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Home , Chronon, Theory of relativity

Proc. Nati. Acad. Sci. USA Vol. 89, pp. 10222-10226, November 1992 In search of a physical of KENNETH J. Hsu Eidgendssische Technische Hochschule, 8092 Zurich, Switzerland Contributed by Kenneth J. Hsu, May 13, 1992

ABSTRACT The variable time considered in 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 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 , the indeterminancy has been variously interpreted; one ofthose, is proposed to designate elementary particles of the theory of hidden variable (7), suggested that there are time in parallel to the atom in . Considerations of 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 . 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 ," 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 , star, or the blooming of a flower. The temporal is not or beauty and hope .... Which end is nearer to God, beauty necessarily measurable by the ticking of a , 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 . With the scientific preoccupation with Knowledge of God and Nature was held in 1987 at Castel observations, 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 . Eventually another class of elemen- of creatio ex nihilo (creation out of nothing) in the 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 () 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 when they speak of beauty and hope. of time. The Meaning of Time Experimental Verification of The 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 , nor . 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 ; 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 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 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 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 variable?) in this equation, we have and that its per-share price went below 100 francs and above 110 francs 10 that . 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 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 , 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. The chronon serves to sequence and to order events in the Explosivity is a hidden variable that causes indetermi- temporal world. When I go to a butcher shop, I wait for my nancy. Explosivity in a stock is its price instability, which is turn until the persons who have come before me are served. related to the small size ofcapital investment ofthe company The chronon activates an action, and chronon capture is, in and to its widely fluctuating earnings because ofcomplicated this case, sequencing. The sequencing appears random to a economic factors. Could explosivity be similarly explained casual stranger, but there could be a predictability, if he only for nuclear interactions? knows that the many factors in our daily routines render it inevitable that I always come to the butcher shop after my Fractal Geometry of Time neighbor. We are not able to answer why one uranium throws out its a particle before its neighbor because we do not know It seems paradoxical that I should select the seemingly the intricacies of the daily life of the subatomic world. chaotic price fluctuations in the stock market to illustrate the Each radioactive isotope has its constant half-life. Again I statistically deterministic half-life of radioactive decays. might choose an from life to Stock-price fluctuations are not regular, nor are they chaotic. example daily serve as a parable. If a sufficiently long-term record is available, the fractal Let us assume that the fluctuation in the price of the stock of geometry of variations can be demonstrated. It is common a certain bank has been very regular: the unit price always knowledge that the variation of daily change in unit price reaches a minimum of 100 francs every year after the divi- (magnitude M) is small; I used to listen to monotonous stock dend is paid. Assume also that I had 100,000 francs in the market reports that IBM was up 1/4 and General Motors was bank and that I gave my broker a standing order 10 years ago down 1/8, etc. Occasionally, the market rallied or crashed. that he should spend half of my cash in the account to Small daily changes are very, very frequent (large values of purchase stocks when the price of the stock drops down to frequency, F), and big jumps are rare (small values of F). 100 francs per share, the half-life of my saving account has Richard Voss (8) made a spectral analysis ofthe daily change thus been 1 year. Since all my cash is gone in 10 years, I might in IBM stock and found the relation say my bank has captured 10 chronons to activate the 10 sales. The cash account has a constant half-life because the F = c/MD, nearly regular fluctuation ofthe price ofthat particular stock. Now, my cash account could have had a different half-life, if where c is an empirical constant and D is the fractal dimen- I had given an order that the shares would only be purchased sion of the phenomenon. This is similar to the well-known when the unit Gutenberg-Richter relation in seismology (9): thousands of price fell down to 10 francs. Then I might have small earthquakes happen every year, but very large ones to wait for a long time, or I might say that "the cross section happen only once a or a . Replacing frequency of chronon capture is very small." by occurrence per unit time (xlt), Raup (10) introduced the concept of waiting time r for each occurrence (X = 1) of Explosivity of Time magnitude M

The chronon concept can be built into the basic equation of log r=D log M - c. the quantum . Substituting frequency by cycles per unit time and assuming that the number ofcycles is a function Applying this concept in daily life to a subatomic scale, the of chronon capture, we have waiting time for the release ofan a particle is a function ofthe magnitude of the task involved. It is no big deal for those in hv = E2-E1 = h-flX)/t. radium but Herculean indeed for those in thorium. The Downloaded by guest on September 26, 2021 10224 Physics: Hsd Proc. Natl. Acad. Sci. USA 89 (1992) waiting-time concept gives a statistical predictability of different types of chronons are involved in catalysis, the events, with its own uncertainty principle: a magnitude 3-4 reactions could be written as earthquake is certainly taking place every few some- where on earth, but we don't know where, or a magnitude 8-9 HCOOH 1+ A1203 + X (type C)] = earthquake is certain to take place in the Bay Area of California, but we don't know exactly when. The uncer- CO + H20 [+ A1203 + X (type C)] tainty, in this case, has nothing to do with interference by the measurements of an observer but is a consequence of the and very complicated physical variables influencing the capture HCOOH [+ ZnO + (type D)] = of chronons by earthquake faults. X CO2 + H2 [+ ZnO + X (type D)]. "Size" and "Type" of Chronons Like the branching ratio of40K, the relative proportion ofthe Chronons, like atoms, are not of the same size: large chro- two kinds ofreaction products is dependent upon the relative nons causing large events are either rare or difficult to efficacy of the catalysts . capture. Chronons, like atoms, may belong to different types: such a postulate could serve to explain the strange phenom- Chronons in Life enon of why a potassium atom will change sometimes, by i decay, into a calcium atom and at some other time, by Dead bodies decay; only the living live and grow. Life can be capture, into an argon atom. Applying the chronon described by what it is not: life is not death. Life is thus not concept, we may write: only made of protons, neutrons, and electrons; there is vitality in the living. We speak of dead animals, dead plants, 40K + X(type A)-4Ca + e and, in our profession, also of "dead carbon." A dead carbon is not a dead tree, which may have "live" carbon atoms (14C) and in it; a dead carbon consists only of 12C and 13C and is devoid of the radiocarbon atoms capable of capturing chronons. 40K + e +x(type B)- 40A. Using the analogy, one could define one aspect of life as the ability for body cells to capture chronons. The branching ratio of potassium decay could thus be Paraphrasing the fission of uranium atoms after neutron considered a manifestation of the different capturing cross capture, the chronon concept relates cell fission to chronon sections for chronon types A and B: more potassium atoms capture: fertilization, or beginning of life, is activated by the decay into calcium than into argon because ofthe larger cross capture of a chronon, and living cells have the potential of section for type A. capturing more chronons for more cell divisions. In the framework of this concept, living cells in plants capture not Chronons as Catalysts only photons but also chronons in photosynthesis. Studies of aging indicate that living cells die after 50 If the activation of all events requires the capture of chro- divisions (11), or after they have captured 50 chronons. The nons, one might wonder if their supply might soon be aging cells look different from newly born cells; the work of exhausted. Is it possible that chronons are not always con- chronons is verifiable. Eventually an organism is dead when sumed but may act as a catalyst to trigger events? cells in vital organs of a body have lost their ability for The mystery of catalysis is exemplified by the oxidation of chronon capture. Biologic clocks are wonders, because we sulfur dioxide: do not understand the work of chronons. Some seem to be built in genetic codes: an eventual understanding of chronon 2SO2 + 02= 2SO3. interactions might yield the answer to the question of why The reaction should but does not take place under normal lemmings rush to the sea every 4 years, why some bamboos circumstances, because the reaction rate is too slow. The will only bloom after a century, or why locust swarms presence of NO speeds up the reaction through stepwise suddenly appear at regular intervals. reactions involving the catalyst: Flow of Chronons in Neurologic Time 2NO + 02= 2NO2 Time and space, to neuroscientists, are human perceptions. 2NO2 + 2SO2 = 2NO + 2SO3 Time is perceived by persons through transmittal of electric impulses by neurons. The impulses are not themselves chro- 2S02 + 02 (+ 2NO) = 2SO3 (+ 2NO). nons, yet their transmission could be considered an interac- tion of neurons and chronons. The process carrying an In thejargon of chemistry, we say that NO is not involved in impulse away from a neuron is called an axon, and the the reaction; it only acts as a catalyst. Why should the process bringing toward a neuron is called a dendrite. The catalytic reactions be faster? Various explanations have been speed of transmittal of an impulse could be correlated to the suggested. By introducing the chronon concept, one could flux of energy in the physical world, or claim that a chronon has been captured as a nonmaterial catalyst and that the chronon needed for the reaction is more i = dX/dt. easily captured by the catalyst. The catalytic reaction could thus be written as Impulses are electric current, traveling at speeds of 1-100 m/sec and at frequencies in the microsecond range. Our 2SO2 + 02 (+ 2NO + X) = 2SO3 (+ 2NO + ) perception oftime is thus apparently governed by the efficacy of such neuron transmittal of information. Oliver Sacks (12) The role of chemical catalysts also illustrates the role of in his popular book Awakenings stated that a person who different kinds of chronons in radioactivity. The same sub- suffers from severe Parkinsonian or postencyphalic syn- stance (e.g., HCOOH) can be induced to react differently by dromes loses "his inner sense of scale and pace, and hence different catalysts (e.g., A1203 or ZnO). By assuming that the incontinent and retardations, the magnifi- Downloaded by guest on September 26, 2021 Physics: HsO Proc. Natl. Acad. Sci. USA 89 (1992) 10225

cations and minifications. The Parkinsonian is lost in space stored in our brains as 0 chronons and 1 chronons. Such an and time, bereft of any inner scale, or metric . ..." analogy permits us to visualize the mechanism of neuron A scale in the physical sense is a constant, a convention, transmission of information: the electric pulse observed is a like a ruler or a clock. And we may say of the Parkinsonian manifestation ofthe interaction of0 chronons and 1 chronons that his inner rulers and scales are all awry, as in the famous with the neurons. We thus further acquire an insight into the painting by Salvador Dali, which shows a multitude ofclocks mechanism ofmemorization. The microchips in our brain, be all going at different rates and registering different times, a they cells or molecules, store the 0 chronons and 1 chronons metaphor, perhaps, for Parkinsonism (the Parkinsonism that like those in a high-speed computer. Perhaps this is the Dali himself was beginning to feel). Parkinsonian metaphor in difference between animals and plants: we have the capacity effect provides rulers and clocks to make for the shattered, of storing structured chronons in our brain, whereas the the delirious, metric chaos-the chaos of broken clocks and plants do not. rulers-which is the Parkinsonian mind. Parkinsonian clocks do not tick away like a cesium clock. A Field Theory for the Flow of Chronons Time stood, for all practical purposes, still for postencephalic patients. The flux of time in them is suspended, while the The Tang poet Li Pei asked, "How much water has escaped ticked away; days, , and years went by. to the east?" comparing the passage of time to the flow of When a postencephalic patient upon his awakening thought Yangtze River. Newton also linked the flow oftime to that of that he went into a coma only when in fact 20 or 30 a continuously running river. He believed, however, "abso- years had gone by, he was telling us his experience that there and mathematical of itself and of its own had been little neuron while he was in a state lute, true, time, transport of nature, flows equably without relation to anything external, coma. and by another name is called duration" (17). Thus defined, Chronons in Aevum the duration is the tempus of Thomas Aquinas; it is the tick-tick time. What is "the not absolute, the untrue, the Chronons interact with spatial objects in the physical world; non-mathematical time," which does not flow equably, being chronons interact with the living cells in the neurological related to things external? Newton and his successors said world to transmit sensual perception or information. This very little about the nonlinearity of time. perception, this information, and the thought processes are The absolute space is homogeneous and isotropic (18) but neither physical nor biological. The entities are real but are the physical space is neither because of the objects in it. In divorced from the material bond; they consist of time in the a theatre, the stage itself is bare, but spatial objects move aevum world of Thomas Aquinas. about. If the absolute time is likewise homogeneous and In 1976 the evolutionary biologist Richard Dawkins (13) isotropic, the physical time is neither. The clocks may tick innovated the terms "ideosphere" and "memes" as imma- away regularly during the 3 of performance, but a terial analogues to terms biosphere and genes. Examples of theatre performance consists not only of spatial objects his memes are tunes, ideas, catch phrases, clothes fashions, moving about, but the drama consists of events-the se- and ways of making pots or of building arches. Just as genes quencing and ordering of temporal objects in the framework propagate themselves in the gene pool by leaping from body ofthe tick-tick time. What is the dynamics of sequencing and to body, so memes propagate themselves in the meme pool ordering? by leaping from brain to brain. Memes are supposedly written Li Pei's and Newton's river models are kinematic, and in some "universal memetic code" in each persons's brain, rivers have a size, a form, and other spatial attributes. and memes, like genes, are susceptible to variation or dis- Temporal objects are not material; they are formless, but tortion-the analogue to mutation. nevertheless dynamic. The movement of formless objects in Long before Dawkins, the great French mathematician space has been described by the field concept: there are Henri Poincard postulated "immaterial atoms" as the indis- gravitational fields, electric fields, magnetic fields, etc. Ap- pensable constituents of ideas (14). "Permit me a rough plying the principle ofanalogy, chronons could be postulated comparison," he wrote. "Figure the elements of our to flow a "temporal field," comparable to the flow of combinations (full-fledged ideas) as something like the groundwater under hydrodynamic potential or the flow of hooked atoms ofEpicurus. During the complete repose ofthe electrons in an electric field. Darcy's law of groundwater mind, these atoms are motionless; so this complete rest may motion, formulated in terms of a volume rate of water be indefinitely prolonged without the atoms meeting, and crossing a unit area normal to the flow direction q, can be consequently without any combination between them. On the expressed by the Laplacian equation (19) other hand, during a period ofapparent rest and unconscious work, certain of them are put in motion. They flash in every q = o-E= -or grad 4. direction like the molecules ofgas in the kinematic theory of gases. Then their mutual impacts may produce new combi- This relation finds a physical and a mathematical analogy in nations." the flow of electricity New combinations, or new memes, are new ideas, new theories. Poincard's "atoms" and "molecules" were called i= aE= -or grad V, "notions" and "memories" by Lewis Thomas (15). Hof- stadter (16) went a step further and concluded that "ideas are where i is the current density, Cis the electrical conductivity, simply variations on themes already enunciated," and his E is the electrical field intensity, and V is the electrical concept of "flickering clusters" makes an analogy to hydro- potential. Consequently, analogue models portraying the gen bonding in water. conductance of electricity in a field of variable resistance I found the analogy ofPoincare's vision ofimpacting atoms have been constructed to simulate the flow ofgroundwater in and Dawson's of memes fascinating. Memes are molecules of a medium of variable permeability. thought, and they consist of atoms of thoughts or "hooked Using the field equation to describe the flow of time, we up" units of information. What is the atomic or subatomic have to introduce, in addition to the one describing the flow structure of information? Using a computer as an analogy, in of chronons dV, the flux of chronons A, the temporal con- which all information is stored in some ordered sequence of ductance a, and the temporal potential 4, and we have to Os and Is, one could imagine that information and ideas are adopt a concept of multidimensional time. By using the Downloaded by guest on September 26, 2021 10226 Physics: HsO Proc. Natl. Acad. Sci. USA 89 (1992) mathematical analogue, the equation for the flow of time in Is it possible to analyze the phenomenon of probability a temporal field is amplitude in terms of the chronon concept? Through the innovation of probability amplitude, Feynman resolved the dx/dt = A=-a grad+. particle-wave duality paradox in quantum physics (21). Could we substitute probability amplitude by cross section of chro- The field equation for time thus gives adefinition ofa chronon non capture? as The title of this paper is "In search of a physical theory of dX= Adt= -a grad dt. time," and I suggest that such a theory will have to consider 0 the functioning of elementary particles of time. The search The flux of chronons is the change dX per unit time. The has barely begun. What would we have known ifwe had spent equivalent expressions in the flow of time in a temporal field as much time in science to investigate the atomic structure of and that of water with volume Q in spatial field are thus temporal and aeval objects as we do the atomic structure of spatial objects? Is chronon the hidden variable in quantum A = dX/dt physics? Is a consideration ofthe temporal field going to lead to a unified field theory? Could we acquire a deep under- and standing of the origin of life and the origin of knowledge through a consideration of the role of chronons? q = dQ/dt. I shall never know. Spatial objects, such as planets, in steady-state motions are with rate; the absolute time The ideas on chronons evolved when I was giving a seminar last interacting chronons at a linear year on the Fractal Geometry of Time at the California Institute of of Newton is linear. In the case of radioactive decay, how- Technology. I was inspired by weekly discussions with participants ever, the flux per unit radioactive mass (dA/dm) is statisti- ofthe seminar, especially Don Anderson, Yuk L. Yong, Peter Wiley, cally time-independent, but the flux (A) per initial mass of and Barclay Kamb. The idea was further explored when I visited radioactive substance is time-dependent: the flux depends Jerry Winterer, Frank Dickson, John Crowell, Gary Ernst, and upon the number of atoms (N) present that are not yet several other friends in California. Anderson and Yong read the first disintegrated (7): draft of the manuscript; Judith McKenzie, David Olgaard, Helmut Weissert, and Christine and Peter Hsu read the final draft. Their A = -N(dN/dt). comments led to improvements. Since the number N decays with time, the flux of disinte- 1. Feynman, R. (1990) The Character of Physical Law (MIT Press, grating particles varies accordingly. Relating X and t by A, one Cambridge, MA). 