Welcome to the Amateur Scientist Web Page

Why "amateur"?  Because science is way too important to be left to the professionals.

Note:  You can view my essays by clicking on the links beneath the images of their front pages, which opens a page in Google Drive displaying the essay as in the screen shot below.  Depending on the device and browser you use, saving a copy of the essay can be a bit tricky.  Clicking on the Download Icon shown below may require you to sign into a Google account to complete the download.  To get around Google's sign-in requirement, try clicking the Print Icon shown below instead.  Doing this using Chrome, Safari or Firefox browsers displays the essay on a separate page where you can download or save a copy of it on your device as a PDF file without signing in to Google.  With other browsers, your mileage may vary.  

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My Journey

I was trained as a professional engineer and throughout my career I completely bought into the current scientific paradigm known as material reductionism, which is defined according to pbs.org as  "the view that only the material world (matter) is truly real, and that all processes and realities observed in the universe can be explained by reducing them down to their most basic scientific components, e.g., atoms, molecules, and everything else thought to make up what we know as 'matter.'"  Engineers are served well by this paradigm because our task is centered around making "things" more functional, more efficient, and less expensive, and breaking things apart is a good way of finding out how they work, and reassembling the parts is how we design things.

From a young age I was interested in pure physics because it would presumably lead me to understand how reality works.  However, I concluded that a career in pure physics, outside of academia, would not be a viable way for me to earn a living, so I pursued an engineering career instead.  Over the years, I picked up a superficial understanding of general relativity and quantum mechanics by browsing through scientific journals and devouring science books aimed at lay audiences.  After I retired as a practicing engineer, I pursued those topics in earnest to see if I could crack the reality code, while applying a common-sense approach that I had mastered as an engineer.  

All human beings are endowed with the power of reason, and I used it to examine a number of statements that scientists repeat over and over, such as "quantum mechanics and general relativity are incompatible" and "black holes exist" and "the brain produces consciousness."   To my surprise, I discovered there was no basis for many "facts" widely accepted by scientists, so I began searching for a different scientific paradigm that could correctly solve the reality riddle.  My approach to the problem was based on what Sherlock Holmes famously remarked to Dr. John Watson:  "How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?" I had taken an information theory course in college based on the pioneering work of the great Claude Shannon.  Applying the knowledge I gained from this course led to the realization that there is the deep underlying connection between information theory and quantum physics, where the the so-called "laws" of classical physics emerge naturally from the law of large numbers and the central limit theorem.  Furthermore, it convinced me that information is not a description of physical things; instead it represents uncertainty, which is nothing other than a state of consciousness.  Following this course led me to accept the proposition articulated by James Jeans that the universe is a great thought instead of a great machine. 

In the end, I doubt Ultimate Truth will be in the form of one or more equations, but rather an idea that may be impossible to express through mathematics or human language.  As John Wheeler stated,  "Behind it all is surely an idea so simple, so beautiful, that when we grasp it - in a decade, a century, or a millennium - we will all say to each other, how could it have been otherwise? How could we have been so stupid?"  My journey isn't over, but what I've discovered so far is documented in essays you can download below, plus some additional comments that follow them on this web page.

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And Here Are the Essays ...

. . . presented below in the order they were written over more than a decade.  Reading the essays in chronological order, you will notice my philosophy concerning science has evolved considerably over the years, progressing from "thing-in-itself' realism into a form of idealism where all things are re-created in the eternal "Now" moment.  Most of my essays have lettered appendices I added to the original essays, sometimes over a period of years.  These appendices also reveal an evolution in thinking, and they might directly contradict conclusions I had reached previously.  I allow those glaring inconsistencies to remain plain view, for as Ralph Waldo Emerson stated, "A foolish consistency is the hobgoblin of little minds, adored by little statesmen and philosophers and divines.  With consistency a great soul has simply nothing to do.  He may as well concern himself with his shadow on the wall." 

As a retired engineer and an amateur scientist, I am very familiar with the laws of nature and the scientific method.  The astounding technological advances of the 20th century were a direct result of scientific inquiry.  Einstein's theory of relativity, quantum mechanics, and the standard model were all amazing feats of human intellect.  Yet despite this amazing progress, I have the uneasy feeling that science is incapable of solving the deeper mysteries of reality, and in fact may be leading mankind away from the fundamental truth.  For the most part, science has devolved into building models that mimic empirical data (which is basically what engineers do) instead of creating theories based on first principles and then using empirical data to validate or falsify them.  I wrote down my thoughts on these matters in an essay "Is Science Solving the Reality Riddle?"  An image of essay's cover is shown below, along with a link to the essay.  You are encouraged to view or download any of my essays free of charge and share them with whomever you want. 

Click Here to Download "Is Science Solving the Reality Riddle?" 

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After some degree of reflection, I was able to identify the problem posed in "Is Science Solving the Reality Riddle?"  I now believe that the current reductionist paradigm that forms the basis for all of modern science needs to be fundamentally changed.  I reached the conclusion that order, including what we consider to be the "laws of nature," emerge from chaotic processes.  These ideas are expressed in a follow-up essay "Order, Chaos and the End of Reductionism."  An image of the cover is shown below with its link the direct download.  If you enjoyed my first essay, I think you'll enjoy the second one even more.

Click Here to Download "Order, Chaos and the End of Reductionism" 

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After completing "Is Science Solving the Reality Riddle?" and "Order, Chaos, and the End of Reductionism," I thought it would be a good idea to summarize what I concluded in a third essay, entitled "Manifesto of an Amateur Scientist."  The "Manifesto" is very much a work in progress, so whenever a new idea or conclusion pops into my head or I read about one I like, I number it and write it down.  Some of the earlier ideas seem to be contradicted by the later ones, but that's okay.  I left the earlier ones in the essay anyway, but red-lined some of them if they turned out to be completely wrong so as not to mislead the reader.  I believe that every rational scientist, whether a professional or an amateur, needs to be prepared to modify his or her beliefs from time to time. Those who aren't willing to budge away from long-held beliefs in spite of a mountain of contradictory evidence are practicing a form of religion instead of science.  The image of the essay's cover and the link to the direct download are shown below.  Feel free to view, download, and share it.

Click Here to Download  "Manifesto of an Amateur Scientist" 

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Shortly after starting "Manifesto of an Amateur Scientist," I felt a need to vent.  Science is under attack by religious fundamentalists who seem to think that teaching science infringes on their First Amendment rights, and also by special interest groups who think that addressing climate change somehow infringe on their right to pollute and endanger the planet.  I thought it was time to set the record straight, at least on the issue of climate change.  Unfortunately, scientists are terrible at public relations, and seem to be unable to explain their theories to the general population in a straightforward, believable fashion.  I took a stab at explaining climate change without using the misleading term "greenhouse effect."  While I was at it, I took a close look at the ozone depletion conjecture, and concluded it was based entirely on voodoo chemistry that violates the second law of thermodynamics.  The bottom line is that scientists can't win over the public by making up stuff; they have to make their case by stating facts.  This is explained in my essay "Global Warming Is Real."  Below are the essay's cover and its link to the direct download.

Click Here to Download "Global Warming Is Real" 

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The next two essays delve into topics that are more mystical and metaphysical than scientific.  The first essay, "Are We All Alone?" is an inquiry of whether humans were ever in contact with supernatural or alien beings.  The second essay is "Teachings from Near Death Experiences," which tries to explore whether consciousness can and does survive physical death. I tried to stick with scientific principles as much as possible when examining these topics, recognizing of course that these areas are normally not considered part of science.  I hope you'll enjoy taking a "Magical Mystery Tour" through these two essays. 

Click Here to Download "Are We All Alone?" 

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Click Here to Download "Teachings from Near Death Experiences" 

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There has been a flurry of activity lately surrounding the latest black-hole information paradox -- the AMPS firewall.  This has caused one of the leading theoretical physicists of our time to question the validity of Orthodox Holology:  Stephen Hawking published a very brief paper shortly before his death, suggesting that the sacred razor-thin event horizon may be a lot fuzzier than everyone had previously thought.  I believe he became disillusioned with the concept of a classical black hole, which he helped invent, due to a mounting number of paradoxes and internal contradictions associated with the event horizon.  His modified version of a black hole was derisively called a "fuzzball" by the orthodox scientific community.  The properties of Hawking's fuzzball are similar to those of Abhas Mitra's eternally-collapsing object (ECO).  Sadly, the collective cognitive dissonance of scientific community is a wonder to behold.  They have paid little or no attention to either Hawking's final paper or Mitra's elegant proof that true black holes exist only in the imaginations of mathematicians.  In the following essay, I claim that the black hole event horizon cannot possibly exist, and I give a very concise proof of why this must be so.  An alternative view of large, collapsing celestial objects is proposed. 

Click Here to Download "Why There Are No True Black Holes" 

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Nature is quirky.  Whenever the puzzle pieces don't quite match up, She changes them so they will fit.  The results often seem bizarre and nonsensical, but the more you study Nature, the more you realize how profoundly wise Nature is.  It all started with a thought experiment Albert Einstein said he imagined around the age 16.  The young Einstein wondered what would happen if he chased a light beam and caught up with it.  This essay was inspired by the National Geographic television series "Genius," which is itself a work of genius.  The essay describes two of the most important discoveries in science, both made by the same man over the course of a decade (1905 - 1915).  This is directed at an audience of amateur scientists like myself, approaching the special and general theories of relativity from underlying principles and deriving as much as possible using basic geometry and a bit of calculus.  I did not go into the depth needed to become a true "relativist," which would require a working knowledge of four-dimensional curvatures and tensor algebra.  Nevertheless, I think any amateur scientist would get something worthwhile from this essay.

