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Removing Myths and Fantasies from Science
An Amateur Scientist’s Recommendations
by John Winders
The image above provided under a CC0 public domain license courtesy of kai Stachowiak
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.
Science is a process of discovery where ideas are proposed and put to the test. The worst three words
in the scientific lexicon are: Let. Us. Assume. A theory must never be built around assumptions unless
those assumptions have been thoroughly tested and vetted. Otherwise, if any one of those assumptions
turns out to be a myth, the entire theory becomes a fantasy. Unfortunately, the current scientific
literature is littered with statements that are widely accepted as facts and get repeated over and over,
but some of them are actually myths that produce fantasies.
I must confess that throughout my engineering career, I accepted mathematical and scientific facts
handed down to me without really examining or questioning them. I considered proving a math
theorem in a homework assignment to be a complete waste of time. After all, if René Descartes had
already proved the theorem, then why should I prove it all over again? Engineers are mainly interested
in how things work instead of why. As an engineer, science and mathematics were simply tools to get
answers by “plug ‘n chug.” Newton’s laws were facts because they worked.
When I retired from engineering and started my hobby as an amateur scientist, I began questioning
everything I thought I already knew about science. To my surprise and horror, I discovered current
scientific literature is littered with big lies, little fibs and half truths. When a statement made by a
famous and well-respected author is published, whether in a peer-reviewed journal or a popular science
book, there is a tendency for others in the field to blindly accept the statement and repeat it ad infinitum
without examining or challenging it. Statements become facts when they are disseminated far and
wide, but they might actually be myths, leading to theoretical dead ends and wasting time, money, and
careers.1
False narratives gum up the gears of scientific progress, causing them to grind to a halt. A
growing number of scientists suspect science is currently in crisis, which I believe might be true
because so many myths have been accepted as facts.
There are a few scientific myths that are particularly egregious because they are repeated so often by so
many authors that they have become scientific mantras.
Two of the Biggest Myths
1. Quantum mechanics is incompatible with the general theory of relativity. Conclusion:
those theories are incomplete and must be scrapped and replaced with a single Theory of
Everything (TOE) that will make them compatible.
2. There are four forces in nature: Strong nuclear, weak nuclear, electromagnetic and
gravitational. The Grand Unification Theory (GUT) has successfully merged the first
three forces into a single force at high energies, but the force of gravity stubbornly refuses
to be unified with the other three. Conclusion: A TOE must therefore unify all four forces.
These two myths produced the fantasy that the anticipated TOE will explain everything about nature in
one fell swoop, from the motions of stars and planets, to the evolution of the universe, to the properties
of atoms. This promise has become the Holy Grail of science and the singular goal of theoretical
physicists worldwide. There have been several candidate theories put forth to achieve this goal, e.g.
string theory, M-theory, and loop quantum gravity. Some attempt to unravel the TOE by going through
the back door by first unifying and quantizing the “four forces of nature,” which will then lead to the
TOE afterward. So far, progress has been disappointing, as noted in Wikipedia on this subject:
“At present, there is no candidate theory of everything that includes the standard model of particle physics
and general relativity and that, at the same time, is able to calculate the fine structure constant or the mass
of the electron. Most particle physicists expect that the outcome of the ongoing experiments – the search
1 Albert Einstein spent much of his career between 1915 and his death in 1955 chasing winged unicorns, led by a false
hope that gravitation could and should somehow be modified to resemble particle physics.
for new particles at the large particle accelerators and for dark matter2
– are needed in order to provide
further input for a TOE.”
I’ll be very disappointed if most particle physicists really believe the discovery of the TOE requires a
search for new particles. Without a working theory to indicate what the signals of “new” particles will
look like, how could researchers find them through the noise emanating from particle accelerators?
Scientific theories are supposed be based on first principles and then predict things, like new particles,
not invented ad hoc to fit data points. TOE candidates like as string theory have already predicted
“new” particles that were never found, so they should be scrapped. Large accelerators consume huge
expenditures of human and economic capital without producing much useful knowledge.3
Let’s examine the first of the biggest myths in more detail.4
Both the general theory of relativity and
quantum mechanics have been hailed as two of the greatest achievements of the human mind.
Quantum Electrodynamics (QED), falling under the umbrella of quantum mechanics, has made
predictions shown to be accurate to within ten parts in one billion, while every single prediction made
by general relativity has been experimentally verified. There is only one reality, not two, and two
theories that are so successful in describing different facets of the same reality cannot possibly be
“incompatible” with each other. It’s absurd to criticize the general theory of relativity because it can’t
be used to compute the fine-structure constant or dismiss the Schrödinger equation because it can’t be
applied to orbital mechanics.5
Yet even though the two theories apply to completely different levels of
reality, they must actually turn out to be codependent if a TOE exists.
I now turn to the second of the biggest myths. There are only three forces of nature: Strong nuclear,
weak nuclear, and electromagnetic. Gravity is not a force, which is the very reason it stubbornly
refuses to be unified with the “other” three forces.6
The entire premise that inspired Albert Einstein to
work on the general theory of relativity for ten long years was his realization that when observers fall
freely under the influence of gravity, they feel no force whatsoever. If gravity were a force, Einstein
would have to explain why this force just happens to exactly cancel the force of acceleration, F = m a.
He could not explain it, so he deduced the “cancellation” is due to the fact that the “force” of gravity
actually is the force of acceleration (the equivalence principle).
The Correct Interpretation of Gravity
Gravity defines the geodesic paths of objects in perpetual motion through space-time. The only time
forces enter the picture is when objects are diverted from their geodesic paths, and electromagnetism is
the only long-range force that can divert them. Sitting on my chair, I feel a force pushing upward on
my tush. But that force is not the force of gravity, it’s the electromagnetic force applied by the surface
of the chair keeping me from following my geodesic path toward the center of the Earth.
So what exactly is a geodesic path? It’s simply the longest path between two points in space-time,
which also happens to be the maximum amount of proper time accumulated by a clock traveling
between those two points, so any path different than a geodesic path represents a “short cut” through
space-time. In the absence of gravity, space-time becomes “flat” meaning all geodesic paths are
straight lines in space. Under the influence of gravity, space becomes “warped,” causing geodesic
2 Dark matter is another myth. Follow the link to Erik Verlinder’s theory of entropic gravity in Footnote 10.
3 The Large Hadron Collider had an original price tag of €7.5 billion. It went into service in 2008, and it currently
employs employs roughly 10,000 scientists, engineers, and technicians with an annual budget of around € 890 million.
The only important discoveries that have resulted so far from all this expensive effort is evidence that the elusive Higgs
boson probably exists and mini black holes don’t.
4 I must confess that I accepted this myth for a long time until I started examining it for myself.
5 Claiming they are incompatible is equivalent to claiming that your hands and feet are incompatible because you don’t
walk on your hands and don’t grasp things with your feet.
6 Particle physicists keep searching in vain for the elusive graviton, the “messenger particle” of the “gravitational force.”
The graviton will never be found because it doesn’t exist.
for new particles at the large particle accelerators and for dark matter2
– are needed in order to provide
further input for a TOE.”
I’ll be very disappointed if most particle physicists really believe the discovery of the TOE requires a
search for new particles. Without a working theory to indicate what the signals of “new” particles will
look like, how could researchers find them through the noise emanating from particle accelerators?
Scientific theories are supposed be based on first principles and then predict things, like new particles,
not invented ad hoc to fit data points. TOE candidates like as string theory have already predicted
“new” particles that were never found, so they should be scrapped. Large accelerators consume huge
expenditures of human and economic capital without producing much useful knowledge.3
Let’s examine the first of the biggest myths in more detail.4
Both the general theory of relativity and
quantum mechanics have been hailed as two of the greatest achievements of the human mind.
Quantum Electrodynamics (QED), falling under the umbrella of quantum mechanics, has made
predictions shown to be accurate to within ten parts in one billion, while every single prediction made
by general relativity has been experimentally verified. There is only one reality, not two, and two
theories that are so successful in describing different facets of the same reality cannot possibly be
“incompatible” with each other. It’s absurd to criticize the general theory of relativity because it can’t
be used to compute the fine-structure constant or dismiss the Schrödinger equation because it can’t be
applied to orbital mechanics.5
Yet even though the two theories apply to completely different levels of
reality, they must actually turn out to be codependent if a TOE exists.
I now turn to the second of the biggest myths. There are only three forces of nature: Strong nuclear,
weak nuclear, and electromagnetic. Gravity is not a force, which is the very reason it stubbornly
refuses to be unified with the “other” three forces.6
The entire premise that inspired Albert Einstein to
work on the general theory of relativity for ten long years was his realization that when observers fall
freely under the influence of gravity, they feel no force whatsoever. If gravity were a force, Einstein
would have to explain why this force just happens to exactly cancel the force of acceleration, F = m a.
He could not explain it, so he deduced the “cancellation” is due to the fact that the “force” of gravity
actually is the force of acceleration (the equivalence principle).
The Correct Interpretation of Gravity
Gravity defines the geodesic paths of objects in perpetual motion through space-time. The only time
forces enter the picture is when objects are diverted from their geodesic paths, and electromagnetism is
the only long-range force that can divert them. Sitting on my chair, I feel a force pushing upward on
my tush. But that force is not the force of gravity, it’s the electromagnetic force applied by the surface
of the chair keeping me from following my geodesic path toward the center of the Earth.
So what exactly is a geodesic path? It’s simply the longest path between two points in space-time,
which also happens to be the maximum amount of proper time accumulated by a clock traveling
between those two points, so any path different than a geodesic path represents a “short cut” through
space-time. In the absence of gravity, space-time becomes “flat” meaning all geodesic paths are
straight lines in space. Under the influence of gravity, space becomes “warped,” causing geodesic
2 Dark matter is another myth. Follow the link to Erik Verlinder’s theory of entropic gravity in Footnote 10.
3 The Large Hadron Collider had an original price tag of €7.5 billion. It went into service in 2008, and it currently
employs employs roughly 10,000 scientists, engineers, and technicians with an annual budget of around € 890 million.
The only important discoveries that have resulted so far from all this expensive effort is evidence that the elusive Higgs
boson probably exists and mini black holes don’t.
4 I must confess that I accepted this myth for a long time until I started examining it for myself.
5 Claiming they are incompatible is equivalent to claiming that your hands and feet are incompatible because you don’t
walk on your hands and don’t grasp things with your feet.
6 Particle physicists keep searching in vain for the elusive graviton, the “messenger particle” of the “gravitational force.”
The graviton will never be found because it doesn’t exist.
duplicated precisely. Amazingly, there are physicists living in the 21st
century who actually believe in a
version of the Laplacian fantasy they call the “the block universe,” where time travel is allowed.
Compare Einstein’s relativistic world with Niels Bohr’s quantum-mechanical world according to the
Copenhagen interpretation, where no definite quantum states even exist until they are actually
observed. Einstein rejected the Copenhagen interpretation insisting, “God does not play dice with the
universe.”11
In 1935, Einstein and two of his associates, Boris Podolsky and Nathan Rosen, published a
famous paper claiming quantum mechanics is “incomplete” because it lacks a mechanism that allows
quantum states to be deduced a priori. Claiming that quantum mechanics is incomplete because it
lacks causality is a classic case of begging the question; there was no convincing reason why causality
is needed in order to make QM “complete.” Einstein et al just assumed that it is.
The debate continued without resolution until 1964, when John Stuart Bell published a paper proving
that statistical correlations of quantum measurements will violate a particular inequality if and only if
the Copenhagen interpretation is correct. It became possible in the 1980s to test the inequality
experimentally, and the results of those experiments conclusively settled the issue: Although large
ensembles of quantum measurements do conform to predictable and repeatable statistics, it is
fundamentally impossible to deduce a priori the outcome of any quantum measurement.
Shannon’s entropy is solely a function of probabilities, S(p1, p2, … , pN). There is a common
misconception that probabilities determine outcomes, when in fact outcomes determine probabilities.
If the state of a system could be determined a priori without taking measurements, then one of the
probabilities would be equal to one and all the others would equal zero. In those cases, S = 0. Thus,
entropy would be meaningless in a deterministic, causal world. Rolling dice and spinning roulette
wheels may appear to be random processes, but they are not; they are chaotic processes instead.
Chaotic processes generate “pseudo-random” results where extremely small variations in initial
conditions produce very significant changes in outcomes, yet these outcomes are still very much
deterministic and repeatable. In contrast, it has been proven experimentally by violations of Bell’s
inequality that quantum processes are neither predictable nor repeatable and therefore they must be
truly random (stochastic). Stochastic Process = Quantum Process. Therefore, entropy can only exist
where there is true stochasticity; i.e., it exists only at the quantum level of reality.
If gravitation is an entropic process tending to maximize uncertainty, then the general theory of
relativity, which is really the theory of gravity, must also rest on a foundation of entropy. This can only
occur if there is a hidden, yet real, connection between general relativity and quantum mechanics.
Thermodynamics reveals another connection between general relativity quantum mechanics. The
general relativity field equations have an exact solution for a spherical mass, known as the
Schwarzschild equation. Thanu Padmanabham published a paper in 2009 paper entitled
“Thermodynamical Aspects of Gravity: New Insights.”12
In that paper he showed the Schwarzschild
solution at the boundary is mathematically equivalent to the fundamental equation of thermodynamics.
My essay “The Universe on a Tee Shirt” explains the significance of this “boundary” in much greater
detail than is needed here.13
Let it suffice to say that space-timed has thermodynamic properties
corresponding to energy, pressure, temperature and entropy, just like a material substance, and that
space, time, matter and energy are all just different manifestations of entropy.14
In other words, the entire physical universe rests on a foundation of uncertainty, which only truly exists
at the quantum level of reality. Space and time emerge in the causal world, but they are also the stage
11 There is some irony in that statement because a roll of the dice isn’t actually random but deterministic.
12 “Thermodynamical Aspects of Gravity: New Insights” is available for download from ArXiv here.
13 “The Universe on a Tee Shirt” is available for download here.
14 Entropy can be expressed in bits or nats. One one cubic meter of empty space is comprised of 1.44 × 1043
nats and one
joule of energy at a temperature of 300K is equivalent to 2.42 × 1020
nats.
upon which quantum events occur. Therefore, it should now be obvious that both facets of reality are
interlocked and codependent. There is no “incompatibility” between them.
Correcting the Two Biggest Myths
Scientific progress being held back by big lies, little lies, and half truths. Every assumption must be
examined and validated before it can be accepted. Just because a famous or well-liked person makes a
statement, there is no reason to blindly accept it and repeat it. There already is a Theory of Everything
hidden in plain sight. Very few have found it simply because they are looking in the wrong places.
The TOE will reveal itself after making the following changes to some basic assumptions.
1) There are four three fundamental forces in nature: Strong nuclear, weak nuclear, and
electromagnetism, and gravity. Gravity is not a force; it alters the geodesic paths of objects
moving through space-time in order to maximize entropy.
2) General relativity and quantum mechanics are incompatible with each other. General relativity
and quantum mechanics are linked through entropy, which is one of the thermodynamic
properties of space-time.
The Mother of All Fantasies: Black Holes
In the past several decades, it seems that black holes are a central part of most of research papers in
theoretical physics. Black holes are sand boxes where outlandish theories are erected like great sand
castles, but the fact is that proving any conclusions using black holes is tantamount to dividing by zero
to prove that 1=2. It’s unfortunate that entire careers and reputations are resting the assumption that
black holes exist without anyone seriously examining how they could form in the first place.
My essay “Why There Are No True Black Holes,”15
points out a number of contradictions showing why
black holes can’t exist. The fundamental fallacy stems from a misapplication of the Schwarzschild
solution. Every spherical body has something called a Schwarzshild radius, RS, proportional to the
body’s positive mass-energy. In order to calculate RS, you must include the entire mass-energy of the
object, both inside and outside RS in the calculation. The size of RS for the Earth is quite small, about
one inch, but all the Earth’s mass-energy from its center to its surface must be included. Strictly
speaking, not including the space beyond the surface is arbitrary, and it’s not allowed in a formal
solution to the general relativity field equations. You could get away with ignoring the surrounding
space if it were truly empty, but it’s really not. Yet assuming space is empty will still yield very good
approximate solutions to practical problems as long as gravitation is weak.
In truth, the space surrounding the Earth is filled with negative gravitational energy, and ordinarily this
energy is negligible compared to the positive mass-energy of the material in the Earth’s core, mantle,
and crust. However, if you try to form a black hole by compressing the mass-energy until it almost fits
inside RS, an enormous amount of negative gravitational energy fills the surrounding space, which will
cancel out some of the mass-energy.16
The cancellation must now be accounted for because it causes
RS to shrink. It can be shown that no matter how much a material object is compressed, RS always
shrinks below the outside radius of the object, meaning no true event horizon can ever form. If an
object could be compressed down to the size of its Schwarzschild radius, the negative gravitational
energy surrounding it would cancel out all its mass-energy, reducing RS to zero.17
15 “Why There Are No True Black Holes” is available for download here.
16 It is easily shown that if a mass were lowered onto a hypothetical event horizon using a pulley system, the liberated
energy would equal 100% of the energy equivalent of the mass being lowered, thus adding zero mass to the black hole.
17 Theoretical physicist Abhas Mitra of the Bhabha Atomic Research Centre in Mumbai, India came up with a similar
conclusion. He proved that the value for the mass of a black hole is not a free parameter that can simply be plugged
into the Schwarzschild equation. A correct solution of the general relativity field equations shows an event horizon can
only form around a mass when it has a value equal to zero. A copy of his paper is available for download here.
Black holes have challenged theoretical physicists with a long list of paradoxes and contradictions,
which have not been successfully resolved and are swept under the rug instead. It’s clear that Nature
hates paradoxes and contradictions, so She will snuff out any black hole before an event horizon can
form, and She has unlimited amounts of negative gravitational energy at Her disposal to do this.
Astronomers and astrophysicists have observed a number of objects called “black hole candidates”
because from a distance they seem to resemble what black holes might look like. So if those objects
are not really black holes, then what are they? Abhas Mitra refers to them as Eternally Collapsing
Objects (ECOs). An ECO is an extremely compact object surrounded by an enormous gravitational
field that bends light and produces time dilation that slows down all physical processes in its vicinity to
a virtual standstill, giving an ECO the appearance of a “black hole” when seen from a distance.
Because of the gravitational time dilation, the ECO continues to shrink at an ever-decreasing rate,
allowing it to approach but never reach the Schwarzschild radius, and never forming a true event
horizon. In other words, an ECO is a pseudo black hole without an event horizon. Interestingly,
Robert Oppenheimer and Hartland Snyder came to a similar conclusion in a paper published in 1939.
They considered only the gravitational time-dilation effect without the mass-cancellation effect of
negative gravitational energy surrounding the object, concluding a black hole might theoretically form
through gravitational collapse, but the process would take forever.
Given the fact that black holes are either impossible or would take forever to form, then how can
theoretical physicists claim they exist in a universe less than 14 billion years old? Well, it’s very easy.
They simply magically insert all of an object’s mass-energy inside its Schwarzschild radius without
explaining how it got there, ignoring the massive amount of negative gravitational energy surrounding
it. With a wave of a hand they say, “Let us assume a black hole has formed,” and go on to invent all
sorts of weird and wonderful fantasies borrowed from science fiction, such as worm holes and time
tunnels, while diverting their eyes from the multiple paradoxes and contradictions that inevitably arise
as a result. Starting out with the statement, “Let us assume X” without proving X is feasible or even
possible is a very bad habit to get into, but it happens all too often in the theoretical physics community
and it impedes scientific advancement.
The Way Forward
Jacob Bekenstein and Stephen Hawking published groundbreaking work involving quantum mechanics
and thermodynamics on black-hole event horizons. Was all their work for naught? Not at all. A sphere
of mass-energy cannot be compressed into a black hole because negative gravitational energy exterior
to the Schwarzschild radius cancels out mass-energy; however, a black hole would be possible if there
were no exterior. This is the case for the universe as a whole because by definition, the universe is
singular without an exterior. In other words, the universe could very well be a black hole having an
event horizon as defined by the Schwarzschild equation, and the Bekenstein-Hawking equation could
then be applied to it. Earlier, I mentioned Thanu Padmanabham’s paper, showing the solution of the
equation at the “boundary” possesses the thermodynamic properties of energy, pressure, temperature
and entropy.18
It is now clear that this “boundary” could only exist for an object with no exterior. This
makes the work of Bekenstein and Hawking even more relevant and important, because instead of
merely describing the thermodynamic properties of a collapsed star, it describes thermodynamic
properties at the boundary of the universe itself, which agrees with Padmanabham’s work.
According to the Schwarzschild equation, the event horizon is a static moment frozen in time, and close
inspection of the equation reveals the radius below the event horizon, r < RS, really points in a temporal
direction instead of a spatial direction. In other words, space and time exchange places inside the black
18 It should be noted that the energy tensor found in the general relativity field equations describe an elastic solid that
resists compression, shear, and torsion. Thus, space-time is analogous to a solid having elastic properties along with
thermodynamic properties.
hole. Physicists engage in quite a bit of hand waving when they try to describe exactly what the
interior of a black hole represents, but according to the common myth, locations inside the event
horizon aren’t locations in space, they are points in the future of everything that had previously passed
through the event horizon.19
At the center of the black hole, at r = 0, there is a singularity where all the
futures converge into a single moment in time – maybe where everything in the past, present and future
happens all at once? You’re not alone if you have trouble making sense of that fantasy.
The TOE Finally Emerges
A black hole starts making sense by shifting thinking away from a collapsed object surrounded by a
static event horizon somewhere out in space, and recognize the Bekenstein-Hawking equation applies
to an expanding event horizon of the entire universe. Rather than a single frozen moment in time, an
expanding event horizon is a series of sequential moments. The interior region surrounded by the event
horizon is a temporal region, as indicated by the Schwarzschild solution, which contains the residue of
previous moments the expanding boundary left behind. The center of the interior temporal region is
the point where the past of everything converges – the Beginning. The event horizon expands at the
speed of light, making it impossible to travel into the past.
By keeping the general theory of relativity and quantum mechanics exactly as they are instead of jerry
rigging them to match some preconceived notion of how they ought to be, a TOE emerges
automatically. There are no conflicts or incompatibilities between the dual descriptions of nature. Both
are complete unto themselves and yet are mutually codependent. Everything happening in the universe
– including us – occurs on the expanding event horizon20
governed by quantum mechanics and
thermodynamics. The general theory of relativity governs the dynamics of the space-time continuum, a
four-dimensional hyperbolic sphere of negative curvature defined by the Minkowski metric.
There is one temporal dimension and three spatial dimensions. The number three is not arbitrary.
