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Q - UMCS
K O M I T E T
R E D A K C Y J N Y
REDAKTOR
NACZELNY
Ryszard Szczygieł
REDAKTORZY
A
SEKCJI
MATHEMATICA
Stanisław Prus
CHEMIA
Jacek Goworek
PHYSICA
Stanisław Hałas
AI
INFORMATICA
Wiesław Kamiński
B
GEOGRAPHIA,
AA
AAA
GEOLOGIA ETC.
C
BIOLOGIA
DD
MEDICINA
VETERINARIA
Maria Łanczont
Wanda Małek
Krzysztof Kostro
E
AGRICULTURA
Barbara Kołodziej
EE
ZOOTECHNICA
Marek Babicz
HORTICULTURA
Robert Gruszecki
EEE
F
HISTORIA
Małgorzata Willaume
PHILOLOGIAE
Barbara Boniecka
G
IUS
Lech Dubel
H
OECONOMIA
Jerzy Węcławski
I
PHILOSOPHIA
FF
– SOCIOLOGIA
J
Lesław Hostyński
PAEDAGOGIA
– PSYCHOLOGIA
Grażyna Krasowicz-Kupis
K
POLITOLOGIA
Maria Marczewska-Rytko
L
ARTES
Gabriela Klauza
U N I V E R S I TAT I S M A R I A E C U R I E - S K Ł O D O W S K A
SECTIO AAA
PHYSICA
VOL. LXVII
U N I W E R S Y T E T
2012
M A R I I C U R I E-S K Ł O D O W S K I E J
I S S N 0 1 3 7 - 6 8 6 1
REDAKTOR SEKCJI
STANISŁAW HAŁAS
OPRACOWANIE REDAKCYJNE
JADWIGA BRANICKA
PROJEKT OKŁADKI
I STRON TYTUŁOWYCH
JERZY DURAKIEWICZ
SKŁAD I ŁAMANIE
MARIAN GRUDZIŃSKI
ISSN 0137-6861
WYDAWNICTWO UNIWERSYTETU MARII CURIE-SKŁODOWSKIEJ
20-031 Lublin, pl. Marii Curie-Skłodowskiej 5, tel. (81) 537-53-04
e-mail: [email protected]
http://www.umcs.lublin.pl/wydawnictwo
Dział Handlowy: tel./faks 81 537-53-02
e-mail: [email protected]
DRUK: Elpil, 08-110 Siedlce, ul. Artyleryjska 11
Nakład 125 egz.
ANNALES
U N I V E R S I TAT I S MAR IAE C U R I E - S K Ł O D O W S KA
LUBLIN – POLONIA
VOL. LXVII
SECTIO AAA
2012
Spis treści
Table of contents
LESZEK WÓJCIK
Prof. dr hab. Bogdan Adamczyk (1930–2011)
– wspomnienie pośmiertne...................................................................... 7
Professor Bogdan Adamczyk (1930–2011) – posthumous recollections
LESZEK WÓJCIK
Dorobek naukowy prof. dr. hab. Bogdana Adamczyka........................... 15
List of scientific papers contributed by Professor Bogdan Adamczyk
Jan Sielewiesiuk, Agata Łopaciuk
Regulation of gene expression by Goodwin’s loop with many genes..... 33
Regulacja ekspresji genów w pętli Goodwina z wieloma genami
Davide Fiscaletti, Amrit S. Sorli
Three-dimensional space as a medium of quantum entanglement.......... 47
Trójwymiarowa przestrzeń jako ośrodek splątania kwantowego
10.2478/v10246-012-0011-8
ANNALES
U N I V E R S I TAT I S MAR IAE C U R I E - S K Ł O D O W S KA
LUBLIN – POLONIA
VOL. LXVII
SECTIO AAA
2012
LESZEK WÓJCIK
Prof. dr hab. Bogdan Adamczyk (1930–2011)
– wspomnienie pośmiertne
Professor Bogdan Adamczyk (1930–2011) – posthumous recollections
7 października 2011 r. zmarł profesor
Bogdan Adamczyk.
Urodził się 4 sierpnia 1930 r. w Lublinie. Całe swoje życie naukowe związał
z kierunkiem fizyki uniwersyteckiej UMCS
w Lublinie.
Jeszcze przed maturą w 1949 r. pracował przez pewien czas jako laborant prywatny u prof. Stanisława Ziemeckiego. Studia na fizyce w Uniwersytecie Marii Curie-Skłodowskiej rozpoczął w 1950 r., przy
czym prawie rok przeleżał w gipsie po ciężkim wypadku motocyklowym. W listopadzie 1953 r., jeszcze jako student fizyki,
został zaangażowany na stanowisko laboranta u prof. Wacława Staszewskiego.
Jak wspominał, prof. Staszewski otoczył Go niemalże ojcowską opieką
i wprowadził do swego zespołu badawczego. Z tego okresu pochodzą materiały
do pierwszych wspólnych z prof. Staszewskim publikacji, m.in. w „Acta Physica
Polonica” i „Journal of Acoustic Society of America”.
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LESZEK WÓJCIK
Po roku pracy awansuje na stanowisko zastępcy asystenta, a później – asystenta. Pracę magisterską pt. Centra barwne w kryształach NaCl wykonał pod kierunkiem prof. Stanisława Ziemeckiego i bezpośrednią opieką wtedy jeszcze magistra Mieczysława Subotowicza, uzyskując w roku 1955 tytuł magistra fizyki
i awansując na stanowisko starszego asystenta.
Po ukończeniu studiów w 1955 r. Bogdan Adamczyk związał się z Zespołem
Badawczym kierowanym przez prof. Włodzimierza Żuka, późniejszego kierownika Katedry Fizyki Doświadczalnej UMCS. Pod jego kierunkiem wykonał pracę doktorską pt. Spektrometr mas z polem elektrycznym o częstości radiowej i nieliniowym rozkładzie potencjału, uzyskując w roku 1963 tytuł doktora i awansując
na stanowisko adiunkta.
Schemat spektrometru z polem elektrycznym o częstości radiowej.
W roku 1957 Bogdan Adamczyk, jeszcze wówczas ciężko jąkający się,
przypadkowo dokonał bardzo ważnej dla siebie i nie tylko dla siebie obserwacji
nad głęboką studnią w ogrodzie swoich rodziców. Stwierdził całkowitą łatwość
mówienia podczas wypowiadania słów w obecności echa własnego głosu. Spostrzeżenie to zapoczątkowało prowadzone przez całe życie badania nad mową
jąkających się. Prowadził je również na terenie Poradni Foniatrycznej w Lublinie, gdzie był zatrudniony przez kilkanaście lat. Pracował też jako terapeuta na
koloniach dla dzieci jąkających się, zorganizowanych przez Wojewódzką Poradnię Foniatryczną w Lublinie. Kolonie odbywały się w Zwierzyńcu n. Wieprzem
(1959), oraz na obozach – turnusach terapeutycznych zorganizowanych przez
Polski Związek Jąkających się: w Muszynie (1993), Myślenicach (1994), Wójtowicach (1995) i Darłówku (1996).
Głównym rezultatem jego badań nad mową ludzi jąkających się stała się
nowa metoda terapii, tzw. metoda ECHO, oraz tzw. echotelefoniczny system korekcji, obejmujący swym zasięgiem cały kraj.
Swoje życie naukowe Profesor poświęcił dwom dziedzinom – fizyce oraz korekcji mowy ludzi jąkających się (szczególnie dzieci i młodzieży). W tych ostatnich badaniach wspierały Go dr Wiesława Kuniszyk-Jóźkowiak oraz dr Elżbieta
Smołka. Prof. B. Adamczyk był promotorem ich prac doktorskich.
Prof. dr hab. Bogdan Adamczyk (1930–2011)
9
Bardzo ważnym okresem w Jego życiu był dziewięciomiesięczny staż w kierowanym przez prof. J. Kistemakera FOM Instituut voor Atom -en Molecuulfysica w Amsterdamie w 1965 r. B. Adamczyk prowadził tam badania nad jonizacją niektórych atomów i molekuł gazu elektronami. Wyznaczał przekroje czynne na jonizację.
Do pomiaru bezwzględnych przekrojów czynnych na jonizację niezbędna
jest wiedza o tym, ile jonów określonego rodzaju zostało wytworzonych przez jeden elektron na jednostkowej drodze w obszarze jonizacji. Z nielicznymi wyjątkami do badania przekrojów czynnych używane były konwencjonalne spektrometry mas. Niestety, spektrometry te miały niewielki współczynnik transmisji
jonów na drodze od źródła do kolektora. Jeszcze większą wadą było to, że współczynnik transmisji zależał w nieznany sposób od masy jonów i energii elektronów, dając w rezultacie zniekształcenia krzywych wydajności jonizacji. Jedyną
drogą do zabezpieczenia przed tym była taka konstrukcja aparatury, która zapewniałaby całkowitą transmisję jonów między źródłem a kolektorem. B. L. Schram,
B. Adamczyk i A. J. H. Boerboom zbudowali cykloidalny spektrometr mas ze
skrzyżowanymi polami elektrycznym i magnetycznym o wysokim, prawie stuprocentowym współczynniku transmisji jonów na drodze od źródła do kolektora jonów.
Na zdjęciu powyżej przedstawiony jest fragment publikacji nt. cykloidalnego spektrometru mas.
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LESZEK WÓJCIK
Zastosowanie jednorodnych pól – magnetycznego B i jednorodnego pola
elektrycznego E prostopadłego do B sprawia, że jony bez początkowej energii
kinetycznej będą poruszać się po cykloidach. Kiedy posiadają początkową energię kinetyczną, wtedy tory są trochoidami. Ponadto, taka konfiguracja pól zapewnia podwójne ogniskowanie jonów – zarówno co do kierunku, jak i energii. Jony
określonego rodzaju, poruszające się wewnątrz analizatora, mają wspólne ognisko niezależne od ich prędkości początkowych i początkowych kierunków. Jony
poruszające się w kierunku pola magnetycznego są ogniskowane wzdłuż linii prostej. Jeśli chcemy, żeby wyprodukowane jony były w całości wyciągnięte ze źródła i zogniskowane na kolektorze jonów, to taką właśnie możliwość daje spektrometr cykloidalny.
Część analizującą cykloidalnego spektrometru mas przedstawia rysunek powyżej.
Po zakończeniu pomiarów w FOM Instituut voor Atom -en Molecuulfysica
w Amsterdamie, część analizująca spektrometru zastała przywieziona do Polski
i stała się podstawą konstrukcji cykloidalnego spektrometru mas w Katedrze Fizyki UMCS. Za pomocą tego spektrometru prof. B. Adamczyk i jego współpracownicy – dr L. Wójcik i dr K. Bederski przeprowadzili później wiele
pomiarów przekrojów czynnych na jonizację atomów i molekuł gazu elektronami o energii od kilkunastu do 1000 eV. Uzyskane rezultaty były podstawą ich
prac doktorskich. Wyniki pomiarów opublikowano w czasopismach o światowym
zasięgu.
Bogdan Adamczyk na stanowisko docenta został powołany jeszcze przed habilitacją w roku 1969. Kolokwium habilitacyjne odbyło się w 1971 r., na podstawie pracy pt. Pomiary przekrojów czynnych na jonizację pojedynczą i wielokrotną atomów He, Ne i Ar elektronami przy pomocy spektrometru mas z całkowitą
transmisją jonów. Problematykę tę kontynuował w ramach dalszej współpracy
Prof. dr hab. Bogdan Adamczyk (1930–2011)
11
z FOM Instituut, przebywając na kolejnych stażach w latach 1972 oraz 1985. Pobyt w Holandii wykorzystał także do współpracy z ośrodkiem psychoanalitycznym
Uniwersytetu w Lejdzie, gdzie prof. Bastiaans zaangażował Go jako autora metody ECHO. Prof. B. Adamczyk otworzył drogę do staży naukowych w Holandii
innym fizykom z naszego ośrodka naukowego.
Podczas jednego ze staży naukowych w Amsterdamie prof. B. Adamczyk
zrealizował własny projekt badania dyfuzji CO2, He, Ar przez skórę człowieka
w różnych jej miejscach przy wykorzystaniu spektrometru mas. Badania przeprowadzane były podczas oddychania mieszaniną O2+He lub O2+Ar oraz bezpośrednio po odłączeniu mieszaniny i oddychaniu powietrzem. Opóźnienie czasowe i natężenie wydalanego CO2, He i Ar były wyznaczane w wielu różnych miejscach na ciele człowieka.
W 1978 r. twórca FOM Instituut – prof. J. Kistemaker otrzymał doktorat honoris causa Uniwersytetu Marii Curie-Skłodowskiej. Prof. B. Adamczyk był promotorem tego doktoratu.
Na zdjęciu prof. J. Kistemaker z małżonką po ceremonii nadania tytułu doktora honoris causa
UMCS, obok po prawej profesorowie B. Adamczyk, A. J. H. Boerboom i A. E. de Vries.
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LESZEK WÓJCIK
W latach 1970–1980 propagowana była w całym kraju współpraca wyższych
uczelni z zakładami przemysłowymi, których wówczas było w regionie znacznie
więcej niż teraz i które posiadały odpowiednie fundusze na sponsorowanie w ramach tej współpracy różnorodnych badań naukowych.
Profesor Adamczyk nawiązał dość aktywną współpracę pomiędzy Zakładem Fizyki Stosowanej Instytutu Fizyki UMCS a Wytwórnią Sprzętu Komunikacyjnego w Świdniku. Prowadzone w tym zakresie badania dotyczyły zagadnień związanych z technologią klejenia metalowych elementów śmigłowców. Na
etacie Wytwórni Sprzętu Komunikacyjnego zatrudniony został Józef Dąbek, student fizyki (magistrant), który prowadził szereg badań z tego zakresu. Rezultaty przeprowadzonych badań były podstawą Jego pracy magisterskiej, a później
doktoratu.
Badania na rzecz Wytwórni Sprzętu Komunikacyjnego w Świdniku, a potem na rzecz Ośrodka Badawczo-Rozwojowego przy WSK, pod kierunkiem profesora Adamczyka, trwały przez dobrych kilkanaście lat, a ich efektem, miedzy
innymi, było wykonanie blisko dwudziestu prac magisterskich. Trudno w sposób
wymierny ocenić, jakie korzyści zyskała WSK Świdnik.
W roku 1976 powołał do życia Zakład Fizyki Stosowanej. Kierował nim nieprzerwanie do roku 2000. Zakład Fizyki Stosowanej nie tylko podejmował określoną tematykę badawczą, ale także oferował specjalności kształcenia studentów
IV i V roku fizyki.
W 1978 r., korzystając ze współpracy Uniwersytetu z Lock Haven State
College, B. Adamczyk wyjechał na cztery miesiące do USA, gdzie w Laboratorium Human Performance Research w Pennsylvania State University zainicjował
i przeprowadził badania nad składem powietrza wydychanego przez jąkających
się podczas mówienia. W ramach tego pobytu wygłosił w Filadelfii, San Francisco, Los Angeles i Houston odczyty zarówno na temat prowadzonych przez siebie badań z zakresu spektrometrii mas, jak i problematyki związanej z jąkaniem.
Tytuł profesora B. Adamczyk uzyskał w 1980 r.
Oprócz wymienionych wcześniej badań z zakresu spektrometrii mas oraz
związanych z korekcją mowy ludzi jąkających prowadzone były badania mające
na celu modelowanie optyczne efuzyjnych wiązek molekularnych. Badane były
zjawiska jonizacyjne zachodzące na przecięciu wiązek molekularnych z wiązką elektronową. Współpracownikiem prof. B. Adamczyka był mgr Leszek Michalak, który opracował kilka metod komputerowej symulacji wiązek molekularnych. Wiązki takie emitowane były przez wąską szczelinę i przez prostokątny kanał. Badano zależność natężeń prądów jonowych od pozycji względem szczeliny
(wylotu kanału). Uzyskane wyniki porównano z wynikami otrzymanymi przy zastosowaniu modelu optycznego. Leszek Michalak zrealizował z tej dziedziny swą
pracę doktorską i habilitacyjną. Prowadzone były również badania dyfuzji gazu
Prof. dr hab. Bogdan Adamczyk (1930–2011)
13
przez ośrodki porowate, m.in. dwutlenku węgla przez warstwę ziarna. Współpracowniczką prof. B. Adamczyka była dr B. Aramowicz. Profesor był promotorem jej pracy doktorskiej. Badania prowadzone były we współpracy z Instytutem
Agrofizyki PAN w Lublinie. Miały one też znaczenie praktyczne związane z przechowywaniem ziarna w silosach.
W 1985 r. profesor gościł w laboratorium prof. Dońca w Dubnej, gdzie zajmował się wielokrotną jonizacją atomów i molekuł gazu.
Profesor B. Adamczyk był bardzo aktywnym pracownikiem naukowym. Wyniki badań własnych i swoich współpracowników przedstawiał na wielu konferencjach i sympozjach, m.in.: w Wiedniu, Interlaken, Pradze, Dublinie, Kopenhadze, Houston, Oslo, Budapeszcie, Belgradzie, Starej Zagorze, Amsterdamie,
Tokio, Kioto, Barcelonie, Kalkucie, Aligarh, Rostoku, Kolonii, Rotterdamie
i Tampere. Do momentu odejścia na emeryturę w roku 2000 wypromował ponad
130 magistrów fizyki i 9 doktorów. Na podstawie prac zrealizowanych w Zakładzie Fizyki Stosowanej odbyły się 4 kolokwia habilitacyjne.
W 1990 r. B. Adamczyk został powołany na stanowisko profesora zwyczajnego. Kierował wieloma tematami w ramach problemów centralnie koordynowanych. Przez wiele lat był wiceprzewodniczącym Rady Naukowej Instytutu Agrofizyki PAN, z którą to placówką współpracował, prowadząc badania w zakresie
transportu gazu w ośrodkach porowatych.
Był członkiem PTF oraz przez jedną kadencję przewodniczącym Lubelskiego Oddziału PTF. Należał do Lubelskiego Towarzystwa Naukowego oraz European Physical Society. Od roku 1963 roku był członkiem założycielem Polskiego
Towarzystwa Logopedycznego, od roku 1974 pierwszym przewodniczącym PTL,
a od roku 1990 redaktorem naczelnym rocznika „Logopedia”. Był członkiem założycielem i członkiem Zarządu Głównego Polskiego Towarzystwa Próżniowego.
Oprócz aktywności naukowej należy podkreślić jego zaangażowanie organizacyjne. W latach 1970–1978 był wicedyrektorem Instytutu Fizyki i następnie jego
dyrektorem przez dwie kadencje w latach 1978–1987.
