I have maintained since the beginning that Relativity is defined by the need for transforms. If we require transforms, then Relativity is fundamentally true. Even if we require transforms only due to the Doppler effect, that still implies Relativity. The rest is a matter of interpretation and math. Einstein sometimes interpreted Relativity in the wrong way, and all his math is wrong, but fundamentally he was correct. We do require transforms, and we require transforms that are of the general form he gave to us. Our job is therefore to correct the math and the interpretation, in those places it fails.

Concerning General Relativity, the question becomes, “Do we need to apply these transforms to accelerations, to combine relativity with gravity?” Yes. Einstein was completely correct in this, so General Relativity must be fundamentally true. Einstein also manages to get the right numerical answer—or near the right answer—with his curved math and space, so we must give him some credit. But we must disagree with him in several ways. As I have pointed out in other papers, the curved math wasn’t necessary. It adds a needless complexity. Even for those who do not or cannot accept expansion theory, GR can be done with a much simpler math. That is to say, even if you want to keep gravity as a pulling force, it is much more efficient to reverse the accelerations in the math, and then apply the time differentials. This method is mathematically allowed, and it gets the right answer much more directly and with much less work. It also clarifies the mechanics. The simpler math puts the motions and forces in a higher focus than Einstein’s math was able to do, so that whatever your mechanics may be, you will have a firmer grasp of it with the simpler math.

This paper will clarify a second major disagreement I have with Einstein. I first wrote about this disagreement in my paper on the Born-Einstein letters, but I thought it best to expand it here under its own title, due to its importance. Not only does Einstein choose a curved math, he chooses a curved field. He lets his math define his field, so that the curvature of one is the curvature of the other. I have already proved that this was simply a choice. I proved it in the most direct manner possible, by making a different choice and showing that it also got the correct answer. Einstein had implied that curved math was necessary, but that is false. The math can be done in either a curved field or a rectilinear field, with either curved math or Euclidean math.

But because the field is curved, certain mechanical properties are given to the field, and certain fundamental dynamical facts are the outcome. In letter 99 of the Born-Einstein letters, Einstein says, ''the gravitational equations would still be convincing because they avoid the inertial system (the phantom which affects everything but which is not itself affected).'' This quote cannot be circled and highlighted enough. In Einstein’s mathematical expression of GR, the inertial system is avoided, by Einstein’s own admission. What does that mean? It has been taken to mean that the equations have to do with acceleration, acceleration is “non-inertial”, and therefore the equations are non-inertial. This interpretation allows readers to pass over this quote of Einstein without pausing. But clearly Einstein could not have meant that in this quote. It would be silly to state something so obvious to another top physicist, much less to then call the inertial system a “phantom which affects everything but which is not itself affected.” In saying that he had “bypassed the inertial system,” Einstein was saying that he had bypassed the dynamical system of forces: he had bypassed the inertial system of Newton—based on force—which acted as a phantom by determining all motions. In Einstein’s math, the motions were determined by pre-existing curves, or by differentials from point to point in the field, not by phantasmagorical Newtonian forces at a distance. Einstein’s field is not an inertial or dynamical system, it is a mathematical system. A body in the system does not move in a curve because it feels a force, it moves in a curve because the space is curved, and the space is curved because the math is curved. It moves in a curve while feeling no forces!

Einstein saw this as a great advance, since it seemed to cleverly sidestep Newton’s problem of force at a distance. Newton had defined force, mass, and acceleration as functions of one another, but since the acceleration was a pull, the force appeared to be transmitted through empty space, with no physical mechanism. Einstein did not provide a physical mechanism: gravitons were of no interest to Einstein himself, as a mediating particle of this force. No, gravitons were proposed by Einstein only as carriers of gravity waves, and were proposed as fundamental field particles only after Einstein, by people who did not understand his concepts. Einstein did not want or need a mediating field particle, because his equations already avoided the inertial system. The equations were expressly chosen to avoid the inertial system, and without an inertial system, you don’t need to explain forces or accelerations. In fact, in Einstein’s equations, all forces and accelerations are only apparent. There is no centripetal acceleration, since the field is already curved. And even a body in freefall is not really accelerating. According to Einstein’s math, a body in freefall is experiencing a constant velocity, according to its own local measurements. It is simply moving into adjacent field “levels” where velocity is measured differently. Since these levels are not equivalent, mathematically, you need GR transforms to go from one to the other. The difference in velocities at different levels is therefore not a real acceleration, it is only a difference in transforms. According to Einstein’s postulates, the body does not accelerate, the transforms do.

Physicists after Einstein have continued to sell this interpretation as a thing of great mathematical and theoretical beauty, since it seems to solve Newton’s problem with one flick of the switch. The problem is, it solves the problem only by hiding it in the math. Einstein avoids the inertial system by making his math the cause of the motions. The curved math does all the physical work, with no need of real forces or accelerations. But clearly this is a cheat of gigantic proportions. It is beyond belief that he was never called on it. He was never called on it because no one understood how this curved math was really working, or how powerful it was as a heuristic tool. The only ones who understood the math, those like Hilbert and Klein and Weyl and Minkowski, were thrilled to have it used in a famous physical theory. So they weren’t going to spill the beans. The mathematicians were the ones who had proposed the equations in the first place. And no one else could see through the veils.

To say it again, the problem is that you cannot let your math carry your forces. The math should represent motions, not cause them. In Einstein’s field equations, the motions are caused by the field curvature, and the field curvature is caused by the math. So it is the math that causes the motions. In curved math, the math becomes a force. The math becomes the first cause, the impetus to motion. The math replaces the inertial system. That is not a theoretical advance, that is a theoretical and mathematical cheat.

Look closely: Einstein has hidden the mechanism in his math, and, although the question is begged most assuredly, no one has seen where to beg it. Einstein has given us a curved field around a planet (say), so that we no longer have to ask how that planet acts on its moon. The field is curved and the moon follows the curve. But the question begged is this: “How does the planet act upon the field, to curve it?” With Einstein’s equations, the field curvature is given to us automatically. The math is curved before the first question or the first manipulation. So we forget to ask for a mechanical reason for the curvature, or a mechanical cause. At the very least we need a physical link between the planet and its field. “Why is the curvature greater nearer the planet and less farther away?” To this, Einstein has no possible answer. He has already matched his math to the known field, so any answer he could give would be circular. For Einstein, the answer is, “The gravitational field acts like it does because that is what a gravitational field is. We are given an experimental fact, and I have matched my equations to it. That is what physics is. What further answer is possible?”

If Einstein had given this particular answer, he would have been following the dodge of Feynman. When pressed on theoretical contradictions, Feynman would always dodge into this “experimental” stronghold and bar all the windows. Physicists in the 20^th century loved this dodge, since it immediately pegged the opponent as some sort of metaphysician. It was if to say, “I am a hard scientist, and we hard scientists—opposed to, say, psychologists or sociologists—are tied to facts. We limit ourselves to questions that can be decided by experimental outcome. We don’t have time for metaphysical questions and squishy philosophical problems."

As if logic were a squishy metaphysical question. As if consistency were a limp philosophical problem. As if physicists were allowed to propose theories in which there was no connection between the facts and the math, or as if mathematicians were allowed to propose equations in which there was no connection between the postulates and the deductions, between the axioms and the proofs.

To get back to Einstein, his answer is a dodge because physics is and always has been more than matching a set of equations to an experiment. If the equations imply physical facts, the physicist should be able to make some physical connection between the equations and the facts. Otherwise you just have a math with no theory. Claiming that the math is the theory is like claiming that the roof is the floor.

To be more specific, there is an easy reply to the question “What further answer is possible?” That reply is: given a planet and a curved field around it, we want a causal mechanism for that curvature. If the planet is the cause of the curvature, as Einstein certainly implies that it is, then we must have a mechanism, or at least the theory of a mechanism. If we don’t, then the field is just as mysterious and un-physical as was Newton’s field of forces at a distance. In fact, curvature IS a force at a distance, since the field is at a distance from the Earth.

Notice that in that last paragraph I am not pointing out a metaphysical problem, I am pointing out a mechanical one.

An even greater mechanical problem comes when we look at impulse to motion in the field. This is what I have called “the biggest black hole in GR” in my title. If we have no real forces and accelerations in the field—all motions being caused by the field curvature at each point—then we have no impulse to motion on a non-moving object in the field. If we PLACE an object at some altitude over the Earth, and use Newton’s field theory, we can explain its immediate fall by a force between that object and the Earth. Using the theory of expansion, we can explain its fall by the real motion of the Earth toward it. Using Einstein’s field theory, we cannot explain its fall. Yes, if it is already moving in any direction, we can explain its subsequent motion by field differentials. If it is already falling, we can explain its continued fall and continued apparent acceleration by field differentials. If it is in orbit, we can explain its continued orbit by the curvature of the math. Using Einstein’s field equations, we can explain any motion except falling from a state of rest. There is no mechanism in Einstein’s field to push the resting object from one level to the next lower one. Since there is no inertial or dynamical field, nothing is or can be impelling the body to move from one point to the other. Ironically, Einstein’s equations cover any possible motion in the field except motion from rest.

Amazingly, this point has never been raised, and it has never been raised because it is hidden in plain sight. It is so basic that no one has thought to look at it. Everyone knows that objects fall in a gravitational field, so how could a set of field equations fail to contain that? It doesn’t seem possible, so no one has checked it. But it turns out that it is the one experimental fact that disproves Einstein’s field equations. An object placed in a gravitational field will fall, therefore the curved math cannot be correct.

Once stated, this problem is so unanswerable it becomes humorous. If an apologist for Einstein attempted to refute me, he or she would have to say something like, “No, Einstein’s field equations do allow for motion in this case, since the equations not only create field differentials, as you put it, they create field potentials. As with the magnetic field, these potentials are perfectly capable of causing motion from a state of rest.”

If the apologist said this, he or she would be claiming that a field of no forces could move a body from a state of rest just by mathematical differences between one point and another. He or she would be claiming that a real mass could achieve a velocity from a state of rest with no force upon it, no inertial or dynamical system, no collision, no emission, and no mediating field particle. In other words, according to this “physicist”, a real body can be moved by nothing other than math.

I put it this way in order to try to pre-empt what I know I cannot pre-empt. No matter how foolish I make them appear beforehand, “physicists” will not be deterred from saying exactly what I just said they will say. They will say it, they will not admit it is un-physical, and it will not bother them one way or the other. I know this because they have been doing it for decades, without a moment’s guilt or hesitation. These are the sort of people who will stand in front of the Sun and tell you it is night, and then get mad when you don’t believe them. They are not only impervious to logic, they are impervious to all experiment. You could literally blind them with that Sun, and they would only use their blindness as proof it was dark.

This experimental fact is not proof of expansion theory, since no experimental fact is proof of a theory (see Karl Popper). But it is proof against Einstein’s theory. Einstein’s theory, like Newton’s, cannot be correct, for strictly experimental reasons. We have to come up with something better.

That something must be something that is more mechanical, not less mechanical. Which is why string theory should be immediately dumped as a nuisance. Expansion theory may or may not be correct, but, joined to my new E/M field theory, it is already much superior to either Newton or Einstein. It avoids this black hole of GR, it avoids the black hole of the stable orbit (see my paper on Celestial Mechanics), and it explains hundreds of things neither Newton nor Einstein could explain.

You will say, if that is so, why do I continue to confirm that GR is true? Didn’t I just accuse Einstein of a gigantic fraud, in using curved math to cause his motions? Didn’t I just show that the curved field was physically false?

Yes, but despite all that, GR is still true. Einstein’s axioms and math are both false, but GR—defined as the need for transforms that include both the gravitational accelerations and the time differentials—is true. Expansion theory does not overthrow GR, it includes it and re-interprets it, in a more consistent field math and more consistent logic. When I do field equations with my own math and theory, I have to do relativity transforms within the gravity accelerations, and in doing that I am doing General Relativity. Einstein’s GR is fatally flawed, but GR, as a broader physical theory, is only confirmed by my corrections to it. In the long run, what I have done is correct Relativity, not overthrow it.