Miles Mathis: The Aberration of Starlight is an Expanding Earth
| Please note that this paper is a simplification by me of a paper or papers written and copyrighted by Miles Mathis on his site. I have replaced "I" and "my" with "MM" to show that he is talking. All links within the papers, not yet simplified, are linked directly to the Miles Mathis site and will appear in another tab. (It will be clear which of these are Miles Mathis originals because they will be still contain "I" and "my".) The original papers on his site are the ultimate and correct source. All contributions to his papers and ordering of his books should be made on his site. (This paper incorporates Miles Mathis' third5 paper, gr4 paper), and first part of the aberr paper up until Airy.) |
Einstein Eddington
Background
The aberration of starlight was historically considered the most convincing data in support of Einstein's curved space hypothesis. (It is now most commonly called bending or deflection of starlight, but is really aberration.) He is said to have predicted it, have given us a number for it, and it was found to be so. It must be noted that Newtonian physics also implies the bending of starlight, once light is known to be a particle. Newton’s gravity will affect light just as much as General Relativity. Newton said so explicitly. You don’t need curved space for the aberration of starlight, you only need light to have a mass equivalent. Eddington even did the math and found his own number for this.
However, it most be noted that Einstein originally got the wrong number for both the bending of light by the sun and the precession of the perihelion of Mercury. (See Problems with General Relativity: Curved Space is Unnecessary and the Inertial System is Ignored) In his first equations, he found less than half the known amount for Mercury and exactly half the correct amount for the sun. (See "Perihelion Precession of Mercury Explained" and also for the similar solution as in this thesis.) He corrected his number for Mercury up, to match the known number, so this was not a prediction. It was a postdiction. This correction to the field equations doubled his prediction for the sun. This might be considered a true prediction, in a way, since the number for the sun was unknown at the time. But it is important to realize that this "prediction" was mathematically linked to the postdiction on Mercury. If Einstein had not known the number for Mercury, he would never have known that he needed to correct the math. It is interesting to realize that his underlying theory allowed either number--either his first number or the doubling of that number. So his claim that his math evolved perfectly out of unquestionable axioms is completely false.
Both Newton and Einstein postulated the existence of a field produced in some mysterious way by the sun. Newton thought matter in the field felt a tug; Einstein, that matter followed a curved path, without a tug. In Problems with General Relativity: Curved Space is Unnecessary and the Inertial System is Ignored a third view is offered, a view that turns both "fields" inside out.
In Solution to the Ellipse problem MM shows that the production of an ellipse with a ball and a rubber band produced a field that was inside out. It was backwards. The force on the rubber band must be greater at apogee than at perigee, which is the opposite of a gravitational field. The "field of the rubber band" varied with the inverse square law, but it got stronger with greater distance, not weaker.
Referring to Einstein's chapter [ch. XX] on gravity in his book Relativity, after showing the equivalence of gravity and acceleration (with his elevator car in space), he said, "Now we might easily suppose that the existence of a gravitational field is always only an apparent one." But, he continued, "It is impossible to choose a body of reference from which the gravitational field of the earth vanishes."
Einstein’s elevator car is the thought problem that led Miles Mathis to work seriously on expansion theory. The question arises can the gravitational field of the sun be caused only by motion, and can we explain the bending of starlight by this motion? Einstein said no, because he did not want to propose expansion, but it seems to offer the best explanation as will be shown.
It turns out that aberration is among the simplest things to explain with expansion. Let us say we have data before us that shows that light from a star on the far side of the sun has not arrived on earth in a straight line. It has curved in getting to us. How do we come to that conclusion? Simple. Before the light from the star got to the sun, it was travelling in line x, the line it always travels in when not affected by the sun. From the sun to the earth, it was travelling in line y, roughly. The difference in the lines is the angle of refraction. Now let us ask, is there any other possible movement that could explain this "refraction." There is one other, though no one has ever put it forward: Something besides the light has moved. You will say, what? What else could have been refracted?
Well, nothing else is in a position to be refracted or bent, but there are a couple of other movements that could explain the appearance of a bending of starlight. At first it seemed that the expansion of the sun would explain it most easily, but then not.
Diagrammed above is an expanding sun here. Look at the starlight arriving at the earth. From the vicinity of the sun to the earth you have "seen" it move from right to the left. You expected it at point a, it arrived at point b, on the earth. Therefore you conclude that it must have been refracted. But now go to the background of this movement. What is the beam of starlight refracting relative to? What is the light moving with regard to? The sun, of course. Either the beam of starlight has moved from right to left, or the right edge of the sun has moved from left to right. In other words, the sun has moved into the space that the beam of light just passed. The light was not refracted, the background moved. The sun is the background, and it moved.
The aberration of starlight is either:
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History has chosen (1), but (2) is a better explanation.
Obviously the right edge of the sun cannot move by itself. The sun cannot just shift to the right for no reason; nor can the sun bulge on the right side and leave the left side standing. So what Miles Mathis have theorized is an expansion of the sun, as a whole, in all directions. From the time the starlight hit the vicinity of the sun until the time it reached us, the sun grew a tiny bit. This “bit” is the same bit that the starlight is supposed to have refracted.
Some scientists have looked quickly at the figure above and said, "That won't work. According to your diagram, we should see the star with the sun as its background—meaning, not at all. It would be lost in the sun. Or, during a total eclipse, we would see your star within the circle of the eclipse! You are saying that the light from the star is not curved or refracted; that there is no aberration. You are saying the light is arriving from the star to the earth in a straight line. Therefore, if we follow your line back from the earth to the sun, we hit the bigger sun. This means that your star would be invisible—not because it is behind the sun, but because the sun is behind your vector, drowning it out. Or, in a total eclipse, your vector would be incident with the moon."