Brał czynny udział w popularyzacji fizyki, m.in. uczestnicząc w corocznie organizowanych Pokazach z Fizyki zainicjowanych w 1953 r. przez prof. W. Staszewskiego.
Prof. Adamczyk był laureatem nagród Ministra Nauki i Szkolnictwa Wyższego i Techniki, Ministra Zdrowia i Opieki Społecznej, Ministra Edukacji Narodowej, Sekretarza Naukowego Polskiej Akademii Nauk, Polskiego Towarzystwa Fizycznego i innych. Za swoje dokonania w zakresie terapii jąkania został wybrany
w plebiscycie telewizyjnym w roku 1965 „Polakiem Roku’’.
Prof. B. Adamczyk miał wielu współpracowników. W Zakładzie Fizyki
Stosowanej, którego był twórcą, pracowali: Bogusława Aramowicz, Krzysztof
Bederski, Jan Cytawa, Jan Czarnota, Józef Dąbek, Krzysztof Głuch, Krystyna
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LESZEK WÓJCIK
Gołaszewska, Ferdynand Jagiełło, Małgorzata Klepacka, Barbara Kozłowiec,
Wiesława Kuniszyk-Jóźkowiak, Artur Kwiatkowski, Elżbieta Marcinkowska,
Artur Markowski, Marek Rafalski, Leszek Michalak, Arkadiusz Musur, Tadeusz
Olech, Paweł Pałczyński, Andrzej Pelc, Barbara Raczek, Anna Smolira, Elżbieta
Smołka, Tadeusz Stański, Piotr Staszewski, Sylwia Ptasińska, Michał Sztubecki,
Witold Szyszko, Waldemar Suszyński, Arkadiusz Wiśniewski i Leszek Wójcik.
Wspominał:
prof. dr Leszek Wójcik
10.2478/v10246-012-0012-7
ANNALES
U N I V E R S I TAT I S MAR IAE C U R I E - S K Ł O D O W S KA
LUBLIN – POLONIA
VOL. LXVII
SECTIO AAA
2012
LESZEK WÓJCIK
Dorobek naukowy prof. dr. hab. Bogdana Adamczyka
List of scientific papers contributed by Professor Bogdan Adamczyk
Spektrometria mas i zjawiska jonizacyjne
MASS SPECTROMETRY AND IONIZATION PHENOMENA
1. B. Adamczyk: Radiofrequency mass spectrometer with flat-cylinder system of
analyzing electrodes, Biul. Lub. Tow. Nauk., 2 (1961), 108–109.
2. B. Adamczyk, A. J. Boerboom, B. J. Schram, J. Kistemaker: Partial ionization cross section of He, Ne, H2, and CH4 for electrons from 20 to 500 eV, J.
Chem. Phys., 44 (1966), 4540–4541.
3. B. L. Schram, B. Adamczyk, A. J. H. Boerboom, J. Kistemaker: A cycloidal
mass spectrometer with 100% collection efficiency, J. Scient. Instrum., 43
(1966), 638–640.
4. B. Adamczyk, A. J. H. Boerboom, J. Kistemaker: A mass spectrometer for
continuous analysis of gaseous compounds excreted by human skin, J. App.
Physiology, 21 (1966), 1903–1906.
5. B. Adamczyk: Cykloidalny spektrometr mas z całkowitą transmisją jonów,
Annales UMCS, sec. AA, 24/25, (1969/70), 142–156.
6. B. Adamczyk: Pojedyncza i wielokrotna jonizacja atomów He, Ne i Ar elektronami o energii 25–600 eV, Annales UMCS, sec. AA, 24/25 (1969/70),
157–170.
7. B. Adamczyk, S. Hałas: Jonizacja i dysocjacja cząsteczek azotu elektronami o energii od 25 do 600 eV, Annales UMCS, Sec. AA 24/25 (1969/70),
180–186.
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LESZEK WÓJCIK
8. B. Adamczyk: Pomiary przekrojów czynnych na jonizację i dysocjację cząsteczek wody elektronami, Folia Soc. Scient. Lubl. sec. C, 12, (1971), 13–16.
9. B. Adamczyk, A. J. H. Boerboom, and M. Łukasiewicz: Partial ionization
cross section of carbon dioxide by electrons (25–600 eV), Int. J. Mass Spectr.
Ion Phys., 9 (1972), 407–412.
10. S. Hałas, B. Adamczyk: Cross sections for the production of N2+, N+ and N2+
from nitrogen by electrons in energy range 16–600 eV, Int. J. Mass Spectr.
Ion Phys., 10 (1972/73), 157–160.
11. B. Adamczyk, A. J. H. Boerboom, J. Kistemaker: Mass spectrometric study
of the dymamics of gas transport through human skin to the lungs, J. Appl.
Physiol., 34, 5 (1973), 718–721.
12. B. Adamczyk, A. J. H. Boerboom, A. E. de Vries: Second order pressure dependence of fragment peaks in mass spectra of water, methane and carbon
dioxide, Int. J. Mass Spectr. Ion Phys., 12 (1973), 314–315.
13. B. Adamczyk, K. Bederski, L. Wójcik, A. Wasiak: Przekroje czynne na jonizację tlenu elektronami, Folia Soc. Scient. Lubl. Mat-Fiz-Chem, 15 (1973),
85–87.
14. B. Adamczyk, K. Zawalska: Anomalna produkcja jonów D2+ przy jonizacji
D2O i CD4 elektronami, Folia Soc. Scient. Lubl., Mat-Fiz-Chem, 16 (1974),
43–45.
15. B. Adamczyk, K. Bederski, W. Szyszko, L. Wójcik: Przekroje czynne na jonizację argonu elektronami, Folia Soc. Scient. Lubl. Mat-Fiz-Chem, 17 1/2
(1976), 135–138.
16. K. Bederski, L. Wójcik, B. Adamczyk, T. Stański: Pomiary przekrojów czynnych na jonizację NO i CO2 elektronami, Folia Soc. Scient. Lubl., Mat-FizChem, 18, 2 (1976), 163–166.
17. B. Adamczyk, K. Bederski, W. Szyszko, L. Wójcik: Źródło jonów do badań
przekrojów czynnych na jonizację atomów i molekuł elektronami, Folia Soc.
Scient. Lubl., Mat-Fiz-Chem, 18, 2 (1976), 167–172.
18. L. Wójcik, B. Adamczyk: Automatyczna lokalizacja wiązki jonów na kolektorze cykloidalnego spektrometru mas, Folia Soc. Scient. Lubl. Mat-Fiz-Chem,
18, 2 (1976), 181–183.
19. B. Adamczyk, K. Bederski, L. Wójcik, T. Stański: Pomiary przekrojów czynnych na jonizację CO, N2, O2, N2O, Ar elektronami o energii 25 do 1000 eV,
Folia Soc. Scient. Lubl., Mat-Fiz-Chem, 18, 2 (1976), 217–221.
20. B. Adamczyk, B. Aramowicz, K. Bederski, L. Wójcik: Ołówkowe termoemisyjne źródło jonów, Annales UMCS, sec. AA, 28 (1973), 361–367.
21. B. Adamczyk, L. Wójcik, K. Bederski, M. Pleszczyński: Ogniskujące działanie niejednorodnego pola elektrycznego w cykloidalnym spektrometrze mas,
Annales UMCS, sec. AA, 28, (1973), 369–375.
Dorobek NAUKOWy prof. dr. hab. Bogdana Adamczyka
17
22. L. Wójcik, K. Bederski, B. Adamczyk, M. Pleszczyński: Przekroje czynne na
wytwarzanie jonów O2+, O+, O22+, O2+ przy bombardowaniu tlenu elektronami, Annales UMCS, sec. AA, 28 (1973), 421–426.
23. B. Adamczyk, B. Aramowicz, K. Bederski, L. Wójcik: Pencil type thermoemission ion source, Advances in Mass Spectrometry, 8, Heyden and Son
Ltd., London (1980), 1798–1799.
24. K. Bederski, L. Wójcik, B. Adamczyk: Ionization of ammonia by electron
impact at 25–1000 eV, Int. J. Mass Spectr. Ion Phys., 35 (1980), 171–178.
25. T. Stański, B. Adamczyk, P. Pałczyński: Dwukolektorowy cykloidalny spektrometr mas do badania oddziaływań elektronów z wiązkami atomowymi
i molekularnymi, I Konferencja Naukowa „Technologia Elektronowa” Wrocław–Karpacz, 24–27 września 1980, Prace Naukowe Politechniki Wrocławskiej, 24 (1980), 53–55.
26. B. Adamczyk: Niektóre zastosowania spektrometru mas jako analizatora
gazu, Zeszyty Problemowe Postępów Nauk Rolniczych, 237 (1981), 185–
199.
27. B. Adamczyk, E. Chomicz, L. Gładyszewski, S. Hałas, C. Harańczyk, M. Kisielewicz, A. Latuszyński, J. Lis, D. Mączka, W. Rosiński, J. Sielewiesiuk,
G. Skrzetuska–Matusiewicz, J. Szaran, J. M. Zinkiewicz, W. Żuk: Spektrometria mas i elektromagnetyczna separacja izotopów, pod redakcją W. Żuka,
PWN, Warszawa (1980), 1–489.
28. B. Adamczyk: Sylwetka prof. J. Kistemakera, akt nadania tytułu doktora honoris causa profesorowi dr. Jacobowi Kistemakerowi 23 października 1978.
Sprawozdanie z działalności Uniwersytetu Marii Curie-Skłodowskiej w roku
akad. 1978/1979, UMCS (1981), 32–35.
29. B. Adamczyk: Spektrometria mas i elektromagnetyczna separacja izotopów
w lubelskim ośrodku fizyki, Annales UMCS, sec. AAA, 36/37, 1 (1981/82),
1–11.
30. B. Adamczyk: Wybrane zagadnienia spektrometrii mas w lubelskim ośrodku fizyki – pamięci Prof. Włodzimierza Żuka, Materiały 120. Konwersatorium Spektrometrii Atomowej Emisyjnej, Absorbcyjnej i Spektrometrii Mas,
UMCS, Lublin 13–15 czerwca 1983 (1983), 5–10.
31. B. Adamczyk, J. Dąbek: New type of the “pencil” thermoemission ion source,
Int. J. Mass Spectr. Ion Phys., 46 (1983), 39–42.
32. T. Stański, B. Adamczyk: Measurements of dissociative ionization cross
section of SF6 , by using double collector cycloidal mass spectrometer, Int.
J. Mass Spectr. Ion Phys., 46 (1983), 31–34.
33. B. Adamczyk, L. Michalak: Badanie rozkładu natężenia wiązki atomowej
w źródle jonów spektrometru mas przy użyciu modelu optycznego, Annales
UMCS, sec AAA, 38, 15 (1983), 179–189.
18
LESZEK WÓJCIK
34. B. Adamczyk: Kalkulacja rozkładu natężenia wiązki molekularnej w źródle
jonów z wiązką elektronową. Folia Soc. Sci. Lubl. Mat-Fiz-Chem, 26 (1984),
9–12.
35. A. Wiśniewski, B. Adamczyk: Rola elektronów wtórnych w procesie wytwarzania jonów wiązką elektronową, Folia Soc. Sci. Lubl. Mat-Fiz-Chem, 26,
1 (1984), 13–16.
36. A. Wiśniewski, B. Adamczyk: Wpływ konfiguracji pól: elektrycznego i magnetycznego na efekty wyróżniania mas w źródle jonów z wiązką elektronową, Folia Soc. Sci. Lubl. Mat-Fiz-Chem 26, 1 (1984), 17–20.
37. B. Adamczyk, L. Michalak, Characteristics of effusive molecular beam
crossed by electron beam, Annales UMCS, sec. AAA, 40/41, 1 (1985/1986),
1–8.
38. B. Adamczyk, L. Michalak, Modeling of the molecular beam intensity distribution in the ion source of mass spectrometer by means of light beam, Int.
J. Mass Spectrom. Ion Processes, 69, (1986), 163–174.
39. B. Adamczyk, L. Michalak: Effusive molecular beam crossed by electron
beam and the optical model of this effect, Int. J. Mass Spectrom. Ion Processes, 71 (1986), 211–220.
40. B. Adamczyk, L. Michalak: Electron ionization of effusion molecular beam
emitted by a rectangular channel and optical model of this effect, Int. J. Mass
Spectrom. Ion Processes, 74 (1986), 319–326.
41. J. Dąbek, B. Adamczyk: Mass spectrometric investigation of pencil thermoemission ion source, Int. J. Mass Spectrom. Ion Processes, 75 (1987), 55–61.
42. L. Michalak, B. Adamczyk: Ion molecular reaction as an effect of crossing
a highly non-homogeneous effusion molecular beam with an electron beam,
Int. J. Mass Spectrom. Ion Processes, 85 (1988), 319–326.
43. B. Adamczyk, A. J. H. Boerboom, J. Kistemaker: Mass spectrometric temperature investigation of gas transport through a human body to the lungs,
Biomedical Environmental Mass Spectrometry, 16 (1988), 455–456.
44. B. Adamczyk, W. Genuit, J. J. Boon: A simple approach to the dynamics headspace analysis of volatile flavours using a gas chromatograph-photoionization mass spectrometer, Biomedical and Environmental Mass Spectrometry,
16 (1988), 373–375.
45. B. Adamczyk, K. Bederski, L. Wójcik: Mass spectrometric investigation of
dissociative ionization of toxic gases by electrons at 20–1000 eV, Biomedical
and Environmental Mass Spectrometry, 16 (1988), 415–417.
46. L. Michalak, B. Adamczyk: Investigation of chemical processes in corona
discharge by means of quadrupole mass spectrometer, Rapid Communication
in Mass Spectrometry, 2 (1988), 244–245.
Dorobek NAUKOWy prof. dr. hab. Bogdana Adamczyka
19
47. L. Michalak, B. Adamczyk: Mass spectrometric investigation of dynamics
of ozone and nitric oxide synthesis in the corona discharge, Nukleonika, 33
(1988), 301–314.
48. J. Dąbek, B. Adamczyk: Al+ beam generation by means of the pencil type thermoemission ion source, Phys. Stat. Sol. (a) 112 (1989), 829–833.
49. J. Dąbek B. Adamczyk: The application of the pencil thermoemission ion
source for determination of the isotopic ratio 7Li:6Li in a monocrystalline
LiF sample, Int. J. Mass Spectrom. Ion Processes, 90 (1989), 187–191.
50. B. Adamczyk, L. Michalak: Symulacja świetlna efuzyjnych wiązek molekularnych, Elektronika (wkładka: Technika Próżniowa i Technologie Elektropróżniowe) 7/9 (1990), 68–69.
51. J. Dąbek, B. Adamczyk: Termoemisyjne źródła wiązek jonowych, Elektronika, 10 (1990), 12–17.
52. B. Adamczyk, L. Michalak, E. Marcinkowska: Modeling of the molecular
beam intensity distribution by means of infrared beam, Int. J. Mass Spectrometry Ion Processes, 105 (1991), 55–61.
53. B. Adamczyk, L. Michalak: Effusion Molecular Beams of High Intensity
Crossed by an Electron Beam: Optical Modelling, Application in Mass Spectrometry, Ion Molecule Reactions, in: Advances in Atomic and Molecular
Physics, ed. M. S. Z. Chaghtai, Today and Tommorow’s Printers and Publishers, New Delhi (1991).
54 L. Michalak, B. Adamczyk, E. Marcinkowska: Temperature effect of ion/molecule reactions in water molecular beam crossed by an electrons beam, Int.
J. Mass Spectrom. Ion Processes, 107 (1991), 9–16.
55. L. Michalak, B. Adamczyk: Light simulation of molecular beam epitaxy, Vacuum 42, 12 (1991), 735–739.
56. B. Adamczyk, L. Michalak, E. Marcinkowska, Optical simulation of effusion
molecular beam for MBE, Sixth European Conference on Molecular Beam
Epitaxy and Related Growth Methods (EURO MBE–90) April 21–24, 1991,
Tampere Hall, Tampere, Finland, Tampere University of Technology, 1991–
Cp3.
57. B. Adamczyk, L. Michalak, E. Marcinkowska: Optical Modeling of MBE system, Vacuum 42, 15 (1991), 971–977.
58. L. Michalak, B. Adamczyk, M. A. Herman: Optical imulation of the beam
flux distribution from molecular beam epitaxy effusion sources, Vacuum, 43
(1992), 341–345.
59. B. Adamczyk, L. Michalak: Effusion Molecular Beams of High Intensity
Crossed by an Electron Beam: Optical Modelling, Application in Mass Spectrometry, Ion-Molecule Reactions, Advanced in Atomic and Molecular Physics, (1992), 245–266, Proc. 7th Nat. Workshop and Conf. on Atomic and Mo-
20
LESZEK WÓJCIK
lecular Physics, ed. M. S. Z. Chaghtai, Today & Tomorrow’s Printers, New
Delhi 1992.
60. L. Michalak, B. Adamczyk: Calculations of a Molecular Beam Intensity Distribution from an Effusion Hole, Proc. Ninth European Conference on Dynamics of Molecular Collisions MOLEC IX, August 30 – September 4, 1992,
Prague, Czechoslovakia (1992), 80–81.
61. L. Michalak, B. Adamczyk, M. A. Herman: Optical Simulation of the Beam
Flux Distribution from Molecular Beam Epitaxy Effusion Sources, Vacuum,
43 (1992), 341–345.
62. L. Michalak, B. Adamczyk: Calculations of a Molecular Beam Intensity Distribution from an Effusion Hole, Proc. Ninth European Conference on Dynamics of Molecular Collisions MOLEC IX, August 30 – September 4, 1992,
Prague, Czechoslovakia.
63. B. Adamczyk: Mass Spectrometric Investigations of Ion-Molecular Reactions
in Gases, Selected Experiments, Sympozjum Naukowe Plazma ’93, Warszawa, 29–30 września 1993.
64. L. Wójcik, K. Bederski, B. Adamczyk: J. A. Herman: Mass Spectrometric
Measurements of Ion-Molecule Reaction, Sympozjum Naukowe Plazma ’93,
Warszawa, 29–30 września 1993.
65. B. Adamczyk, L. Michalak, E. Marcinkowska: Investigations of Ionization
Processes on the Crossing of an Effusion Molecular Beam with an Electron
Beam, Sympozjum Naukowe Plazma ’93, Badania i zastosowania plazmy,
Warszawa, 29–30 wrzesień 1993.
66. B. Adamczyk, L. Michalak: Niejednorodne Efuzyjne Wiązki Molekularne i Ich
Zastosowanie, 3, Szkoła Mielno ’92, Nowoczesne Technologie Próżniowe,
26–28 listopada 1992, Koszalin (1993), 21–38.
