General Relativity - A Moon Experiment to Confirm It

Finally Actually Confirming General Relativity with a Simple Experiment

Time is passing now, here on Earth, at a DIFFERENT rate than it is passing on the surface of the Moon! Not a lot, but certainly by several parts in a billion. That is about 1/95 of a second every year.

The assumption of absoluteness in the rate of passage of time is not actually true!

This is a direct and obvious result of Einstein's General Relativity, where a gravitational field, such as we have on Earth, causes an 'acceleration due to gravity' which has an equivalence to a physical acceleration in deep space, such as due to a rocket engine. The presence of the gravitational field causes a very tiny 'warping' of the time dimension of space-time, per Einstein. The fact that the Earth has a greater acceleration due to gravity on our surface than the Moon has, causes this 'warping' to be slightly different. This means that time physically passes at slightly different rates on the surface of the Earth and the surface of the Moon.

Time in a free-falling elevator cage is also passing at a slightly different rate than we are normally used to! (but by an even smaller differential than mentioned above.)

By around 1926, the Time Dilation consequence of Special Relativity was experimentally well demonstrated. When very high-energy cosmic rays from outer space impact atomic nuclei high in the Earth's atmosphere, some Mu mesons are often created due to such collisions. It is well-known that mu mesons decay very rapidly (average lifetime of around 0.000 001 52 second) and that even at the speed of light, they MUST decay within about 0.28 mile or so of where they were created. However, research labs on the surface of the Earth, many miles below, easily detect those mu-mesons. The ONLY possible explanation for this is due to the Time Dilation effect of Special Relativity. For the mu mesons, their enormous (constant) velocity causes (Time Dilation) time to appear (TO US) to pass much more SLOWLY than it does for us. And so those mu-mesons actually have plenty of time to travel the distance of many miles to the labs. To the mu-mesons, our atmosphere looks like it is less than 0.28 mile thick, and so it is totally logical to be able to get to the surface, without disobeying the speed of light being the fastest possible. There have been countless other experimental confirmations of the Time Dilation effects of Special Relativity.

No experiment to STRICTLY confirm the effects of General Relativity has ever been done. (There are IMPLIED results of some experiments regarding the Sun that are sometimes cited, but they all involve many assumptions which may or may not be valid.)

Einstein had noted that a gravitational field of any star or planet causes a (local) acceleration due to gravity which appears to be identical to a constant acceleration of a rocket in deep space. This was the basis for what he called General Relativity. Einstein presented thought-experiments where a person was in a rocket that was resting on a launching pad on Earth, experiencing the sensation of the gravitational field effect of an acceleration of 32 feet per second per second, while also describing another person was in an identical rocket in deep space which had its rocket engine accelerating the rocket with a constant 32 feet per second per second actual acceleration. Einstein noted that these two people would be in identical environments, where any experiment done by one would have identical results if done by the other. He then built General Relativity on that premise.

Further study convinced Einstein that the accelerations of General Relativity had consequences regarding changes in the apparent X, Y, Z coordinate dimension measurements, as well as similar changes regarding the rate of the passage of time. The set of Equations that Einstein came up with for General Relativity (nearly 100 years ago) were so immensely complicated that even today, they have never been fully solved. Therefore, no one yet knows the precise consequences of General Relativity. Around 1960, shortly after Einstein died, some Physicists made several assumptions which enabled mathematical solutions to be found, but the validity of those assumptions has always been argued. The specific point here is that all Physicists are confident that General Relativity causes SOME effects regarding the rate of the passage of time, but no reliable information has yet been found to prove it. Sadly, lacking any actual ability to achieve that mathematical solution, virtually all Physicists have simply adopted another assumption, that the Time Dilation effect of Special Relativity must also apply during General Relativity.

The logic provided in the linked presentation just below indicates that that assumption must be wrong, and that the reality must be exactly the opposite effect, that there must be a Time Compression effect which occurs during General Relativity. This proposed Time Compression effect seems to resolve many problemmatical details in modern Physics, and makes Physics far more logic-based than it has been in recent decades, where much of Physics seems to have become speculation-based.

Please see Twins Paradox of Relativity Is Absolutely Wrong which includes the Physics and logical proof that General Relativity causes an OPPOSITE effect from Special Relativity. Where we all know that Time Dilation occurs during Special Relativity (that is, without any acceleration), we also prove there that an opposite effect, which we call Time Compression, occurs during General Relativity (that is, during times of acceleration).

Einstein's thought-experiments shows that whichever of these two effects actually occurs during General Relativity, either Time Dilation or Time Compression, the same effect must be true for situations in gravitational fields, such as for us on the surface of the Earth, or for the environment on the surface of our nearby Moon.

I believe that a very simple and inexpensive experiment can be done, which would quickly and absolutely show the actual truth of the situation.

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This presentation was first placed on the Internet in January 2009.

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Einstein first presented Relativity, but he recognized that there are two very different situations which must be considered, which he called Special Relativity and General Relativity.

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 longer distance before decaying. From the mu-meson's point-of-view, 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/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 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 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 (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 un-manned 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 earth-based atomic clocks is 9,192,631,770 cycles per second.

In the slightly weaker gravitational field of the Moon, I believe that the Moon-based 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 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 in a gravitational field by a factor which is generally called the Equivalence Factor and is given as
1 + (a * d)/2 / c2.

We know that the gravitational field on the surface of the Moon (a) is around 1.62519 meter / sec2. We know that the RADIUS of the Moon (d) is around 1.738 * 106 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 time-speeding 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 / sec2. 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 time-speeding factor on the surface of the Earth as compared to open deep space.

Accepting that Earth-borne 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 Moon-based Cesium clock would run at 9,192,631,766.94 cycles per second. These figures indicate that an Earth-based Cesium clock should run 3.06 cycles per second faster than an identical Moon-based Cesium clock should run. In any hour, that would mean the two identical Cesium clocks would tick


This implies that we on Earth age faster than we would 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 0.011 second faster on Earth per year than in deep space.

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.


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 0.011 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 non-Physicists, 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 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!


This Time Speeding effect certainly might be very significant near white dwarf stars or other extremely dense objects. Say that the gravitation there was 150,000,000 times what it is here (if that is possible), and that the object was 1000 kilometers in radius. My calculations indicate that time would pass there at around 2% faster than the rate that we measure it passing. Say that the gravitation there was 150,000,000,000 times what it is here (if that is possible), and that the object was also 1000 kilometers in radius. My calculations indicate that time would pass there at 16 times the rate that we measure it passing.

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.


Most important of all, the fact that no one has yet been able to fully solve the full set of ten Tensor equations of General Relativity, means that no one has ever really known for sure about any effects on the rate of the passage of time. It was traditional to ASSUME that the same Time Dilation MUST occur during General Relativity (acceleration) as it certainly does during Special Relativity (constant velocity, no acceleration). No one seems to have ever questioned the validity of those assumptions and that conclusion! As a Physicist, I feel it necessary to question EVERYTHING! My presentation regarding the Twins Paradox proves that that very popular idea is not remotely true and is not even possible. (Twins Paradox of Relativity Is Absolutely Wrong ). That presentation includes the logic and the conclusion there that GR must have Time Compression rather than Time Dilation, exactly the OPPOSITE effect of what nearly every Physicist now assumes to be the case!

So such a experiment (on the Moon and on the Earth) is needed to demonstrate that GR has Time-rate 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!


The scientific community needs to know this simple bit of knowledge, of such simple and inexpensive experiments!


This presentation was first placed on the Internet in January 2009.


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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago