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Special Relativity refers to the situation where an object is traveling at a CONSTANT VELOCITY relative to an observer. We have long known that it is real and that it has the time dilation effects that Einstein had calculated for it. We mentioned above that one of the first such experiments (around 1926) involved cosmic rays hitting molecules near the very top of the Earth's atmosphere at incredibly high impact force. The impact shatters the molecules into a lot of smaller pieces, some of which are mumesons or also called muons. We know in a laboratory how long a mumeson exists before it then again disintegrates into yet other particles. All scientists knew that even at the speed of light, a mumeson could not quite travel half a mile before disappearing as it decayed into other particles.
The proof of time dilation was that laboratories on the surface of the Earth, many miles below, were detecting those mumesons! That should have been impossible! A mumeson was created maybe 50 miles high in the atmosphere, and it was known to not be able to even go half a mile before decaying. So there was NO chance whatever that any mumeson could possibly get down to Earthbased labs to be detected. Time dilation was the ONLY possible explanation! From OUR pointofview, the mumeson's rate of time passage was far slower than ours, where it was able to make that longer distance before decaying. From the mumeson's pointofview, the thickness of the Earth's atmosphere was less than 0.28 mile, so there is no problem of getting all the way through it before decaying (even though time seemed to pass at normal speed for the mu meson!)
But the far more interesting subject is that regarding General Relativity. Where Special Relativity dealt with CONSTANT VELOCITY, in other words, NO ACCELERATION, General Relativity is about the many situations where accelerations occur.
One specific example of Einstein became very well known. In a pair of thought experiments, he proposed either two elevators or two rocket ships. In the elevators, he had one elevator carriage out in deep space where there was no gravitation applying, while for the other elevator, he cut the cables supporting the elevator carriage which was in the Earth's gravitational field, where the elevator then fell downward with ever increasing velocity, but with constant acceleration. He noted that an occupant of that falling elevator would be floating in the elevator, along with everything else there (at least if air friction was not considered and until it hit the bottom!) and that he would not be able to do any experiment to find any difference from if he was in the other elevator carriage floating free in deep space. Relativity. In the one case, there was no net acceleration because there were two effects, one of the Earth's gravitational field and the other from the acceleration of the free fall, which totaled exactly zero, just like is true in outer space. Einstein concluded that meant that an acceleration due to motion must be exactly interchangeable with an acceleration due to the gravity of a planet.
Time Passes Faster Here on Earth than on the Moon
Einstein's rocket thought experiment showed a little more. His experiment was to have two identical rockets. One is (forever) sitting on a launch pad, being subjected to the 32 ft/sec^{2} effect of the gravitational field of the Earth. The other space ship would be in deep space, far away from any planet's gravitation, but accelerating due to everrunning rocket engines at exactly 32 ft/sec^{2}. He noted here as well that the two occupants could never do any experiment to tell which situation was really their case. Again, an acceleration due to acceleration of motion cannot be distinguished from the effects of a gravitational field.
As it turns out, the equations for General Relativity are astoundingly complex, and after 100 years NO ONE has yet fully solved them! But virtually all Physicists agree that there MUST be some sort of effect regarding some modification of the rate of time passage which must exist in General Relativity. Unfortunately, being unable to actually solve the equations, they all ASSUMED that the timeeffect was the SAME as for Special Relativity, which turns out to be exactly OPPOSITE of what is certainly true.
Around 1960, a few years after Einstein's death, some Physicists applied some (wrong) simplifications to the set of (insoluble) Tensor Calculus equations that Einstein presented as describing General Relativity. Even then, all Physicists realized that in applying such modifications to the equations in order to be able to solve them, there was a good chance that the real precision of the original GR equations might have been lost. But there was immediately nearly universal adoption of the modifications.
Since no one has yet completely solved the set of ten tensor calculus equations of General Relativity, no one actually has ever known what that effect might actually be. There is a UNIVERSAL ASSUMPTION that a Time Dilation effect must apply. There is absolutely NO actual basis for making such an assumption! I firmly believe that it is entirely based on a flaw in the modifications done to the equations! In fact, my research regarding analyzing the alleged Twins Paradox and in studying those equations of General Relativity, have established to me that the exact OPPOSITE is actually true! During acceleration or when within a gravitational field, that time passes FASTER than it would in deep space without acceleration. I have given this the name of Time Speeding.
Given the preambles above, an extremely obvious experiment seem to be needed to be done! It is convincing and accurate.
(I proposed this experiment early in 2006 to NASA)
A small unmanned rocket would take a set of several accurate atomic Cesium clocks to a spot on the surface of the Moon and gently plop them down on the surface there. Radio links would be required to be able to compare those clocks' readings with the readings of an identical set of atomic clocks here in a laboratory on Earth. That's the entire experiment!
Specifically, the precise known frequency of the Cesium atoms on earthbased atomic clocks is 9,192,631,770 cycles per second.
In the slightly weaker gravitational field of the Moon, I believe that the Moonbased atomic clocks should have a frequency very slightly slower, that is, around 9,192,631,767 cycles per second. This is only slightly more than 3 cycles per second different, or around 10,976 different numbers of ticks per hour.
The difference is not much, only about 1/95 of a second slower per year on the surface of the Moon.
Actually, a longheld concept, called the Equivalence Principle, which
states that the effects of acceleration and the effects of a gravitational
field are indistinguishable, due to General Relativity, also has
long provided support for my research and my proposed experiment.
If any environment is subject to either a gravitational field or
an actual spatial acceleration, then that Equivalence Principle
states that General Relativity MUST cause
time to pass FASTER in a gravitational field by a factor which is
generally called the Equivalence Factor and is given as
1 + (a * d)/2 / c^{2}.
We know that the gravitational field on the surface of the Moon (a) is around 1.62519 meter / sec^{2}. We know that the RADIUS of the Moon (d) is around 1.738 * 10^{6} meters. And we know that the speed of light is about 299,792.458 kilometers/sec. If we plug those numbers into the commonly accepted Equivalency Principle factor above, we can see that the factor is therefore 1.000 000 000 015 732 (note that this factor is more than 1.0000 and so there is a timespeeding factor as compared to open deep space.
Over a period of one calendar year, that would imply that time passage on the surface of the Moon should have GAINED around 0.00049 second during that year, as compared to the rate of time passage in deep space. This is not a large interval of time, but to Physicists, it is huge!
We must now do the same math for the surface of the Earth. We know that the gravitational field on the surface of the Earth (a) is around 9.82 meter / sec^{2}. We know that the RADIUS of the Earth (d) is around 6 378 137 meters. We know that the speed of light is about 299 792.458 km/sec. If we plug those numbers into the commonly accepted Equivalency Principle factor above, we can see that the factor is 1.000 000 000 348 445 (note that this factor is more than 1.000 000 and so there is a timespeeding factor on the surface of the Earth as compared to open deep space.
Accepting that Earthborne Cesium clocks run at 9,192,631,770 cycles per second, this would then be a rate for a deep space Cesium clock of 9,192,631,766.80 cycles per second.
And a Moonbased Cesium clock would run at 9,192,631,766.94 cycles per second. These figures indicate that an Earthbased Cesium clock should run 3.06 cycles per second faster than an identical Moonbased Cesium clock should run. In any hour, that would mean the two identical Cesium clocks would tick
So, if MY calculations turn out to be correct, then we on Earth age around 0.011 second faster per year than if we had lived on the Moon's surface. The important fact is that time passes faster here on Earth than it does on the surface of the Moon, by a significant and detectable amount.
I am not sure that this tiny difference would ever be useful or important for any experiment on Earth. But see that if the Moon and Earth clocks were exactly synchronized on January first of some year, then after an entire year (of about 31 million seconds), the two clocks should be different by about 0.011 second! In Physics, that is a HUGE difference!
A (young) Physicist in California is researching even smaller effects related to the Moon, which seem to me to be certain to fail for being too small for any instrumentation to ever actually detect. But he rather arrogantly simply blew MY Research off as absolutely irrelevant, and he even told me to stop bothering him (after a total of TWO brief communications)! The majority of Physicists DO tend to be incredibly arrogant when around nonPhysicists, but I was amazed to be treated as being totally ignorant. I have no doubt that he is absolutely wrong regarding MY Research, especially since he made a clear point of NOT even more than scanning my information. He also made some statements which show his understanding of the accuracy and consistency of atomic clocks is sadly lacking! I can only hope that he takes more care in the Research which HE is being paid to do! He DID claim to totally accept the Equivalence Principle, but it seemed clear that he had no idea of its implications and consequences! In a rather clear act of total disrespect for me as a Physicist, he even chose to "teach me" the difference between Special Relativity and General Relativity. I suppose I was lucky that he chose to explain it in words for a Fourth Grade child, where I had a chance of understanding his explanation!. I found that rather sad regarding how superficial he seemed to be. And how selfcentered he clearly behaved. MOST Physicists recognize that people like me who received a Degree in Physics from the University of Chicago, might actually even KNOW most of the letters of the alphabet!
Such a situation might change a lot of attitudes regarding what is happening in such bizarre environments. If we now believe that material is orbiting at virtually the speed of light, but if time was actually passing there at 45 times as fast as we realize, then the ACTUAL velocity there may only be 1/45th of what we think it is! In other words, we might MOT need to dream up bizarre ideas to explain relativistic rotational speeds, IF that is not even close to actually being the case!
Additionally, for Pulsars and Quasars and other objects which seem to us to be generating impossible amounts of radiation, this might provide an interesting new insight! If light from 16 actual seconds of radiation, all arrives here during one second, we would see it to be 16 times as BRIGHT as it actually is! Again, some of the bizarre ideas which have been presented to try to describe such observations might NOT actually be necessary at all!
Additionally, we believe that some such objects are rotating at astounding rates. If time is passing there at 16 times or 1000 times of what we experience and believe, then the ACTUAL rotation rate might only be 1/16th or 1/1000th of what we now think it is, and in many cases, that might put the object back into being less exotic than has been assumed.
There are other characteristics that we see in extremely distant objects which might be explained more logically than previous explanations have ever provided.
So such a experiment (on the Moon and on the Earth) is needed to demonstrate that GR has Timerate speeding rather than Time Dilation, and that time passes MORE QUICKLY here on Earth than it does in deep space. The experiment would also show if my calculations are accurate or not. (No one else has ever even tried to GUESS at how fast their (alleged) time dilation occurred during acceleration! It is NOT Time Dilation at all and is actually Time Speeding during acceleration and deceleration. I even derived an equation there to give that Time Speeding factor for any situation!)
There is even the possibility that an aspect in the equations might cause even GREATER effects on the Moon and the Earth than calculated above. All this certainly makes experimentally confirming General Relativity to be very important!
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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago