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How the Principle Of Equivalence Disproves The Relationship Between The Warping Of General Relativity's Space-Time and Gravity
The Principle Of Equivalence And The Tempo Field Theory Are Fully Compatible.

The principle of equivalence is perhaps the most powerful illustrative tool in the locker of relativistic science. The correct application of well established physical laws, has lifted the principle of equivalence, from the diffident and modest position it has occupied for most of the last century, that of being merely an approximation of the principles of nature, to that of nature's direct representation and delineation, enabling it to be used as an incisive tool. It has become the expression of the symmetry and harmony that exists between acceleration, speed, time dilation, energy, redshift, frequency of light, the speed of light, and quantum gravity. For a theory to be taken seriously it must comply in all respects with the principle. Initially it was widely considered that general relativity did so. Indeed it was thought to have been formed from a correct application of the principle. However, it can now be incontrovertibly demonstrated that this is not the case. It can be shown that special and general relativity only pay lip service to the principle and do not conform to it fully when it is rigorously applied, thereby failing to comply with their own criterion. The Tempo field theory is the only current model that complies with the principle of equivalence in all respects and this fact alone, constitutes a paradigm shift in the disciplines of relativistic astrophysics, cosmology and quantum physics.

The purpose of this Paper is to support with fresh examples and evidence, the conclusions arrived at in Chapter 7 of my book 'Time - The Hidden Dimensions of the Missing Physics'. In so doing, I wish to put forward several aspects of the 'Principle of Equivalence' that I have neglected or only touched upon in the book. Because of their profound importance to physics in general and to the Tempo field theory in particular, they deserve to be dealt with fully and with special emphasis.

(1) How The Principle Of Equivalence Proves Time Dilation To Be Independent Of Gravity.

In the following paragraphs it will be conclusively demonstrated that the principle of equivalence has time dilation taking place where there is a constant gravitational effect. Conversely, general relativity requires the opposite, by demanding time and space to be warped relative to gravity: so that the greater the time dilation the stronger must be the gravitational field synonymous with it. It is important to grasp the difference between the erroneous postulate of general relativity, which time warps with gravity, and the contrasting absence of such effect, in the principle of equivalence. It means that our ideas on the form that gravity has, have to be changed, as it can now be appreciated that there can be time dilation without gravity but there cannot be gravity without time dilation, in the form of a field. Natural examples of this can be found in the world. For instance at the centre of the Earth, where gravity is zero but time dilation will be at a maximum. The reasoning for this given in the Tempo field model is, that because the maximum time dilation is at the centre of the time field, it is a uniform point, where there is no time differential, to cause a gravitational effect, (see Papers on 'Time' and 'Quantum Gravity' and my book 'Time - The Hidden Dimensions Of The Missing Physics'). The inevitable result of this is that time must be the agent for gravity and not the other way about. The principle of equivalence contradicts general relativity in this regard, but accords with the Tempo field model, where it is the time differential and not merely time dilation that causes gravitational effect. It is this principle, which goes to the heart of quantum gravity, (see Papers on 'Time' and 'Quantum Gravity'). If gravitational effect does not warp time, it cannot warp space-time either, leaving the concept of space-time redundant.

The original thought experiment that initially demonstrated the principle of equivalence, can be used to establish how time dilation is independent of gravitational effect. Imagine a closed box being accelerated in outer space, with a beam of light shining from one side of the box to the other. If it is accelerated at the constant rate of 1G, the gravitational effect in the box will be constant similar to Earth. To an observer in the box, the beam of light will appear to bend as if under a constant gravitational effect equal to Earth-gravity. However, while this is happening, its speed will be increasing all the time. A consequence of its increasing speed will be a corresponding increase in its time dilation, in spite of the fact that the gravitational effect on the beam of light is constant.

The Tempo field model explains that the box in which there is an artificial gravitational effect, with the consequent bending of the light beam, has within it a simulated time field equivalent in form to that which causes gravity on Earth. The time differential in this instance, is occasioned by the box's acceleration, whereas, on Earth it is relative to a body's proximity to the mass of the Earth. The simulated time field allows a differential in time dilation between the source of the light and when the light reaches the far wall. This is because when the photons reach the wall, the box will be travelling faster than when they left their source on the opposite wall. This creates a time differential across the box, which simulates a time field.

The symmetry here lies in the fact that, [as seen in the Paper on 'Quantum Gravity'], natural gravitational effect results when a quantum energy wave such as light, is in an actual time field. It is the time differential across the quantum wave, that gives it the propensity to move in the direction of maximum time dilation. It is this propensity to move that we call gravity, (see Papers on 'Time' and 'Quantum Gravity').

