*“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.

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