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stuart-boehmer · 5 months ago

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Counterfactuality, Quantum Superposition and Reality: What is a Photon?

If we want to understand quantum electrodynamics as a theory of cause and effect, we must look at the Hamiltonian, specifically, the interaction Hamiltonian between the electronic and electromagnetic fields.

The electromagnetic vector potential, A, appears in Hint. In the usual formulation, A is represented as an operator times a field strength (a function of (x,y,z,t)). The relevant operator is not the photon particle number operator, but the photon annihilation operator. This is where the trouble begins.

A photon is not a particle in the Nineteenth Century sense, a small billiard ball with structure and measurable properties. It is defined dynamically: changes in the photon number create a non-zero potential, A, while, based on Nineteenth Century understandings, we would expect the photon to possess a certain spatial field, A(x,y,z), analogous to the Coulomb field of a classical electron. That is, we would expect A to be defined in terms of the photon particle number operator.

The state of matter in classical theory was defined by the positions and momenta of all the particles comprising the system being studied, e.g., the solar system or hydrogen atom. But quantum field theory understands the world in terms of a superposition of states of the wave vector. The more we think about the meaning of this statement, the more perplexing and untenable it becomes. The standard, Born interpretation of the wave vector is that it represents in some way the state of knowledge of the experimenter. Does this mean that the world is created by the consciousness of some experimentalist at CERN? It is unclear exactly what it means, but this line of thought clearly runs into a dead end and we must pursue other avenues of understanding.

Let us now digress a little and discuss how to interpret the meaning of experiments on entanglement of photons or electrons. The theory of entanglement is usually framed in terms of elementary quantum mechanics, where photons or electrons are understood as particles, but we have just seen that they are not particles in any meaningful sense of the term. Let us therefore attempt to sketch the outline of a field-theoretic understanding of what this phenomenon may be.

Let us describe electron spin entanglement experiments phenomenologically, free of theoretical interpretation. We create two correlated low intensity electron beams at a certain point and separate them to large remove where they interact with magnetic fields of random orientations and they are resolved into two separate beams normal to the magnetic field and the relative intensities of the four resulting beams are measured.

The theoreticians explain what has happened something like this: Two electrons with correlated spins are created at some point and separated to distant remove where they interact with magnetic fields of random orientations and their spin components are measured. The value of the spin is determined only in the act of measurement, explaining why two beams of spin up and down relative to the direction of the magnetic field are observed, whatever the direction of the magnetic field may be.

Of course, all this is hand-waving, balderdash and double-talk, but let us not pause here to argue about it further, but let us move right along and cut to the chase, moving, in Nietzsche’s words, as the Ganges flows instead of as the tortoise crawls, or, at best, as the frog leaps.

We have just seen that in a field-theoretic understanding, the photon is not a particle with structure and measurable properties. We presume that a similar statement could be made apropos the electron or, indeed, any quantum particle.

Thus, spin is not a property of the electron, nor, for that matter, is momentum nor any other property that might be attributed to a classical particle.

Experiments can be understood and described only in phenomenological terms. They cannot be explained or visualized in terms of atoms, particles, electrons, photons, quarks or what have you.

Nietzsche was correct: there is no reality deeper than appearances. There is no terra firma, no material substratum, no earth residuum holding it up.

It is a kaleidoscope of nonsense.

Thus, to end the 100+ year debate apropos the meaning of quantum theory: it is a matter of shut up and calculate after all, much to the chagrin of the Einsteins, the Bells, the Schroedingers and kindred spirits.

It is primitive artificial intelligence.

Thus, summarily ends the Human Legacy of trying to understand existence and trying to figure out what the hell it is all about.

In the future, the discipline of physics will disappear, and engineers will just use models generated by AI of whatever invention they are trying to build or whatever phenomenon they are trying to study. These models will just be one tool in a tool kit consisting of things like serendipity and trial and error. The new engineers will be Citizen Kanes, who don’t know how to run a newspaper but just try one thing and another; some of it will work and some of it won’t. This is probably a pretty good description of how the Romans built the aqueducts with no understanding of fluid mechanics or how the Egyptians built the pyramids with no understanding of structural analysis.

