General Relativity Time Dilation Logical Error

General Relativity Time Dilation Logical Error

A Major Error in Modern Physics

Neglect of General Relativity

NASA intentionally neglected General Relativity when they decided that they were going to try to prove Special Relativity with their Hafele-Keating experiment in October 1971. By ignoring the effect of General Relativity, NASA guaranteed that that experiment would be a dismal failure, and it was.

Around 1880, math was developed by Lorentz and FitzGerald which later became the math basis for the Special Relativity effect of Time Dilation. Unfortunately, little in our Universe is known really precisely. The size (radius) (r) of any planet or satellite is generally not known very well, so our knowledge of the circumference (2 π*r) is usually not precise, although we often know the rotation rate (t) of many objects quite accurately. Therefore, our knowledge of the rotational velocity (v) is often not known very precisely, with a single exception. That Exception is the Earth. We know the Equatorial Radius of the Earth extremely accurately, to around one meter precision, of the 6,378.137 ±0.001 kilometer radius (r) (or one part in around 6,000,000). We also know the length of our Sidereal Day (t) to impressively great precision, 86,164.0905 seconds, better than one one-ten-thousandth of a second accuracy. Therefore, we know the velocity of the rotation of the Earth’s equator (v) (circumference divided by Sidereal day length) at precisely 1,674.366 102 km/hr, which is 0.465101695 km/sec, far more accurately than any other measurement in outer space. We see that the Lorentz factor () or the Time Dilation factor of Special Relativity only depends on that velocity (v) and the speed of light (c), 299,792.458 km/sec, which was defined as exactly this number. Therefore, we can use the Lorentz formula to calculate the Apparent Time Dilation Factor (of Special Relativity) for someone standing at the surface of the Equator of the Earth to impressive 18-digit precision. It dawned on me that the Equator of the Earth is the only location in the Universe where we can calculate that Time Dilation Factor so accurately that gives us  = 0.999999999998796560 .

I was impressed by the amazing precision which we can be assured of for the Apparent Time Dilation factor, for that single location of the Equator of the Earth. At first, I did not see any reason for wanting to know this number so precisely, except for being a Physicist who obsesses on such things. All I saw was that the Time Dilation effect of Special Relativity is amazingly tiny, only a difference of about one part in a trillion in the 31 million seconds of a year, or about 1/30,000 second per year difference for a guy standing at the Equator of the Earth.

When calculations are done to such extreme precision, it becomes critically important to make such observations from a location that Physicists call an "Inertial Rest Frame of Reference". This means that the point of observation must be devoid of all velocity and acceleration. This pretty much rules out observing from almost anywhere on Earth, because we are both whizzing around with the spinning Earth's surface and also accelerating straight downward with a Centripetal Acceleration to follow our downward curved circular path around the Earth. Consequently, there are only two acceptable locations where we can make these really accurate observations of our Equatorial man, which are the North Pole and the South Pole. From any other location on Earth, which is constantly accelerating downward, that would affect the precision that we are pursuing. Actually, that is why NASA had failed at the Hafele-Keating experiment with the jet airliners circling the Earth. However, our North Pole observer IS at an Inertial Rest Frame of Reference, so he would accurately see the Apparent Time Dilation effect of Special Relativity of our Equator man which we have calculated,  = 0.999999999998796560 .

I then decided to look into General Relativity. Einstein had described a very important “thought experiment” which is important. Einstein described two identical rockets, each with a scientist inside. One of the rockets is sitting stationary on the surface of the Earth (therefore dealing with the 9.8 m/s2 gravitational field of the Earth with no acceleration). The other rocket is in deep space far from Earth and not subject to any gravitational field. This second rocket has a motor which is constantly running to mechanically accelerate the rocket at exactly 9.8 m/s2. Einstein was showing that the “mechanical acceleration” has the exact same effect as the “gravitational field of the Earth”. Einstein called this “Equivalency”. He noted that if the rockets did not have any windows, then the two occupants could never do any experiments to know which of the two rockets they were in, again referring to the exact Equivalence of a gravitational field and of a mechanically generated acceleration.

A formula is used in Theoretical Physics regarding this Equivalence of a gravitational field and a mechanical acceleration in General Relativity, and I decided to try to use it to calculate the possible Apparent time-rate effect of General Relativity. That Equivalency factor is . This factor only relies on the accurate radius of the Earth (d), the well-known radial centripetal acceleration (downward toward the center of the Earth) (a), and the speed of light (c). We know each of these three values extremely accurately for the Earth, and especially for the Equator of the Earth. The centripetal acceleration seems to be an unfamiliar concept to some people, but it is a standard concept for anything which travels in a circular path (such as us as we go around the Earth every day). That “central acceleration” is simply v2/r, which explained the sideways leaning that many High School students learned and which got created when they did donuts in their cars in a parking lot. You can look up the accurate value of the downward Centripetal Acceleration at the Equator of the Earth in the Handbook of Chemistry and Physics.

