We discuss the meaning of quantum theory and conclude that, indeed, the proper interpretation is ... more We discuss the meaning of quantum theory and conclude that, indeed, the proper interpretation is "shut up and calculate!" It is primitive AI, a data compression scheme.
measurements: if q is determined exactly, so is p (specif.: p = (h/2[pi])dS/dq), but due to this ... more 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.
I will have more to say about the following in a more detailed post later, but for now, a thought... more 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 language-based 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)
The theory that "life" is just an optical illusion caused by a very complicated inanimate biochem... more 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…
First, allow me to interject that the idea that I am about to describe seems more extensive than ... more 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:" H 1 is the first class of hypernumber, of cardinality of the power set of the reals, c 1 := 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 hypernumber 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, H 2 = power set of those of the first class, whose "integers" and "digits" are H 1 numbers, with the density of H 1 numbers. This set has cardinality c 2 := 2^c 1. And, more generally, we can continue in a sequence of HN with cardinality c N := 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?
PLANAR BLACK HOLE Stuart Boehmer, MSc Physics I have fully worked out the interior solution of a ... more 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/c 2 is incorrect, as I stated in my former missive-but now I am more certain of the result.
According to a formula of Tolman ("Relativity, Thermodynamics and Cosmology," Clarendon Press, 19... more 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, g mn , and the space-time metric, G mn , is not g mn = G mn , but g mn = G mn-G 0m G 0n /G 00. Therefore, a singularity coincident with the ergosphere is found to occur in the g 33 component of the spatial metric (where u 3 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 g 11 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 g 11 := 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 := du 3 /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,u 2) and w(r,u 2) 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.
In a non-inertial reference frame in relativity (and all real reference frames are non-inertial; ... more In a non-inertial reference frame in relativity (and all real reference frames are non-inertial; special relativity is just a theoretical abstraction), synchronization by light signals based on the constancy and isotropy of the speed of light do not work. Thus, we must define synchronization by the more fundamental (and, in inertial frames, equivalent) procedure of slowly transporting a clock between two locations: I get out of my chair & travel to yours across the room and make a direct comparison of our watches. In non-inertial reference frames in relativity, I find that the concept of "synchronization" of clocks is path dependent. This means that there is no real concept of synchronization. For example, if clock B is to the north and east of A, they may appear to be synchronized if A travels first to the north, then to the east, while perhaps not if A travels first to the east then to the north. Thus, the question whether A and B "are" synchronized has no definite answer. This has an astonishing consequence for the concepts of (spatially extended) "objects," "observers," and the sense of "self." A spatially extended object (or person or "self") does not exist at what could be meaningfully construed as a single "instant" of time-what is the "now," in light of the forgoing? The concepts of "object" and "self" are interrelated in a sort of feedback loop: which is the chicken, and which is the egg? As Nietzsche said: "How much rudimentary psychology [i.e., street psychology; intuition] resides in your atom, my dear physicists!"
In this paper, we study hypersphere (sectional curvature, K, = constant > 0), pseudosphere (K < 0... more In this paper, we study hypersphere (sectional curvature, K, = constant > 0), pseudosphere (K < 0) and flat (K = 0) solutions of the Einstein Field Equations corresponding to uniform density and pressure. We, incidentally, confirm that Mach's Principle obtains in General Relativity, i.e., the rotation of space (causing centrifugal, Coriolis and Euler forces) is intimately bound with the rotation of matter. Gödel thought that he had found a rotating solution of the Einstein Field Equations, but his solution may be summarily dismissed because it is nonphysical, containing two time-like coordinates, t and φ (and he
We derive conditions on possible solutions of the Einstein Field Equations that guarantee their p... more We derive conditions on possible solutions of the Einstein Field Equations that guarantee their physical reality. These conditions eliminate several famous "solutions" of the EFE extant in the literature, including event horizons, ergospheres and "time travel" or closed time loops.
We discuss the fact that what is known as the "cosmological" constant of the Einstein Field Equat... more We discuss the fact that what is known as the "cosmological" constant of the Einstein Field Equations, usually taken to be a fundamental constant of Nature, like h or c, is really just an adjustable constant of integration, adaptable to whatever physical problem is at hand.