Rotational symmetry requires the conservation of angular momentum, which can only be defined in
three dimensions. The single temporal dimension is asymmetrical (curved) because there is a definite
direction in time. The Minkowski metric defines hyperbolic sphere having a uniform negative
curvature. Unlike an ordinary sphere having positive curvature, every point on a hypersphere’s surface
curves away from the center of curvature instead of toward it. Since the hypersphere has no exterior
(because nothing exists beyond the universe) all observations must point inward from the boundary to
past events recorded in the hypersphere’s interior. Any straight line projected in any direction from any
point on the boundary must eventually arrive at the center of the hypersphere, at the Beginning.
Two Remaining Potential Myths
There are two very fundamental “laws” of nature that could turn out to be myths: 1) The total amount
of mass-energy in the universe is constant, and 2) Newton’s constant, G, does not change. If the TOE
as outlined above is true, then both of those two laws are false. Since the temporal dimension is
asymmetric, Noether’s theorem cannot allow the law of conservation of mass-energy to apply to the
universe as a whole. If TU is the age of the universe and the boundary expands at the speed of light,
then in order to satisfy the Bekenstein-Hawking equation, the total mass-energy of the universe must be
proportional to TU squared and G is not constant but a variable21
proportional to 1 / TU. I admit these
predictions are very bold and controversial and I would love to see them honestly examined and tested.
19 This presents another argument against the possibility of forming a black hole. Objects seen approaching the event
horizon by a distant observer never actually reach it. And yet objects must have passed through the event horizon in the
observer’s frame, otherwise the black hole wouldn’t exist. It’s another paradox that’s been swept under the rug.
20 Event horizon is very apt description, because it’s the boundary where all events must occur. The past and future do not
actually exist because the past lying below the event horizon is a frozen residue left behind by the expanding event
horizon, and the future lies in a non-existent region outside the universe above the event horizon.
21 Precise laboratory measurements of G have shown anomalous fluctuations over time that cannot easily be explained.
Chasing Rainbows
The photograph below22
shows a double rainbow over a beautiful landscape. The bottom rainbow
appears to start at a clump of tress on the left and end in a stand of trees on the right.
However, if we would attempt to reach the end of the rainbow by heading off in the direction of the
arrow, we would soon discover that we could never reach the end because it would keep receding away
from us. In other words, the “end of the rainbow” doesn’t exist, and in fact, the rainbow itself isn’t real
either. Every observer looking out over this landscape from a different location sees a slightly different
“rainbow” created within the observer’s own consciousness. The experience of seeing a rainbow is
very real, while the physical rainbow itself is not.
We live in a radically-relativistic universe with no absolutes, where “reality” depends entirely on the
observer’s frame of reference. Like the rainbow, the experience is real, but the physical universe we
think we are experiencing is not. According to my Theory of Everything, reality only exists in the Now
moment, a true event horizon on the surface of a hyperbolic sphere23
having a negative curvature and a
radius expanding at the speed of light. At the center of the hyperbolic sphere is a temporal Beginning,
which sets the “age” of the universe (at the present Now) at ~14 billion years.24
Any direction an observer can point to will always point toward the Beginning; however, the Beginning
recedes from all observers at the speed of light. Thus, no matter how fast or how far the observer
travels, it never recedes more slowly than the speed of light and it cannot be approached or overtaken.
In this respect, chasing the Beginning is like chasing a light beam. So the question is, “If the Beginning
can neither be observed nor approached, does it even exist?” Although I cannot prove it, I believe the
answer is “no.” The “Beginning” is an illusion like the “end” of a rainbow. It’s a virtual or apparent
point in time our consciousness creates based on the assumption25
of linear time. I suspect the true
nature of time is logarithmic instead of linear, which simply means the age of the universe was never
zero; instead, it diminishes to smaller and smaller orders of magnitude toward an infinite past.
22 Photograph courtesy of Binyamin Mellish, under CC0/Public Domain license: https://www.goodfreephotos.com
23 A hyperbolic sphere curves away from its center of curvature at every point on its surface instead of toward it. It is
impossible to imagine what such an object looks like in three dimensions, and yet this is what our universe actually is.
24 The “standard” cosmological model purports the universal age is ~14 billion years. But that number is based on an
assumption that the gravitational parameter, G, is a constant. If G is inversely proportional to time, very distant galaxies
would have greater intrinsic brightness, so their true distances would be greater than is supposed in the standard model.
The end result is the true distance from the Beginning to Now is likely greater than ~14 billion years.
25 Like most areas of science, the current cosmological model is filled with unproven assumptions that are mistaken as
“facts.” The truth of every assumption must be verified by observation or derived through reason.
Attempting to Imagine the Unimaginable
J.B.S. Haldane was a British polymath and philosopher who made major contributions in the fields of
biology, genetics and statistics. Contemplating the universe as a whole, he once remarked, “Now my
own suspicion is that the universe is not only queerer than we suppose, but queerer than we can
suppose.” What we humans can suppose about the physical universe is based on a faulty, inaccurate
model bound by what our physical senses reveal; in other words, we suppose a fantasy.
Whether you were a cave man living in the Pleistocene, or a 21st
century cosmologist, that model is the
same three-dimensional Euclidean geometry envisioned by Galileo and Newton. Animal species
employ a three-dimensional space filled with objects in motion as their working model because it is
optimally suited for enabling them to survive and reproduce in a small-scale terrestrial environment.
There is no need for humans or any other species to comprehend the totality of the universe because
doing that would have no direct benefit to their survival or well being. So when we look up into the
night sky into the vastness of the universe, we can only comprehend what consists of an outward
projection of our small-scale model of a three-dimensional Euclidean world instead of witnessing its
truly grand four-dimensional hyperbolic geometry. Humans possess awesome powers of reason and
abstract mathematics that give us a glimpse of reality, but it is only that – a glimpse. We simply cannot
truly comprehend reality because our internal models have been conditioned by our sense of sight,
which is based upon (and limited by) the propagation of light according to Maxwell’s equations.
Shortly after Einstein published his special theory of relativity in 1905, the brilliant mathematician
Hermann Minkowski26
combined time and three-dimensional Euclidean space into a four-dimensional
space-time manifold, known as the Minkowski metric. This metric provides “distances” in space-time
that are invariant for all observers, regardless of their relative positions or motions. Minkowski space-
time also describes a universe having a hyperbolic geometry, without any boundary that separates its
interior from an exterior.
An ordinary Euclidean sphere is is easy for us to imagine because our three-dimensional model world
is filled with them. Ordinary spheres have two-dimensional surfaces separating insides from outsides.
When physicists contemplate the meaning of the Schwarzschild equation, their minds automatically
jump to envisioning a static Euclidean sphere hanging in space with a surface they call an “event
horizon,” a one-way boundary separating the interior of the sphere (a black hole) from its exterior (the
rest of the universe). What the Schwarzschild equation really describes is a hyperbolic sphere without
an exterior; however, no human mind can form a proper mental image of such an object.27
When looking into the sky in any direction, every observer is always looking directly toward the center
of the universal hyperbolic sphere. Galaxies equidistant from an observer appear to lie on the surfaces
of ordinary spheres curving toward the observer and away from the center. Those galaxies do in fact lie
on surfaces curving away from the center because they lie on negatively-curved hyperbolic boundaries
of the past. But projecting our three-dimensional Euclidean space model onto the universe creates a
contradiction: As the distances to those galaxies increase, the spherical surfaces surrounding us upon
which they lie appear to increase in size also. In reality, those surfaces are hyperbolic spheres and they
must decrease in size as their distances from us increase, because the radii between them and the center
of the hypersphere decrease. This simple example shows how the universe really is queerer than we
can suppose, and why the Euclidean models we attempt to impose on it are mostly fantasies.
26 Minkowski was acquainted with young Einstein prior to the publication of special relativity, and referred to him as “a
lazy dog” who “never bothered with mathematics at all.” To his credit, Einstein embraced Minkowski’s space-time and
incorporated it into his general theory of relativity, and is doubtful that he could have achieved success had he not done
that.
27 According to Hilbert’s theorem, hyperbolic geometry does not have a model in three-dimensional Euclidean geometry;
however, images of hyperbolic objects can be projected onto Euclidean spaces as shown here.
Unraveling the Hard Problem
I believe every serious scientific inquiry must ultimately encounter the question of consciousness,
namely, “What is it?” Philosophers have pondered this problem for centuries, whereas until recently
physicalists generally have tried to ignore or dismiss it. Philosopher David Chalmers described the
problem in the following terms:
“The hard problem of consciousness (Chalmers 1995) is the problem of explaining the relationship between physical
phenomena, such as brain processes, and experience (i.e., phenomenal consciousness, or mental states/events with
phenomenal qualities or qualia). Why are physical processes ever accompanied by experience? And why does a given
physical process generate the specific experience it does—why an experience of red rather than green, for example?”28
Lately, an increasing number of physicists and neurologists are promoting their own theories about
what consciousness is (or isn’t). These specialists are divided into two camps: 1) Those who believe
consciousness is produced by the brain, and 2) those who don’t believe consciousness exists. Yes, I’ve
read articles by authors who assert consciousness is an illusion29
, and the brain somehow tricks itself
into believing this illusion is real; however, it isn’t clear how the brain, essentially a data processor,
could possibly be tricked, let alone trick itself, into “believing” anything. The corollary to this
argument, of course, is that an artificial data-processing machine having sufficient complexity could
also trick itself into believing it is conscious, leading to one of the most glaring scientific myths:
Extraordinarily Complex Data Processing → Consciousness
I am convinced the hard problem stems from the fact that qualia, like the state of consciousness itself,
cannot be compared to, or defined in terms of, any exterior objects. You simply cannot describe the
experience of “red” to someone who is color blind or explain to an unconscious machine or a computer
algorithm what it’s like to be conscious. Physicalists attempt to define “red” as a specific range of
wavelengths of light. While those wavelengths do stimulate an interior experience we label as “red,”
we also experience “red” with our eyes closed and while dreaming. “Red” is not physical.
When the brain is active, either awake or dreaming, there is a reality show in progress that is being
observed by something or someone. But the brain is not the observer; it is among exterior objects
being observed, serving as a conduit through which the “Great Objective Reality Show” streams into
our consciousness. It would be silly to conclude that stopping the show by shutting down the brain also
shuts down the observer, any more than turning off a television monitor shuts down the viewer.
Author Donald Hoffman compares our experiences to icons on a computer screen.30
Computer icons
are symbols representing files and applications the user can access. But those symbols are not the files
or applications themselves. Likewise, the true nature of objective reality is very different than the
images we use to comprehend and interact with the reality they represent. We saw earlier how we
perceive our world as a model conforming to Euclidean geometry, whereas the true geometry of the
universe is hyperbolic. Qualia, in many different forms, are the only things consciousness perceives.
In conclusion, consciousness cannot be defined because it is unobservable and therefore it cannot be
approached through symbolic languages or mental icons. Consciousness isn’t part of “objective
reality” or constrained by it; instead, it is fundamental and complete unto itself. Being unconstrained
by space or time, consciousness is boundless and therefore singular. Physicist James Jeans noted, “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 to be an accidental intruder into
the realm of matter … we ought rather hail it as the creator and governor of the realm of matter.”
28 Robert J. Howell and Torin Alter (2009), Scholarpedia, 4(6):4948.
29 Even some philosophers, such as Daniel Dennett, are completely on board with the position that human consciousness
and free will are the results of purely physical processes.
30 Reference: “The Case Against Reality: Why Evolution Hid the Truth from Our Eyes”
Truisms → Myths → Fantasies
Since the invention of quantum mechanics, a significant number of theoretical physicists have adopted
a reductionist position that all physical objects – in fact the entire universe – can be reduced to wave
functions. It’s true that physical objects are comprised of elementary particles, which in turn can be
represented as wave equations, at least under some conditions. However, this truism as led to persistent
myths and outright fantasies. One such myth is the so-called “measurement problem.”