67. L. Wójcik, K. Bederski, B. Adamczyk: J. A. Herman: Mass Spectrometric
Measurements of Ion-Molecule Reaction, Sympozjum Naukowe Plazma ’93,
Warszawa, 29–30 września 1993, 111–114.
68. B. Adamczyk, L. Michalak, E. Marcinkowska: Infrared Simulation of Effusion Molecular Beams, in: Optoelectronic Science and Engineering ’94, (eds)
Da-Heng Wang, A. Consortini, J. B. Breckinridge, Proc. SPIE 2321 (1994),
369–371.
69. B. Adamczyk, L. Michalak: Optical simulation of effusion molecular beam,
Slovenian-Hungarian-Croatian-Austrian Sixth Joint Vacuum Conference, 4 –
7 April 1995, Bled, Slovenia.
70. B. Adamczyk, L. Michalak: Optical simulation of effusion molecular beam,
J. Exp. Theor. Phys., A4 (1995), 113–124.
71. B. Adamczyk: Mass spectrometer in selected biomedical investigations, Proc.
of VIth Scientific Conference on Electron Technology ELTE ’97, 6–9 May
1997, Krynica Górska, 2 (1997), 225–228, in Polish.
Dorobek NAUKOWy prof. dr. hab. Bogdana Adamczyka
21
72. A. Markowski, L. Micjalak, B. Adamczyk: Generation of ions on the crossing of the electron or photon beam with an effusion molecular beam, Proc. of
the 7th Joint Vacuum Conference of Hungary, Austria, Croatia and Slovenia,
26–29 May 1997, Debrecen, Hungary, 261–262.
73. B. Adamczyk: Mass-spectrometric investigations “on-line” of ionization and
dissociation of gases by electron impact, in: 1st Congress of the Polish Vacuum Society, Kraków, 25–30 May 1998, Abstracts, O.I.1 (1998), in Polish.
74. B. Adamczyk: Mass-spectrometric investigations “on-line” of ionization
and dissociation of gases by electron impact, Proceedings of 1st Congress
of the Polish Vacuum Society, Kraków, 25–30 May 1998, Wyd. Uniw.
Jagiellońskiego, 1 (1998), 37–41, in Polish.
LOGOPEDIA – PROBLEMY JĄKANIA
LOGOPAEDICS – STUTTERING PROBLEMS
1. B. Adamczyk: Adwendung des Apparates fur die Erzeugung von künstlichem
Wiederhall bei Behandlung des Stotterns, Folia Phoniatrica, 11 (1959), 216–
218.
2. B. Adamczyk: O możliwości prowadzenia na terenie szkoły ćwiczeń rehabilitacyjnych z jąkającymi się przy pomocy aparatu wytwarzającego echo, Logopedia, 1 (1960), 19–23.
3. B. Adamczyk: Modèle du bégaiement bas sur retarde auditufdu feedback /
echo artificiel/ Proceedings of the First International Congress of Cybernetics Medicine, Naples, (1960), 1–4.
4. B. Adamczyk: Próba wyjaśnienia mechanizmu jąkania się, Logopedia, 2
(1963), 12–18.
5. B. Adamczyk: Nowa metoda korekcji mowy u jąkających się przy pomocy
sztucznego echa, Otolaryngologia Polska, 17 (1963), 482–484.
6. B. Adamczyk: Korekcja mowy u jąkających się przeprowadzona drogą telefoniczną z zastosowaniem sztucznego echa, Otolaryngologia Polska, 17
(1963), 479–481.
7. W. Czarnecka-Paplińska, B. Adamczyk, W. Wojciechowski: Eksperymentalne kolonie dla dzieci jąkających się, Otolaryngologia Polska 17 (1963),
485–486.
8. B. Adamczyk: Echo-telefoniczny system korekcji mowy u jąkających się, Logopedia, 5 (1964), 29–37.
9. B. Adamczyk: Die Ergebnisse der Behandlung des Stotterns durch das Telephonosystem, De Therapia Vocis et Loquelae Societatis Internationalis
Logopediae et Phoniatriae XIII Congressus Vindobonae Anno MCMLXV,
1 (1965), 433–435.
22
LESZEK WÓJCIK
10. B. Adamczyk: Psychoterapeutische Faktoren der Behandlung des Stotterens
mit der “Echo method”, Folia Phoniatrica, 21 (1969), 300–306.
11. B. Adamczyk: Echo leczy, „Polska”, 6, (1965), also in English, French, Spanish, German, and Swedish, 38–39.
12. B. Adamczyk, W. Kuniszyk: Application of speach reverberation by stammering therapy, 9th Conference of Physiological Acoustics and Psychoacoustics, The High Tatras, 31st August – 4th September 1971, 7–10.
13. B. Adamczyk: Psychoterapia i trening w metodzie “Echo”, Logopedia 10
(1971), 46–52.
14. B. Adamczyk, L. Wójcik: Spiralna akustyczna linia opóźniejąca jako korektor mowy, Folia Soc. Sci. Lubl. sec C, 12 (1971), 9–12.
15. B. Adamczyk, E. Sadowska, W. Kuniszyk-Jóźkowiak: Influence of Reverberation on Stuttering, Folia Phoniatrica, 27 (1975), 1–5.
16. B. Adamczyk, E. Sadowska, W. Kuniszyk-Jóźkowiak: Oddziaływanie pogłosu na mowę jąkających się, Logopedia, 12 (1975), 47–54.
17. B. Adamczyk, W. Kuniszyk–Jóźkowiak, E. Sadowska: Wpływ zespołowego
mówienia na mowę jąkających się, Logopedia, 12 (1975), 55–68.
18. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka, F. Jagiełło: Propagacja
fal podłużnych w stalowych sprężynach śrubowych, Folia Soc. Sci. Lubl.,
Mat-Fiz-Chem. 17, ½ (1976), 129–133.
19. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka, F. Jagiełło: Rozchodzenie
się fal w stalowych spiralach śrubowych, Annales UMCS, AA, 29 (1974/75),
281–287.
20. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Sadowska: Correction effect
in chorus speaking by stuttering people, XV-th International Congress of
Logopaedics and Phoniatrics Iterlaken, August 25–29, 1974, (eds) E. Loebell,
S. Karger – Basel, (1976) 1–5.
21. B. Adamczyk, E. Smołka, W. Kuniszyk: Czynnik chóralnego mówienia
w niektórych metodach terapii jąkania, Studia Logopedica, Materiały Ogólnopolskiego Sympozjum 5–7 IX 1974 i 27–28 V, Uniwersytet Marii Curie-Skłodowskiej, Zakład Logopedii, Lublin (1976), 5–13.
22. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka: Synchronizacja mówienia z echem i pogłosem w terapii jąkania, Prace XXIV Otwartego Seminarium z Akustyki, Gdańsk, Władysławowo, Wrzesień 1977, (1977), 37–40.
23. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka: Echo reverberation correlation by influence on stuttering, 17th Int. Congr. Logopedics and Phoniatrics, Copenhagen 1977 (1977), 311–317.
24 B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka, F. Jagiełło: Próba badania współruchów u jąkających się przy użyciu czujnika drgań, Logopedia, 13
(1978), 43–47.
Dorobek NAUKOWy prof. dr. hab. Bogdana Adamczyka
23
25. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka: Oddziaływanie bodźców
akustycznych na proces jąkania, in: Akustyka mowy i diagnostyka akustyczna, Praca zbiorowa pod red. Janusza Kacprowskiego, IPPT PAN Warszawa
1980, 75–101.
26. W. Kuniszyk-Jóźkowiak, B. Adamczyk: Wpływ filtrowanego echa i pogłosu
na prędkość mówienia, Archiwum Akustyki, 18, 3, (1983), 285–294.
27. E. Smołka, B. Adamczyk: Pomiary częstotliwości podstawowej przy oddziaływaniu echa i pogłosu na proces mówienia jąkających się, Logopedia, 14/15
(1983), 50–55.
28. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka: Eksperymentalne zastosowanie korektora pogłosowego w terapii jąkających się, Logopedia, 14/15
(1983), 39–49.
29. B. Adamczyk, W. Kuniszyk-Jóźkowiak E. Smołka: Stymulacja i kontrola procesu mówienia u jąkających się, in: Akustyka w technice i medycynie,
Przegląd wyników badań w problemie międzyresortowym MR I-24 w latach
1981–1985, Koordynator prof. dr hab. Jerzy Ranachowski, IPPT PAN, Warszawa 1985, 239–244.
30. B. Adamczyk, W. Kuniszyk-Jóźkowiak: Effect of echo reverberation of
restricted information capacity on speech process, Folia Phoniatrica, 39,
(1987), 9–17.
31. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka: Integrated stimulation
of speech of stutterers by means of acoustical, optical and tactile signals,
Logopedics and Phoniatrics, Proceedings of the XXth Congress of the International Association of Logopedics and Phoniatrics, 3rd–7th August 1986,
Sasakawa Hall and Miyako Inn Tokyo (1986), 227–273.
32. L. Kaczmarek, B. Adamczyk (red.): Jąkanie, Materiały IX Naukowego Zjazdu Polskiego Towarzystwa Logopedycznego, Lublin 24–25 września 1987,
(1987), 1–83.
33. B. Adamczyk: 30 lat metody „echo”, in: Jąkanie, pod redakcją L. Kaczmarka
i B. Adamczyka, Lublin 1987, 7–14.
34. B. Adamczyk: Stowarzyszenie jąkających się na świecie, in: Jąkanie, pod redakcją L. Kaczmarka i B. Adamczyka, Lublin 1987, 15–19.
35. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka: Zastosowanie zintegrowanego akustyczno-optycznego korektora mowy w terapii jąkających się in:
Jąkanie, pod redakcją L. Kaczmarka i B. Adamczyka, Lublin 1987, 20–23.
36. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka: Stymulacja kanałem słuchowym, wzrokowym i dotykowym procesu mówienia jąkających się, Prace
IPPT IFTR Reports, 2.23 – akustyka mowy, 29/1987, Warszawa 1987, 3–20.
37. W. Kuniszyk-Jóźkowiak, B. Adamczyk: Effect of auditory and tactile echo
and reverberation on stuttering, Proceedings – Supplement of 15 Congress
24
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
LESZEK WÓJCIK
of Union of the European Phoniatricians, (eds) G. Kittel and B. Schurenberg.
Erlangen, 14–18 September, 1988 (1988), 103–105.
B. Adamczyk: My great adventage with stuttering, Second International Conference on Self-help in Stuttering, Cologne, 11–14 August 1989, Abstract
(1989), 100.
W. Kuniszyk-Jóźkowiak, B. Adamczyk: The effect of tactile echo and reverberation on speach fluency on stutterers, International Journal of Rehabilitation Research, 12/3/ (1989), 312–317.
W. Kuniszyk-Jóźkowiak, B. Adamczyk, E. Smołka: Integrated auditory-visual – tactile echo in the speach therapy of stutterers, XXIst Congress of the
international Association of Logopedics and Phoniatics, August 6–10, 1989,
Prague, Proceedings, Vol. I (1990), 119–121.
W. Kuniszyk-Jóźkowiak, B. Adamczyk: Correlation between speach velocity
decrease and speach fluency in stutterers under echo reverberation, XXIst
Congress of the International Association of Logopedics and Phoniatrics, August 6–10, 1989, Prague, Proceedings , Vol. I (1990), 152–154.
E. Smołka B. Adamczyk: The effect of echo and reverberation transmitted
by the auditory and visual channels of stuttering, XXIst Congress of the
International Association of Logopedics and Phoniatrics, August 6–10, 1989,
Prague, Proceedings, Vol. I (1990), 179–181.
B. Adamczyk, Z. Tarkowski (red.): Logopedia 17, Współczesne trendy w logopedii, Materiały X Naukowego Zjazdu Polskiego Towarzystwa Logopedycznego, Lublin 21 i 22 września 1990, UMCS (1990), 1–164.
B. Adamczyk, W. Kuniszyk-Jóźkowiak, T. Szydło: Ocena przez ośrodki logopedyczne terapii jąkania przy użyciu echo-korektora mowy, in: Współczesne
trendy w logopedii, Logopedia, 17, red. B. Adamczyk i Z. Tarkowski (1990),
9–17.
B. Adamczyk, E. Smołka: B. Saran: Wzrokowy autostymulator mowy dla jąkających się, in: Współczesne trendy w logopedii, Logopedia, 17, (red.) B.
Adamczyk i Z. Tarkowski (1990), 19–24.
E. Smołka, W. Kuniszyk-Jóźkowiak, B. Adamczyk, B. Koc-Kozłowiec: Zastosowanie echa w postaci sygnałów akustycznych, optycznych i dotykowych
w terapii jąkania, in: Współczesne trendy w logopedii, Logopedia, 17, red.
B. Adamczyk i Z. Tarkowski (1990), 117–123.
B. Adamczyk (ed.): Logopedia 18 (1991), 1–152.
B. Adamczyk, Motywacja w terapii jąkania, Logopedia, 18 (1991), 15–19.
B. Koc-Kozłowiec, B. Adamczyk: Fonetyczna analiza jąkania, Logopedia,
18 (1991), 59–64.
B. Adamczyk (ed.): Logopedia, 19 (1992), 5–8.
B. Adamczyk: Zawartość tlenu i dwutlenku węgla w powietrzu wydychanym
przez jąkających się, Logopedia, 19 (1992), 5–8.
Dorobek NAUKOWy prof. dr. hab. Bogdana Adamczyka
25
52. E. Smołka, B. Adamczyk: Influence of visual echo and visual reverberation
on speech fluency in stutterers, Int. J. Rehabilitation Research, 15 (1992),
134–139.
53. B. Adamczyk (ed.): Logopedia 19 (1992), 1–76.
54. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka: Sterowanie procesem
mówienia jąkających się sygnałami akustycznymi, optycznymi i dotykowymi, Problemy współczesnej psychologii, (eds) A. Biela, Cz. Walesa, Lublin, 2
(1992), 817–825.
55. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka: Sterowanie procesem
mówienia jąkających się sygnałami akustycznymi, optycznymi i dotykowymi, Problemy współczesnej psychologii, (eds) A. Biela, Cz. Walesa, Lublin,
2 (1992), 817–825.
56. B. Adamczyk, E. Smołka, W. Kuniszyk-Jóźkowiak: Oneskorená akustická,
optická a dotykowá spätná väzbá (echo a reverberácia) v terapii zajakavosti,
Komplexná Rehabilitácia pri poruchách reči a sluchu, Zostavil Dr Jozef Baláž, Bratislava, 1992, 39–42.
57. B. Adamczyk: Motivation of Stutterer in Speech Therapy, Folia Phoniatrica,
XXIInd World Congress of the International Association of Logopedics and
Phoniatrics, August 9–14, 1992, Hannover, Germany, 44 (1992), 3–4.
58. B. Adamczyk: Zawartość tlenu i dwutlenku węgla w powietrzu wydychanym
przez jąkającego się podczas mówienia, Logopedia, 19 (1992).
59. E. Smołka, B. Adamczyk: Influence of visual echo and visual reverberation
on speech fluency in stutterers, International Journal of Rehabilitation Research, 15 (1992), 134–139.
60. E. Smołka, B. Adamczyk: Visual Feedback for Stuttering Therapy, Folia Phoniatrica, XXIInd World Congress of the International Association of Logopedics and Phoniatrics, August 9–14, 1992, Hannover, Germany, 44 (1992), 75.
61. E. Smołka, B. Adamczyk: Visual Feedback for Stuttering Therapy, Institute
of Physics Annual Report 1992, 91.
62. B. Adamczyk: The concentration of oxygen and carbon dioxide in air expired
by stutterer during speaking, Institute of Physics Annual Report 1992, 83.
63. B. Adamczyk: Motivation of Stutterer in Speech Therapy, Folia Phoniatrica,
XXIInd World Congress of the International Association of Logopedics and
Phoniatrics, August 9–14, 1992, Hannover, Germany.
64. B. Adamczyk: Koncentrácia kyslika a kyslićnika uhlićiteho vo vydychavosti
vzduchu u zajakavajuceho poćas reći, VII Celeśtátnu Logopedickú Konferenciu s medzinárodnou úćast’ou, 22–24 októbra, 1992, Żilina, Czechoslovakia.
65. E. Smołka, B. Adamczyk: Visual Feedback for Stuttering Therapy, Proceedings of the XXIInd World Congress of the International Association of
26
LESZEK WÓJCIK
Logopedics and Phoniatrics, August 9–14, 1992, Hannover, Germany, (ed.)
E. Loebell, Hannover, 1993, paper no. 100 (3 pages).
66. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka: Pojęcie synchronizacji
w mówieniu chóralnym z echem i pogłosem w terapii jąkania, Logopedia, 20
(1993), 5–15.
67. B. Adamczyk (ed.): Logopedia, 20 (1993) 1–197.
68. B. Adamczyk: Problemy Zaikovosti, Vedecká Konferencia s medzinárodnou
úćast’ou, Michalovce, 30.06–2.07 1993, Slovakia.
69. B. Adamczyk: Stuttering therapy with the “echo method”, Proceedings of
the 1st World Congress on Fluency Disorders, 8–12 August, 1994, Journal of
Fluency Disorders, 9 (1994), 147.
70. B. Adamczyk: Video-echo in stuttering therapy, IV Congress of People Who
Stutter, 26–29 July 1995, Linkoping, Sweden.
71. B. Adamczyk: Stuttering therapy with the “echo” method, Proceedings of
the 1st World Congress on Fluency Disorders, 8–12 August 1994, Munich,
Germany, (1995), 291–295.
72. W. Kuniszyk-Jóźkowiak, E. Smołka, B. Adamczyk: Effect of acoustical, visual and tactile echo on speech fluency of stutterers, Fol. Phoniatr. Logopaed.
48 (1996), 193–200.
73. B. Adamczyk (ed.): Logopedia, 23 (1996), 1–246.
74. B. Adamczyk: The 33th Anniversary of the Polish Logopedic Society, Logopedia, 23 (1996) 5–8, in Polish.
75. B. Adamczyk: Department of Applied Physics, Maria Curie-Skłodowska University, Lublin. Forty years of investigating stuttering, Logopedia, 23 (1996),
9–25, in Polish.
76. B. Adamczyk, W. Kunszyk-Jóźkowiak, E. Smołka (eds.): Who is who in the
Polish Logopediae, PTL, Lublin, 1996, 1–230, in Polish.
77. B. Adamczyk, Video-echo-talking puppet as a delayed auditory-visual feedback aid for stutterers, Fourth Oxford Dysfluency Conference, St. Catherine’s
College, Oxford, England, 26–29 June 1996, Abstracts, p. 4.
78. B. Adamczyk, B. Raczek: Correlations between the CO2 Concentration in
the Air Exhaled While Speaking and Speech Fluency, Institute of Physics
Annual Report 1996, 87.