This Equivalency formula regarding the General Relativity time-rate effect on the man at the Equator gives us an Apparent General Relativistic time-rate Equivalency Factor of 1.000000000001203440 .

At first, I did not realize the importance of the relationship between those two amazingly precise numbers. I knew that they both referred to a Apparent tiny difference in time-rate. One is due to effects of Special Relativity and the other is due to effects of General Relativity. I did notice that they each referred to a Apparent time-rate differences of about one part in a trillion. I was first mystified that they seemed to be in opposite directions! One seemed to be an Apparent Time Dilation (SR) and the other seemed to be an opposite of some sort of “Apparent time speeding” (GR).

I eventually realized that we are all forever circling the Earth in our daily path, which means that, no matter where we are on Earth, we are forever subject to the Apparent SR effect of our velocity, and we are also forever subject to the Apparent GR effect of our downward (central) acceleration. So I realized that I could not avoid having to consider both of the Relativistic Apparent time-rate effects, so I had to multiply the two Apparent time-rate numbers mentioned above, to know the total Apparent Relativistic time-rate effect on that man standing at the Equator.

I was rather shocked to see the product of those two time-rate factors to be 1.000000000000000000 000 000 . In other words, the two Apparent Relativistic time-rate effects amazingly exactly cancel each other out. We have long known that Special Relativity would cause the appearance of a tiny difference of time-rate, which we call Apparent Time Dilation, but we can never see it because it is invariably always exactly canceled out by an exact opposite Apparent time-rate effect of General Relativity.

( ) The Equivalency Factor used above (and shown again here) is commonly used in Theoretical Relativistic Physics but it is actually very, very slightly incorrect. The a * d factors used in the Equivalency factor formula can be exactly replaced by v2, by a standard Newtonian motion formula v2 = a * d. There is still a factor of 1/2 that exists, but when a number is very close to ONE, the square root of that number is then very very close to 1 + 1/2 of that value. This formula is actually slightly more precise, but for our man at the Equator of the Earth, the improvement in accuracy is only in about the twentieth digit, and everyone has ignored it. Please note that this (precise) equation for the Equivalency Factor looks exactly like the Lorentz factor used above in the Special Relativity calculation except that it has a + sign where the Lorentz factor formula has a - sign.

If you have actually done both of these Relativistic time-rate calculations, you may have seen that the product of the two calculations is actually different from 1.000000000000000 in about the 20th digit. This comment actually clears up why the product of the two numbers given above is only precise to about 20 digits, because the (correct) square root is used in one term and the 1/2 approximation is used in the other. If we use the correct form of the Equivalency Formula, the Net Relativistic Effect is always exactly 1.00000...

We have another motion that we might think we know as precisely, but we do not. How many thousands of years have we known the yearly path of the Sun across our skies? That is due to our Earth's annual orbit around the Sun. The same calculations as above can be used to calculate the SR and GR Apparent time-rate effects of that motion of ours. We certainly know the length of our sidereal year very accurately, but surprisingly, we do not know the radius of our orbit around the Sun very accurately at all. Yes, it is about 1.495 * 108 kilometers radius. Disappointingly, that radius of the Earth's orbit has an enormous error factor, around ± 100,000 kilometers. Because of this poor accuracy, we similarly do not know the precise velocity of the Earth in orbiting the Sun (to only four digits accuracy). This is actually because the only evidence we have for calculating those two values is from Newton's gravitational equation. There is a Gravitational Constant in that equation that we know surprisingly poorly. While all of the other “constants” of science are known to about ten digit precision or better, the Gravitational Constant is only known to about three digit precision (6.674 * 10-11 m3/sec2/kg), as we have not been capable of doing gravitational experiments very accurately, although scientists have tried for 300 years since Newton derived that equation. The result is disappointing. We only know the mass of the Earth (or anything else) to about three-digit precision (5.97 * 1021 metric tonnes). We only know our velocity in traveling around the Sun as about 29.85 km/second. We only know the radius of the Earth's orbit around the Sun as being about 1.495 * 108 kilometers.

As a result of this, where we used the Lorentz Equation and Equivalence Principle formula above for the Equator man circling the Earth every day, the numbers which apply for our orbiting the Sun are far less precise. The Apparent time-rate effect given by the Lorentz equation is 0.999999995 . And the Apparent time-rate effect given by the Equivalence formula is 1.00000000495 . Both of these effects are much greater than the time-rate effects of the Earth spinning as we travel around the Sun much faster than we spin on our axis. They each would result in an Apparent effect of about 1/6 of a second per year. However, like for our spinning on our axis every day, both the SR and GR opposing effects constantly and continuously affect us, so we have to multiply the two values just given, which again must result in a net Apparent Relativistic time-rate effect of 1.0000000000000000, as they also cancel each other out for us.

