Proc. Nati. Acad. Sci. USA Vol. 89, pp. 10222-10226, November 1992 Physics In search of a physical theory of time KENNETH J. Hsu Eidgendssische Technische Hochschule, 8092 Zurich, Switzerland Contributed by Kenneth J. Hsu, May 13, 1992 ABSTRACT The variable time considered in science is a as far as it goes, but that it was incomplete (5), it is the belief measurement. The relation of time to other variables is ex- of conventional quantum theories that individual quantum pressed in rates, and the variable time is seldom explicitly events are radically uncaused; only their overall statistical included in equations describing chemical reactions or radio- pattern is prescribed (6). The indeterminancy caused the active decays. Recalling that the Greek word atom is applicable famous man to protest that God does not play dice. This to indivisible particles in both spatial and temporal worlds, the indeterminancy has been variously interpreted; one ofthose, term chronon is proposed to designate elementary particles of the theory of hidden variable (7), suggested that there are time in parallel to the atom in space. Considerations of minute causal factors, admittedly unknown so far, that ac- interactions ofchronons with material and nonmaterial objects tually determine the outcome of individual, seemingly ran- could promote understanding of several paradoxes in physical dom measurements (6). We enter the realm oftheology ifGod and biological sciences. is the ultimate Hidden Variable (4). Science searches in the hidden variable in time, the real time, not the parameter t There is a gap between real experience and the fundamental expressing time measurements. physical laws. "Everything in physical science is a lot of Objects in space are substantial, be they a mountain, a star, Feynman once or a flower. Objects in time, or events, are not substantial, but protons, neutrons, and electrons," Richard they are real, be they the rise of a mountain, the motion of a stated, "while in daily life we talked about men and history, star, or the blooming of a flower. The temporal reality is not or beauty and hope .... Which end is nearer to God, beauty necessarily measurable by the ticking of a clock, but the and hope or the fundamental laws?" (1). He pleaded for an reality is underlined by the observable manifestations of the end of this communication gap: "To stand at either end, and interaction of time and the spatial objects involved. What to walk off that end of the pier only, hoping that out in that does time consist of? direction is the complete understanding is a mistake." A step Atoms were considered by the Greeks to be elementary in the right direction was taken when a symposium on Our particles of the world. With the scientific preoccupation with Knowledge of God and Nature was held in 1987 at Castel observations, matter in space is perceived, reduced into Gandolfo, Vatican, to commemorate the Newton tercente- atoms, and later reduced into protons, neutrons, electrons, nary. Scientists found expressions in the theological concept and the other fermions. Eventually another class of elemen- of creatio ex nihilo (creation out of nothing) in the Big Bang tary particles (the bosons) was recognized: they include theory and that of creatio continua (continuous creation) in photons, gravitons, and gluons, which mediate electromag- the theory of evolution (2), noting nihilo is t = 0 and the netic, gravitational, and strong and weak interactions. The continua is the flow of time. The variables relating to time world consists, however, not only of matter, and the word find their expressions in quantum physics in frequency, atom (arouov) in Greek means indivisible, be it a constituent half-life, chance, probability amplitude, etc. The concept of of an object in space or in time. The Greek word crovu&ev time seems thus the bridge to link the two shores: time is a means in an instant, or an indivisible unit oftime; the Greeks scale in physical sciences, time is a scale in history, including envisaged thus not only substantial atoms in space, but also history of earth (geology) and of life (evolution), and time is temporal atoms in time. To distinguish the two, I suggest that a theme for contemplation by theologians and philosophers we use the word chronon to describe the elementary particle when they speak of beauty and hope. of time. The Meaning of Time Experimental Verification of Chronons The theory of relativity has led some of us to think of time as Chronons are not material: they have neither volume, nor a dimensional variable in a material or substantial world; we mass, nor momentum, nor electric charge. They could be were walking farther away from the other end of Feynman's conceived of as a kind of boson, and their existence is pier where beauty and hope are buried. Time is, however, not theoretically intelligible and experimentally detectable as the only definable on the basis of physical measurements. There result oftheir interactions with other elementary particles. In are biological clocks; there are neurological clocks. There are describing the quantum world, R. J. Russell (5) stated: "As even philosophical clocks: Thomas Aquinas distinguished ordered, regular and constant as are the rocks, tables and three types of duration of time: tempus, measurable by flowers of our world of experience, at close range matter change; aevum, tempus that has escaped the bonds ofmatter; seems to be ruled by a chaos of unpredictable change. For and aeternitas, duration experienced by God (3). example, though all the atoms in a kilogram of uranium are Seeking truth in a substantial world is a recent develop- identical, and though on the average a predictable number of ment in human intellectual endeavor. The quantum theory them will decay in a specified amount of time no one knows gives us "beautiful and transparent patterns of the world, how to predict in advance which atom actually will decay, or (4)" a physical world that is neither mechanical nor chaotic. why it did and its neighbours didn't." Or why does this Although Einstein agreed that quantum physics was correct happen for radium C' after only one thousandth of a second while the not so different thorium will not oblige until ten The publication costs of this article were defrayed in part by page charge thousand million years have gone by (22). Are there exper- payment. This article must therefore be hereby marked "advertisement" imental observations that may provide an explanation, how- in accordance with 18 U.S.C. §1734 solely to indicate this fact. ever imperfect, of those questions? 10222 Downloaded by guest on September 26, 2021 Physics: HsO Proc. Natl. Acad. Sci. USA 89 (1992) 10223 The decay reaction of a uranium atom is commonly ex- The relation implies that the change in energy state is pressed by the relation dependent upon chronon capture per unit time. We can again use an example of stock purchase to convey the meaning of -*8U 234Th + a particle. such a physical formula. Assume that my friends and I both would like to buy a 100-franc ticket for an evening at the opera The equation does not state when it is its turn to give off an and that we could use only the annual profit of playing the a particle. What is missing is a consideration of the role of stock market to buy this ticket. Assume further that I found time. Introducing the chronon as a new variable X (the hidden a stock that went up and down cyclically almost every month variable?) in this equation, we have and that its per-share price went below 100 francs and above 110 francs 10 times that year. My program to buy at 100 and 2 +8U+ 234Th + a particle. to sell at 110 has realized a profit of 100 francs for the opera ticket. My friend, however, programmed to buy and sell In scientific we could that an uranium another stock, which went through only two such cycles that jargon then, say year, has realized only a profit of 20 francs, not enough for atom will decay if it captures a chronon, as when we say that the ticket. In thejargon of chrononic theory, I might say that the atom splits if it captures a neutron. We theorize on I could go to the opera because I had captured 10 chronons, neutron capture on the basis of capturing cross section, and and my friend could not because he had only captured 2, not we could try to explain the different rates of radioactive enough to initiate the action of theatre going. decay of the various radioactive atoms in the language of A stock price that oscillates with high frequency is said to cross-sectional area of chronon capture. be a stock ofhigh explosivity (8) (large xl'). The principle that one can cash in more profitably on a buy-and-sell program of The Meaning of Chronon Capture a stock of high explosivity can be applied to explain the different cross sections ofchronon capturing. We might recall A man on the street has difficulty in thinking ofcatching light, Gamow's picture of a particles rattling around nuclei before but scientists have no difficulty in devising detectors of they shoot out. Now those inside radium C nuclei have photons. Similarly we could consider the detection of a apparently far greater explosivity than those rattling inside particles by a Geiger counter as verification of chronon thorium nuclei, implying that many more chronons were capture by a uranium atom. But what is a chronon, the captured per unit time by radium than by thorium, causing the invisible and the immaterial? difference in their rates of decay.