We carefully criticize Alcubierre's analysis of a solution to the Einstein Field Equations which ... more We carefully criticize Alcubierre's analysis of a solution to the Einstein Field Equations which he claims represents hyper-fast (fasterthan-light) travel in general relativity. We show that his solution is really just a solution of special relativity, reducible to the usual Twin Paradox, and that his conclusions are completely fatitiutous.
We study the Einstein Field Equations in a two-dimensional spacetime, and we find that they do no... more We study the Einstein Field Equations in a two-dimensional spacetime, and we find that they do not approach anything like the Newtonian Limit as → ∞. Neither theory, General Relativity or the Newtonian Theory, has any empirical basis except in a four-dimensional space-time, which is what the one and only reality we know, apparently, is.
We derive conditions on possible solutions of the Einstein Field Equations that guarantee their p... more We derive conditions on possible solutions of the Einstein Field Equations that guarantee their physical reality. These conditions eliminate several famous "solutions" of the EFE extant in the literature, including event horizons, ergospheres and "time travel" or closed time loops.
I have posted the following summary of some of my recent results on black hole theory on Academia... more I have posted the following summary of some of my recent results on black hole theory on Academia.edu, ResearchGate & stuartboehmer.com:-
1 There are no black holes. Main result: the minimum value of what Schwarzschild calls r is 2GM/c^2, not 0; this eliminates negative values of G00 (four-metric) and g11 (spatial metric) and, along with it, a lot of nonsense. Just about any text on black hole theory contains an account of the region 0 < r < 2GM/c^2, which is hereby rendered completely obsolete. The interior environment is just matter of extreme density and pressure, an extreme neutron star—no event horizons, &c.
We solve the problem of rigid motion in special relativity in completeness, forswearing the use o... more We solve the problem of rigid motion in special relativity in completeness, forswearing the use of the 4-D geometrical methods usually associated with relativity, for pedagogical reasons. We eventually reduce the problem to a system of coupled linear nonhomogeneous ordinary differential equations. We find that any rotation of the rigid reference frame must be independent of time. We clarify the issues associated with Bell's notorious rocket paradox and we discuss the problem of hyperbolic motion from multiple viewpoints. We conjecture that any rigid accelerated body must experience regions of shock in which there is a transition to fluid motion, and we discuss the hypothesis that the Schwarzchild surface of a black hole is just such a shock front.
We consider the case of a planar gravitating object in General Relativity and find glaring incons... more We consider the case of a planar gravitating object in General Relativity and find glaring inconsistencies in the Einstein Field Equations. 1 Introduction. Consider an object (something approximating a black hole, if you will) distributed in the − plane of constant density, , for finite thickness, −ℎ < < 0. This corresponds to the case of a constant gravitational field in the z-direction in Newtonian gravity-the simple case you learned in High School where projectiles follow parabolic trajectories & escape velocity is ∞-i.e., nothing can escape the gravity: a projectile shot with any velocity upward returns to earth. The mass per unit area is finite = ℎ; the gravitational field depends on this finite quantity and not the total mass of the plane, which is infinite-both in the relativistic & Newtonian case. However, there are easily calculable contradictions in the Einstein Field Equations [EFE], as we will see in this brief missive.
We discuss the meaning of quantum theory and conclude that, indeed, the proper interpretation is ... more We discuss the meaning of quantum theory and conclude that, indeed, the proper interpretation is "shut up and calculate!" It is primitive AI, a data compression scheme.
measurements: if q is determined exactly, so is p (specif.: p = (h/2[pi])dS/dq), but due to this ... more 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.
I will have more to say about the following in a more detailed post later, but for now, a thought... more 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 language-based 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)
The theory that "life" is just an optical illusion caused by a very complicated inanimate biochem... more 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…
First, allow me to interject that the idea that I am about to describe seems more extensive than ... more 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:" H 1 is the first class of hypernumber, of cardinality of the power set of the reals, c 1 := 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 hypernumber 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, H 2 = power set of those of the first class, whose "integers" and "digits" are H 1 numbers, with the density of H 1 numbers. This set has cardinality c 2 := 2^c 1. And, more generally, we can continue in a sequence of HN with cardinality c N := 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?
PLANAR BLACK HOLE Stuart Boehmer, MSc Physics I have fully worked out the interior solution of a ... more 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/c 2 is incorrect, as I stated in my former missive-but now I am more certain of the result.
According to a formula of Tolman ("Relativity, Thermodynamics and Cosmology," Clarendon Press, 19... more 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, g mn , and the space-time metric, G mn , is not g mn = G mn , but g mn = G mn-G 0m G 0n /G 00. Therefore, a singularity coincident with the ergosphere is found to occur in the g 33 component of the spatial metric (where u 3 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 g 11 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 g 11 := 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 := du 3 /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,u 2) and w(r,u 2) 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.
In a non-inertial reference frame in relativity (and all real reference frames are non-inertial; ... more In a non-inertial reference frame in relativity (and all real reference frames are non-inertial; special relativity is just a theoretical abstraction), synchronization by light signals based on the constancy and isotropy of the speed of light do not work. Thus, we must define synchronization by the more fundamental (and, in inertial frames, equivalent) procedure of slowly transporting a clock between two locations: I get out of my chair & travel to yours across the room and make a direct comparison of our watches. In non-inertial reference frames in relativity, I find that the concept of "synchronization" of clocks is path dependent. This means that there is no real concept of synchronization. For example, if clock B is to the north and east of A, they may appear to be synchronized if A travels first to the north, then to the east, while perhaps not if A travels first to the east then to the north. Thus, the question whether A and B "are" synchronized has no definite answer. This has an astonishing consequence for the concepts of (spatially extended) "objects," "observers," and the sense of "self." A spatially extended object (or person or "self") does not exist at what could be meaningfully construed as a single "instant" of time-what is the "now," in light of the forgoing? The concepts of "object" and "self" are interrelated in a sort of feedback loop: which is the chicken, and which is the egg? As Nietzsche said: "How much rudimentary psychology [i.e., street psychology; intuition] resides in your atom, my dear physicists!"
In this paper, we study hypersphere (sectional curvature, K, = constant > 0), pseudosphere (K < 0... more In this paper, we study hypersphere (sectional curvature, K, = constant > 0), pseudosphere (K < 0) and flat (K = 0) solutions of the Einstein Field Equations corresponding to uniform density and pressure. We, incidentally, confirm that Mach's Principle obtains in General Relativity, i.e., the rotation of space (causing centrifugal, Coriolis and Euler forces) is intimately bound with the rotation of matter. Gödel thought that he had found a rotating solution of the Einstein Field Equations, but his solution may be summarily dismissed because it is nonphysical, containing two time-like coordinates, t and φ (and he
We derive conditions on possible solutions of the Einstein Field Equations that guarantee their p... more We derive conditions on possible solutions of the Einstein Field Equations that guarantee their physical reality. These conditions eliminate several famous "solutions" of the EFE extant in the literature, including event horizons, ergospheres and "time travel" or closed time loops.
We discuss the fact that what is known as the "cosmological" constant of the Einstein Field Equat... more We discuss the fact that what is known as the "cosmological" constant of the Einstein Field Equations, usually taken to be a fundamental constant of Nature, like h or c, is really just an adjustable constant of integration, adaptable to whatever physical problem is at hand.
We carefully criticize Alcubierre's analysis of a solution to the Einstein Field Equations which ... more We carefully criticize Alcubierre's analysis of a solution to the Einstein Field Equations which he claims represents hyper-fast (fasterthan-light) travel in general relativity. We show that his solution is really just a solution of special relativity, reducible to the usual Twin Paradox, and that his conclusions are completely fatitiutous.
We study the Einstein Field Equations in a two-dimensional spacetime, and we find that they do no... more We study the Einstein Field Equations in a two-dimensional spacetime, and we find that they do not approach anything like the Newtonian Limit as → ∞. Neither theory, General Relativity or the Newtonian Theory, has any empirical basis except in a four-dimensional space-time, which is what the one and only reality we know, apparently, is.
We derive conditions on possible solutions of the Einstein Field Equations that guarantee their p... more We derive conditions on possible solutions of the Einstein Field Equations that guarantee their physical reality. These conditions eliminate several famous "solutions" of the EFE extant in the literature, including event horizons, ergospheres and "time travel" or closed time loops.