Click Here to Download "Relativity in Easy Steps" 

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For a long time, theoretical physicists have dreamed of the day when the general theory of relativity and quantum mechanics would be combined to create the Theory of Everything. It's often stated that such a theory would be so simple and concise that the whole thing could be condensed into a simple equation that would fit on a T-shirt.  It was clear to me that classic material reductionism could not provide a path to that laudable goal, so I undertook an investigation to see what could replace it. That investigation spanned almost 4½ years, and it was documented step-by-step in my essay "Order, Chaos and the End of Reductionism."  This research led me to several dead ends, blind alleys, and self contradictions. What I ultimately discovered was that Einstein's field equations of the general theory of relativity actually provide an exact solution for the universe as a whole, but are approximations for weak-field interactions on smaller scales. Combining this principle with the principle of maximal entropy led to some surprising conclusions, summarized by a simple equation of state for the entire universe that can easily fit on a T-shirt that captures the essence of the Theory of Everything.  This equation of state is shown on the cover of my essay "The Universe on a Tee Shirt," below, with a direct link to the essay. 

Click Here to Download "The Universe on a Tee Shirt" 

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The General Theory of Relativity has some surprising hidden meanings that even its author didn't realize were there.  What I discovered through my examination of GR truly surprised me and I hope it will surprise you.  I'm sure not even Albert Einstein himself could have guessed at all the implications contained in his theory.  The key to the hidden secrets is understanding the full implications temporal asymmetry (time curvature) and the fact that the Schwarzschild metric and the Bekenstein-Hawking equation do not describe an event horizon of an isolated "black hole" within the universe, but instead they describe an expanding event horizon surrounding the entire universe − the Now moment.  Furthermore, rearranging the terms of the Schwarzschild metric at the horizon yields the thermodynamic equation T dS − dE = P dV, meaning the event horizon has thermodynamic properties of temperature, entropy, internal energy and pressure.  Recognizing the fact that we live on an event horizon is the key to unifying GR and QM.  I intended "The Hidden Secrets of General Relativity Revealed" to be a brief summary that covers a few of most significant of the hidden secrets in order to get my points across without bogging down the reader with too many facts.  Because I kept it as brief and easy to read as possible, critics could argue that the claims are based on too little evidence.  However, a much more comprehensive analysis can be found in my earlier essays, particularly "Relativity in Easy Steps" and "The Universe on a Tee Shirt."  Here I used just a smidgen of math because I know a lot of people − including myself − are intimidated by essays that have too much math in them.  I think the essay will delight the Idealists among us, and I hope it won't be too confusing or annoying to those who are still stuck in the Materialist camp.     

Click Here to Download "The Hidden Secrets of General Relativity Revealed" 

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A growing number of science authors, including Jim Baggott, Alexander Unzicker, Sheilla Jones, and Lee Smolin, have written about the so-called crisis in physics.  The ongoing quest to unify Einstein's theory of gravity and quantum mechanics has so far produced a few interesting mathematical models and elaborate sand-castle fantasies, but these have mostly proven to be dead ends.  Einstein, Bohr and the members of his Copenhagen team, Bekenstein and Hawking have provided all the necessary pieces to the puzzle and everything need to assemble them once the scientific myths and fantasies are abandoned.  The instructions for assembling those pieces into a comprehensive Theory of Everything are hidden in plain sight but the best and brightest theoretical minds can't find them because they have been accepting some long-standing myths as facts that keep pointing them in the wrong directions.  This essay exposes a few of the most egregious myths and fantasies that continue to restrain scientific progress, explained in easy-to-understand prose.  Note:  If I were to pick out one of my essays that other amateur scientists should read first, it would be "Removing Myths and Fantasies from Science."  I intentionally directed this essay to readers who have keen interests in science without having formal scientific or mathematical backgrounds.  It is relatively short and provides a summary of my other essays without having to plow through heavy mathematics. 

Click Here to Download "Removing Myths and Fantasies from Science" 

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Soon after Albert Einstein published his general theory of relativity in 1915, Karl Schwarzschild derived an exact solution of the GR field equations for a spherical gravitating body, which was modified by David Hilbert and became known as the Schwarzschild metric. This was misconstrued to be what scientists thought was the description of a "black hole."  Even after Einstein published a paper in 1939 that proved that a physical black hole is impossible based on general relativity, this false belief gained speed and spread relentlessly until it became a matter of faith among scientists, despite a long series of contradictions and paradoxes that would inevitably arise from it.  Nevertheless, a few scientists broke free from cognitive dissonance and are speaking out, notably Abhas Mitra and Laura Mersini-Houghton, who have shown that the black hole candidates (BHCs) that astronomers purportedly have found are actually very massive stars that have partially collapsed, and are in the process of shedding mass and halting their collapse before turning into black holes. It turns out that the mathematics upon which the black-hole fallacy is based is entirely sound, but the problem is misinterpreting and ignoring what the mathematics is trying to tell us. By turning the black hole inside out, the correct mathematical interpretation emerges that leads to a radical discovery revealed in the following essay.

Click Here to Download "The Inside-Out Black Hole" 

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John Archibald Wheeler was one of the last of the great scientist-philosophers.  He wore his science on his sleeve and wasn't ever afraid to go out on a limb with novel ideas or to admit he was wrong, even engaging in brainstorming sessions in front of large audiences.  One problem he encountered is how the universe could be both self-contained and logically consistent, in light of Gödel's incompleteness theorem.  This led him to conclude that we live in a participatory universe where perceptions of phenomena are created by the observer instead of being preordained as an objective reality.  He coined the term "It from Bit" as his typical terse and pithy way of referring to this hypothesis.  The following essay highlights the salient features of Wheeler's radical departure from Materialism, pointing out some very important facts about the oft-misused term "information."  These issues are discussed in several other of my essays, but they bear repeating here again because these must be properly understood in order to grasp the full depth and significance of Wheeler's hypothesis.  This essay concludes with my own extrapolation of "It from Bit" relating it to the cosmological model developed in previous my essays, as summarized in "The Amateur Scientist's Cosmology in a Nutshell" further down this page, along with a surprising discovery:  Time and causality depend on the existence of acausal quantum uncertainty!  I think this essay may be my magnum opus, the most important essay published to date on this site because it really gets to the bottom of of reality.

Click Here to Download "It from Bit"

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In 1937 James Jeans wrote, "Today there is a wide measure of agreement, which on the physical side of science approaches almost unanimity, that the stream of knowledge is heading towards a non-mechanical reality; the universe begins to look more like a great thought than like a 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."  Shortly after Jeans wrote this, the onset of WWII redirected the stream of knowledge back to the machine, as scientific research morphed into gigantic engineering projects committed to building weapons of mass destruction.  Ever since then, scientific research based on material reductionism and supported by "Big Science" exemplified by the massive LHC project has been stumbling into one blind alley after another, finally reaching its culmination in string theory.  Recently however, the stream of knowledge has begun shifting back again toward a non-mechanical, holographic model of the universe with consciousness as its foundation.  This shift is clearly reflected in the writings of John Archibald Wheeler during the decade preceding his death in 2008 and of others in the scientific establishment who lately have begun to think outside the traditional box.  This two-page essay is a capsule summary of my interpretation of a consciousness-based holographic universe.

Click Here to Download "The Cosmic Hologram" 

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In the early days of quantum mechanics, the 1920s, the so-called "wave function collapse" or "measurement problem" arose.  The problem centered around the question of at what point is the final result decided upon when a measurement of a quantum particle is made.  Some physicists believed the role of the observer was critical, and that the decision was made only when someone, preferably a human being, looked at the measurement causing the Schrödinger wave equation to "collapse."  Others, including Erwin Schrödinger himself, thought this idea was ridiculous,  Heated debates over the measurement problem have raged for almost a century without reaching a unanimous opinion among those in the physics community.  Physicists in the Copenhagen Interpretation camp, originally under the leadership of Danish physicist Niels Bohr, simply shrugged their shoulders at all the commotion and said, "Shut up and calculate."  Several solutions to the problem have been offered, such as quantum field theory, which bypasses the question of measuring quantum particles altogether by changing quantum particles into field excitations.  According to a biography of John A. Wheeler, his career was divided into three parts, the first two parts being "everything is particles" and "everything is fields."  In 1956 one of his students, Hugh Everett III, developed the many worlds interpretation (MWI) as his doctoral thesis at Princeton University.  According to MWI, the Schrödinger wave equation doesn't ever collapse.  Instead, the entire universe splits into as many parts as necessary, perhaps an infinite number, so that every possible result of a quantum measurement become realities in different universes.  A number of notable scientists have embraced MWI, although many others reject it and consider it to be a ridiculous idea.   In the essay below, I uncover a serious mathematical problem with MWI as it is currently formulated and offer my own alternative interpretation called  the "Many Alices Interpretation."

Click Here to Download "Many Alices Interpretation" 

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The following mantra is repeated over and over in scientific journals, books,  magazines and on science web sites:  "General relativity is incompatible with quantum physics."  This myth stems from two fallacies.   Fallacy number one is that gravity is a force.  Anyone who is at all familiar with general relativity should know better.  The sole reason that Albert Einstein worked on general relativity for ten long years between 1905 and 1915 was because he realized that gravity is not a force, contrary to popular opinion at the time.  If it were a force, he would have just shrugged his shoulders and said, "Well the force of acceleration of a falling object  just happens to cancel out the gravitational force for some unknown reason," and be done with it.   He recalls his realization that a falling man feels no force as "the happiest moment of my life."  Fallacy number two is material reductionism, which holds that a whole is equal to the sum of its parts.  Scientists who stubbornly cling to reductionism expect objects in the classical world to behave in similar ways as their constituent parts in the quantum world.  Unlike electromagnetism, the gravitational "force" cannot be described as an exchange of non-existent force carriers called "gravitons" and the predictable behavior of tables and chairs is not all similar to the somewhat strange indeterminate behavior quantum particles.  These observations result in the "incompatibility" myth.  I hope this essay explodes the myth and shows why the quantum and the classical worlds are actually perfect reflections of each other. 

Click here to download "Relativity and Quantum Mechanics Are Not Incompatible" 

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Physicists, cosmologists, and metaphysicists have many unanswered questions like, “How did the universe begin?”, “Are there other universes beyond our own?”, “What is the true shape and geometry of the universe?”, “What are the fundamental constituents of matter and their interactions?”, “Why is there something instead of nothing?”, and the Biggie, “How did the universe come into being?”  Some physicists brush off the last question by proclaiming it emerged from “a quantum fluctuation” in the vacuum.  But as John A. Wheeler observed, “The quantum theory of fluctuations of geometry tells us that the concepts of ‘before’ and ‘after’ lose all application at distances of order the Planck length or less.  If the concept of time fails anywhere, it must fail everywhere.”  Wheeler eventually arrived at his own conclusion, “Omnibus ex nihil ducendis sufficit unum (one principle suffices to obtain everything from nothing).”  The search for that one principle occupied much of Wheeler’s time near the end of his career, and he sometimes expressed it as a “self-excited circuit” based on the principle that “the boundary of a boundary is zero.” Gottfried Leibniz defined the fundamental unit of existence from a concept known as Monadology, wherein monads are the simplest, most basic units of existence, characterized by their internal activity, each perceiving and reflecting existence from its own unique perspective.  The following essay is explores the idea of how time and space could have emerged from nothing – a dimensionless, boundless, timeless, and spaceless Source – followed by everything else called physical reality.

Click here to download "The Source" 

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The first part of the following essay on gravity is a broad summary (of an admitted non-expert) about string theory, which began in the 1960s. It started out as a way to model quantum interactions using classical mechanics (a category error) and has morphed into a catch-all theory that is used to connect (non-existent) black holes with quantum mechanics. It has been extended to superstring theory with eleven dimensions, where gravity seems to pop out automatically, which was supposed to be the Holy Grail of Physics – the Grand Unification Theory.  String theory mathematics are judged to be “beautiful,” despite the fact it are excruciatingly difficult to perform, and its solutions don’t seem to converge. By the 1980s there were five separate string theories, when the leading string theorist, Edward Witten, proclaimed that all five were actually different flavors of one overarching theory named M-Theory. Despite failure of M-Theory to provide any testable predictions and the fact nobody knows exactly what M-Theory is, it currently “the only game in town,” although it seems that the promised theory of quantum gravity will have to wait a while longer.  As string theorist Nathan Seiberg quipped, "If there is something beyond string theory, we will call it string theory." The second part of this essay contrasts the search for gravity via string theory against a theory of gravity based on spacetime entropy and how the entropic model emerges naturally (and almost effortlessly) from the Minkowski equation and the Bekenstein-Hawking equation at the spacetime boundary. There are some surprising twists to that story, including a testable predictions that Newton’s gravitation constant, G, is not constant, and the radius of the known observable universe is twice as large as the currently-accepted value of 13.8 billion light years, which observations through the James Webb Telescope have already hinted at.   Here’s another twist:   Based on entropic gravity, G in the Beginning was 10^39 times larger than G in the present, closing the so-called hierarchy problem that troubles physicists.

Click here to download "Gravity: Superstrings or Entropy?" 

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The next very short essay is way out of character and off-topic from my others, but it’s a topic I’ve given a great deal of thought about over my adult life; namely investing in the stock market. I’m certainly not a stock “guru” by any means, but I have an excellent B.S. detector, and this essay exposes some of the B.S. stock market fantasies that people buy into.  It explains why stock trading alone is a zero-sum game equivalent to poker, why trying to undo bad investment decisions made in the past is a terrible economic strategy, and why the winners in the stock trading game are in the minority.  On a positive note, I’m convinced there is a strategy where investors can base their decisions on the true values of shares in real time instead of basing them on unrealistic current prices and over-promised future prices.  In short, it is a simple arbitrage method that spots mismatches in those true values of shares in real time and will steer investors into “buying low and selling high” automatically without having to use a crystal ball to figure out what to buy and when to sell it.  Anyway, here is my unsolicited (and unbiased) advice for what it’s worth.

Click here to download "How to Play the Stock Market" 

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I hope you find my essays above interesting even if you don't necessarily agree with them.

Yours truly,

The Amateur Scientist

(shown above at the start of his career)

Feedback

If you would like to comment or questions about these essays or anything else on this site, you can send an email to this address:  Amateurscientist@hotmail.com  

I'll try to respond to all serious inquiries, but please be patient if I don't get back to you right away.

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Further Reading

If you think some of my ideas are controversial, check out these mind-blowing articles by Robert L. Kurucz of the Harvard-Smithsonian Center for Astrophysics:

Elementary Physics in the Cellular Automaton Universe 

Radiatively-Driven Cosmology In The Cellular Automaton Universe

Conventional wisdom among cosmologists states that galaxies aggregated around spherical halos made of dark matter.  In my essay "Is Science Solving the Reality Riddle?" I show why it is highly improbable that such dark-matter halos could form naturally.  

I recently stumbled upon a paper by Pavel Kroupa that seems to disprove the very existence of dark matter halos:

The Dark Matter Crisis: Falsification of the Current Standard Model of Cosmology

Please check out Trespassing on Einstein's Lawn, by Amanda Gefter, another true amateur scientist.  Her book is simply a joy to read.  It tells a story of a father/daughter pursuit of what is real, which they decided must be invariant, or the same for all observers.  They made a preliminary list of potential invariants on a napkin, but crossed them off one at a time when they discovered they were observer-dependent.  In the end, they determined that nothing in the universe is invariant; hence nothing in the universe is real!  Consciousness wasn't included on Gefter's preliminary list of invariants, but it turns out that pure consciousness is the only thing that isn't observer-dependent, and therefore it's the only thing that's real.  I believe deep scientific explorations ultimately all lead to the conclusion that idealism is the correct interpretation.

Abhas Mitra is an astrophysicist and an adjunct professor at Bhabha National Science Institute in Mumbai, India.  He's from the "old school" and knows the difference between physical reality and making assumptions.  He questions conventional wisdom, exposing fallacies about things others take for granted, such as the big bang theory and black holes.  His papers are controversial, but as far as I can tell nobody has found any flaws in them.  If you're able to handle the technical and mathematical details, I think you'll enjoy these three papers:

Non-occurrence of Trapped Surfaces and Black Holes in Spherical Gravitational Collapse: An Abridged Version

No Uniform Density Star in General Relativity

The fallacy of Oppenheimer Snyder Collapse:  No General Relativistic Collapse at All, No Black Hole, No Physical Singularity

In addition, in 2021 Mitra published a well-researched book entitled The Rise and Fall of the Black Hole Paradigm.   In it, he explains why no object having mass can be contained within its Swarzschild radius and goes on to list all the physicists and mathematicians who have reached the conclusion he did:  That the so-called black hole event horizon is non-physical and the mass of a true black hole must be zero.  The book is easy to understand and it has no abstruse mathematics to confuse the reader.

Alone in the Universe, by John Gribbin, echoes many of the same conclusions in my essay "Are We All Alone?"  It presents a very sound rationale why our solar system, its location in the galaxy, and the Earth itself are very special -- unique perhaps -- and how unlikely it is for a technological civilization like ours to emerge anywhere else but here.  In fact Gribbin believes we may be utterly alone in the Milky Way, although I'm not quite that pessimistic.  I do agree with him on another point:  There will be no "second chance" for a human-like civilization to arise if there is another mass extinction on Earth, which is quite likely to happen.

The Life and Death of Planet Earth, by Peter Ward and Donald Brownlee, presents the "big picture" of life on Earth and its climate over the past half billion years.  We are currently on the knife's edge of climate change, and the future of life on Earth does not look good.  This book provided reference material for Appendix B of my essay "Global Warming is Real."  This (the book, not my essay) is a must read.

Marina Cortês and Lee Smolin co-authored an award-winning paper The Universe as a Process of Unique Events, which completely demolishes the deeply-flawed notion of a block universe.  Congratulations to Drs. Cortês and Smolin for winning their prize, and keep up the good work!

Shoichi Toyabe of Chuo University in Japan, along with several colleagues, performed a truly ground-breaking experiment, where they literally created energy from information as described in This Article.  In my opinion, this experiment ranks up there with the experiments performed by Alain Aspect and others that demonstrated violations of Bell's inequality and dispelled for once and for all the notion that a quantum wave function contains local hidden variables.  The Toyabe experiment demonstrates that a physical "something" can come from a non-physical "nothing," in agreement with the Szilard equality.  I believe this explains how the universe came into being.  Instead of a singular, explosive big-bang event where all mass-energy was created suddenly at once, creation might involve a much more gradual evolution where mass-energy condenses from a vacuum filled with information, a process continuing up until the present.   

