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A Revaluation of Time and Velocity
and the Concept of Relativity

© Miles Mathis

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' time paper and rel1 paper.)

The paper is to present definition of time that is as little abstract as possible. What we are aiming at is a definition that describes time as something that we measure. Only that. One might call it an operational definition. This definition is not an explanation of what time means (or has come to mean) philosophically or epistemologically. It is an explanation of what time is in our experimental or everyday use of it.

Time needs to be defined as simply a measurement of movement. This is its most direct definition. Whenever we measure time, we measure movement. We cannot measure time without measuring movement. The concept of time is dependent upon the concept of movement. Without movement, there is no time. Every clock measures movement: the vibration of a cesium atom, the swing of pendulum, the movement of a second hand.

In this way time can be thought of as a distance measurement. When we measure distance, we measure movement. We measure the change in position. When we measure time, we measure the same thing, but give it another name. Why would we do this? Why give two names and two concepts to the same thing? Distance and Time. In fact, when comparing one to the other, time is just another, comparative, measurement of distance.


The measurement of time is necessary to the measurement of velocity. It may be that time was not even "invented," in the modern sense, until someone first thought of the idea of velocity. Velocity is the measurement of the change in position of one thing (the object in question) relative to the change in position of another thing (the cesium atom, or the pendulum, etc.). Once you have conceived of the idea of velocity in this way, you realize that it can be measured in only one way: Compare the unknown movement to a known movement. That is, find something in your world that moves as uniformly as possible, and let that be your clock. Then compare your unknown movement to the movement of your clock. That is what velocity is.

You might ask, how can one know that something moves "as uniformly as possible" without already having an idea of time? You cannot. But MM maintains that this idea of time—as simply a commonsense idea of uniformity of movement—is the only operational idea of time we have ever had. The initial idea of time, historically, or instinctively, is the idea of uniform movement. The first clock must have been chosen on this basis, just as the very latest atomic clock is chosen on this basis.

Also notice that there has never been any way to test the uniformity of a clock, except relative to another clock. The first clock must have been chosen based mainly on instinct. The ancient who chose the swinging pendulum because it swung the same number of times per day was comparing it to another clock—the sun. If he was smart he counted his pendulum swings from sunup to sunup, rather than sunup to sundown, and so avoided the variation in length of daylight. And if he was very smart, he continued to look for even better natural clocks to fine-tune his measurements by. But notice that as long as the sun was his standard, he had to assume that the sun was a good clock—he took for granted that one day was the same length as the next.

In judging the uniformity of natural clocks, like the sun or the stars, our ancient would resort to comparing them to his pendulum clock. How did he know that the sidereal clock was more accurate than the solar clock? By comparing it to his pendulum. He corrected his pendulum by the sun and corrected the sun by his pendulum.

In this way you can see that there never was an idea of "absolute time." Time was always a relative measurement. It had to be. It was relative to a given clock, a clock chosen mostly by instinct. For there was never any way to prove that the given clock was absolutely uniform. It was only more uniform relative to clocks that were already relative to other clocks.

So time is not a measurement of "time." Time is a measurement of the movement in or on a given clock. And this given clock is uniform only by definition. It is uniform relative to a standard clock. One that has been defined as uniform. This standard clock cannot be proven to be uniform. It is only believed to be more uniform, based on previous definitions and previous clocks.

In this sense, time is not absolute. There is not, and cannot be, a clock that is known to be absolutely uniform. This is a statement of logic. A clock known to be absolutely uniform is a reductio ad absurdum. For us to know the clock was absolutely uniform would require us to have a previous clock by which to measure it. A clock may be defined as absolutely uniform. That is, we may decide, quite freely, to define some vibration of the background radiation of the big bang to be absolutely uniform. But we cannot know the truth of that definition.

Every measurement of time is a relative measurement, in this sense. It is relative to a standard clock, defined as standard. Time is also a relative measurement in the sense that it is dependent upon a measurement of distance. The time concept is relative to the distance concept.


Now that we have an operational definition of time, we may proceed to an operational description of the calculation of velocity. Velocity is a relative measurement of the change in position of an object relative to the change in position of (the internal workings of) a clock. We usually write this as distance-over-time. d/t. MM maintains that this is exactly the same as distance-over-distance. If we had written miles per hour, we might have written miles per miles. For we might have remembered that our clock is a little something in movement, and the movement inside the clock might be expressed in our denominator just as easily as the "time"on the clock. A pendulum travels some distance each second, and so does a cesium atom or a pulse of light. In calling the distance traveled a "second" instead of a mile or a foot or an angstrom, we are simply choosing terminology that suits us. But the fact remains: in terms of measurement, what is being measured by a clock is distance.

In the calculation of velocity, one makes one basic assumption. One must assume that there is indeed a relationship between the measurement of the object in question and the measurement of the clock. If one is comparing two things, one must assume that the two things are comparable. Thus one must assume that the distance that is being measured is the same sort of distance that is being measured with a clock. In a velocity equation, one really has distance-over-distance. For the equation to make any sense at all, one must assume that the concept in the numerator is equivalent to the concept in the denominator. That is, one must assume continuity, therefore one must assume that the measuring rod of the object-distance is the same measuring rod of the clock-distance and that the background is the same for the clock and the object. In mathematical terms, one must assume that the clock and the object are in the same co-ordinate system. If they are not, then it would be foolish to compare them. It would be foolish to put one over the other in an equation.

Think of it this way. A velocity equation states that the object (of the numerator) moves a certain distance relative to the movement of another object—the workings of a clock (the denominator). "Relative to" means that the first thing is related to the second thing. If they are in different co-ordinate systems, they are not related to each other, and it would be senseless to put them in the same equation.

So the basic assumption of a velocity equation is that the object and the clock are related. They are in the same co-ordinate system. Or, to put it another way, space is continuous from the object to the clock. If it were not, there could be no velocity equation.

If time is actually a measurement of distance, then wherever space is continuous, time is also continuous. This being true, it follows that wherever there is an attempt to measure velocity, there is an assumption that time and space are continuous. There is an assumption that all local measurements are equivalent. Without this assumption, no equations are possible.

In this sense, time is absolute. Time is assumed to be invariable from point to point, throughout space. This assumption is what allows for the measurement of velocity. [This says nothing about measuring moving clocks as will be shown in "An Algebraic Correction to Special Relativity and Refutation of Gamma" In fact he findings of Einstein's Special Relativity are valid, in the main. But in order to calculate the slowing of moving clocks, from a distance, one must assume they are not slow, locally.]

It is said that Einstein did not make this assumption—of absolute time—when he began his calculations in Special Relativity. It is said he did not make the Newtonian assumption of absolute and continuous space and time (one big co-ordinate system); nor did he make the assumption in a more limited sense, as MM does above. He did not assume the equivalence of local time. It is said that he proceeded without this assumption, and by proceeding without it proved that local time, in my sense, is meaningless. According to the canon, one may now speak of ones own local time. But speaking of the local time in another place is a faux pas.

MM will show in other papers that Einstein hid his assumption very well, but it was there nonetheless. What is the only assumption that most people will admit that Einstein carried into Special Relativity? What was his "only" given? The constancy of the speed of light. But if the speed of light is the same in every co-ordinate system, then that, by itself, assures that the local time of every co-ordinate system is equal to that of every other. If light goes 300,000 km/s in every system, then the ratio of kilometers to seconds in every system must be equal. Either that, or the statement "light has a constant speed" has no meaning. It is a contradiction to say that light has a constant speed, but that its time when measured in another system may be different than ours, then to say that light has a constant speed has no meaning.

It does not matter that their time is "different than ours." When they measure the speed of light, they will not be using our watches. That their watches are relative to ours will not enter into the velocity equation they use at all. To measure the speed of light, they will divide the distance light goes in their system by the distance their little cesium atom wobbles. The relationship of light to a cesium atom in their system is the same as in ours, so they will not only see the light go the same speed, they will see it go the same distance we do.

Notice this has nothing really to do with cesium atoms. It has to do with the relationship between distance and time in their system. If their time is slow relative to ours, it surely does not mean that they will measure it differently. Einstein says they will get the number 300,000 km/s, just like us. You might think that their second is slower, so that the distance must be longer than 300,000 kilometers in order to equal the same speed. But this is not looking at it from their perspective. They are not going to divide the distance they see light travel by one and a half pendulum swings, for instance, or by 1.5 seconds, or by some extra number of cesium wobbles. They are going to divide the distance by one second, just like we do. And they are going to call it one second, no matter what you or I think of the matter—no matter how long or short that second looks to us. Einstein says that according to them, light will be going 300,000 km/s. They define one second as being one tick of their own clock, just like we do. Therefore, they will see light travel 300,000 kms during that tick.

It is true that if we could see the light in their system from our system (which we can't—by the time we see it, it is in our system) it would appear to have traveled a shorter (or longer) distance—since those clocks over there are slow (or fast). But that is not the question. The question is what do they see. They see the same thing we do. This is not of the nature of a guess. It is a deduction. If the speed of light is given as a constant in every system, then every system must have equivalent local time.

The smartest scientists have understood this, even when they were a bit unclear about Relativity as a whole. Richard Feynman, for instance, who many would call the smartest physicist since Einstein, explicitly believed in what MM is calling local time and distance. On page 94 of Feynman Lectures on Gravitation, he talks of "absolute time separation" and "proper time". This was his admission not only of local measurement, but of the universal equivalence of local measurement. He understood that you cannot link various systems with any transforms whatsoever unless you assume the equivalence of all local time.

Four-dimensional Space

Minkowski is known as the father of four-dimensional space. In his theory, time becomes a fourth dimension, mathematically equivalent to x, y, and z. In fact, by setting his quadratic equation equal to 1, instead of to zero, Minkowski implied that time travels at a right angle to all three of the other dimensions. It was therefore equivalent to a spatial vector, travelling orthogonally. It so doing, it created what mathematicians call symmetry. The t variable could then be incorporated into matrices as an absolute equal to the other distance variables.

This theory was appealing to those who are attracted to mathematical esoterica, but unfortunately it is completely false.

As MM has shown, time is a measurement of movement. Without movement there is no time. But this movement already has a direction, determined by x, y, z: it cannot be given a secondary vector. All motion is a vector, and that vector must coincide to some distance vector within the 3-d continuum x, y, z. So to state that time has a vector outside this continuum is false. If time is a measurement of motion and all motion is contained in x, y, z, then time cannot be outside of or external or superadded to x, y, z.

Nor can it be thought of as mathematically symmetrical to the three distance variables. It is a second measurement of distance, as MM has shown, so it can certainly be thought of as a distance variable. But it is not the same sort of variable, theoretically. It is different because it is not really a variable at all. It is a postulate. You may not include it with the others simply because the others rely on it. Meaning that you may not have all four variables as variables at the same time. If time is unknown at the same time that x, y, and z are unknown, then all four are unknowable. If x, y and z are thought of as fields, then t is a subfield. If x, y and z are thought of as axes, then t is a defining axis or "axiom axis". It is not strictly equivalent to the other three. Including it in matrices in the way that is now done is therefore dangerous. Theory is lost, postulates are hidden from view, and mathematical errors are the consequence.

If that critique of Minkowski was a bit abstract for some, think of it this way: Velocity is distance over time, right? Distance and time are both vectors. They have direction. Well, you can't put orthogonal vectors in a ratio or a fraction and expect to get a value for your velocity vector. If you have one vector over another, and the vector in the denominator is at a right angle to the vector in the numerator, you have a serious problem. One of the first rules of vector algebra tells us that you can't just divide one number by the other; but this is what happens every time we find a velocity. We simply divide the distance by the time. Which means one of two things must be the case. Either all our historical velocities are wrong, or Minkowski is wrong. The time vector is not at a right angle to any possible distance vector. (See more on Minkowski in Problems with General Relativity; Curved Space is Unnecessary.)

Conclusion

MM was asked by a reader of another paper whether he ultimately thought time was absolute or not. You can see that this is not such a simple question. MM had to ask, "absolute in what sense?" As MM has shown, time is assumed to be absolute in the sense of being equivalent from one system to another. We must make this assumption in order to calculate velocities, among other things. This does not mean that it is absolute, of course. It means that we must define it as having continuity from our immediate vicinity to any vicinity we want information about. If we do not assume time and space continuity, we cannot hope to build meaningful equations. A universe without continuity is a universe without equations, without mathematics, and without science.

However, time is not absolute in the sense of absolutely precise, or absolutely known. It is a concept based on the idea of uniform movement, but the concept allows of only relative measurement. A movement can be known to be more or less uniform, but not absolutely uniform.

Likewise, time is not an absolute in the sense that many "classicists" appear to mean when they mean by it that Special Relativity is wrong. Objects moving at a distance, including of course clocks, look different than objects at hand. And velocity and acceleration influence the appearance of distant objects in quantifiable and dramatic ways. Time dilation is a fact.

Time is also dependent upon, and therefore relative to, movement. In a sense, time is nothing but a second measurement of movement. Displacement is movement. Time is movement. Time is displacement. Time is the displacement of the reference body.


Relativity as a Concept
(A Break in the Pioneer Case)

This paper is meant to prepare the reader for a serious analysis of Einstein’s equations. Most readers seem to enter any analysis with extremely strong prejudices, and they are likely to enter this particular problem with prejudices that are almost religious. No matter how simple and transparent the math is, no one will consider it if they do not imagine the possibility that it may be correct. To provide this possibility, MM has constructed here a short overview of the concepts. This will allow the reader to place the math in a proper framework.

Most think that they are already aware of the framework, but Relativity has remained uncorrectable for a century due to the fact that no one—not one person—has fully understood the framework, including Einstein himself. It is for this reason that MM must show where the framework must be extended and altered in the simplest possible language. An understanding of the framework is necessary in order for MM's mathematical corrections are to mean anything to you at all. MM is not proposing any esoteric ideas or concepts, inventing particles or fields and nor will it be proved that light can go faster than c or that Relativity is a myth. MM is merely making small mathematical and conceptual alterations to Special Relativity that will make it even stronger and more useful.

That Relativity is true is a given. The finite speed of light does require us to use transforms. There is no doubt of it. These transforms will give us time dilation and length contraction. Einstein was absolutely correct in that. But his theory, as he presented it, was still flawed and incomplete. Even Einstein knew this. He told his followers explicitly that no theory was ever finished, and especially not his. That is why he continued to work on it until his death. He was not just working on General Relativity, either. He was working until the end trying to understand all the implications of his first postulates. He did not succeed. He left Relativity with many basic errors embedded in it, errors that have not been corrected to this day.

Before presenting the mathematical corrections, it is therefore best to make clear to the reader the conceptual mistakes of Einstein and current theory. Absolutely everyone, Einstein included, thought that the transforms were transforming variables in one coordinate system to variables in another coordinate system. But this is not what the transforms do, mathematically or operationally. In any given experiment, what the transforms do is transform incoming data to local data.

Let us use the Pioneer spacecraft as our example. If the engineers at JPL apply the transforms to the problem, what exactly are they doing and what are they finding? All would say that they are transforming a moving coordinate system that is far away from the earth to the earth’s system. In some sense this is correct, but it is not precisely correct. It is not correct enough to avoid confusion. What is really being transformed is data from the distant system to the earth’s system. Relativity is primarily a theory of observation and measurement. Therefore all our data is observed or measured data. That is what Relativity means. Newton could gather data without considering who gathered it or where. But Einstein correctly pointed out that we could no longer do this if we wanted to get the right answer. The finite speed of light demanded that we take into consideration who was gathering data and where. If we wanted to get the right answer we either had to make all our measurements near at hand, where the speed of light did not affect our numbers, or we had to do transforms on the numbers. Most data that arrived from any distance would be affected by the E/M waves it was arriving on. We would now have to consider the time separation and the velocity of the object we were receiving data from.

This means that in any transform we have two sets of numbers. We have our local numbers for things, like the length of a meter rod and the length of a second, and we have the data coming in from a distance. We want to apply our meter rod and second to this incoming data, so that we know what it means, but how do we do it? Einstein gave us transforms and these transforms (usually) work. Great. But with the Pioneer Anomaly the transforms are a tiny bit off. What could be wrong?

What is wrong is very simple, though it is beastly difficult to discover if you have already made it to the end of your understanding of Relativity and your acceptance of it is set in stone. The only way to find the error is to go back to the very beginning and start over. This is what MM did and this is what he discovered:

To do a transform you have to assign a set of variables to your incoming data. You can make them primed variables, for example. This is what Einstein did. But conceptually you are not finished. You now have to assign your coordinate system. It is not enough to make a variable assignment. You have to also define your new coordinate system. This is where the central error is made. In the Pioneer example, the data is coming from the spacecraft, so Einstein and everyone else defines the primed coordinate system as belonging to the spacecraft. But this is false. What we receive on earth is just data. We are measuring or observing not the spacecraft itself, but information arriving from the spacecraft. In other words, we are seeing how the spacecraft looks to us, not how the spacecraft looks to itself.

The whole reason we have to do a transform in the first place is that the finite speed of light is skewing the data. The information from the spacecraft is arriving late to us, compared to when it was experienced by the spacecraft, and it is arriving with time periods stretched out and meters compressed and so forth, as we know. We do the transform in order to correct this. The transform gives us numbers that we can compare to local numbers and make sense of. But if the finite speed of light is skewing the numbers, then logically the numbers must have been unskewed back at the spacecraft. The spacecraft is not emitting funky data, we are receiving funky data. It is the distance between us, and the finite speed of light, that is causing the difference. Therefore, the spacecraft, which is no distance from itself and is not seeing itself with light that has had to travel long distances, must be experiencing normal local data.

This means that the transform is not expressing a difference between the numbers of the spacecraft and the numbers on the earth. The transform is expressing a difference between numbers arriving at the earth on E/M waves and numbers on earth arriving from a negligible distance. To put it another way, x’ is not how the length of the spacecraft looks to the spacecraft, it is how the length of the spacecraft looks to us, from a long distance away. Therefore you cannot give x’ to the spacecraft. You must give x’ to the data only.

A doubter will say, “But don’t we see things locally with light, too? All our information, local as well as distant, arrives on E/M waves.” True, but the E/M waves do not skew nearby data, since there is no time lag. To get time dilation and length contraction, the light has to travel some appreciable distance or the velocity of the measured object must be very very great. When we define local time and length we do not define it relative to clocks or meter rods that are far away or rushing about. We define it relative to clocks and meter rods that are nearby and at rest relative to us, as observers.

A reader will say, “Maybe, but what difference does it make? You seem to be making very subtle conceptual distinctions, but this is just semantics or metaphysics. Relativity is not philosophy; it is math.”

Yes, but all applied math must be applied correctly. Incorrect variable or field assignments are not metaphysical errors. They are mathematical errors that will and must lead to mistakes in calculation. This is exactly what has happened with the Pioneer Anomaly.

This is how the field misassignment has affected the math of Special Relativity:

Two of the fundamental equations and assumptions of SR concern the movement of light in the two fields or coordinate systems.

x = ct
x’ = ct’
The first equation is how light travels relative to us here on earth. The x and t variables are our own local variables. MM has no problem with this equation.

The second equation is how light travels in the other field. But there is no other analogous field, in a strict sense. What MM means is that x’ and t’ are how the spacecraft’s lengths and times look to us. How do we put c into that data, if it just data? In what sense is data a field that light can travel in?

It’s not. We can’t do it, mathematically or conceptually. We have to find some other way to solve. We know empirically that time dilates and lengths contract, so we can develop simple equations that express that. As time dilates, the period gets longer, by definition. So within the pseudo-field of our data, time and length are inversely proportional.

xt = Kx’t’
where K is an unknown constant. Now we simply use the two equations we have so far and solve.
x = ct
xt = Kx’t’
ct2 = Kx’t’
x’ = ct2/Kt’
x’ ≠ ct’

Someone may say,
x’ = ct’ may still be true according to your equations if
t2/Kt’ = t’
K = t2/t’2
But x’ = ct’ cannot possibly be true, since if both x = ct and x’ = ct’ are true then x and t must change in direct proportion. This would be
x = ct
x’ = ct’
c = x/t = x’/t’
that is a direct proportion. But that contradicts mountains of empirical data. The period does not get shorter as the length gets shorter. Just the reverse. This means that Einstein has accepted as one of his first equations an equation that contradicts all current data and all data that he was trying to explain. He knows that time dilates and that dilation means a larger period. He says it explicitly in the book 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." And yet the equation x’ = ct’ must mean that time speeds up. This is a terrible error.

A reader will say, “With an error of that magnitude, how does he end up getting a transform [γ] that works so well?” He achieves this with a compensation of errors, and by knowing what he needs at the end. The Lorentz transforms already existed—that is why they bear the name of Lorentz and not Einstein. It was empirically known what equations were needed, and Einstein simply supplied the derivation. Lorentz’s math was pure heuristics, since it was applied to the data after the fact. Lorentz’s math was not predictive, it was compensatory. Everyone knows that. But so was Einstein’s math. The transformations are a direct outcome of the Michelson null outcome. The only difference between Lorentz’s heuristics and Einstein’s is that Einstein collected and invented several important axioms. Most of these axioms are true, as MM has said above. Einstein made real contributions to the problem and deserves much credit. But Einstein did not get everything right. Both his math and his theory were and remain incomplete. His errors have caused a mountain of confusion and are now causing experimental errors. These errors must be corrected if we are to continue to make progress in kinematics.

The equation x’ = ct’ has never been corrected. It is a fundamental part of gamma and still exists in the derivation of the tensors. Importing tensor calculus into SR did nothing to correct the equation. The only way to correct gamma is to jettison x’ = ct’ and start over. That is what I have done in all my papers. The full derivation of new transforms may be found in the paper: An Algebraic Correction to Special Relativity and Refutation of Gamma.

The specific problem confronting the scientists working on the Pioneer Anomaly is that the motions of their spacecraft are not analogous to the motions Einstein and Lorentz were attempting to explain. Gamma comes very close to correctly transforming the variables in the thought problems given at the time, including the interferometer. But the relative trajectories in these thought problems do not match the relative trajectories in the Pioneer problem. Spacecraft do not recede from the earth in the same way that light travels through an interferometer or what have you. MM has shown in all my various papers that trajectory must always be a consideration.

Following Einstein, current theory accepts that all trajectories are equivalent with regard to Relativity. That is, you do not need to consider direction or angles or curves, only velocity. This is false. MM has proven beyond any doubt that direction is of paramount importance. The transforms are completely different for objects approaching than for objects receding. Objects moving at tangents or angles to the line of sight of the observer require more complex transforms. Since the motions of the spacecrafts in question are quite complex, the transforms must be equally complex. Gamma is not sufficient to do the job, no matter how much tensor calculus you bring in to bolster it. In fact, the current transforms are so partial and insufficient that is may be considered a mathematical miracle that they work at all. That they come within any fraction of the correct answer can only be attributed to the great imagination and ingenuity of the mathematicians and engineers who use them.

Someone may ask, “So what does this mean about distant objects? Are they in our field or not? You are saying that the local numbers of the spacecraft are basically the same as ours. Their meter rods and seconds are the same as ours. The time and length differences are only apparent, since it is the data that is skewed, not the spacecraft itself. Doesn’t this put us right back in the universe of Newton? And doesn’t this mean that all the ‘cranks and crackpots’ on the web are right?”

Not at all. Some of the so-called crackpots have had their points, but everyone in both camps—believers and non-believers alike—all share the distinction of being pretty spectacularly wrong, including Einstein himself. The single mistake MM has related above is of awesome dimension, considering that Einstein had his whole lifetime to spot it and make a correction. None of the great believers or non-believers have ever spotted it either, including Bertrand Russell, Herbert Dingle, and Richard Feynman. It appears that no one living or dead has spotted it or any of the other major algebraic errors that MM relates. Therefore, all the finger-pointing and name-calling should immediately end. None of the believers or non-believers are or have been in any position to judge their neighbors.

For it turns out that the truth is almost precisely in the middle. The non-believers believe that Relativity is false. But in the end, Relativity is simply the necessary existence of transforms. If transforms are necessary, then Relativity is true. Those who believe that transforms are not necessary have either never been on the receiving end of any data or have never done any math, or both.

As for the believers, they have also strayed far a-field. They have pretended to an understanding they never had. They have tried to force upon us twin paradoxes and varying atomic clocks in airplanes and all manner of other mysteries and mystifications. They have hidden behind imposing maths like the tensor calculus while they could not spot or correct simple algebraic errors. They have filled the blackboard with Hamiltonians and Lagrangians and other multiple abstractions while they have been unable to comprehend simple circular motion or the physical basis of the derivative. They have belittled philosophers and mathematicians while themselves making astounding mathematical and philosophical errors. They have accused others of being metaphysicians while they themselves have become the most naïve idealists imaginable.

But the answer is that, no, we are not back to Newton, not by the furthest stretch of the imagination. That all data from a distance requires a transform is a huge step forward, and Einstein deserves his place in this. The recognition of a time separation with any distance separation is also quite different from Newton, and crucial. Relativity allows us to do many things in mechanics and kinematics that we could not have hoped to do in the 19th century. It allows us to show the physical genesis of the inverse square law, which Newton could not hope to do. Newton derived the law but could not explain what caused it. Relativity has allowed me to do this. (See Derivation of the Inverse Square Law..) No doubt Relativity will allow us to solve many problems that have not even been discovered yet, problems still embedded in classical and current theories.

The equivalence of all local time is not a return to Newton, since all local measurements are incommensurate when measured from a distance. Newton and Galileo did not believe this and could not have expressed it if they had. In fact, there was no local time for Newton since he saw no use for it. MM has defined local time in relation to relative time. Newton had no relative time, therefore he could have no local time. He only had universal time. Newton thought it was “now” everywhere. But we know that this is not true. If we look at Saturn in a telescope, the picture we see is not “now”. It is Saturn some seconds ago. If we look at a distant star, that twinkle is some years old. And so on. Very different from Newton, and true. This is proof of Relativity in itself. Time separation is Relativity. The consequences of that alone are huge, in the history of physics and astronomy.

In addition, redshifts and blueshifts of data due to relative motion have been known since the 1600’s, when Rømer saw them from Io. MM does not mean shifts of light, but shifts of data. The data from Io was seen to vary depending on the relative motions of the earth and Io. This was Relativity, and Einstein’s transforms can be applied to Io to discover the variance. Why? Because any periodic motion can be considered a clock. The eclipses of Io were periodic, so Rømer was seeing a clock in the sky from a distance. The same is true of pulsars, which are clocks in the sky. Their periods are known to vary depending on relative motion. This variance is Relativity. The periods of pulsars shorten if the pulsar is moving toward us; slow down if the pulsars is moving away. This is a Doppler Effect on clocks, which is the same thing as Relativity. And it contradicts the current interpretation of Relativity as being the same for all relative motion. The rate of moving clocks does not always slow down. Pulsars are moving clocks and they speed up when they approach us.


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