Time fascinates me! The two sentences which most grabbed my attention in this article were "the key to understanding time may be to study the fundamental physics of timekeeping" and "the arrow of time, causing time to move forward rather than backwards, (has nothing) to do with our human, conscious experience". These remind me of something I once saw on TV (I'm not sure but I think it might have been in one of the "Monty Python" shows). They were discussing the nature of time and one of the characters said timekeeping - a clock which has 60 minutes in an hour, 24 hours in a day - was only thought up as a joke and was never meant to be taken seriously. Using quantum mechanics and general relativity plus things like the Riemann hypothesis, the inverse-square law, binary digits, and topology; this adaptation of my science-journal article "Riemann hypothesis supports topological propulsion and faster-than-light travel through space-time" (https://medcraveonline.com/AAOAJ/AAOAJ-06-00159.pdf) should show that our invention of timekeeping - and thus our human, conscious experience - could explain time's nature in a quantum gravity universe. This means it's no joke and must be taken very seriously.
Anybody can go on the Internet and look at an image of the Mobius strip. The Mobius, in both our hypothetical reality and as an online image, is two dimensional and can obviously be programmed/coded/drawn by computer. This means it's composed of BITS (the binary digits of 1 and 0, which can represent electrical pulses being "on" or "off"). Then two strips combine into a figure-8 Klein bottle which is immersed (not embedded) in the 3rd dimension (clocklike Wick rotation^ is electronically programmed into the strips and bottles to produce the 4th dimension of time). And trillions of strips and bottles respectively form electromagnetism's photons and gravity's gravitons.
The physicist and science historian Abraham Pais wrote that "In 1924 the scientist Wolfgang Pauli was the first to propose a doubling of electron states due to a two-valued non-classical "hidden rotation". (7) Extending the ideas of "doubling", "two-valued" and "hidden rotation" from the quantum spin Pauli had in mind to the Mobius strip being a basic, fundamental unit of reality; it can be seen that Pauli's proposal has an analogy to this article. The doubled Mobius strips (doubled to form a figure-8 Klein bottle) could be produced by the two-valued binary-digit system used in electronics. The bottles possess a hidden rotation, now identified as adaptive Wick rotation, which gives a fourth dimension to space-time.
Figure 1 - the Mobius Strip (source: http://www.clker.com/cliparts/3/7/ a/9/1220546534781713951lummie_Mobius_Strip.svg.hi.png) The Mobius strip is a closed surface with no distinction between inside and outside. Thanks to quantum mechanics' entanglement applying on macroscopic scales,* this doesn't refer only to the surface itself. This results in the space-time of our universe existing everywhere and everywhen. The inside and outside of the universe's energy and mass are continuous when it's composed of Mobius strips and figure-8 Klein bottles acting macroscopically - there cannot be other universes outside our infinite and eternal universe, and there's no universe with different laws of physics (such a state of supposed multiple universes is called the multiverse).
* "Physicists now believe that entanglement between particles exists everywhere, all the time, and have recently found shocking evidence that it affects the wider, 'macroscopic' world that we inhabit." (8) Though the effect is measured for distances in space, the inseparability of space and time means that moments of time can become entangled too. (9)
Figure 2 - MOBIUS DOUBLET (FIGURE-8 KLEIN BOTTLE) (source: https://upload.wikimedia.org/wikipedia/commons/7/73/KleinBottleFigure8-01.png) Note that the positive curvature fits together with the negative curvature to produce the outline of a doughnut which is technically flat (see the reference to Vanessa Janek (10). When many doublets are placed together, binary digits can fill in any gaps or voids in the same way that computers can morph a picture on a screen and extrapolate a small patch of blue sky to make a sky that's blue from horizon to horizon. Morphing by bits can also delete a single doublet's central "hole". But the doublet doesn't become multiply connected like the doughnut. Merely the doughnut's outline is adopted - the doublet retains the property of being simply connected, a property necessary for space-time's infinity. (Informally, if an object in space consists of one piece - the constituent two Mobius strips now have the outline of one doughnut - and no longer has any "holes" that pass all the way through it, it is called simply-connected. A flat universe that is also simply connected implies an infinite universe. (11)
^ Figure 3 - WICK ROTATION: "The complex plane reveals i's special relationship with cycles via the circle of i, also known as Wick rotation. Whenever a point on the complex plane is multiplied by i, it moves a quarter rotation around the origin or center of the plane." [Figure and quote from (12)] The Riemann hypothesis, proposed in 1859 by the German mathematician Georg Friedrich Bernhard Riemann, is fascinating. It seems to fit these ideas on various subjects in physics very well. The Riemann hypothesis doesn't just apply to the distribution of prime numbers but can also apply to the fundamental structure of the mathematical universe's space-time. In mapping the distribution of prime numbers, the Riemann hypothesis is concerned with the locations of "nontrivial zeros" on the "critical line", and says these zeros must lie on the vertical line of the complex number plane i.e. on the y-axis in Fig. 3. Besides having a real part, zeros in the critical line (the y-axis) have an imaginary part. This is reflected in the real +1 and -1 of the x-axis in Fig. 3, as well as by the imaginary +i and -i of the y-axis. In the upper half-plane of Fig. 3, a quarter rotation plus a quarter rotation equals a half - both quadrants begin with positive values and ¼ + ¼ = ½. (The Riemann hypothesis states that the real part of every nontrivial zero must be 1/2.) While in the lower half-plane, both quadrants begin with negative numbers and a quarter rotation plus a negative quarter rotation equals zero: 1/4 + (-1/4) = 0. In the Riemann zeta function, there are infinitely many zeros on the critical line. This suggests the y-axis is literally infinite. To truly be infinite, the gravitational and electromagnetic waves it represents cannot be restricted to the up-down direction but must include all directions. That means it would include the horizontal direction and interact with the x-axis - with the waves rotating to produce ordinary mass (and wave-particle duality) in the x-axis' space-time,* and dark matter in the y-axis' imaginary space-time.
* The inverse-square law states that the force between two particles becomes infinite if the distance by which they're separated goes to zero. Remembering that gravitation partly depends on the distance between the centres of objects, the separation only goes to zero when those centres occupy identical space-time coordinates (not merely when the objects' sides are touching). That is - infinity equals the total elimination of distance, or zero. The infinite, eternal cosmos could possess this absence of distance in space and time (deletion of the 3rd dimension) via the electronic mechanism of binary digits which would make the universe as malleable and flexible as any image on a computer screen. If infinity is the total deletion of distance in space-time, there is nothing to rule out instant intergalactic travel or time travel to the past and future. Infinity does not equal nothing - nor does zero. Zero would be something if it's paired with one to form the binary digits used in computers and electronics. Could the universe, and life, have begun with all the brains of past and future history acquiring increasingly sophisticated knowledge of time and space? Then an extra-dimensional hyperspace might be used to access the infinite past and purposely switch the digits composing the universe from 1 to 0 or vice versa (this switching would be comparable to the quantum fluctuations associated with Big Bang theory). Renormalization is a mathematical procedure for cancelling infinities. At present, it's regarded as a prerequisite for a useful theory and is part of attempts to unite general relativity with quantum mechanics. But if the Big Bang never happened, we'd be living in an infinite and eternal cosmos. Removing infinities mathematically (or by any other means) would be an error and retaining the infinite values would point the way to deeper understanding of the universe.
