I was impressed by the amazing precision which we can be assured of,
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 effect of Time Dilation 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.

I then decided to look into **General Relativity**. Einstein described a
"thought experiment" which is important. Einstein described
two identical rockets, one of which is sitting stationary on the surface
of the Earth (therefore dealing with the 9.8 m/s^{2} gravitational
field of the Earth, and no acceleration),
and the other of which is in deep space far from Earth and not subject to
any gravitational field. This rocket has a motor which is constantly
running to mechanically accelerate the rocket at exactly 9.8 m/s^{2}.
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 know which of
the two rockets they were in, again referring to the **Equivalence of a
gravitational field and of a mechanically generated acceleration**.

A well-known formula is used in Physics regarding this **Equivalence** of a gravitation field
and acceleration in **General Relativity**, and I decided to try to use
it to calculate the possible time-rate effect of General Relativity.
That Equivalency formula is
This formula also 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**), each of which we know really
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. That "central acceleration" is simply
v^{2}/r, which many High School students learned and which got
used when they did donuts in their cars in a parking lot.

This formula regarding the man at the Equator circling the Earth every day
gives us a Relativistic Equivalency Factor of
**1.000 000 000 001 203 440.**

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 difference in time-rate. I DID notice that they each
referred to a time-rate difference of about one part in a trillion.
I was first mystified that they seemed to be in opposite directions!
One seemed to be a Time Dilation (SR) and the other seemed to be an
**opposite** of some sort of "time speeding" (GR).

I eventually realized that we are **forever** circling the Earth in
our daily path, which means that we are forever subject to the SR
effect of our velocity, and we are also forever subject to the GR
effect of our downward (central) acceleration. So **I realized that I
could not avoid having to consider BOTH of the Relativistic time-rate
effects**, so I had to **multiply** the two time-rate numbers mentioned
above, to know the total 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 1.000 000 000 000 000 000 000 000 . In other words, the two
relativistic effects amazingly exactly cancel each other out. Special
Relativity would cause the appearance of a tiny difference of time-rate,
**but we can never see it because it is invariably always exactly canceled
out by an exact opposite time-rate effect of General Relativity**.

The Equivalency Factor used above (and shown here again) is commonly used in Relativistic Physics but it is
very, very slightly incorrect. The a * d factors used in the Equivalency
factor can be exactly replaced by v^{2}, by a standard Newtonian
motion formula v^{2} = 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 close to 1 + 1/2 of that number. 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 a + sign exists where a - sign does
there. This comment actually clears up why the product of
the two given above is only precise to about 20 digits, because the
(correct) square root is used in one and the 1/2 approximation is
used in the other.

We have another motion that we might think we know as precisely, but we do not, that of our Earth's annual orbit around the Sun. The same calculations as above can be used to calculate the SR and GR 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. We also do not know the precise velocity of the Earth in orbiting the Sun very accurately. 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. Where 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, as we have not been capable of doing gravitational experiments very acccurately, 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 * 10

As a result of this, using the Lorentz Equation and Equivalence Principle formula used above for the man circling the Earth every day, the numbers which apply for our orbiting the Sun are far less precise. The time-rate effect given by the Lorentz equation is 0.999 999 995 . And the time-rate effect given by the Equivalence formula is 1.000 000 004 95. Both of these effects are much greater than the 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 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 effects constantly and continuously affect us, so we have to multiply the two values just given, which again results in a NET Relativistic time-rate effect of 1.000 000 000 000 000 0, as they also camcel 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 15 second), decaying into 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 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!** 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, 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!) **Time Dilation is a consequence of great CONSTANT
VELOCITY**.

**An incredible important "detail" has always been absolutely
overlooked by scientists!** 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 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
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 both General
Relativity and Special Relativity.

**Only a single location in the Universe exists where we have truly
precise data where we can calculate Einstein's Special Relativity and its
Time Dilation factor to eighteen-digit accuracy. It is for a man
standing at the Equator of the Earth, who is 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, such as when standing at the North Pole. Due to the

**For that same man at the Equator, we can also calculate the precise
time-rate effect of Einstein's General Relativity, also to better than
eighteen-digit precision.** This results in
the **Relativistic Equivalency Factor (
)**
being 1.000 000 000 001 203 440.
That is then the **General Relativity** time-rate factor as observed
from the North Pole on the person standing at
the Equator being **1.000 000 000 001 203 440**.
(That is more than 1.000 so it is an observed time-speeding effect) (due to
the Equator man's centripetal radially downward **acceleration**).

The Special and General Relativistic time-rate factors always both
constantly apply and so we must multiply these two time-rate factors to get
the net time-rate effect of Relativity on that Equator man. The result is
**1.000 000 000 000 000
000** (within experimental error). **This is a precise mathematical
proof that the two Relativistic time-rate effects exactly cancel each other
out** (for you at the North Pole viewing the person at the Equator).

**General Relativity has exactly the
opposite time-rate effect from what all Physicists believe to be true**.
**It does not have a "time slowing effect"
of Time Dilation, but instead has a "time speeding effect" which
totally changes everything in many fields of modern Physics.**
A very precise math proof follows. All
"time travel" speculations are certainly impossible. The
popular Twins Paradox story is also impossible. **Many entire fields
of modern Physics are based on this wrong assumption.**
NASA has sadly tried many experiments
which ignored General Relativity which turned out to be total failures,
including the rather famous Hafele-Keating experiment in October 1971. The
famous Kip Thorne believes that speculative "wormholes" exist. The
famous Stephen Hawking spent half an hour in his recent *
"Genius"* TV series in trying to
prove a wrong assumption of his about Cesium clocks on a mountain. Time passes
on the surface of the Moon slightly more slowly than it does here on Earth.
(Due to the different strengths of the gravitational fields of the Earth
and Moon, **a Moon clock would run about one ninetieth of a second slower
per year than an identical clock here on Earth).** The math to prove
this is quite simple, and you can even confirm that this is the truth.
**The following math is indisputable and precise.**

We live our lives on the surface of the Earth, where we constantly
daily rotate at around 1000 mph, **so Einstein's
Special Relativity clearly applies to us**. We also "ride in a daily
curved circle" (around the Earth) in that same process, which means that we
also constantly accelerate (radially downward), so that **Einstein's
General Relativity also applies to us.** (We
call this centripetal acceleration). (The *Handbook of Chemistry and Physics* provides the precise
centripetal acceleration value for the Equator.) **
These effects are both easy to calculate and it turns out that
mathematically their time-rate consequences are exactly opposite each other! **One
(SR) is a Dilation (slowing) of apparent time-rate while the other (GR) is a
Speeding of apparent time-rate. They always exactly cancel each
other's net effects out for us! **There is and
can be no net Relativistic time-rate effect on us!
That is equally true for people in their homes, for
Astronauts who orbit the Earth in the ISS, and even in airliners which circle
the Earth. **The precise math proof of this new perspective follows.

**Please note one very important detail which no one seems to realize.
In Relativity, the person or event being watched does not actually
change in any way. No "time travel" ever occurs to him or is even
possible. No goofy experiences ever occur in his life. He lives a mundane
life. Only the (usually distant) observer sees any appearance where
the rate of time passage seems to have changed.**
(He also observes some other apparent effects, such as apparent change in
inertial mass and in radial distances, also by the same ß factor. None of
these phenomena is actually sensed by the moving person).

We place you to be standing at the North Pole, where
you are neither moving nor accelerating due to the daily spinning of the
Earth. You will be our "stationary, Inertial observer" for the following analysis of the
movements of a man who is standing at the Equator of the Earth.
The factors regarding the time-rate effects of both Special and General
Relativity are extremely minimal for us on the Earth, but they are easy to
calculate. To calculate the **Time Dilation
Effect of Special Relativity**, a person standing at the Equator
"orbits" at precisely 1,674.366 102 km/hr, "orbiting" with
the surface of the Earth every sidereal day.
(Equatorial circumference divided by the length of a sidereal day, both precisely
known measurements of the Earth). This is the same as 0.465 101 695
km/sec (v). We know that the speed of light (c) is 299,792.458 km/sec.
Hendrik Lorentz and George FitzGerald discovered the well-known formula which
is the Time Dilation time-rate factor ß (which is
)

that gives us **0.999 999 999 998 796 560**
(which is less than 1.000 so it is an observed time-slowing effect**
) **as the**
Time Dilation time-rate (slowing) factor** which you (at the North
Pole) observe for that person standing at the Equator due to
**Special Relativity** due to the rotational
speed (not "experienced" by him at the Equator but only as seen
by you, a motionless observer).

For the **time-rate Effect of General
Relativity**, for that person at the Equator of the Earth we have a **
6,378,137 meter Equatorial Earth radius (d) **and his
radially downward centripetal acceleration **(a)** there is **
0.033 915 785** m/sec^{2}. This results in the **
Equivalency Factor **(
)
being **1.000 000 000 001 203 440** . That is then the **General
Relativity time-rate factor ** (as observed from the North Pole) on the
person standing at the Equator being
**1.000 000 000 001 203 440** . (That is more
than 1.000 so it is a time-speeding effect**) **(due
to acceleration) (due to the radially downward centripetal acceleration
of the Equator man).

Since **both** Relativistic effects constantly exist, we must
multiply these two factors to determine the net
Relativistic time effect. That is: SR Time Dilation factor of **
0.999 999 999 998 796 560 **times the GR time-rate
factor of **1.000 000 000 001 203 440**. That results in the net
Relativistic time-rate effect being exactly **1.000 000 000 000 000 000**
(within experimental error). **This is a precise mathematical proof that the
two Relativistic time-rate effects exactly cancel each other out** (for
you viewing the person at the Equator).

A dreadful logical blunder occurred in Physics in the early 1960s and
it was never fixed. **Even NASA believed that
an orbiting satellite or even a conventional airliner circling the Earth, only
experienced the effect of Einstein's Special Relativity and Time Dilation,
and ignored all effects of General Relativity.**
That was and is wrong. Well, misleading, because NASA did not seem to realize
that both Special Relativity and General Relativity always constantly apply at the same
time. **NASA had totally neglected to consider the
effects of General Relativity**. NASA had (wrongly) assumed that we
on Earth are in what we Physicists call an Inertial Rest Frame of Reference
(that is, there is no acceleration acting on us.) **
It turns out easy to mathematically prove that, for any object that is
circling a massive planet like Earth, as in the precise math example above,
both effects exist, and that they exactly cancel each other out! **One
is due to the speed of the motion (SR) and the other is due to the radial acceleration
of the motion (GR), as Einstein had clearly explained.

During the 1960s, NASA included Cesium clocks on a number of earth
satellites, to try to prove that their assumption about Time Dilation applied,
but all those experiments dreadfully failed. NASA even performed a rather
famous (but wrong) experiment in October 1971 to try to prove that (wrong
assumption) that only Time Dilation was acting, by sending sets of four
identical Cesium clocks both ways around the Earth in conventional airliners,
in the **Hafele-Keating experiment**.
That experiment wound up with results which were worthless, well within the
experimental margin of error.

A popular claim is that if identical twin brothers were born on Earth,
and one went to the ISS (International Space Station) for ten years, the
brother who remained on Earth would be able to detect a slightly slower aging
of his brother on the ISS, due to Time Dilation. The calculated effect of
Einstein's Time Dilation would only be a fraction of one second difference in
age, but using identical Cesium (atomic) clocks, that would be easy to detect.
**That claim is wrongly based on the Earth twin
being in an Inertial Rest Frame of Reference that was not accelerating, such
that only Time Dilation would apply. That claim was also wrongly based on the
ISS twin not being in such an Inertial Rest Frame of Reference. **

We on Earth (incorrectly) think we are in such a non-accelerating**
**Inertial Rest Frame of Reference! (Of
course, for thousands of years we also thought we lived on a flat Earth that
was not moving at all!) However, we each revolve around the Earth once every
day, at high speed in a curved circular path, which means we are also each
constantly accelerating (radially downward) in a circle. **
And so NASA and everyone else (incorrectly) assumed that such satellite
and airliner Time Dilation effects would be experimentally detected. **

**Here is the problem!**

The passengers on the ISS ** also** think they are
in a non-accelerating** **Inertial
Rest Frame of Reference, since they also do not sense any acceleration. If we
make a slight adjustment to that story of twins, we can see an obvious
demonstration of the logical blunder they had done (and which everyone still
accepts as correct!) Consider that a family had lived on the ISS and they had
twins, and one of those sons decided to take a rocket ship trip to the surface
of the Earth (for ten years). The "non-traveling" brother who stayed
on the ISS would see that his brother (on Earth) was living more slowly than he
was living, due to Time Dilation, which he could prove by a comparison of
cesium clocks. If we looked at everything from the perspective of the ISS
rather than the Earth, and the ISS twin brother compared his Cesium clock with
one he could watch on Earth, Einstein's Time Dilation would (seem to) require
that he would **also** see that the
Earth clock was running slower than his own Cesium clock was running.