In the simulated time field, the correct proportional amount of movement to match the matching gravitational effect is symmetrically provided by the motion of the box. The Tempo field model does not, as in general relativity, lay the emphasis, exclusively, on the physical effect of the acceleration moving the box away from the light beam while in transit across the box. While it acknowledges the effect, it shifts the emphasis, by showing that the box's acceleration progressively increases its speed and time dilation. This simulates the constant ratio required for the increasing time differential between the walls of the box, and the increasing speed of the photons.

To an observer in the box, the acceleration of the box has the effect of letting him see the photons arc downwards as if under gravity, while at the same time, generating a constant ratio of the mean speed of the photons to the difference between the time dilations of the two walls. This constant ratio, is equal to that which would, in a real time field, produce an equivalent gravitational effect.

(2) How The Principle Of Equivalence Proves The Speed Of Light Is Not A Constant.

The propagation of light within the principle of equivalence creates insurmountable problems for the proponents of special and general relativity. Both those theories require the speed of light to be a constant, while the principle of equivalence indicates the opposite to be true. It requires the speed of light to vary with the time dilation of the observer in the box, in pleasing conformity with the Tempo field model. This change in our understanding of the propagation of light, is directly counter to theories that have prevailed for the past hundred years. Despite such longevity, the Tempo field theory now indicates four different ways of proving the veracity of the change, as follows:-

(a) How The Principle Of Equivalence Proves That Distance For A Body Does Not Shorten In Its Line Of Travel.

In order to keep the speed of light notionally constant at 300,000 kilometers a second, special and general relativity requires distance to shrink in the line of travel of the box, while at the same time, inside the box distance has to remain normal. However, as we have seen in the Paper entitled 'The Variation of the Measurement of Distance Rejected', this is a built-in contradiction. In order for gravity to be simulated in the box, the distance travelled by the box through space, has to be the same measured internally as externally. The Tempo field model avoids this by making the speed of light a variable proportional to the observer's time dilation, obviating the necessity to alter distance.

(b) How The Principle Of Equivalence Enables An Observer On Earth To See The Speed Of Light To Be Equal In The Box And On Earth, Ensuring Simultaneity.

As we have seen, the principle of equivalence calls for the speed of light across the box to vary with the time dilation in the box. General relativity entails the opposite. That theory requires the speed of light across the box to be constant, regardless of the dilating [slowing] of time in the box. Such a notion would result in the light in the box having to become slower relative to 'fixed' Earth-time. In other words, if time in the box is slower relative to an observer on Earth, then so also, for that observer, must be the speed of light in the box. This is simply impossible. It is a postulate for the propagation of light, that an observer on Earth must measure the speed of light to be the same, in the box and on Earth. An observer on Earth and in the box must see the light leave the source and arrive at the opposite wall, at the same instants, even though, because of their different time dilations, they will each measure different intervals between the two instants.

The requirement is precisely met, when the parameters of the Tempo field model are applied to the principle of equivalence in the box. It is achieved in that model, by virtue of the fact that for an observer in the box, as his time dilates, the speed of light for him proportionally increases. As a consequence of this, an observer on Earth, looking at the beam of light crossing the distant box, with that constant proportionality of time dilation to the speed of light in the box, will have the same constant of proportionality as light propagated on Earth. This enables the observer on Earth to measure the speed of light in the box and on Earth, to be the same, and therefore, constant. Consequently, subject only to the travel time of the light to reach the observer on Earth, the observer in the box and on Earth will see events in the box simultaneously, relative only to their distance and without any other reference to time. This is an important step forward, as it improves on general relativity, which requires events to occur at different times in different inertial frames. It brings back the now into physics.

(c) How The Principle Of Equivalence Provides For A Ray Of Light In The Box To Be Repeatable and Reversible.

The following problem revealed by the principle of equivalence, is one that the reader will not find covered, that is to say, resolved, in any of the text books on cosmology. It is however, of paramount importance, pulling together all the problems that we have seen resolved by the Tempo field theory. Its resulting successful determination comprises a paradigm shift in cosmological thinking. It irrevocably moves us away from our reliance on special and general relativity, requiring all the many theories that have been developed from them, to be questioned afresh.

The problem is that notwithstanding that general relativity correctly predicts the bending of a beam of light when crossing the accelerating box, the reasoning given is flawed. This is because the manner of propagation of the light, does not accord with experience.