We do not have as accurate data as for the radius of the Earth, but the same results apply, that, for us on Earth, the two Relativistic time-rate effects exactly cancel each other out for us.

We certainly know that incredibly energetic cosmic rays hit some molecules near the top of our atmosphere which shatters some atoms, forming Muons up there. We know in laboratories how long Muons exist before decaying. It is around a half-millionth of a second, (0.000 002 197 second), decaying into electrons and yet other particles. All scientists knew that even at the speed of light, an average Muon could not quite travel half a mile (0.3999 mile or 2110 feet) before disappearing as it decayed into other particles.

The first experimental proof of Time Dilation was that laboratories on the surface of the Earth, many miles below, were detecting those Muons! In 1941, the Rossi-Hall experiment first demonstrated the situation, followed by many more. That should have been impossible!

A Muon, which was created maybe 50 miles high in the atmosphere, was known to not be able to even go half a mile before decaying. So there was no chance whatever that any Muon could possibly get down to Earth-based labs to be detected. Time Dilation was the only possible explanation! Here is the scientific explanation of that experiment. From our human point-of-view, the Muon’s velocity was sooo fast (0.9954c) that its Apparent Time Dilation rate of time passage was far slower than ours, around 1/100 as fast, where it was able to make that far longer distance trip before decaying. From the Muon’s point-of-view, the scientific explanation was different, but again due to the extremely fast differential velocity, the Apparent 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 seems to pass at normal rate for the Muon!)

we know that the 50-mile-thick atmosphere did not shrink to half a mile thick, but due to the Apparent Time Dilation as seen by the Muon, it Appears to.

Time Dilation is a consequence of great constant velocity.

An incredible important “detail” has always been absolutely overlooked by scientists! The science should be corrected now. Slightly before that trip by the Muon, a cosmic ray accelerated the relatively stationary Muon particle in our upper atmosphere up to very near the speed of light (measured to be 0.995c to 0.9954c). That means that, for an extremely brief moment, the Muon experienced fantastic General Relativity, which has an opposing Apparent time-rate effect on the Muon. In fact, when the Muon crashed to Earth in the laboratory, it again has to experience fantastic acceleration (actually, extreme deceleration) which causes bremsstrahlung radiation in stopping. Yes, in our reference frame, we see the Muon appear to live a hundred times longer during the constant-velocity trip down to Earth, but we do not have any equipment which is capable of detecting the Apparent time-rate effect of the intense acceleration, that is, due to General Relativity. No scientist in a hundred years has recognized this fact! Every one of those Muons experienced an entire trip, which included General Relativity, then Special Relativity, and then General Relativity.

The total time involved for the entire Muon trip, acceleration due to the Cosmic Ray creating the Muon, then the trip down through the atmosphere to the Earth-based laboratory and then sudden deceleration and the bremsstrahlung radiation, is exactly the same total time, whether seen by the Muon or by an Earth scientist. As we showed in our calculations for the Earth Equator man, the acceleration and deceleration portions of the trip cause opposite Apparent time-rate effects from the much more easily observed Apparent (time dilation) time-rate changes in the Muon trip down through our atmosphere.

Only a single location in the Universe exists where we have truly precise data where we can calculate Einstein’s Special Relativity and its Apparent Time Dilation factor to eighteen-digit accuracy. It is for a man standing at the Equator of the Earth, who is rapidly rotating with our planet.

For true precision, we need to observe this from an Inertial Rest Frame of Reference in order to be able to use Euclidean Geometry (also called Plane Geometry). Our observer cannot be accelerating, so he or she needs to be standing at the North Pole. Due to the Apparent Time Dilation Effect of Special Relativity, this observer would see such a rapidly moving Equator man appear to have time pass slightly slower. Hendrik Lorentz and George FitzGerald discovered the well-known formula which is the Time Dilation time-rate factor ß (which is ) that gives us 0.999999999998796560 . (That is less than 1.000 so it is an observed apparent time-slowing effect) as the Time Dilation time-rate factor which you(at the North Pole) see occurringfor the personstanding at the Equatordue to Special Relativity due to the rotational speed. (It is not “experienced” by the guy at the Equator but it is only as seen by you, a motionless observer). We know this so precisely because we accurately know the size of the Earth and its rotational speed (the sidereal length of day).

For that same man at the Equator, we can also calculate the precise apparent time-rate perception effect of Einstein’s General Relativity, also to better than eighteen-digit precision. This results in the Apparent Relativistic Equivalency Factor() being1.000000000001203440. That is then the Apparent General Relativity time-rate factor as observed from the North Pole on the personstanding at the Equator being 1.000000000001203440 . (That is more than 1.000 so it is an observed time-speeding effect) (this is due to the Equator man’s centripetal radially downward acceleration).