Bardeen’s attitude was that the meaning of a theory was embodied in the technology it produced. Once that technology is created, the theories and the textbooks become superfluous and may be discarded.

Life happens on the double-quick.

If you blinked, you missed the major transformative shift that just happened.

Goodbye, physicists! You are relics!

The study of physics theories based upon materialistic concepts such as general relativity or elementary quantum mechanics or even the a-materialistic quantum electrodynamics could live on as art forms, like the study of mathematics. Human reason is a form of art—concepts such as matter, object, number, the sense of self, or the fictions of identity, boundary and permanence are great artistic masterpieces and should be appreciated as such. They are among the noblest creations of the human spirit, testimony that giants once walked upon the earth. These subjects continue to remain interesting as ends in themselves, though cynics and realists might dismiss the activity of study of these subjects as something with the existential import of solving crossword puzzles.

The human mind is a learning engine, the most advanced AI system in existence at this time. It can solve any problem, even in a chaotic and lawless environment, by adjusting the statistical weights of its synaptic firing thresholds even without any visualizable model of the world. If one is hungry, he can find a way of foraging for apples even in an environment where all order has broken down, though his explanations of how he managed to do this might bear little or no relation to what actually happened. The hand is wittier than the brain. Everyone who has ever flown down the interstate on autopilot knows this. This, too, is the meaning of the quantum theory: shut up and calculate!

AFTERWORD

If we absolutely insist upon moving as the frog leaps, we could conduct experiments based upon calculations such as the following:-

The electron annihilation operator, a0, is a 2 X 2 matrix with four elements, three zeroes and a one. We could replace it in the quantum electrodynamic definition of the field operator Helectron, the Hamiltonian of the electronic field, by a = a0 + e, where e was a 2 X 2 matrix consisting of four elements, each a small, nonzero number. We could then calculate the implied modification to any observable effect that suited our fancy, for example, the Fermi-Dirac statistics for electrons. Or, alternatively, we could do something similar for the photon annihilation operator and calculate the implied modification to the blackbody spectrum and by observing the Sun or, in the controlled environment of the laboratory, by observing the radiation coming from a small aperture in an oven of varying temperatures, the experimentalist could determine the small quantities, e.

If any of them were found to be different from zero within the statistical significance of the observational error, that would provide proof that not even the frogs and tortoises among us could doubt.

But is it really necessary? Does not the fact that, although some of the brightest minds on Earth have set their sights on the problem, the question of what the quantum theory means has remained controversial and unresolved for over one hundred years, from its very inception, provide prima facie evidence that something counterintuitive is going on here?

One last parting thought: our perception of and understanding of the material world is based upon lies. For example, when you look at a fountain pen, you are not seeing the fountain pen, but, presumably, an image of it created in your brain or mind. It is “in here,” not “out there.” But it seems “out there.” Our mind is lying to us about the very nature of our perception of the fountain pen, and the common man in the streets lives his whole life without once giving thought to or even being aware of this fundamental fact. Not only a fountain pen, but your lover too. Wrap your head around this one! The explanation is that the brain projects it so that it seems “out there,” like, presumably, it really is. How does the brain do this? Somehow. By faculty of some faculty. Truly a solid scientific explanation!

Reality, as Howard Bloom avers, is a shared hallucination. Or, in the words of Arthur Schopenhauer, it is a waking dream. Even Einstein, toward the end, was saying things like reality is an illusion, albeit a very persistent one.

All our explanations are double talk, circular reasoning and trying to understand an infinite reality with a finite number of words of shifting and indefinite meaning. Given such a basis of the human condition, how the human mind finds itself immersed in the world of phenomenon, how can we hope to sort things out and arrive at the “objective” Truth? Clearly, we cannot; it is the ultimate Gordian Knot. It cannot be disentangled; it can only be cut through with the sword of Alexander. That is, we must give up seeking for knowledge and learn to become wise, living life as human beings were meant to live it. Perhaps, out there, somewhere in the vastness, is a species capable of understanding, but we are not that species. Like Kafka, we must give it up and return to the human fold. Only then can we live happily ever after. This is what God intended for us in the Garden of Eden. A return to innocence, a new Paradise on Earth, is within our reach! Look not to the Heavens; Man will be his own Salvation.

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stuart-boehmer · 5 months ago

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The World is a Kaleidoscope of Nonsense

The World is A Kaleidoscope of Nonsense.

Science is a form of art. Its concepts are anthropomorphic analogies. For example, the concept of force is an abstraction of the muscle sensations we have when pushing, pulling or lifting a heavy object. There is nothing any more real about this system of thought than any other. All human thought is Art. And one does need faith to believe in scientific theories. Any evidence that they work is heavily cherry picked. When Newton computed the ephemerides of the moon to check his then-new theory of gravitation, he ruthlessly ignored any observations that contradicted his calculations. Such a procedure has historically been a factor in the "confirmation" of any scientific theory to date including the most modern. The statistical outliers are swept under the rug as "insignificant.". There is a way to avoid this, but it would not be something recognizable as a respectable "theory" based upon concepts that we could visualize or "understand.". That procedure is this:- For example if one has made 10,000 measurements, set up a system of equations with 10,000 adjustable parameters. Then one could hit all the data points on the mark and there would be no cherry picking. Physics as curve fitting. Ultimately that is all it is anyway. If a theory makes an incorrect prediction, we summarily replace it with another theory that hits more of the data points more closely. Bardeen's attitude was that the meaning of a theory is embodied in the technological objects that it helps to produce, along with healthy doses of serendipity and trial and error. Once the technology has been created the textbooks and theories become superfluous and they may be thrown out. Bardeen was correct: Nature cannot be understood. It is a kaleidoscope of nonsense. Einstein did not understand this when he stated that the most incomprehensible thing about experience is that it can be comprehended. It cannot be comprehended. It IS. It is what it is and frail mortals who can succumb at any moment to a lowly bacterium are in no position to explain it or comprehend it. Weinberg states in his monograph on Quantum Field Theory that the business of physics research is geared towards coming into an understanding of why Nature is as it is and no other. But I dunno, it seems to me that She might have a mind of Her own. The human mind is a learning engine that can solve the two fundamental problems of human existence—food and sex foraging—given any set of circumstances, and learning engines, as any computer scientist knows, are based on modifying synaptic weights with new experience, that is, by curve fitting, not grand theories and explanations. We could learn to navigate any environment, however chaotic and lawless. There might be a species out there somewhere capable of understanding this world of sensuality and mendacity, but we are not It! Imhotep II, the artiste formerly known as Stuart Edward Boehmer

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stuart-boehmer · 5 months ago

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New Formulation of Quantum Theory

New Formulation of Quantum Theory.

I have developed a new formulation of quantum mechanics and quantum field theory (QED) based upon the Madelung formulation.

It is contrary to Born's formulation: there is no uncertainty principle for individual measurements: if q is determined exactly, so is p (specif.: p = (h/2[pi])dS/dq), but due to this correlation between p and q (dS/dq is a function of q), the usual uncertainty relation between uncertainty in q over multiple measurements and the same for p holds.

From this, a P(q,p) that is globally non-negative (unlike the Wigner Distribution) can trivially be constructed from the theorem relating P(p,q) to P(p|q) (viz., P(p,q)=P(p|q)P(q)).

Thus, I have interpreted the physical significance of the wave function and completely solved the quantum measurement problem, and it is not the Copenhagen interpretation nor "bake a cake, regardless of what that means objectively and perform your experiment; the classical theory of reality tells you how to do this though the real world is a black box." It is trivially the usual probability theory and thus reduces identically to the classical "measurement problem."

My extension to QED/QFT is anti-atomistic: the particle creation and absorption operators have nothing to do with particles/electrons/photons but are just quantities appearing in the electric fields, magnetic fields and current density. I have therefore answered the question, "What is a photon?" that so troubled Einstein.

Similarly spin is not an intrinsic angular momentum but just a quantity appearing in the quantum Hamiltonian. It is not surprising or paradoxical that non-classical quantities should appear in quantum theory--it is, after all, a different theory based upon different concepts.

New Physics Galore!

And I can suggest all sorts of experimental effects to search for.

For example, the theory may be not only non-atomistic but even non-materialistic if the "particle" creation and annihilation operators are slightly modified: then one may not exactly have E = nhf, where n is an integer, for the possible energy levels of the electromagnetic field and, similarly, the electron current density might not exactly equal an integer number of quantum units of current density. Might something like this be the explanation of dark matter?

And if the particle creation/annihilation operators could be modified radically, reality would not be recognizable at all in the materialist world view. What kind of reality would such a world appear to be? What concepts replacing matter, space and time would we have?

Reality might be dualist or pluralist: there might be fields unrelated to electrical, magnetic and gravity fields, etc.--e.g., different fields for each aspect of life: one, for example, for psychology and consciousness; thus Dennett may be wrong and consciousness may not arise solely from the material electrochemical activity in the brain, but be caused by a new kind of field that interacted with the usual "material" reality. Similarly, perhaps life can spring only from life and the explanation entirely in terms of the properties of inanimate matter (e.g., DNA) may not be possible, and we would have a return to something like Nineteenth Century Vitalism.

And the possibilities multiply profusely; this is just an all-too-brief overview.

My prospects are looking up! If there is anything to any of this, with my directions on where to look to discover new physics, I should definitely be on track for the Nobel.

Like Mandelbrot and Einstein I have transformed how we understand reality by creating a whole new world from nothing, simply giving people eyes to see what was right in front of them all along.

I have ended the 100+ year debate on the meaning of quantum theory and, despite Feynman's warning not to do so, I have gone down the rabbit hole and emerged triumphant. Though there was a lifetime of preparation and study, these thoughts flooded in of one piece just today, in the space of a single afternoon.

Stuart Edward Boehmer MSc Physics (2004)

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stuart-boehmer · 5 months ago

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Spatial Perception and Reality

I will have more to say about the following in a more detailed post later, but for now, a thought "hot off the press":-

Some schizophrenics sometimes have the experience that someone on the other side of the room is inside their physical bodies.

Such statements are currently dismissed as deranged, as anomalies in spatial perceptions.

But I have profound reasons to suspect that they have reverted to a more naked experience of reality, that of the pre-verbal infant, unmediated by the brainwashing adult indoctrination into a materialistic experience of this reality.

We shouldn't dismiss them as sick or deranged or "crazy." Perhaps we should adopt the attitude of a student, "This is interesting; tell me more!" Perhaps they know something we others do not. Perhaps new, idealist, theories of physics could be derived from a serious study and attempt to understand their viewpoints.

Today, we no longer speak of the "brain" versus the "body," but of the "brain-body." It is one unified, integrated system: the nervous system is distributed throughout the body and chemicals in the gut have a non-trivial effect on mood, wakefulness, etc. The location of the brain and consciousness is no longer regarded as confined to the interior of the skull. Who says that the complete location of the brain-body is confined to what we normal people perceive as within the boundaries of the physical body? Is there evidence that pre-verbal infants have this perception before receiving language-materialistic brainwashing by their adult parents?

Stuart Edward Boehmer, MSc Physics (2004)

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stuart-boehmer · 5 months ago

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My Book is still Unwritten.

I have sat under the Bodhi Tree. I have much to teach. I want to pay it forward. I may give up physics and literature and become a spiritual motivator like Eckhart Tolle or Mihaly Csikszentmihalyi. My Book is still unwritten.

Stuart Edward Boehmer.

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stuart-boehmer · 6 months ago

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Self awareness

Calmness and deliberateness in all one's actions and words. Be aware of yourself at all times. Be cognizant of the image one is projecting. This is the best advice I can give on how to ignite Flow.

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stuart-boehmer · 6 months ago

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Enlightenment

I have sat under the Bodhi Tree. I have much to teach. Stuart Edward Boehmer MSc. Physics (2004)

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stuart-boehmer · 6 months ago

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GOD AND INDIFFERENCE

The opposite of love is not hate but indifference.

The fact that nature is indifferent--be it materialist or idealist--is the proof that God does not exist.

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stuart-boehmer · 6 months ago

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THE QUICK AND THE DEAD

Arrive. Raise Hell. Leave.

Don't dwell on any one thing too long. Life is a bird on the wing.

Don't explain the joke.

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stuart-boehmer · 6 months ago

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VITALISM & AI

VITALISM AND AI

Stuart Boehmer MSc Physics (2004)

The theory that “life” is just an optical illusion caused by a very complicated inanimate biochemical process (DNA) is incorrect.

Life can spring only from life. The vitalism of the Eighteenth and early Nineteenth Centuries is apparently correct, after all.

The artificial intelligence of the future will come from genetic engineering, not by building ever more advanced pocket calculators…the Boehmer Test of Consciousness: I’ll believe that a computer MAY be conscious when it refuses to work w/o pay. 😊

The creation of a smarter, healthier, stronger human species for the future is the ultimate goal of genetic research. Today’s Man is a relic…

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stuart-boehmer · 6 months ago

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TWO DISCOVERIES IN MATHEMATICAL PHILOSOPHY

1 HYPERNUMBERS

First, allow me to interject that the idea that I am about to describe seems more extensive than the hyper-reals of non-standard analysis and is not to be confused with them.

The hyper-reals, in my understanding (and I haven’t yet thoroughly studied non-standard analysis, so this may be a mis-perception), are just an alternative description of the real number system with the same cardinality of the reals—the power set of the naturals, c := 2^(aleph-null). according to a book I have on non-standard analysis by Mark Davis published in 1977 & 2005, to the date of publication, only one theorem of real analysis has been proven by non-standard methods—not too powerful a method?

Now to describe what I mean by “hyper-numbers:” H1 is the first class of hypernumber, of cardinality of the power set of the reals, c1 := 2^c. The “integers” of this number system are reals, with the density of the reals—no “first,” “second,” &c., integers & the “digits” of a hyper-number of first class are reals, with the density of the reals—no “first,” “second,” &c., digits.

From this, we can likewise define hyper-numbers of the second class, H2 = power set of those of the first class, whose “integers” and “digits” are H1 numbers, with the density of H1 numbers. This set has cardinality c2 := 2^c1.

And, more generally, we can continue in a sequence of HN with cardinality cN := 2^c(N-1), where N is any finite natural number. Consider N = 100, N= 1,000,000, or N = 2^100!

Mind blowing!

I’d like to study this theory in detail someday, maybe establishing a formal theory by proving a few seminal theorems. Right now, I’m still busy completing and writing up my theory of black holes for publication in a peer-reviewed journal (as you may know if you’ve been reading my prior missives)—pretty bland stuff by comparison, no?

2 THE INEFFABLES. IDEALISM AND REALITY.

In quantum theory there is the well-known Wigner Probability Density Distribution [WQPD], which is not necessarily globally > or = 0 (and what, pray tell, does it mean that your chances of, say, getting lung cancer under certain circumstances is -5%?). In quantum theory, however, it remains the case that the probability density of a single observable is always globally > or = 0. This seems to have something to do with the hypothesis that any discrete or single (continuous) observable has a presumed exact value that can be determined exactly in a single measurement (while, for example, q, position, and p, momentum, cannot both be determined exactly simultaneously—the uncertainty principle +, really, only one thing can be measured at a time; perhaps this has something to do with why the WQPD may sometimes be < 0).

But what quantity can be measured to arbitrary precision with any real measuring instrument (I mean out to aleph-null decimal places), and in what conceivable machine or human memory device could all these digits be recorded or written down for even just one measurement, let alone scads of them?

Thus, I conjecture that not even the probability of a single (continuous) observable or variable need be globally > or = 0—and, indeed, why not dispense as well with the stipulation that it be normalized to unity (i.e., that the “total probability” = 100%)? What if sometimes the attempt to measure a quantity didn’t result in anything that could be represented by a number, or that, though it was in principle a number, it couldn’t be measured or calculated (like Chaitin’s Omega—the “probability” that a computer program loaded with a specific input would ever stop and not get caught in an infinite loop [the Turing “halting problem”])?

This brings me to my concept of “ineffables”—things that cannot, even in principle, be expressed by measurable or calculable “numbers” (isn’t the number concept itself an ineffable itself—WHAT IS a “number” [or, similarly, WHAT DOES it “mean” to “mean”?]. Mind you, I’m not looking for definitions in terms of other words—the attempt to describe an infinite reality with a paltry 100,000 or 300,000 words [the English language, the language with the most extensive vocabulary by far on earth] is really pathetic, and, ultimately, a vicious circle [all the words in a dictionary must be defined by other words—or by “pointing” to something: when you point to something, a dog will assume you’re trying to draw attention to your finger, not the object being “pointed” to—and, how do you point to “love” or “growth”?]).

Ineffables that we can mention, besides Chaitin’s Omega, are Cantor’s “Absolute” (infinity), which he associated with God, and consciousness, not to mention “color” (I mean the raw, conscious experience of a color, not its wavelength or frequency—I very much doubt that telling a congenitally blind person that the wavelength of blue light is 4000 Angstroms would in any way convey what a sighted person experiences as the sky).

What of the phenomenon of synesthesia, where a person might associate colors with music or numbers? And who says that what I experience as blue, if I could experience it through your sensory system, I might not experience as teal or red—or the note C-flat (synesthesia again!)? Science can describe only the “average,” “typical” case—these machines that can determine what a person is thinking about fairly accurately describe only what is common in the experience—what can be described in the public sphere. To what is atypical or unique in an experience—the private, subjective, world—science will forever be blind. Study your Nietzsche!—these things have been known a long time!

Mind blowing!

This is another thing that makes my continued interest in black hole theory look bland by comparison, no?

The notion that “empirical facts” can always be reduced quantitatively to numbers is hereby completely exploded. And the Hawkings of the world are not concerned with matters of “mere” philosophy! They’re missing half the fun! Why DO we perform our experiments if not precisely to interpret them and adjust our pardi pris to what they are trying so desperately to tell us about how the world really is—do we continue to stick to our dogmas in defiance of proper understanding of the evidence? Are we just to be content with the literal results of our piddlin’ experiments conducted in the sterile, controlled environment of the laboratory and not venture a guess as to what might be happening in the “wild?”

My feelings towards religion are mixed—part Hobbesian materialistic, quantitative atheist/tea kettle agnostic (Russell’s phrase), part Berkeleyian fundamentalist idealist-theist. There are NO certainties in life—but how much education is required to understand this! I would venture that the entire purpose of education (as opposed to the vocational training that the modern university system has devolved into) is precisely to depart some sense of just how small the collective knowledge of Man is (Feynman once famously calculated that every document ever produced—most of it the dross of phone books, suspense novels, restaurant receipts, X-rated movies, &c; the true knowledge is a very small percentage of even this tiny amount—could be stored on an ideal memory device of approximately one cubic centimeter—one seventeenth of a cubic inch!), let alone what is known to a single individual, be he a sports news anchor or the highest of artistic geniuses.

Dogma is never pretty nor correct. How arrogant—let alone unimaginative—is a person to think that he is in possession of even a single atom of the “Truth!”

As a banner in a church I attend states, “God is too big to fit into one religion.”

COEXIST!!

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stuart-boehmer · 6 months ago

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PLANAR BLACK HOLE

Stuart Boehmer, MSc Physics

I have fully worked out the interior solution of a black hole defined by an object of finite thickness and density in the z-plane.

Under certain conditions, the gravitational field strength, g, (see my prior missive, “Theory of Black Holes”) can approach infinity. But my calculations indicate that, as pressure gives out and there is a contraction, g is restored to smaller, finite values, allowing pressure to rebuild and equilibrium is re-established without a runaway contraction to a plane of zero thickness and infinite density.

Thus, as I suspected, Chandrasekhar’s contraction theory does not apply here.

This is good: very probably, the same result will obtain for a Schwarzschild sphere (the interior solution for which was worked out by Schwarzschild himself in 1916) and the standard picture of a black hole as a point-mass-singularity surrounded by a space-time singularity at distance 2GM/c2 is incorrect, as I stated in my former missive—but now I am more certain of the result.

