A Quantum of Time:
Limits, Constants, and Thermodynamics
Edward Renner
1984
Limits and Constants
What are constants and limits? How are they both the same and different? And what is their role in defining reality and the fundamental forces of the universe? By definition, a constant is a discrete number or a set relationship between some variables resulting in a fixed number (comprised of the value’s units of measurement), and is generally used to describe or define some aspect of reality; i.e., p , c, h, e, R, n,… etc. A limit, on the other hand, is a value used to describe an uppermost or lowermost value for some aspect of reality; e.g., ¥ , Absolute Zero (0° K), Speed of Light (c). And yet, some constants can be limits when they contain two or more variables, such as c according to the Special Theory of Relativity. Although the velocity of c can be slower in media of different transparent densities, it can be pushed to higher velocities in those same media (resulting Cerenkov radiation release); however, it’s absolute velocity is still that of in a vacuum, thus it’s limit. So if c can be both a constant and a limit (to v), then one or both of c’s units (d and/or t) may also be constants, limits, or both; i.e., c = d/t = (l ¦ ) = 3.0x1010cm/s (en vacuo).
This paper is a presumption that time, a fundamental dimensional aspect of our universe, is not a unbroken continuum, but rather a series of fixed instants separated by a set interval at our present point in the thermodynamic/entropic evolution of the universe; and exists as a time quantum inherent in all physical systems. Although the very existence of a time quantum is more important than it’s interval, the interval is at least as important as the comparative strengths/values of the four fundamental forces of nature in determining the structure and processes of our universe’s existence.
A Time Quantum (tq)
According to quantum theory, a quantum is a discreet and minimal unit or packet of energy, and all interactions that take place within the universe do so as multiples of those energy quanta. So why should time be any different if all interactions are also time dependent?
The deterministic treatment of applied force and other revisions in the Laws of Motion by William O. Davis (1961, 1962, 1967) and other physicists, have allowed scientists to calculate the smallest meaningful interval of time for any finite system (6.27x10- 24 s), a value independently arrived at stochastically by Hermann Von Schelling (1963), from physical assumptions made by Gilbert Plass (1961), and from theoretical estimates made by Werner Heisenberg (1956). This value is believed to be a universal constant that determines many other constants in our universe; such as the speed of light (c) and Planck’s Constant (h) - both of which can be derived from this time quanta or vice-versa using Davis Mechanics.
Alternative theoretical values for a quantum of time, named a chronon by Robert Levi (1927), have been derived from quantum mechanics and General & Special Relativity, and were proposed to create a theory of quantum gravity. One such value proposed by Piero Caldirola (1980) is 6.97x10- 24 s, a value very close to that derived by Davis Mechanics. Max Planck also proposed a minimal unit of time, called Planck time, but his value was 5.39x10- 44 s and was derived to mark the beginning of the universe, not set a continuing time quantum. However, the one thing all such theories have in common is that they all propose some kind of time quanta as a unit of time, inferring that time is not a continuous/undivided dimension, but “granular“; and this granularity would extend into and effect all physical processes that involve matter, energy, and the interaction of fundamental forces.
The concept of a time quantum rather than a continuum makes sense when you analogously consider quantum physics and the concept of a quantum universe and infinity. Even though the concept of infinity is mathematically sound and provable, its existence is actually confined to the paradigms and symbolic representations of the mathematics, yet has no actual physical manifestation within our universe; i.e., although our universe is finite but unbounded (expanding into the infinite), it is not infinite in itself, but rather confined to the finite space it creates as it expands. Thus a time quanta concept may be very important in accounting for the quantized nature of our universe at all levels.
By accepting the existence of a time quanta, we can understand why certain constants are constant. For instance, the speed of light (c) is a constant composed of distance per unit time (d/t), meaning that both of these factors or dimensions must vary in synch as a quintessential manifestation of the space-time continuum. A time quantum would mean that time is composed of fixed moments separated by a mathematically infinite (or finite?) number of diverging probabilities, and can be viewed as a half-sine-like wave with 0 probability after one time quantum followed by a growing probability distribution until the next time quanta occurred, thereby “fixing” that particular moment and resetting the probability distribution(s). This process would be governed by the laws of entropy and thermodynamics, meaning that backwards travel along the same time line would be virtually impossible because of the 0 probability time well after a time quantum instant, and/or the necessity to alter the duration of a past time quantum (with a consequential energetic and highly disruptive ripple effect moving up and down the time stream).
FIGURE 1 - Space-Time via Time Quantum Perspective - 3D (or 2D) Time instants connected by sine-like probability distributions. Each instant is one (retrospectively fixed) time-probability dimension of the multiverse. Between the instants would lie n-number of other probability instants with the potential for other possible realities or time lines. Entropy provides directionality to the ‘arrow of time’ and backwards time travel (re-entering a fixed time instant) would encounter a 0 probability well.
However, if backwards time travel was possible, then any attempt to enter a time quantum instant that was already “written” (past) would have to create a new time quanta sequence/ time stream at that point; thus creating an alternate and parallel universe. This new universe would diverge from the past time stream the moment you created it, and all changes you might make would have no effect on the sequential series of fixed events in the universe you left (and create no ripple effect up and down the timeline). That is, assuming that present and future events cannot effect or influence events of the past (as some Quantum Theorists have proposed). In this perspective, an overview of Hawking’s feather-of-time would resemble a sequential series of connected probability tufts, with each probability line having the potential to create a new future sequence; although each probability line in the tuft would be limited in how far it could diverge from the past main probability line by the collapse of probabilities when a time quanta became fixed. Attempts at backwards time travel would just create another fractal probability sequence in the probability tuft series (a Multiverse). The following figure is an attempt to diagrammatically show this alternate view.
FIGURE 2 -The Arrow/Feather of Time vs. the Tufted Feather and the Fractal Feather of a Multiverse with Backward Time Travel Allowed. Hawking’s feather of time is a linear time line with the present fixing the past and proceeding to one probability or another. In a multiverse view of this perspective, each probability line could result in a different future. The Tufted Feather is the same except it is broken up into a series of probability distributions with fixed moments/time-quanta sandwiching them. The Fractal Feather allows all probabilities to exist as separate time lines in a Multiverse, with backward time travel conditionally allowed by creating alternate time streams.
Thus time would function as 3 (or 2?) dimensional moments or instants (like frames in a motion picture), where intervening non-moments are outside of our space-time frame of existence; yet the separated instants providing a retrospective illusion of a continuous 4th (and 3rd ?) dimension (as only the time quanta moments constitute our reality). Perhaps a universe with no quantum of time (a continuous unregulated time frame/4th dimension) would run out soon after it came into existence; like a clock without a regulated release of spring energy. This view of space-time can be visualized as a sort-of slinky toy, where an unregulated (continuous time) universe would be like un-stretched coils touching one another, and a linear trace from one end of the slinky to the other would be just a few inches long. However, when time is quantized and stretched out as in our universe, the slinky can be dozens of feet long depending on the distance between the coils. The time quantum would be the distance between coils and space dimensions the coils and path along the coils, while total spring/coil tension might represent the total energy, mass (“coagulated” energy), and temperature of that universe. Thus, our universe’s time quantum may be a fundamental and necessary constant, like the period of a pendulum, torsion balance, or oscillating spring constant for regulating the existence of space-time and the relationships between the fundamental forces; i.e., the reason our universe exists or persists as it does.
If time came into being during the Big Bang, then it should have started at zero and increased in value until the universe (~Higgs Field) cooled enough to let matter come into existence (“congeal“), thus creating a time quanta at a value consistent with inflation until it reached its (approximate) present value. Thus the time quantum may still be slowly changing in keeping with the expansion rate (and cooling) of the universe. Yet, because any knowledge of existence/ reality is confined to the fixed moments of time, there probably is no measurable way of discerning time expansion or contraction directly. However, the background radiation temperature and its history in our universe may give an insight into this question, as EM radiation has a wavelength, frequency and temperature associated with each light quanta, and thus has a time quantum component.
Distance Quantum (dq) and Thermodynamic Limits
If the speed of light is a constant because of a time quantum, then that must mean there is also a smallest meaningful unit of distance based on the unit values of c; which is calculated from this constant as 1.88x10-13 cm (Davis, 1963; Heisenberg, 1956). Using Planck’s proposed absolute time of 5.39x10- 44s, we can also calculate a Planck smallest distance (again using c) of 1.617x10-33cm. The significance of these values (among other things) may be that one or the other (or more) of these distances/lengths could represent the smallest possible wavelength of light thus its highest possible frequency at a particular time in the universe (1/tq = ¦ max):
(Davis, et al) c = l ¦ = dq/tq = 1.88x10-13 cm / 6.27x10-24 s = 3.0x1010cm/s
or
(Planck) c = d/t = 1.617x10-33cm / 5.39x10- 44s
(1) l
min ¦
max (Davis) ®
¦
max = 1 / 6.27x10-24s = 1.595x1023
Hz
and
(2) l
min ¦
max (Planck) ®
¦
max = 1 / 5.39x10- 44s = 1.85x1043Hz
(3) Wheeler-Planck ¦
max calculation (from l
min) = 1.6x1035 Hz
(1) Davis, et al® Tmax = 1.595x10²³ Hz / 5.88x1010 Hz K-1 = 2.71x1012 K
(2) Wheeler-Planck ®
Twp = 1.6x1035 Hz / 5.88x1010 Hz K-1 = 2.72x1024 K
(3) Planck ®
Tp = 1.85x1043 Hz / 5.88x1010 Hz K-1 = 3.15x1032 K
(4) Planck’s Absolute Hot ®
Tmax = 1.417x1032 K
1.4168x1032 K · 5.88x1010 Hz K-1 = 8.33x1042 Hz ® dq = 1/¦ max = 1.2x10-43s
A value less than the Planck Time of 5.39x10- 44s, but not that much less. Since we can’t ask Planck to elaborate on this discrepancy, we can only speculate on what took place at these various times and temperatures.
The highest temperature (Planck’s Absolute hot, 1.4168x1032 K) was proposed as the point where all known physics ceases to exist or can come into existence¯ . This would mean that if a time quantum came into existence at the moment of the Big Bang, it would have to have grown from zero to 1.2x10-43s in about 10-42s. Further, Planck’s estimated time value of 5.39x10-44s may possibly be when time itself actually came into being as a dimension of physics, thus subsequently allowing the fundamental forces to come into being one by one and begin creating structure in a cooling and expanding universe.
The intermediate temperature derived from the Wheeler-Planck calculation for maximum frequency (1.6x1035 Hz = 2.72x1024 K ® 6.25x10-36 s) seems to represent the point where the Electroweak epoch began (10-36 s after the Big Bang) and the temperature had dropped enough to allow the strong force to separate from the electroweak force. The electroweak epoch ended when the Inflationary epoch began (~10-32s), a point when the universe had cooled more and was now composed of a quark-gluon plasma. This Inflationary epoch lasted until ~10-24s when the universe had cooled/expanded enough to let various states of matter form as the quark-gluon plasma congealed.
The lowest calculated temperature (Davis, 2.71x1012 K ® 6.27x10-24s) seems to coincide with a threshold time (~10-24s) and temperature where thermal energy separates protons and neutrons (overcomes the strong nuclear force and decouples matter and radiation), and where the electron-positron flux is in thermal equilibrium with EM radiation and contributes to the black body spectrum. This temperature also coincides with the experimental temperature at which a quark-gluon plasma was formed at Cern: QGP~ 2×1012 K and up to 4.06x1012 K (where the melting point of more stubborn mesons built of heavy quarks could occur). Thus at temperatures/ energies greater than this, physical baryonic matter systems would breakdown into a quark-gluon plasma. Since the Davis, Heisenberg, et al time quantum was derived/proposed as the smallest meaningful time interval for any finite physical system, it would make sense that where the possibility of physical systems breakdown, so would the applicability / co-incidence of a time quantum.
Based upon the above, the time quantum may have come into existence at ~10-24s (after the Big Bang and as a set time interval) and then gradually expanded to its present value of 6.27x10-24s as the universe continued cooling and expanding. Thus the time quantum may have originated as a manifestation of quantum thermodynamics and the cooling of the Big Bang, both marking the epochs of creation and eventually becoming “frozen” into / inexorably linked to matter and energy at about 10-24s after the Big Bang; i.e.:
0 (Big Bang) ® 10-44s (Planck time) ® 10-43s/1032K (Absolute hot) ®
10-36s /1024 K (Electroweak epoch) ® 10-32s /1021K (Inflationary epoch) ®
10-24s /1012 K (strong nuclear force, matter, time quantum) ® nucleosynthesis
~1018s /2.7 K (Present) ® tq = 6.27x10-24s
Even though the cooling rate of the universe at the present time is for all intents and purposes negligible, the time quantum may still be able to grow as the universe continues expanding and the cosmic background radiation continues dropping from its present temperature of about 2.7° K. Thus it appears as though time, and the quantum of time as a discreet quantum thermodynamic constant, was created out of the Big Bang as did matter, energy, and the fundamental forces of nature. Since Absolute zero (0° K) appears to be an unreachable limit, time in all probability should not run out for many billions of years.
REFERENCES
http://en.wikipedia.org/wiki/Black_body_radiation
http://lasp.colorado.edu/~bagenal/1010/SESSIONS/13.Light.html
http://en.wikipedia.org/wiki/Quark%E2%80%93gluon_plasma
http://en.wikipedia.org/wiki/Momentum_space
http://en.wikipedia.org/wiki/Chronology_of_the_universe
An old idea but one of growing acceptance.
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