79. W. Kuniszyk-Jóźkowiak, E. Smołka, B. Adamczyk: Effect of Acoustical,
Visual and Tactile Reverberation on Speech Fluency of Stutterers, Institute of
Physics Annual Report 1996, 93.
80. W. Kuniszyk-Jóźkowiak, B. Adamczyk: Auditory-Tactile Echo-Reverberating Stutterers’ Speech Corrector, Institute of Physics Annual Report 1996,
95.
81. B. Adamczyk, E. Smołka: The Influence of Video-Echo on the Speaking Process, Institute of Physics Annual Report 1996, 99.
Dorobek NAUKOWy prof. dr. hab. Bogdana Adamczyka
27
82. B. Adamczyk (ed.): Logopedia, 24 (1997), 1–136.
83. B. Adamczyk: Application of audio-echo, video-echo and reverberation in
stuttering therapy in summer or winter camps conditions, Proc. of the Logopedic Workshop “Diagnosis and Therapy of Stutterers”, Augustów, Poland,
5–8 June 1997, 46–52, in Polish.
84. B. Adamczyk, E. Smołka: Professor Leon Kaczmarek as the founder and editor of “Logopedia”, Logopedia, 24 (1997), 15–21.
85. W. Kuniszyk-Jóźkowiak, B. Adamczyk: Auditory tactile echo-reverberating
stutterers’ speach corrector, in: Optoelectronic and Electronic Sensors II,
(ed.) Z. Jankiewicz, Proc. SPIE 3054 (1997), 240–244.
86. B. Raczek, B. Adamczyk: Concentration of carbon dioxide in the air exhaled
while speaking as an index of speaking ergonomics, Proc. of the Logopedic
Workshop “Diagnosis and Therapy of Stutterers”, Augustów, Poland, 5–8
June 1997, 53–58, in Polish.
87. B. Raczek, B. Adamczyk: Electric model RC as a model of emission of CO2
in process of respiration and speaking, Proc. of Xth National Scientific Conference “Biocybernetics and Biomedical Engineering”, Warsaw, Poland, 4–6
December 1997, Warszawa, 87–91, in Polish.
88. B. Adamczyk (ed.): Logopedia, 25 (1998), 1–196.
89. B. Adamczyk: Stutttering as an iceberg, Logopedia, 25 (1998), 15–18, in Polish.
90. B. Adamczyk: Forty years of investigations on application of echo and reverberation in the stuttering therapy, in: 5th World Congress for People who
Stutter, Johannesburg, 5–9 July 1998, Summaries, 17, Johannesburg (1998).
91. B. Adamczyk: Audio-video-echo talking duck in stuttering therapy, in: XXIV
Congress of International Association of Logopedics and Phoniatrics, Amsterdam, 23–27 August 1998, Program and Abstract Book, 6–7, Amsterdam
(1998).
92. B. Adamczyk: Stuttering as an Iceberg, Institute of Physics Annual Report
1998, 85.
93. B. Raczek, B. Adamczyk, M. Jarecka: Capnographic Measurement Level of
CO2 in the Air Exhaled while Speaking, Institute of Physics Annual Report
1998, 97.
94. B. Adamczyk (ed.): Logopedia, 26 (1999) (251 pages), in Polish.
95. B. Adamczyk: From President of Polish Logopedical Society, Logopedia, 26
(1999), 3–7, in Polish.
96. B. Adamczyk: Stuttering therapy for poor but willing people, Logopedia, 26
(1999), 15–26, in Polish.
97. B. Adamczyk: My Great Adventure with Polish Logopedic Society,
Wiadomości Uniwersyteckie UMCS, 10 (1999), 18–19, in Polish.
28
LESZEK WÓJCIK
98. B. Raczek, B. Adamczyk, A. Prószyński: Emission of CO2 exhaled Chile
eluent or disfluent speaking, Proc. of XI National Conference of “Biocybernetics and Biomedical Engineering”, Warszawa (1999), 324–328, in Polish.
99. B. Adamczyk:, Audio-Video-Echo “Talking Duck” in Stuttering Therapy,
Proceedings of 24th Congress of International Association of Logopedics and
Phoniatrics, (eds) Ph. Dejonckere, H. F. M. Peters, 2 (1999), 683–686.
100. B. Adamczyk: Stuttering therapy for the poor but willing, Institute of Physics Annual Report 1999, 73.
101. B. Raczek, B. Adamczyk: Concentration of CO2 in the air exhaled by stutterers and fluent speakers during speaking, Institute of Physics Annual Report 1999, 89.
102. B. Raczek, B. Adamczyk: Changes of concentration of CO2 while fluent or
influent speaking, Proc. of XLVIth Open Seminar of Acoustics, Kraków –
Zakopane, 14–17 September 1999, 125–130, in Polish.
103. B. Raczek, B. Adamczyk: Emission in the Speaking Process of Stutterers
and Fluent Speakers, Maintenance and Reliability, 7 (2000), 29–37.
AGROFIZYKA
AGROPHYSICS
1. B. Adamczyk, B. Aramowicz, T. Olech, S. Gruszeczki, Z. Tryniecki: Pomiary
wymiany gazowej w suchych ziarnach pszenicy układów hel-powietrze, dwutlenek węgla-powietrze, Folia Soc. Sci. Lubl. Mat-Fiz-Chem, 18, 1 (1976),
61–66.
2. B. Adamczyk, B. Aramowicz, T. Olech, M. Piłat: Oporowo-pojemnościowy
model pomiaru wymiany gazowej w ziarnistych ciałach porowatych, Folia
Soc. Sci. Lubl. Mat-Fiz-Chem, 18, 1 (1976), 55–60.
3. B. Adamczyk, B. Aramowicz, K. Gołaszewska, T. Olech: Transport niektórych gazów atomowych i molekularnych przez złoże nasion pszenicy, Roczniki Nauk Rolniczych, 72–C–4 (1977), 137–145.
4. B. Adamczyk, B. Aramowicz, K. Gołaszewska, T. Olech: Problem pomiaru
parametrów wymiany gazowej w ziarnistych ciałach porowatych, Folia Soc.
Sci Lubl., Mat-Fiz-Chem, 19 (1977), 85–88.
5. B. Adamczyk, B. Aramowicz, K. Gołaszewska, T. Olech: Wymiana gazowa
w suchym ziarnie pszenicy, Roczniki Nauk Rolniczych, 73–C–2 (1978), 9–16.
6. B. Adamczyk, B. Aramowicz, K. Gołaszewska, T. Olech: Transport of gases in dry weat grain, Zeszyty Problemowe Postępów Nauk Rolniczych, 203
(1978), 301–305.
7. B. Adamczyk, B. Aramowicz, K. Gołaszewska, T. Olech: Diffusion of gases
through a layer of wheat grain, Zeszyty Problemowe Postępów Nauk Rolniczych, 203 (1978), 309–311.
Dorobek NAUKOWy prof. dr. hab. Bogdana Adamczyka
29
8. B. Adamczyk, B. Aramowicz, K. Gołaszewska, T. Olech: Modelowanie procesów dyfuzyjnych w ośrodkach porowatych, Roczniki Nauk Rolniczych,
73–C–4 (1978), 175–185.
9. B. Adamczyk, B. Aramowicz, K. Gołaszewska: Wyznaczanie parametrów
wymiany gazowej w suchych ziarnach pszenicy, Roczniki Nauk Rolniczych,
74–C–2 (1980), 7–16.
10. B. Adamczyk, B. Aramowicz, K. Gołaszewska, P. Pałczyński, T. Stański,
B. Styk: Pomiary parametrów dyfuzyjnych warstwy ziarna zbóż, Roczniki
Nauk Rolniczych, 74-C-5 (1980), 9–16.
11. B. Adamczyk, B. Aramowicz: The effect of some factors on the diffusion
properties of wheat grain, Proceedings of the II International Conference
on Physical Properties of Agricultural Materials, Gödölö, Hungary, 26–28
August 1980, 7, 84 (1980), 1–7.
12. B. Adamczyk, B. Aramowicz, K. Gołaszewska-Malec, B. Styk: Badanie
wpływu niektórych parametrów agrotechnicznych na parametry dyfuzyjne
warstwy ziarna pszenicy ozimej, Roczniki Nauk Rolniczych, C-75-1 (1981),
199–266.
13. B. Aramowicz, B. Kornas-Czuwar, B. Adamczyk: Parametry dyfuzyjne warstwy modelowo uszkodzonego ziarna pszenicy, Zeszyty Problemowe Postępów Nauk Rolniczych, 258 (1983), 471–477.
14. B. Adamczyk, B. Aramowicz, P. Staszewski: Anwendungsmöglihkeit der
Massenspektometric in der Gasen- un Wasser Bewegungsuntersuchung in
manchen biologischen System, Physic Und Landwirschaft, Beträge der 3.
Wissenschaftlichen Tagung Agrophysik, vom 3. bis 6. December 1984 in
schloss Reihardsbrunn, DDR, 124–127.
15. B. Adamczyk, B. Aramowicz, P. Staszewski: Parametry dyfuzyjne ziarniaków trzech odmian pszenicy zróżnicowanych pod względem czynników agrotechnicznych, Roczniki Nauk Rolniczych, 76–C–1 (1985), 127–131.
16. B. Adamczyk, B. Aramowicz, P. Staszewski: The effect of fertilization level
on the process of difussion of helium in wheat grain, Zeszyty Problemowe
Postępów Nauk Rolniczych, 304 (1985), 81–84.
17. B. Adamczyk, B. Aramowicz, P. Staszewski, S. Grundas, Gas diffusion and
absorption of stain in wheat grain with various internal stuctures, Zeszyty
Problemowe Postępów Nauk Rolniczych, 304 (1985), 85–89.
18. B. Adamczyk, B. Aramowicz, P. Staszewski: Proces dyfuzji gazu w ziarniakach pszenicy poddanych obciążeniom mechanicznym, Zeszyty Problemowe
Postępów Nauk Rolniczych, 320 (1987), 59–62.
19. B. Aramowicz, B. Adamczyk, A. Musur: The investigation of water transport
in wheat grain using D2O as labeled water, Trietija Nacjonale Simpozijum
Fiziki-Sielskostopansko Proizwodstwo, Pleven, Bulgaria, 28–30 September
(1989) 70–73.
30
LESZEK WÓJCIK
20. B. Aramowicz, B. Adamczyk, A. Musur: Methods of investigation into moisture transport in cereal grain using D2O as the labeled water, 4th International
Conference on Physical Properties of Agriculture Materials and Their Influence on Technical Processes, Rostock, September 4–8, 1989, vol. 1 (1989),
20–25.
21. B. Aramowicz, B. Adamczyk, A. Musur: A method of water transport in
wheat grains using Deuterium Oxide D2O as labeled water, Zeszyty Problemowe Postępów Nauk Rolniczych, 370, (1989), 7–10.
22. B. Aramowicz, B. Adamczyk, A. Musur: Investigation into moisture transport parameters in wheat grain using D2O as labeled water, Drying 91, ed.
A. S. Mujumdar, I. Filkova, Elsevier, Amsterdam (1992), 423–434.
23. B. Aramowicz, B. Adamczyk, A. Musur, Water–Vapour Parameters in the
Wheat Grain of Various Endosperm Structure, Institute of Physics Annual
Report 1992, 85.
24. B. Aramowicz, B. Adamczyk, A. Musur: Water vapour transport/sorption
studies in wheat grain and silica gel, 5th International Conference on Physical
Properties of Agricultural Materials, Bonn, September 6–8, (1993), 15.
25. B. Aramowicz, B. Adamczyk, A. Musur, B. Styk: Investigations of the Moisture Sorption Process in the Wheat Grain Using D2O as the Labelled Water,
Zeszyty Problemowe Postępów Nauk Rolniczych, 399, (1993), 1–6.
INNE PUBLIKACJE
OTHER PUBLICATIONS
1. B. Adamczyk, W. Staszewski: On the longitudinal attraction and repulsion
of spheres in vibrating air, Acta Phys. Pol., 15 (1956), 43–47.
2. W. Staszewski, B. Adamczyk: O siłach pomiędzy kulkami w polu akustycznym, Prace II Seminarium Otwartego z Akustyki, Olsztyn (1955), 95–102.
3. W. Staszewski, B. Adamczyk: Spontaneous electrification of dust figures in
Kundt’s tube, J. Acoust. Soc. America, 30 (1958), 987–989.
4. B. Adamczyk, B. Michalak, E. Urbańska: A new method of telemeasurements
of deviations from monolinearity of helicopter blades, Folia Soc. Sci. Lubl. 2
(1962), 128–129.
5. B. Adamczyk, Z. Kozyra, M. Sobolewska: Mercurial collector with low level
of resistance noise, Folia Soc. Sci. Lubl. 2 (19620, 126–127.
6. B. Adamczyk: Prostownik iskrowy, Fizyka w Szkole, 2 (1955), 89–99.
7. B. Adamczyk: Destylarka wodna-automat z ogrzewaniem elektrolitycznym
i chłodzeniem powietrznym, Chemia w Szkole, 35 (1957), 267–271.
8. B. Adamczyk, E. Dowgird: Obserwacja miraży na szosie, Fizyka w Szkole, 5
(1957), 292–295.
Dorobek NAUKOWy prof. dr. hab. Bogdana Adamczyka
31
9. B. Adamczyk, B. Wierciak: Pomiary izotopowe, Fizyka w Szkole, 4 (1957),
241–243.
10. B. Adamczyk, W. Grunwald, S. Kapiszewski, J. Mielnik, M. Piasecka,
B. Wierciak: Pracownia Fizyczna (red.) E. Dowgird, Lublin (1958), 1–178.
11. B. Adamczyk, M. Subotowicz: Profesor Wacław Staszewski (1892–1970),
Postępy Fizyki, 21, 4 (1970), 431–436.
12. B. Adamczyk, M. Łukasiewicz, L. Wójcik, T. Głazowski, D. Adach: Issliedowanie zamaslennosti anodirowannych powierchnostiej, Zawodskaja Laboratoria, 3 (1973), 307.
13. B. Adamczyk, L. Wójcik, M. Łukasiewicz, T. Głazowski, D. Adach: Zastosowanie efektu zwilżania przy badaniu zatłuszczenia powierzchni blach duraluminiowych anodowanych, Folia Soc. Sci. Lubl. Mat-Fiz-Chem, 17, 1/2
(1976), 11–16.
14. B. Adamczyk, M. Łukasiewicz, L. Wójcik, J. Dąbek, D. Adach, T. Głazowski:
Fluorescencyjna metoda wykrywania zatłuszczenia zmywaczy i powierzchni
duraluminiowej, Folia Soc. Sci. Lubl. Mat-Fiz-Chem, 17, 1/2 (1976), 17–20.
15. B. Adamczyk: An optical metod of Tele-measurement of nonlinearity of helicopter propeller blades, Physics in Industry, (eds) E. O’Mongain and C. P.
O’Toole, Pergamon Press, Oxford–New York, (1976), 151–155.
16. J. Dąbek, B. Adamczyk, Z. Rybczyński, M. Plewa: Badanie korelacji pomiędzy gazową przepuszczalnościa klejonych powierzchni a jakością klejenia,
Folia Soc. Sci. Lubl. Mat-Fiz-Chem, 19 (1977) 13–16.
17. B. Adamczyk: Professor dr Emanuel Trembaczowski (1924–1993), Wiadomości Uniwersyteckie, 3, 3 (19), Lublin, (1993).
18. B. Adamczyk: Poster Seminars for the 4th and 5th Year Students of Physics
(Teaching Methods at Universities), Institute of Physics Annual Report 1993,
85.
19. B. Adamczyk: U Brata Alberta. Rozmowa z księdzem Janem Mazurem, Listy
Rotariańskie, 3, 4 (6), 1993, 16.
20. B. Adamczyk: Professor dr Emanuel Trembaczowski (1924–1993), Wiadomości Uniwersyteckie, 3, 3 (19), Lublin, (1993).
21. B. Adamczyk, T. Durakiewicz: Próżnia jako temat na XXXIV Pokazach z Fizyki, Lublin 1993, Technologia Elektronowa, V Konferencja Naukowa ELTE
’94, Szczyrk, kwiecień 1994.
22. B. Adamczyk: Pół wieku fizyki w UMCS. II. Ośrodek fizyki doświadczalnej
UMCS w latach 1976–1994, Annales UMCS, Physica AAA (1994), 45–64.
23. B. Adamczyk: Department of Applied Physics at the Institute of Physics in
the 50-th Anniversary of Maria Curie-Skłodowska University, Institute of
Physics Annual Report 1994, 76.
32
LESZEK WÓJCIK
24. B. Adamczyk: My View of the Present Institute of Physics in the 50-th Anniversary of Maria Curie-Skłodowska University, Institute of Physics Annual
Report 1994, 75.
25. B. Adamczyk: Zakład Fizyki Stosowanej IF UMCS w 50-lecie Uniwersytetu,
Annales UMCS, Physica AAA (1994), 115–138.
26. B. Adamczyk: Video-Echo – Talking Puppet as a Delayed Auditory – Visual
Feedback Aid for Stutterers, Institute of Physics Annual Report 1995, 67.
27. B. Adamczyk: My Adventure with Agrophysics, Polish Society of Agrophysics, Biuletyn Informacyjny, 8 (1999), 7–11, in Polish.
28. B. Adamczyk, L. Michalak: Ecological experiments on physics, XI “School
Physics with Elements of Agrophysics”, Lublin, 27–28 September 1999,
Wyd. Nauk. FRNA 2 (1999), 13–21, in Polish.
PATENTY
PATENTS
1. B. Adamczyk: Sposób korekcji mowy drogą telefoniczną oraz urządzenie do
stosowania tego sposobu, Patent nr 47696 (1964), zgłoszono (submitted in)
1962.
2. B. Adamczyk: Sposób zdalnego pomiaru niewspółtorowości łopat wirnika nośnego śmigłowca i urządzenie do stosowania tego sposobu, Patent nr
78389 (1976), zgłoszono (submitted in) 1972.
3. B. Adamczyk, B. Aramowicz: Termoemisyjne źródło jonów, Patent nr 86074
(1978), (submitted in) zgłoszono 1974.
4. B. Adamczyk, J. Dąbek, J. Koperwas: Sposób oceny przydatności duraluminiowych powierzchni anodowanych do klejenia, Patent nr 96725 (1979),
zgłoszono (submitted in) 1979.
5. T. Olech, B. Adamczyk, J. Siewielec, J. Dąbek: Sposób i urządzenie do oceny przydatności duraluminiowych powierzchni do klejenia, Patent nr 131276
(1986), zgłoszono (submitted in) 1979.
6. B. Adamczyk, W. Kuniszyk-Jóźkowiak, E. Smołka, Z. Bieżyca: Pogłosowy
korektor mowy, Patent nr 122489 (1986), zgłoszono (submitted in) 1979.
7. B. Adamczyk, W. Kuniszyk-Jóźkowiak, Z. Skorzyński, J. Czarnota: Echo-rewerberacyjny korektor mowy dla jąkających się, Patent nr 130362 (1986),
zgłoszono (submitted in) 1980.
10.2478/v10246-012-0013-6
ANNALES
U N I V E R S I TAT I S MAR IAE C U R I E - S K Ł O D O W S KA
LUBLIN – POLONIA
VOL. LXVII
SECTIO AAA
2012
Biophysics Department, Institute of Physies, Maria Curie-Skłodowska University
pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, e-mail: [email protected]
Jan Sielewiesiuk, Agata Łopaciuk
Regulation of gene expression by Goodwin’s loop with many genes
Regulacja ekspresji genów w pętli Goodwina z wieloma genami
ABSTRACT
The paper presents a simple analysis of a long Goodwin’s loop containing many genes. The
genes form a closed series. The rate of transcription of any gene is up or down regulated by the
protein product of the preceding gene. We describe the loop with a system of ordinary differential
equations of order s. Oscillatory solutions of the system are possible at the odd number of repressions
and any number of inductions if the product of all Hill’s coefficients, related to both repressions and
inductions, is larger than:
.
1. INTRODUCTION
We analyze loops of processes with negative or positive feedback. The most
frequently considered realizations of such loops are some genes, whose expression
is, directly or indirectly, regulated by their protein products. Since its invention
by Goodwin in 1965 [1, 2], many papers have been devoted to this system (see
[5] for review). S. Müller and co-authors [4] analyzed general properties of
a long loop containing a number of genes repressed by products of the preceding
gene. Their loop consisted of alternating transcription and translation reactions.
They explored conditions for the existence of oscillatory solutions, multiple
equilibriums and heteroclinic orbits. H. Smith [6] considered a loop containing
a number of repressed genes, which he described by ordinary differential
34
Jan Sielewiesiuk, Agata Łopaciuk
equations with a delay. Invernizzi and Treu [3] have analyzed a long loop with
a single repressed gene. In their system, a protein was produced as a result of the
gene transcription and translation. After numerous transformations, this protein
acquired the form capable of repression of the gene. All mentioned authors
used more general derivations than we do. They arrived at the conclusion that
oscillations are possible under condition, which is much like that mentioned
in Abstract. Our consideration is much simpler and includes the case with
many genes with repressed or induced transcription. We hope that it will be more
intelligible to undergraduate students.
2. THE SCHEME OF THE MODEL
We wish to analyze dynamical features of the loops containing both repressed
and induced genes, whose products (proteins) undergo many changes before their
interaction with the next gene. Let us assume that the loop contains a number of
genes. Some of those genes are down regulated and some of them are up regulated
by proteins encoded in the loop. The structure of the system is sketched in Figure
1. For the rate of transcription we accept the usual formulae of cooperative
kinetics [1]. We assume that the rates of repressed and induced transcriptions are
respectively proportional to
or to
; x is a concentration of the
transcription factor ( protein), a and b are constants and n is the Hill coefficient.
Fig. 1. Goodwin’s loop with a few up- and down- regulated genes. Symbols X1, Xp+1, Xq+1 refer
to mRNA. The rest of Xi denote proteins, gj are regulated genes
Regulation of gene expression by Goodwin’s loop with many genes
35
3. GOODWIN’S LOOP CONTAINING SINGLE REPRESSED GENE
Goodwin’s loop containing single repressed gene can be represented by a set
of ordinary differential equations (1):
x&1 =
a
− x1 ,
1 + xsl
(1)
x&i = hi xi −1 − ki xi ,
i = 2, 3,..., s
where dimensionless variables xi are used with unit concentration adjusted to a
concentration of xs , which makes the rate of transcription equal to the half of its
maximum value a. The unit time is equal to the mean lifetime of mRNA (x1). In
equations (1), l is the Hill coefficient of cooperativity. The symbols hi and ki refer
to rate constants of synthesis (hi) and decay (ki) of the corresponding species.
The system (1) has a single equilibrium point determined by the relations:
s
xi =
∏k
j =i +1
s
j
∏ hj
xs ,
i = 1,..., s − 1.
(2)
j =i +1
s
a
= α xs ,
1 + xsl
α=
∏k
j
∏h
j
j =2
s
j =2
,
where xi denotes the values of the corresponding variable xi in equilibrium
points. The derivative of the nonlinear term in the first equation of (1) with respect
to xs is:
∂f1 − alxsl −1 ,
=
∂xs 1 + xsl 2
(
(3)
)
where f1 replaces the function on the right of the first equation (1).
In the equilibrium point the value of this derivative (see (2)) can be expressed
as:
.
(4)
The diagonal of the Jacobian matrix of the system (1) consists of the
species decay rate constants (kj). Positions (j, j-1) cover the rate constants for the
36
Jan Sielewiesiuk, Agata Łopaciuk
production of corresponding species (hj). The position (1, s) is occupied by the
derivative g. The structure of the Jacobian determines the following equation for
its eigenvalues (λ):
.
(5)
At what values of parameters does the equilibrium become unstable?
Is it possible they have a Hopf bifurcation in this system? Sufficiently simple
analytical solution of (5) can be found only for s=1 or s=2. One could find an
answer to the second question, assuming for (5) pure imaginary λ and searching
for conditions consistent with such an assumption. This way is effective for s not
higher than 6. For the higher orders, equation (5) can be solved analytically only
under severe simplification that the system has very high symmetry. If we assume
that all k j = 1 , then (5) can be written as:
s
(1 + λ ) s = g ∏ h j (cos π + i sin π ) .
(6)
j =2
It follows from (6) that
1
1
s
s

(2k + 1)π + i ⋅  g s h  s sin (2k + 1)π ,
λk = −1 +  g ∏ h j  cos
 ∏ j
s
s
 j =2 
 j =2 
k = 0,1..., s − 1.
(7 )
(7)
The equilibrium will be unstable if the real part of any λ is positive. So far as
we are looking for the minimum conditions of the equilibrium destabilization, we
should consider those roots (7), which have the largest real parts. The two complex
conjugate roots λ0 and λs-1 have the highest real parts. They will be positive and
consistent with (4), if
.
(8)
, one
Taking into account the definition of the α (2) and the assumption
can conclude that double inequality (8) can be satisfied only under the condition
.
(9)
Regulation of gene expression by Goodwin’s loop with many genes
37
So, Hopf bifurcation in system (1) is possible, if the Hill coefficient for
cooperative repression is high enough and s ≥ 3. Let us note two features of the
eigenvalues (7). All of them are placed in a complex plane on the circle with the
radius equal to
(10)
centered at the point (-1, 0). In the particular case
.
(10a)
At the bifurcation, when Re(λ0)=0,
.
and
(11)
The imaginary part of this eigenvalue, or the cyclic frequency of small
oscillations around the equilibrium, is given by (11).
4. GOODWIN’S LOOP CONTAINING A SINGLE INDUCED GENE
The system of equations describing such a loop differs from the system (1)
solely in the first equation referring to transcription.
x&1 =
a xsl
− x1
1 + xsl
x&i = hi xi −1 − ki xi ,
(12)
i = 2, 3,..., s .
We can repeat calculations similarly to those done in the previous section and
obtain corresponding relations determining the coordinates of equilibrium points:
(13)
38
Jan Sielewiesiuk, Agata Łopaciuk
where α is defined exactly in the same way as in (2). As it follows from (13), the
equilibrium is found in the origin of coordinates. Other equilibrium points can be
found at xs≠0.
.
(14)
The left hand side of (14) has a maximum at x sl = l − 1 . The additional points
of equilibrium exist, when the maximum value of this function is higher than α/a.
In the opposite case, graphs of the functions of xs on the left and on the right sides
of (14) will have no common points and equation (14) will have no real solutions:
.
(15)
The derivative of the nonlinear term in (12) is
∂f1
alxsl −1 .
=
∂xs 1 + xsl 2
(
(16)
)
The derivative (16) has the structure which is fully analogical to that of (3).
They differ only by the sign. Let us note that the derivative (16) is equal to zero in
the origin of coordinates. The value of this derivative in other equilibrium points
can be obtained by inserting a from (14) into (16). This results in formula:
.
(17)
The Jacobian structure of the system (12) is exactly the same as it was in (1).
In consequence, characteristic equation of eigenvalues will also have the same
structure:
.
(18)
This time, however, the right hand side of the equation is not negative. It
follows immediately from (16) that equilibrium in the origin of coordinates is
Regulation of gene expression by Goodwin’s loop with many genes
39
stable for any physically meaningful values of the rate constants. For g=0 the
solution of (18) becomes
.
All of the eigenvalues are real and negative and the equilibrium is stable.
Polynomial in λ on the left of (18) is a monotonously increasing function of its
argument for positive λ. For λ=0, the polynomial has the value
eigenvalues appear only for
.
. Positive real
(19)
The case of both sides of (19) equal to each other corresponds to a saddle-node
bifurcation. Taking into account that g satisfies at the same time (17), we arrive
at the conclusion that bifurcation takes place for equilibrium value of xs,, when
x sl = l − 1 . So, the condition for the existence of nonzero equilibrium points and
the condition for unstable equilibrium are the same. Let us shortly consider the
very symmetrical case with all kj=1. In such a case characteristic equation (18)
acquires the shape:
.
(20)
And eigenvalues are:
.
There is at least one real eigenvalue (λ0). It will be positive when the inequality
(22) is satisfied.
.
(22)
In this case (kj=1) inequalities (22) and (19) are equivalent. At a maximum
transcription rate (a) which is high enough in comparison with the overall rate of
proteins decay (15), the loop under consideration is a bistable trigger with one
40
Jan Sielewiesiuk, Agata Łopaciuk
of the stable equilibrium points in the origin of coordinates and the second at
. In the opposite case the system has only one equilibrium with all of
the variables equal to zero.
5. GOODWIN’S LOOP CONTAINING MANY REGULATED GENES
We will not present in detail the systems with two regulated genes. It can be
shown that a loop containing two repressed genes behaves as a bistable trigger
at high enough maximum rate of transcription. Two stable equilibrium points
correspond to high concentrations of one of the regulating proteins and low
concentrations of the other. There is no equilibrium in the origin of coordinates.
There are no oscillations, either.
At the low rate of transcription, a loop containing two induced genes behaves
like the loop with a single induced gene. It can have an equilibrium point for
all the variables equal to zero. Alternatively, it can have two additional points of
equilibrium outside the origin of coordinates. One of these points is unstable and
the second one is stable. The loop behaves then as a bistable trigger.
As an example of the loop with many regulated genes we are going to discuss
the loop containing three regulated genes. One of these genes is repressed and
two of them are induced. The system can be represented by a set of ordinary
differential equations (23):
(23)
Nonlinear expressions in equations 1, q+1 and r+1 refer to gene transcription
with a repression or induction. Dynamical variables with the mentioned indices
refer to mRNA concentration. The rest of variables denotes concentrations of
proteins. Equations (23) have been written in a dimensionless form. The unit time
Regulation of gene expression by Goodwin’s loop with many genes
41
is equal to the mean lifetime of the mRNA, whose concentration is denoted by
x1 in equations (23). Parameters R2 and R3 denote the ratio of the decay constants
between xq+1, xr+1 and x1 respectively. Concentrations units are not the same for
all variables. It follows from equations 1, q+1 and r+1 in (23) that unit values of
xs, xq and xr make the rates of corresponding transcriptions equal to halves of their
maximum values. The variables x1…xq are expressed in the same units as xq. The
variables xq+1 …xr have the same concentration units as xr. Similarly, variables
xr+1 …xs have the same concentration units as xs. Equating the right sides of linear
equations in (23), we can relate equilibrium values of all the variables to those of
xq , xr and xs .
(24)
(25)
.
(26)
Equilibrium values of xq, xr and xs can be obtained from equations (27):
.
(27)
To linearize the system (23), we will calculate derivatives of the nonlinear
terms with respect to their arguments:
∂f1 − C1l xsl −1
=
,
∂xs
1 + xsl 2
(
)
∂f q +1
∂xq
=
C2 m xqm −1
(1 + x )
m
q
,
2
∂f r +1 C3n xrn −1 .
=
∂xr
1 + xrn 2
(
)
(28)
42
Jan Sielewiesiuk, Agata Łopaciuk
The symbols f1 , fq+1 and fr+1 refer to functions in the right sides of the
corresponding equations in (23). If we put the values of C1, C2 and C3 obtained
from (27) into (28), we will arrive to expressions for the values of the derivatives
in the equilibrium point:
(29)
(30)
.
(31)
Let us notice that the absolute value of the product
(32)
has an upper bound equal to the limit value at x s → ∞ and x q = x r = 0 (32).
Now, we ought to find eigenvalues of the Jacobian matrix of the system.
(33)
We have to transform the determinant (33) into polynomial and solve the
resulting equation. The Jacobian contains two nonzero terms in each row. One of
these terms is situated on the main diagonal, in the position (j, j) and is equal to
the rate constant of decay of the respective substance. The other nonzero terms,
the rate synthesis constants of the respective substances, have positions (j, j-1).
Regulation of gene expression by Goodwin’s loop with many genes
43
In the rows 1, q+1 and r+1, the values of derivatives of the terms describing
transcription are placed in these positions instead of rate constants of synthesis.
Derivatives are positive in the case of induction and they are negative in the case
of repression. In the first row the derivative g1 is situated in the position (1, s).
Equation (33) is equivalent to polynomial equation (34).
(34)
Because of the repression, there is no equilibrium in the origin of coordinates.
Neither of derivatives g is equal to zero, but their product can be positive or
negative. When the right hand side of (34) is positive, the system has a phase
portrait of a trigger. When it is negative, the system evolves similar to that with
one repressed gene. If parameters satisfy some additional condition, the system
will be able to show auto-oscillations. These conditions consist in high enough
maximum rates of transcription (C1 , C 2 , C 3 ) and decay constants R2 , R3 , k j
not too much different from 1. In the particular case of the system (23) the product
of gi and the right side of (34) is negative.
Equation (34) has no simple solution in general case. But it is solvable under
quite severe conditions that
(
.
)
(35)
The conditions (35) are equivalent to the assumption that all reagents of the
system have the same mean rate constants of their decay. If it is so, then equation
(34) can be written as
(36)
Let us to notice that under condition (35) the absolute value of g1g2g3 (32)
(37)
Taking into account that, according to (24–26 and 35)
(38)
44
Jan Sielewiesiuk, Agata Łopaciuk
we obtain the relation (39):
.
(39)
The insertion of (39) into (36) results in the equation for eigenvalues λ.
.
(40)
It is evident that the absolute value of the right hand part of (40) satisfies the
inequality:
.
(41)
In the case of the negative product of derivatives, at odd number of repressions, the equation (40) can be written as:
.
(42)
and
.
(43)
All of the eigenvalues (43) are located on a circle with the radius R
with the centre in the point (-1, 0) on the complex plane.
Im λ
Re λ
Fig. 2. Eigenvalues (21): a) R<1, b) R=1, c) R>1
1
s
and
Regulation of gene expression by Goodwin’s loop with many genes
45
The roots λ0 and λs-1 have the same and the largest real part. Equilibrium of our
system will be destabilized through Hopf bifurcation when the real part of these
eigenvalues becomes positive. It happens when
.
(44)
At the same time R should satisfy the inequality (41). It is possible, if
.
(45)
Relation (45) and a negative product of nonlinear term derivatives in (23)
constitute the necessary conditions of Hopf bifurcation in the system with a single
repressed and two induced genes. This result can be generalized on a long loop
with an odd number of repressed genes and with any number of induced genes.
So, an oscillatory solution is possible in a Goodwin’s loop when it contains an
odd number of repressed genes and has the product of Hill coefficients higher
than
, where s is the number of chemical species participating in the
loop or the order of the system of ordinary differential equations describing the
loop. The main requirement for the existence of oscillatory solutions in the loops
under consideration is an odd number of repressed genes. However, the presence
of cooperative induction makes the product of Hill coefficients higher. On the
other hand, at the presence of many protein interconvertions, even described by
linear equations, s is higher and the extreme left side of (45) is lower. Both factors
make oscillatory solution more probable.
references
[1]Goodwin, B. C., Oscillatory behavior in enzymatic control processes, Advances in Enzyme
Regulation 3 (1965), 425–438.
[2]Goodwin, B. C., An entrainment model for timed enzyme synthesis in bacteria, Nature 209
(1966), 479-481.
[3] Invernizzi, S., Treu, G., Quantitative analysis of the Hopf bifurcation in the Goodwin
n-dimensional metabolic control system, J. Math. Biol. 29 (1991), 733–742.
[4] Müller, S., Hofbauer, J., Endler, L., Flamm, Ch., Widder, S., Schuster, P., A generalized model
of the repressilator, J. Math. Biol. 53 (2006), 905–937.
[5] Purcell, O., Savery, N. J., Grierson, C. S., di Bernardo, M., A comparative analysis of synthetic
genetic oscillators, J. R. Soc. Interface, doi:10.1098/rsif.2010.0183, Published online.
[6] Smith, H., Oscillations and multiple steady states in a cyclic gene model with repression, J.
Math. Biol. 25 (1987), 169–190.
10.2478/v10246-012-0014-5
ANNALES
U N I V E R S I TAT I S MAR IAE C U R I E - S K Ł O D O W S KA
LUBLIN – POLONIA
VOL. LXVII
SECTIO AAA
2012
SpaceLife Institute, via Roncaglia 35, 61047 San Lorenzo in Campo (PU), Italy
e-mails: [email protected],[email protected]
Davide Fiscaletti*, Amrit S. Sorli
Three-dimensional space as a medium of quantum entanglement
Trójwymiarowa przestrzeń jako ośrodek splątania kwantowego
ABSTRACT
Most physicists today still conceptualize time as a part of the physical space in which material
objects move, although time has never been observed and measured as a part of the space. The
concept of time here presented is that time measured with clocks is merely the numerical order of
material change, i.e. motion in a three-dimensional space. In special relativity the Minkowskian
four-dimensional space-time can be replaced with a three-dimensional space where time does not
represent a fourth coordinate of space but must be considered merely as a mathematical quantity
measuring the numerical order of material changes. By quantum entanglement the three-dimensional
space is a medium of a direct information transfer between quantum particles. Numerical order of
non-local correlations between subatomic particles in EPR-type experiments and other immediate
quantum processes is zero in the sense that the three-dimensional space acts as an immediate
information medium between them.
Key words: space, time, numerical order of material change, run of clocks, photon motion,
quantum entanglement, quantum entropy, symmetrized quantum potential
1. Introduction
In Newtonian physics, as well as in standard quantum mechanics, time is
postulated as a special physical quantity and plays the role of the independent
variable of physical evolution. Newton or Hamilton equations, as well as the
Schrödinger equation, are introduced on the basis of the underlying assumption
* corresponding author
48
Davide Fiscaletti, Amrit S. Sorli
that an idealized, absolute time t in which the dynamics is defined, exists. However,
it is an elementary observation that we never really measure this idealized time t,
that this idealized, absolute time does not ever appear in laboratory measurements:
we rather measure the frequency, speed and numerical order of material changes.
What experimentally exists is only the motion of a system and the tick of
a clock. What we realize in every experiment is comparing the motion of the
physical system under consideration with the motion of a peculiar clock described
by a peculiar tick T. This means that the duration of material motions has not
a primary physical existence, that time as humans perceive it does not exist as an
absolute quantity, that time does not flow on its own as an independent variable
and thus does not exist as a primary physical reality.
Changes of the state of the universe and, at the same time, changes of the
state of any physical system can be considered the primary phenomena which
generate evolution of the universe. This evolution can be described by introducing
a mathematical parameter, which provides only the ordering of events. In the article
Projection evolution and delay choice experiment, A. Góźdź and K. Stefańska
have shown that an evolution parameter, “numerical order”, which provides only
the order of events, can be easily introduced [1]. In the reference [2], the authors
of this article have gone beyond by suggesting the following concept of time:
according to this view, the symbol of time t in all mathematical formalisms of
physics is a number which represents the numerical order of material change,
i.e. motion and therefore, only the numerical order of the motion of the system
under consideration, which is obtained by the clock under consideration, exists.
In the Minkowskian arena of the Special Theory of Relativity the fourth
coordinate X 4 of space is spatial, too. X 4 is a product of imaginary number i ,
light speed c , and the numerical order t of a physical event: X4 = i · c · t. On
the basis of the mathematical expression of the fourth coordinate, the Minkowski
arena is a four-dimensional (4D) space [3]. In the recent article Special theory of
relativity in a three-dimensional Euclidean space [4] the authors have shown that
Minkowski 4D space can be replaced with a three-dimensional Euclidean space
with Galilean transformations
X '= X − v ⋅ t
Y '= Y
Z '= Z
X 4 = i ⋅c ⋅t
(1)
for the three spatial dimensions and Selleri’s transformation
v2
t' = 1− 2 ⋅ t
c
(2)
Three-dimensional space as a medium of quantum entanglement
49
for the rate of clocks. The Galilean transformations are valid for both the observers
O and O’ in inertial systems o and o’. The transformation of the speed of clocks
given by Selleri’s formalism [5, 6, 7] shows clearly that the speed of the moving
clock does not depend on the spatial coordinates but is linked only with the speed
v of the inertial system o’. In the formalisms (1) and (2), time and space are two
separated entities. Equations (1) and (2) determine an arena of Special Relativity
in which the temporal coordinate must be clearly considered as a different entity
with respect to the spatial coordinates just because the transformation of the
speed of clocks between the two inertial systems does not depend on the spatial
coordinates. Selleri’s results seem thus to suggest that the three spatial coordinates
of the two inertial systems turn out to have a primary ontological status, define
an arena that must be considered more fundamental than the standard space-time
coordinates interpreted in the sense of Einstein. On the basis of equations (1)
and (2) one can assume that the real arena of Special Relativity is not a mixed
3D+T space-time but rather a three-dimensional (3D) space and that time does
not represent a fourth coordinate of space but exists merely as a mathematical
quantity measuring the numerical order of material changes.
The main idea which is at the basis of this article is that evolution in the universe
occurs in a 3D space. The article is structured in the following manner. In chapter
2 we will illustrate in what sense a timeless 3D space (where time exists only as
a numerical order of events) is the fundamental arena of physical processes (and
we will indicate some current research which point in this direction). In chapter
3 we will mention some predictions of our model in the relativistic domain and
propose a way in which our theory of space and time could be falsified. Finally, in
chapter 4 we will show that, as regards non-local correlations between subatomic
particles, the 3D space acts as a direct medium of quantum information transfer
(in the picture of Bohm’s quantum potential and then of a symmetrized quantum
potential).
2. THREE-DIMENSIONAL SPACE AS A FUNDAMENTAL ARENA OF PHYSICS
In his paper Time and Classical and Quantum Mechanics: Indeterminacy
versus Discontinuity Lynds argues that between time and space there is always a
difference: “The fact that imaginary numbers when computing space-time intervals
and path integrals do not facilitate that when multiplied by i , that time intervals
become basically identical to dimensions of space. Imaginary numbers show up
in space-time intervals when space and time separations are combined at near
the speed of light, and spatial separations are small, comparing to time intervals.
What this illustrates is that although space and time are interwoven in Minkowski
space-time, and time is the fourth dimension, time is not spatial dimension: time
is always time, and space is always space, as those i ' s keep showing us. There is
50
Davide Fiscaletti, Amrit S. Sorli
always a difference. If there is any degree of space, regardless of how microscopic,
there would appear to be inherent continuity i.e. interval in time” [8].
Although Lynds’ conclusion that time is time and space is always space may
appear a little questionable (the imaginary space-time interval, in fact, means only
an impossibility to connect the points under consideration by a signal equal or
slower than the speed of light), according to the authors there is nothing wrong in
assuming that time and space are different in their nature, that time is a different
entity from space, that time is not a spatial dimension. The crucial starting
hypothesis of the view suggested in this paper is that time and space are different
in their nature and that the difference between space and time is the following: the
fundamental arena of the universe is a 3D space and time is a numerical order of
material changes that take place in space.
On the other hand, many researchers are challenged with the view that
time is not a fundamental arena of the universe. For example, in their paper The
Mathematical Role of Time and Space-Time in Classical Physics, Newton C. A. da
Costa and Adonai S. Sant’Anna show that time as a fundamental physical arena in
which material changes take place can be eliminated: “We use Padoa’s principle
of independence of primitive symbols in axiomatic systems in order to discuss
the mathematical role of time and space-time in some classical physical theories.
We show that time is eliminable in Newtonian mechanics and that space-time is
also dispensable in Hamiltonian mechanics, Maxwell’s electromagnetic theory,
the Dirac electron, classical gauge fields, and general relativity” [9].
According to several current studies, the mathematical model of space-time
does not correspond indeed to a physical reality and a “state space” or a “timeless space” can be proposed as the fundamental arena. In particular, Girelli, Liberati and Sindoni have developed a toy model in which they have shown how the
Lorentzian signature and a dynamical space-time can emerge from a non-dynamical Euclidean space, with no diffeomorphisms invariance built in. In this sense
this toy-model provides an example where time is not fundamental, but simply an
emerging feature [10]. In more detail, this model suggests that at the basis of the
arena of the universe there is some type of “condensation”, so that the condensate
µν
is described by a manifold R 4 equipped with the Euclidean metric δ µv
. Both the
condensate and the fundamental theory are timeless. The condensate is characterized by a set of scalar fields Ψi x µ , i=1, 2, 3. Their emerging Lagrangian L is invariant under the Euclidean Poincarè group ISO(4) and has thus the general shape
( )
L = F ( X 1 , X 2 , X 3 ) = f ( X 1 ) + f ( X 2 ) + f ( X 3 ) ; X i = δ µvµν ∂ µ Ψi ∂ν Ψi . (3)
( )
The equations of motion for the fields Ψi x µ are given by
Three-dimensional space as a medium of quantum entanglement
 ∂2F

 ∂F µ 
(∂ µ X j )∂ µ Ψi + ∂F ∂ µ ∂ µ Ψi  .
∂ µ 
∂ Ψi  = 0 = ∑ 
 ∂X i

( )
j
 ∂X ∂X
 i j
∂X i


51
(4)
The fields Ψi x µ can be expressed as Ψi = ψ i + ϕ i where ϕ i are
perturbations which encode both the gravitational and matter degrees of freedom
and the functions ψ i are classical solutions (of the above Eq. (4)). The Lagrangian
for the perturbations ϕ i is given by
F (X 1 , X 2 , X 3 ) + ∑
j
2
3
∂F
(X )δX j + 1 ∑ ∂ F (X )δX jδX k + 1 ∑ ∂ F (X )δX jδX kδX l
∂X j
2 jkjk ∂X j ∂X k
6 jkl ∂X j ∂X k ∂X l
(5)
µν
where X i = δ µv
∂ µψ i ∂νψ i and δX i = 2δ µψ i ∂ µψ i ∂ µ ϕ i ∂ µ ϕ i .
Different choices of the solutions ψ i lead to different metrics
(6).
The toy model developed by Girelli, Liberati and Sindoni shows that at
a fundamental level space is a timeless condensate, that time as humans perceive
it is only an emerging feature and that different solutions of the equations of
motion of the fields characterizing this condensate determine different metrics
of the space-time background. If in a timeless background different metrics
are possible and time represents only an emerging feature, this means that, at
a fundamental level, time cannot be considered a physical arena, a primary physical
reality and that in order to describe physically the evolution clocks provide only
a parameter which orders events.
But in what sense clocks provide only the numerical order of a physical event,
how can a clock act in a space that, at a fundamental level, is timeless? In this regard,
in the recent article The nature of time: from a timeless Hamiltonian framework to
clock time metrology, Prati has underlined that Hamiltonian mechanics, both in the
classical domain and in quantum field theory, is rigorously well defined without
the concept of an absolute, idealized time. Prati has shown that in a timeless
Hamiltonian framework a physical system S, if complex enough, can be separated
in a subsystem S2 whose dynamics is described, and another cyclic subsystem
S1 which behaves as a clock [11]. The cyclic subsystem acts as a clock reference
used for the operative definition of time. An important result of Prati’s research is
that, as a consequence of the gauge invariance (which transforms one parametric
time into another in a way that they are all equivalent) the complex system S can
be separated in many ways in a part which constitutes the clock and the rest. But,
52
Davide Fiscaletti, Amrit S. Sorli
now, what does it mean, in physical terms, that a complex physical system can be
separated in many ways in a subsystem whose dynamics is described and another
subsystem which behaves as a clock? This means clearly that the time provided
by each subsystem which acts as a clock cannot be considered as an absolute
quantity, and therefore that time as an idealized quantity that flows on its own does
not exist: only the ticking of each subsystem acting as a clock exists as physical
reality. This implies, in other words, that each subsystem which acts as a clock
provides only a description of the dynamics of the other subsystem and that this
description is tightly linked to ticking of the clock-subsystem. In synthesis, one
can say that each clock-subsystem provides only a measuring reference system for
the dynamics of the other subsystem and that this reference system is not absolute;
one can say that each subsystem that acts as a clock provides only the numerical
order of the dynamics of the other subsystem.
Moreover, recently Pavsic developed a Kaluza-Klein-type model in which
the ordinary spacetime of general relativity is replaced with a configuration space
C, a multidimensional manifold equipped with metric, connection and curvature
[12]. Inside this model Pavsic showed that the ordinary general relativistic theory
for a many particle system is only a special case that derives from a more general
action in the configuration space C for a particular block diagonal metric. The
most general action has the form
½
(7)
where X M ≡ X iµ (with µ = 0, 1, 2, 3 and i=1, 2,…,N, N being the number of
the particles in the configuration) are the coordinates of the point particles of the
system, M has the role of mass in C, τ is an arbitrary monotonically increasing
parameter and GMN is the metric. The action is proportional to the length of a
worldline in C. The ordinary general relativistic theory for a many particle system
derives from the action (7) in the special case
(8).
Inside Pavsic’s model, the metric in the configurations space C is not fixed
but is dynamical, so that the total action contains a kinetic term for GMN:
Three-dimensional space as a medium of quantum entanglement
53
(9)
where
(10)
and
(11)
where R is the curvature scalar in C.
In Pavsic’s model, the fact that, on the basis of equations (7), (9), (10) and
(11), the action of a system of N particles in the general relativistic domain does
not depend explicitly on an idealized time but only on an arbitrary monotonically
increasing parameter τ , according to the authors, means that in general relativity
time does not exist as a primary physical reality but is only a mathematical device
and that the parameter τ represents just a measuring device of the mathematical
numerical order of material changes, characterizing the system of N particles
under consideration.
In synthesis (also taking into account some current research) according to
the authors of this paper, it is legitimate to assume that the fundamental arena in
which material changes take place is a 3D space and that time is a different entity
from space, is not a primary physical reality that flows on its own: it exists only
as a numerical order of material changes measured with clocks. In the universe,
material changes are running in space only while time, being merely a mathematical
measuring system, is a static concept: it indicates exclusively a numerical order
of material changes. Past instants t −n ...t −2 , t −1 , present the moment t 0 and future
instants t 1,t 2 ...t n exist only as a numerical order of material change in a 3D space.
One can move in space only and not in time. Hypothetical travels in time are not
possible.
3. ABOUT THE PREDICTIONS AND THE FALSIFIABILITY OF THE HERE PRESENTED
THEORY OF SPACE AND TIME
As regards the predictions of the model of space and time proposed by the
authors, it is important to mention that, in virtue of equations (1) and (2), there is
no “time dilation” and there is no “length contraction” in the direction of motion
of an inertial system (as it is known in the Special Theory of Relativity). In fact,
54
Davide Fiscaletti, Amrit S. Sorli
on the one hand, it is not true that dilation of time as a 4th coordinate of space
causes clocks to have a slower rate: what really exists in different inertial systems
is the relative velocity of material change (including the run of clocks). On the
other hand, as regards “length contraction” some other research leads to the same
conclusions of our model. Since 1905, when the Special Theory of Relativity was
published, there has been no experimental data on “length contraction” [13].
As regards the possibility to falsify our model, let us consider the falsifiability
of the following two statements, A and B:
A. for all experiments, time t has the same ontological nature of the 3D space
and therefore is a fundamental physical entity in which a given experiment occurs;
B. for all experiments, time t, when measured with clocks, is merely
a numerical order of material change taking place in a 3D space, which is
a fundamental physical entity in which a given experiment occurs.
Statement A has no basis in the elementary visual perception. This is its
weak point. Statement A is falsifiable by an experiment in which time t does not
exist. Such an experiment is, for example, the Coulomb experiment with a torsion
balance to measure electrostatic interaction between two metal-coated balls
endowed with charges q1 and q 2 respectively. The Coulomb experiment implies
the following mathematical formalism as regards the electrostatic force between
the two metal-coated balls:
F = Ke
q1 q 2
r 2 (12)
where r is their distance.
In this experiment, time is not present as the fundamental entity in which
the experiment takes place. To consider statement A as correct, it should be
proven that the Coulomb experiment does not take place in space only but also
in time, and that time does not affect the electrostatic interaction between the two
metal-coated balls. Without this proof this experiment indicates statement A is
wrong: formalism (12) indicates experiment takes place only in the 3D space as
a fundamental physical entity, not in time.
In the analogous way, in Newton’s measuring of gravitational force between
two material objects, time t as the fundamental physical entity does not exist.
Measurement of the gravitational force implies the following mathematical
formalism of gravitational force between two material objects of masses m1 and
m2 situated at distance r:
F =G
m1m2
(13).
r2
Three-dimensional space as a medium of quantum entanglement
55
In this experiment, time is not present as the fundamental physical entity in
which the experiment takes place. To consider statement A as correct it should
be proven that this experiment takes place in time and that time does not affect
gravitational force between the two material objects. Without this proof the
experiment indicates that statement A is wrong: formalism (13) indicates the
experiment takes place only in the 3D space as a fundamental entity, not in time.
Statement B has its basis in the elementary visual perception. This is its
strong point. Ocular experience confirms that clocks measure the numerical order
of material changes in 3D space as a fundamental entity in which an experiment
occurs. Statement B is falsifiable by an experiment where time t measured
with clocks is not the numerical order of material changes. Such an experiment
would prove statement B to be wrong; such an experiment is not known yet. An
experiment where there is no time is not disproving statement B.
4. BY QUANTUM ENTANGLEMENT 3D SPACE IS A DIRECT MEDIUM
OF QUANTUM INFORMATION TRANSFER
According to the concept of space-time, all physical phenomena happen in
space and time. This concept cannot explain those physical phenomena where
information transfer is immediate. For these phenomena the elapsed clock run
is zero. We can appropriately call these phenomena as “immediate physical
phenomena”. If phenomena would happen in time as some physical reality,
time could never be zero. The core of this article is to present a new concept
of space-time as a timeless 3D physical reality where measurable time obtained
with clocks is only a numerical order of physical phenomena. Immediate physical
phenomena have no numerical order. Immediate physical phenomena are
immediate information transfers carried directly by the 3D space which originates
from a 3D vacuum. In the quantum domain, examples of such phenomena are: the
non-local correlations between quantum particles in EPR-type experiments and
other immediate physical phenomena like tunneling or quantum entanglements
regarding the continuous variable systems or the quantum excitations from one
atom to another in Fermi’s two-atom system [14–17].
On the other hand, it is important to mention that also quantum electrodynamics
predicts the existence of immediate physical phenomena. The QED allows for
0-time phenomena for virtual photons which do not obey normal conservation laws
and other rules. These virtual processes of exchange of space-like virtual photons
are not related to transfer of any real physical quantity but are characterized by
interchange forces which act instantaneously thanks to the medium of space.
The fundamental quantum process underlying applications as disparate as the
gyromagnetic ratio of the electron and electrical machinery is the so-called
56
Davide Fiscaletti, Amrit S. Sorli
Møller scattering ee → ee. In J. H. Field’s paper Quantum electrodynamics and
experiment demonstrate the nonretarded nature of electrodynamical force fields,
a detailed analysis of the quantum amplitude for the Møller scattering shows
that the corresponding intercharge force acts instantaneously: on the basis of the
lowest order Feynman diagram, each virtual photon in the Møller scattering is
both emitted and absorbed at the same instant, so that the corresponding force is
transmitted instantaneously [18].
According to the view suggested by the authors of this article, immediate
physical phenomena are characterized by a zero numerical order independently on
the motion of the observer. Therefore, in this approach the interesting perspective
is opened that the zero numerical order regarding the immediate information
transfer turns out to have an ontological status similar to the maximum of the light
speed of the special theory of relativity.
As we know, in quantum mechanics the world is described by a wave function. The wave function of an isolated microsystem evolves freely according to
the Schrodinger evolution, that is certainly one of the most important equations of
physics, as it allows us to understand the behaviour of many materials and physical systems, like for example semiconductors and lasers. Quantum mechanics was
however originally formulated as a theory of quantum microsystems that interact
with classical macrosystems. In the original formulation of the theory, the interaction of a quantum microsystem S with a classical macrosystem O is described
in terms of “quantum measurements” [19, 20]. After the microsystem S under
consideration interacts with its surroundings, the microsystem and its surroundings then become entangled and they are in a quantum mechanical superposition.
