The Missing Sentence in Einstein’s General Relativity

“Many—perhaps most—of the great issues of science are qualitative, not quantitative, even in physics and chemistry. Equations and measurements are useful when and only when they are related to proof; but proof or disproof comes first and is in fact strongest when it is absolutely convincing without any quantitative measurement.

Or to say it another way, you can catch phenomena in a logical box or in a mathematical box. The logical box is coarse but strong. The mathematical box is fine-grained but flimsy. The mathematical box is a beautiful way of wrapping up a problem, but it will not hold the phenomena unless they have been caught in a logical box to begin with.”

—John R. Platt, Science,1964

Albert Einstein’s canonical 1916 paper titled “The Foundation of the Generalized Theory of Relativity” contained many implied assumptions. His concept of “spacetime” (Raumzeit in the original German) was based on an understanding among scientists that the terms “space,” “time,” and “dimensions” had a clearly understood meaning. They were primarily mathematical meanings, space being the hypothetical container of all physical things in the universe, time the measure of the duration or persistence of those things, and dimensions, the measurable qualities of space and time. Of course, no one had ever experienced space, in and of itself, it couldn’t be seen, felt, or tasted. Time could only be measured as whatever fraction one chose of certain regular variable of experience, passage of the sun across the heavens, the cycles of day and night, the seasons in certain parts of the world. And dimensions were how one located objects relative to some reference point, or determined their size and shape relative to other “things.” Again, no one had seen, tasted, felt, or perceived in any way any physical substance of space, time, or a dimension. They were seen as not measurable, not perceivable qualities of the universe.

So why did Einstein choose to use them to describe the workings of that special phenomenon we call gravity. We may never know, but one reason might be that they were conveniently available mathematically and had been used by other mathematicians to relate to actual physical entities, notably by Poincaré, and Minkowski. They ended up as fundamental assumptions in his mathematical theory of gravity, and were accepted as fundamental, with few, if any questions as real, physical entities with real, physical characteristics.

But just imagine how, if Einstein had made these assumptions clear at the beginning, if he had opened his paper with the following sentence, what might have been the intellectual consequences?

“Let us assume that the hypothetical entity we designate as “space” is, in and of itself, a real physical entity, and that it possesses three unique characteristics we will call spatial dimensions, themselves possessing real physical characteristics, designated as “up-down,”, “right-left”, and “to-from,” measuring its value in spatial units; and further, that the hypothetical entity we call “time” is a real physical entity, and that it possesses as a unique characteristic a fourth dimension, measuring its value in time units “forward and back.” If we accept these assumptions, then the source and origin of the phenomenon we call “gravity” can be explained as follows.”

On reading the full paper it is clear to the reader that these assumptions are implicit in the words that follow, else the published text would not have physical meaning and would constitute only a hypothetical exercise in mathematics. However, the text is explicit in asserting that it constitutes a generalization of the assertions of the prior work, Special Relativity (On the electrodynamics of moving bodies, 1905), in order to include gravity in its purview. Einstein was a consummate mathematician. His formulae are elegant, consistent, and complete, but because of their non-physical assumptions they fail to reflect a physical, even a logical, reality. Rather, they are derived from a geometry, not from observations of the physical world.

To understand the theory’s assertions in full it is necessary to define its terminology as clearly as possible. The two key questions of course are: What is space? Is it a true physical entity that we can identify, locate? Can it or portions of it be described as to its nature and composition? Or is it alternatively like other real things, a magnetic field, for instance, only describable and its existence inferred from, its effect on other entities? Can we measure its intensity, direction or substance? is there proof that it is “real,” either logical or mathematical?

And what is time? Is it a force, moving one direction? Is it malleable independently of objects, events, phenomena? Like the question concerning space, can we examine a portion of it and determine its physical characteristics? None of these questions have generated an unequivocal answer. “It’s just there, everybody knows that!” is a common answer. And “everybody knows what time is!”

The most generalizable definition of space seems to be that it is the hypothetical container of all of the identifiable entities contained in what we call the universe. Its physical characteristics are hard to define except that it is unmeasurable in its extent and unfathomable in its depth. Descriptions of “outer space” usually specify that it is essentially “empty” except for the identifiable heavenly bodies like stars, planets, galaxies, etc. and clouds or nearly invisible wisps of hydrogen gas, cosmic dust, or in the most extreme sense, something called “quantum fluctuations,” an unknown substance, that participates in also unknown behaviors and causations. It is also referenced as “the vacuum” with the admonition that it is not really the same as the technical definition of a vacuum, that is, a space within a container that has been mechanically evacuated of all air, etc. It is, in astronomy, most usually considered to be that empty space between the stars “out there.”

In recent years, based primarily on anomalous observations of the behaviors of planetary and galaxial movements, what has been called gravitational lensing and the like, and on calculations of the numbers and assumed mass of what we can actually see in the night sky, space is also thought to contain mysterious substances thought to play a part in these anomalies. These have been named “dark energy” and “dark matter” and their total contribution to the mass of the universe has been more or less precisely calculated. So, space is not just an empty container, not a true vacuum. But what exactly is it then? And how can we best understand it?

When Isaac Newton was developing his mathematical models of the behaviors of the planets, he found that solving the relative gravitational influence of three or more planetary bodies was extremely difficult using the mathematical tools of his time, so he conveniently chose to ignore the effect of the moon on the orbit of the earth around the sun to obtain a useful approximation. Later, when Albert Einstein offered an newer model of the structure of the universe, he assumed that empty space was, in fact, actually empty. While earlier scholars and cosmologists felt the need for space to be a substance, to account for the transmission of light, for example, Einstein’s mathematical model of the universe had no need of substance, so an early assumption of an all-pervasive “ether” could be left out of his equations. Even though he later conceded that there must be something filling his “space” for the things he said were happening there to actually exist, he never made allowance for them in his equations. On the other hand, he left in place the assumption that the hypothetical “space” itself had physical characteristics, that is, it could be stretched, curved, distorted, etc. in the neighborhood of massive objects like planets that Newton earlier had assumed were exerting a force of attraction on other nearby and distant bodies. This force was called gravity.

In Einstein’s new construction of the universe, all is contained in what he called a spacetime continuum. A continuum in mathematics is considered a smooth, unbroken entity without interruptions or breaks. In one definition, it expressed as: a continuous sequence in which adjacent elements are not perceptibly different from each other, although the extremes may be quite distinct. In General Relativity’s continuum, there are no indicated or assumed limits. There exists an entire branch of mathematics for these entities called continuum mechanics.

To make his mathematics of the universe work, Einstein drew on the prior efforts of two other geniuses, Henri Poincaré and Hermann Minkowski who had developed systems that added a fourth variable, time, to the three accepted spatial dimensions. Adding time was important in describing systems in motion. But adding time was also problematical, because time, like space, was an entity that lacked real, physical attributes. It was not something you could see, taste, smell, touch. All it’s necessary attributes for a role in the physical world had to be arbitrarily added to it.

A very early writer on almost every subject, St. Augustine of Hippo, in the 5th century wrote, “I think I know what time is, until someone asks me to explain it. If nothing had ever occurred, the there would be no need for a concept of past time. If nothing were yet to occur, there would be no need for future time. If nothing were, there would be no need for present time.” And Newton said, “In another sense, time might be considered as simply duration.”

The concept of time is inextricably tied to the existence of “things,” their persistence, their duration. In the words of the joke, “Time is just one damn thing after another.” What time is not is a mysterious giant clockwork out among the stars measuring out our days.

So, Einstein’s physical universe, it’s observable behaviors, motions, forces had to be derived from those of two, until now, nonexistent entities, space. the hypothetical container, and time, the hypothetical measure of continued existence. Spacetime, is then a construct meld together by something called dimensions, but dimensions, in the real world, are simply systems of measurement, not physical entities in and of themselves.

So, if Einstein had made his assumptions explicit, instead of leaving the impression that, somehow, space and time were real entities, with physical characteristics enabling them to be bent, curved, compressed. extended, how would we today be explaining the orbits of the planets and stars, how would we be explaining the phenomena of gravitational lensing. Would we still be looking at Newton’s laws of motion? Or would we be seeking a new approach, looking at our last hundred years of observations and emerging patterns with different eyes, perhaps? Or would we have found a new paradigm, re-examining another concept to explain the speed of light, gravity, magnetism? Would there still be a search for the link between relativity and quantum mechanics, say, or would QM also be looking in other directions (It has it’s own contradictions to resolve, of course)?

Make no mistake, Albert Einstein was a true genius, in conceptual thinking, in mathematics. And he sensed that there was something missing in his theory. He hinted at that in his talk at Leyden in 1920, when he said , in effect, “the presence of an ether is essential for the theory of relativity to work..” So why do we still see “space” as empty? How do we explain how light and other electromagnetic phenomena are transmitted ? What is the reason light has a fixed speed limit? How can we speak to our friends instantly, so to speak, across the world? Surely there is a medium that bears those signals. General Relativity, that is, Einstein’s theory, has been useful, but why have we ignored its faulty assumptions? General Relativity is an elegant mathematical box. The corresponding logical box is, unfortunately, a poorly constructed container based on unprovable, unsupportable assumptions.

Space is not a thing. Time is not a thing. Dimensions are not things. They cannot be observed, manipulated, bent, curved, deflected, or managed in any way by human action or by cosmological or gravitational forces. They cannot be isolated in the laboratory, examined in the field, tested, or potentially disproven. Their existence or nonexistence cannot be objectively shown. And yet. . . . one of the principal “standard models” of physics and cosmology rests on the exactly opposite assumptions, that these hypothetical man-made concepts, measuring systems, imaginary constructs, are in fact, real things. I think 100 years is long enough to depend on this illusion.


About Charles Scurlock

Charles is a recently retired architect/planner and generalist problem-solver with a lifelong interest in science, physics, and cosmology, and the workings of the human mind. He has started this blog in the interest of sharing his ideas with others of like-(or not so like) minds.
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3 Responses to The Missing Sentence in Einstein’s General Relativity

  1. Guy Burneko says:

    You do cut to the chase…..

  2. Michael Boyd says:

    Photons [light] has no inertia and photoelectric effect is only a property of non-bonding electron orbitals in matter, not anything to do with gravitation what ever. The simplest flaw I see is it fails to address the anti-symmetric nature between the mass of electrons (electron……….0.00091×10-27 kg ) and protons (proton………….1.6726 x 10-27 kg ) and how that effects the flow [mobility] of the different types of charge, protons[holes] and electrons. Since the form of energy the light weight electrons produce is light [mass-less photons] and the force of energy protons produce is attractive gravity [massive gravitons] therefore I assume EM and gravitation are not directly related, but only indirectly instead. In order to understand why gravity is different [stronger] close-up you have to understand the theory of gravitation being what’s called the large extra-dimension…

    Theoretical physicists Arkani-Hamed, Dimopoulos and Dvali pointed [2], out that prior to now, gravity had not been measured below a distance of about a millimeter. They whose model is known as ADD, suggest that there could be extra dimensions as large as a millimeter in diameter. In particle physics, the ADD model, also known as the model with large extra dimensions [1], offers an alternative scenario to explain the weakness of gravity relative to the other forces. This theory requires that the fields of the standard model are confined to a four-dimensional membrane, while gravity propagates in several additional spatial dimensions that are large compared to the Planck scale.

    Theoretical physics typically treats the Planck scale as the highest energy scale and all dimensional parameters are measured in terms of the Planck scale. In models of large extra dimensions the fundamental scale is much lower than the Planck scale. This occurs because the power law of gravity changes. For example, assuming r is the distance between the gravitational induction sensor and the spinning disk; when there are two extra dimensions of size d, the power law of gravity is 1/r4 for objects with r <> d. This relationship suggests if we want the Planck scale to be equal to the next accelerator energy (1 TeV) we should take d approximately 1mm.

    As suggested by ADD, gravity could be just as strong as the other forces but only felt strongly at short distances. Scientists funded by the European Space Agency have measured the gravitational equivalent of a magnetic field for the first time in a laboratory. Just as a moving electrical charge creates a magnetic field, so a moving mass generates a gravitomagnetic field. According to Einstein’s Theory of General Relativity, the effect is virtually negligible. However Tajmar [3] have measured the effect in a laboratory. Their experiment involves a ring of superconducting material rotating up to 6,500 times a minute.

    My hypothesis is that protons [holes in the semiconductor junction] in all forms of matter and their presence in our location in the universe, this is the source of the attractive force of gravity in the vicinity of matter. My discovery is at 100nm distance away the force of gravity is magnified and can be harnessed to produce gravitomagnetic induction with my invention, the mass spin-valve or gravitational rectifier, due to this gravity large extra dimension. The other novel thing I discovered in the absence of matter produces a repulsive anti-gravity force that is much weaker then the gravity force and balloon like. Electrons however do not contribute enough mass to really effect gravitation in any significant way.

    The GMR head in the device sees the magnetic image at 100nm distance and something else? The way my device distinguishes the EM from the gravitation is using Maxwell’s right hand rule for magnetic induction. Using that rule I know the edges of my nano-features on a spinning disk will produce a magnetic induction signal that is dependent on the direction of the magnetization of the magnetic media on the disk which I can control by change the bias applied to the write transducer [a microscopic metal coil] on the head in the disk drive assembly. Notice the direction of the gravitomagnetic signal shown doesn’t change however; that’s because that force field’s direction depends on the presence or absence of matter.

    Effects of geometry on gravitational fields and time
    The geometry of matter, or lack there of, causes a force field to be produced that I could measure. The reason gravitation is a direct tensor is because it has two components one is the normal gravitational energy produced by the presence of matter’s nucleus in the universe and the other what we call repulsive anti-gravity or dark energy is produced by its absence. But the tensor for gravity is much stronger than anti-gravity since the absence of mass produces only about 16% of the magnitude for the same volume (geometry). Some other differences are normal gravity is much stronger below 1 mm from matter than it is above that distance; as is the antigravity force. I found for normal gravity above 1 mm it is consistently linear with distance; while antigravity is ~ 0. That means the force is 1/r^2 above 1mm and 1/r^4 below 1 mm but that means gravity is still linear with distance within both regions of normal gravity space time. Antigravity on the other hand is a third order force repulsive force tensor whose force fields are like that of balloon with their force field’s strength being strongest at the membrane of the balloon and weak inside.

    Regarding the gravitational temporal relation both forms of gravitation experience the same amount of frame dragging as described in Einstein’s General Relativity theory; so doesn’t that means Time must be the substance between gravitational energy and EM energy that makes up our existence? Time must be a substance. That’s because gravitational space time is produced by hole states of matter and electromagnetism spacetime (EM or light) is produced by electron states of matter. QM is built on EM space time; not gravitational space time. However Special Relativity is built on EM space time while General Relativity is built on gravitational space time. The manifold of events in spacetime are a “substance” which exists independently of the matter within it…Special Relativity and General Relativity created a conundrum for Einstein that he tried to resolve unsuccessfully to unit the two theory in to one grand unified field theory. My discovery is that while the speed of light is constant that’s not true for gravitation. It can be slower in speed and faster too. Einstein focused to much on the speed of light and not enough on the “holes” all around him. That’s where the gravitation is. That “electromagnetism is in spacetime A” let’s call that space-time “{EM} space-time”, and this is what Einstein’s “Zur Elektrodynamik bewegter Korper”[4] (“On the Electrodynamics of Moving Bodies”) described which reconciles Maxwell’s equations for electricity and magnetism with the laws of mechanics, by introducing major changes to mechanics close to the speed of light. This later became known as Einstein’s special theory of relativity (SR).[5][6] That “gravitation is in spacetime B” let’s call that space-time “{G}space-time” and this is what Einstein’s General relativity (GR) describes. According to general relativity,[7] the observed gravitational attraction between masses results from the “warping of space and time by those masses”. When I write about this “manifold of events in spacetime are a “substance” which exists independently of the matter within it” this “manifold of events in spacetime” is this property that makes Time; as we measure it; the emergent {positive arrow of time}. Therefore time is a vector which direction depends on your position in our universe which is created by a change of energy states between gravitation to electromagnetism; and visa versa.

    Theoretical Implications of Nano-scale Quantum Gravitomagnetism
    In the event horizon of a black hole gravity is faster than the speed of light. In that domain light is forbidden. Einstein’s problem was he only understood the universe from the side of electrons not the holes side that dominates it. If you think of empty space as a high density of holes and matter as regions where electron density is higher then you see Einstein Dirac etc…, where blinded by the light produced by electrons…, that’s why they couldn’t see the holes in the universe all around them.

    The mass of a neutron is greater than the mass of a proton because the neutron contains a proton, contains an electron with some subatomic particles.

    Neutron stars are collapsed matter leaving only neutrons at the atomic scale that makes up the neutron star and black holes are nearly identical but made of protons [holes] instead.

    Black holes are black not because light doesn’t escape but because black holes are made of holes [collapsed protons] where light is not present because there are no electrons to absorb the light for re-emission of the light.

    My hypothesis is that protons [holes in the semiconductor junction] in all forms of matter and their presence in our location in the universe, this is the source of the attractive force of gravity in the vicinity of matter. My discovery is at 100nm the force of gravity is magnified and can be harnessed to produce gravitomagnetic induction with my invention the mass spin-valve or gravitational rectifier due to this gravity large extra dimension. The other novel thing I discovered is the absence of matter produces a repulsive anti-gravity force that is much weaker then the gravity force and balloon like. Electrons however do not contribute enough mass to real effect gravitation in any real way as far as I can measure.

    [1] ANTONIADIS, N., ARKANI-HAMED, N., DIMOPOULOS, S., DVALI, G. New dimensions at a millimeter to a Fermi and superstrings at a TeV. arXiv: hep-ph/9804398, 1998.
    [2] ARKANI-HAMED, N., DIMOPOULOS, S., DVALI, G. The Hierarchy problem and new dimensions at a millimeter. arXiv: hepph/9803315, 1998.
    [3] TAJMAR, M., MATOS, C.J. Gravitomagnetic Fields in Rotating Superconductors to Solve Tate’s Cooper Pair Mass Anomaly. arXiv: gr-qc/060786, 2006.
    [4] EINSTEIN, A. Zur Elektrodynamik bewegter Korper. Annalen der Physik 17: 891-921, 1905.
    [5] EINSTEIN, A.; GROSSMANN, M. Entwurf einer verallgemeinerten Relativitatstheorie und einer Theorie der Gravitation. Zeitschrift fur Mathematik und Physik 62: 225-261, 1913.
    [6] EINSTEIN, A. Die Grundlage der allgemeinen Relativitatstheorie. Annalen der Physik, 49, 1916.
    [7] HILBERT, D., Die Grundlagen der Physik. Mathematische Annalen, 92, 1924.

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