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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 mu-mesons or also called muons. We know in a laboratory how long a mu-meson exists before it then again disintegrates into yet other particles. All scientists knew that even at the speed of light, a mu-meson 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 mu-mesons! That should have been impossible! A mu-meson 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 mu-meson could possibly get down to Earth-based labs to be detected. Time dilation was the ONLY possible explanation! From OUR point-of-view, the mu-meson's rate of time passage was far slower than ours, where it was able to make that distance before decaying. From the mu-meson's point-of-view, the thickness of the Earth's atmosphere was less than half a 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 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/sec2 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 ever-running rocket engines at exactly 32 ft/sec2. 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 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 time-effect 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 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 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 Compression.
Given these two preambles above, each of three extremely obvious experiments seem to be needed to be done! The first is the more convincing, and accurate, I suspect!
Specifically, the precise known frequency of the Cesium atoms on earth-based atomic clocks is 9,192,631,770 cycles per second.
The gravitational field of the Moon is about 1/6 that of Earth. Instead of the 32 ft/sec2 or 9.8 m/sec2 that we experience on Earth, on the surface of the Moon, it is instead about 5 ft/sec2 or 1.6 m/sec2.
In my efforts at solving Einstein's General Relativity equations, I find results which suggest that the rate of time passage on the Moon will be MEASURABLY different than here on Earth. On the order of about 1/48 of a second slower per year.
Actually, a long-held 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 by a factor which is generally given as
1 + (a * d) / c2.
We know that the gravitational field on the surface of the Moon (a) is around 1.6 meter / sec2. We know that the DISTANCE from the Earth observer to the surface of the Moon (d) is around 4 * 108 meters. And we know that the speed of light is about 3 * 108 meters/sec. If we plug those numbers into the commonly accepted Equivalency Principle factor above, we can see that the factor is therefore 1 + 7.1 * 10-9, or 1.000 000 007 1
I personally have grave reservations regarding the claim of (d) being the DISTANCE to an observed object. There is absolutely no logical reason why that should be the case. Instead, my calculations indicate that it is actually the (gravitational-related) RADIUS distance of the object creating the gravitational field, in this case, the Moon, but we will continue with the calculations based on the Equivalence Principle here. Over a period of one calendar year, that would imply that time passage on the surface of the Moon should have GAINED around 0.224 second during that year. This is not a large interval of time, but to Physicists, it is huge!
We must now also determine the perceived situation ON the Moon regarding how fast time appears to be passing on Earth! We know that the gravitational field on the surface of the Earth (a) is around 9.8 meter / sec2. We know that the DISTANCE from the Moon observer to the surface of the Earth (d) is around 4 * 108 meters. And we know that the speed of light is about 3 * 108 meters/sec. If we plug those numbers into the commonly accepted Equivalency Principle factor above, we can see that the factor is therefore 1 + 4.36 * 10-8, or 1.000 000 043 6
This implies that IF the assumptions made in the Equivalency Principle were valid, then the precise frequency of the Cesium atoms on a Moon-based atomic clocks should be 9,192,631,365 cycles per second. This is about 405 counts DIFFERENT each second!
Over a period of one calendar year, that would imply that time passage on the surface of the Earth should have GAINED around 1.374 second during that year. This is about six times the difference, as seen from the Moon as the difference as seen from the Earth. The two observers would conclude that they experienced different rates of time during a calendar year of the difference of these two amounts, that is 1.150 second per year. THIS would be an EASILY DETECTED AND MEASURED difference in the rate of time passage!
Specifically, considering the Moon first: We know that the gravitational field on the surface of the Moon (a) is around 1.6 meter / sec2. We know that the RADIUS of the Moon (d) is around 1.74 * 106 meters. And we know that the speed of light is about 3 * 108 meters/sec. If we plug those numbers into the formula above for the Equivalency Principle, we can see that the factor is therefore 1 + 3.1 * 10-11, or 1.000 000 000 031
MY result is substantially smaller than the traditional version of the Equivalence Principle seems to give. On the surface of the Moon, my calculations suggest that time must be passing only a tiny bit faster than in deep space, only around 0.001 second faster per year.
Now, we consider the Earth: We know that the gravitational field on the surface of the Earth (a) is around 9.8 meter / sec2. We know that the RADIUS of the Earth (d) is around 6.38 * 106 meters. And we know that the speed of light is about 3 * 108 meters/sec. If we plug those numbers into the formula above for the Equivalency Principle, we can see that the factor is therefore 1 + 69.4 * 10-11, or 1.000 000 000 696
This implies that by MY calculations, then the precise frequency of the Cesium atoms on a Moon-based atomic clocks should be 9,192,631,764 cycles per second. This is about 6 counts DIFFERENT each second!
This implies that we on Earth age faster than on the Moon, or as compared to deep space, by about 23 times as much difference. It still only results in a small effect, being around 0.022 second faster per year than in deep space.
If we do these calculations for someone on the surface of the Sun, a year would pass about 6.7 seconds faster!
So, if MY calculations turn out to be correct, then we on Earth age around 0.021 second faster than if we had lived on the Moon's surface. My result is substantially smaller than the value calculated from the traditional understanding of the Equivalence Principle (which would be more than one full second per year), but the important fact is that we BOTH AGREE that time passes faster here on Earth than it does on the surface of the Moon, by a significant and detectable amount.
Granted that the differences would not be noticeable or would ever interfere in any experiments. They appear to be extremely minimal for any acceleration that we humans could possibly cause, or due to any gravitational field which we might be able to survive!
But the simple FACT that time, as measured here on Earth, is likely to be DIFFERENT than the passage of time on other planets or moons or in outer space, suggests that a basic assumption in Astrophysics might be incorrect.
