The Universe on a Tee Shirt

The Universe on a Tee Shirt (A TOE According to One Amateur Scientist)

by John Winders

Note to my readers: You can access and download this essay and my other essays through the Amateur Scientist Essays website under Direct Downloads at the following URL: https://sites.google.com/site/amateurscientistessays/ You are free to download and share all of my essays without any restrictions, although it would be very nice to credit my work when quoting directly from them.

For a long time, theoretical physicists have dreamed of the day when the general theory of relativity and quantum mechanics would be combined to create the Theory of Everything. It often stated that such a theory would be so simple and concise that the whole thing could be condensed into a simple equation that would fit on a T-shirt.

It was clear to me that classic material reductionism could not provide a path to that laudable goal, so I undertook an investigation to see what could replace it. That investigation spanned almost 4½ years, and it was documented step-by-step in my essay Order, Chaos and the End of Reductionism, which you can access from my Amateur Scientist Web Page. This research led me to several dead ends, blind alleys, and self contradictions; however, I never deleted or changed any of my mistakes in order to preserve and document the evolution of my thinking along each step of the way.

The essay presented here is just a condensation of that much longer essay. The equation on the cover would easily fit on a T-shirt and I think it really does capture the essence of the Theory of Everything. dEU / dtU = 2 π k T c3 tU / ħ G You'll note that the four fundamental constants of nature are here: Boltzmann's constant, k, the speed of light constant, c, Planck's constant, ħ, and Newton's gravitation constant, G. Astute readers who are familiar with the Bekenstein-Hawking theory will notice a piece of the Bekenstein equation is found in it. I believe this is the equation of state of the universe that describes expansion in terms of increasing mass-energy, EU, with respect to a universal time parameter, tU. You might object, “Wait a minute. I thought mass-energy is conserved.” Well, mass-energy is conserved over short time intervals where time-displacement symmetry is valid. What I discovered, however, is there is no time-displacement symmetry over cosmological time scales, and there's a good reason for that.

The other thing I discovered is the gravitational constant, G, is not really constant after all, and there's a good reason for that too. So come with me on a short journey to find out what those reasons are. Because this essay is fairly brief, so you may have a bit of trouble following the derivation of my theory; therefore, I urge to to go over to the web site and review Order, Chaos and the End of Reductionism, especially Appendices W, X and Y, which go into much more detail.

In its most basic form, reductionism is an approach to understanding the nature of complex things by reducing them to the interactions of their parts, or to simpler or more fundamental things.

Engineers and physicists use reductionism to explain reality. I came to the conclusion that there are three different classes of interactions in nature: 1. Deterministic, linear, reversible, certain 2. Deterministic, non-linear, irreversible, predictable in the forward direction 3. Non-deterministic, irreversible, unpredictable (probabilistic) Reductionism is concerned mainly with the first class of interactions; however, they only apply to the most trivial of situations, such as two bodies orbiting around each other and simple harmonic motion. The vast majority of interactions in nature are in the second class, commonly referred to as chaotic interactions. Ironically, it seems that the highly-complex order we observe in the universe emerges essentially from chaos. Take for example weather patterns, like a hurricane, born from chaos and yet having an identity and a quasi-stable structure. The giant red spot on Jupiter is a permanent hurricane that has persisted for at least 187 years.

Since reductionism is only capable of examining the simplest and most trivial examples of order, I chose the title Order, Chaos and the End of Reductionism to reflect the fact that order and chaos 1

begin where reductionism ends. Another interpretation is that reductionism is at an end as a viable scientific philosophy going forward. As long as you examine nature through linear, deterministic and reversible interactions, you are only seeing reality through a tiny keyhole. How sad it is that a majority of scientists still consider reductionism as the preferred default method of solving science.

String theory is touted as the whiz-bang cutting edge of theoretical physics, but I perceive oldfashioned reductionism at its core.

The third class of interactions are stochastic, random, and completely unpredictable. These interactions lie at the heart of quantum mechanics. Oddly enough, some extremely brilliant theoretical physicists (including Albert Einstein up till his death) deny the very existence of stochastic interactions, believing that some underlying local hidden variables are involved instead.

I confess being guilty of thinking that chaotic interactions might be used as substitutes for stochastic processes, but I was definitely wrong. Experimental violations of Bell's inequality put that idea to rest, and in the face of such incontrovertible evidence as this I'm amazed there are theoretical physicists who still cling to determinism.

The core of my thesis is this: Entropy equals information. Entropy has been completely misunderstood by many leading scientists, who try to label it as “missing information” or “hidden information” or even “negative information.” This misconception stems from the fact that order and entropy are indeed opposites. People tend to prefer order over disorder, so they equate entropy to something very negative and undesirable. On the other hand, people love information – the more the better. After all, we live in the “information age” with the Internet offering us cool things like Wikipedia, Facebook, Twitter, and Instagram. So how can something “good” like information possibly be the same as something so obviously “bad” like entropy? First off, you need to know information is defined, which unfortunately most physicists do not. Claude Shannon figured it out in the 1940s, and it has everything to do with probability and uncertainty. Suppose there are N possible outcomes of some interaction, each with a certain probability, pr. Shannon concluded that the amount of information, S, contained in that set of outcomes is as follows.

S = – ∑ pr log2 pr

, r = 1, 2, 3, … , N

If an outcome is certain; i.e., if any of the probabilities in the set should equal one, then there is zero information in that set. Suppose I call someone on the phone and inform them it's Saturday. How much information did I relate to that person if he already knew it was Saturday? The answer is zero, because there was no uncertainty on his part about the day of the week. But now suppose that person just woke up from a coma and had no idea what day it was, so all days are equally probable to him. For N equally-probable outcomes, the above equation reduces to S = log2 N. Stating that it's Saturday provides log2 7 bits of information to that person. If you notice, S = log2 N is identical to Boltzmann's definition of thermodynamic entropy, except Bolzmann used the natural logarithm instead of the base-2 logarithm and he stuck a constant, kB, in front of it: S = kB Ln N. Once you come to grips with the fact that entropy = information, then it's apparent that information cannot exist without uncertainty. So which class of interactions in nature involves uncertainty?

Well, the first class clearly doesn't because all outcomes can be uniquely solved in both forward and reverse directions. A single planet revolving around a star will stay in that orbit forever unless it is perturbed by some outside force. You can determine the exact location of that planet billions of years into the future or billions of years into the past using a simple formula that describes an ellipse with a time parameter, t.

Can information come from a chaos? It might seem that chaos could provide randomness and uncertainty, but this is not the case. Chaotic processes are still deterministic because there is a unique relationship between the current state and subsequent states. Thus, every repetition of a chaotic process will produce exactly the same sequence of events. This is not true in the reverse 2

direction due to one-to-many relationships between the current state and previous states, rendering chaotic processes irreversible. Thus, irreversibility alone does not generate true uncertainty, at least going forward. Chaotic interactions can rearrange bits, and even make them unrecognizable, but they cannot create new bits. Only the third class of stochastic interactions can introduce the uncertainty that information requires.

Chaos produces fractal patterns, and these patterns are widespread in nature. So at one point in this investigation, I thought the universe itself might be a colossal fractal. Fractal patterns have extremely high – or one might even say infinite – levels of complexity that can be generated by very simple non-linear functions. Fractals have the properties of scale-invariance and self-similarity, where large-scale features are repeated over and over on smaller scales. Those features are not necessarily repeated exactly, however. The Mandelbrot set is one of the most widely-known fractals, having a prominent circular feature that appears over and over again on smaller scales. On the smallest scales, this circular feature gradually gives way to different features. You can try this yourself using the interactive Mandelbrot Viewer.

I used to think the general relativity field equations could only be applied to small-scale systems, but I was very wrong. What I discovered is that Einstein actually had stumbled on a set of equations that provides an exact description for the entire universe, and that pattern is only repeated as an approximation for smaller scales involving weak-field interactions. In other words, the universe is a fractal having an exact overall solution given by the Schwarzschild equation, but this equation is not necessarily an exact solution for smaller scales.

A recurrent theme in this throughout my investigation is that the most important – and perhaps the only – law of nature is the statement that entropy of isolated systems cannot decrease. This is the famous second law of thermodynamics, which really should be the zeroth law of the universe because it underlies causality itself. Since entropy and information are equivalent, this law means that information cannot be destroyed. Some scientists try to trivialize this law by saying that there's just a tendency for entropy to increase because it's more likely to increase than to decrease. They say given enough time (and patience) you'll see an isolated system inevitably repeat some previous lower-entropy state. I state unequivocally that this is not just unlikely, but it's impossible because it would be tantamount to destroying information and causing “unhappening” of previous events.

As a corollary to the second law of thermodynamics, I came up with what I call the “postreductionist universal law” stated as follows: “Every change maximizes the total degrees of freedom of the universe.”

The phrase “total degrees of freedom” sounds kind of nice, which is why I chose it. But the logarithm of total degrees of freedom equals total entropy, so what this really means is that every change maximizes the entropy of the universe. Not only can entropy never decrease, it must always increase to the maximum extent possible. Taking this idea to the limit, I postulated we live in a moment of maximally-increasing entropy, which addresses – and maybe solves – the mystery of time. What clocks are actually measuring are increases in entropy reflected as a reduction in curvature of the universe unfolding around them, as explained in the following paragraphs.

Solving the Schwarzchild equation yields R = 2 E G / c2 describing a sphere of radius R, where E is the mass-energy of the system, G is the gravitational parameter, and c is the speed of light.

Maximizing the total degrees of freedom (entropy) of the universe means the universe is in a permanent state of maximal entropy, so the only way to further increase entropy is through expansion. The maximum rate of expansion can be attained if R increases at the speed of light by introducing the concept of universal time, tU, where R = c tU. The idea that there could be such a thing as universal time is anathema to physicists. After all, we 3

are told space and time are relative, not absolute. However, tU isn't the Newtonian notion of simultaneity across space. Instead, tU marks the progress of universal expansion, and while R has a dimension of length, it should be thought of as an expanding radius of curvature around a temporal center, with a surface surrounding the center at a distance R = c tU marking the present moment. No clock can run ahead of tU because no clock can run ahead of the present moment. A free-falling body will keep up with tU, except when a force acts on the body causing acceleration and its proper time to lag behind tU. Observing objects at some distance in any direction, we observe them when the universe had a radius R' < c tU. Those objects will fall behind us in time and will appear to recede from us in space, resulting in the cosmological red shift. Objects at at distance R = c tU will be receding at the speed of light and will be at the edge of our horizon. Substituting c tU for R in the Schwarzschild equation results in E G = ½ c3 tU. This means either the total mass-energy of the universe or the gravitational parameter must increase over time, or both. As it turns out, the gravitational parameter decreases over time, being proportional to tU – 1, so E must increase in proportion to tU 2.

If the universe is in a state of maximal entropy, we can apply the Bekenstein equation to it. By combining the Bekenstein and Szilárd equations, we get the following equation of state. dEU = (k T c3 / 4 ħ G) dA

, where A is the expanding surface area of uniform curvature, 4 π R2.

dA = 8 π R dR dA / dtU = 8 π R dR / dtU = 8 π c R \ dEU / dtU = 2 π k T c4 R / ħ G = 2 π k T c3 tU / ħ G The above equation of state combines the four fundamental constants k, c, ħ, and G (although G is really a variable, being inversely proportional to tU). The temperature of the universe, T, is inversely proportional to tU also, so the ratio T / G equals a constant that can be evaluated using the current temperature of the universe and the measured value of the gravitational constant.

According to the Bekenstein equation, the total entropy expressed in bits is proportional to the area of uniform curvature, 4 π R2 , divided by 4 Ln 2 times the Planck area, G ħ / c3. Since the Planck area is proportional to tU–1, total entropy is proportional to tU3. There must have been a time in the past when the total entropy of the universe was equal to one bit, which I would guess is the minimum amount of information that has meaning; the information associated with a coin toss. The value of tU corresponding to a single bit of entropy would be my idea of “The Beginning.”

Information from the past is encoded into the present moment. Linear and chaotic interactions transform those bits according to the laws of determinism without any loss of information, obeying the second law of thermodynamics, a.k.a. the zeroth law of the universe. Meanwhile, stochastic interactions are laying new bits of information at an increasing rate across an ever-expanding surface of uniform curvature corresponding to the present moment.