According to current quantum theory, an elementary particle that is unobserved ceases to exist as a
particle and turns into a wave function, which represents the future quantum properties of the particle in
terms of probabilities. When those quantum properties are measured, the probabilities become
actualities, and the wave function “collapses” and is replaced by a particle. The “problem” is that
nobody knows the precise mechanism that causes the so-called “collapse.”
This situation reminds me of an amazing catch by Willie Mays in the first game of the 1954 World
Series between the New York Giants and the Cleveland Indians at the Polo Grounds in Manhattan.
It was the top of the 8th
inning with the game tied 2-2 with Cleveland outfielder Vic Wertz at bat. Wertz
crushed a pitch from Giants’ reliever Don Liddle, and center fielder Mays took off running full-speed
toward deep center field with his back to the ball. Without ever looking back at the ball, Mays reached
out and caught it over his left shoulder 420 feet from home plate, only a few steps from the wall in
center field. The instant before Mays made the catch is shown above, left.
According to some quantum interpretations, objects exist in physical form only while they are observed
by conscious observers. Now suppose everybody, including Mays, had looked away from ball as it left
Wertz’s bat. The ball would then have immediately turned into a wave function defining the
probabilities of measuring the ball at particular locations in spacetime. The wave function would
evolve deterministically, radiating outward from home plate with a bent conical shape as shown in the
figure above, right, terminating at the blue patch on the Earth’s surface in center field where the ball
had a high probability of being “measured” when (and if) it landed.
In a brief moment, Mays observed the initial state of the ball as it left the vicinity of home plate, using
both visual and audible clues, such as the crack of the bat when the ball was struck. In addition to the
initial trajectory of the ball through spacetime, he observed the location of the ball over home plate and
the angle of the bat as it was struck, determining its spin causing the ball to hook or slice through the
air. He also took the wind velocity into account, as well as the humidity and atmospheric pressure. All
of those data were factored into a wave function terminating at that high-probability blue area in center
field. When Mays arrived at that precise location in spacetime, he reached out and “measured” the ball
by catching it in his glove. The wave function collapsed and a ball appeared in its place, but
unfortunately, to this day nobody knows why or how the “measurement” made this happen; ergo,
instead of just being an amazing catch, it is yet another example of a fundamental “measurement
problem” that has plagued and undermined physics since quantum mechanics was invented.
Of course, the above narrative is ridiculous. No “wave function” evolved from home plate to center
field; it existed entirely inside Willie Mays’ mind. It “collapsed” as soon as the ball went into Mays’
glove because it ceased to have any relevance. But as silly as this narrative is, there are a large number
of theoretical physicists who continue to agonize over the “collapse of the quantum wave function” as
if a wave function were a physical object instead of simply a mathematical formula defining the
probabilities of future quantum states. Their inability to separate the model from the thing itself has led
to elaborate workarounds and fantasies to explain how and why the “collapse” occurs.
One such fantasy is Hugh Everett’s many worlds interpretation (MWI).31
It solves the measurement
problem by not allowing the wave function to collapse at all. Instead, reality exists as a quantum
superposition of all possible measurements that could be made. Each time a conscious being measures
a state, reality splits into as many renditions as there are other quantum states to be measured. The
minimum number of split realities would be two, as in the case of measuring the up/down spin of an
electron; however, a single measurement could easily cause one reality to split into billions of other
separate realities. Also, a measurement anywhere in the universe would cause splits everywhere else.
For example, Willie Mays catching a ball could result in countless other versions of reality where the
ball sails into the stands, bounces off the wall, drops to the ground, or hits Willie in the head. But it
doesn’t end there. As conscious beings, we must also split into as many versions of ourselves as
necessary to inhabit the complete set of possible realities. Nevertheless, it seems MWI has very
specific rules keeping us consciously isolated and unaware of our other doppelganger selves.32
The underlying fallacy behind the measurement problem myth can be traced back to Schrödinger’s Cat
thought experiment, where a device triggered by a radioactive decay has a 50/50 chance of killing a cat
in a sealed box within a fixed time interval. That being the case, the state of the cat is in an alive/dead
superposition until a very smart guy in a white lab coat peers into the box, causing the superposition to
“collapse.” This scenario is based on the truism that a when a classical object, such as a cat, interacts
with a quantum particle, their wave functions combine. If the particle is in superposition, then
supposedly the cat is also. Without knowing how or why, only a conscious observer is able to break
this impasse, causing the wave function to collapse to reveal the cat’s final physical, objective state. In
other words, objective reality is continually being created solely by conscious observers like us.
The fallacy behind this myth is that a macroscopic quantum measuring device doesn’t have just two
either/or states, but a veritable googolplex33
of states. Schrödinger’s cat herself, whose wave function
combines with the radioactive particle that could ultimately kill her, has myriad states corresponding to
an alive cat and others corresponding to a dead cat. She can remain in a superposition if both states are
nearly identical with only a very tiny energy gap, ΔE, between them. However, if there is a significant
energy gap, the two states will spontaneously decohere within a very short time interval, Δτ ~ /
ℏ ΔE,
where is Planck’s constant. For example, a superposition of two quantum states with
ℏ ΔE equal to one
joule would decohere spontaneously within ~10 -34
sec. It would not be possible for a cat to remain in
an alive/dead superposition for any measurable length of time, so the entire premise of Schrödinger’s
thought experiment is false. As a result, the “measurement problem” is a myth and there was no
justification for ginning up a fantasy like MWI in order to solve it.
31 Some authors refer to this as the many worlds theory, but a valid scientific theory must make testable predictions, or at
least possess observable evidence to support it, and MWI does neither.
32 Splitting consciousness into many parts is no problem for physicalists who maintain consciousness is produced by a
physical brain. However, some theorists consider splitting a consciousness as particularly problematic – even more
more problematic than merely splitting planets and galaxies. So they offer another possibility, namely that each of us
has only one consciousness that actually survives these splits – our other “selves” then become zombies without
consciousness. If that were the case, then statistically speaking, most or all of the inhabitants of any given reality would
be zombies instead of conscious beings, which might explain the current state of society I find myself living in.
33 If you’re unfamiliar with the term googolplex, it’s an unimaginably large number. It’s equal to ten raised to the power
of one googol, where a googol is equal to ten raised to the power of one hundred. 1 googolplex = 1010
100
.
Abductive Reasoning → False Equivalences → Fantasies
Science is rife with theories based on abductive reasoning, defined as forming an hypothesis based on
the simplest and most likely conclusion drawn from observations. It is often articulated by the
common expression, “If it looks like a duck, swims like a duck, and quacks like a duck, then it
probably is a duck.” Abductive reasoning tends to produce false equivalences, where a few shared
characteristics between two or more items are oversimplified, or additional factors are ignored.
Jacques de Vaucanson (1709-1782) invented a mechanical “duck” that “digested” corn kernels, as
depicted below, right. Although Vaucanson’s model may have shared one characteristic with a real
duck, concluding the two are interchangeable clearly would be a false equivalence error.
≠
Charles Sanders Pierce (1839-1914) is credited with inventing abductive reasoning, but there were
much earlier examples, such as the Ptolemaic model of the universe, a fantasy that matched the simple
“observation” that the Sun, Moon, planets, and stars revolve around the Earth. When more detailed
observations contradict a model based on false equivalences, “refinements” must be made to the model
to force it into alignment with the new observations. Refinements to circular planetary orbits in the
form of epicylces had to be made over the years until the Ptolemaic model finally had to be scrapped
and replaced by a more accurate heliocentric model featuring Johannes Kepler’s elliptical orbits.
I strongly suspect string theory models are based on abductive reasoning leading to equivalence errors.
In 1968, theoretical physicist Gabriele Veneziano discovered an Euler beta function formula that
accurately matches the observed scattering amplitudes of strongly-interacting mesons. Using abductive
reasoning, this formula thus became known as the Veneziano amplitude model. The only missing piece
was a physical mechanism that could explain why strongly-interacting mesons obey the Veneziano
amplitude model. Here, the history gets a little fuzzy. Some scientific historians, who refer to Leonard
Susskind as the “Godfather of String Theory,” give him credit for modeling the meson as a tiny string
with electrical charges on each end. Others credit Veneziano himself as modeling two scattering
mesons as four “open-string tachyons.”34
In either case, the simplified abductive reasoning behind
string theory is that if you shrink physical strings to Planck-scale dimensions and fling them at each
other (while still treating them as classical objects obeying Newton’s laws of motion), their scattering
angles would match the Veneziano amplitude model. Therefore, mesons = tiny strings.35
The obvious fallacy is imagining any object on the scale of the Planck length (~10 -35
meter) would
behave anything like a classical vibrating string, having a definite location in spacetime and moving
according to Newtonian laws. The Heisenberg uncertainty principle alone would rub out any
semblance of definite shapes, sizes, locations, or motions for any such objects. The truth of the matter
is that scattering is a quantum interaction, analyzed using Feynman diagrams, not a physical interaction
like colliding billiard balls. Events on quantum scales are stochastic, and lack any causal mechanisms,
so by definition any theories based on such “mechanisms” are fantasies.
34 In case you’re wondering, a tachyon is a particle traveling through space faster than the speed of light, which of course
violates causality. That alone leads me to believe there is a fundamental flaw with this “mechanism.”
35 It turns out that string models predict other particles that should exist but have failed to materialize in the real world.
Nevertheless, an army of string theorists forge ahead unhindered by such apparent factual discrepancies.
Chasing Rainbows
The photograph below22
shows a double rainbow over a beautiful landscape. The bottom rainbow
appears to start at a clump of tress on the left and end in a stand of trees on the right.
However, if we would attempt to reach the end of the rainbow by heading off in the direction of the
arrow, we would soon discover that we could never reach the end because it would keep receding away
from us. In other words, the “end of the rainbow” doesn’t exist, and in fact, the rainbow itself isn’t real
either. Every observer looking out over this landscape from a different location sees a slightly different
“rainbow” created within the observer’s own consciousness. The experience of seeing a rainbow is
very real, while the physical rainbow itself is not.
We live in a radically-relativistic universe with no absolutes, where “reality” depends entirely on the
observer’s frame of reference. Like the rainbow, the experience is real, but the physical universe we
think we are experiencing is not. According to my Theory of Everything, reality only exists in the Now
moment, a true event horizon on the surface of a hyperbolic sphere23
having a negative curvature and a
radius expanding at the speed of light. At the center of the hyperbolic sphere is a temporal Beginning,
which sets the “age” of the universe (at the present Now) at ~14 billion years.24
Any direction an observer can point to will always point toward the Beginning; however, the Beginning
recedes from all observers at the speed of light. Thus, no matter how fast or how far the observer
travels, it never recedes more slowly than the speed of light and it cannot be approached or overtaken.
In this respect, chasing the Beginning is like chasing a light beam. So the question is, “If the Beginning
can neither be observed nor approached, does it even exist?” Although I cannot prove it, I believe the
answer is “no.” The “Beginning” is an illusion like the “end” of a rainbow. It’s a virtual or apparent
point in time our consciousness creates based on the assumption25
of linear time. I suspect the true
nature of time is logarithmic instead of linear, which simply means the age of the universe was never
zero; instead, it diminishes to smaller and smaller orders of magnitude toward an infinite past.
22 Photograph courtesy of Binyamin Mellish, under CC0/Public Domain license: https://www.goodfreephotos.com
23 A hyperbolic sphere curves away from its center of curvature at every point on its surface instead of toward it. It is
impossible to imagine what such an object looks like in three dimensions, and yet this is what our universe actually is.
