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Papers by Stuart Boehmer

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.

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.

SCIREA journal of physics, May 22, 2021

SCIREA journal of physics, Apr 19, 2021

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.

European Journal of Applied Sciences, 2023

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.

Today I defied Richard Feynman's advice to not waste your time & went down the qu... more Today I defied Richard Feynman's advice to not waste your time & went down the quantum rabbit hole and figured out what the theory MEANS. Whether I'm a skilled enough mathematician to pull off the specific calculations is another matter. The idea involves observing a qm system (II) with another system (I) treating I only in the classical limit. The idea of speaking of II only in relation to its effect on I is the essence of the Copenhagen interpretation promoted by Niels Bohr and Werner Heisenberg. The theory is materialistic regarding I, but agnostic regarding the nature of II-maybe someone could even figure out how to apply it to the question of consciousness, which like quantum systems, we know about only through inference-even in the case of our own consciousness, according to the famous perspectives of Julian Jaynes ("The Bicameral Mind & The Origin of Consciousness"-a book which today, admittedly, isn't taken very seriously by serious scholars). In any case it has the potential to give "nuts and bolts" meaning to bizarre qm statements s.a. "qm particles can be in two places at once" & such things as wave-particle duality and bizarre phenomena such as the double slit expt. or the delayed choice expt., &c., &c....

. The question of the illusoriness of time is discussed and a position against the idea is taken.

We discuss the meaning of quantum theory, in particular, the question of whether reality is subje... more We discuss the meaning of quantum theory, in particular, the question of whether reality is subjective (observer-dependent), per the claims of one version of the multi-faceted "Copenhagen Interpretation" and conclude that it is not, any more so than is the classical, pre-quantum theory-and for the same reason, viz., it is built in by assumption. To drive this point home, in the final section we derive a general "phase space" representation of the quantum mechanics of an individual free particle characterized by a parameter, L, which refers to a property of the measuring instrument (observer), and show that the expectation value of any operator is independent of L.

We discuss whether the mathematical ideal of a black hole can exist in nature. We conclude that ... more We discuss whether the mathematical ideal of a black hole can exist in nature. We conclude that the objects which have been observed, popularly called black holes, are mere approximations to the ideal, much as natural shock waves are approximations to the mathematical ideal of an abrupt discontinuity in pressure & density.

We establish that the 3-geometry of any rigid motion attainable from rest is Euclidean. This is a... more We establish that the 3-geometry of any rigid motion attainable from rest is Euclidean. This is a direct consequence of the Born rigidity condition. Rotation has a non-Euclidean 3-geometry and thus arbitrary rotation is not possible; hence Bona's theory to the contrary is untenable. Along the way we solve Bell's notorious rocket paradox.

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.

SCIREA Journal of Physics, 2021

SCIREA journal of physics, May 22, 2021

SCIREA journal of physics, Apr 19, 2021

European Journal of Applied Sciences, 2023

. The question of the illusoriness of time is discussed and a position against the idea is taken.

SCIREA Journal of Physics, 2021

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.

European Journal of Applied Sciences, 2023

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.

Check out my blog at stuartboehmer2.blogspot.com

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 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.