All mass is composed of gravitational and electromagnetic waves, according to vector-tensor-scalar (VTS) geometry inspired by the title of Einstein's 1919 paper "Do gravitational fields play an essential role in the structure of elementary particles?" Both types of waves possess retarded and advanced* components which travel forwards and backwards in time, cancelling one another and entangling all masses. Wick rotation (time) is built into the Mobius strips and figure-8 Klein bottles composing electromagnetism's photons and gravitation's gravitons. Therefore, all time (the entire past and present and future) is united into one thing just as all space and all mass are united into one thing. (If time only passed rectilinearly - from past to present to future - the idea of waves travelling back in time would make no sense at all. But if time is curvilinear - with past, present, and future interconnected - time must be able to move from future to present to past.) (Unity of past/present/future may remove the issue of non-simultaneity - in special relativity - because the timing or sequence of events being different in different frames of reference can only exist if past/present/future are separate. The concepts of cause and effect are no longer separate when all periods of time are united, and everything can happen "at once". This is similar to watching a DVD - every event on the DVD exists at once since the whole DVD exists but we're only aware of sights and sounds occurring in each tiny fraction of a second.) This view of time removes the "arrow of time" (where events only move from past to future) - although the DVD analogy shows how cause and effect occur in our perceptions even when everything happens at once.
* "When we solve (19th-century Scottish physicist James Clerk) Maxwell's equations for light, we find not one but two solutions: a 'retarded' wave, which represents the standard motion of light from one point to another; but also an 'advanced' wave, where the light beam goes backward in time. Engineers have simply dismissed the advanced wave as a mathematical curiosity since the retarded waves so accurately predicted the behavior of radio, microwaves, TV, radar, and X-rays. But for physicists, the advanced wave has been a nagging problem for the past century." (14)
Stars and galaxies etc. send us retarded light which, through spectroscopy, gives an approximate measurement of how long that light has been travelling (the distance to the astronomical body). The light includes an advanced component that reaches back into the past, producing a measurement that significantly exceeds the real distance. The farther away a star or galaxy is, the more the advanced part of waves from it will reach into the past, giving us a greater inaccuracy regarding its true distance. This increase is analogous to redshift increasing with distance. We might call it readshift - re(tarded) ad(vanced) shift. Readshift would explain the astronomical results which were interpreted as accelerating expansion of the universe. Surveyed supernovas would appear fainter, therefore apparently farther away than they truly are. Unless advanced waves are considered a possibility, the only rational way to move a supernova from its apparent, distant position to its true nearer location is to conclude the universe has expanded.
Besides those listed in the references, acknowledgements go to the following -
a) In 1990, John Wheeler (1911-2008) suggested that information is fundamental to the physics of the universe. According to this "it from bit" doctrine, all things physical are information-theoretic in origin.
b) Erik Verlinde says gravity is not a fundamental force of nature, but an emergent phenomenon. In the same way that temperature arises from the movement of microscopic particles, gravity emerges from the changes of fundamental bits of information, stored in the very structure of spacetime.
c) Cosmologist Max Tegmark hypothesizes that mathematical formulas create reality
d) "Pioneered (in the late 1980's) by Rafael Sorkin, a physicist at the Perimeter Institute in Waterloo, Canada, the theory (causal sets) postulates that the building blocks of space-time are simple mathematical points that are connected by links, with each link pointing from past to future."
(e) Prof. Edward Fredkin, pioneer of cellular automata and digital physics.
(f) Luca Rajabi, Principal Investigator at Mobilis Solutions Group in the USA, who gave me enlightening discussions on researchgate.net about the Mobius strip and Einstein's views on dimensions.
7. Pais A. Niels Bohr's Times. Oxford Clarendon Press; 1991. p 201.
8. The Weirdest Link. New Scientist. 2004;181(2440):32.
9. Brukner C, Taylor S, Cheung S, et al. Quantum Entanglement in Time. Arxiv. 2004.
10. Janek V. What Shape is the Universe? 2015.
11. Luminet JP, Rey ML. Cosmic Topology. Phys Rep. 1995;254(3):135- 214.
12.Welch K. The Meaning of Imaginary Time: Creativity's Dialog with Timelessness. Word Press. 2015.
13.Hardy AS. Elements of Quaternions. 1881.
14.Kaku M. Physics of the Impossible. Penguin Books. 2008:276-277.