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stuart-boehmer · 6 months ago

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APROPOS KERR METRIC AND INTERIOR SOLUTION

APROPOS THE VACUUM KERR METRIC AND INTERIOR KERR SOLUTION

Stuart Boehmer

According to a formula of Tolman (“Relativity, Thermodynamics and Cosmology,” Clarendon Press, 1934), with which apparently most authors are unfamiliar, and which can easily be reproduced with a little careful thought, the relationship between the spatial metric, gmn, and the space-time metric, Gmn, is not gmn = Gmn, but gmn = Gmn – G0mG0n/G00.

Therefore, a singularity coincident with the ergosphere is found to occur in the g33 component of the spatial metric (where u3 is the longitude), thereby rendering the standard vacuum Kerr metric theoretically useless as a practical model of a rotating black hole (see my prior missive, “Theory of Black Holes,” apropos my thought on singularities occurring in nature—the mathematical trick I used there to render impotent the singularity in g11 at the Schwarzschild radius doesn’t seem to work here).

Thus, in order to find a practical working model, there seems to be no shortcut except to do the hard work of solving the full, interior problem, including the consequent vacuum solution for the region of space exterior to the rotating dead star. This remains an open problem, but with the assistance of machine computation it is conceptually trivial, as we shall describe presently.

Define the problem in this way for specificity: use spherical polar coordinates where r is the radial distance from the center along a path of constant co-latitude and longitude (therefore g11 := 1). I see no reason to complicate matters by using the hyperbolic elliptic coordinate system chosen by Kerr. The black hole or dead star is assumed to be spherical (density a nonzero constant inside a sphere of radius r = R) and rotating with constant angular velocity w := du3/dt. Because, as we are about to describe, the solution is in terms of Taylor series, there is no a priori reason we cannot use general functions d(r,u2) and w(r,u2) expanded as Taylor series with known coefficients).

At this point, allow me to parenthetically describe the process of “Involution” (W. Seiler, Springer, 2009) for solving any differential equation or system of differential equations in terms of Taylor series and justify it as being just as good (and, for purposes of practical calculation in no way inferior to) finding a solution in terms of “elementary” functions—the obsession for which no doubt contributes to the fact that this conceptually trivial problem has remained open so long. Indeed, this method could be used to solve any problem in any theory of physics and no “open problems” should remain anywhere in the entire discipline of physics, conceptually.

The method is this: expand all known and unknown functions in terms of Taylor series; the known functions have known coefficients, and the unknown functions have unknown coefficients which can be derived recursively by equating the coefficients of like powers of the coordinates, by the standard procedure. See what I mean by “trivial?”

Now some old-fashioned people may object that any sound theory must be construed in terms of “elementary” functions, which are in some sense “known.” Of course, the only elementary functions except for polynomials are the trigonometric, hyperbolic trigonometric and exponential functions—all of which can be reduced to the exponential function, which in turn can be accurately calculated in terms of—guess what?—Taylor series or some equivalent infinite recursive process.

These days, we might regard elliptic integrals as elementary functions and there is an elaborate algebraic theory reducing the evaluation of an arbitrary elliptic function to those of the first, second and third kinds, but no one is interested in this theory any longer—it is simpler to just evaluate in terms of Taylor series by machine computation (the “NI” in UNIAC and ENIAC stand for “Numerical Integrator”—that is why computers were invented!).

Conclusion: computation by machine is just as respectable as any reduction to elementary functions—and there is no escaping the use of machine computation when calculating numerical values of “elementary” functions anyway!

The method of involution is often described as reducing calculus to algebra, because, of course, machine computation must terminate in a finite number of steps and the Taylor series just turns out to be polynomials of high degree. Polynomials are, ultimately, the only functions whose numerical values can be computed in a finite number of steps.

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stuart-boehmer · 6 months ago

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theory of black holes

THEORY OF BLACK HOLES

Stuart Boehmer

After many years of thinking about black hole theory, I think that I may have finally hit upon a consistent, unified theory.

An “event horizon” is usually defined in the literature as a place where a component of the spatial metric, gmn becomes infinite—this occurs only when one chooses poor spatial coordinates to define the problem. It can always be eliminated by a transformation of spatial coordinates.

For example, in the vacuum Schwarzschild metric, the radial distance from the origin is not Schwarzschild’s radial coordinate (here denoted by r*), but r := INTEGRAL(dr*/[1-(2GM/c2r*)]. This is an elementary quadrature which can be looked up in any table of integrals and it is both the function r(r*) and its inverse r*(r) are und to be singularity-free. Thus, we have eliminated the “event horizon.” g11 is not singular but becomes := 1 and the 22 and 33 components of the spatial metric are proportional to r*(r)^2, which is also has no singularities.

Also, the standard literature defines an “ergosphere” as a place where the G00 component of the space-time metric becomes zero. Alternatively, it is a place where the escape velocity equals c, which means light cannot escape this surface. In the case of the Schwarzschild vacuum horizon, because in the popular imagination an event horizon is a surface from which light cannot escape. By defining the “gravitational field strength,” gm, in a way that gives the Newtonian Limit (when c à infinity), we find that another definition of the ergosphere (when c does not à infinity) is where the gravitational field strength becomes infinite.

I make it an axiom that singularities (infinities and discontinuities) do not occur in nature, but may exist as theoretical abstractions only (e.g., the idealization of an atmospheric shock wave as a sharp discontinuity in pressure and density: in reality, the small, but real, viscosity of the air serves to give the shock wave a nonzero thickness).

Therefore, gravity never is infinite and, consequently, the escape velocity never equals or exceeds c anywhere in a realistic solution. Therefore, light can always escape the surface of any real black hole, albeit however slowly.

The full interior solution to the interior Schwarzschild problem was published by Schwarzschild himself in 1916. But apropos the vacuum solution, the ergosphere is coincident with the physical singularity at r = 0, which corresponds (upon evaluating the quadrature given ibid.) to r* = 2GM/c2.

The standard picture of a black hole as a point mass singularity surrounded by a space-time singularity at distance 2GM/c2 is incorrect.

One last note: Chandrasekhar’s theory is that a black hole will ineluctably collapse into a point singularity; however, my calculations indicate that the collapse will halt at a point where the gravitational field strength at the surface reduces to a point where pressure can once again balance it out and restore equilibrium. When we observe the surface of a black hole, we are in fact seeing the surface of a dead star (an extreme version of a neutron star), not some putative “Schwarzschild surface” at distance 2GM/c2.

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stuart-boehmer · 6 months ago

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OVERCOMING ALCOHOLISM

FIRST STEP IN OVERCOMING ALCOHOLISM

Stuart Boehmer

The first step in overcoming alcoholism, according to Alcoholic’s Anonymous [AA] is to “accept” that one has a problem. But my question is, “How can one ‘accept’ that on has a problem if one does not recognize in fact that it is a problem?”

The first step, as I have learned from my own personal experience, is learning to see your problem as a problem.

The problem with the brain of an alcoholic, like the brain of a psychopath, is that it is not wired to see one’s behavior as a problem. One thinks of it as a justifiable, even normal, way of life.

A psychopath’s brain is hardwired differently than the rest of us—he is almost a different species of beast—and there is no hope that learning through life experiences can change him.

But it is different with the alcoholic. The mis-wiring is a function of learning and life experiences and can be undone with time, learning and reflection.

I have no insight into how this learning is to take place; for me it “just happened,” and, I believe, I’m not really addicted to the alcohol per se—I have no cravings when I go for a spell without a drink—but to the paraphernalia, the whiskey glasses and carafes. “You can’t just put tea or water in those!” I tell myself dogmatically. So, I’m one of the lucky ones in this sense—it’s easy to cut myself off with no more than a few drinks.

As for the value of therapy, I find it somewhat dubious—AA or therapy (and my therapist recommended AA strongly, almost requiring it before he was willing to provide further therapy), either one, all the talk about alcohol just made me want to go out to a bar and have a drink afterwards.

Perhaps the greatest stimulus and learning experience for me was simply the repeated observation that the kinds of drunks that populate the bars tend to be silly and obnoxious (listen to the way they laugh when “living it up), and I decided that I didn’t want to be like that any longer.

I have no real advice to offer, just these observations, which I have found personally helpful. I hope that they can do something similar for you or a loved one if you or they suffer from this affliction.

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