Indeterminism, Time Arrow, and Prediction
作者:
F. J. Belinfante,
期刊:
AIP Conference Proceedings
(AIP Available online 1974)
卷期:
Volume 16,
issue 1
页码: 157-175
ISSN:0094-243X
年代: 1974
DOI:10.1063/1.2948444
出版商: AIP
数据来源: AIP
摘要:
Life in general, and man's memory in particular, determine a preferred direction in time (“time arrow”). It is made plausible that the time direction in which the entropy increases is this same time arrow.In quantum theory, wave functions describe not real (single) physical systems, but ensembles of systems. Reduction of wave packets corresponds to treating a system as a member of a new ensemble. Similarly, splitting an electromagnetic field into IN‐field plus retarded field, or into OUT‐field plus advanced field, corresponds to different ensembles describing a scattering on which only partial information is available. Our desire to ascribe a source to any light observed is the reason for usually preferring retarded fields over advanced fields. Independent of the fact that retardation of light waves is shown experimentally by Fizeau's measurement of the velocity of light,Afterthought Oneshows that an eye‐object interaction by advanced fields would violate the second law of thermodynamics. This would relate the time arrow of electromagnetism to the one of life. A puzzle remains when this is applied to light traveling between stars and interstellar dust.The time arrow of cosmology (time direction of expansion of the universe) is sometimes related to the time arrow of life by an extension of Olbers' paradox. An example worked out inAfterthought Twoshows that this generalization of Olbers' paradox is not justified.Afterthought Threecontains some speculations about possible correlations between the time arrows of cosmology and of life.The time arrow of quantum theory is determined by the fact that quantum theory in general predicts future probabilities, and that it can retrodict (postdict) probabilities of the past only under specific conditions that often are not satisfied. This asymmetry becomes more understandable when quantum theory is applied to sequences of nonideal (irreproducible) measurements separated by the use of gadgetry that prepareschoseninitial conditions for the next measurement. The entering here ofchoiceindicates a relation between the mind with its built‐in time arrow, and the choice of the ensembles to which quantum theory then is applied objectively.We shall now return to the style of yesterday's meeting, talking about generalities. The only difference is that I will be thinking in terms of quantum theory instead of classical theory. Therefore the wordIndeterminismin the title of this talk.
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