I have posted the following summary of some of my recent results on black hole theory on Academia... more I have posted the following summary of some of my recent results on black hole theory on Academia.edu, ResearchGate & stuartboehmer.com:-
1 There are no black holes. Main result: the minimum value of what Schwarzschild calls r is 2GM/c^2, not 0; this eliminates negative values of G00 (four-metric) and g11 (spatial metric) and, along with it, a lot of nonsense. Just about any text on black hole theory contains an account of the region 0 < r < 2GM/c^2, which is hereby rendered completely obsolete. The interior environment is just matter of extreme density and pressure, an extreme neutron star—no event horizons, &c.
We solve the problem of rigid motion in special relativity in completeness, forswearing the use o... more We solve the problem of rigid motion in special relativity in completeness, forswearing the use of the 4-D geometrical methods usually associated with relativity, for pedagogical reasons. We eventually reduce the problem to a system of coupled linear nonhomogeneous ordinary differential equations. We find that any rotation of the rigid reference frame must be independent of time. We clarify the issues associated with Bell's notorious rocket paradox and we discuss the problem of hyperbolic motion from multiple viewpoints. We conjecture that any rigid accelerated body must experience regions of shock in which there is a transition to fluid motion, and we discuss the hypothesis that the Schwarzchild surface of a black hole is just such a shock front.
We consider the case of a planar gravitating object in General Relativity and find glaring incons... more We consider the case of a planar gravitating object in General Relativity and find glaring inconsistencies in the Einstein Field Equations. 1 Introduction. Consider an object (something approximating a black hole, if you will) distributed in the − plane of constant density, , for finite thickness, −ℎ < < 0. This corresponds to the case of a constant gravitational field in the z-direction in Newtonian gravity-the simple case you learned in High School where projectiles follow parabolic trajectories & escape velocity is ∞-i.e., nothing can escape the gravity: a projectile shot with any velocity upward returns to earth. The mass per unit area is finite = ℎ; the gravitational field depends on this finite quantity and not the total mass of the plane, which is infinite-both in the relativistic & Newtonian case. However, there are easily calculable contradictions in the Einstein Field Equations [EFE], as we will see in this brief missive.
This paper continues my look into the Minkowski paradox & explores its relationship to Mach's Pri... more This paper continues my look into the Minkowski paradox & explores its relationship to Mach's Principle.
We announce our discovery that the cosmological constant is actually an adjustable constant of in... more We announce our discovery that the cosmological constant is actually an adjustable constant of integration.
We present general relativity in what I call normal form, decomposing the 4-metric, , into a grav... more We present general relativity in what I call normal form, decomposing the 4-metric, , into a gravitational vector potential, , in terms of which the gravitational field strength, , is defined as and the spatial metric,. Gravity is a force and the putative "curvature of space-time" reputedly responsible for it can be reduced to the three components, of the 4-metric. The curvature of space is regarded as an effect of gravity rather than a cause and gravity is a vector potential field, , not a tensor potential field,. Notation.
Abstract.
I can show that the minimum value of what Schwarzschild calls r is 2GM/c2. Of course, ... more Abstract. I can show that the minimum value of what Schwarzschild calls r is 2GM/c2. Of course, r (denote it by u) is not the radial distance from the origin (denote that by r). Therefore, the Schwarzschild solution doesn’t really have an event horizon—it is coincident with the central singularity. (u = 2GM/c2 corresponds to r = 0.) Calculations follow.
We consider the case of a planar gravitating object in General Relativity and find glaring incons... more We consider the case of a planar gravitating object in General Relativity and find glaring inconsistencies in the Einstein Field Equations.
We find that the Wigner Probability Distribution has a fully classical interpretation, and that t... more We find that the Wigner Probability Distribution has a fully classical interpretation, and that the microscopic world is not a "black box" (per the Copenhagen Interpretation). Probability represents our state of knowledge of a system. However, in quantum theory, as opposed to classical theory, cause and effect is at the level of our state of knowledge, (,), not the state of the world, (,). Quantum theory is idealistic in the sense of Berkeley: the world is a conscious, shared hallucination.
We discuss "temporal drift," my term for the degree to which clocks in a fixed reference frame di... more We discuss "temporal drift," my term for the degree to which clocks in a fixed reference frame dis-synchronize with distance as defined by slow clock transport in both pre-relativistic ("classical") and relativistic physics. Then we demonstrate that the usual expression for length contraction is unaffected by temporal drift, although there is a subtlety in the definition of velocity when temporal drift is present. Then we demonstrate the invariance of the line element in relativity and show that the off-diagonal terms of the 4-metric are intimately related to the temporal drift when is chosen to equal. Finally, we investigate temporal drift and synchrony in accelerating and rotating frames and find that temporal drift is irreducible in these cases.
We discuss an ontology for quantum theory based on the fact that it is a theory of observation an... more We discuss an ontology for quantum theory based on the fact that it is a theory of observation and measurement, not a theory about "reality." It is similar to the Copenhagen Interpretation of Bohr and Heisenberg in many respects, but there is one difference. This paper may be regarded as a mathematical formalization of the Copenhagen Interpretation.
This paper is inspired by a paper of Fayngold [1] in which he claimed that one-way superluminal s... more This paper is inspired by a paper of Fayngold [1] in which he claimed that one-way superluminal signaling is impossible. He stated that he felt that he hadn't proven that one-way tachyon travel was impossible, just that one-way transfer superluminal of information is impossible (couldn't we attach a letter to our tachyon?). But in this paper, we go further and show that tachyon travel-one-way as well as two-way-is impossible, provided that we accept the very intuitive notion that a particle cannot arrive at a point before it departed the same point in some reference frame. 1 Introduction.
We analyze carefully the premise made in Bell's analysis of his non-locality theorem that measure... more We analyze carefully the premise made in Bell's analysis of his non-locality theorem that measurements made at distant locations cannot influence those made locally and find that it is false. This vitiates his famous theorem and allows us to conclude that quantum theory is local and realistic (in the sense that it is premised upon a single materialistic world which is common to all observers at different points in space or in different reference frames); i.e., a "hidden variables" theory, with no superluminal influences or "spooky action at a distance," but just the result of correlations among the spins which are established at a common origin.
The thesis of this paper is based upon the observation that the Lorentz Transformation probably i... more The thesis of this paper is based upon the observation that the Lorentz Transformation probably is not exact to an arbitrary degree of precision-nothing manmade ever is-and therefore the concept of a "space-time manifold" in which time is inseparably bound with space disintegrates and must be replaced by what I call "space with time" or "temporal geometry" which is contrasted with the static geometries of Euclid, Bolyai and Riemann as well as the absolute time of Newton by including in spatial geometry a time parameter which dynamically interacts with spatial variables but is not identical with them as in the Minkowskian conception (which can degenerate into a completely absurd "block space time" in which everything is written out in advance for all time-nature, by contrast, is dynamic and chaotic, not static. In the words of a song by Natasha Bedingfield, "Your book is still unwritten.") The four-metric, , is merely a convenient mathematical auxiliary variable with no direct physical meaning. We define a force as any deviation from a spatial geodesic (thus returning to Newton's original conception), because, among other things, a space-time geodesic cannot be meaningfully defined if there is no space-time manifold, and in that case, gravity is a force. The much ballyhooed "curvature of space-time" (which is said to be the cause of gravity) will be found to be caused entirely by a vector-like potential, , and not the full tensor potential,. We close in our conclusion with some remarks on empiricism and the flaw in trying to develop theories intellectually rather than being guided exclusively by trying to explain empirical results, an activity that has become popular since the-in my opinion, unfortunateunique example of the development of the General Theory of relativity.
We consider the case of constantly accelerated frames and rotating frames in the Special Theory o... more We consider the case of constantly accelerated frames and rotating frames in the Special Theory of Relativity. We find that both cases have surfaces homologous to an event horizon at the point where the velocity of the non-inertial reference frame, , with respect to an arbitrary but fixed global inertial frame, , becomes and space variables become time-like and the time variable becomes space-like. We conjecture that this is impossible and that one must transfer to another reference frame which becomes non-rigid at least slightly before reaching the event horizon and where space variables are globally space-like and never null or time-like and time variables are globally time-like, never null or space-like. We conjecture, moreover, that in relativity any rigid non-inertial reference frame must have an event horizon somewhere; we also conjecture that this is not a reference frame that could occur in nature and whose space and time variables could be used for meaningful physical analysis. In that case, one must transfer to another reference frame which is non-rigid and in which no event horizon occurs. Mathematical
We discuss "temporal drift," my term for the degree to which clocks in a fixed reference frame ge... more We discuss "temporal drift," my term for the degree to which clocks in a fixed reference frame get out of synchrony with distance as defined by slow clock transport in both prerelativistic ("classical") and relativistic physics. We find a subtle paradox in special relativity that doesn't appear in classical theory regarding the calculation of the apparent length of a moving rod compared with its proper length when temporal drift is present. The resolution of the paradox is an open question.
In this paper we adopt a novel approach to finding the Newtonian Limit of the Einstein Field Equa... more In this paper we adopt a novel approach to finding the Newtonian Limit of the Einstein Field Equations and find, among other things, that the gravitational field is properly defined by a vector potential rather than a scalar potential. This approach also explains the
In 1949 Kurt Gödel found a solution to the Einstein Field Equations of General Relativity which h... more In 1949 Kurt Gödel found a solution to the Einstein Field Equations of General Relativity which he believed contained a closed time-like curve which could be slightly perturbed to allow reverse time travel-a time machine. Apparently, he was not conversant with the Sagnac effect whereby two clocks on a rotating sphere do not give the same reading at the same time. This effect has been observed and today is routinely used to maintain synchrony of satellites in the Global Positioning System. We discuss the general theory of the Sagnac effect and show how it debunks Gödel's argument. Several closed time-like curve solutions have been found by other authors over the years, but our guess, without having methodically examined each case, is that they all succumb to the same analysis.
We show that, contrary to the prevailing opinion, coordinates in General Relativity do have physi... more We show that, contrary to the prevailing opinion, coordinates in General Relativity do have physical meanings and that coordinates are essentially reference frames. A coordinate singularity such as an event horizon is actually a pathology in the reference frame and can be eliminated only by a velocity boost or change of reference frame. In this light we discuss the case of constant acceleration in special relativity and the Schwarzchild and Kerr metrics in General Relativity. We find, among other things, that what in the Kerr metric is often called the ergosphere is really the event horizon and that what is usually called the event horizon, being inside the real event horizon and physically inaccessible, is just another (physically uninteresting) coordinate singularity which, however, has the peculiar property of being one-dimensional rather than two-dimensional.
We discuss the attempt to reform the interpretation of relativity by saying that the Cosmic Micro... more We discuss the attempt to reform the interpretation of relativity by saying that the Cosmic Microwave Background [CMB] determines a sort of "absolute space" where we can return to the ideas of Newton (as amended by Lorentz and Poincarè).
We resolve the twin paradox of special relativity by tediously considering two space time paths i... more We resolve the twin paradox of special relativity by tediously considering two space time paths in detail.
We show that violation of Bell's theorem has little to do with quantum mechanics, locality or cau... more We show that violation of Bell's theorem has little to do with quantum mechanics, locality or causality, but merely with whether or not particles are independent entities. If they are not, then there would be violations even in classical mechanics with a non-negative Liouville probability distribution.
Uploads
Papers by Stuart Boehmer
1 There are no black holes. Main result: the minimum value of what Schwarzschild calls r is 2GM/c^2, not 0; this eliminates negative values of G00 (four-metric) and g11 (spatial metric) and, along with it, a lot of nonsense. Just about any text on black hole theory contains an account of the region 0 < r < 2GM/c^2, which is hereby rendered completely obsolete. The interior environment is just matter of extreme density and pressure, an extreme neutron star—no event horizons, &c.
1 There are no black holes. Main result: the minimum value of what Schwarzschild calls r is 2GM/c^2, not 0; this eliminates negative values of G00 (four-metric) and g11 (spatial metric) and, along with it, a lot of nonsense. Just about any text on black hole theory contains an account of the region 0 < r < 2GM/c^2, which is hereby rendered completely obsolete. The interior environment is just matter of extreme density and pressure, an extreme neutron star—no event horizons, &c.
I can show that the minimum value of what Schwarzschild calls r is 2GM/c2. Of course, r (denote it by u) is not the radial distance from the origin (denote that by r).
Therefore, the Schwarzschild solution doesn’t really have an event horizon—it is coincident with the central singularity. (u = 2GM/c2 corresponds to r = 0.)
Calculations follow.