It is a difficult situation to construct in your head, but these scientists are wrong. They have not done a thorough study of the diagram or the problem. Imagine we are studying the problem at a total eclipse, and have our telescope trained on the edge of the sun. We photograph the star just beyond the edge of the sun. We know it is a star that should not be there. According to our charts, it should be behind the sun. So far, so good. But now we have to analyze the operation of photographing the star. The light that has developed our photograph is coming from the star and the sun. The light from both travels the same speed and covers the distance from the sun to the earth in the same time. Therefore, our photograph is a photograph of the starlight just as it passes the sun. We are looking at a situation that existed in the vicinity of the sun around eight minutes ago. Therefore, all we know is that eight minutes ago, the light from the star was just wide of the edge of the sun, seen from the earth.
If this is true then if you follow the line back from the earth to the sun in the diagram, you do not hit the sun at t2, you hit the sun at t1—the smaller sun. This is because as you follow the line away from the earth, you must go back in time a bit. When you reach the sun, you are eight minutes in the past: t1 is eight minutes in the past; t2 is when the light hits the photographic plate. Therefore the starlight is not drowned out by the sun anymore than theirs is. Nor is it within the eclipse.
It is at this point in his explanation that MM recognized a flaw. If the sun is eight minutes in the past on a photographic plate, then all our measurements of the sun must be eight minutes old. Specifically, when we measure the optical width of the sun to determine its size, we are measuring a sun that is eight minutes old. Therefore, when we used our star charts to determine which stars should be obscured by the sun, we were using a sun that was eight minutes old there, too. And this means that we cannot go eight minutes in the past in order to find a smaller sun—one we can make our starlight pass in a straight line. We are already in the past, regarding all current measurements on the sun. The sun may be expanding, but if so, it is expanding after our photograph was taken. Its expansion thereby cannot be part of our data in this problem.
If it is not the sun expanding, then there is still another body expanding in this problem: the earth. If the earth is expanding at 9.8 m/s2, then after eight minutes it will have moved over a million meters in every direction.
s = at2/2= [(9.8 m/s2)(499s)2]/2
= 1,220,105m
At t1, the time the photograph was taken of the eclipse, the earth was represented by the smaller circle and would have been blocked from the light of the star unless it was bent. But at t2, eight minutes later, the right side of the earth will have moved far enough to the right to capture the starlight with no bend.
This means that it is the expansion of the earth that is responsible for the appearance of aberration, not the expansion of the sun.
Einstein's theory is being used to surpass him! Relativity makes this new theory possible. It is relativity that allows us to see that the time of the sun and the time of the earth are not equivalent. A distance separation implies a necessary time separation. The fact that our photographic plate of the eclipse is a picture of the vicinity of the sun eight minutes ago is crucial to MM's solution. That eight minute gap allows the earth to expand enough to capture starlight that it is not predicted to be able to capture. The prediction fails because it was based on an earth that was the same size at t1 and t2.
This explanation allows Miles Mathis to make a very important prediction of his own. Eddington confirmed Einstein’s prediction only because his telescope was positioned on the correct side of the earth. You can see from MM's second diagram that only the right side of the earth would be in a position to capture the starlight. In fact, a telescope positioned on the left side of the earth looking at a star on the right side of the sun would find just the opposite “bending”. Rather than seeing stars it was predicted not to see, it would not see stars it was predicted to see. The sun would seem to be blocking even more starlight than it should. And a telescope positioned in the middle of the earth would see the sun blocking (almost) exactly what it was predicted to be, since that position would benefit least from the expansion of the earth during the eight minutes. Astronomers should put this prediction to the test during an eclipse, comparing the aberration from different positions on earth. If expansion theory is true, then they will see very different outcomes from what current theory predicts.
In fact, Miles Mathis provides a number for his prediction, using very simple math. The number above for the expansion of the earth in 499 seconds to calculate a maximum apparent bending must be corrected a bit in order to fit it into the calculation. The light from the star would intersect the sun at a tangent, therefore we must add the radius of the sun to the distance to the sun in order to find the length of that line. Which gives us an extra 2 seconds for the light to reach the earth. Which changes our expansion of the earth to:
s = at2/2 = [(9.78 m/s2)(501s)2]/2
= 1,230,000m
Now, if the telescope is positioned on the earth as far right in MM's diagram as it can go, then the angle at the sun would be:
tan θ = 1,230,000m/1.51 x 1011m
θ = 1.68 seconds of arc
[To see why this number does not match the current number 1.75 is shown further down where gamma causes the current equations to fail. The number 1.75 is an outcome of the current equations, not of the newest measurements.]
Telescopes positioned further toward the middle of the earth would find less bending, and telescopes on the left side of the earth would find stars obscured that shouldn't even be obscured by the solar disk.
Notice that MM has found a number that is absurdly close to Einstein's first number (1.7s) without General Relativity or Newton. It makes one wonder if Einstein's numbers were not finessed in order to match the math above. MM's math is simple and straightforward and does not require any curved fields, transforms, or tensors. It does not require non-Euclidean geometry or a host of new assumptions. It only requires applying the number for the gravity of the earth to a real acceleration of the earth outwards. You can see for yourself how blindingly easy the calculation is.
In comparison, let us look at Einstein’s math. In 1911, he provided this equation in his paper On the Influence of Gravitation on the Propagation of Light:
a = (1/c2)∫(kM/r2)(cosθds)
where the integral is taken from θ = π/2 to θ = -π/2.
Unfortunately, this equation gave him .83 arc seconds, a number that history has conveniently forgotten.
In 1916, in The Foundation of the General Theory of Relativity, Einstein got serious with his math. He gave us this equation:
B = ∫(∂γ/∂x1)(dx2)
Where the integral is taken from +∞ to -∞, and
γ = √(-g44/g22)
So we have an integral of partial derivatives, one of which is the transform gamma expressed as the square root of the negative ratio of two tensors. From all this Einstein gets the number 1.7 arc seconds.
MM gets the same number from this equation:
θ = tan-1(gt2/2)/d
Where g is the acceleration of the earth and d is the distance to the sun. Is this not simpler than a full derivation. The so-called free data in Einstein’s equations is considerable. There is not a speck of free data in the Miles Mathis equation. His "field strength" is 100%.
Even if the expansion theory is not true, it is highly interesting to see that the correct number can be achieved in such a direct manner.
In Problems with General Relativity: Curved Space is Unnecessary and the Inertial System is Ignored, it is shown that the Gaussian fields were unnecessary to the theory. Whatever physical form the field actually took, one could construct a Euclidean sub-field beneath it in which to do simpler math. This means that even if the actual physical field is non-Euclidean, the math does not have to match the field. Modern mathematicians have been famous for claiming that you can apply any math you want to a problem, as long as you do it in the right way. And they are correct.
Minkowski answered his critics by saying that his fields were a mathematical convenience: he did not need to prove their physical reality, he only needed to get the right answer. In this, he was right. Any math that does not contain false postulates is as good as any other math. (Minkowski’s math contains several false postulates, as shown elsewhere. It contains the false postulates of Einstein (like x = ct) and it adds to them the false postulate that time travels at a right angle to x, y, z.) But modern mathematicians have used this as an excuse for test-driving all sorts of esoteric maths. MM turns the tables on them by showing a simple algebraic solution, in a Euclidean field, that undercuts their tensor calculus.
All that was done here to achieve the solution is to reverse the acceleration vector of gravity. This creates a square flat field and allows me to do all the math in a simple way. Once the final number is achieved, one can leave the field as it is or to take it back to the way it was. If one believes in expansion theory, then one leaves the vector pointing out from the center of the earth in this problem. If one believes in Newton or Einstein and want to return to a curved field, then the vector can be reverses pointing at the center of the earth. This changes the theory but does not affect the math. This proves a claim from an earlier Miles Mathis paper that solved a complex problem of curvature—a problem that Einstein used tensors to solve—without Gaussian coordinates.
A Prediction for Jupiter
My prediction above is so broad that it does not have to wait for an eclipse. It can be decided tomorrow by pointing a large telescope at Jupiter and comparing starlight on the left side to starlight on the right side. Jupiter is 2097 light seconds away from earth, which gives the earth more than four times as long to expand. Let’s predict a maximum aberration:
θ = tan-1(gt2/2)/d
= 7 seconds of arc
This is a major deviation from Einstein, since he predicted .02 seconds of arc for Jupiter, based on the gravity of Jupiter. Miles Mathis has dismissed the gravity of Jupiter as a consideration, requiring only the distance to Jupiter from the earth. This means that we should be able to see way around Jupiter, provided that we take our picture off the right edge of Jupiter from the right side of the earth. If we take a picture off the left edge of Jupiter from the same telescope, we will find many stars obscured that should not be. An additional 7 seconds of arc (roughly—the tangent there will not be exactly 180 degrees from our first tangent, but close enough) should be obscured by the left edge.
Of course, the number 7 seconds of arc applies only when the earth is closest to Jupiter. MM used 4.2AU as the distance to Jupiter, which is the earth's nearest pass (roughly). Even greater apparent aberration could be achieved by placing earth at different positions relative to Jupiter. Let us put the earth sideways to the sun, for instance, and do the math.
tanθ = 3.3 x 107m/7.80071 x 1011m
θ = 8.76 seconds of arc
Positions of the earth much further than this away from Jupiter will not be experimentally feasible, since Jupiter will be up only during the day.
From this diagram, it is clear that viewings of Jupiter (or the solar eclipse) must be done as close to the horizon as possible. Only in this way can the astronomer be sure that he is positioned as far to the edge of the earth, relative to Jupiter, as possible. This brings other factors into play, but it is unavoidable.
As one final peculiarity of the experiment, notice that the scientist will actually be studying the top and bottom edges of Jupiter, as he sees it on the horizon, not the left and right edges. The telescope is positioned on the far right edge of the earth relative to Jupiter, in the diagram. But if we imagine a little man standing on the earth at that position, his head must be pointing due right also. If we rotate the whole diagram so that he is standing up like we are, then he will be studying the top and bottom edges of Jupiter as he sees it. The top edge will give him the number for theta above, allowing him to see around Jupiter a bit; the bottom edge will obscure stars that he expects to see.
The experimental difficulties of this viewing would make it unlikely to yield results, except that there is such a huge difference from edge to edge. Also notice that it can be measured from the same location—we don’t need to travel or to compare data from different telescopes. And it does not even require great precision. The clumsiest measurements will show a variation from side to side, if it exists as MM predicts. Seven or eight seconds of arc can be seen by medium sized telescopes, even on the horizon, provided the location and atmospheric conditions are optimal. The only thing that takes special care is in choosing the location. A telescope positioned near the middle of the earth, relative to Jupiter, will show almost no aberration and therefore almost no variation.
Now that we have thoroughly explored this problem both mathematically and theoretically, we are in a position to see why Einstein’s prediction has never been completely verified by data from eclipses. After Einstein’s fame had already been achieved by Eddington, Eddington’s method was called into question. It was found that he had pushed his data strongly in the direction of Einstein. New experiments in the 20’s and 30’s failed to verify the number 1.7, and all experiments since have been inconclusive. It is now easy to see why. Given the current explanation of aberration, scientists have not expected that the position on earth of their telescopes was important, except as regards normal considerations like clarity. That they never factored in what MM has shown must be the main consideration, if MM's theory is true. Different positions on earth must give us radically different numbers, from +θ on one edge to zero in the middle to –θ on the other edge. The variation in Eddington’s numbers at the two different locations can now be explained as (mainly) a difference in longitude. Brazil and the west coast of Africa are about 30o apart, and could not possibly see the same aberration.
The expansion of both the sun and the earth is not as counterintuitive as it first seems. Most of us already accept the fact that the universe as a whole is expanding. Due to redshifts it is generally accepted that on large scales, objects like galaxies are fleeing one another. We accept macro-expansion. Furthermore, it is commonly believed that the center of the universe is everywhere. If this is true, it implies that expansion is not just going on "out there," billions of miles away. It is going on right here, in our own solar system. And macro-expansion implies micro-expansion. Large areas are made up of small areas. Large areas can hardly expand without the expansion of the small areas they contain. Therefore absolute expansion—or the expansion of the universe at all levels—should not be so difficult to accept. It would be more surprising, if the universe were only expanding at a macro-level. That would require a greater explanation than expansion regardless of scale.
Most physicists will reply that it is assumed that the Big Bang is the cause of macro-expansion. Micro-expansion has not been seriously considered because up to now it was thought that at smaller scales gravity had caused clumping. That is, within galaxies, and especially within solar systems, Hubble-type redshifts had been overcome long ago. In order to create smaller structures like galaxies, the initial Big Bang explosion has had to be overcome somehow. Galaxies fleeing each other, or other larger redshifts, are just leftover expansion that gravity could not touch.
All of this is pretty much unexamined theory, though. No one but Dirac, that MM knows about, ever hypothesized absolute expansion, and he never tied it to gravity. The feasibility of micro-expansion—within existing matter—has never been put to the test. Besides, micro-expansion does not really contradict current cosmological theory, as a whole. As a cosmological mechanism, micro-expansion works in precisely the same way as gravity, as you see. It clumps. The great qualitative difference is that it implies that there is a continual "banging" in the universe. The Big Bang was not a one-time event, in the past. It is happening right now. Every point in the universe, or at least those inhabited by matter, is expanding spherically.
Beyond this, MM has already reminded the reader that current theory contains an expansion theory, although it does not tie it to existing matter. Einstein’s Lambda is an expansion of space, an expansion that is now being assigned by various theoretical physicists to new types of matter. Einstein never proposed a mechanism for the expansion of space—using it mainly as a fudge factor—and newer theory also has no mechanism. Even the avant garde theories like string theory do not explain how their new particles, strings of particles, or relationships create the space expansion given to Lambda.
Those who do not believe in the Big Bang will say that MM's analogy to large-scale expansions may fail, but even if it does, this failure will not much affect me. It is convenient to tie micro-expansion to macro-expansion, but this connection is not a necessary one. A universe that is not expanding at the macro-level only tells us that galaxies are not fleeing one another. Galaxies can be in equilibrium with or without the expansion of matter. You could even theorize a shrinking universe with expanding matter. The expansion of matter fits equally well into any known cosmological theory. Every theory contains some equation for gravity. Expansion is just a different explanation of the genesis of that equation, not a different final number. My theory is explained in a single step: turn the acceleration vector (due to gravity) around. Once you do that, you will still have to explain why galaxies do or do not flee one another.
In summation, you will have noticed that according to MM's theory, light is not bent. Its aberration is only apparent. Gravity is a motion, not a force field, so that it cannot affect the path of light. Therefore light must always travel in a straight line. In one sense this brings us back to Newton. In many other ways, you will have seen that MM has gone well beyond both Newton and Einstein. Neither man had the theoretical stomach for the real expansion of matter. It is unlikely that Newton ever seriously toyed with the idea. Einstein proberly did, but he preferred to give an expansion to space. Space expansion is just avant garde enough and esoteric enough to slip under the radar, especially if you tag it with Λ or "the cosmological constant". But the expansion of matter, which implies the expansion of the earth, was too avant even for Einstein. You can steal a man’s watch, but beware of stealing the ground beneath his feet. He may applaud the former as a miracle of prestidigitation; he will likely find the latter a sacrilege.
Go to Bending of Starlight
by the Planets
(Experimental Proof of my Theory) on MM's site where his observations proved his theory to be true.
Gravity at the Quantum Level
The (claimed) zero size of gravity at the quantum level is more proof of the theory above. We are told that at the quantum level, the size of gravity is on the order of 10-40. But this is not strictly true. This number is arrived at by a complex calculation that takes into account the strength of gravity at the macrolevel and the relative size of the quantum level. But empirically, no interaction of gravity at the quantum level has ever been found. In experiment, there is no gravity at the quantum level.
We are told that this is because 10-40 is so very small. We would have to be able to measure to an accuracy of something like 34 decimal places in order to be able to discover it relative to other forces at that level. But of course our inability to measure it might also be explained by the fact that it is not there in the form we expect.
In part 2 of this series on the Third Wave, MM showed that the atomic orbit was explained by a combination of the acceleration of the mass of the nucleus and electron outward and by charge. MM replaced replaced gravity by the acceleration of mass, so you can see that gravity is there at the quantum level, in some form. But notice that in MM's theory it is not a force. It is motion.
Currently the orbit is explained completely in terms of charge. If either gravity or expansion is a partial cause of the orbit, then its effect will be unseen by current theory.
Current theory finds no gravity at the quantum level because it is looking in the wrong place. It proposes that the nucleus is somehow attracting the electron, despite using the E/M field, which is an exclusionary field. Current theory cannot explain the mechanism of this attraction (with an exchange of particles, for instance), but if the electron is attracted to the nucleus by charge, then there will be no use for any other “force” to create the field. In short, by trying to explain the orbit only with charge, current theory has overlooked the place of gravity at the quantum level. Gravity at the quantum level exists in the form given it—as a real expansion outward of both the nucleus and the electron.
In the final analysis, MM's theory says that the expansion of mass exists at all levels, but it exists most fundamentally, and most simply, at the quantum level. This would put an analogue of gravity at the quantum level. But, this analogue of gravity is not a force. Therefore it does not require any unification with other forces or fields, at least not in the way that was previously thought.
As the basic motion in the universe, it intersects the E/M field and all other known and unknown fields. Only in this way can it be unified with other interactions. In The Nucleus is kept together by Gravity; there is no Strong Force and "Gravity at the Quantum Level, MM has shown the strong force can be replaced by gravity at the quantum level, and that at the quantum level can be calculated from known numbers, giving us a field that is actually 1022 more powerful than now thought.
In fact, let us now calculate the force due to acceleration of mass, and see if it is of a proper size to fit the strong force. Here is the value calculated for the proton:
a = 6.06 x 10-13m/s2
F = ma = 1 x 10-39v4
At first this seems way too low for the strong force, and would appear to be proportional to macro-gravity. It is what is predicted by current theory for gravity at the quantum level, and does not begin to explain the strong force as predicted by QCD. However, the reason that the strong force is thought to be so strong is that it has to overcome the electric force. In "How Elements are Built - A Mechanical Explanation of the Periodic Table" MM shows that nucleons do not have any E/M exclusion inside the nucleus, due to the way protons and neutrons stack. If this is true, then the strong force would not have to overcome it.
You will say, "But this contradicts the charge on the nucleus. You cannot turn off the E/M field to get rid of the strong force and then turn it back on to explain the charge on the nucleus." This can be done, as long as the E/M field of the nucleus is external to the nucleus. The E/M field does not permeate the inner spaces of the nucleus. The nucleus repels the electron, it does not repel itself. Protons in a nucleus do not repel each other or nearby neutrons. Their joint field sets up around them. The spins of the individual protons and neutrons do not create radiation within the nucleus; only the summed spins create radiation and therefore the E/M field, which field surrounds but does not penetrate the nucleus. This is quite easy to propose and diagram, as you can see by following the last link.
More Problems with General Relativity - Gamma fails again
Abstract: MM shows that the current number for bending of starlight by the Sun, 1.75, is incorrect. MM shows precisely why the number is incorrect, pulling apart the field equations to show the simple mathematical errors. Then MM show's that his number, 1.68, is correct, even given the most recent experiments. It is correct because MM's correction to gamma and the field equations yields precisely a 4% error. 1.75 minus 4% is 1.68. After correcting the errors in the equations, the experiments confirm MM's math and falsify Einstein's math.
In an email a sympathetic reader was worried that MM's theory might be dismissed out of hand because MM's number for bending of starlight by the Sun did not match the current number. In several papers MM has shown that the number should be around 1.68. The current number from experiment is 1.75, and this number comes from very respected data, including data from VLBI (very long baseline interferometry) and from Hipparchos, an optical satellite. However, MM does not need to question either experiment, since the problem is once again with the math. If we look at the equations that these physicists and astronomers are using to achieve the number 1.75, we quickly see that they are using the term gamma. For instance, if we go to Physicsword.com* we find that the bending by the Sun converges on (1 + γ)/2. Since MM has shown in An Algebraic Correction to Special Relativity and Refutation of Gamma that gamma is false, being achieved by faulty math, this equation cannot give us the correct number.
Let us look at this in more detail, to see if we can find the cause of the difference between 1.68 and 1.75. Current physicists are still using Einstein's equations for gamma: nothing has been corrected in the past century***. According to Einstein, γ = t/t' = x/x' = m/m'. That is, gamma is the straight transform due to time or distance separation, or to mass increase. Problem is, in that last triple equation, time and distance transform in the same way: as one gets larger the other does, too. Time and distance are in direction proportion, as you see. But this is opposite to what Einstein intended and stated in clear sentences.** Einstein wanted time and distance to transform in the opposite way, in inverse proportion. Time dilation and length contraction happen at the same time, with the same object, but dilation and contraction are opposites. Dilation is the act of getting bigger and contraction is the act of getting smaller. That is the definition of each word, and Einstein knew that when he used them. When time dilates, the period gets larger; when length contracts, the length gets shorter. So x and t should change inversely. Unfortunately, his math does not match his intentions, his statements, or his theory.
MM has corrected Einstein's math, but kept to his intentions, his statements, and his theory (mostly) intact. That is why MM denies that he has overturned Relativity, only corrected the math. After the embarrassingly simple corrections, neither t/t' nor x/x' is equal to γ.
We have to completely delete gamma from all the field equations, since it is not true under any circumstances. MM has shown that the math has to be redone from the ground up, to include the already known fact that time and length change in opposite ways. Now, since MM's new transform, like gamma, is not a constant, it will vary depending on the problem at hand. Here we are looking at bending in the field of the Sun, and fortunately MM has already done that math in Perihelion Precession of Mercury Explained where MM corrects Mercury's precession and thus knows exactly how much Einstein's field equations are wrong in the field of the Sun. They are off by exactly 4%, as MM shows in the third part of that paper (see the sub-section where MM corrects the number 528). In other words, MM shows that the difference between gamma and his corrected transform, in the field of the Sun, is 4%. Therefore, MM could have predicted that current physicists would be 4% wrong, as long as they used gamma to develop their number. MM did not predict it, or mention it at all, because he has not kept up with these latest experiments on bending. In his papers, MM still assumed the number is 1.7, because that was Einstein's number. After his experiences at Wikipedia, MM no longer wastes breath arguing in forums or elsewhere online, so he has to be prompted sometimes by MM's readers. In this case, it was fortuitous to brought up-to-date on this, since it provides strong confirmation of MM's number 1.68.
As you see, the current number is not proof against MM's theory and math, it is proof FOR MM's theory and math. The difference between 1.75 and 1.68 is 4%. It is the current number 1.75 that is false, and I have shown precisely why it is false. It is false because the field equations are wrong. The experiments are correct, but the math is wrong.
Using Solve General Relativity Problems without the Tensor Calculus (In about 1/100th the time) MM derives the number 1.68 without using any transforms at all. MM simply reverses the gravitational field, a la Einstein's equivalence principle, and this allows him to find the number 1.68 without any pulling forces, traditional gravitational forces, or curvature of any kind. Reversing the field gives me a Euclidean background, and using that background he can find an angle of deflection in three lines of math:
s=(9.8m/s2)(500s)2/2=1,225,000m
tanθ=1,225,000m/1.5x1011m
θ = 1.68 seconds of arc
In other papers, MM corrects Einstein's transforms, correcting the time, length, and the mass transforms separately, as has been the custom in E ≠ mc2 (Gamma is Kappa) . But to correct the number 1.75 requires that one uses use all three transforms. Einstein's field equations include mass, length, and time, so we must transform all three simultaneously. For this reason, MM cannot simply show you a difference between gamma and his transform in a single equation. Einstein uses gamma in all three transforms, so when we see gamma in a final equation, as it is used at Physicsworld, it is a sort of compressed transform. Another way to state that is to remind you that the field equations express a force. It requires a gravitational force to curve space. Since force is equal to the dimensions of kilogram meter per second squared, we have to include mass, length and time transforms, all three at the same time. Force will not vary like mass alone or time alone or length alone. Force must vary as the force equation varies, so we must look at how time separation affects each parameter.
Now, Einstein never recognizes this subtlety, which is why his equations are incomplete. Yes, he looks at the mass transform in the curved field, but his math does not include the fact MM has just related: the force cannot vary like the separate transforms, since force is defined as a mass times an acceleration. To be specific, MM shows in the paper on Mercury (Perihelion Precession of Mercury Explained that length would increase by a factor of 1.04, time would decrease by a factor of 1.04, and mass would increase by a factor of 1.57. Therefore, according to the force equation, force would increase by 1.51.
F = (1.57)(1.04)/(1.04)2 = 1.51
The difference between 1.51 and 1.57 is 4%. Einstein ties his field equations to the mass transform, not the force transform, so he is 4% off. Current theory has not corrected Einstein, so they are still 4% off. That is why and where they get the number 1.75.
A final interesting question begged by all this, but never asked by anyone before MM, is how current physicists explain MM's number 1.68. You will say it is not up to them to explain it, since it is MM's number; that needs to be explained, but in a very real and direct way, it is Einstein's number, which also makes it their number. To get this number, MM just follows Einstein's equivalence postulate or principle. In his books, Einstein famously states that there is no mathematical difference between acceleration up and gravity down. He shows this with his elevator car in space, and the thought problem and postulate are still accepted as true. This means that we should be able to invert the field with no numerical difference. That is what equivalence means: it is a mathematical equivalence, not just a theoretical equivalence. Einstein says the number for acceleration and gravity should be the same. If this is so, then why does the inverted field give us a different number than the normal field? The inverted field gives us 1.68 and the normal field gives us 1.75. Why? How do mainstream physicists explain this? They have not been able to show that MM has done the math wrong, but if they want to believe in the equivalence principle, they must show that. They cannot claim to believe in equivalence and then fail to address the difference between 1.68 and 1.75. If MM is wrong in this paper, and the difference is not caused by Einstein's mathematical error, how is it caused? Mainstream physicists must either show a mathematical cause of the difference, or they must give up the equivalence principle.
As it is, they seem proud that their number is different than “mine”, since it seems to them to imply that they are correct and MM is not. But they have not appeared to recognize that the deviation between the two numbers is also a problem for them. It is a problem because it conflicts with the equivalence principle. To confirm Einstein, they should have matched experiment to equivalence, which would have given them 1.68. To confirm Einstein, gamma should have confirmed equivalence. It doesn't, but they have swept this problem under the rug. MM has just solved it. How do they solve it?
***Addendum: This same reader wrote back to say that gamma is no longer simply Einstein's mass transform, in the latest incarnations of GR. He sent me to the Parameterized post-Newtonian formalism page at Wikipedia as proof of this. There, gamma is the amount the space curvature gij is curved by a unit rest mass. MM told the reader that to achieve this "tensorized" gamma, one must still use the old gamma, which was and still is 1/√[1 - (v2/c2)]. Contemporary physicists try to hide behind more and more new math, but the new math is supported by the old math, so that if the old equations are wrong, the new ones must be, too. Beyond that, MM has already shown that all the PPN math is false bombast. In E ≠ mc2 (Gamma is Kappa) on mass increase, MM shows it is errors in the math that lead to an expanded equation, whereby Einstein's kinetic energy equation is said to approach Newton's at a limit. In other words, Einstein derives an equation with infinite terms, and tells us the first term is Newtonian. The other terms apply to the Relativistic deviation from Newton. But Einstein achieves this equation with ordered terms only by bad math. Once MM corrects the math (in part 7 of his paper), the mass transform is in a different form, one that is not in a series like that. To be specific, there is no square root to expand by the power series. The mass transform is 1 - [v2/(2c2 - 3cv)]. No square root. This means that the PPN math is all manufactured from nothing, including all the fake beta-delta categories of Will, Ni, Misner, and all the rest. There are not seven parameters, or ten or twelve, since each parameter is dependent on the power series. There is no square root, so there is no power series, so there is no PPN.
*http://physicsworld.com/cws/article/print/21148/1/PWrel4_01-05
**Relativity, Ch.XII, p. 37. "As judged from K, the clock is moving with the velocity v ; as judged from this reference body, the time which elapses between two strokes of the clock is not one second but [γ] seconds, i.e. a somewhat larger time. As a consequence, the clock goes more slowly than when at rest."
A relook at the 19th century mess once again related to Relativity
and the problem of aberration, giving corrections to Einstein's equations and experiments.
In previous papers on Relativity: The Error of the M/M Interferometer and Solving General Relativity Problems without the Tensor Calculus (In about 1/100th the time), and the Aberration discussion above which analyzed the equations on bending of starlight by the Sun. People have called this the aberration of starlight, but here MM looks at starlight as it comes into a telescope. In this situation, it has long been known that you have to tilt your telescope a bit to best capture light from specific stars, and that this was due to the motion of the Earth relative to the star. Equations were developed long ago [1728] that allowed astronomers to do that, and the classical equations were good enough for the job. However, Einstein reran the equations using his Relativity updates, finding a slight correction. However, since the relativistic second-order effect was still far below the attainable accuracy of observation at the time of Einstein's death, aberration has never confirmed or disproved his equations. It is now claimed by some that we possess this accuracy to check the equations, but this has not been done.
MM will show that although a Relativity update was necessary to the old equations, Einstein provided the
wrong one. We can see that just from the form of his final equations:
u'x = (ux – v)/ (1 – ux v/c2)
u'y = uy / γ(1 – ux v/c2)
Since we see gamma (γ) there, we know those equations must be wrong. MM has disproved gamma from the ground up, going line-by-line through all of Einstein's proofs . A second major problem is that Einstein used his addition-of-velocities equation to solve this, but that was unnecessary. There is only one relative motion here, that being the Earth relative to the star (or the star relative to the Earth, but not both). Again, you can tell that just from the form of the equation. In the pair of equations, we only have the speed of light and the speed of the Earth v. The variables ux and uy are both components of c here, so they aren't separable from c. Remember, in Einstein's addition-of-velocities equation, you have to have two velocities on the right side, not counting c.
W = (v + u)/(1 + vu/c2)
That is the addition-of-velocities equation, straight from mainstream textbooks. In that equation, neither v nor u are components of c. They are components of W, in a way, but not of c. Therefore, in the pair of equations above, we simply don't have enough velocity assignments to use this addition-of- velocities equation. This makes the proposed solution a rather obvious hash. It means Einstein couldn't really figure out how to apply his own equations to the problem.
It also explains the labeling of the x and y components of c, which seemed odd to me at first glance. Why label them uy and uy? Why not cy and cy? This is obviously done to fool you into thinking they fit Einstein's addition-of-velocity equation somehow, which already contains a variable labeled u. But they don't.
We must suppose that Einstein used his addition of velocities equation because he was following the form of the classical equation, which uses a “Galilean” addition of velocities. This was unfortunate, since the classical equation is also a hash. In the classical equation, we also find x and y components of c. The 19th century physicists couldn't really have been expected to see that as a mistake, but Einstein should have recognized it for one immediately.
Which brings us to the third major problem of both the classical and relativistic equations: the breaking down of c into x and y components. That is disallowed by Einstein's own rules, as MM has shown in many previous papers. Since c sets the field, you aren't allowed to give light x and y components. This is one of the mistakes of the light clock, the M/M interferometer , and so on. Instead, you must let everything else move relative to the light, giving all the other velocities x and y components, instead of the light. I will remind you what I mean just below.
In An Algebraic Correction to Special Relativity and Refutation of Gamma Part VI, MM shows how to solve this problem in the most efficient manner. To start with, to add these Relativity corrections to the classical equations, we have to know where the Earth is in its orbit. That is, we have to include whether the Earth is moving toward or away from the star. In Einstein's equations, it doesn't matter, since in them all motion causes time dilation. But in MM's corrections, this is no longer true. The solution will be very slightly different when you are moving toward the star and away from the star. One will cause time dilation and the other time compression. For instance, if you are looking at a star that is near the ecliptic, the Earth will be moving toward it half the year and away half the year. Well, we won't be able to use the same Relativity correction to the classical equations both times. Direction matters .
Of course this means the Relativity corrections apply mainly at the apsides of our created ellipse. This is a bit ironic, since it is the sideways motion to the star that causes the main effect in the classical equation. The classical equation doesn't even track the y motion of the Earth, as you see: the given velocity v is in the x-direction, which is mainly perpendicular to the light coming from the star. But the less y motion the Earth has relative to the star, the less the Relativity correction. In fact, there is no Relativity correction when θ=90. The maximum Relativity correction is at θ=0 and θ=180, and this is because the Earth is then moving most quickly toward or away from the star.
To solve in the most efficient manner, we must give the motion to the star. As Einstein taught from the beginning, any observer can define himself as stationary, measuring the universe from his own position. And to run the equations in the cleanest form, you must define yourself as stationary, so that your local system has no velocity. If you don't do that, you are guaranteed to get into a mess pretty fast. This is the way that Relativity equations often misfire, and Einstein's own equations in this problem are misfiring for this reason. As you see above, he is trying to give the Earth the motion, which forces him to give the light ray x and y components. Anytime you give a light beam x and y components, you are guaranteed to go astray, and that is because doing so breaks one of the cardinal rules of Relativity: Einstein's Postulate 2. Einstein has broken his own Second Postulate here. Light does not travel in a coordinate system of its own. The motion of light is what sets any and all coordinate systems, but light itself does not travel in any one of them. Light is a special case , and Einstein admits that from the very beginning. But if you give light x and y components, you have put it into some coordinate system. The variables x and y are coordinates. You have broken Postulate 2.