If the macrosystem O interacts with the variable q of the microsystem S, and S
is in a superposition of states of different values of q, then the macrosystem O
measures only one of the values of q, and the interaction modifies the state of S by
projecting it into a state with that value: in every measurement the wave function
of a microsystem collapses into the state specified by the outcome of the measurement. But, is the collapse of the wave function instantaneous? Do properties of
subatomic systems become manifest suddenly? When precisely can we say that a
given event has happened?
In this regard, in his book The Landscape of Theoretical Physics: A Global
View, Pavsic proposes the old idea (which appears however a little questionable)
that the collapse of the wave function happens at the moment when the information
about the interaction between the microsystem and the macrosystem arrives in the
observer’s brain: according to this view, there would be no collapse until the signal
reaches the observer’s brain [21]. As regards the question of when precisely a
quantum event happens, when precisely properties of subatomic systems become
manifest, according to the authors, Rovelli’s view seems more interesting. It has
Three-dimensional space as a medium of quantum entanglement
57
shown that the quantum theory gives a precise answer to this question. Rovelli
has found that: (i) a precise (operational) sense can be given to the question
of the timing of the measurement; (ii) we can compute the time at which the
measurement happens using standard quantum techniques; (iii) the interpretation
of the physical meaning of this time is no more problematic than the interpretation
of any other quantum result [22]. Rovelli showed that the question “When does
the measurement happen?” is quantum mechanical in nature, and not classical.
Therefore, its answer must be probabilistic. For example, the sentence “half way
through a measurement” would mean that the measurement is just “happened with
1/2 probability”, or “already realized in half of the repetitions of the experiment”.
The second idea is that the question “When does the measurement happen?” does
not regard the measured quantum system S alone, but rather the coupled system
formed by the observed system S and the observer system O. Therefore, the
appropriate theoretical setting for answering this question is the quantum theory
of the two coupled systems. In more detail, Rovelli has introduced an operator
measuring whether or not the measurement has happened. By considering the
simple case of a physical system S (for example an electron) that interacts with
another physical system O (an apparatus measuring the spin of the electron) and
that the interaction between S and O qualifies as a quantum measurement of the
variable q of the system S, if we suppose that q has only two eigenvalues a and b,
during the interaction between S and O, the state of the combined system S-O is
(14)
where a and b are the eigenstates of q corresponding to the eigenvalues a and
b respectively, O
a a and O
a b are the states of O that can be identified as “the
pointer of the apparatus indicates that q has value a” and “the pointer of the apparatus indicates that q has value b”, respectively. When the combined system
S-0 is in the state (14), a definite correlation between the pointer variable, with
a a and O
a b , and the system variable, with eigenstates a and b ,
eigenstates O
is established.
For some reason, at some point, we have to (or we can) replace the pure state
(14) with a mixed state. Equivalently, we replace (14) with either
(15)
or
(16)
58
Davide Fiscaletti, Amrit S. Sorli
2
2
where, of course, the probability of having one or the other is ca and cb respectively. If the wave function has collapsed, and the state is either (15) or (16),
the correlation between the pointer variable and the system variable is present
as well.
Rovelli focuses attention on the question of what we can say about the precise
time t at which the wave function changes from (14) to either (15) or (16) and
the quantity q acquires correspondingly a definite value. In this regard, Rovelli
has found that the operator M which measures the timing of the measurement is
defined as the projection operator on the subspace spanned by the two states ψ a
and ψ b : M = ψ a ψ a + ψ b ψ b . M turns out to be a self-adjoint operator
on the Hilbert space of the coupled system S-O. It may admit an interpretation
as an observable property of the coupled system S-O. In all the eigenstates of
M with eigenvalue 1 the pointer variable correctly indicates the value of q. In all
the eigenstates of M with eigenvalue 0, it does not. Therefore, M has the following
interpretation: M = 1 means that the pointer (correctly) measures q. M = 0 means
that it does not. Now, when the pointer of the apparatus correctly measures the
value of the observed quantity, we say that the measurement has happened.
Therefore we can say that M = 1 has the physical interpretation “the measurement
has happened”, and M = 0 has the physical interpretation “the measurement has
not happened”. By applying standard quantum mechanical rules to this operator,
at every time t, we can compute a precise (although probabilistic) answer to the
question whether or not the measurement has happened: the probability that the
measurement has happened at time t is given by relation P(t ) = ψ (t ) M ψ (t )
where ψ (t ) is the state of the coupled system during the Schrödinger evolution.
The probability density p (t ) that the measurement happens between time t and
time t+dt is
(17)
where H is the total Hamiltonian. For a good measurement in which P(t ) grows
smoothly and monotonically from zero to one, p (t ) will be a “bell shaped”
curve, defining the time at which the measurement happens, and its quantum
dispersion.
Now, in the picture of our model of space and time according to which the
fundamental arena of physics is a 3D space and clocks provide a numerical order
of events, Rovelli’s results can be read in the following manner. The operator
M can be interpreted as the operator which measures the numerical order of
a measurement during the interaction between a subatomic system and an
apparatus; the probability density (17) defines the numerical order associated
with the actualization of a measurement. Moreover, on the basis of the treatment
Three-dimensional space as a medium of quantum entanglement
59
made here, one can conclude that the fundamental essence, the fundamental arena
of measurement processes is represented by the correlation, in the 3D space,
between a physical system and an apparatus and thus by the entangled state (14)
in the sense that it is just by starting from this state that one can compute the
numerical order corresponding with the actualization of the measured property of
the physical system under consideration. The quantum superposition, the quantum
entanglement between the measured physical system and the apparatus can be
considered the fundamental reality of space in the quantum domain. Now, the
crucial point introduced by the authors of this article is that by means of quantum
entanglement, in virtue of some fundamental phenomena in which the elapsed
clock run for them to happen is zero, the 3D timeless space (where time exists
only as a numerical order of material changes) acts as an immediate medium of
information transfer between the systems under consideration.
In order to illustrate in detail in what sense a 3D space acts as an immediate
medium of information transfer in immediate physical phenomena regarding the
quantum domain by means of quantum entanglement, the best way is to consider
the classic example of EPR-type experiment given by Bohm [23] in 1951. We
have a physical system given by a molecule of total spin 0 composed by two spin
½ atoms in a singlet state:
r r
r
r
ψ ( x1 , x2 ) = f1 (x1 ) f 2 (x2 )
r
1
(u+ v− − u−v+ ) (18)
2
r
where f1 ( x1 ) , f 2 ( x2 ) are non-overlapping packet functions, u± are the
eigenfunctions of the spin operator sˆz1 in the z-direction pertaining to particle 1,
and v± are the eigenfunctions of the spin operator sˆz 2 in the z-direction pertaining
h
2
h
2
to particle 2: sˆz1 u± = ± u± , sˆz 2 v± = ± v± . Let us suppose we perform a spin
measurement on the particle 1 in the z-direction when the molecule is in such
a state. And let us suppose, moreover, that we obtain the result spin up for this
particle 1. Then, according to the usual quantum theory, the wave function (18)
reduces to the first of its summands:
ψ → f1 f 2u+ v−
(19).
The result of the measurement carried out on the particle 1 leads us to have
knowledge about the state of the unmeasured system 2: if the particle 1 is found
in the state of spin up, we know immediately that the particle 2 is in the state v_,
which indicates that the particle 2 has spin down. But this outcome regarding
particle 2 depends on the kind of measurement carried out on particle 1. In fact,
by performing different types of measurement on particle 1 we will bring about
60
Davide Fiscaletti, Amrit S. Sorli
distinct states of the particle 2. This means that as regards spin measurements
there are correlations between the two particles. By considering the particles 1 and
2 separately, one can think about a strange influence of one particle onto the other.
A measurement on one of the two particles automatically fixes also the state of
the other particle, independently of the distance between them. Although the two
partial systems (the particle 1 and the particle 2) are clearly separated in space
(in the conventional sense that the outcomes of position measurements on the
two systems are widely separated), indeed they cannot be considered physically
separated because the state of the particle 2 is indeed instantaneously influenced
by the kind of measurements made on the particle 1. Bohm’s example shows
therefore clearly that entanglement in spin space implies non-locality and nonseparability in Euclidean three-dimensional space: this comes about because the
spin measurements couple the spin and space variables1.
As we have illustrated through Bohm’s example, the surprising fact regarding
the quantum entanglement lies in the fact that the results of the measurement of the
spin of two particles are 100% correlated, if for both particles we measure the spin
along the same direction. According to Bell’s theorem, it is not possible to interpret
all the correlations between the two particles regarding the spin measurements by
assuming that the two particles are born with the relative instructions about how to
behave [24]. But then in what way can we interpret the fact that the measurement
of a particle defines in what state the other particle is found, independently of
the distance? In 1935, after EPR’s work, Bohr suggested that the two entangled
particles, independently of their distance, continue to constitute an unity, a single
system: the two particles have not an autonomous existence. Below we will show
that this Bohr’s interpretation can receive a natural basis, if space is considered as
the medium of information transfers in quantum physics.
According to the previsions of the quantum theory, in EPR-type experiments
the transmission of the information has zero numerical order. If the state of the
second particle changes instantaneously after the measurement on the first particle,
this fact does not imply a transmission of the information at a higher speed than
light speed because we can not influence the outcome of the first measurement.
According to the authors, the information between the two particles is instantaneous
thanks to the medium of space. A 3D space (where time is not a primary physical
reality but exists only as a numerical order of material change) can be considered
the fundamental medium which can explain the non-local correlations determined
by entanglement in Bohm’s example. One can say that the state of the particle 2
is instantaneously influenced by the kind of measurements regarding the particle
1 because space acts as an immediate information medium between the two particles.
It is also important to underline that if one assumes the quantum interference as a fundamental
property, independent of space separation of quantum mechanical systems, the non-locality becomes
a natural phenomenon.
1
Three-dimensional space as a medium of quantum entanglement
61
It is the medium of the 3D space which produces an instantaneous connection
between the two particles as regards the spin measurements: by disturbing system
1, system 2 is instantaneously influenced despite the big distance separating the
two systems thanks to space which acts as an immediate information medium and
puts them in an immediate contact.
It is important to emphasize here that the interpretation of quantum
entanglement and non-locality as immediate physical phenomena determined
by a timeless 3D space that acts as an immediate information medium appears
legitimate in virtue of the fact that quantum entanglement and non-locality
cannot be explained by invoking a mechanism of entities that are transmitters of
information between the particles under consideration: there is no information
signal in the form of a photon or some other particle travelling between particles
1 and 2 of Bohm’s example. The time of information transfer between particle
1 and particle 2 is zero [25]. Information between particle 1 and particle 2 has
not duration: this suggests that there is a fundamental medium that acts as an
immediate information medium. And in this article the point of view suggested
by the authors is just that this fundamental medium is a 3D space where time
exists only as a numerical order of material change. The 3D space is an immediate
information medium that is informing particle 1 about the behaviour of particle
2 and vice versa. It is the 3D space medium which determines an immediate
information transfer and allows us to explain why and in what sense, in an EPR
experiment, two particles coming from the same source and going away, remain
joined by a mysterious link, why and in what sense if we intervene on one of the
two particles, also the other feels the effects instantaneously despite the relevant
distances separating it [26].
It is important to stress that the idea of the 3D space as a direct, immediate
information medium between subatomic particles follows as a natural development
from Bohm’s quantum potential. As we know, in his classic works of 1952 and
1953 [27, 28], Bohm showed that if we interpret each individual physical system
as composed by a corpuscle and a wave guiding it, the movement of the corpuscle
guided by the wave happens in agreement with the law of motion which assumes
the following form
2
∂S ∇S
h2 ∇2R
+
−
+ V = 0 (20)
∂t
2m 2m R
(where R is the absolute value and S is the phase of the wave function, h is Planck’s
reduced constant, m is the mass of the particle and V is the classic potential).
This equation is equal to the classical equation of Hamilton-Jacobi except for the
appearance of the additional term
62
Davide Fiscaletti, Amrit S. Sorli
Q=−
h2 ∇2R
(21)
2m R
having the dimension of an energy and containing Planck constant and therefore
appropriately defined quantum potential.
The treatment provided by relations (20) and (21) can be extended
in a simple way to many-body systems. If we consider a wave function
, defined on the configuration space R 3 N of a system
of N particles, the movement of this system under the action of the wave ψ
happens in agreement to the law of motion
2
where
∂S N ∇ i S
+∑
+ Q + V = 0 (22)
∂t i =1 2mi
2
h 2 ∇i R
(23)
Q = ∑−
2mi R
i =1
N
is the many-body quantum potential. The equation of motion of the i-th in the
particle, within the limit of big separations, can also be written in the following
form
r
∂ 2 xi
r r
r
r
mi 2 = −[∇ i Q( x1 , x2 ,..., xn ) + ∇ iVi ( xi )] (24)
∂t
which is a quantum Newton law for a many-body system. Equation (24) shows
that the contribution to the total force acting on the i-th particle coming from the
quantum potential, i.e. ∇ i Q , is a function of the positions of all the other particles
and thus in general does not decrease with distance.
The quantum potential is the crucial entity which allows us to understand
the features of the quantum world determined by Bohm’s version of quantum
mechanics. The mathematical expression of quantum potential shows that this
entity does not have the usual properties expected from a classic potential.
Relations (21) and (23) tell us clearly that the quantum potential depends on how
the amplitude of the wave function varies in the 3D space. The presence of Laplace
operator indicates that the action of this potential is space-like, namely creates
onto the particles a non-local, instantaneous action. In relations (21) and (23) the
appearance of the absolute value of the wave function in the denominator also
explains why the quantum potential can produce strong long-range effects that
do not necessarily fall off with distance and so the typical properties of entangled
wave functions. Thus even though the wave function spreads out, the effects of the
Three-dimensional space as a medium of quantum entanglement
63
quantum potential need not necessarily decrease (as the equation of motion (24)
of the many-body systems shows clearly, the total force acting on the i-th particle
coming from the quantum potential, i.e. ∇ i Q , does not necessarily fall off with
distance and indeed the forces between two particles of a many-body system may
become stronger, even if ψ may decrease in this limit). This is just the type of
behaviour required to explain EPR-type correlations.
If we examine the expression of the quantum potential in the two-slit experiment, we may find that it depends on the width of the slits, their distance apart
and the momentum of the particle. In other words, the quantum potential has a
contextual nature, namely brings global information on the process and its environment. It contains instantaneous information about the overall experimental
arrangement. Moreover, this information can be regarded as being active in the
sense that it modifies the behaviour of the particle. In a double-slit experiment,
for example, if one of the two slits is closed the quantum potential changes, and
this information arrives instantaneously to the particle, which behaves as a consequence.
Now, the fact that the quantum potential produces a space-like and active
information means that it cannot be seen as an external entity in space but as an
entity which contains spatial information, as an entity which represents space.
On the basis of the fact that the quantum potential has an instantaneous action
and contains active information about the environment, one can say that it is
space which is the medium responsible for the behaviour of quantum particles.
Considering the double-slit experiment, the information that quantum potential
transmits to the particle is instantaneous just because it is spatial information, is
linked to the 3D space.
In virtue of its features, the quantum potential can be considered a geometric entity, the information determined by the quantum potential is a type of geometric information “woven” into space. Quantum potential has a geometric nature just because it has a contextual nature, contains global information on the
environment in which the experiment is performed and at the same time it is a dynamical entity just because its information about the process and the environment
is active, determines the behaviour of the particles.
In this geometric picture one can say that the quantum potential indicates,
contains the geometric properties of space from which the quantum force, and
thus the behaviour of quantum particles, derive. Considering the double-slit
experiment, the fact that the quantum potential is linked with the width of the slits,
their distance apart and the momentum of the particle, namely that brings global
information on the environment means that it describes the geometric properties
of the experimental arrangement (and therefore of space) which determine the
quantum force and the behaviour of the particle. And the presence of Laplace
operator (and of the absolute value of the wave function in the denominator)
64
Davide Fiscaletti, Amrit S. Sorli
indicates that the geometric properties contained in the quantum potential
determine a non-local, instantaneous action. We can say therefore that Bohm’s
theory manages to make manifest this essential feature of quantum mechanics,
just by means of the geometric properties of space described and expressed by
the quantum potential. As regards the geometric nature of the quantum potential
and the non-local nature of the interactions in physical space, one can also say,
by paraphrasing J. A. Wheeler’s famous saying about general relativity, that the
evolution of the state of a quantum system changes active global information, and
this in turn influences the state of the quantum system, redesigning the non-local
geometry of the universe.
In synthesis, according to the authors, in virtue of the space-like action of the
quantum potential, the medium of the 3D space has a crucial role in determining
the motion and the behaviour of subatomic particles. On the basis of the equations
(21) and (23), one can say that it is space which is the medium responsible for the
behaviour of quantum particles. One can say that equations (21) and (23) of the
quantum potential contain the idea of space as an immediate information medium
in an implicit way.
In particular, if we consider a many-body quantum process (such as for
example the case of an EPR-type experiment, of two subatomic particles, first
joined and then separated and carried away at big distances one from the other), we
can say that the 3D physical space assumes the special “state” represented by the
quantum potential (23), and this allows an instantaneous communication between
the particles under consideration [29]. If we examine the situation considered by
Bohm in 1951 (illustrated before) we can say that it is the state of space in the
form of the quantum potential (23) which produces an instantaneous connection
between the two particles as regards the spin measurements: by disturbing system
1, system 2 may indeed be instantaneously influenced despite a big distance
between the two systems thanks to the features of space which put them in an
immediate communication.
In synthesis, one can say that in EPR-type experiments the quantum potential
(23) makes the 3D physical space an “immediate information medium” between
elementary particles. In EPR-type experiments the behaviour of a subatomic
particle is influenced instantaneously by the other particle thanks to the 3D space
which functions as an immediate information medium in virtue of the geometric
properties represented by the quantum potential (23).
