Cosmic Time as an Emergent Property of Cosmic Thermodynamics

This paper, in conjunction with recent Flat Space Cosmology (FSC) publica-tions, provides theoretical support for cosmic time being an emergent property of cosmic entropy and temperature. Therefore, if Verlinde’s “emergent gravity” theory is correct, both time and gravity are most fundamentally emergent properties of cosmic thermodynamics. Since emergent properties within complex systems with a huge number of degrees of freedom are often not definable at the smallest scales, these results suggest that quantum time and quantum gravity may be no more definable than consciousness within two connecting neurons. String theorists now struggling to define quantum space-time and quantum gravity should bear this in mind.


Introduction and Background
A common dictionary definition of time is that it is "the measure of duration".
However, this definition is somewhat unsatisfying, because "duration" is simply a synonym for "time". Einstein's definition of time as "what a clock measures" is correct, of course, but gets us no closer to a fundamental understanding of time.
The difficulty with the philosophical question "What is time?" is that one cannot define time in a fundamental way using only words, because any word definition of time invariably must use another word which can only be defined in terms of time [1].
The only alternative to defining time in words is to use a more rigorous form How to cite this paper: Tatum of symbolic logic, namely mathematics. Mathematics is essentially rigorous logic without the use of words, with the only exception to rigor being that some beginning set of assumptions ultimately derived from word logic is necessary as a starting point of any mathematical derivation. As proven in Godel's theorem, all mathematical systems must start with at least one unprovable assumption.
Aside from issues concerning starting assumptions, even with the use of mathematical equations, it is not necessarily easy to define time in a fundamental way. Every student of elementary physics learns the equation vt = s, where v stands for velocity, t stands for time, and s stands for distance travelled. Algebraic rearrangement defines time by t = s/v (i.e., time as distance divided by ve- It was not until the 19 th and early 20 th centuries that time could be redefined in a non-Newtonian way. The first important breakthrough appears to have been Maxwell's discovery of a fundamental velocity (i.e., speed of light c) which was entirely derivable from Faraday's laws of electromagnetism, which did not incorporate a time variable! Then, in 1905, Einstein conclusively proved that c is a fundamental constant of nature which is completely unshackled from the Newtonian concept of absolute time, and the tautological time definitions that come with it.
Of even greater importance, for the purposes of this introduction, was Ludwig Boltzmann's concept of entropy, which also did not incorporate a time variable.
Entropy allowed for a probabilistic, but inevitable, sequence progression (i.e., progressive change) within highly complex systems with many degrees of freedom, including the cosmos itself. Unfortunately, Boltzmann didn't live long enough to see the potential cosmic consequences of his second law definition, because the universe in his day was widely believed to be infinite, eternal and unchanging.
It was not until Edwin Hubble's discovery of an expanding universe that

Results
An entropic arrow of cosmic time is rigorously defined in FSC according to the following equation wherein t represents cosmic time, L p represents the Planck length, c is speed of light and S is the square root of Bekenstein-Hawking's entropy S at time t [see Equation (1)]. As detailed in the FSC references [4] and [5], Bekenstein-Hawking's entropy is a unitless ratio, and the correct-scaling entropy term in FSC is S . The reason for this is simply that cosmic entropy in terms of S scales in exactly the same way as cosmic time t (60.63 logs of 10 from the Planck scale). Furthermore, the FSC "Universal Temperature" T U scale [5], which is defined in a one-to-one correspondence to the Kelvin scale T by T U = 2 T , scales downward from the Planck scale temperature by 60.63 logs of 10 as time scales upward from the Planck scale time by 60.63 logs of 10. This allows for a thermodynamic arrow of time in the form of wherein T U and T are defined as above and the other terms are well-known constants.

Discussion
The above FSC definitions of cosmic time are in terms of cosmic entropy S , cosmic Universal Temperature T U , and temperature T in the Kelvin scale. Thus, in this cosmological model, cosmic time appears to be fundamentally an emergent property of cosmic thermodynamics. Furthermore, Erik Verlinde has re-cently suggested very persuasively that gravity and its manifestations (including dark matter and dark energy) are also emergent properties of cosmic entropy [6] [7]. The paper entitled "Clues to the Fundamental Nature of Gravity, Dark Energy and Dark Matter"  shows how FSC appears to be the cosmological model correlate to Verlinde's "emergent gravity" theory. Furthermore, as detailed in the July 2018 Journal of Modern Physics paper entitled "A Potentially Useful Dark Matter Index" [8], there now appear to be at least four recent observational studies [9] [10] [11] [12] in support of Verlinde's "emergent gravity" theory, particularly with respect to observations currently attributed to "dark matter." In addition, our own July 2018 Journal of Modern Physics paper entitled "Equivalence between a Gravity Field and an Unruh Acceleration Temperature Field as a Possible Clue to 'Dark Matter'" [13] provides further theoretical support for "dark matter" not actually being particulate in nature. Thus, it appears likely that additional persuasive evidence in support of Verlinde's "emergent gravity" theory will be forthcoming.

Summary and Conclusions
The current paper, in conjunction with recent FSC publications, provides theoretical support for cosmic time being an emergent property of cosmic entropy and temperature. Therefore, if Verlinde's "emergent gravity" theory is correct, both time and gravity are most fundamentally emergent properties of cosmic thermodynamics. Since emergent properties within complex systems with a huge number of degrees of freedom are often not definable at the smallest scales, quantum time and quantum gravity may be no more definable than consciousness within two connecting neurons. String theorists now struggling to define quantum space-time and quantum gravity should bear this in mind.