So you must give the motion to the star. In current theory, they call this relativistic beaming, but it is the same thing as aberration of starlight (supposing it is a star that is beaming). It just means we let the light source move rather than the observer of it. This creates an apparent reverse ellipse in the star's motion, which mirrors the Earth's ellipse around the Sun. That is what they originally meant by “aberration.” They meant that the star didn't stay still if you took a long exposure.
So let us solve for one position of the Earth in its orbit. We can then use this illustration MM created for his earlier Relativity paper:
We then let the blinker be the star. Instead of the Earth having a velocity at an angle to the star, we hold the eye still and let the star have an angle relative to the Earth. Light then travels on one of the lines labeled x'. If we need to give one of the motions x and y components, we give them to the star's motion, not to the motion of the light. If we solve for position 2, say, we find
c = x2'/t
x2'2 = x1'2
+ y12
- 2y1 x1cos135
But since we are tracking these distant motions from our own system, we can't use v'. That is the local velocity of the star, not the velocity we will experience measure on Earth. So we must transform it:
v = v'/[1 + (v'/c)]
From this, we see that it is v that is being transformed by Relativity, and that it will be transformed in different ways for different angles. It will also be transformed differently for different directions. As I already said, direction matters. If the star is moving toward the Earth, we use a different velocity transform:
v = v'/[1 - (v'/c)]
You will say that should reverse the angle, but it doesn't. It only changes the amount we add. Here is the classical equation for aberration, for instance:
tanφ = sinθ/[(v/c) + cosθ]
Changing the value of v up or down slightly will not reverse the value of the entire equation, it will only change the amount we add to cosθ.
So you see, all that was necessary was for Einstein to relativize that velocity variable v, by using a simple transform. He needed to do that to properly import it into the equation next to c. The problem with Bradley's classical equation was that his term hv/c was naïve. Once we have a finite speed of light, and information carried by that light, the classical transform x = x'v/c no longer works. Instead we must use (supposing motion away): x = x'/[1 – (v/c)]
This is admitted even by those who still claim to be anti-Relativists, since that simple transform is used on frequency. In the frequency transform, almost no one admits the term is a Relativity transform, but that is exactly what it is. So Bradley and those who came after him could have perfected and extended their classical equation without any help from Einstein or Relativity. All they had to do is import the frequency transform in the right way, realizing it applied to lengths just as much as to frequencies.
MM will now correct the equations from the ground up. To start with, we have to jettison the x and y components of c from the classical equation. To do that, we simply let the light arrive on a line we define as setting the perpendicular, and then give the star's motion x and y components relative to that. The easiest thing to do is put the star at the zenith and give it a reverse motion v at some given angle.
cosφ = v'x/v'
tanθ = v'x/c
tanθ = cosφ(v'/c)
Theta then gives us the tilt of our telescope. That simplifies the math considerably, and clarifies the mechanics as well. Only problem is, do we know v' and φ? Well, assuming the Sun is not in quick motion relative to the star, we should be able to use the velocity of Earth in orbit, as they do in current equations. Do we know φ? Well, it is calculable, since we know the position of the star relative to the ecliptic. Even if we didn't, we could calculate it straight from the aberration itself. In other words, we would have to track the star's aberration for some amount of time, at least enough to find an apside. We then match it to the apside of the Earth's orbit, and we then know how the Earth is moving relative to the star.
Now for the Relativity correction. Just as we ignored vy in the classical solution, we ignore v xin the Relativistic solution. The vertical component of v is the only thing that will give us a correction due to Relativity, since it is the only thing that will act to compress the data. Since the star is moving slightly toward the Earth, we use this velocity transform:
vy = v'y/ [1 – (v'y/c)]
This changes the apparent length of vy in our triangle, which also changes the apparent length of v. The
velocity v will have appeared to increase. But vx will not be affected by this transform.
sinφ = vy/v
vsinφ = v'y/ [1 – (v'y/c)]
v'xtanφ = v'y
vsinφ = v'xtanφ/ [1 – (v'xtanφ /c)]
v = v'xtanφ /sinφ [1 – (v'xtanφ /c)]
Now we just replace v' with v, to make the Relativity correction:
tanθ = cosφ(v'/c)
tanθ = cosφv'xtanφ /sinφ[c – (v'xtanφ)]
v'cosφ = v'x
tanθ = v'cosφcosφtanφ /sinφ[c – (v'cosφtanφ)]
tanθ = v'cosφ /[c – (v'sinφ)]
Now let us look at one of the complaints of anti-Relativists. They will say this whole demonstration is flawed, because if one draws those vectors as MM has done in his illustration, it implies that whatever is moving along that hypotenuse is going over c. Even Relativists will not draw it that way, for the same reason. They would rather break Postulate Two than draw a hypotenuse like that. We may assume that is why they give the x and y components to c rather than to v. At least in that case they don't have to draw or imply this hypotenuse.
But it is not against any rules of Relativity to draw that hypotenuse. That vector is a compound vector, and isn't applied to any one body. Relativity says that no body may be diagrammed as going over c; it does not say that no field result can be over c. That hypotenuse is a compound of the motion of the light and the motion of the Earth. It is the vector addition of c and v. So the light is not going over c. It is diagrammed and defined as going c, no more, no less. The hypotenuse does not belong to the light. The adjacent leg belongs to the light.
This should all be obvious, since if field results over c were not allowed, aberration of starlight would be an impossibility. Redshifts and blueshifts would be an impossibility. All these things are indication of motion relative to light, and any time you have motion relative to light, you will be diagramming a field result over c. Motion relative to light simply means you are adding or subtracting some number from c. That is allowed. Einstein did it all the time, as we see straight from his equations. His equations contain the term (c – v) all over the place. If you can have (c – v) you can also have (c + v), which is simply this field result over c. That is exactly how you get redshifts.