Several years ago, I had done some earlier calculations, which were based more directly on Einstein's set of ten Tensor Calculus equations. Those results are slightly different than the above results due to either approach to the Equivalency Principle factor. THOSE results of mine suggest that on the Earth's surface, time should pass very slightly FASTER than it does in open space, but by a Time Compression factor of approximately 1.000 000 003 5
On the Moon, that Time Compression factor should be 1.000 000 001 1
This implies that IF my analysis of Einstein's set of ten equations is valid, then the precise frequency of the Cesium atoms on a Moon-based atomic clocks should be 9,192,631,748 cycles per second. This is about 22 counts DIFFERENT each second!
Those calculations which were based on Einstein's equations resulted in an annual difference of around 0.076 second, which is between the other two calculations shown above. They were very complex and difficult calculations, not like the simple formula as given by the Equivalence Principle.
So, I believe that clocks on the Moon and Earth should show an annual difference of 1.150 second, or 0.076 second, or 0.021 second, in all cases where we age faster here on Earth due to our stronger gravity.
Actually whether either set of my calculations are correct or whether the Equivalency Principle factor is correct, ALL indicate that we should definitely see a measurably different rate of time passage on the Moon as compared to what we experience on Earth. If the Equivalency Principle formula is true, then the experimental results would be several times easier to detect, as both sets of my numbers give slightly smaller values for the effect.
The two IDENTICAL sets of atomic clocks therefore would run at DIFFERENT speeds (but only really small differences!) Of course, the timing signal from the Moon would have to be corrected for the exact transit time due to the varying distance the Moon was at that instant, but that is easy to do!
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 0.021 second! In Physics, that is a HUGE difference!
Again, if the Equivalency Principle formula happens to be accurate, then the difference after that year would be around 1.150 second, slightly more of a difference. In the one case, I am now more than a minute older than I would have been had I lived my entire life on the surface of the Moon. In the other case, (by MY calculations), I am only a little more than one second older than if I had been born on the Moon!
A (young) Physicist in California is researching even smaller effects related to the Moon, which are likely to be too small for any instrumentation to ever actually detect, but he simply blew MY Research off as absolutely irrelevant, and he even told me to stop bothering him (after a total of TWO brief communications)! 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 attempting to do! He DID claim to totally accept the Equivalence Principle, but it seemed clear that he had no idea if 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 self-centered 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!
The two clocks are exactly synchronized, with the elevator cage at the top of the building. Then the support for the elevator cage is cut so that that atomic clock plunges down the elevator shaft. It would ACCELERATE at the standard 32 ft/sec/sec. If that elevator shaft were 1600 feet tall, the downwardly accelerating atomic clock would fall for just over 7 seconds. It would only get up to about 150 mph during those seven seconds so air friction and terminal velocity would not significantly apply, and correction factors could be applied.
Inside that falling elevator cage, the NET acceleration would be zero, just as if it were in deep space far from Earth. And so the General Relativity effect on the passage of time would occur, which is necessarily different for the two atomic clocks. They would necessarily run at different rates during that seven second interval.
Unfortunately, the different rate of time passage is very small. By my calculations based on Einstein's equations, the difference should only be about one part in more than a billion. If that is correct, then the two clocks should only get out of synchronization by around one two-hundred-millionth of a second (5 * 10-9 second), in that available 7 seconds of the experiment. That IS a difference which might be large enough to experimentally detect and to measure.
It would not give the accuracy of a year of monitoring the Moon-based atomic clocks, but at least it would be a fairly simple and inexpensive experiment to prove the Time Compression consequence of General Relativity.
If this same experiment could be performed in a falling spacecraft, the time interval might be extended. For example, if the orbiting International Space Station was to (somehow) "drop" an atomic clock, it would plunge straight down through the atmosphere for quite a few seconds before it would burn up in the atmosphere. However, to DO that might not be easy. The atomic clock would have to be launched rearward to cancel the orbital velocity of the Space Station. Maybe an unmanned small rocket could be launched straight upward to a few hundred miles, where it could then fall straight back downward those few hundred miles (before the atomic clock would again burn up in the atmosphere).
This is a REALLY small difference in gravitational field strength, even though you would find that a 200 pound man at the Equator was seen to weight 201 pounds at the North Pole!
Regarding this General Relativity effect, the differences in the two clocks would be VERY tiny indeed! By the Equivalence Principle formula, the clocks would only have a single count difference in 18 seconds! Both of my calculations indicate even smaller differences, either one count difference in either six minutes or twenty minutes.
Cesium clocks ARE accurate enough and consistent enough to show even such minimal differences. But Statistical Analysis would likely be necessary due to the possibility of external effects.
Whether communication links between two clocks that far apart could ever be sufficient to detect such tiny fluctuations where the clocks gain and lose such a tiny amount of time to each other each day, is uncertain. But if such a communication link could be arranged, that should provide a second or third confirmation of the time effects of General Relativity.
This effect is even far smaller than the Pole / Equator results would be, but it WOULD be a repeating effect every 13 hours, which might aid in the Statistical Analysis of the data.
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 know, 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 either of these experiments (on the Moon or on the Earth) is needed to demonstrate that GR has Time Compression rather than Time Dilation, that time passes MORE QUICKLY here on Earth than it does in deep space. The experiment(s) would also show if my calculations are accurate or not, or if the traditional Equivalence Principle assumptions are valid or not! (No one else has ever even tried to GUESS at how fast their time dilation occurred during acceleration! It is NOT Time Dilation at all and is actually Time Compression during acceleration and deceleration. I even derived an equation there to give that Time Compression ratio 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!
C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago