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.
EU = π k T c3 tU
2
/ 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 old-
fashioned 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 “post-
reductionist 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 → EU = π k T c3 tU
2
/ 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 tU
3. 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 3.08 × 10-27
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.
4

SUMMARY
• There are three kinds of interactions: linear, deterministic, reversible; non-linear,
deterministic, chaotic, irreversible; stochastic, probabilistic, irreversible.
• Entropy is equivalent to information.
• Information requires uncertainty; thus, only stochastic interactions are capable of producing
information.
• Linear and chaotic deterministic interactions preserve and transform information in causal
space according to the “laws of nature.”
• Causal space has one time dimension, requiring three spatial dimensions because they must
match the number of rotational degrees of freedom.
• A free-falling observer is incapable of measuring any spatial curvature of three-dimensional
space because of rotational symmetry.
• 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.
• Order emerges from chaotic interactions as fractal-like patterns that repeat on different
spatial and temporal scales.
• The universe is a fractal with the properties of scale-invariance and self-similarity.
• 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. However, the radius of the universal pseudosphere is exactly twice this value.
• 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.
• There exists a universal time parameter, tU, which marks the expansion of the universe.
• The universe expands maximally at a rate dR / dtU that is bounded by the speed of light, c.
• 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.
• 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.
• The quantity of mass-energy in the universe increases in proportion to tU
2.
• The quantity of entropy-information in the universe increases in proportion to tU
3.
• 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 = 1 / (8π G tU
2
) k T / 2 ħ G tU, with a present value
of 980 3.08 × 10-27
kg/m3
.
5

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.
6

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 tU
2, while entropy (which drives expansion) is proportional to tU
3. 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.
7

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.
8

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.
4 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.
10

Addendum – Revised Calculation of the Vacuum Energy Density
The TOE is still a work in progress and I want to preserve everything for the record, including my
mistakes.7
My preliminary estimate of the vacuum mass-energy density, ρ, was based on the
assumption that the cosmological temperature, T, is approximately equal to the CMB temperature of
2.73 K. In my essay The Hidden Secrets of General Relativity Revealed, the cosmological
temperature was calculated as the temperature of the expanding Bekenstein-Hawking surface,
which is strictly a function of the age of the universe:
T = ħ / (4π tU k)
This value turned out to be much, much smaller than 2.73 K. Based on this calculation, the
cosmological temperature is 1.37 × 10 -30
K, which reduces my original estimate of ρ (980 kg/m3
) by
30 orders of magnitude! Combining ρ = k T / 2 ħ G tU with the above expression for T reduces ρ to
the following simple formula.
ρ = 1 / (8π G tU
2
)
Using the current measured value of G and assuming tU ≈ 14 billion years = 4.4 × 1017
seconds, we
get the following result.
ρ = 3.08 × 10-27
kg/m3
Earlier I mentioned the so-called “vacuum catastrophe” producing wildly different estimates of
vacuum energy density depending on which methodology is used. The Hubble-constant
methodology places ρ between 6.4 × 10-27
kg/m3
to 7.2 × 10 -27
kg/m3
, and happily my new value is
just below this range. It should be noted, however, that there is a significant amount of hand
waving associated with all currently-accepted cosmological models8
, especially those models
featuring a so-called “accelerating expansion of the universe.” In each case, astronomical distance
measurements are off because they’re based on the assumption that universal expansion has been
slowing down over time9
instead of maintaining a constant rate, c. In contrast, ρ derived from my
TOE is based entirely on first principles and uses only a single astronomical measurement, tU .
In conclusion, although I made a serious error in assuming T is the same as the CMB temperature,
the huge discrepancy between 1.37 × 10 -30
K and 2.73 K might be explained if the latter value (the
observed temperature of all radiating matter in the universe after all red shifts are taken into
account) is not strongly coupled with the cosmological temperature. In other words, the two
temperatures decrease over time at different rates and are “disconnected” from each other because
the universe is in a perpetual state of disequilibrium due to expansion. It is possible, however, that
the two temperatures could asymptotically converge over time if the universe would attain a state of
equilibrium.
7 The mistakes I made in this essay are shown as strike-through characters in the text.
8 A universal model having a contemporaneous volume with a fixed amount of mass-energy fundamentally wrong.
The “interior volume” of the universe is a mirage: Reality is embedded in an asymmetric temporal surface with
curvature diminishing over time and an implied radius of curvature, R = tU c; however, R should never be
interpreted as the radius of a contemporaneous spherical volume. Furthermore, the amount of mass-energy
distributed throughout this fictitious volume is not constant, as assumed in most of the prevailing cosmological
models. Instead, the total mass-energy is distributed across Bekenstein-Hawking surfaces of uniform temporal
curvatures while increasing in proportion to tU
2
.
9 To compound the problem, there’s a consensus among cosmologists that the universe just recently has decided to
“accelerate” its expansion, needing “dark energy” to fuel this acceleration. Then there’s the problem of spiral
galaxies appearing to rotate much faster than they should according to Newton’s law of gravity, needing “dark
matter” to boost their rotational speeds. No wonder the field of cosmology is such a hopeless mess. (By the way,
Erik Verlinde’s thermodynamic theory of gravity solves the rotational problem naturally without including dark
matter. Kudos to Verlinde for having the courage to promote a very unpopular idea.)
12

Appendix E – Cosmic Goldilocks
Soon after Einstein completed his masterpiece, the General Theory of Relativity, he noticed the GR
field equations revealed a disturbing property of the universe; namely, that gravitating matter
distributed throughout space would cause it to collapse. Einstein fixed that problem by inserting a
so-called cosmological term, Λ gμν, into the field equations, which was used to exactly cancel out
the mass causing gravitational collapse. Physically, Λ is a fixed quantity of energy per unit volume
of empty space. In contrast, the density of gravitating matter decreases with volume because the
total amount of matter in the bulk universe is assumed to be constant. This produces a highly
unstable condition: If the volume of the universe should grow by just a smidgen, this would result
in runaway expansion, and if the volume of the universe should shrink by just a smidgen, it would
ultimately lead to the very collapse that Einstein feared. In order to keep things in balance, Λ would
have to be ridiculously fine-tuned, just like the porridge in the story of Goldilocks: not too hot and
not too cold, but just right.
Eventually, Einstein gave up on his cosmological constant after it was discovered that the universe
is indeed expanding. So once Λ gμν was removed from the GR field equations, gravitating matter
would simply slow down the expansion. This raised another question: Would gravitating matter
lose its grip and allow the universe to expand forever, or would it be powerful enough to reverse the
expansion and lead to a Big Crunch? Well, it turned out that the universe is perfectly flat, and it’s
poised at very the edge of eternal expansion (an open universe with negative curvature) and
ultimate collapse (a closed universe with positive curvature). This led to another serious Goldilocks
issue, called the “flatness problem.” Alan Guth came to the rescue with his inflation theory, which
seemed to solve the problem, at least for the time being.10
Then a few more monkey wrenches were thrown in. Spiral galaxies appear to rotate much faster
than they ought to according to Newton’s law of gravity and the amount of visible matter these
galaxies contain. To fix that problem, cosmologists concluded that there must be enormous
spherical clouds of invisible “dark matter” embedded in those galaxies. The problem is that there is
way more “dark matter” needed to fix the anomalous rotations than there is ordinary matter.11
This
would surely result in a very closed universe and a very rapid collapse, so an ad hoc solution
popped up again: Einstein’s old cosmological constant, Λ, given a new name, “dark energy.” But
in order to keep the universe nearly flat with all that “dark matter,” there had to be a lot of it. Of
course, now we’re right back to the Goldilocks problem of how Nature achieved such a delicate
balance between so much “dark matter” and “dark energy.”12
Then in 1998 is was discovered that
just about now, exactly 13.8 billion years after the big bang, “dark energy” took over, and the
universal expansion is speeding up!13
In fact, it’s speeding up so much that the universe will be torn
apart in a hypothetical “Big Rip” at some point – maybe in our not too distant future.
10 Guth’s inflation model solves the riddle of how the universe got so perfectly flat by postulating an inflation event
that occurred just before the Big Bang. Here, the universe inexplicably underwent an exponentially-increasing
expansion, and then it stopped just as inexplicably as it started. This dramatic expansion conveniently “ironed out”
all the wrinkles in space-time and flattened it out perfectly.
11 Estimates vary, but a rule of thumb is the universe has five times as much “dark matter” as regular matter.
12 So here’s the latest rundown: 68% of the universe is “dark energy,” 27% is “dark matter,” and only 5% is ordinary
matter. Of course none of this is true, but it illustrates how hopelessly messed up the cosmological model is.
13 One might ask why the expansion decided to accelerate just as the human species evolved, crawled down from the
trees, walked out of the African savanna, invented agriculture, science, mathematics and telescopes, and finally
formulated a general theory of relativity that explains all of this. Wouldn’t it have been much more plausible for the
acceleration to start either much earlier or much later than this special moment in time? Is it possible that
cosmological distances to remote objects using astronomical observations are way off due to a faulty model, and the
Hubble expansion is actually perfectly linear?
13

Then the so-called Vacuum Catastrophe made matters even worse. According to quantum
electrodynamics (QED), empty space is filled with energy in the form of virtual particles, and this
form of “dark energy” produces the same effect as Einstein’s cosmological constant. The problem
is when all the virtual particles are added up, they amount to one ginormous amount of energy; an
amount 120 orders of magnitude more than is needed to balance out all the gravitating mass. The
proponents of QED are unwilling to admit their theory is wrong, so they believe something must be
canceling out all this energy, but they just don’t know what it might be.
Here’s another way of looking at the balancing act between gravity and Λ. According to general
relativity, there is a cosmological pressure, Pc, associated with space-time that is equal to minus the
energy density of the vacuum, ρe. Contrary to intuition, a negative cosmological pressure pushes
space apart whereas a positive pressure pulls it together. (Because gravitational energy is negative,
it generates positive pressure by definition.) The universal expansion rate will slow down when net
Pc is positive and speed up when net Pc is negative. According to current models of a bulk universe
based on general relativity, vacuum energy density is constant, so if the initial expansion rate was
great enough, at some point the universe will cross over into negative pressure territory and lead to
the “Big Rip.” Well let’s see how my TOE balances positive and negative pressures.
Thanu Padmanabham published a paper in 2009 entitled “Thermodynamical Aspects of Gravity:
New Insights” showing there is a deep connection between general relativity and thermodynamics.
In particular, he shows the Schwarzschild solution of the field equations at an event horizon is
mathematically equivalent to the fundamental thermodynamic equation T dS – dE = P dV, where P
is interpreted as a cosmological pressure, Pc. If we are actually living on such an event horizon, this
equation would describe our world. Dividing both sides of the equation by dV,
Pc = T dS / dV – dE / dV = T dS / dV – ρe
There are two components of Pc: A positive term, Pm = T dS / dV, corresponds to gravitating mass
and a negative term, Pe = – ρe, correspons to vacuum energy density.
In the preceding Addendum to this essay, the vacuum energy density, ρ, was expressed as mass
density, in kg/m3
:
ρ = 1 / (8π G tU
2
)
Using the mass-energy equivalency, e = m c2
, we convert ρ into energy density, ρe. Since this term
in the equation is a negative quantity, it represents negative pressure that accelerates expansion.
Pe = – ρe = – c2
/ (8π G tU
2
)
The positive term in the thermodynamic equation, Pm = T dS / dV represents positive pressure that
decelerates expansion.
Pm = T dS / dV = T (dS / dA) (dA / dV) = T (k c3
/ 4 G ħ) (2 / R)
In the Addendum, T = ħ / (4π tU k), and of course R = c tU, as usual. Substituting those values of T
and R in the above expression for Pm, we get
Pm = c2
/ (8π G tU
2
)
⸫ Pc = T dS / dV – dE / dV = c2
/ (8π G tU
2
) – c2
/ (8π G tU
2
) = 0
Positive and negative pressures automatically cancel each other when space is considered to be the
surface of an expanding event horizon and basing it on a thermodynamic model instead of a bulk
volume. This eliminates Goldilocks problems requiring contrived solutions. As Einstein famously
said, “We cannot solve our problems with the same thinking we used when we created them.” It’s
time to abandon the kind of thinking that led to these problems in the first place.
14

Appendix F – Natural Units of Measure
Most objects with we are familiar have a height, a width and a depth, otherwise known as volume,
and are have contemporaneous parts, meaning all parts coexist in the same moments of time. A
contemporaneous object like a bowling ball has a mass that can be weighed on a scale, and a
volume that can found by measuring the circumference with a tape measure. People (including
most cosmologists) tend to envision the entire volume of the universe as a contemporaneous object.
But as I’ve shown, the only contemporaneous features of the universe are two-dimensional
Bekenstein-Hawking event horizons with a Schwarzschild solutions equivalent to the fundamental
thermodynamic equation.
Space has three degrees of freedom with volume is defined as height × width × depth. Any
arbitrary direction chosen as “depth” automatically points toward a temporal Beginning. With one
degree of freedom assigned to “depth,” two other degrees of freedom are perpendicular to time and
to each other, and lie on a contemporaneous, expanding Bekenstein-Hawking surface with a radius
of curvature, R = c tU. Space has rotational symmetry, so all three dimensions are “depth” directions
pointing back toward the past. In other words, a spatial volume is not a contemporaneous object,
but is rather a container of residual information left over from the past. The larger the volume
becomes, the less contemporaneous it is.
Cosmological temperature, T, and Newton’s gravitational parameter, G, decrease over cosmological
time while the quantity of information, H, per unit volume is constant. This is shown as follows,
starting out with the fundamental thermodynamic equation at the horizon with P = 0.
T dS = dE
dS / dV = T -1
dE / dV = c2
/ (8π T G tU
2
) recalling ρe from Appendix E
Dividing the above expression by k converts entropy, S, into information, HN, expressed as nats.
dHN / dV = c2
/ (8π k T G tU
2
)
The above expression has dimensions of m -3
(the nat being a pure number). Furthermore, we can
see that G tU
2
k T is constant, so dHN / dV indeed has a constant value, which can be calculated by
substituting the present-day values of G, T, and tU into the above equation.
dHN / dV = 1.44 × 1043
nat / m3
The volume corresponding to one nat of information, VN, is found by inverting dHN / dV. The
natural length, l N, and natural time, tN, follow directly from this value.
VN = (dHN / dV) -1
= 6.94 × 10 -44
m3
l N = VN
1/3
= 4.11 × 10 -15
m
tN = l N / c = 1.37 × 10 -23
sec
Finally, the natural unit of mass, MN, is defined by the quantum of angular momentum, ħ, and using
the dimensions of angular momentum: L = Mass × Velocity × Length.
MN = ħ / (c l N ) = 8.52 × 10 –29
kg
Conventional science considers Planck units as fundamental, but those units change over time as
Newton’s parameter, G, decreases over time. The natural units of measure above were derived from
thermodynamic properties of Bekenstein-Hawking surfaces of uniform temporal curvature instead
of the GR equations of non-contemporaneous bulk volume. The natural units of measure are
fundamental because they do not change over time.
15

Appendix G – The Impossible TOE Geometry
The TOE presented in this essay is based on an expanding temporal surface having a decreasing
uniform curvature, κ = 1 / R, with a radius of curvature measured in spatial units R = c tU. Space is
perfectly symmetrical with three orthogonal degrees of freedom (aka dimensions) per Noether’s
theorems. This leads to a rather peculiar type of geometry.
The Minkowski metric defines four-dimensional space-time as follows.
c2
dτ2
= (dx0)2
+ (dx1)2
+ (dx2)2
+ (dx3)2
The variable τ is proper time as measured by a clock moving through space-time. The variable
x0 = i c t, is the radius of the time coordinate expressed in spatial units (where i2
≡ -1). The variables
x1, x2, and x3 are the customary three dimensions of space. The reciprocal of radius x0 squared is the
Gaussian curvature, K = 1 / (i c t)2
< 0, signifying time has negative curvature.14
The significance of
negative curvature is that it folds away from the center of curvature everywhere instead of folding
inward and around it; this kind of curvature is impossible to visualize in ordinary Cartesian space.
The figure below is a schematic diagram of the geometry I’m trying to describe. An arrow labeled
(x) points away from an observer, O, toward the Beginning. The two remaining degrees of
freedom, (y) and (z) lie in a flat space-like plane orthogonal to (x), which is tangent to the blue
temporal surface at the point O (“Here” and “Now”). Due to its negative curvature, the temporal
surface bends away from the center of curvature, separating the observer’s past, to the left of the
surface, from the future, to the right. As tU increases, the temporal surface becomes more flat (its
Gaussian curvature becoming less negative). It’s very important to remember, however, that the
temporal is not an ordinary sphere embedded “within” three-dimensional space. It sits entirely
outside space in an “imaginary dimension” owing to its imaginary radius, i c t.
Traveling within the red plane trace paths left of the temporal surface. This is strictly forbidden
because those paths go back in time, which can only be attained at speeds faster than light. Also,
the observer cannot see, hear, touch, taste, or smell anything lying on that plane. Objects in the
space-like plane will be accessible only in the observer’s future. Each observer experiences reality
differently as it evolves over time, so this scheme is radically relativistic, observer-dependent, and
14 A 2-dimensional surface of uniform negative curvature is a pseudosphere, having a surface area equal to 4π |R|2
, the
same as an ordinary sphere.
16

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
configured in any of 2
68,719,000,000
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) → Ontological 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.
5 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.
6 Except that the conventional western Deity is said to reside “above” the universe instead of “below” it.
11

Appendix H – Empty Space Finally Weighs In
Information is equivalent to mass-energy, and every cubic meter of space contains the same quantity
of information, 1.44 × 1043
nats. So one might reasonably ask how much a cubic meter of “empty”
space weighs. The answer depends on the cosmological temperature, T, because the ratio of mass-
energy to information is proportional to T according to the Szilárd equation.
The Addendum to this essay determined the mass-energy density of space taking T into account:
ρ = 1 / (8π G tU
2
) kg / m3
By inspection, ρ is proportional to 1/tU because G tU is constant. As tU → 0, ρ → ∞. The state of
infinite density is the “singularity” in the Big Bang model.17
Incremental mass, dM, is equal to ρ times incremental volume dV = 4π R2
dR = 4π c3
tU
2
dtU.
dM = 4π c3
tU
2
dtU / (8π G tU
2
) = c3
tU dtU / (2 G tU)
Since (2 G tU ) is a constant, we can substitute present-day values, GP and tP, into the denominator.
The total mass-energy of the universe, M, is then found by integrating dM over 0 ≤ tU ≤ tP .
M = c3
/ (2 GP tP) ∫ tU dtU = c3
tP
2
/ (4 GP tP) = c2
R / (4 GP)
Solving for the radius, R,
R = 4 GP M / c2
R is exactly twice the Schwarzschild radius, RS, corresponding to the mass M. Accordingly, M is
one half the mass corresponding to RS.18
There is another principle on which my TOE is based, which is a function of a constant quantity,
namely the information density per unit volume and per unit surface area.19
According the
Bekenstein-Hawking principle, the information contained within a volume cannot exceed the
information capacity of the surface surrounding it, and my TOE hinges on it. So let’s see if that
principle holds when applying the relationships derived in this essay.
Let ρHV = uniform information density per unit volume = c2
/ (8π kT G tU
2
)
Let ρHA = uniform information density per unit surface area = c3
/ (4 ħ G)
The Bekenstein-Hawking information limit can be expressed by the following inequality.
∫V
ρHV dV ≤ ∫A
ρHA dA .
Since ρHV and ρHA are constants, the inequality can be written as follows.
dV/dA ≤ ρHA / ρHV
dV/dA = ½ R = ½ c tU ≤ [c3
/ (4 ħ G)] [ 8π kT G tU
2
/ c2
]
From the Addendum we learned T = ħ / ( 4π tU k). Making this substitution, everything on the right-
17 However, unlike other cosmological big-bang models, my TOE does not postulate total mass-energy is constant.
Instead, total mass-energy increases because information, the mass-energy equivalent, increases in proportion to
total volume. This is allowed because time is asymmetric, making the law of mass-energy conservation invalid.
18 A sphere of constant density has a mass proportional to its volume, but a sphere saturated with information becomes
a Schwarzschild sphere having a mass proportional to its radius: MS = c2
R / 2G. A pseudosphere has half the
volume and would weigh half as much as an ordinary sphere if both have the same density and the same radius.
This might explain the 1:2 ratio of M : MS.
19 The information density per unit area is constant across a B-H surface in “information saturation.”
18

hand side of the inequality reduces to ½ c tU.
The inequality ½ c tU ≤ ½ c tU is true, and it also shows the volume is always in a state of
“information saturation” limited by the information capacity of the B-H area. Therefore, the
numerical relationships involving mass-energy, information, temperature, time, space, and
gravitation in the TOE fit together perfectly and they point back to the fundamental B-H theorem.
One might reasonably ask the following questions: “If information is equivalent to mass-energy
and empty space is already saturated with information, then how can planets, stars, galaxies, etc. be
added to the vacuum without exceeding the B-H limit and causing information overflow? Must we
invent some sort of ‘dark energy’ to cancel out the excess mass-energy?” Fortunately for the sake
of science, my answer to the second question is “No.”
Now I’ll answer the first question. According to Wheeler’s “it from bit” principle, mass-energy is
information in condensed form. All the raw material needed to all the fundamental particles
comprising the physical universe is already available from the vacuum itself. But you may object,
“The amount of mass in a lump of clay is far greater than the equivalent mass of the information
contained in the lump’s volume.” Your objection would certainly be true based on the current
cosmological temperature, on the order of 10 -30
K. But according to the Szilárd equation, all we
have to do to increase mass is to raise the temperature of the vacuum. This is similar to quantum
field theory, which says mass-energy is an excitation of an underlying quantum field. In this case,
the underlying quantum field is space and time itself with its thermodynamic properties, and it can
be excited by raising its temperature. The lump of clay could be seen as a “hot spot” in the vacuum.
The vacuum (cosmological) temperature is proportional to curvature: T∝ 1/tU ∝ 1/R = κ. In other
words, a local “hot spot” increases local curvature. You could even go as far to say that mass and
curvature are equivalent.20
It’s extremely important to make a distinction between information and data. Information measures
the number of ways bits could be arranged, while data represent a particular arrangement of bits.
Think of empty space as a digital thumb drive where all the bits are scrambled in a completely
random arrangement with no recognizable patterns. When data are entered into this thumb drive,
the bits are arranged into patterns that represent physical reality (“it from bit”). Arranging bits
doesn’t reduce the number of ways they could still be arranged, so no information is actually lost by
arranging them. However, the arrangement does remove some uncertainty, and information is
thereby converted into the form of recognizable physical objects (mostly particles) with much
higher temperatures and mass-energies than the random background vacuum information at
prevailing cosmological temperatures.
Because there’s a 1:1 correspondence between the number of bits on the temporal surface and the
number of bits in the so-called volume it surrounds, this brings about the radical idea of a 1:1
correspondence between events on a 2-dimensional holographic surface and events unfolding in a
3-dimensional space (the hologram). This is the holographic principle, which is gaining some
traction in the science community. It is based on something called AdS/CFT correspondence, where
AdS stands for Anti-de Sitter space and CFT stands for conformal field theory.21
It would be a serious mistake to interpret the holographic principle as being two equivalent versions
20 Albert Einstein and Nathan Rosen got the idea in 1935 that the elementary particles (there were only a couple of
known elementary particles at that time) are actually tiny knots in space-time geometry. Unfortunately, their idea
didn’t go anywhere. Today, theoretical physicists are shamelessly using the Einstein-Rosen paper to justify their
own wild sci fi fantasies involving “wormholes” and “time tunnels” reaching out into far-away regions of space.
I’ve read their paper and they mentioned no such thing, and in fact they explicitly warned against making that kind
erroneous conclusion from their equations.
21 AdS is an n-dimensional manifold with negative curvature. Its boundary is equivalent to Minkowski space-time. I
have no way of describing what conformal field theory is, except to say it’s way over my head.
19

of reality occurring simultaneously in two very remote places. According to my TOE, the space
surrounding the observer is an historical record of what has already happened on an earlier temporal
surface. In other words, the correspondence isn’t taking place in real time at all. Events appearing
close to the observer happened on recent temporal surfaces, while events appearing farther away
happened on earlier temporal surfaces. Objects observed “out there” are just a data trail left behind
the temporal surface. The area of that surface increases in proportion to tU
2
and the information
density on its surface, ρHA, increases in proportion to tU owing to a decreasing gravitational
parameter, G. Thus, the residue of information left behind in the vacuum then has constant density
per unit volume.22
Seeing the hologram unfold in 3-D is like watching a movie, except different
images appearing simultaneously on the screen could have formed on different temporal surfaces at
very different times depending on their relative distances from the observer. The rules of special
relativity link those non-contemporaneous images together causally.
CAUTION: Please do not misinterpret the schematic diagram below as a three-dimensional
representation of physical reality. It is impossible to imagine (or draw) actual physical reality in
three dimensions. The spaghetti shapes emerging from the blue curved surface are high-energy hot
spot data forming on a cold temporal surface as it unfolds into the future at the speed of light. The
temporal surface sheds those data along with other information from its surface into the volume it
leaves behind on the left. The residual hot-spot data are then interpreted as “particles” observed
moving and evolving in space-time. The colors correspond to temperatures, red being the coolest
and yellow being the hottest. Hotter temperatures correspond to higher mass-energies per unit
information. The “particles” trace “world lines” that start and end in space-time. For example, the
yellow line began at an earlier time than the red and orange lines in this diagram.
As previously cautioned, the above diagram is a schematic representation only. I consider so-called
“world lines” as a bad representation of reality in general, because time is an imaginary distance
(i c t), so it shouldn’t be shown as part of a “block universe” or similar representation as if it were
another spatial dimension with a real distance. Also, the hot spots should be thought of as spread
out over an entire temporal surface instead of emerging from specific locations as shown above.
Unlike other models based on the holographic principle, this TOE places the mind of the observer
within the expanding holographic surface (the temporal surface) instead of in the middle of the
hologram (space) with the holographic surface far away. The mind finds the hologram image so
convincing that it projects itself into the middle of this image. Taking our experiences from a 2-
dimensional holographic surface and projecting them onto a participatory 3-dimensional hologram
is a truly amazing feat. It’s a cosmic magic show the mind performs for itself.23
22 The information density per unit volume can be considered a never-changing fundamental constant like the speed of
light, c. As shown in Appendix F, fundamental units of length, time, and mass are based on this quantity.
23 The Sanskrit word māyā ( माया ) is describes the illusory or false aspect of reality. It literally means “magic show”
or “illusion.”
20

Appendix I – Life in the Hologram
The English physicist James Jeans was famously quoted as follows.
“Today there is a wide measure of agreement, which on the physical side of science approaches almost
to unanimity, that the stream of knowledge is heading towards a non-mechanical reality; the universe
begins to look more like a great thought than like a great machine. Mind no longer appears as an
accidental intruder into the realm of matter; we are beginning to suspect that we ought rather to hail it as
a creator and governor of the realm of matter.”
We have seen that the physical universe (aka space-time) we assume exists around us is just an
historical record of information and data in an expanding 2-dimensional Now. Would it make any
sense to be in an historical record instead of being in Now? How else could we be other than being
in Now? So the idea that we are really in Now but choose to mentally project ourselves into a
space-time hologram of the past may not be too far-fetched.
Chris Niebauer, a neuropsychologist and author, has made extensive studies about how the left and
right hemispheres of the human brain operate. He made the following observation.24
“… the right brain is key in spatial processing. Rather than focusing on one thing at a time, the right
brain senses the whole picture – both the things themselves and the spaces in between. One could say
that the right brain understands that a figure is determined by its background; something the left brain
tends to overlook.
The truth is that no figure could exist without the background and the shape of the background is
dependent upon the figure.”
In other words, the brain’s left hemisphere25
focuses mostly on material objects, while ignoring the
“empty” spaces between them. But what would reality look like if there were no spaces between
objects? And as we saw in Appendix H, space is filled to the brim with information. In fact, even
the tiny spaces between the atomic nucleus and the electron shells surrounding them are filled with
“virtual particles” that affect the properties of atoms. So empty space matters even if it is ignored.
The diagram below depicts how things are organized in an observer’s space-time hologram. Space
runs horizontally and time runs vertically. An observer, O, sits atop a light cone, whose surface is
defined by the light paths from distant objects to the observer, as shown by the dashed lines
arranged in a circle 360° around the vertical axis of the cone. All visible objects lie along this ultra-
thin surface.26
As far as the observer is concerned, nothing exists outside the cone. The only objects that exist are
shown as colored spheres within the cone or along its surface. The spheres are embedded in a blue
volume of “empty space,” which we know is filled with information. Objects visible along the
24 From Niebauer’s book No Self No Problem, Page 97.
25 Some consider the left hemisphere as the “seat of consciousness” or the “thinking” part of the brain.
26 Only two spatial dimensions can be shown. In actual space-time, the 3-dimensional cone is a 4-dimensional
hypercone. All visible objects lie along the ultra-thin 3-dimensional surface of a hypercone.
21

cone’s surface include stars, galaxies, and everything else the observer can see with the naked eye
or through telescopes. Objects inside the cone’s surface are not visible, but they do have causal
impacts on the observer. For instance, the observer’s great-great-great grandparents living inside
the light cone (all currently deceased) are not visible to the observer; however, the observer’s DNA
came from all 32 of those individuals and they are thus very much causally linked. The observer
cannot see dinosaurs living inside the light cone roaming the Earth, but the observer can study the
fossils they left behind and imagine what those creatures may have looked like.
The problem with the space-time version of reality is that light paths along the surface of the light
mix space and time together. This is a consequence of the brain’s inability to envision 4-
dimensional hyperbolic space-time where three space axes are real and one time axis is imaginary.
So in order to produce a working model the brain can process and the mind can comprehend, the
time dimension had to be combined with one of the space dimensions, the one pointing away from
the observer. This leads to an illusion of objects “out there” being contemporaneous, whereas they
are really separated by both distance and time by in-between spaces filled with information.
Objects in the space-time hologram are organized according to their relevance to the observer.
Contemporaneous objects close to the observer are generally more relevant than objects separated
from the observer by time and distance. Since the mind of the observer is attached to a physical
brain with limited processing power, the most relevant objects appear large and sharp to the
observer having much higher resolutions than the least relevant objects, which appear small and
fuzzy with poor resolution. Objects inside your home are much more relevant to your survival than
objects in the Andromeda galaxy, so the former are given much higher priorities in your space-time
hologram.
The total information within the non-contemporaneous volume of space-time equals the information
distributed across the expanding temporal surface, HS = π c5
tU
2
/ ħ G. The hologram created by the
observer significantly limits this information in a number of ways.
1. The location of the observer in the hologram is the apex of a “light cone” (actually the center of a
4-dimensional hypercone)27
and it excludes all information outside the hyperscone’s surface.
The hologram of one observer excludes at least a part of every other observer’s hologram.
2. The “vastness of space” that seems so impressive to the observer is only the 3-dimensional outer
surface of the hypercone. This surface is razor-thin in comparison to the interior of the
hypercone, where everything else is causally-linked to the observer yet completely invisible.
3. Objects in the hologram are organized according to the relevance to the observer. There are far
fewer data bits available for observing distant objects than close-up objects.
4. Spaces between objects in the hologram are filled with much more information than the objects
themselves, yet this space appears “empty” and is generally ignored by the observer. As
Niebauer notes, figures are determined as much by their backgrounds as the figures themselves.
The observer can zoom in on distant objects by relocating nearer to them. This involves travel,
which is restricted by the laws of special relativity, and of course travel alters the hologram.
The reader might object to the statement that observers “create” their own holograms. The counter
argument is that every hologram is uniquely observer-centric and it can be altered by reorienting the
observer. This would not be the case if there were only a single, universal hologram. As James
Jeans said, “Mind no longer appears as an accidental intruder into the realm of matter; we are
beginning to suspect that we ought rather to hail it as a creator and governor of the realm of matter.”
27 The equation of a hypercone is x2
+ y2
+ z2
– w2
= 0. It is the same as the Minkowski metric for the path light
follows, where τ = 0 and w = c t.
22

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