24 The “standard” cosmological model purports the universal age is ~14 billion years. But that number is based on an
assumption that the gravitational parameter, G, is a constant. If G is inversely proportional to time, very distant galaxies
would have greater intrinsic brightness, so their true distances would be greater than is supposed in the standard model.
The end result is the true distance from the Beginning to Now is likely greater than ~14 billion years.
25 Like most areas of science, the current cosmological model is filled with unproven assumptions that are mistaken as
“facts.” The truth of every assumption must be verified by observation or derived through reason.

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Removing Myths and Fantasies from Science

  • 1. Removing Myths and Fantasies from Science An Amateur Scientist’s Recommendations by John Winders The image above provided under a CC0 public domain license courtesy of kai Stachowiak
  • 2. 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.
  • 3. Science is a process of discovery where ideas are proposed and put to the test. The worst three words in the scientific lexicon are: Let. Us. Assume. A theory must never be built around assumptions unless those assumptions have been thoroughly tested and vetted. Otherwise, if any one of those assumptions turns out to be a myth, the entire theory becomes a fantasy. Unfortunately, the current scientific literature is littered with statements that are widely accepted as facts and get repeated over and over, but some of them are actually myths that produce fantasies. I must confess that throughout my engineering career, I accepted mathematical and scientific facts handed down to me without really examining or questioning them. I considered proving a math theorem in a homework assignment to be a complete waste of time. After all, if René Descartes had already proved the theorem, then why should I prove it all over again? Engineers are mainly interested in how things work instead of why. As an engineer, science and mathematics were simply tools to get answers by “plug ‘n chug.” Newton’s laws were facts because they worked. When I retired from engineering and started my hobby as an amateur scientist, I began questioning everything I thought I already knew about science. To my surprise and horror, I discovered current scientific literature is littered with big lies, little fibs and half truths. When a statement made by a famous and well-respected author is published, whether in a peer-reviewed journal or a popular science book, there is a tendency for others in the field to blindly accept the statement and repeat it ad infinitum without examining or challenging it. Statements become facts when they are disseminated far and wide, but they might actually be myths, leading to theoretical dead ends and wasting time, money, and careers.1 False narratives gum up the gears of scientific progress, causing them to grind to a halt. A growing number of scientists suspect science is currently in crisis, which I believe might be true because so many myths have been accepted as facts. There are a few scientific myths that are particularly egregious because they are repeated so often by so many authors that they have become scientific mantras. Two of the Biggest Myths 1. Quantum mechanics is incompatible with the general theory of relativity. Conclusion: those theories are incomplete and must be scrapped and replaced with a single Theory of Everything (TOE) that will make them compatible. 2. There are four forces in nature: Strong nuclear, weak nuclear, electromagnetic and gravitational. The Grand Unification Theory (GUT) has successfully merged the first three forces into a single force at high energies, but the force of gravity stubbornly refuses to be unified with the other three. Conclusion: A TOE must therefore unify all four forces. These two myths produced the fantasy that the anticipated TOE will explain everything about nature in one fell swoop, from the motions of stars and planets, to the evolution of the universe, to the properties of atoms. This promise has become the Holy Grail of science and the singular goal of theoretical physicists worldwide. There have been several candidate theories put forth to achieve this goal, e.g. string theory, M-theory, and loop quantum gravity. Some attempt to unravel the TOE by going through the back door by first unifying and quantizing the “four forces of nature,” which will then lead to the TOE afterward. So far, progress has been disappointing, as noted in Wikipedia on this subject: “At present, there is no candidate theory of everything that includes the standard model of particle physics and general relativity and that, at the same time, is able to calculate the fine structure constant or the mass of the electron. Most particle physicists expect that the outcome of the ongoing experiments – the search 1 Albert Einstein spent much of his career between 1915 and his death in 1955 chasing winged unicorns, led by a false hope that gravitation could and should somehow be modified to resemble particle physics.
  • 4. for new particles at the large particle accelerators and for dark matter2 – are needed in order to provide further input for a TOE.” I’ll be very disappointed if most particle physicists really believe the discovery of the TOE requires a search for new particles. Without a working theory to indicate what the signals of “new” particles will look like, how could researchers find them through the noise emanating from particle accelerators? Scientific theories are supposed be based on first principles and then predict things, like new particles, not invented ad hoc to fit data points. TOE candidates like as string theory have already predicted “new” particles that were never found, so they should be scrapped. Large accelerators consume huge expenditures of human and economic capital without producing much useful knowledge.3 Let’s examine the first of the biggest myths in more detail.4 Both the general theory of relativity and quantum mechanics have been hailed as two of the greatest achievements of the human mind. Quantum Electrodynamics (QED), falling under the umbrella of quantum mechanics, has made predictions shown to be accurate to within ten parts in one billion, while every single prediction made by general relativity has been experimentally verified. There is only one reality, not two, and two theories that are so successful in describing different facets of the same reality cannot possibly be “incompatible” with each other. It’s absurd to criticize the general theory of relativity because it can’t be used to compute the fine-structure constant or dismiss the Schrödinger equation because it can’t be applied to orbital mechanics.5 Yet even though the two theories apply to completely different levels of reality, they must actually turn out to be codependent if a TOE exists. I now turn to the second of the biggest myths. There are only three forces of nature: Strong nuclear, weak nuclear, and electromagnetic. Gravity is not a force, which is the very reason it stubbornly refuses to be unified with the “other” three forces.6 The entire premise that inspired Albert Einstein to work on the general theory of relativity for ten long years was his realization that when observers fall freely under the influence of gravity, they feel no force whatsoever. If gravity were a force, Einstein would have to explain why this force just happens to exactly cancel the force of acceleration, F = m a. He could not explain it, so he deduced the “cancellation” is due to the fact that the “force” of gravity actually is the force of acceleration (the equivalence principle). The Correct Interpretation of Gravity Gravity defines the geodesic paths of objects in perpetual motion through space-time. The only time forces enter the picture is when objects are diverted from their geodesic paths, and electromagnetism is the only long-range force that can divert them. Sitting on my chair, I feel a force pushing upward on my tush. But that force is not the force of gravity, it’s the electromagnetic force applied by the surface of the chair keeping me from following my geodesic path toward the center of the Earth. So what exactly is a geodesic path? It’s simply the longest path between two points in space-time, which also happens to be the maximum amount of proper time accumulated by a clock traveling between those two points, so any path different than a geodesic path represents a “short cut” through space-time. In the absence of gravity, space-time becomes “flat” meaning all geodesic paths are straight lines in space. Under the influence of gravity, space becomes “warped,” causing geodesic 2 Dark matter is another myth. Follow the link to Erik Verlinder’s theory of entropic gravity in Footnote 10. 3 The Large Hadron Collider had an original price tag of €7.5 billion. It went into service in 2008, and it currently employs employs roughly 10,000 scientists, engineers, and technicians with an annual budget of around € 890 million. The only important discoveries that have resulted so far from all this expensive effort is evidence that the elusive Higgs boson probably exists and mini black holes don’t. 4 I must confess that I accepted this myth for a long time until I started examining it for myself. 5 Claiming they are incompatible is equivalent to claiming that your hands and feet are incompatible because you don’t walk on your hands and don’t grasp things with your feet. 6 Particle physicists keep searching in vain for the elusive graviton, the “messenger particle” of the “gravitational force.” The graviton will never be found because it doesn’t exist.
  • 5. for new particles at the large particle accelerators and for dark matter2 – are needed in order to provide further input for a TOE.” I’ll be very disappointed if most particle physicists really believe the discovery of the TOE requires a search for new particles. Without a working theory to indicate what the signals of “new” particles will look like, how could researchers find them through the noise emanating from particle accelerators? Scientific theories are supposed be based on first principles and then predict things, like new particles, not invented ad hoc to fit data points. TOE candidates like as string theory have already predicted “new” particles that were never found, so they should be scrapped. Large accelerators consume huge expenditures of human and economic capital without producing much useful knowledge.3 Let’s examine the first of the biggest myths in more detail.4 Both the general theory of relativity and quantum mechanics have been hailed as two of the greatest achievements of the human mind. Quantum Electrodynamics (QED), falling under the umbrella of quantum mechanics, has made predictions shown to be accurate to within ten parts in one billion, while every single prediction made by general relativity has been experimentally verified. There is only one reality, not two, and two theories that are so successful in describing different facets of the same reality cannot possibly be “incompatible” with each other. It’s absurd to criticize the general theory of relativity because it can’t be used to compute the fine-structure constant or dismiss the Schrödinger equation because it can’t be applied to orbital mechanics.5 Yet even though the two theories apply to completely different levels of reality, they must actually turn out to be codependent if a TOE exists. I now turn to the second of the biggest myths. There are only three forces of nature: Strong nuclear, weak nuclear, and electromagnetic. Gravity is not a force, which is the very reason it stubbornly refuses to be unified with the “other” three forces.6 The entire premise that inspired Albert Einstein to work on the general theory of relativity for ten long years was his realization that when observers fall freely under the influence of gravity, they feel no force whatsoever. If gravity were a force, Einstein would have to explain why this force just happens to exactly cancel the force of acceleration, F = m a. He could not explain it, so he deduced the “cancellation” is due to the fact that the “force” of gravity actually is the force of acceleration (the equivalence principle). The Correct Interpretation of Gravity Gravity defines the geodesic paths of objects in perpetual motion through space-time. The only time forces enter the picture is when objects are diverted from their geodesic paths, and electromagnetism is the only long-range force that can divert them. Sitting on my chair, I feel a force pushing upward on my tush. But that force is not the force of gravity, it’s the electromagnetic force applied by the surface of the chair keeping me from following my geodesic path toward the center of the Earth. So what exactly is a geodesic path? It’s simply the longest path between two points in space-time, which also happens to be the maximum amount of proper time accumulated by a clock traveling between those two points, so any path different than a geodesic path represents a “short cut” through space-time. In the absence of gravity, space-time becomes “flat” meaning all geodesic paths are straight lines in space. Under the influence of gravity, space becomes “warped,” causing geodesic 2 Dark matter is another myth. Follow the link to Erik Verlinder’s theory of entropic gravity in Footnote 10. 3 The Large Hadron Collider had an original price tag of €7.5 billion. It went into service in 2008, and it currently employs employs roughly 10,000 scientists, engineers, and technicians with an annual budget of around € 890 million. The only important discoveries that have resulted so far from all this expensive effort is evidence that the elusive Higgs boson probably exists and mini black holes don’t. 4 I must confess that I accepted this myth for a long time until I started examining it for myself. 5 Claiming they are incompatible is equivalent to claiming that your hands and feet are incompatible because you don’t walk on your hands and don’t grasp things with your feet. 6 Particle physicists keep searching in vain for the elusive graviton, the “messenger particle” of the “gravitational force.” The graviton will never be found because it doesn’t exist.
  • 6. duplicated precisely. Amazingly, there are physicists living in the 21st century who actually believe in a version of the Laplacian fantasy they call the “the block universe,” where time travel is allowed. Compare Einstein’s relativistic world with Niels Bohr’s quantum-mechanical world according to the Copenhagen interpretation, where no definite quantum states even exist until they are actually observed. Einstein rejected the Copenhagen interpretation insisting, “God does not play dice with the universe.”11 In 1935, Einstein and two of his associates, Boris Podolsky and Nathan Rosen, published a famous paper claiming quantum mechanics is “incomplete” because it lacks a mechanism that allows quantum states to be deduced a priori. Claiming that quantum mechanics is incomplete because it lacks causality is a classic case of begging the question; there was no convincing reason why causality is needed in order to make QM “complete.” Einstein et al just assumed that it is. The debate continued without resolution until 1964, when John Stuart Bell published a paper proving that statistical correlations of quantum measurements will violate a particular inequality if and only if the Copenhagen interpretation is correct. It became possible in the 1980s to test the inequality experimentally, and the results of those experiments conclusively settled the issue: Although large ensembles of quantum measurements do conform to predictable and repeatable statistics, it is fundamentally impossible to deduce a priori the outcome of any quantum measurement. Shannon’s entropy is solely a function of probabilities, S(p1, p2, … , pN). There is a common misconception that probabilities determine outcomes, when in fact outcomes determine probabilities. If the state of a system could be determined a priori without taking measurements, then one of the probabilities would be equal to one and all the others would equal zero. In those cases, S = 0. Thus, entropy would be meaningless in a deterministic, causal world. Rolling dice and spinning roulette wheels may appear to be random processes, but they are not; they are chaotic processes instead. Chaotic processes generate “pseudo-random” results where extremely small variations in initial conditions produce very significant changes in outcomes, yet these outcomes are still very much deterministic and repeatable. In contrast, it has been proven experimentally by violations of Bell’s inequality that quantum processes are neither predictable nor repeatable and therefore they must be truly random (stochastic). Stochastic Process = Quantum Process. Therefore, entropy can only exist where there is true stochasticity; i.e., it exists only at the quantum level of reality. If gravitation is an entropic process tending to maximize uncertainty, then the general theory of relativity, which is really the theory of gravity, must also rest on a foundation of entropy. This can only occur if there is a hidden, yet real, connection between general relativity and quantum mechanics. Thermodynamics reveals another connection between general relativity quantum mechanics. The general relativity field equations have an exact solution for a spherical mass, known as the Schwarzschild equation. Thanu Padmanabham published a paper in 2009 paper entitled “Thermodynamical Aspects of Gravity: New Insights.”12 In that paper he showed the Schwarzschild solution at the boundary is mathematically equivalent to the fundamental equation of thermodynamics. My essay “The Universe on a Tee Shirt” explains the significance of this “boundary” in much greater detail than is needed here.13 Let it suffice to say that space-timed has thermodynamic properties corresponding to energy, pressure, temperature and entropy, just like a material substance, and that space, time, matter and energy are all just different manifestations of entropy.14 In other words, the entire physical universe rests on a foundation of uncertainty, which only truly exists at the quantum level of reality. Space and time emerge in the causal world, but they are also the stage 11 There is some irony in that statement because a roll of the dice isn’t actually random but deterministic. 12 “Thermodynamical Aspects of Gravity: New Insights” is available for download from ArXiv here. 13 “The Universe on a Tee Shirt” is available for download here. 14 Entropy can be expressed in bits or nats. One one cubic meter of empty space is comprised of 1.44 × 1043 nats and one joule of energy at a temperature of 300K is equivalent to 2.42 × 1020 nats.
  • 7. upon which quantum events occur. Therefore, it should now be obvious that both facets of reality are interlocked and codependent. There is no “incompatibility” between them. Correcting the Two Biggest Myths Scientific progress being held back by big lies, little lies, and half truths. Every assumption must be examined and validated before it can be accepted. Just because a famous or well-liked person makes a statement, there is no reason to blindly accept it and repeat it. There already is a Theory of Everything hidden in plain sight. Very few have found it simply because they are looking in the wrong places. The TOE will reveal itself after making the following changes to some basic assumptions. 1) There are four three fundamental forces in nature: Strong nuclear, weak nuclear, and electromagnetism, and gravity. Gravity is not a force; it alters the geodesic paths of objects moving through space-time in order to maximize entropy. 2) General relativity and quantum mechanics are incompatible with each other. General relativity and quantum mechanics are linked through entropy, which is one of the thermodynamic properties of space-time. The Mother of All Fantasies: Black Holes In the past several decades, it seems that black holes are a central part of most of research papers in theoretical physics. Black holes are sand boxes where outlandish theories are erected like great sand castles, but the fact is that proving any conclusions using black holes is tantamount to dividing by zero to prove that 1=2. It’s unfortunate that entire careers and reputations are resting the assumption that black holes exist without anyone seriously examining how they could form in the first place. My essay “Why There Are No True Black Holes,”15 points out a number of contradictions showing why black holes can’t exist. The fundamental fallacy stems from a misapplication of the Schwarzschild solution. Every spherical body has something called a Schwarzshild radius, RS, proportional to the body’s positive mass-energy. In order to calculate RS, you must include the entire mass-energy of the object, both inside and outside RS in the calculation. The size of RS for the Earth is quite small, about one inch, but all the Earth’s mass-energy from its center to its surface must be included. Strictly speaking, not including the space beyond the surface is arbitrary, and it’s not allowed in a formal solution to the general relativity field equations. You could get away with ignoring the surrounding space if it were truly empty, but it’s really not. Yet assuming space is empty will still yield very good approximate solutions to practical problems as long as gravitation is weak. In truth, the space surrounding the Earth is filled with negative gravitational energy, and ordinarily this energy is negligible compared to the positive mass-energy of the material in the Earth’s core, mantle, and crust. However, if you try to form a black hole by compressing the mass-energy until it almost fits inside RS, an enormous amount of negative gravitational energy fills the surrounding space, which will cancel out some of the mass-energy.16 The cancellation must now be accounted for because it causes RS to shrink. It can be shown that no matter how much a material object is compressed, RS always shrinks below the outside radius of the object, meaning no true event horizon can ever form. If an object could be compressed down to the size of its Schwarzschild radius, the negative gravitational energy surrounding it would cancel out all its mass-energy, reducing RS to zero.17 15 “Why There Are No True Black Holes” is available for download here. 16 It is easily shown that if a mass were lowered onto a hypothetical event horizon using a pulley system, the liberated energy would equal 100% of the energy equivalent of the mass being lowered, thus adding zero mass to the black hole. 17 Theoretical physicist Abhas Mitra of the Bhabha Atomic Research Centre in Mumbai, India came up with a similar conclusion. He proved that the value for the mass of a black hole is not a free parameter that can simply be plugged into the Schwarzschild equation. A correct solution of the general relativity field equations shows an event horizon can only form around a mass when it has a value equal to zero. A copy of his paper is available for download here.
  • 8. Black holes have challenged theoretical physicists with a long list of paradoxes and contradictions, which have not been successfully resolved and are swept under the rug instead. It’s clear that Nature hates paradoxes and contradictions, so She will snuff out any black hole before an event horizon can form, and She has unlimited amounts of negative gravitational energy at Her disposal to do this. Astronomers and astrophysicists have observed a number of objects called “black hole candidates” because from a distance they seem to resemble what black holes might look like. So if those objects are not really black holes, then what are they? Abhas Mitra refers to them as Eternally Collapsing Objects (ECOs). An ECO is an extremely compact object surrounded by an enormous gravitational field that bends light and produces time dilation that slows down all physical processes in its vicinity to a virtual standstill, giving an ECO the appearance of a “black hole” when seen from a distance. Because of the gravitational time dilation, the ECO continues to shrink at an ever-decreasing rate, allowing it to approach but never reach the Schwarzschild radius, and never forming a true event horizon. In other words, an ECO is a pseudo black hole without an event horizon. Interestingly, Robert Oppenheimer and Hartland Snyder came to a similar conclusion in a paper published in 1939. They considered only the gravitational time-dilation effect without the mass-cancellation effect of negative gravitational energy surrounding the object, concluding a black hole might theoretically form through gravitational collapse, but the process would take forever. Given the fact that black holes are either impossible or would take forever to form, then how can theoretical physicists claim they exist in a universe less than 14 billion years old? Well, it’s very easy. They simply magically insert all of an object’s mass-energy inside its Schwarzschild radius without explaining how it got there, ignoring the massive amount of negative gravitational energy surrounding it. With a wave of a hand they say, “Let us assume a black hole has formed,” and go on to invent all sorts of weird and wonderful fantasies borrowed from science fiction, such as worm holes and time tunnels, while diverting their eyes from the multiple paradoxes and contradictions that inevitably arise as a result. Starting out with the statement, “Let us assume X” without proving X is feasible or even possible is a very bad habit to get into, but it happens all too often in the theoretical physics community and it impedes scientific advancement. The Way Forward Jacob Bekenstein and Stephen Hawking published groundbreaking work involving quantum mechanics and thermodynamics on black-hole event horizons. Was all their work for naught? Not at all. A sphere of mass-energy cannot be compressed into a black hole because negative gravitational energy exterior to the Schwarzschild radius cancels out mass-energy; however, a black hole would be possible if there were no exterior. This is the case for the universe as a whole because by definition, the universe is singular without an exterior. In other words, the universe could very well be a black hole having an event horizon as defined by the Schwarzschild equation, and the Bekenstein-Hawking equation could then be applied to it. Earlier, I mentioned Thanu Padmanabham’s paper, showing the solution of the equation at the “boundary” possesses the thermodynamic properties of energy, pressure, temperature and entropy.18 It is now clear that this “boundary” could only exist for an object with no exterior. This makes the work of Bekenstein and Hawking even more relevant and important, because instead of merely describing the thermodynamic properties of a collapsed star, it describes thermodynamic properties at the boundary of the universe itself, which agrees with Padmanabham’s work. According to the Schwarzschild equation, the event horizon is a static moment frozen in time, and close inspection of the equation reveals the radius below the event horizon, r < RS, really points in a temporal direction instead of a spatial direction. In other words, space and time exchange places inside the black 18 It should be noted that the energy tensor found in the general relativity field equations describe an elastic solid that resists compression, shear, and torsion. Thus, space-time is analogous to a solid having elastic properties along with thermodynamic properties.
  • 9. hole. Physicists engage in quite a bit of hand waving when they try to describe exactly what the interior of a black hole represents, but according to the common myth, locations inside the event horizon aren’t locations in space, they are points in the future of everything that had previously passed through the event horizon.19 At the center of the black hole, at r = 0, there is a singularity where all the futures converge into a single moment in time – maybe where everything in the past, present and future happens all at once? You’re not alone if you have trouble making sense of that fantasy. The TOE Finally Emerges A black hole starts making sense by shifting thinking away from a collapsed object surrounded by a static event horizon somewhere out in space, and recognize the Bekenstein-Hawking equation applies to an expanding event horizon of the entire universe. Rather than a single frozen moment in time, an expanding event horizon is a series of sequential moments. The interior region surrounded by the event horizon is a temporal region, as indicated by the Schwarzschild solution, which contains the residue of previous moments the expanding boundary left behind. The center of the interior temporal region is the point where the past of everything converges – the Beginning. The event horizon expands at the speed of light, making it impossible to travel into the past. By keeping the general theory of relativity and quantum mechanics exactly as they are instead of jerry rigging them to match some preconceived notion of how they ought to be, a TOE emerges automatically. There are no conflicts or incompatibilities between the dual descriptions of nature. Both are complete unto themselves and yet are mutually codependent. Everything happening in the universe – including us – occurs on the expanding event horizon20 governed by quantum mechanics and thermodynamics. The general theory of relativity governs the dynamics of the space-time continuum, a four-dimensional hyperbolic sphere of negative curvature defined by the Minkowski metric. There is one temporal dimension and three spatial dimensions. The number three is not arbitrary. Rotational symmetry requires the conservation of angular momentum, which can only be defined in three dimensions. The single temporal dimension is asymmetrical (curved) because there is a definite direction in time. The Minkowski metric defines hyperbolic sphere having a uniform negative curvature. Unlike an ordinary sphere having positive curvature, every point on a hypersphere’s surface curves away from the center of curvature instead of toward it. Since the hypersphere has no exterior (because nothing exists beyond the universe) all observations must point inward from the boundary to past events recorded in the hypersphere’s interior. Any straight line projected in any direction from any point on the boundary must eventually arrive at the center of the hypersphere, at the Beginning. Two Remaining Potential Myths There are two very fundamental “laws” of nature that could turn out to be myths: 1) The total amount of mass-energy in the universe is constant, and 2) Newton’s constant, G, does not change. If the TOE as outlined above is true, then both of those two laws are false. Since the temporal dimension is asymmetric, Noether’s theorem cannot allow the law of conservation of mass-energy to apply to the universe as a whole. If TU is the age of the universe and the boundary expands at the speed of light, then in order to satisfy the Bekenstein-Hawking equation, the total mass-energy of the universe must be proportional to TU squared and G is not constant but a variable21 proportional to 1 / TU. I admit these predictions are very bold and controversial and I would love to see them honestly examined and tested. 19 This presents another argument against the possibility of forming a black hole. Objects seen approaching the event horizon by a distant observer never actually reach it. And yet objects must have passed through the event horizon in the observer’s frame, otherwise the black hole wouldn’t exist. It’s another paradox that’s been swept under the rug. 20 Event horizon is very apt description, because it’s the boundary where all events must occur. The past and future do not actually exist because the past lying below the event horizon is a frozen residue left behind by the expanding event horizon, and the future lies in a non-existent region outside the universe above the event horizon. 21 Precise laboratory measurements of G have shown anomalous fluctuations over time that cannot easily be explained.