This problem was first noted by Einstein's friend and colleague Ehrenfest, who was a professor at Leiden. He had spotted the failure of general relativity to comply with the Principle of Equivalence, for the propagation of light across the box. Ehrenfest In 1913, wrote a short precise Paper, pointing out that if light was propagated across the box, like it is on Earth, it would be possible to reflect it back to its source, (see the Collected Scientific Papers:- North-Holland, 1959 ). That is to say, rays of light are repeatable and reversible. He showed that general relativity does not accomplish this, for light in the accelerating box. Einstein chose to ignore Ehrenfest's Paper, probably because he had no answer to it. Certainly, there is no answer to be found in general relativity, where the speed of light is required to be a constant. However, the problem is resolved in the Tempo field theory, where the speed of light increases as the time in the box dilates.

The solution is in the fact that for an observer in the box, the speed of light is constantly increasing commensurate with his increasing speed and time dilation. As we have seen above, this means we can derive a constant for the situation in the box. The constant is the ratio of the increasing differential in time dilation between the two walls to the increasing mean speed of the light passing between them. This constant takes no account of the direction the light is travelling in, making the light beam repeatable and reversible for the principle of equivalence.

Of course, this constant ratio is also pertinent for a similar beam of light on Earth. On Earth the mean speed of the light would have to be measured from a point midway between the time dilations of the source of the light and the mirror positioned to reflect the beam back. This measuring point, would be half way in height between the source and the mirror. [This is because time contracts the further away one gets from the mass of the Earth]. The difficulty is that the variables on Earth, are so small that we do not yet have the techniques to measure them, (see Part 4 of the Paper E= mc2).

(d) How The Principle Of Equivalence Provides For The Full Bending Of Light Without The Need For The Warping Of Space.

The new concept, that the Tempo field theory allows the light in the box to behave and bend to the full extent as that on Earth, alerts us to a deep flaw in general relativity, that from the beginning has confused our thinking and led us down false trails. Einstein's 1911 calculation for the bending of light, was based on a misunderstanding of the Principle of Equivalence. When he found that his calculations for the principle, only indicated a bending of the light beam by an amount that was half of the correct value, he passed it off by regarding the principle as being in some way limited. In other words, the symmetry of nature in the form of the principle had got it wrong, not him.

Einstein did not go looking for the missing half in his interpretation of the principle, but looked for a separate explanation that he could add to the half he already had. He argued that his1911 calculation was only in respect of the warping of time, and that the missing half could be attributed to the warping of space. This gave rise to the theory of general relativity, which of course gave the value it was designed for, from his new theory of gravitation. Einstein purported that his revised calculation included an extra deflection attributable to the notional warping of space, [but without explanation as to the causal physics for the phenomenon]. He argued that his previous calculation had only taken into account the warping of time.

In so doing, he ignored the implications of this argument on the Principle of Equivalence. For an observer in the box, the error is clear: the bending of a ray of light, when his box is accelerated, cannot be half as large as when it is at rest in a gravitational field. Otherwise, acceleration that simulates a time differential and gravitation are not interchangeable and symmetric, leaving us without a principle of equivalence.

The Tempo field theory provides the correct parameters to fit the principle of equivalence when simulating gravity, answering the quandary of the missing half. The problem that goes to the core of the matter, is the old chestnut, that , in general relativity, the frequency and speed of light crossing the box, has to remain constant for an observer in the box. As a consequence of this interpretation, as the box speeds up and its seconds dilate, time slows down, effectively slowing down the frequency and speed of the light. On the other hand, in the Tempo field model as the time dilates the frequency and speed of the light has to go up, (see Papers 'Time' and 'Quantum Gravity').

This yields the result that the change in frequency or energy of light, required to bend it, in accordance with the gravitational effect of general relativity, is half that of the Tempo field model. This result is obtained because the Tempo field model starts from a frequency value that is twice that of general relativity. Demonstrably, in the principle of equivalence, the energy used in bending the beam of light is fully accounted for by the Tempo field model. In quantitative terms, the Tempo field model of gravity, will always be twice that indicated by general relativity in the principle of equivalence, without the need for the bending of space.

All that remains to be done, to resolve all aspects of the problem, is to show how the amount of the bending of the light beam physically equates to the actual distance travelled by the box, relative to the speed of the light passing across it. In doing this only normal distance and real time, as in the Tempo field theory may be relied on, thereby, setting apart that theory from Special and general relativity. This differentiation comes about because in its endeavour to keep the speed of light constant, and the speed of all moving bodies below such constant, special and general relativity introduce a postulate that distance as measured from the moving body, shortens in the line of its travel, relative to its speed. They also require the box, as measured from Earth, to foreshorten in its line of travel, in proportion to its speed. It will be shown that it is the resultant notional shortening of distance in the line of travel of the box, together with the constant speed of the light across the box, which is at the root of the problem. The principle of equivalence will do this, by showing that it works perfectly without them in accord with the Tempo field model.

The question to be resolved is:- if an observer in the box, by whatever means are available to him in general relativity, sees the downward bending of a ray of light passing across the box in accordance with a given gravitational effect, can an observer on Earth using the same model of general relativity, see an identical amount of bending? The answer is a definite no, which can be understood when it is appreciated, that the observer on Earth, can rely on the principle of equivalence only if there is an equivalent foreshortening of distance, in real life, with which a comparison can be made. In general relativity the foreshortening of the box, is remote from real life, being a mathematical fiction, required to keep the speed of light constant. The fiction is shown however, to be inadmissible when applied to observers outside the box. For example, let the observer in the box, adjusts its speed and measurement of distance in its line of travel, so that the light beam looks to him as if it were bent in a gravitational field. Because an observer on Earth has to see the box foreshortened in its line of travel, the Earthbound observer, must see the light beam bent by a lesser foreshortened amount. Furthermore, if the observer is successful in keeping the gravitational effect in the box constant, then despite his efforts, the Earthbound observer will nevertheless, by virtue of the increasing foreshortening of the box as it speeds up, see the amount of the bending gradually reduce towards zero, the closer the speed of the box gets to the speed of light on Earth. Such requirements of general relativity are simply impossible, being misconceived and unnecessary, as shown by the fact that the Tempo field model does not require them.

More bizarre requirements of general relativity, are exemplified when matters relative to the box are further considered. In a futile attempt to keep the speed of the box below the constant 'c' for the speed of light, different parameters are muddled together. I will try to explain the muddle if only to show that the mathematical fictions that constitute it, do not work and are not necessary.

First let us consider how things are for an observer in the box. If matters are arranged so that he feels as if he is in a gravitational field of 1g, then he must be being accelerated at the rate of 9.8 metres per second per second, as measured from inside the box. This is generally accepted and is common ground. It must therefore be the case, that there is nothing to stop the box speeding up without limit. The box could accelerate until it was going at an infinite speed. This is a great embarrassment in general relativity, as it is not allowed in that model. In that model the speed of all objects, including the box, have to be limited to 'c'. In general relativity, a way had to be found, without altering the box's internal gravitational effect, to notionally make the rate of acceleration of the box, when observed externally, gradually reduce as its time stretches. The acceleration needs to gradually reduce until it reaches zero, to coincide with the box reaching the limiting speed. This is supposedly done, by adopting the mathematical fiction, of measuring distance relative to the box, differently on the outside to that of the inside, (see Paper - 'The Variability of the Measurement of Distance Rejected'). This strange new system requires distance outside the box to foreshortened in the line of its travel, proportionally to its speed and time dilation, while distance remains normal inside the box, that is to say, its internal dimensions remain unaltered. If this could be done, it would mean that the box's rate of acceleration would reduce externally while remaining constant internally. To compound the implausibility of this dichotomy, it is found to be necessary to introduce a separate time dilation from that of the box. This is called for, in order to have the beam of light inside the box, continue to hit the far wall at the same point all the time, as in a constant gravitational field. The notional reason for this, is that as the box is seen on the outside to slow down, so the speed of the light across the box has to slow down synchronously with it, to maintain the constant effect. Regrettably, because it is impossible, this creates more difficulties than it solves. For instance, the laws for the propagation of light, make it impossible for an external observer to see the beam of light in the box, slower than a beam of light in his own time dilation. Furthermore, even if he could, the point down the wall where the beam lands would be in mathematical terms, only half the distance down that it should be for a gravitational effect of 1g. This is because the external foreshortening of distance for the box, slows the rate of acceleration of its walls. The implausible consequence of this was supposed to be that the walls of the box do not internally accelerate away from the photons crossing it, fast enough. We are now left with a ragbag of fictions, which do not fit with either the principle of equivalence or any other scientific principle, and when all comes to all, only give half an answer.

The general relativistic model is reduced to a tissue of inconceivable mathematical fictions, suggesting a missing half of the gravitational effect in the box. When these are swept away, and the full amount of time dilation is allowed for, without the foreshortening of distance, and with the increase in the speed of light across the box, then all anomalies disappear, and the missing half is restored. There is now full compliance with the principle of equivalence, corroborating and endorsing the Tempo field theory. In that model, distance, time dilation and acceleration have their full values, leaving the beam of light free to bend the correct amount, as viewed from both inside and outside the box.

It is now manifest that the Tempo field theory in conjunction with the principle of equivalence, resolves the quandary of the missing half of gravitational effect and the bending of light. There is no missing half to find, and consequently, there is no warping of space. Naturally, this has profound adverse implications for all theories derived from general relativity.

For further reading see 'Time - The Hidden Dimensions Of The Missing Physics' and other Papers on this website.