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of Curved Space
by Miles Mathis
In a previous paper I have shown that the curved space of General Relativity can be made rectilinear with one simple mathematical manipulation. Just as Minkowski made the four-vector field symmetrical with one simple postulate, I have made curved space non-curved with one even simpler postulate. The difference is that my postulate is true and his is false.
Minkowski's idea was to use hyperbolic math to express the field, let the time variable be represented by i, and postulate that time was moving orthogonally to x,y,z. Mathematically this was beautiful; physically it was simply false, as I have shown in another paper.
My idea was to use Einstein’s own postulate of equivalence to reverse the central field vector g. This flattened out all the bending of light in the gravitational field and allowed me to express the math with highschool algebra, in a rectilinear field. It also allowed me to solve 40-page tensor problems in one paragraph.
Now, it is true that my postulate is not physically demonstrable as correct. My mechanics relies on internal consistency and simplicity, like any other mechanics or any other theory. However, I have falsified Minkowski's postulate: it is not correct. Minkowski's math implies a physical mechanics that we know is not the case, experimentally. I have also falsified several of Einstein’s postulates, which are not correct. Einstein's math does not work in many logical and experimental situations. But my postulate is both mathematically and logically consistent. It corrects a large number of old problems and does not create any new ones. It stands until someone falsifies it.
Before I offer my newest critique of curved space, one that I think is fatal to it, let me quickly gloss my previous critiques. As I said, my primary critique is mathematical. I have shown that the gravitational field can be expressed as a rectilinear field, even after we import Special Relativity and the finite speed of light into it. I have shown that I can solve problems in this field with simple algebra, and do so in an 80th of the time it takes to solve them with tensor calculus and curved space. For the modern scientists who claim to care about nothing except math and experiment, that should be enough. They can follow my calculations and "shut up" (as their master Feynman told them). But some few may still have logical problems. These few may eye my math like I have eyed Minkowski's. That is, they will not want to accept that all matter is accelerating outward spherically, no matter what the math says. Nor will they want to accept it only as a mathematical postulate, reversing it later to suit the physics they believe in. They will demand to know what is really going on—and I admire them for that stance. This paper is to address their concerns.
The first logical critique I made of curved space was in my article on tides. I showed that tidal theory relied completely on Newtonian forces at a distance. This theory is wholly dependent on uneven forces on an extended body, forces which do not pertain with curved space. An orbiter traveling in curved space would not logically be expected to feel the same tidal forces as an orbiter traveling in a Newtonian orbit, and this has nothing at all to do with SR or the speed of light. It has to do with the vectors or tensors caused by the field.
This is true with only one body, but it is much more obvious once you introduce a second body. The second body, say the Moon, is also warping the space around it. The warp around the Moon is convex, like the warp around the Earth. Problem is, the influence is going both ways. The Moon is supposed to be causing tides on the Earth at the same time that the Earth is causing tides on the Moon. So is the space in between the Earth and the Moon convex or concave? It must be one or the other. Space cannot curve two different ways at the same time. Nor can it be a vector addition of the curvatures. If the two bodies flatten out the curves of the other, they also must flatten out the effects. The curvature is both mathematical and physical. If the curve is flattened, the tide is gone. In General Relativity, the space is the field. They are the same thing. Unless Einstein meant to propose that we have an infinite number of gravitational fields interpenetrating eachother with no collisions or effects, his postulate is a non-starter. And if this is the case, there is really no reason to assign any or all of these fields to space. Moreover, if this is the case, his math becomes even more bulky—both as math and as metaphysics—than it was before. He now has a nearly infinite number of curved fields to express simultaneously, as against my one rectilinear field.
Which brings us to the central thesis of this paper. Everyone knows that Einstein used Maxwell's electrical field as the blueprint for his gravitational field. He did this mainly because the finite speed of light had already been incorporated into the electrical field. The problem comes when you compare the two fields. I will use as an example the field created by a bar magnet, since we all have in our heads the illustration of it from our textbooks. You will remember that the field lines curve. Did you ever go back to that illustration and ask, "Does that mean that space curves around a bar magnet?" Probably not. Most people assume that space and the electrical field are two different things. The electrical field can curve or not curve, but that says nothing about space. The electrical field is assumed to inhabit space, but it is not space itself.
Why do we make a different assumption with the gravitational field? Or, to put it another way, why do we allow Einstein to make that assumption for us and then never seriously question that assumption in a century? Einstein chose a curved math. He tells us that he had to choose a curved math, since no rectilinear math could be applied to the problem. I have shown that this is false. He chose a curved math because a very impressive curved math was flitting around looking for a partner. It was a PR move. Then, when he was done, he told us that the math was the physics. The math is the space. The field is the vacuum.
Notice how similar this is, as a sales tactic, to Quantum Mechanics. Both theories are basically mathematical, but they tack on a metaphysics at the end. This metaphysics very hamhandedly says that the math is the physics. The math curves therefore the space curves. End of argument. In QED, the math causes logical inconsistencies, therefore there are inherent logical inconsistencies in nature that we must accept. End of argument.
But the math curves due to the fact that Einstein quite freely chose to use a curved math. It therefore says nothing about the physical space that the math inhabits. Like the electrical field, the gravitational field can be seen simply as a field. As an abstraction. Logically, the curvature of the math or the field says nothing about the curvature of space. Why should gravity be the fundamental defining field of space any more than the electrical field? Why does the gravitational field get applied directly to space when the electrical field doesn’t?
None of these logical questions are ever asked. They were immediately buried and they have remained buried.
Curved space is bad theory, since curved fields do not imply curved space. The curved gravitational field is a bad theory, since it is unnecessary. The curvature is completely caused by the math, but it is not necessary to choose that math. Math that is much simpler and more transparent is readily available, and it gives you the same answers in 1/80th the time.
If one of your first demands on celestial mechanics is that it avoid the idea of universal expansion, then, yes, you will be led to a curved gravitational field. Einstein was correct in that. But he was not correct to imply that the idea of universal expansion was impossible. Expansion is a rather simple mechanical concept, and it should not be dismissed prejudicially. Einstein dismissed the idea in one sentence, with no argumentation or explanation. He did this despite the fact that all his paragraphs leading up to this dismissal led logically—one might say inexorably—to the idea of expansion.
Einstein was a revolutionary, but he was also very attached to the idea of equilibrium. We all know that he spent decades trying to make GR match his prejudice that the universe was stable—neither expanding nor contracting as a whole. This prejudice basically destroyed him, as a mathematician. But he also had another similar prejudice, concerning the equilibrium of visible objects like the Earth and Moon and people and animals. In the book Relativity, he says that, "it is impossible to choose a body of reference such that, as judged from it, the gravitational field of the earth (in its entirety) vanishes." While this would seem to be true on a first reading, it is not to the point, theoretically or mathematically. He thinks that it implies that he cannot create a rectilinear math, but I have shown that this is false. You do not need to choose a body of reference like he is talking about in order to create a rectilinear math. All you have to do is redefine a pull as a push, and his postulate of equivalence allows us to make that redefinition. His story of the man in the chest does precisely that. He reverses the acceleration vector, and shows that no mathematical or physical contradiction is the result. This allows us to reverse the central acceleration vector of gravity. Because this acceleration vector points in all directions spherically, the gravitational field of the earth vanishes. Or, to be more precise, the field does not vanish, it simply becomes rectilinear and expresses itself by real outward motion instead of an apparent inward pull.
Einstein implies that this field reversal is not worth theorizing. He implies that because it is impossible to choose the body of reference he mentions, it must be impossible to follow this line of theory. But it is by no means impossible. If you are prepared to accept universal expansion, then it is simple to follow this line of theory, as I have shown. In fact, once you have done this, you can then go back and find a body of reference that fits his description. Your body of reference must be expanding at the same relative rate the earth is, in which case the gravitational field of the earth vanishes, in Einstein’s sense of vanish. The only reference body that is impossible to choose is one that is not expanding. Einstein is not really honest enough here, or rigorous enough. He should have said, "It is impossible to choose a body of reference [stable in size relative to the vacuum] such that, as judged from it, the gravitational field of the earth (in its entirety) vanishes." That is true. But that impossibility is just a mechanical prejudice. We do not know for a physical fact that all objects in the universe are stable in size relative to the vacuum, or relative to ten seconds ago. Therefore he is discarding theory not on logical grounds or mechanical grounds or mathematical grounds, but on a prejudice.
All of this is almost beside the point, however, given the current state of physics. Most physicists and mathematicians accept the math of Minkowski, and they accept it because (they think) it works. They don’t care whether time physically travels at a right angle to x,y,z, because the postulate is simply a mathematical one. Given that, there is no reason why they should not welcome my rectilinear gravitational field, even if they believe it is or may be physically false. They should be able to accept my vector reversal as a simple mathematical postulate, one that greatly simplifies the equations. Einstein himself gave me the vector reversal, with his own postulate of equivalence. All I have done is apply it in a mathematically consistent way. If these scientists and mathematicians are consistent and logical, they must accept my equations as a great advance.
And, if they are truly revolutionary and non-prejudicial, I think they must accept my mechanics as well. Universal expansion has ten times the explanatory power and none of the inconsistencies of the Standard Model. I admit that it is incomplete, but it is already more complete than the Standard Model. It is superior as math, is simple and transparent, is falsified by no experiments, and beautifully explains many of the paradoxes and dead ends of current theory. It makes predictions that are immediately verifiable and makes no appeals to faith or authority. That is what a good theory should be.
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