  • 10. Chasing Rainbows The photograph below22 shows a double rainbow over a beautiful landscape. The bottom rainbow appears to start at a clump of tress on the left and end in a stand of trees on the right. However, if we would attempt to reach the end of the rainbow by heading off in the direction of the arrow, we would soon discover that we could never reach the end because it would keep receding away from us. In other words, the “end of the rainbow” doesn’t exist, and in fact, the rainbow itself isn’t real either. Every observer looking out over this landscape from a different location sees a slightly different “rainbow” created within the observer’s own consciousness. The experience of seeing a rainbow is very real, while the physical rainbow itself is not. We live in a radically-relativistic universe with no absolutes, where “reality” depends entirely on the observer’s frame of reference. Like the rainbow, the experience is real, but the physical universe we think we are experiencing is not. According to my Theory of Everything, reality only exists in the Now moment, a true event horizon on the surface of a hyperbolic sphere23 having a negative curvature and a radius expanding at the speed of light. At the center of the hyperbolic sphere is a temporal Beginning, which sets the “age” of the universe (at the present Now) at ~14 billion years.24 Any direction an observer can point to will always point toward the Beginning; however, the Beginning recedes from all observers at the speed of light. Thus, no matter how fast or how far the observer travels, it never recedes more slowly than the speed of light and it cannot be approached or overtaken. In this respect, chasing the Beginning is like chasing a light beam. So the question is, “If the Beginning can neither be observed nor approached, does it even exist?” Although I cannot prove it, I believe the answer is “no.” The “Beginning” is an illusion like the “end” of a rainbow. It’s a virtual or apparent point in time our consciousness creates based on the assumption25 of linear time. I suspect the true nature of time is logarithmic instead of linear, which simply means the age of the universe was never zero; instead, it diminishes to smaller and smaller orders of magnitude toward an infinite past. 22 Photograph courtesy of Binyamin Mellish, under CC0/Public Domain license: https://www.goodfreephotos.com 23 A hyperbolic sphere curves away from its center of curvature at every point on its surface instead of toward it. It is impossible to imagine what such an object looks like in three dimensions, and yet this is what our universe actually is. 24 The “standard” cosmological model purports the universal age is ~14 billion years. But that number is based on an assumption that the gravitational parameter, G, is a constant. If G is inversely proportional to time, very distant galaxies would have greater intrinsic brightness, so their true distances would be greater than is supposed in the standard model. The end result is the true distance from the Beginning to Now is likely greater than ~14 billion years. 25 Like most areas of science, the current cosmological model is filled with unproven assumptions that are mistaken as “facts.” The truth of every assumption must be verified by observation or derived through reason.
  • 11. Attempting to Imagine the Unimaginable J.B.S. Haldane was a British polymath and philosopher who made major contributions in the fields of biology, genetics and statistics. Contemplating the universe as a whole, he once remarked, “Now my own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose.” What we humans can suppose about the physical universe is based on a faulty, inaccurate model bound by what our physical senses reveal; in other words, we suppose a fantasy. Whether you were a cave man living in the Pleistocene, or a 21st century cosmologist, that model is the same three-dimensional Euclidean geometry envisioned by Galileo and Newton. Animal species employ a three-dimensional space filled with objects in motion as their working model because it is optimally suited for enabling them to survive and reproduce in a small-scale terrestrial environment. There is no need for humans or any other species to comprehend the totality of the universe because doing that would have no direct benefit to their survival or well being. So when we look up into the night sky into the vastness of the universe, we can only comprehend what consists of an outward projection of our small-scale model of a three-dimensional Euclidean world instead of witnessing its truly grand four-dimensional hyperbolic geometry. Humans possess awesome powers of reason and abstract mathematics that give us a glimpse of reality, but it is only that – a glimpse. We simply cannot truly comprehend reality because our internal models have been conditioned by our sense of sight, which is based upon (and limited by) the propagation of light according to Maxwell’s equations. Shortly after Einstein published his special theory of relativity in 1905, the brilliant mathematician Hermann Minkowski26 combined time and three-dimensional Euclidean space into a four-dimensional space-time manifold, known as the Minkowski metric. This metric provides “distances” in space-time that are invariant for all observers, regardless of their relative positions or motions. Minkowski space- time also describes a universe having a hyperbolic geometry, without any boundary that separates its interior from an exterior. An ordinary Euclidean sphere is is easy for us to imagine because our three-dimensional model world is filled with them. Ordinary spheres have two-dimensional surfaces separating insides from outsides. When physicists contemplate the meaning of the Schwarzschild equation, their minds automatically jump to envisioning a static Euclidean sphere hanging in space with a surface they call an “event horizon,” a one-way boundary separating the interior of the sphere (a black hole) from its exterior (the rest of the universe). What the Schwarzschild equation really describes is a hyperbolic sphere without an exterior; however, no human mind can form a proper mental image of such an object.27 When looking into the sky in any direction, every observer is always looking directly toward the center of the universal hyperbolic sphere. Galaxies equidistant from an observer appear to lie on the surfaces of ordinary spheres curving toward the observer and away from the center. Those galaxies do in fact lie on surfaces curving away from the center because they lie on negatively-curved hyperbolic boundaries of the past. But projecting our three-dimensional Euclidean space model onto the universe creates a contradiction: As the distances to those galaxies increase, the spherical surfaces surrounding us upon which they lie appear to increase in size also. In reality, those surfaces are hyperbolic spheres and they must decrease in size as their distances from us increase, because the radii between them and the center of the hypersphere decrease. This simple example shows how the universe really is queerer than we can suppose, and why the Euclidean models we attempt to impose on it are mostly fantasies. 26 Minkowski was acquainted with young Einstein prior to the publication of special relativity, and referred to him as “a lazy dog” who “never bothered with mathematics at all.” To his credit, Einstein embraced Minkowski’s space-time and incorporated it into his general theory of relativity, and is doubtful that he could have achieved success had he not done that. 27 According to Hilbert’s theorem, hyperbolic geometry does not have a model in three-dimensional Euclidean geometry; however, images of hyperbolic objects can be projected onto Euclidean spaces as shown here.
  • 12. Unraveling the Hard Problem I believe every serious scientific inquiry must ultimately encounter the question of consciousness, namely, “What is it?” Philosophers have pondered this problem for centuries, whereas until recently physicalists generally have tried to ignore or dismiss it. Philosopher David Chalmers described the problem in the following terms: “The hard problem of consciousness (Chalmers 1995) is the problem of explaining the relationship between physical phenomena, such as brain processes, and experience (i.e., phenomenal consciousness, or mental states/events with phenomenal qualities or qualia). Why are physical processes ever accompanied by experience? And why does a given physical process generate the specific experience it does—why an experience of red rather than green, for example?”28 Lately, an increasing number of physicists and neurologists are promoting their own theories about what consciousness is (or isn’t). These specialists are divided into two camps: 1) Those who believe consciousness is produced by the brain, and 2) those who don’t believe consciousness exists. Yes, I’ve read articles by authors who assert consciousness is an illusion29 , and the brain somehow tricks itself into believing this illusion is real; however, it isn’t clear how the brain, essentially a data processor, could possibly be tricked, let alone trick itself, into “believing” anything. The corollary to this argument, of course, is that an artificial data-processing machine having sufficient complexity could also trick itself into believing it is conscious, leading to one of the most glaring scientific myths: Extraordinarily Complex Data Processing → Consciousness I am convinced the hard problem stems from the fact that qualia, like the state of consciousness itself, cannot be compared to, or defined in terms of, any exterior objects. You simply cannot describe the experience of “red” to someone who is color blind or explain to an unconscious machine or a computer algorithm what it’s like to be conscious. Physicalists attempt to define “red” as a specific range of wavelengths of light. While those wavelengths do stimulate an interior experience we label as “red,” we also experience “red” with our eyes closed and while dreaming. “Red” is not physical. When the brain is active, either awake or dreaming, there is a reality show in progress that is being observed by something or someone. But the brain is not the observer; it is among exterior objects being observed, serving as a conduit through which the “Great Objective Reality Show” streams into our consciousness. It would be silly to conclude that stopping the show by shutting down the brain also shuts down the observer, any more than turning off a television monitor shuts down the viewer. Author Donald Hoffman compares our experiences to icons on a computer screen.30 Computer icons are symbols representing files and applications the user can access. But those symbols are not the files or applications themselves. Likewise, the true nature of objective reality is very different than the images we use to comprehend and interact with the reality they represent. We saw earlier how we perceive our world as a model conforming to Euclidean geometry, whereas the true geometry of the universe is hyperbolic. Qualia, in many different forms, are the only things consciousness perceives. In conclusion, consciousness cannot be defined because it is unobservable and therefore it cannot be approached through symbolic languages or mental icons. Consciousness isn’t part of “objective reality” or constrained by it; instead, it is fundamental and complete unto itself. Being unconstrained by space or time, consciousness is boundless and therefore singular. Physicist James Jeans noted, “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 to be an accidental intruder into the realm of matter … we ought rather hail it as the creator and governor of the realm of matter.” 28 Robert J. Howell and Torin Alter (2009), Scholarpedia, 4(6):4948. 29 Even some philosophers, such as Daniel Dennett, are completely on board with the position that human consciousness and free will are the results of purely physical processes. 30 Reference: “The Case Against Reality: Why Evolution Hid the Truth from Our Eyes”
  • 13. Truisms → Myths → Fantasies Since the invention of quantum mechanics, a significant number of theoretical physicists have adopted a reductionist position that all physical objects – in fact the entire universe – can be reduced to wave functions. It’s true that physical objects are comprised of elementary particles, which in turn can be represented as wave equations, at least under some conditions. However, this truism as led to persistent myths and outright fantasies. One such myth is the so-called “measurement problem.” According to current quantum theory, an elementary particle that is unobserved ceases to exist as a particle and turns into a wave function, which represents the future quantum properties of the particle in terms of probabilities. When those quantum properties are measured, the probabilities become actualities, and the wave function “collapses” and is replaced by a particle. The “problem” is that nobody knows the precise mechanism that causes the so-called “collapse.” This situation reminds me of an amazing catch by Willie Mays in the first game of the 1954 World Series between the New York Giants and the Cleveland Indians at the Polo Grounds in Manhattan. It was the top of the 8th inning with the game tied 2-2 with Cleveland outfielder Vic Wertz at bat. Wertz crushed a pitch from Giants’ reliever Don Liddle, and center fielder Mays took off running full-speed toward deep center field with his back to the ball. Without ever looking back at the ball, Mays reached out and caught it over his left shoulder 420 feet from home plate, only a few steps from the wall in center field. The instant before Mays made the catch is shown above, left. According to some quantum interpretations, objects exist in physical form only while they are observed by conscious observers. Now suppose everybody, including Mays, had looked away from ball as it left Wertz’s bat. The ball would then have immediately turned into a wave function defining the probabilities of measuring the ball at particular locations in spacetime. The wave function would evolve deterministically, radiating outward from home plate with a bent conical shape as shown in the figure above, right, terminating at the blue patch on the Earth’s surface in center field where the ball had a high probability of being “measured” when (and if) it landed. In a brief moment, Mays observed the initial state of the ball as it left the vicinity of home plate, using both visual and audible clues, such as the crack of the bat when the ball was struck. In addition to the initial trajectory of the ball through spacetime, he observed the location of the ball over home plate and the angle of the bat as it was struck, determining its spin causing the ball to hook or slice through the air. He also took the wind velocity into account, as well as the humidity and atmospheric pressure. All of those data were factored into a wave function terminating at that high-probability blue area in center field. When Mays arrived at that precise location in spacetime, he reached out and “measured” the ball by catching it in his glove. The wave function collapsed and a ball appeared in its place, but unfortunately, to this day nobody knows why or how the “measurement” made this happen; ergo, instead of just being an amazing catch, it is yet another example of a fundamental “measurement problem” that has plagued and undermined physics since quantum mechanics was invented.
  • 14. Of course, the above narrative is ridiculous. No “wave function” evolved from home plate to center field; it existed entirely inside Willie Mays’ mind. It “collapsed” as soon as the ball went into Mays’ glove because it ceased to have any relevance. But as silly as this narrative is, there are a large number of theoretical physicists who continue to agonize over the “collapse of the quantum wave function” as if a wave function were a physical object instead of simply a mathematical formula defining the probabilities of future quantum states. Their inability to separate the model from the thing itself has led to elaborate workarounds and fantasies to explain how and why the “collapse” occurs. One such fantasy is Hugh Everett’s many worlds interpretation (MWI).31 It solves the measurement problem by not allowing the wave function to collapse at all. Instead, reality exists as a quantum superposition of all possible measurements that could be made. Each time a conscious being measures a state, reality splits into as many renditions as there are other quantum states to be measured. The minimum number of split realities would be two, as in the case of measuring the up/down spin of an electron; however, a single measurement could easily cause one reality to split into billions of other separate realities. Also, a measurement anywhere in the universe would cause splits everywhere else. For example, Willie Mays catching a ball could result in countless other versions of reality where the ball sails into the stands, bounces off the wall, drops to the ground, or hits Willie in the head. But it doesn’t end there. As conscious beings, we must also split into as many versions of ourselves as necessary to inhabit the complete set of possible realities. Nevertheless, it seems MWI has very specific rules keeping us consciously isolated and unaware of our other doppelganger selves.32 The underlying fallacy behind the measurement problem myth can be traced back to Schrödinger’s Cat thought experiment, where a device triggered by a radioactive decay has a 50/50 chance of killing a cat in a sealed box within a fixed time interval. That being the case, the state of the cat is in an alive/dead superposition until a very smart guy in a white lab coat peers into the box, causing the superposition to “collapse.” This scenario is based on the truism that a when a classical object, such as a cat, interacts with a quantum particle, their wave functions combine. If the particle is in superposition, then supposedly the cat is also. Without knowing how or why, only a conscious observer is able to break this impasse, causing the wave function to collapse to reveal the cat’s final physical, objective state. In other words, objective reality is continually being created solely by conscious observers like us. The fallacy behind this myth is that a macroscopic quantum measuring device doesn’t have just two either/or states, but a veritable googolplex33 of states. Schrödinger’s cat herself, whose wave function combines with the radioactive particle that could ultimately kill her, has myriad states corresponding to an alive cat and others corresponding to a dead cat. She can remain in a superposition if both states are nearly identical with only a very tiny energy gap, ΔE, between them. However, if there is a significant energy gap, the two states will spontaneously decohere within a very short time interval, Δτ ~ / ℏ ΔE, where is Planck’s constant. For example, a superposition of two quantum states with ℏ ΔE equal to one joule would decohere spontaneously within ~10 -34 sec. It would not be possible for a cat to remain in an alive/dead superposition for any measurable length of time, so the entire premise of Schrödinger’s thought experiment is false. As a result, the “measurement problem” is a myth and there was no justification for ginning up a fantasy like MWI in order to solve it. 31 Some authors refer to this as the many worlds theory, but a valid scientific theory must make testable predictions, or at least possess observable evidence to support it, and MWI does neither. 32 Splitting consciousness into many parts is no problem for physicalists who maintain consciousness is produced by a physical brain. However, some theorists consider splitting a consciousness as particularly problematic – even more more problematic than merely splitting planets and galaxies. So they offer another possibility, namely that each of us has only one consciousness that actually survives these splits – our other “selves” then become zombies without consciousness. If that were the case, then statistically speaking, most or all of the inhabitants of any given reality would be zombies instead of conscious beings, which might explain the current state of society I find myself living in. 33 If you’re unfamiliar with the term googolplex, it’s an unimaginably large number. It’s equal to ten raised to the power of one googol, where a googol is equal to ten raised to the power of one hundred. 1 googolplex = 1010 100 .
  • 15. Abductive Reasoning → False Equivalences → Fantasies Science is rife with theories based on abductive reasoning, defined as forming an hypothesis based on the simplest and most likely conclusion drawn from observations. It is often articulated by the common expression, “If it looks like a duck, swims like a duck, and quacks like a duck, then it probably is a duck.” Abductive reasoning tends to produce false equivalences, where a few shared characteristics between two or more items are oversimplified, or additional factors are ignored. Jacques de Vaucanson (1709-1782) invented a mechanical “duck” that “digested” corn kernels, as depicted below, right. Although Vaucanson’s model may have shared one characteristic with a real duck, concluding the two are interchangeable clearly would be a false equivalence error. ≠ Charles Sanders Pierce (1839-1914) is credited with inventing abductive reasoning, but there were much earlier examples, such as the Ptolemaic model of the universe, a fantasy that matched the simple “observation” that the Sun, Moon, planets, and stars revolve around the Earth. When more detailed observations contradict a model based on false equivalences, “refinements” must be made to the model to force it into alignment with the new observations. Refinements to circular planetary orbits in the form of epicylces had to be made over the years until the Ptolemaic model finally had to be scrapped and replaced by a more accurate heliocentric model featuring Johannes Kepler’s elliptical orbits. I strongly suspect string theory models are based on abductive reasoning leading to equivalence errors. In 1968, theoretical physicist Gabriele Veneziano discovered an Euler beta function formula that accurately matches the observed scattering amplitudes of strongly-interacting mesons. Using abductive reasoning, this formula thus became known as the Veneziano amplitude model. The only missing piece was a physical mechanism that could explain why strongly-interacting mesons obey the Veneziano amplitude model. Here, the history gets a little fuzzy. Some scientific historians, who refer to Leonard Susskind as the “Godfather of String Theory,” give him credit for modeling the meson as a tiny string with electrical charges on each end. Others credit Veneziano himself as modeling two scattering mesons as four “open-string tachyons.”34 In either case, the simplified abductive reasoning behind string theory is that if you shrink physical strings to Planck-scale dimensions and fling them at each other (while still treating them as classical objects obeying Newton’s laws of motion), their scattering angles would match the Veneziano amplitude model. Therefore, mesons = tiny strings.35 The obvious fallacy is imagining any object on the scale of the Planck length (~10 -35 meter) would behave anything like a classical vibrating string, having a definite location in spacetime and moving according to Newtonian laws. The Heisenberg uncertainty principle alone would rub out any semblance of definite shapes, sizes, locations, or motions for any such objects. The truth of the matter is that scattering is a quantum interaction, analyzed using Feynman diagrams, not a physical interaction like colliding billiard balls. Events on quantum scales are stochastic, and lack any causal mechanisms, so by definition any theories based on such “mechanisms” are fantasies. 34 In case you’re wondering, a tachyon is a particle traveling through space faster than the speed of light, which of course violates causality. That alone leads me to believe there is a fundamental flaw with this “mechanism.” 35 It turns out that string models predict other particles that should exist but have failed to materialize in the real world. Nevertheless, an army of string theorists forge ahead unhindered by such apparent factual discrepancies.
  • 16. Chasing Rainbows The photograph below22 shows a double rainbow over a beautiful landscape. The bottom rainbow appears to start at a clump of tress on the left and end in a stand of trees on the right. However, if we would attempt to reach the end of the rainbow by heading off in the direction of the arrow, we would soon discover that we could never reach the end because it would keep receding away from us. In other words, the “end of the rainbow” doesn’t exist, and in fact, the rainbow itself isn’t real either. Every observer looking out over this landscape from a different location sees a slightly different “rainbow” created within the observer’s own consciousness. The experience of seeing a rainbow is very real, while the physical rainbow itself is not. We live in a radically-relativistic universe with no absolutes, where “reality” depends entirely on the observer’s frame of reference. Like the rainbow, the experience is real, but the physical universe we think we are experiencing is not. According to my Theory of Everything, reality only exists in the Now moment, a true event horizon on the surface of a hyperbolic sphere23 having a negative curvature and a radius expanding at the speed of light. At the center of the hyperbolic sphere is a temporal Beginning, which sets the “age” of the universe (at the present Now) at ~14 billion years.24 Any direction an observer can point to will always point toward the Beginning; however, the Beginning recedes from all observers at the speed of light. Thus, no matter how fast or how far the observer travels, it never recedes more slowly than the speed of light and it cannot be approached or overtaken. In this respect, chasing the Beginning is like chasing a light beam. So the question is, “If the Beginning can neither be observed nor approached, does it even exist?” Although I cannot prove it, I believe the answer is “no.” The “Beginning” is an illusion like the “end” of a rainbow. It’s a virtual or apparent point in time our consciousness creates based on the assumption25 of linear time. I suspect the true nature of time is logarithmic instead of linear, which simply means the age of the universe was never zero; instead, it diminishes to smaller and smaller orders of magnitude toward an infinite past. 22 Photograph courtesy of Binyamin Mellish, under CC0/Public Domain license: https://www.goodfreephotos.com 23 A hyperbolic sphere curves away from its center of curvature at every point on its surface instead of toward it. It is impossible to imagine what such an object looks like in three dimensions, and yet this is what our universe actually is. 24 The “standard” cosmological model purports the universal age is ~14 billion years. But that number is based on an assumption that the gravitational parameter, G, is a constant. If G is inversely proportional to time, very distant galaxies would have greater intrinsic brightness, so their true distances would be greater than is supposed in the standard model. The end result is the true distance from the Beginning to Now is likely greater than ~14 billion years. 25 Like most areas of science, the current cosmological model is filled with unproven assumptions that are mistaken as “facts.” The truth of every assumption must be verified by observation or derived through reason.