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The Perihelion Precession Part 1
In 1859 LeVerrier did a extended classical solution of the problem of Mercury's precession. This solution showed that Newton’s and Kepler's equations fell short of the empirical data by a margin that could not be assigned to instrument failure or other error. This margin—38 seconds then, 45 second in Einstein’s time, and now 43 seconds of arc per century—became the holy grail of a thousand theories. Some like LeVerrier searched for another perturbing body in the region of the Sun to explain the discrepancy—a hidden moon of Mercury or a tiny inner planet. Part 2
Now for the second part of my critique. The entire analysis above assumes that GR is at least correct in principle, and that the historical analysis is at least correct in principle. All I do is show that both were misused. I leave upon the possibility that GR could be applied to the problem in a complete and logical way, and that if it were, the correct total might be achieved, though in a different way than we have been told. For instance, even admitting all my points above, it is possible that the number 43 is correct, it is possible the given total is correct, and it is possible that we can achieve that total by raising the perturbation total and lowering the equinox total, or something like that. Some will say that I have answered my own question: I complain that GR is not mechanical and they will reply, no, it is geometric. It therefore requires no mechanical explanation. But this is a transparent dodge. Even if I accept that space is no longer physical and that it is now a mathematical abstraction, I still may ask how matter curves the math. Einstein never denied that the Sun was physical. How does the Sun curve the mathematical field? Physicists now hide behind the math at every opportunity, pretending that mathematical fields can be postulated with no questions asked or allowed. If you want a curved field, you propose one, that is all. If someone asks you why it is curved, you claim that math is abstract and it can be anything we want: questions about math are disallowed. But this is absurd. Applied math is not pure, and it is not metaphysical to ask questions about application. Metaphysics or semantics has nothing to do with it. The question is definitional or operational or logical, and is fully allowed. To deny this is to claim that you may not ask physical questions about physics. And this is not Einstein's only problem. Newton had one big hole in his dynamics, but Einstein has many. The second major hole can be seen in perturbation theory, where he has to explain distant forces without forces. His fields have no forces, remember. Motions are caused only by travelling field disruptions, in the form of curves. Unfortunately this leaves us with travelling waves that somehow do not mechanically influence eachother. The curvature of space affects masses in that space, but does not curve other curves. Curves moving through curved space do not become more curved. For instance, Venus can send a wave to Mercury, as a carrier of its perturbation, and this wave travels across and against a much larger wave receding from the Sun. Mysteriously, the Sun's wave does not tamp down the wave from Venus at all. It is as if Einstein's gravity field is not one field, but an infinite number of interpenetrating fields, where no curvature affects any other. If this is so, then it is like no other field we know. And it is certainly not mechanical. In any field mediated by particles, we would expect the particles to collide occasionally, creating interference. This cannot be so in the Solar system, since to explain the perturbations we see, we must assume non-interfering gravity waves. As I said in another paper, the Earth raises tides on the Moon, and the Moon raises tides on the Earth, which means the curve is curving both ways at the same time, with no interference. As with Newton, gravitational forces interpenetrate with zero resistance. Regarding the magic of Newton's force at a distance, this is no surprise; but given a mathematical field of curvature, or a field of gravitons, this is a grave contradiction. This is clear regarding the graviton, I think, but it should be clear in the mathematical field by itself, even without the gravition. How can the curves affect mass if they cannot affect eachother? Some waves or particles can be imagined to pass eachother with little effect, like neutrinos, for example. But neutrinos also pass through matter with little effect. A gravity wave must affect matter—that is why it is proposed in the first place. It must either be substantial or insubstantial. If it is insubstantial enough stack infinitely with no interference, it cannot be substantial enough to move matter; and if it is substantial enough to move matter, it cannot be so transparent as to stack infinitely. Likewise, if gravity is thought of only as a mathematical curve, it cannot curve only in the presence of matter and uncurve in the presence of other curves. It either travels in the field or it does not. If it travels in the field as a curve, then it must curve the field. If it curves the field, then other curves moving through the same field must interact with it. Einstein wants it both ways. He wants to get rid of space, having only the curves created by the math. This would mean that the curves define the interactions entirely. The curves are the mechanics. But then he wants the waves to act in unmechanical ways, as if they are only mathematical abstractions. No, it is even more than this, since even mathematical abstractions must affect eachother. Curves in mathematical space cannot pass eachother without effect, unless they are specifically defined in non-physical ways. Einstein wants to define his curves in non-physical ways and then imagine that they affect matter! So they travel as non-physical mathematical abstractions and then suddenly, in the presence of matter, they become highly interactive. GR has no logical or mechanical consistency. In fact, it has even less consistency than Newton’s classical field. This does not make Newton better; it makes both Newton and Einstein fatally wrong. My theory of gravity solves all these problems directly, by proposing that every apparent force resolves to simple linear motion. There are no curves, no gravity waves, no gravitons, no attractions, no forces, no tensor calculus, no forces at a distance, no spooky forces, no paradoxes, no supraluminal speeds, no virtual particles, no Higgs bosons, no strings, and no non-mechanical ideas. Everything resolves to motion, even gravity, mass, and inertia. Part 3
Here I will apply my simplified equations and dynamics to Mercury's orbit and see if I get the number 45. As you will remember from my simple solution to starlight deflection, I solved by taking Einstein's principle of equivalence literally. That is, to create a rectilinear field, I flipped all gravitational acceleration vectors, allowing the material bodies to expand. This may seem at first like a huge amount of precession, but remember that we never see this kind of precession from the Earth. As I will show, we must subtract the Earth's own precession due to curvature to achieve a usable figure, and we have never done this. If you look at all the glosses of Einstein's problem, including the latest updates, you will see that no one calculates the Earth's precession due to curvature. This is because they mistakenly think the number is negligible. They think that Einstein's 1.7 number applies only to the deflection of starlight and not to the Earth's field curvature. ^{6} But, following Einstein, they have misunderstood the entire gravitational field and its mechanical causes. I will calculate the Earth’s curvature below and show that it gives us a number that fits the current data in all important ways.To show that my new equations have not mirrored and corrected Einstein's by some sort of accident or coincidence, let us apply them now to the Earth. In a previous paper I showed that the total curvature of the field at the distance of the Earth's orbit is 3.36 arc secs. I achieved that this way: s = at ^{2}/2 = [(9.78 m/s^{2})(501s)^{2}]/2 = 1,230,000mtanθ = 1,230,000m/1.51 x 10 ^{11}mθ = 1.68 seconds of arc These equations I have simply imported from my paper on Solar deflection. This is my famous GR solution in three lines of math. It gives us the apparent bending of light from the Sun, as seen by an observer. It also gives us the angle of expansion in one direction. Doubling that represents expansion both prograde and retrograde and therefore stands for the curvature of the whole orbital field. Hence the number 3.36. [To see why this number 1.68 does not match the current number 1.75, go here. I show that gamma causes the current equations to fail. The number 1.75 is an outcome of the current equations, not of the newest measurements.] Now let us find the precession of the Earth due to this curvature or expansion. We will do it the same way we found Mercury's. a = v ^{2}/r = (2.94 x 104)^{2} /(1.50 x 1011) = .00573m/s^{2} v _{t} = √(a^{2} + 2ar) = 41,400m/s (41,400m/s)(365 days) = (2.45m/s)(6,160,000 days) (7.71 x 10 ^{5} )(1.68 arc secs) = 6,160,000 daysP_{E} = 76.8 arcsec/yr.Now, if we subtract Mercury's precession from the Earth's, we achieve the apparent precession of Mercury as seen from the Earth. This is the number we want. This gives us a difference of ΔP = .8 arcsec/yr
Or 80 arc secs per century. Therefore we will see Mercury precess about 80 arc seconds per century, due to curvature of the field alone. This is almost double Einstein's 43, which is enough to disprove his math and postulates. It also means that we will have to re-figure the perturbation total. The number 528 from above cannot be correct, as I said, since that is a Newtonian number, not a Relativistic number.But first let us look at something very interesting. Now that we have a number for Mercury's precession due to curvature, we must return to our equations and consider what it means. Notice that if you divide 365 days (the Earth year) by 88 days (the Mercury year) you get 4.15. If we take our very first number for curvature, .39, take half to express only the curvature in one direction (for the orbital direction in space) and multiply by 4.15 we get .8/yr. That is what we just got by a rather involved calculation. That means that the first angle should have been applied to the Mercury year. We could have skipped all the long math and simply written, s = (3.74m/s ^{2})(153.3s)^{2}/2 = 43.9kmtanθ=43,900m/4.6x10 ^{10}mθ = .197 seconds of arc .197 arcsec/88 days = (.39 arcsec/88 days) x (365 days/1 yr) = .8 arcsec/yr = 80 arcsec/century So Einstein could have leapt to the conclusion he did, if he had used the right year and the right angle. He could have taken the angle and applied it to one full orbit of Mercury. His number should have been applied to the Mercury year. But his math gave him absolutely no reason to apply it to one full orbit of the Earth. He calculated the extra curvature of the Sun's field at the distance of Mercury, so what could the orbit of the Earth have to do with that? He also used the wrong angle. He doubled it. This is interesting because historically his first solution got around half the angle of his final solution. Remember that his first lecture on GR found .18 for the angle, as I said above. I have just calculated that it must be about .197. His initial math was better than his final math. For the precession problem, he doesn’t need the curvature of the field in both directions, he only needs the prograde curvature.But how does my abbreviated solution work? How did we skip directly to this field differential of .8 arcsec/yr without considering all the Earth numbers? It works because once you compare the Earth's orbit to Mercury's you must achieve a relative number. What I mean is that simply by using the term 365/88 in our math, we have made the problem a relative one. We are comparing the two orbits, and in doing so we have left the "absolute" field of the Sun. The number we get at the end of the calculations must be Mercury relative to the Earth, not Mercury relative to the Sun. When you import certain terms into equations, those equations bring with them certain assumptions or axioms. They also carry with them certain information. You cannot use them without bringing these axioms and information to bear on the math. The term 365/88 already contains a load of information about the relative motions of Mercury and the Earth, and simply by using it we achieve a final number that includes all that information. We do not have to write all the information as numbers in our equations: it is already implicitly included in the term 365/88. And so we achieve a relative number at the end (.8 arcsec/yr) which is the precession of Mercury relative to Earth's orbit, not the precession of Mercury relative to the Sun. There is a second important point to hit before I move on to perturbations. Notice that the number of days (6,160,000) for a full precession for the Earth is almost the same as a full precession for Mercury (6,220,000). This is not a coincidence. In fact, it gives us a way to check our math above one more time. From the point of view of the Solar field itself, the precession period of both planets should be the same. Why? you may ask. Two reasons: 1) There is no time differential if you measure from the field itself. To put it another way, you don’t have to do an SR transform if you measure from the field. Time differentials and Relativity transforms only apply if you are measuring one motion in the field from another point of motion. You will see what I mean by this in a moment. 2) Expansion is the same for all objects. That is why all objects stay the same relative size, and why we don’t see expansion. If the rate of expansion weren't the same, we would see Mercury changing size. We don’t see that, so the expansion must be equal. Not numerically equal, since 3.7 does not equal 9.8; but relatively equal. We have a variable acceleration here, and the variation is the same. In other words, the rate of change of the two accelerations is equivalent. If this is so regarding expansion, then if we flip the field back over to get Einstein’s curved field, it means that the curvature of the field is the same at both distances. What I mean by that is, another of Einstein's major errors is that he thought the curvature of the field and the field strength were the same thing, but they aren't. The field strength determines the size of the centripetal acceleration vector from the Sun at each distance—.038 for Mercury and .0057 for the Earth, for example. But the curvature that he found with his tensor equations is the change in this field. It is the field variation. That is why it was an addition to the field of Newton. Newton already knew about the field strength of the Sun, and its variation with distance from the Sun. Einstein's equations don't apply to that (although Einstein thought they were just a simple addition to that field). Einstein's equations apply to the change in that field. Newton’s accelerations are rates of change of velocities, and Einstein's GR accelerations are rates of changes of accelerations.
It turns out that the rate of change of acceleration is the same for all planets. If we look at expansion, then all the planets expand at the same rate. If we look at curvature instead (as the inverse of expansion) then we find that the curvature is also the same for all the planets. To a first approximation, Einstein should find the same angle for each planet, since they are all part of the same variable field. He doesn't, and that is a major error. He thought (and physicists still think) that the curvature of the main field is less for the Earth than for Mercury. But it isn’t. The only variation comes from the time differential.Some will say, if your argument is true, it means that the Earth and Mercury should orbit at the same rate. If the curvature is the same, the orbits should be analogous. But those who say this are missing the distinction I just made. The rate of orbit is not caused by the differential or variable field I just described. To a first approximation, the rate of orbit is caused by the planet's "innate" tangential velocity and the Sun's centripetal acceleration at that orbital distance, just as Newton told us. That is the main acceleration or gravitational field. It is a field of acceleration vectors or tensors. But the extra curvature field of Einstein is a differential field: it is the change in acceleration field, due to Relativity. That is why it is an addition to Newton. Einstein's .43 angle for Mercury is part of that differential field, and that is why it is not part of Newton's main analysis. It is a relativistic field, caused by time differentials, as I have shown and will show again in a moment. The precessions and forces caused by that field are only apparent. They are the outcome of time differentials. This means that we have a field that is curved in two separate ways, although Einstein never saw this. Every rate of change implies a curvature, whether we want to use a curved mathematical field to represent it or not. I prefer to straighten out all the curves in my math, since the math becomes a lot easier and more transparent, but Einstein was correct in a sense when he showed that accelerations imply curvatures. Unfortunately, he conflated two rates of change. He tried to express Newton’s gravitational acceleration field as a curvature, which is valid. Accelerations can certainly be expressed mathematically as curves, if one desires. But the variation from Newton is not caused by representing the field as curved, in the first instance. It is caused by adding another curvature to that curvature, and the second curvature is caused by time differentials. That is, it is caused by Relativity. It is caused by the fact that Mercury is separated from the Earth by 499s, and that time cannot be ignored. This time differential creates another rate of change to the field, and that rate has to be added to the curvature of the main gravitational field. So we have two curvatures on top of eachother. One is SR, caused by time, one is GR, caused by gravitational accelerations. Einstein never saw this, and no one since him has seen it. He was never clear on what his curvature was expressing. Because he never clearly separated his two mechanisms, his curved field became confused. He wasn't able to separate out all the events like I do, and his tensors soon became unassignable. Were they expressing the first curvature, the second curvature, or a combination? Often, no one could say. The math was too complex for anyone to really wield. And we now must add to this his basic ignorance of the correct vector analysis, as I will show. True, his tensors acted like complex vectors, but because he couldn't visualize all the interactions, he couldn't say when these vectors or tensors should be added and when subtracted. As I will soon prove beyond any doubt, it is of ultimate importance to your final numbers to know whether your apparent forces or differentials will be prograde or retrograde, and to know this you can't just throw math at the field. You have to intimately understand the field. Let me do a bit more math, and you will see what I mean. The first math I did in this paper was a giant simplification and correction to GR, although it may have seemed difficult to some. The second math I did was even simpler. Now I will simplify even further. We already know that there is an absolute time separation between Mercury and the Earth of 499 seconds. This is no bold claim of mine, it is current wisdom. The mean distance between the two planets is 1AU, and light takes 499 seconds to travel that distance. Therefore, all our measurements on Mercury are 499 seconds old. All our photos from Earth are 499 seconds old. Given that, if Mercury is expanding at 3.7m/s, then it will have continued expanding while we were waiting for the light to get here with our information. Therefore, if we want to compare Mercury now to Earth now, we have to do a Relativity transform. That transform is very simple, given expansion, and we don’t need tensors. We just go back to our first equation and change the time. We let Mercury expand for 499s instead of 153s. s = (3.7m/s ^{2})(499s)^{2}/2 = 460,600mThat tells us how much Mercury has expanded while we are waiting for the light to get here. Now, if we want to relate that to how we see Mercury's orbit or its precession, we have to divide by two, since once again we are only considering motion in one direction in the field. We are only concerned with half the curvature of the field, since Mercury's orbital motion is +x but not also –x. Now we just do the rest of the math: tanθ=230,300m/5.8x10 ^{10}mθ = .82 seconds of arc There it is again, the same number. Confirmation of our angle difference, without even looking at the numbers from the Earth. All we have to do is calculate how much the numbers change between Mercury and the Earth, and we do so by looking at how much light skews the problem directly. That is what Relativity is, whether we are talking about SR or GR. SR is how much the speed of light skews non-acceleration problems, and GR is how much the speed of light skews acceleration problems. Einstein assumed that GR couldn’t be solved in straight-line geometrics, but I have shown that it can. Basically, I have solved GR using SR directly. Using the postulate of expansion, all problems become SR problems, and I can calculate by simply looking at time differentials caused by light, in a straight line. [A very clever person will say, "Wait, you just assumed that was .82 arcsec/yr, whereas you spent any amount of time complaining that Einstein made a per-year assignment in the same way without justification. What could possibly be your justification?" The answer is in the time used in the equations. I use 499s, which is connected to 1AU, which is the average distance of Mercury from the Earth. To get that average, you have to take positions over a full orbit of both bodies, and both bodies are moving relative to the field and the zero-point. The number we get at the end, 499, is therefore an average relative to the bodies in motion, and to their motion. It is a relative number: it is one orbit relative to the other. Another way to look at it is that .82, although it is an angle to the Sun, is an angle as seen from the Earth, not from the Sun. The number is based on the time of 499s, and the Sun or the field itself never experiences that 499s gap. That light gap is between Mercury and the Earth only, so only the Earth sees the angle .82. It is a relative angle, not an absolute angle. It is an angle relative to bodies moving in the field, not an angle relative to the zero-point or the Sun. The time period is the year, since both orbits are defined by the year, and the time in the equation was taken from an average over an Earth year. Perhaps a simpler way to put it is that since 499s is an average time over one full orbit, .82 is an average angle over one full orbit. If we did the full analysis, without averaging, we would have to take into account the fact that at some points in the two relative orbits Mercury appears to move forward from the Earth and at other points it appears to move backward (and at two point it appears to stand still). The angle at nearest approach would be .37 and at farthest it would be 3.0 (and in two points it would be 0.0). 3.37 divided by 4 is equal to .84, so you see that we have a good estimate just from those four points in the orbit. Once I actually average, you can see precisely how the number .82 is connected to the full orbit and the year. The clever person will now say, "If it is an average over a year, then it will be an average over a century as well, won’t it?" No, it won’t. That sort of reasoning would work with linear averaging, but that isn’t the sort of averaging I am doing here, as you can see if you study the mechanics. In orbital motion, a residual angle after one rotation must be given to the precession after that one rotation. That is what precession is. One rotation is one year, in this part of the problem, therefore at the end of each year we collect the average angle and give it to precession. The next year we must collect the same angle again, or another angle if the mechanics changes.]
Now let us move on and look at precession due to perturbations. Even if we accepted the figure of 528 (and we don’t), we must see that the historical analysis, including that of Einstein, is very incomplete. If we go to Wiki today we learn that the Earth has a precession of its perihelion just like Mercury, and that this precession is also thought to be caused by perturbations from other planets. It is called the anomalistic precession of the Earth. Mysteriously, this precession is never included in the analysis of Mercury, although clearly it must affect our measurement of Mercury's total precession. If the Earth and Mercury are both precessing due to perturbations (and we assume they are precessing in the same direction, since both orbits are prograde) then one number has to be subtracted from the other in order to get a resultant precession. To me this seems obvious, but so far it has been ignored by everyone. The given number for anomalistic precession of the Earth is 1157, a number I will take on faith here since it comes from observation, not calculation. Here are the numbers we had before the perturbation correction:
Now for the final analysis. Some will ask how my corrections affect Earth's own precession, so let us look at the numbers again, disregarding Mercury completely. My corrections have to make sense with the Earth alone, as well as with the Mercury/Earth problem.
*Felix Klein and David Hilbert both worked with Einstein on his math, so they are the first to blame. The fact that they either contributed to these errors or utterly failed to notice them is reason enough for the lack of respect I appear to have shown them in other papers. If this paper was useful to you in any way, please consider donating a dollar (or more) to the SAVE THE ARTISTS FOUNDATION. This will allow me to continue writing these "unpublishable" things. Don't be confused by paying Melisa Smith--that is just one of my many |