One of the raging controversies in the scientific community is the “vacuum catastrophe,” referring to the huge discrepancy between the mass-energy vacuum density based on cosmological arguments with an apparent flatness of space and the mass-energy vacuum density of virtual particle pairs based on quantum electrodynamics (QED). Using the model presented in this essay, the value of density, ρ, is found by dividing the rate of change of dEU / dtU by dVU / dtU = 4π R2 dR / dtU, with the assumption that dR / dtU is at the maximum rate, c. The vacuum density is ρ = k T / 2 ħ G tU, and it decreases over time. Based on the known values of the parameters used in the formula, the vacuum density is currently 980 kg / m3, a surprisingly large value. However, it's not nearly as outlandish as the QED value for vacuum density of around 10 106 kg / m3. I'll conclude this essay on the following page with some bullet items that capture the key points of my Theory of Everything.

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SUMMARY

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There are three kinds of interactions: linear, deterministic, reversible; non-linear, deterministic, chaotic, irreversible; stochastic, probabilistic, irreversible.

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Entropy is equivalent to information.

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Information requires uncertainty; thus, only stochastic interactions are capable of producing information.

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Linear and chaotic deterministic interactions preserve and transform information in causal space according to the “laws of nature.”

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Causal space has one time dimension, requiring three spatial dimensions because they must match the number of rotational degrees of freedom.

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A free-falling observer is incapable of measuring any spatial curvature of three-dimensional space because of rotational symmetry.

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Due to the asymmetry of time, there is a radius of temporal curvature, R, expressed in units of length, centered on the beginning of time.

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Order emerges from chaotic interactions as fractal-like patterns that repeat on different spatial and temporal scales.

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The universe is a fractal with the properties of scale-invariance and self-similarity.

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Due to scale-invariance, solutions to the general relativity field equations are exact solutions for the entire universe and approximate solutions for to its sub parts.

•

The Schwarzschild formula R = 2 E G / c2 is an exact formula of a closed system, e.g. the universe.

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The universe is in a permanent state of maximal entropy and so the Bekenstein equation can be applied to it. Thus, the universe must expand in order to accommodate more information.

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There exists a universal time parameter, tU, which marks the expansion of the universe.

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The universe expands maximally at a rate dR / dtU that is bounded by the speed of light, c.

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Since tU corresponds to the present moment, proper time of an observer cannot get ahead of tU. The geodesic paths of free-falling bodies maximize proper time up to the limit of tU.

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Time, having a radius of curvature equal to R, does not have time translation symmetry over cosmological time periods. Thus, the law of conservation of mass-energy does not apply to the universe as a whole.

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The quantity of mass-energy in the universe increases in proportion to tU2.

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The quantity of entropy-information in the universe increases in proportion to tU3.

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There is an equivalency between mass-energy and entropy-information (“it equals bit”).

•

Since mass-energy and entropy-information increase at different rates, they are linked by the Szilárd equation with a decreasing temperature, T, proportional to tU–1.

•

The vacuum density of mass-energy is ρ = k T / 2 ħ G tU, with a present value of 980 kg / m3.

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Appendix A – A Picture Is Worth 1,000 Words The schematic diagram below explains the cosmology of the Theory of Everything.

The universe expands from left to right beginning at a time t' = 0, which can be interpreted as the “big bang” or whatever initial state is appropriate. The magenta curves indicate “now” surfaces of uniform curvature having radii of curvature, R', centered on t' = 0. The present radius of curvature at Here and Now is R = c tU where dR / dtU = c. Looking in any direction, x, y, or z out into space, we see the universe as it was younger and when R' of the “now” surface of uniform curvature was smaller. Because the universe was younger at these locations, their times appear to be lagging behind tU from the vantage point of Here and Now, creating time dilation proportional to the distances Ö x2 + y2 + z2. This is the reason for the cosmological red shift.

Temperatures, T', shown above the red thermometers, are inversely proportional to time t', so true temperatures are proportional to distances Ö x2 + y2 + z2 . However, because of the cosmological red shift, all temperatures appear the same from our vantage point of Here and Now. The so-called cosmic microwave background (CMB) is actually the composite of all temperatures of every era after those temperatures have been red-shifted in proportion to distances. The CMB isn't just one red-shifted temperature from a particular era, but all temperatures after they've been red-shifted.

The radius of curvature always expands at the speed of light at a surface of uniform curvature: dR' / dt' º c. However, the cosmological time dilation slows distant expansion velocities from the vantage point of Here and Now. This makes objects from previous eras appear to recede away from Here and Now, as shown by the green arrows. Thus, the true origin of the Hubble constant is the apparent slowing down of distant recessional velocities from cosmological time dilation.

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Appendix B – The Point of Inflection According to the standard cosmological model (SCM), the universe is currently on the precipice of something big. Since the big bang, gravity has been slowing the rate of universal expansion – until now. Dark energy – also known as the cosmological constant – has caused the rate of expansion to start picking up recently. In the future, the expansion will continue to accelerate, causing a number of cosmologists to fear that space itself will be torn apart. They call this future event “the big rip.”

In calculus, the point of a curve where the slope stops decreasing and starts increasing is called a point of inflection. The size of the universe is now at a point of inflection.

On the other hand, according to my Theory of Everything (TOE), the rate of expansion as expressed by the radius of temporal curvature is, was and always will be equal to the speed of light. The graphs below compare the SCM and TOE models. “Time Since the Beginning” and “Radius” are on normalized scales, where 1.0 = tU » 13 + billion years and 1.0 = R = c tU.

The blue curve corresponds to the SCM and the red line corresponds to my TOE. The point of inflection of the blue curve is occurring at t' = 1.0. The SCM rationale for a rate of expansion that decreases and then increases is as follows. Whereas gravity puts the brakes on expansion, it's becoming a non-factor as the universe expands because no additional matter is being added to the universe. On the other hand, since the density of dark energy is constant, there is more outward “pressure” to expand as the universe gets larger, and this is just now overwhelming the tendency for the universe to collapse under gravity.

Doesn't it seem a bit odd that a once-in-a-universe event such as this would wait until just after the human species had a chance to evolve into intelligent creatures and began to contemplate the universe? Or could it be that astronomers really don't know how big or how old the universe actually is? After all, if distances to the “standard candles” used by astronomers to judge distances are slightly off, then the calculated previous rates of expansion will be off too. The most reliable “standard candles” are in our immediate vicinity, so if the rate of expansion right around us seems to be X, then it just might be that the rate of expansion always has been X. My TOE looks at things differently than SCM: Mass-energy is being added to the universe and it is proportional to tU2, while entropy (which drives expansion) is proportional to tU3. Temperature, being proportional to tU – 1, balances the two, keeping the rate of expansion constant. It's not that the radius of curvature is forced to expand at the speed of light; instead, the speed of light is forced to equal the rate of expansion in order to prevent travel into the past, which would violate causality.

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Appendix C – Some Observations and Experiments One of the most controversial claims of my TOE is that Newton’s so-called constant, G, is a variable that decreases over cosmological time, and I think there is some evidence that suggests G is not constant. Astronomers estimate distances based on apparent luminosities of stars, which decrease by the square of their true distances from Earth, compared to their intrinsic luminosities.

The intrinsic luminosity increases with the star’s diameter and its surface gravity. If the value of G was greater in the past, the intrinsic luminosity of a distant star would be greater than an identical nearby star. In other words, if G were greater in the past distant stars would be actually farther away from Earth than their apparent luminosities would indicate. The following chart shows measurements of the cosmological red shift based on the apparent luminosities of distant stars. The blue circles depict stars with distances computed using “standard candles” based on the assumption that G is a constant. The red circles depict the same stars assuming greater values of G and higher intrinsic luminosities in the past, which shifts their true distances toward the right.

Based on standard cosmology, the rate of expansion of the universe is slowing down. This is shown by the blue line, which bends upward with increasing distance. My TOE claims that the cosmological red shift must be linear over distance since all observers recede from the Beginning at the same speed (c) in their own frames of reference. Based on their greater true intrinsic luminosities, distant stars are shifted from the curved blue line toward the straight red line.1 This doesn’t prove a thing; however, if G does decrease over cosmological time, then it would explain why the observed rate of expansion seems to have slowed down even if the true rate were constant.

Astronomers claim that observations of distant supernovae prove that G has remained constant for billions of years. But this assumes an average star in the past began with the same amount of material as an average star forming today. But if G were significantly greater in the past, couldn’t smaller stars then appear much the same as medium-sized Sun-like stars today?

Observations of Mars clearly indicate remnants of rivers, lakes, and possibly seas on the Martian surface. Although today’s temperatures at the Martian equator can reach 20°C at high noon, the mean surface temperature is −60°C. These chilly temperatures are partly due to the fact that Mars doesn’t have much of an atmosphere, but its doubtful that a thicker atmosphere would make much 1

This means that distances to far away galaxies are greater than indicated from astronomical observations.

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of a difference considering that the “greenhouse effect” from Earth’s relatively thick atmosphere adds only about 30°C to the Earth’s surface temperature. Current models of stellar evolution indicate that the Sun was significantly cooler billions of years ago than it is today, but those models are highly dependent on the surface gravity of a star. So how was it possible for water to flow on Mars in the distant past? One plausible explanation is that if G were larger in the past than it is today, the Sun could have been significantly brighter in the past than the current models indicate.

Gravity is an exceptionally weak “force”2 on small scales, so measuring G requires very precise instruments. The Cavendish torsion balance is the standard instrument for doing these measurements. A schematic diagram of the torsion balance is shown below.

Two spherical orange weights, each with a mass m, are attached to a rod of length L suspended from a thin fiber (shown in green). Two movable blue weights, each with a mass M, are placed in close proximity to the orange weights so that the M-to-m centers are maintained at a fixed distance, a, apart. The blue and orange spheres attract each other by gravity and produce a torque, τ, in the fiber (indicated by the green arrows). G is calculated by measuring the torque in the fiber and applying Newton’s law of gravitation in reverse, as follows.

G = a 2 τ / (L M m) When measuring any physical parameter in a laboratory, random errors produced by all components of the instrument must be taken into account. These errors are combined statistically to produce a range of possible true values around the measured result. For example, if the measured value of X is 1.0 and the combined measurement errors are  0.1, we expect 0.9 < X < 1.1 to the be the true value of X. When multiple measurements are made using the same instrument, the measurements may vary but they should fall within the range of statistical error. This isn’t case with the Cavendish torsion balance; over the years as measurements are getting more precise, researchers have noted anomalous measurements that routinely fall well outside those ranges.

In a 2015 paper (Click this link for the paper), J. D. Anderson of the Jet Propulsion Laboratory and three other authors reported that measured values of G seems to be correlated with the variations in the length of day (LOD) over a 5.9-year periodic cycle. These results are is depicted on the highlyschematic chart on the next page.3 The blue dots represent laboratory measurements of G and the vertical bars indicate instrument error ranges. The solid blue curve represents the LOD over one of several 5.9-year cycles.

2

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I hesitate using the words force and gravity in the same sentence because the General Theory of Relativity clearly shows that gravity isn’t a force; it’s a distortion of space-time that defines trajectories of free-falling bodies. The “force” appear when the body is prevented from following that trajectory. The chair I’m sitting in alters my trajectory through space-time by pushing on my butt. That push is often mislabeled as “gravitational force.”

The actual chart is copyrighted so it can’t be shown here, but you can see it by following the link to the paper.

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As depicted on the chart, most of the blue dots fall outside the instrument-error ranges of other blue dots and follow the length-of-day curve. Anderson and the other authors are quick to point out that they don’t believe a change in the Earth’s rotation itself affects the G measurements, nor do they believe G actually changes. Thus, they are at a loss to explain why measured values of G are correlated with LOD, although they suspect there is a common driver. Some have suggested periodic changes in the Earth’s core affect LOD, which is reasonable. But why would changes in the Earth’s core affect laboratory measurements of G at the surface?

Well here’s my hypothesis: The drivers behind the variations in measurements of G and LOD are true variations in G itself. Gravitational mass and inertial mass are two sides of the same coin. If the true value of G increases, the Earth’s inertia will also increase. Then in order to conserve angular momentum, the Earth’s speed of rotation must slow down, thus increasing the LOD. At any rate, Cavendish torsion balance data strongly suggest that G is not a constant but a variable.4 The fact that the period of G correlates with the period of LOD is interesting, although it might just be a coincidence. But matching amplitudes would really support the hypothesis of a causal connection between them. From the Anderson et al paper, the measurements of G over the 5.9-year LOD cycle vary between 6.672 and 6.675  10 –11 m 3 s – 2 kg – 1. Unfortunately, different labs made these measurements using different instruments with different statistical errors. At any rate, the measurements deviated  0.0225% from the mean value.

I looked up the LOD over a 5.9-year period, and the variations deviated about  1.5 ms from the mean sidereal day of 86,164 sec. These LOD variations are only  0.0000017% compared to the hypothetical  0.0225% variation of G. The angular momentum of a sphere having a mass M and radius R is given by the formula L = ⅘ ω M R2.. The speed of rotation, ω, is inversely proportional to M, so if angular momentum is conserved with G (along with the inertial mass M) truly varying by  0.0225% , the LOD should vary by  19 seconds over a 5.9-year cycle. This is 13,000 times larger than the observed LOD variations, and such a huge discrepancy in LOD observations would seem to show my TOE hypothesis is all wet; however, some relevant facts were left out.

The angular momentum of a sphere is dependent on R2 and the Earth is an obloid sphere, with its radius bulging out at the equator. Since the Earth is not perfectly rigid, the equatorial bulge would move slightly inward as G increases and the rotation slows down. Such a slight decrease in R might almost – but not quite – cancel the slowing down of the rotation due to an increase in inertial mass, M. In other words, a more detailed model of an elastic Earth might show that the data from the observations actually align with the hypothesis that G changes over time and causes LOD to change in synch with G. This warrants some further research in my opinion.

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I still don’t have a clue why G would vary over a 5.9-year cycle, although it should be correlated with the local ambient cosmological temperature. Unfortunately, I don’t know of a way to measure that temperature directly, but I’d love to know if the LODs of other planets in our solar system also follow the same 5.9-year cycle.

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Appendix D – What’s Below the Ontological Basement?

The British physicist Paul Davies famously stated that information occupies the ontological basement of reality. From my own studies over the past decade, I gradually arrived at the same conclusion: Entropy (information) underlies everything we call physical “reality” or “universe” (see two other of my essays Order, Chaos and the End of Reductionism and Relativity in Easy Steps). This implies a hierarchical chain, as follows.

Information → Time → Space → Energy → Matter The last four items in the chain (time, space, energy and matter) form what physicists define as the material universe in its entirety, but there are a growing number of them, like Davies, who are beginning to suspect that these are just the four upper floors of an edifice with a basement below them consisting of information. In fact, some have concluded that the key to a unified theory of quantum physics and gravity lies in the language of information.

The question that remains is whether information is ontologically complete in and of itself. I’ve struggled with that question, and lately have come to the conclusion that it must depend on something else which stands completely apart from time, space, energy and matter. My reasoning is as follows.

Most of us have an intuitive idea of information as having to act on a physical object. For example, flash drives store data using electrical charges applied to billions of tiny transistors. Information (according to Claude Shannon’s definition) requires uncertainty, so if each of those transistors could exist only in one possible state, there would be zero uncertainty about the flash drive’s actual configuration, rendering it useless because it couldn’t store any information. On the other hand, a functional 8 GB flash drive can store 6.8719  10 10 bits of information, meaning the drive may be 68,719,000,000 configured in any of 2 unique configurations, an insane number of possibilities with a huge uncertainty. The flash drive’s information storage function depends entirely on uncertainty.

We can envision physical computer hardware coming off the assembly lines without any firmware, operating system, software, or data. In other words, hardware can exist without containing any information, but, we cannot imagine firmware, an operating system, software or data existing in empty space without the physical hardware. Thus, information truly requires a physical substrate to act upon. The aforementioned Szilárd equation reveals that energy equals information multiplied by the temperature-dependent proportionality factor, kBT, suggesting that a substrate having thermodynamic properties5 must exist for the energy ↔ information equivalence to be valid.

Ontological information relies on a universal substrate I’ll refer to as “Q”.

Q (the universal substrate) → Ontilogical Information (the physical universe) The problem is that Q cannot consist of either matter or energy because mass-energy is just information in a condensed form. This suggests Q must be at least one additional level below Davies’ ontological basement, distinct from the physical universe itself and existing beyond it. The metaphor of physical reality represented by a building with information as its ontological basement is even more appropriate if we represent Q by the soil surrounding and supporting the basement.

The soil can easily exist without the building, but not the other way around. Being outside the physical universe, Q seems similar to the description of the Deity.6 In any case, whatever Q is, it cannot be described or accessed as if it were a physical object.

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In my essay Relativity in Easy Steps, I show how the general relativity field equations can be rearranged to describe a physical “substance” having energy, entropy and temperature, implying that space-time can be thought of as a “field” having physical and thermodynamic properties. Unfortunately, space-time cannot serve as the necessary substrate for information because space and time are both derived from information itself.

Except that the conventional western Deity is said to reside “above” the universe instead of “below” it.

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