However, what makes indeed the 3D space an immediate information
medium in EPR-type correlations? If the space that we perceive seems to be
characterized by local features, from which fundamental entity or structure the
property of the quantum potential to determine the action of the 3D space as an
immediate information medium derives? In this regard, according to the authors, it
is important to mention that in the recent article Bohmian split of the Schrödinger
Three-dimensional space as a medium of quantum entanglement
65
equation onto two equations describing evolution of real functions, Sbitnev
[30] has shown that the quantum potential can be determined as an information
channel into the movement of the particles as a consequence of the fact that it
determines two quantum correctors into the energy of the particle depending on
a more fundamental physical quantity that can be appropriately called “quantum
entropy”. This new way of reading Bohmian mechanics can be called as the
“entropic version” of Bohmian mechanics or, more briefly, “entropic Bohmian
mechanics”. In the case of a one-body system, the quantum entropy is defined by
the logarithmic function
1
S Q = − ln
ln ρ
2
(25a)
r 2
where ρ = ψ ( x ,t ) is the probability density (describing the space-temporal
distribution of the ensemble of particles, namely the density of particles in the
r
element of volume d 3 x around a point x at time t) associated with the wave
r
function ψ ( x, t ) of an individual physical system. In the case of a many-body
system, the quantum entropy is always defined by the logarithmic function
1
S Q = − lln
n ρ (25b)
2
r r
r
2
where here ρ = ψ ( x1 , x2 ,..., x N , t ) is the probability density (describing the
space-temporal distribution of the ensemble of particles, namely the density of
r
particles in the element of volume d 3 x around a point x at time t) associated
r r
r
with the wave function ψ ( x1 , x2 ,..., x N , t ) of the many-body system under
consideration. In the entropic version of Bohmian mechanics, one can assume that
the 3D space distribution of the ensemble of particles describing the individual
physical system under consideration generates a modification of the background
space characterized by the quantity given by equation (25a) (or (25b)). The
quantum entropy ((25a) and (25b)) can be interpreted as the physical entity that,
in the quantum domain, characterizes the degree of order and chaos of the vacuum
– a storage of virtual trajectories supplying optimal ones for particle movement
– which supports the density ρ describing the space-temporal distribution of the
ensemble of particles associated with the wave function under consideration. By
introducing the quantum entropy, for one-body systems, the quantum potential
can be expressed in the following convenient way
Q=−
2
h2
(∇SQ )2 + h ∇ 2 SQ
2m
2m
(
)
(26).
and we obtain the following equation of motion for the corpuscle associated with
r
the wave function ψ ( x, t ) :
66
Davide Fiscaletti, Amrit S. Sorli
∇S
2
h2
h2 2
2
(∇SQ ) + V + ∇ SQ = − ∂S
−
2m 2m
2m
∂t
(
)
(27)
h2
2
which provides an energy conservation law where the term − 2m (∇S Q ) can be
2
interpreted as the quantum corrector of the kinetic energy ∇S of the particle,
2
2m
while the term h (∇ 2 S Q ) can be interpreted as the quantum corrector of the
2m
potential energy V.
In the case of many-body systems, the quantum potential is given by the
following expression
N
Q = ∑[ −
(
2
h2
(∇ i SQ )2 + h ∇i 2 SQ
2mi
2mi
and the equation of motion is
i =1
N
∑
i =1
∇i S
2mi
2
N
−∑
i =1
(
)]
(28)
)
2
N
h2
(∇i SQ )2 + V + ∑ h ∇i 2 SQ = − ∂S
2mi
∂t
i =1 2mi
which provides an energy conservation law where the term
N
−∑
i =1
(29)
h2
(∇ i SQ )2
2mi
can be interpreted as the quantum corrector of the kinetic energy of the manyN
body system, while the term ∑
i =1
(
h2
2
∇ i SQ
2mi
)
can be interpreted as the quantum
corrector of the potential energy.
On the ground of Sbitnev’s results, it becomes thus permissible the following
reading of the quantum potential and of the energy conservation law in quantum
mechanics. The quantum potential derives from the quantum entropy describing
the degree of order and chaos of the background space (namely the modification
in the background space) produced by the density of the ensemble of particles
associated with the wave function under consideration. And, on the basis of
equations (27) and (29), we can say that the quantum entropy determines two
quantum correctors in the energy of the physical system under consideration (of
the kinetic energy and of the potential energy respectively) and without these two
quantum correctors (linked just with the quantum entropy) the total energy of the
system would not be conserved. Moreover, in this entropic approach to Bohmian
mechanics, the classical limit can be expressed by the conditions
(∇S )
Q
2
(
→ ∇ 2 SQ
)
(30)
Three-dimensional space as a medium of quantum entanglement
67
for one-body systems and
(∇ S )
i
Q
2
(
2
→ ∇ i SQ
) (31)
for many-body systems. The quantum dynamics will approach the classical
dynamics when the quantum entropy satisfies conditions (30) (for one-body
systems) or (31) (for many-body systems) which can be considered as the
expression of the correspondence principle in quantum mechanics.
With the introduction of the quantum entropy ((25a) for one-body systems
and (25b) for many body systems) which leads to the energy conservation law
(equation (27) for one-body system and equation (29) for many-body system),
now new light can be shed on the interpretation of the action of the 3D space as
an immediate information medium in EPR-type correlations. In fact, on the basis
of equation (29), one can say that the action of the 3D space as an immediate
information medium derives just from the two quantum correctors to the energy
of the system under consideration, namely from the quantum corrector to the
N
potential energy ∑
N
−∑
i =1
2
h
(∇ i SQ )2
2mi
i =1
(
h2
2
∇ i SQ
2mi
)
and the quantum corrector to the kinetic energy
N
(while the other two terms ∑
i =1
∇i S
2mi
2
and V on the right-hand of
equation (29) determine a local feature of space). The feature of the quantum
potential to make the 3D space an immediate information channel into the
behaviour of quantum particles derives just from the quantum entropy. In other
words, one can see that by introducing the quantum entropy given by equation
(25b), it is just the two quantum correctors to the energy of the system under
consideration, depending on the quantity describing the degree of order and chaos
of the vacuum supporting the density ρ (of the particles associated with the wave
function under consideration) the fundamental element, which at a fundamental
level produces an immediate information medium in the behaviour of the particles
in EPR-type experiments. The space we perceive seems to be characterized by
local features because in our macroscopic domain the quantum entropy satisfies
conditions (30) or (31).
In synthesis, in the entropic version of Bohmian mechanics, one can say that
the quantum entropy, by producing two quantum corrector terms in the energy,
can be indeed interpreted as a sort of intermediary entity between space and the
behaviour of quantum particles, and thus between the non-local action of the
quantum potential and the behaviour of quantum particles. The introduction of the
quantum entropy (given by equation (25a) or (25b)) as the fundamental entity that
determines the behaviour of quantum particles leads to an energy conservation law
in quantum mechanics (expressed by equations (27) and (29)) which lets us realize
what makes indeed the 3D space an immediate information medium in EPR-type
68
Davide Fiscaletti, Amrit S. Sorli
correlations, which in turn lets us realize from which property of the quantum
potential one can derive the action of the 3D space as an immediate information
medium. The ultimate source, the ultimate visiting card which determines the
action of the 3D space as an immediate information medium between quantum
particles is a fundamental vacuum defined by the quantum entropy ((25a) or
(25b)). The quantum entropy, by producing two quantum corrector terms in the
energy, is the fundamental element which gives origin to the non-local action of
the quantum potential.
Now, as regards the instantaneous communication between quantum particles
in EPR-type experiments and the role of the 3D space as a direct information
medium between them, if one imagines to exchange, to invert the roles of the two
particles what happens is always the same type of process, namely an instantaneous
communication between the two particles. In other words, the instantaneous
communication between two particles in EPR experiment is characterized by
a sort of symmetry: it occurs both if one intervenes on one and if one intervenes
on the other. In both cases the same type of process happens and – we can say –
always owing to space which functions as an immediate information medium.
Moreover, if we imagine to film the process of an instantaneous communication
between two subatomic particles in EPR-type experiments backwards, namely
inverting the sign of time, we should expect to see what really happened. Inverting
the sign of time, we have however no guarantee that we obtain something that
corresponds to what physically happens. Although the quantum potential ((21)
for one-body systems and (23) for many-body systems) has a space-like, an
instantaneous action, however it comes from Schrödinger equation which is not
time-symmetric and therefore its expression cannot be considered completely
satisfactory just because it can meet problems inverting the sign of time.
On the basis of these considerations, in order to interpret in the correct way,
also in symmetric terms in exchange of t for –t, the instantaneous communication
between subatomic particles and thus the interpretation of 3D space as an immediate
information medium, in quantum theory in line of principle a symmetry in time
is required. For this reason the authors of this article have recently introduced
a research line based on a symmetrized version of the quantum potential. The
symmetrized quantum potential can explain a symmetric and instantaneous
communication between subatomic particles and thus can be considered as
a better candidate for the state of the 3D space as an immediate information
medium in EPR-type experiments (or, more generally, in each immediate physical
phenomenon). In the case of a system of N particles the symmetrized quantum
potential assumes the form
Three-dimensional space as a medium of quantum entanglement
69
 ∇i 2 R1 


N
h 2  R1  (32)
Q = ∑−
2mi  ∇i 2 R2 
i =1

 −
R2 

where R1 is the absolute value of the wave-function Ψ = R1eiS1 / ħ describing the
forward-time process (solution of the standard Schrödinger equation) and R2 is
the absolute value of the wave-function Ø = R2eiS2 / ħ describing the time-reverse
process (solution of the time-Schrödinger equation). On the basis of equation
(32), we can explain non-local correlations in many-body systems – and thus EPR
experiments – in the correct way (that is, also if one would imagine to film back
the process of these correlations). The symmetrized quantum potential (32) can
be considered the most appropriate candidate to provide a mathematical reality
to a 3D space intended as a direct information medium [31]. In fact, the symmetrized quantum potential is characterized by two components, the one regarding
the forward-time process, the other regarding the time-reverse process. The first
component of the symmetrized quantum potential,
2
h 2 ∇ i R1
Q1 = ∑ −
2mi R1
i =1
N
(33),
which is related to the forward-time process and coincides with the original
Bohm’s quantum potential, is the real physical component which produces
observable effects in the quantum world. As regards the observable effects of
Bohm’s quantum potential, the reader can find details in the results obtained, for
example, by Philippidis, Dewdney, Hiley and Vigier about the classic double-slit
experiment, tunnelling, trajectories of two particles in a potential of harmonic
oscillator, EPR-type experiments, experiments of neutron-interferometry [32,
33]): it expresses the instantaneous action on quantum particles and thus the
immediate action of space on them. The second component,
2
h 2 ∇ i R2
Q2 = ∑
R2
i =1 2mi
N
(34),
is introduced to reproduce in the correct way the time-reverse process of the
instantaneous action and thus it guarantees that the quantum world can be
interpreted correctly with the idea of space as an immediate information medium
if one would imagine to film the process backwards: it must be introduced in order
70
Davide Fiscaletti, Amrit S. Sorli
to recover a symmetry in time in quantum processes, to interpret in the correct
way quantum processes if one would imagine to film that process backwards.
The opposed sign of the second component with respect to the physical first
component (that is, with respect to the original Bohm’s quantum potential) can
be interpreted as a consequence of the idea of the measurable time as a measuring
system of the numerical order of material change: the mathematical features of
the second component of the symmetrized quantum potential imply that it is not
possible to go backwards in the physical time intended as the numerical order of
physical events.
Both the components (33) and (34) of the symmetrized quantum potential can
be considered as physical quantities deriving from the quantum entropy (25b).
The first component can be expressed as
N
Q = ∑[ −
i =1
(
2
h2
(∇ i SQ1 )2 + h ∇ i 2 SQ1
2mi
2mi
)]
(35),
while the second component can be expressed as
(
2
h2
(∇ i SQ 2 )2 − h ∇ i 2 SQ 2
2mi
2mi
N
Q = ∑[
i =1
)]
(36),
1
S Q1 = − ln
ln ρ1 is the quantum entropy defining the degree of order and
where
2
r r
r
2
ρ1 = ψ ( x1 , x2 ,..., x N , t ) ,
chaos of the vacuum for the forward-time processes (where r r
r
ψ ( x1 , x2 ,..., x N , t ) = R1e −iSiS 1 / h being the forward-time may-body wave function, so1
S Q 2 = − ln
ln ρ 2 is the quantum
lution of the standard Schrödinger equation) and 2
entropy defining the degree of order and chaos of the vacuum for the time-reverse
r r
r
processes (where ρ 2 = φ ( xr1 , xr2 ,..., xr N , t ) 2 , φ ( x1 , x2 ,..., x N , t ) = R2 e − iS 2 / h being
the time-reverse many-body wave function, solution of the time-reversed Schrödinger equation). The energy conservation law for the forward-time process is
N
∑
i =1
∇ i S1
2mi
2
N
−∑
i =1
(
)
2
N
h2
(∇ i SQ1 )2 + V + ∑ h ∇ i 2 SQ1 = − ∂S1 ,
2mi
2mi
∂t
i =1
(37)
while the energy conservation law for the reversed-time process is
N
∑
i =1
∇i S2
2mi
2
N
+∑
i =1
(
)
2
N
h2
(∇ i SQ 2 )2 − V − ∑ h ∇ i 2 SQ1 = − ∂S 2
2mi
2mi
∂t
i =1
(38).
On the basis of its mathematical features, the symmetrized quantum potential
Three-dimensional space as a medium of quantum entanglement
71
implies that in the quantum domain a timeless 3D space has a crucial role in determining the motion of a subatomic particle because the symmetrized quantum
potential produces a like-space and instantaneous action on the particles under
consideration and contains active information about the environment and, on the
other hand, implies the concept of time as a numerical order of material change.
In EPR-type experiments (and, more generally, in all immediate physical phenomena regarding the quantum domain) the 3D timeless space acts as an immediate information medium in the sense that the first component of the symmetrized
quantum potential makes physical space an “immediate information medium”
which keeps two elementary particles in an immediate contact (while the second
component of the symmetrized quantum potential reproduces, from the mathematical point of view, the symmetry in time of this communication and the fact that
time exists only as a numerical order of material change). We can call this peculiar interpretation of quantum non-locality as the “immediate symmetric interpretation” of quantum non-locality.
5. CONCLUSIONS
This article shows that a 3D space where time t is exclusively a numerical
order of material changes can be considered a fundamental arena of physical
processes. At a fundamental level, we live in a universe where time measured
by clocks exists exclusively as a numerical order of material changes. Nonlocal correlations in EPR-type experiments are carried directly by the 3D space,
the numerical order t of quantum entanglement is zero in the sense that the 3D
space functions as an immediate information medium. The action of the 3D
space as an immediate information medium derives from the quantum entropy
describing the degree of order and chaos of the vacuum supporting the density
of the particles associated with the wave function under consideration. The
symmetrized quantum potential characterized by the two components (where the
first component coincides with the original Bohm’s quantum potential and the
second component is endowed with an opposed sign with respect to it) seems to be
the most appropriate candidate to represent the mathematical state of the 3D space
as an immediate information medium between subatomic particles that accounts
for entanglement and non-locality (and more generally, for all immediate physical
phenomena in the quantum domain).
references
[1]Góźdź A., Stefańska K., Journal of Physics: Conference Series 104, 012007 (2008).
[2] Sorli A. S., Fiscaletti D., Klinar D., Physics Essays 24, 1 (2011).
[3] Sorli A. S., Fiscaletti D., Klinar D., Physics Essays 23, 2, 330–332 (2010).
[4] Sorli A. S., Fiscaletti D., Physics Essays 25, 1 (2012).
72
Davide Fiscaletti, Amrit S. Sorli
[5] Selleri F., Space and time should be preferred to spacetime – 1, International Workshop
Physics for the 21st Century, 5–9 June 2000.
[6] Selleri F., Space and time should be preferred to spacetime – 2, International Workshop
Physics for the 21st Century, 5–9 June 2000.
[7] Manaresi R., Selleri T., Found. Phys. Lett. 17, 65 (2004).
[8] Lynds P., Found. Phys. Lett. 16, 4, 343–355 (2003).
[9] Newton Da Costa C. A., Adonai S. Sant’Anna, Found. Phys. Lett. 14, 6, 553–563 (2003).
[10]Girelli F., Liberati S., Sindoni L., Is the notion of time really fundamental?, arXiv:0903.4876,
27 Mar 2009.
[11] Prati E., The nature of time: from a timeless hamiltonian framework to clock time metrology,
arXiv:0907.1707v1, 10 Jul 2009.
[12] Pavsic M., Towards the unification of gravity and other interactions: what has been missed,
arXiv:0912.4836v1 [gr-qc], 24 Dec 2009.
[13] Lan B. L., Physics Essays 24, 293 (2011).
[14] Eckle P., Pfeiffer A. N., Cirelli C., Staudte A., Dörner R., Muller H. G., Büttiker M.,
Keller U., Science 322, 5907, 1525–1529 (2008). http://www.sciencemag.org/cgi/content/
short/322/5907/1525.
[15] Pirandola et al. S., A Letters Journal Exploring Frontier of Physics (2008).
[16] Hegerfeldt G. C., Phys. Rev. Lett. 72, 596–599 (1994). http://prola.aps.org/abstract/PRL/v72/
i5/p596_1
[17] Palmer T. N., The Invariant Set Hypothesis: A New Geometric Framework for the Foundations
of Quantum Theory and the Role Played by Gravity, Submitted on 5 Dec 2008, last revised 17
Feb 2009, http://arxiv.org/abs/0812.1148.
[18] Field J. H., Physics of Particles and Nuclei Letters 6, 4, 320–324 (2009).
[19] von Neumann J., Mathematische Grundlagen der Quantenmeckanik, Springer, Berlin 1932.
[20] Heisenberg W., Physics and Philosophy, Harper and Row 1958.
[21] Pavsic M., The Landscape of Theoretical Physics: A Global View, Kluwer Academic
Publishers, Boston–Dordrecht–London 2001.
[22] Rovelli C., Found. Phys. 28, 7, 1031–1043 (1998), e-print arXiv:quant-ph/9802020v3.
[23] Bohm D., Quantum Theory, Prentice-Hall, New York 1951.
[24] Bell J. S., Physics 1, 195–200 (1964).
[25] Sorli A., Sorli I. K., Frontier Perspectives 14, 1, 38–40 (2005).
[26] Fiscaletti D., Electronic Journal of Theoretical Physics 3, 2, 15–20 (2005).
[27] Bohm D., Phys. Rev. 85, 166–193 (1952).
[28] Bohm D., Phys. Rev. 89 (1953).
[29] D. Fiscaletti, Sorli A., Frontier Perspectives 14, 2 (2005/2006).
[30] Sbitnev V. I., Kvantovaya Magiya 5, 1, 1101–1111 (2008). URL http://quantmagic.narod.ru/
volumes/VOL512008/p1101.html.
[31] Fiscaletti D., Sorli A. S., Physics Essays 21, 4, 245–251 (2008).
[32] Philippidis C., Dewdney C., Hiley B., Il Nuovo Cimento B 52, 15 (1979).
[33] Dewdney C., Calculations in the causal interpretation of quantum mechanics, in: Quantum
Uncertainties – Recent and Future Experiments and Interpretations, Plenum Press, New York,
19–40 (1987).

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