2. Russell, R. J., Stoeger, W. R. & Coyne, G. V., eds. (1988) Physics, arrives at the conclusion that the chronon flux has been Philosophy, and Theology: A Common Quest for Understanding decreasing. If we accept the theory that chronons were (Liberia Editrice Vaticana, Vatican). created by the Big Bang, the implication is a logarithmic 3. Peters, T. (1988) in Physics, Philosophy, and Theology: A Common decrease of chronon flux since that time. Quest for Understanding, eds. Russell, R. J., Stoeger, W. R. & Cosmologists have theorized that events must have been Coyne, G. V. (Liberia Editrice Vaticana, Vatican), pp. 273-292. after the Bang; the 4. Tipler, F. J. (1988) in Physics, Philosophy, and Theology: A Com- extremely rapid immediately Big mon Quest for Understanding, eds. Russell, R. J., Stoeger, W. R. went through, during the first second, the quark , the & Coyne, G. V. (Liberia Editrice Vaticana, Vatican), pp. 313-328. proton era, the electron era, and the -ray era, before the first 5. Polkinghorne, J. (1988) in Physics, Philosophy, and Theology: A helium was made at 3 min after the Big Bang (20). After the Common Quest for Understanding, eds. Russell, R. J., Stoeger, initial bursts ofactivity, the fluxes for radioactive decay have W. R. & Coyne, G. V. (Liberia Editrice Vaticana, Vatican), pp. become asymptotically linear. It defies our common sense to 333-341. 6. Russell, R. J. (1988) in Physics, Philosophy, and Theology: A imagine that so much could happen so quickly. On the other Common Quest for Understanding, eds. Russell, R. J., Stoeger, hand, all seems quite reasonable ifthe processes are phrased W. R. & Coyne, G. V. (Liberia Editrice Vaticana, Vatican), pp. in terms of the rate of chronon capture: a great deal of 343-374. chronons were captured to effect the changes during the first 7. Bohm, D. (1952) Phys. Rev. 85, 166-193. 3 min after the Big Bang. If the duration of time is measured 8. Voss, R. F. (1992) in Proceedings ofthe Workshop on Applications by one might conclude that a lot of water flowed under of Fractals and Chaos, eds. Jones, H. & Crilly, T. (Springer, A%, Berlin), in press. the bridge during the brief span of the first 3 min. 9. Gutenberg, B. & Richter, C. F. (1949) Seismicity of the Earth and Associated Phenomena (Princeton Univ. Press, Princeton). Chronon, Chance, and Probability 10. Raup, D. M. (1991) Extinction, Bad Genes or Bad Luck (Norton, New York). In envisaging the chronon as the trigger of an , the near 11. Hayflick, L. (1956) Exp. Cell Res. 37, 614. in is chance. The of 12. Sacks, 0. (1983) Awakenings (Dutton, New York). synonym our everyday language concept 13. Dawkins, R. (1976) The Selflsh Gene (Oxford Univ. Press, New chronon capture is innovated to explore the criticality of York). triggering an event. In classic physics, criticality can be 14. Poincare, H. (1956) in The World ofMathmatics, ed. Newman, J. R. defined by variables with determinable time dependency. (Simon & Schuster, New York), Vol. 4, pp. 2041-2050. The criticality ofdecay ofindividual atoms can, however, not 15. Thomas, L. (1979) The Medusa and the Snail (Viking, New York). be so defined; scientists invented the term half-life to express 16. Hofstadter, D. R. (1985) Metamagical Themas: Questing for the Essence of Mind and Pattern (Basic Books, New York). a statistically determinable time dependency. In Nature and 17. Newton, I. (1687) Philosophiae Naturalis Principia Mathematica, in daily life, criticalities, in many instances, are likewise Cited in De Beauregard, 0. C. (ed.) Time: The Physical Magnitude determined by the "intangibles." Through an application of (Reidel, Dordrecht, The Netherlands). the chronon concept, we might find patterns in the fraternal 18. Gray, J. (1989) Ideas of Space, Euclidean, Non-Euclidean and geometry of time. It may be interesting to note that the only Relativistic (Vintage, London). successful prediction of the earthquakes was the February 19. Hubbert, M. K. (1957) Bull. Assoc. Int. Hydrolog. Sci. 5, 24-59. 20. Calder, N. (1983) Timescale (Hogarth, London). 1975 Haicheng earthquake of China. The criticality for that 21. Feynman, R. (1985) QED The Strange Theory ofLight and Matter prediction was determined on the basis of the temporal (Princeton Univ. Press, Princeton). patterns of the foreshocks, not on the basis of physical 22. Polkinghorne, J. (1985) The Quantum World(Princeton Univ. Press, measurements. Princeton). Downloaded by guest on September 26, 2021