Natalie Wolchover is the author of an article in  "Quantum Information Theory" entitled The New Thermodynamic Understanding of Clocks. "Space,"  Albert Einstein said, "is merely what we measure with a ruler; time is what we measure with a clock."  But there is a growing number of researchers who are beginning to realize that time is inextricably tied to entropy, a.k.a. information.   According to Marcus Huber, leader of the Huber Group at the Institute for Quantum Optics and Quantum Information - Vienna, a clock is actually a thermal machine.  “The irreversibility [of a clock] is really fundamental,” Huber said. “This shift in perspective is what we wanted to explore.”  Gerard Milburn of University of Queensland in Australia flatly stated, “A clock is a flow meter for entropy."  If a clock measures time and is also a flow meter for entropy, then time must equal the flow of entropy.  These statements mesh with the conclusions in several of my essays.  The Now moment is an expanding two-dimensional surface perpetually saturated with entropy, and the surface density of entropy, dS/dA, is proportional to time.  Taking the asymmetry of time into account causes collateral damage from Noether's theorem:  The law of conservation of mass-energy is an approximation that only applies during time intervals when changes to the radius of curvature of the Now surface, Δr/r, are small, and the total mass-energy of the expanding universe must increase.

E.T. Jaynes of Washington University in St. Louis, MO wrote a mind-bending and oft-cited paper The Gibbs Paradox which discusses a scenario where the mixing entropy of two dissimilar gases can be reduced by applying an observer's ability to distinguish between atoms of the mixture and thereby enabling the physical process on a micro level.  Jaynes summarized this scenario by noting, "… our greater knowledge resulting from the discovery of the [ability to distinguish between different atoms] leads us to assign a different entropy change to what may be in fact the identical physical process, down to the exact path of each atom.  But there is nothing 'unphysical' about this, since that greater knowledge corresponds exactly to – because it is due to – our greater capabilities of control over the physical process."  Nevertheless, I think this example shows the physical entropy of a substance is somehow related to "unphysical" uncertainty in the mind of an observer, and this implies the existence of an observer-dependent reality.

James H. Jeans published The Mysterious Universe in 1930.  This remarkable book shows that Jeans and many physicists of that era were way, way ahead of their times.  In fact in my opinion, Jeans was far ahead of most of today's physicists even though his book contained some minor inaccuracies.  For example, Jeans anticipated fusion of four hydrogen atoms into a helium nucleus consisting of four protons and releasing an amount of energy equivalent to the decrease in mass, although the neutron and the strong force had yet not been discovered.  He correctly noted that gravity is not a force, unlike physicists of today who mistakenly keep insisting it is.  Although quantum theory was just in its infancy in 1930, Jeans could see its intimate connection with general relativity, unlike those who currently spout nonsense about a fundamental "incompatibility" between quantum mechanics and gravity.  Like Plato and Aristotle, who are sometimes dismissed as ignoramuses by today's scientific standards, scientists of Jeans' era were much closer to ultimate truth than they are given credit for.  The final chapter of The Mysterious Universe presents the concept of a universal mind, from which human consciousness emerges, and which brings the "physical" universe into existence as a great thought through an act of continuous creation.  I believe this concept is superior to Wheeler's interpretation of retroactive creation by human consciousness. 

Donald Hoffman's The Case Against Reality presents a strong case in support of the hypothesis that our world of tables and chairs is an illusion.  Space, time, energy, and material objects are mere symbols or icons that allow us and other living creatures to respond appropriately to the underlying reality of the Cosmic Hologram, which would otherwise be entirely beyond our comprehension or ability to interact with, and make it impossible to survive.  Imagine  what it would be like if you had to manipulate ones and zeros in your laptop computer's memory instead of  being able to simply click, drag and drop icons on the screen.

Thomas Nagel's 15-page essay What Is It Like to Be a Bat? tackles René Descartes' dualism and David Chalmers' hard problem of consciousness.   His conclusion is that it's not possible to explain any conscious experience in terms of physicalism.  The closer we get to treating a conscious experience objectively, the farther away we get from the experience itself.

Christian Sundberg's book A Walk in the Physical states unequivocally based on his personal experience that being in physical reality is, as Kahlil Gibran described it, being awake in the "deeper dream."  Make of it as you will, but I believe this book encapsulates the principle of idealism.

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 Quotables

Ray Cummings (1887-1957) made this statement in his sci-fi book The Girl in the Golden Atom:  “Time is what keeps everything from happening at once.”  I think this is a perfect explanation of why the universe has time, which is its most indispensable feature. 

John Archibald Wheeler (1911-2008) latched on to Cummings' statement and expanded it to explain why the universe has space.  He said, “Space is what keeps everything from happening to me.”  Wheeler is remembered for making succinct statements throughout his long career.  This one stands out:  "Omnibus ex nihil ducendis sufficit unum."   (One principle suffices to obtain everything from nothing.)  The quest for that one Principle became his lifelong obsession.  Further down the page you will find my interpretation of one of his favorite remarks, "The Boundary of a Boundary is Zero."

Emmy Noether (1882-1935) explained why space has three dimensions:  According to her theorem, there is a relationship between conservation of angular momentum and rotational symmetry.  Angular momentum is the cross product of two vectors, and this cross product can only be represented properly in three dimensions, which is why a physical universe having rotational symmetry cannot have more or less than three dimensions of space.  Time has a single dimension because it is asymmetric with a preferred direction.  All of this is covered in detail in Appendix M of my essay “Order, Chaos and the End of Reductionism.”

Karl Popper (1902-1994) warned about taking shortcuts in order to advance pet theories: “For if we are uncritical we shall always find what we want: we shall look for, and find, confirmations, and we shall look away from, and not see, whatever appears to be overwhelming evidence in favor of a theory which, if approached critically, would have been refuted.”

Yogi Berra (1925-2015) once said, “In theory, practice and theory are the same. In practice, they're different.” This serves to warn us about gedanken experiments used by theoretical physicists to prove a point, especially when those experiments could never be carried out in practice because they're logically flawed or they violate the laws of physics.  Yogi led a secret life as a quantum physicist.  Once he was giving Joe Garagiola directions to his house and he said, "When you come to a fork in the road, take it."  He didn't tell Joe whether he should take the left fork, the right fork, or both of them; he left the choice entirely up to Joe, just as any true quantum physicist would.  Yogi understood quantum uncertainty, saying, "It's tough to make predictions, especially about the future" and, "The future ain't what it used to be."  But remember Yogi said he didn't say half the things he said, so we can't be really sure if he said them.  

Bertrand Russell (1872-1970) hit the nail on the head: “The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.” Being certain is not the same as being right.  (See Akhenaten, below.)

Akhenaten (1380-1335BCE):  "The wise man doubteth often, and changeth his mind; the fool is obstinate, and doubteth not; he knoweth all things but his own ignorance."  Human progress in every field, especially science, comes through a few brave, doubting souls who question conventional wisdom that is set in stone.

Publius Ovidius Naso (4BCE-18CE):  "A new idea is delicate.  It can be killed by a sneer or a yawn; it can be stabbed to death by a quip and worried to death by a frown on the right man's brow."

Jonathan Swift (1667-1745):  "When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him."

Upton Sinclair (1878-1968) told an audience, “It is difficult to get a man to understand something, when his salary depends upon his not understanding it.” In addition to salaries, there are NSF research grants, book royalties, lecture fees, and awards and prizes that keep scientists from understanding things such as why there are no true black holes.

David Chalmers  (1966 - ):  “We won't have a theory of everything without a theory of consciousness.” 

Thomas Nagel (1937 - ):  "Materialism is incomplete even as a theory of the physical world, since the physical world includes conscious organisms among its most striking occupants."  On the other hand, idealism is a complete theory that regards matter as derivative from consciousness.  See the following quotables from Sir James Jeans, Erwin Schrödinger and Max Planck.

Sir James Jeans (1877-1946) was a renowned physicist who came to the conclusion that reality is pure mathematics conceived by a universal mind. “The making of models or pictures to explain mathematical formulae and the phenomena they describe, is not a step towards, but a step away from, reality; it is like making graven images of a spirit.”  Making models is what engineers are supposed to do, not true scientists.

“Today there is a wide measure of agreement, which on the physical side of science approaches almost unanimity, that the stream of knowledge is heading towards a non-mechanical reality; the universe begins to look more like a great thought than like a great machine.  Mind no longer appears as an accidental intruder into the realm of matter; we are beginning to suspect that we ought rather to hail it as a creator and governor of the realm of matter – not of course our individual minds, but the mind in which the atoms out of which our individual minds have grown exist as thoughts.”  The last phrase shown in italics is almost always omitted in the literature, but it definitely appears in the second edition of The Mysterious Universe.  It's possible Jeans added the phrase in the later edition to clarify his position that the creator and governor of the realm of matter is a Universal Mind, opposed to the minds of individual observers, as postulated by John Wheeler and others.  

The "wide measure of agreement, which on the physical side of science approaches almost unanimity" is reflected in statements by Schrödinger and Planck quoted below.

Erwin Schrödinger (1887-1961) was an idealist, as shown by this quote taken from My View of the World:  "If finally we look back at that idea of Mach, we shall realize that it comes as near to the orthodox dogma of the Upanishads as it could possibly do without stating it expressis verbis. The external world and consciousness are one and the same thing." 

Max Planck (1858-1947) made many quoteworthy statements in the course of a very long and productive life.  Here are a few examples.

"I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness."  (It equals bit.)

"New scientific ideas never spring from a communal body, however organized, but rather from the head of an individually inspired researcher who struggles with his problems in lonely thought and unites all his thought on one single point which is his whole world in the moment."  (Science is too important to be left to the professionals.)

"A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it."  (In short, science advances one funeral at a time.)

Claude Shannon (1916-2001), the Father of Information Theory, recalled his predicament of deciding what to name his invention:  "My greatest concern was what to call it. I thought of calling it 'information,' but the word was overly used, so I decided to call it 'uncertainty.'  When I discussed it with John von Neumann, he had a better idea. Von Neumann told me, 'You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one really knows what entropy really is, so in a debate you will always have the advantage.'"  

Information = Uncertainty = Entropy

Alan Watts (1915-1973) had the feeling of being carried along by the edge of the universe – the Now. He is quoted as saying, “I have realized that the past and future are real illusions, that they exist in the present, which is what there is and all there is.”

Isaac Newton (1643-1727) offered some advice about biting off more science than can be chewed. "What certainty can there be in a Philosophy which consists in as many Hypotheses as there are Phaenomena to be explained?  To explain all nature is too difficult a task for any one man or even for any one age.  'Tis much better to do a little with certainty, & leave the rest for others that come after you than to explain all things by conjecture without making sure of any thing."   

Albert Einstein (1879-1955) pondered the following question: "What I'm really interested in is whether God could have made the world in a different way; that is, whether the necessity of logical simplicity leaves any freedom at all."  If scientists proceed under the assumption that the answer to this question is no, they will eventually arrive at Truth.  Otherwise, they will flounder around embracing one flawed theory after the next and never discover the true Order of nature.

Einstein also had this to say about some of the practitioners of science of his time.  "Many kinds of men devote themselves to Science, and not all for the sake of Science herself.  There are some who come into her temple because it offers them the opportunity to display their particular talents.  To this class of men science is a kind of sport in the practice of which they exult, just as an athlete exults in the exercise of his muscular prowess.  There is another class of men who come into the temple to make an offering of their brain pulp in the hope of securing a profitable return.  These men are scientists only by the chance of some circumstance which offered itself when making a choice of career.  If the attending circumstance had been different they might have become politicians or captains of business."

Einstein believed that mathematics is the essential language of science.  However, he warned that there always will be gaps between mathematics and reality:  "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” 

Here's another wonderful quote from Herr Einstein.  "The intuitive mind is a sacred gift and the rational mind is a faithful servant.  We have created a society that honors the servant and has forgotten the gift."  Today's "industrial science" has replaced true visionaries, like Einstein and John S. Bell, with left-brain thinkers with rational minds.  Rational minds are very good at inventing new patterns, whereas the intuitive mind is much better at recognizing patterns that already exist.  Even Einstein himself fell into the trap set by rational thinking, and wasted the latter part of his career trying to invent a theory that unifies general relativity with quantum mechanics when his sought-after unification was staring him right in the face (see my essay  "The Universe on a Tee Shirt" ).

Arthur Eddington (1882-1944) understood that the second law of thermodynamics is not just some statistical "tendency" for entropy to increase, as is purported in many modern popular science books.  Rather, it is the Law of Laws that underlies all of nature.  Eddington said, "The law that entropy always increases holds, I think, the supreme position among the laws of Nature.  If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations.  If it is found to be contradicted by observation - well, these experimentalists do bungle things sometimes.  But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation."  Nothing can occur in a static universe without expansion, and entropy must increase in order for the universe to expand.  In short, time = increasing entropy.

J.B.S. Haldane (1892-1964) was a British polymath, whose main contributions were in the fields of biology, genetics and statistics.  I believe he was an amateur scientist at heart because he had an inherent mistrust of what is perceived through the senses, and thus he didn't pretend to have all the answers.  In a collection of essays entitled "Possible Worlds" published in 1927 he wrote, "Now my own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose."  There is some truth to this statement – the human mind cannot possibly comprehend the true nature of the universe as long as comprehension is limited to what can be perceived through the senses.

Leonard Susskind (1940- ) would sometimes start off his lectures saying, "I don't care if you agree with what I say.  I only want you to remember that I said it."  Then he would say a whole bunch of things that were vaguely mad, as the British science writer Jim Baggott would later recall.  I didn't agree with a lot of things Professor Susskind said either, especially when he talked about entangled black holes, wormholes, and other sci-fi fantasies, which were almost always included in his talks.  But I admired the fact that he had confidence his ideas would ultimately be proven to be true, even if nobody else believed they would, and he was willing to go out on a limb to promote them. I'm like that too, knowing that very few of my ideas promoted on this site will be believed until after I'm long gone from the Earth.

An Anonymous Physics Professor:  "I've always had a sense of guilt over flunking students for not knowing what was later proven to be false." I wonder how many students were flunked for not knowing string theory or the standard cosmological model?

Gottfried Wilhelm Leibniz (1646-1716):  "Every person or substance is like a small world expressing the large world."  Leibniz seems to be describing a holographic, fractal universe, similar to the expression "as above, so below," where the hologram (above) is reflected in all of the parts of the holographic image (below) and vice versa.  If the universe really is holographic, then everything should have a dual nature – a localized, four-dimensional holographic image along with a non-local hologram.  A dimensionless quantum reality expressed through relativistic, dimensional phenomena. Interestingly, the human brain is divided into a left hemisphere, which relates to an individual identity, separated from other identities by space and time, and a right hemisphere, more in tune with a holistic, universal, group identity.  It seems the two hemispheres are often at odds with each other, resulting in much human suffering.  I think we may find "enlightenment" through introspection, integrating two minds into a harmonious One:  "Let he who seeks continue seeking until he finds.  When he finds, he will be troubled.  After he is troubled, he will be astonished, and he will reign over All." - Logon 2, The Gospel of Thomas.

Eric Hoffer (1902-1983):  “We can be absolutely certain only about things we do not understand.”  As a practicing engineer, I was absolutely certain the materialist-reductionist-empiricist approach could solve all scientific riddles.  My absolute certainty about this eroded significantly as I started to understand those riddles.

Elbert Hubbard (1856-1915):  "The recipe for perpetual ignorance is:  Be satisfied with your opinions and content with your knowledge."  Those engaged in the scientific quest can never be 100% certain about prevailing theories and must continuously put them to the test.  To the perpetually ignorant masses, who never question their own opinions, the questioning ethos of the scientific method shows a weakness instead of its abiding strength.

Richard Feynman (1918-1988):   "I would rather have questions that can't be answered than answers that can't be questioned."   Leaving a hard question unanswered  is always preferable to jumping to a conclusion based on an appeal to ignorance, which almost always leads to the wrong answer.

Galileo Galilei  (1564-1642):   "In the sciences, the authority of thousands of opinions is not worth as much as one tiny spark of reason in an individual man."   Galileo had plenty of experience with opinions of authorities (the Roman Church) and he himself had much more than just a spark of reason.

Hunter S. Thompson (1937-2005):  "Yesterday's weirdness is tomorrow's reason why."   Some people are of the opinion that quantum mechanics is weird, and that it is therefore incompatible with classical physics.  What they don't realize is that quantum weirdness is the reason why classical physics  works.

Yoko Ono (1933 - ):  "A dream you dream alone is only a dream.  A dream you dream together is reality."  This is a pretty good description of Idealism.

Kurt Gödel (1906-1978) :  “Either mathematics is too big for the human mind or the human mind is more than a machine.”   There are certain things humans can figure out that no machine (AI) can do based on an algorithm, regardless of how large, complex or "intelligent" the algorithm may be.  You can follow This Link for more on this topic.  Also, see the section entitled "Gödel's Universe" further below on this website.  He also said, "I don't believe in empirical science. I only believe in a priori truth," meaning that there are a priori truths that are completely inaccessible through scientific observation.  For example, we see ourselves as being in the center of an expanding Euclidean sphere looking outward toward the edge instead being on the edge of an expanding hyperbolic sphere looking inward toward the center.  This is the reason why cosmology is such a mess:  It is because cosmologists base their models of the universe on what they see instead of what actually is.

Werner Heisenberg (1901-1976):  "Not only is the Universe stranger than we think, it is stranger than we can think."  Since the geometry of the universe is hyperbolic instead of Euclidean, there is no possibility that we can ever form a mental image of what it actually is.

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Misquotations

I really get annoyed when famous scientists are misquoted by those who want to borrow someone else's reputations to push their own agendas.  Einstein is often misquoted as objecting to quantum mechanics on the grounds that it invokes "spooky action at a distance."  Einstein never uttered those words.   He wrote a letter to Max Born in 1947 where he said physics should represent reality in time and space, free from spukhafte Fernwirkung, which is properly translated from German into English as "spooky long-range effect."   An effect is not the same as an action.  As a matter of fact, long-range quantum effects, not actions, must be instantaneous (spooky) in order to prevent someone from using them to send faster-than-light messages (see my essay "It from Bit" Pp 12-13).  

Physicists who are proponents of entangled black holes, time tunnels, wormholes, and other sci-fi fantasies are fond of calling them "Einstein-Rosen bridges," fraudulently suggesting that Einstein endorsed such nonsense.  The source of this fanciful term was a paper written in 1935 entitled, "The Particle Problem in the General Theory of Relativity," where Einstein and Nathan Rosen attempted to equate the known elementary particles (there were only four of them at the time) with tiny black holes as defined by the exterior Schwarzschild metric.  They realized this produces two singularities at r=0 and r=rs, but those singularities could be eliminated with a clever mathematical trick of the tail known as a change of variable.  Substituting u2 = r – 2m into the Schwarzschild metric rendered the solution smoothly analytical over the range -∞< u<∞.  This produced two congruent sheets; one with u<0 and one with u>0, which some modern physicists completely misrepresent as as being two separate regions of the universe (or possibly two separate universes) connected through a wormhole, aka an Einstein-Rosen bridge.  It is important to note that u is not even a physical dimension; it's the square root of a distance, which is physically meaningless.  (One might ask:  What is the distance of the square root of one meter?)  Furthermore, if those physicists had bothered to read the Einstein-Rosen paper, they would find out that they explicitly warned against mistaking u<0 and u>0 for two different regions of space:  "If we consider once more the solution from the standpoint of the information we have acquired from the Schwarzschild solution, we see that there also the two congruent halves of the space for x1<0 and x1>0 can be interpreted as two sheets each corresponding to the same physical space [emphasis mine]."  It should also be noted that Einstein-Rosen placed the term "bridge" in quotes, referring to the particle being modeled and not a wormhole. 

The following misquote is attributed to Erwin Schrödinger.  "The total number of minds in the universe is one. In fact, consciousness is a singularity phasing within all beings."  Unfortunately, he never said it.  The giveaway is the phrase "phasing within all beings" which is gobbledygook.  Nobody has provided a source for that quote, which first appeared on the Internet in 2016, although Schrödinger died in 1961.  Apparently, somebody who believed in a universal mind simply fabricated this quote by the famous physicist in order to validate their belief.    On the other hand, those who don't believe in a universal mind omit the part of a statement by James Jeans where he strongly suggests a universal mind is the creator and governor of the realm of matter.  By the way, when I asked the AI app ChatGPT where this statement came from, it attributed it to Hungarian philosopher Ervin László.

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The  Great Scientific Debate

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A Metaphor of Science

Albrecht Dürer was a 16th century German artist who created the engraving entitled “Melancholia” shown above. Some believe "Melancholia" was a self portrait, although I really doubt it was. The angel is surrounded by tools and measuring instruments, and she seems to be staring at a stone.  No, Dürer didn't draw in the dashed line; I did that.   The stone has sides in the shape of a pentagon, forming a Platonic solid known as a dodecahedron, which according to the cosmology of ancient Greece, symbolized the universe.  (There were four other Platonic solids:  The tetrahedron, the hexahedron, the octahedron, and the icosahedron, symbolizing the four elements of fire, earth, air, and water.)  

A ladder ascends to Heaven, but the stone is in the angel's way, causing frustration and melancholia.  Hence, the stone represents unsolvable riddles of the universe that block the mind from ascending the ladder of knowledge.  Although Dürer’s sad angel might have been a self portrait, I think she's really a portrait of scientists, both professional and amateur, who are frustrated and depressed because they are unable to fully solve the riddles of the universe.  

Of course, there is an obvious question:  Why would an angel need to climb a ladder when she has wings that enable her to fly?  I like to think of the melancholy angel staring at the stone as a metaphor for scientists clumsily trying to uncover the deep secrets of the universe solely through physical experimentation and observation.  This often just produces disparate sets of data that seem arbitrary, contradictory and confusing.  Instead of staring at stone and hoping it moves away from the ladder, we can use our wings of insight to soar above the stone and understand the reason (λόγος) for it, which is hidden from observation.  This is the only way to penetrate the stone, connect the dots and find the truth within it.

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Embracing the Crazy

In 1979, John Wheeler gave a final lecture on quantum measurement at the University of Texas in Austin.  An article appeared 30 years later in Physics Today written by three attendees at that lecture, who remembered 17 numbered statements Wheeler had written on the blackboard that day (see page 44 of This Article).  Here were the first three of them:

1.  We don't understand how the universe came into being.

2. We will first understand how simple the universe is when we recognize how strange it is.

3.  When we understand how it came into being it will seem so compelling that we will all say how stupid we have been.

The key to understanding the universe is to recognize how crazy it is. To do this, we cannot confine our thinking to what common sense tells us and what seems obvious based on perception.  When we find the answer, we discover that although it is contrary to common sense, it becomes so obvious that we cannot imagine how we missed it.  The "connect the dots" puzzle below illustrates this point.  The object of the puzzle is to connect all nine of the dots using no more than four straight lines connected end-to-end.  

Many people get frustrated by this puzzle because they assume the lines must stay within the 3x3 box when connecting all nine dots, which turns out to be impossible.  When they are shown the solution, below, some people object saying, "Nobody said we could go outside the box!"  Well, nobody said they couldn't.  We can't solve the puzzle by following an old rule that originally seemed so "obvious" and "common-sense" because it just won't work.  A new rule allowing  us to "go outside the box" is now so obvious we wonder how we could have missed it. 

The White Queen in Lewis Caroll's Alice in Wonderland  said, "Why, sometimes I've believed as many as six impossible things before breakfast."   According to quantum theory, there are six or possibly more impossible things we must believe before we can begin to understand the universe.  Here are a few of them.

• Quantum states do not exist until they are observed.

• Quantum objects cannot be  entangled with more than one other quantum object.

• Quantum influences travel instantaneously.

• Unknown arbitrary quantum states cannot be copied.

• Quantum information can never be lost or erased.

Some physicists believe quantum theory is crazy because it contradicts what our perception of reality tells us is "common sense."  For example, it's commonly believed that quantum influences traveling instantaneously must violate relativity because faster-than-light travel is the same as going back in time.  The truth of the matter is, however, that quanta themselves do not exist in either time or space, which seems nonsensical.  But there is a very important reason why quantum influences must travel instantaneously:  Contrary to common sense, if they did travel at speeds below infinity, this would make it possible to violate relativity by sending signals through space faster than light and change the past – the very thing most people would assume would happen if they travel instantaneously!  

The nine dots in the puzzle above represent the physical universe, which we assume is the sum total of everything, like the angel staring at the stone in Dürer's "Melancholia."  The four straight lines connected together represent all of the mathematical tools we have to connect the dots.  But we won't be able to connect all of them unless we extend our thinking beyond the physical universe we perceive.  "But," you may object, "there aren't any dots outside the box."  Sure there are, you just don't see them.

In Hermann Hesse's novel Siddhartha, Govinda listens while his dear friend Siddhartha tries to explain to him the great Truth he discovered.  Govinda's reaction was:  "This Siddhartha is a bizarre person, he expresses bizarre thoughts, his teachings sound foolish."  Words and mathematical symbols will always fall short when using them to describe the Truth.  They can only point the way toward it.

The universe truly is bizarre, but getting through all the craziness is possible if we abandon our conventional, pre-conceived notions of how the universe ought to be and think outside the box.  In other words, we must fully embrace the crazy in order to understand a bizarre universe.  When the complete Theory of Everything is finally revealed, everyone will be amazed at how simple it is and how stupid we were for missing it; a Principle so compelling, so simple, and so obvious that it will be unnecessary, or maybe even impossible, to write it down using mathematical equations.

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The Amateur Scientist's Cosmology in a Nutshell

The universe is everything that exists, and it all comes from information in the present moment -- the temporal Now.  The temporal dimension is asymmetric, meaning it has curvature, with the temporal Now defining a surface of uniform curvature with a center of curvature at the Beginning.  The totality of information is ever-increasing, and the temporal Now must expand in order to accommodate it.

The question is:  Since the temporal Now cannot expand in relation to itself, in relation to what does the temporal Now expand?  The answer is provided by the Minkowski space-time metric:  (c dτ)2 = (c dt)2 – (dr)2 .   The Now surface is defined by dτ = 0, a where proper time, τ, as measured by a clock, comes to a complete stop; thus, the progression of time is equivalent to the radius of curvature of this surface, r, increasing at the speed of light,  dr/dt = c.   The radius of curvature connects asymmetrical time with symmetrical space through c and establishes causal relationships conforming to the principles of the theory of relativity.  The primal radius has three degrees of freedom, commonly referred to as the "three dimensions of space," but when you point in any direction away the Now surface, you always point back along the primal radius toward the Beginning because there is no exterior direction from the Now surface to point to.  Hence, the apparent "three dimensions of space" are just different elements of the same primal dimension pointing back to the origin of the radius of temporal curvature. 

Although space could conceivably have any number of degrees of freedom ("dimensions"), the number three is unique.  Here's why:  Space possesses perfect translational and rotational symmetry because space has no boundaries, no preferred locations and no preferred directions.  According to Noether's theorem, rotational symmetry is equivalent to the conservation of angular momentum, and angular momentum can only be defined mathematically in three dimensions.  Furthermore, conservation of both linear and angular momentum requires the existence of mass (inertia), which is the reason why all objects confined to space must possess mass. 

In contrast, light is massless and so it must be confined to the temporal dimension.  Light "travels" at the speed of light relative to all spatial objects due to the fact the temporal radius expands at the speed of light, dr/dt = c.  The relative speed of space with respect to time endows massless light in the temporal dimension with energy and momentum when it is observed in the spatial dimension of objects possessing mass.  Causality prohibits spatial objects with mass from traveling faster than light relative to any other spatial object in order to prevent them from traveling back toward the Beginning.  Since space has three degrees of freedom, any of which can be a radius of temporal curvature, two other degrees of freedom orthogonal to the radius define a surface tangential to the temporal Now, making the temporal Now somewhat analogous to a two-dimensional temporal sphere surrounding three-dimensional space.  Observers at different locations in the temporal Now are completely cut off from each other in the present moment, but they are causally connected with each other's pasts and futures.  Any object observed at a distance in space is a residue or shadow of the object's "past" left behind the expanding temporal Now.

But in order for the pieces of spacetime to fit together and work properly, spacetime geometry must be hyperbolic instead of Euclidean.  By definition, the Now moment is a surface equidistant from its center of uniform curvature; however unlike the surface of a normal sphere, its curvature is negative, meaning its surface curves away from its center of curvature instead of toward it (don't even try to form an image of this object in your head).  Consequently, when we look "out" into "space" and observe stars and galaxies that are equidistant from us, those objects are also equidistant from their own centers of temporal curvatures, which are closer to the Beginning than we are.  Although space appears to expand at distances farther from us, space actually shrinks because those distances are closer to the Beginning!  The universe we perceive through our sense of sight is like a rainbow; it's a mirage or an illusion (Māyā) produced by our senses.  It is impossible for the human mind to grasp the true nature of the universe by trying to visualize it using geometric models.  Weirdness is an essential aspect of reality in order for it to ultimately make sense, but this cannot be understood through the senses – it can only be grasped through logic and abstract reasoning.

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Materialism vs Idealism

"In The Beginning" is the introductory track of the album "On The Threshold Of A Dream" by one of my favorite music groups, The Moody Blues.  It relates a conversation among the Man, the Establishment, and the Inner Man.  The Man starts out by paraphrasing Descartes:  "I think, I think I am; therefore I am, I think."

The Establishment informs the Man that "our great computer" has a complete record of the Man's DNA ("miles and miles of files of his forefather's fruit") and thus he is nothing more than "magnetic ink."

The Man insists he's more than that, or at least he thinks he must be.

The Inner Man congratulates the Man for seeing beyond the Establishment's Maya ("to perceive the web they weave"), but warns that gaining this insight into his true nature will "rile" the Establishment, causing much tribulation ("piles and piles of trials").  The Inner Man ends the conversation by encouraging the Man to face the human condition with smiles and to "keep on thinking free."

I think this is a wonderful metaphor describing the conflict between materialism and idealism.  Materialism, the scientific paradigm of the 20th and 21st century, asserts that consciousness is a secondary phenomenon emerging from the electrochemical processes within the brain, which belongs to the physical universe consisting of space, time, matter and energy ("the Establishment").  Consciousness is therefore just a seductive illusion.  Idealists take the opposite view by asserting that consciousness is fundamental and the material universe is just the external manifestation of an overarching Universal Consciousness ("the Inner Man"). 

Materialists argue that since consciousness has no ontological foundation, it cannot be real but only an illusion the brain tricks itself into believing.  I think there's a fatal flaw in that argument:  Doesn't the brain already have to be conscious in order to trick itself into believing an illusion?

It is clear that "In The Beginning" embraces idealism over materialism.

Om So Hum (I Am That)

You might want to listen to this audio as you meditate on the above (be sure to turn on your speakers!)   Link to Audio

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Gödel's Universe

In 1931, the great Austrian mathematician, logician and philosopher Kurt Gödel published a landmark proof stating that in any consistent formal mathematical system, there are true statements that are not provable from the system's axioms.  In short, a formal mathematical system can be consistent or complete but not both.

Definition of Consistency:  There is no statement where both the statement and its negation are provable from the axioms.

Definition of Completeness:  Any statement or its negation are provable from the axioms.

The classical universe is equivalent to a formal mathematical system based on a set of axioms expressed as causal laws (the "laws of nature") governing interactions among space, time, matter and energy.  Therefore, the universe itself is either consistent or complete but not both.  An inconsistent universe would be a universe where a cause can give rise to both an effect or its opposite.  Clearly this not the case because experiments based on physical laws are repeatable.  We must then conclude that the universe is consistent and yet it must be incomplete.  By definition, the universe is "all there is" and therefore it must be radically self-referential and complete and consistent at the same time, which seems to violate Gödel's proof.

Here is where quantum mechanics comes in, where the superposition of two quantum states can give rise to an effect or its opposite.  For example if the spin states of an electron are in a superposed up and down state, a spin measurement can produce either an up or down spin state according to a set of probabilities.  The important thing to note is that the results of spin measurements are not subject to any law of cause and effect; the outcomes of those measurements are completely random and impossible to predict from axioms, as proven experimentally by violations of Bell's inequality.  In other words, quantum mechanics is inconsistent according to the above definition, but this inconsistency allows it to be a complete description of quantum reality based on its axioms.  

Per statistics and the law of large numbers, a consistent set of axioms (expressed as the classical laws of nature) will emerge naturally from underlying quantum randomness and inconsistency.  Quantum mechanics is inconsistent yet complete while classical physics is incomplete yet consistent.  Both are subtly and magically joined together, resulting in our universe bounded by completeness and consistency as illustrated below.

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A Metaphor:  The Worlds of Light and Shadow

There are two worlds that coexist in our universe.  The first is the visible world, characterized by the presence of light and matter, such as planets, stars, and galaxies, all moving through spacetime.  This world is rich in sensory experiences, with fragrant flowers, majestic trees, diverse animals, and awe-inspiring sunsets.  It is a world of certainty operating on the principle of cause and effect, where all objects with mass move at a constant speed of light along world lines that bend and twist under the influence of gravity.  It is a world filled with entropy and time without end, marked by cycles of birth, aging, and death, and where everything has its designated place and time.

The second world is the invisible shadow world of quantum physics, where space and time lose their classical meaning, and objects behave as waves and particles, but not both concurrently.  In this world, nothing is certain, and objects can appear and disappear without leaving a trace.  It is a world of entangled particles that share a mysterious connection across great distances, and where entropy is in short supply and gravity is absent.   

Despite their striking differences, the two worlds are not incompatible but are instead interconnected and interdependent.  Each world reflects the other and neither could exist without the other.  The visible world of light, and the invisible world of shadow together form a balanced and harmonious whole that reveals the profound complexity and beauty of the universe.

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Einstein's Warning About Taking Mathematics Too Literally

"Fundamental ideas play the most essential role in forming a physical theory.  Books on physics are full of complicated mathematical formulae.  But thought and ideas, not formulae, are the beginning of every physical theory. The ideas must later take the mathematical form of quantitative theory, to make possible the comparison with experiment. "  -  The Evolution of Physics, 1938

"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” - Lecture on Geometry and Experience, 1921

Pertaining to the second quote, the German word Wirklichkeit was translated into English as "reality," but this word arguably could have been better translated as "actuality."  In either translation, the point Einstein was trying to make was there are inherent gaps between the certain laws of mathematics and the physical reality (or actuality) they describe.

Take for example the following problem.  Alice is a mathematician/gardener who wants to enclose a garden of area, A, within a rectangular perimeter constructed of wooden edging.  Her budget allows a total edging length of 40 meters at a cost of $10 per meter.  She works out two formulas giving the length and width of a rectangle having a 40-meter perimeter in terms of the area, A, as shown in the figure below.

Using the above formulas, Alice creates the table below specifying the dimensions of the rectangle for different sizes of area, and we can see the perimeter in each case is 40 meters long.

Alice notices that her formulas for length and width would allow her to enclose more than 100 square meters within a 40-meter rectangular perimeter.  She decides she would like to enclose a huge garden having an area of 200 square meters inside a 40-meter perimeter, so she sets A=200 in her formulas to work out the length and width of the required edging.

L1 = 10 + 10i  meters

L2 = 10 - 10i  meters

, where i is the square root of negative 1.  She checks the math using the complex values of edging above, and sure enough L1 times L2 equals 200 square meters and the perimeter length is 40 meters.  So now all Alice has to do is run down to the home improvement store and purchase 2 pieces of edging 10+10i  meters long and 2 pieces of edging 10-10i meters long and pay $400  for a total edging length of 40 meters.

The formulas Alice derived work fine up to the point where A=100 square meters, but there is an obvious glitch when A>100.  Here, the laws of mathematics are still certain but they no longer refer to reality because real wooden edging only comes in real lengths and not complex lengths.  

The same thing holds for the exterior Schwarzschild metric on which the "black hole" phenomenon is based.  For an object having spherical symmetry and a total mass m, the Schwarzschild radius is R=2mG/c2.  This works out fine for real objects like the Earth and Sun, whose Schwarzschild radii are mere fractions of their physical sizes.  The problem physics runs into is attempting to squeeze the entire mass of an object like the Earth or Sun within its Schwarzschild radius and forming a "black hole."  A real mass just won't "fit" inside a real radius R=2mG/c2, the same way a real area greater than 100 square meters won't fit inside a real 40-meter perimeter.  

The exterior Schwarzschild equation says an object's mass will "fit" inside R, but this is predicated on two assumptions, namely: a) R is constant, and b) no mass-energy exists in the space surrounding the object.  Neither of those assumptions are true when a real star shrinks.  As the star shrinks, gravitational binding energy is released and negative gravitational energy intensifies in the space surrounding it, decreasing both the star's total mass-energy and R.  (It's easy to show that if one kilogram of mass were lowered from infinity to the surface of a hypothetical "black hole," one kilogram's worth of gravitational binding energy would be released and would entirely cancel the kilogram reaching the surface.)  So what really happens when a star collapses is this:  Enormous amounts of gravitational binding energy are released as the star's surface approaches its Schwarzschild radius, reducing the star's total mass-energy and causing a reduction in R.  As the star continues to shrink, R must always remain smaller than the physical radius of the star, and the inward gravitational pressure will remain finite.  Ultimately,  the pressure reaches equilibrium with the star's internal radiation pressure – the Eddington limit – and the star's physical collapse stops.  The end result is a very hot, eternally-collapsing object (ECO) producing an extremely large spatial curvature and time dilation, but no true "event horizon" will form. 

Borrowing Einstein's words, the laws of mathematics describing a "black hole" are certain, but they don't refer to reality.

The image below is alleged to be a "black hole" in the center of the galaxy Messier 87, recorded by the misnamed Event Horizon Telescope.  In reality, this object is an ECO, or black hole mimicker, as described by astrophysicist Abhas Mitra in his book The Rise and Fall of the Black Hole Paradigm.  Mitra refers to the glowing orange circle as a "photon sphere" surrounding the ECO.   As explained in his book, 

"The photon sphere is 50 per cent larger than the black hole or its mimicker.  Photons moving within the photon sphere vertually remain trapped within it as they need to struggle extremely hard to pierce the photon sphere.  Accordingly, the photon sphere itself acts like a virtual event horizon, and no external observer, no telescope, can peer inside the photon sphere.  For a rotating black hole mimicker, the photon sphere gets replaced by a photon ring at the equatorial plane."

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Anatomy of an ECO

So if Messier 87 isn't a true black hole with an event horizon but an ECO instead, then what accounts for the image produced by the Event Horizon Telescope of totally black region surrounded by an orange ring?  In the diagram below, a physical ECO is a ball of incredibly hot matter shown as a sphere of diameter D.  Within that ball of matter is a somewhat smaller mathematical (non-physical) sphere of diameter Ds equal to twice the Schwarzschild radius of the ECO.  According to general relativity, photons trying to escape the ultra-hot surface of the ECO are trapped within a photon sphere having a diameter DΦ = 1.5Ds.  The photon sphere is an imperfect trap however, and a small percentage of the photons do escape into the surrounding space by scattering off matter particles in the vicinity of the photon sphere.  The tiny bright yellow dot on the left edge of DΦ in the diagram depicts one of the points on surface of the photon sphere from which radiation escapes.

When photons escape tangentially from that spot, their paths bend under the influence of gravity to form a shell in a rounded cone shape as shown in the diagram below.  Once the radiation is far enough away from the light-bending gravitational influence of the ECO, it travels in straight paths, forming a circular shell of radiation that surrounds a totally black interior shadow.  Since there are an infinite number of places around the surface of the photon sphere from which radiation escapes, there are an infinite number of radiation shells emerging from the ECO in every direction.  However only one of these shells is shown in the diagram below, which happens to be the only one directed toward the Earth that is visible to earthbound observers.  The diameter of the central shadow is several times larger than the physical ECO and is impenetrable to distant observers.  However, this shadow is NOT an image of an "event horizon" but rather is simply an optical effect caused by gravitational bending of the radiation escaping from behind the photon sphere.  Extreme gravitational time dilation in the region surrounding the ECO greatly reduces the frequencies of the escaping radiation from gamma-ray and X-ray frequencies to radio frequencies that are picked up on Earth by the Event Horizon Telescope antennas. 

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TOE on a T-Shirt

Physicist and astronomer Adam Frank is quoted as saying this regarding the Theory of Everything (TOE):

 “Once you have this TOE you are done. You know everything there is to know in principle. It will be so simple and elegant that it should be expressible via an equation that fits on a T-shirt.”

I doubt string theory will ever fit on a T-shirt, but I know there is an equation that does fit, and I believe it captures everything there is to know in principle about the universe.  That equation is shown below.

The equation on the T-shirt is the equation of state of the universe at its temporal boundary (the 2-dimensional Now surface) having a radius of curvature, R, increasing at at the speed of light, dR = c dt.   This equation of state also corresponds to the equation of state of the 3-dimensional region within the temporal boundary.

EU = total energy at the temporal boundary

π  = we all know what pi is

kB = Boltzmann constant

T = cosmological temperature at the temporal boundary

c = speed of light

tU = age of the universe (time elapsed since the Beginning)

ħ =  reduced Planck constant

G = Newton’s gravitational parameter on the temporal boundary at tU

Notes: Both G and T are inversely proportional to tU and T/G is a constant = 0.0387 J-K-m3/sec4..  The estimated age of the universe has recently been revised upward to around 26.5 billion years (820 quadrillion seconds). 

Applying this equation, it is possible to show the following.  In the Beginning when the total entropy, H, of the universe was equal to one bit and tU was on the order of 3x10^–24 seconds, gravity would have been 3x10^39 times stronger than it is today.   This is how the promise of "unification of the forces of nature at high energies" is fulfilled.  For details, click on this link:  "Gravity: Superstrings or Entropy?".

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Consciousness Is Fundamental

Experiments conducted by Marcus Huber and his associates at the University of Queensland have shown that clocks measure the flow of entropy.  There are many kinds of clocks, but they are all based on counting physical changes, such as counting the amount of sand flowing through an hourglass, counting the swings of a pendulum, counting the spins of the Earth on its axis, counting the revolutions of the Moon around the Earth, or counting the revolutions of the Earth around the Sun due to the law of gravity.  In other words, temporal distances as measured by physical changes are equivalent to the flow of entropy.  Proper time measured by a clock also corresponds to a distance along a path the clock travels through spacetime.  Thus, spatial of distances are also equivalent to the flow of entropy.  In summary, the physical universe is composed of space, time, gravity, inertia, matter and energy, and all of the above are based on the flow of entropy.

What is entropy?  It is simply the metric of uncertainty, and uncertainty is confusion or a lack of knowledge.  Only consciousness can be in a state of confusion or uncertainty because only consciousness is capable of being in the opposite state of certainty or knowledge.  Without consciousness there is no entropy.  Without entropy there is no physical universe.  In other words, consciousness is fundamental end everything else emerges from it.  Consciousness just simply is.

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The Boundary of a Boundary Is Zero

The late John Archibald Wheeler often repeated the statement, "The boundary of a boundary is zero" when trying to explain his concept of the universe as being a "self-excited circuit."  This statement is mentioned no less than 27 times in Amanda Gefter's book Trespassing on Einstein's Lawn.  Gefter, as well as well as a few of the scientists she interviewed in her book, were unsure what Wheeler actually meant by it.   From his voluminous notebooks he left behind, it seems Wheeler was attempting to boil all of physical reality down to some fundamental Law or Principle that possesses no attributes or dimensions of its own.  In other words, he was trying to describe how everything emerged from essentially nothing.

In topology, the "boundary of a boundary is zero" is a straightforward concept.  It can be represented symbolically as ∂∂=∅, where ∅ symbolizes the null set { }.  Take for example the illustrations below, showing the evolution of spacetime.  

A dimensionless point, 0D, unfurls into 1D, becoming a pair of points forming the boundary of one-dimensional linear time, shown as the figure labeled "1D time" above.  Linear time allows causal events to be ordered in a logical sequence, but this lacks "space" that separates different concurrent or overlapping events from each other.  When 1D time unfurls into 2D, it becomes the 1D circular boundary of an interior 2D hologram of everything happening in the moment.  The circular boundary attains the property of curvature while the boundary of the circular boundary is a null set.  The circular boundary expands in order to accommodate the "flow of time" moment-by-moment.

The 2D time unfurls into 3D, forming "2D time / 3D space" depicted schematically above as the blue 2D temporal boundary enclosing a yellow 3D spherical space.   The temporal boundary retains its property of curvature, which represents temporal asymmetry due to its irreversible expansion into the '"future."  In contrast, interior 3D space must be absolutely symmetrical and flat, and the flatness of 3D space has been confirmed through astronomical measurements.  Cosmologists erroneously call this "the flatness problem," and Alan Guth invented "inflation" to explain it.  In truth, the reason there are three spatially-flat dimensions is simple:  In the absence of acceleration, Noether's theorem requires space to have translational and rotational symmetries in order to conserve linear and angular momenta, which is a very important requirement in order to maintain consistency of physical laws.  Space must be three-dimensional because angular momentum, defined by the cross-product of a momentum vector and a distance vector, can only be consistently defined in three dimensions.  Forming a cross product of two vectors in spaces having fewer or greater dimensions than three are not possible. 

A temporal Beginning exists at the center of 3D space with the radius from the center to the 2D temporal Now boundary increasing at the speed of light.  The 3D region contained within the 2D temporal boundary is timeless, serving as the holographic record of all events that occurred on the expanding Now boundary since the Beginning.  Space is finite and is bounded by time, but there is no escape from it because nothing can approach the temporal boundary as it recedes from the Beginning at the speed of light.  

The final illustration above schematically represents the set {2D time / 3D space} unfurling into four dimensions, becoming the 3D boundary of the 4D Minkowski spacetime manifold.

The takeaway from this illustration is this:  The underlying boundary of the universe is a 0D Singularity that unfurls as a 1D duality; two dimensionless points that are the boundary of linear 1D time.  The 0D Singularity cannot have a boundary because there is no lower dimension that could serve as its boundary.  Therefore, 0D=∂∂∂∂{4D}=∅.  What is the boundless Singularity that is the boundary of everything?  Some ascribe various names to the Singularity, such as God, I Am, Universal Consciousness or simply The Source.  It should be noted that while ∅ can refer to nothing, it can also refer to everything, an infinite set of unrealized possibilities; a set of yes/no questions corresponding corresponding to "bits" of information in Wheeler's "it from bit" postulate.  Those yes/no questions are equivalent to nothing until they are actualized as yes/no decisions as Source unfurls into higher dimensions, and then nothing becomes everything.

The Theory of Everything can be summarized as follows:  ∅ → U