Because they both (incorrectly) believed they were in
non-accelerating Inertial Rest Frames, this must be true, that **both brothers
would measure that the other one was aging more slowly than himself!**

This would be an easy experiment to do, since there are lots of Cesium clocks in Earth laboratories and also several on board the ISS. And it would obviously fail. Only after each of them correctly considered his own acceleration and therefore that General Relativity was acting, would they then resolve the flawed situation.

**When the traveling brother got back home, neither would be younger
or older than the other! **This is true for either version of the story,
whether the family lived on Earth or on the ISS.

**This situation is vaguely similar to
the popular Twins Paradox story, which also happens to be totally wrong due to
neglecting the effects of General Relativity**, but for
slightly different reasons, discussed below.

The logical flaw here is that both clocks and brothers are constantly and continuously accelerating, in the process of the curved paths of circling the center of the Earth.

In an accelerating (non-inertial) Rest Frame of Reference, Einstein
showed that a different set of circumstances must exist, that of **
General Relativity**. Physics even has a
formula called the **Equivalency Principle**,
which can be used to calculate the Time-rate effects of any acceleration (or
'equivalently' the effect of any gravitational field such as due to the Earth).

We know the orbital speed and altitude of the ISS, and we can easily
calculate the strength of the Earth's gravitational field at that orbital
distance. The Time Dilation effect due to the orbital speed of the ISS is a
factor of **0.999 999 999 669**
(calculated below, which is only a difference of less than one part per billion
of time). The time-rate effect due to the orbital acceleration of the ISS is **
1.000 000 000 330** (also calculated below,
which is also a difference of less than one part in a billion of time, but in
the opposite direction!) We must multiply these two numbers to account for the
net Relativistic effects of both speed and acceleration, and the product is
amazingly close to being exactly 1.000 000 000
(actually, 0.999 999 999 998 999 999).

**In other words, for an orbiting ISS satellite, the net effect of the speed and
acceleration is such that there is no Relativistic time change effect!** In
other words, NASA in the 1960s and still, is dead wrong about expecting to see
Time Dilation effects in satellites or airliners, due to a logical failure of
not including the (really obvious) effects of the General Relativity of the
orbital acceleration!

There are even still people today (2016) who aggressively claim that the 1971 experiment should have worked and so they present endless claims about why it didn't. But they do not seem to realize that the experiment failed because it was based on faulty logic, that of ignoring General Relativity.

Up above, we also calculated the Precise Time Dilation Effect and the Equivalency Factor for us who are orbiting on the surface of the Earth as it rotates, and that also shows that the two effects exactly counteract each other and there is no net Relativistic time difference effect due to the Earth spinning.

**This mathematically proves two
interesting new insights! First, that the time effect of acceleration is
opposite that of speed, creating a Time Speeding General Relativity effect
which opposes the known Time Dilation effect of speed and Special Relativity.
Second, for any satellite in a perfectly circular orbit around a symmetric
planet (or star), the time altering effects of the two different Relativitys of
speed and acceleration exactly cancel each other out!**

It is sad that, today, 2015 and 2016, famous Physicists still get this
wrong, and still it is because they totally ignore the consequences of General
Relativity. A currently popular showboating move is to take two Cesium clocks,
which are lavishly bragged about as incredibly precise and reliable, and first
synchronize them. Then one of those atomic clocks is driven up a mountain, and
the (allegedly smart) commentator describes how a Relativity time-rate effect
causes one of the clocks to "run slower" than the other due to the
difference in altitude. **Even the
"infallible"** **Stephen
Hawking demonstrates sadly poor logic in promoting this claim. **A
recent TV series by Hawking (*Genius*)
spent half an hour of valuable TV time in presenting this faulty logic and
conclusions! There are a bunch of logical errors there! At a location which
is a mile higher on a mountain, yes, the gravitational field of the Earth is a
tiny bit weaker, which would have a General Relativity time-rate effect, but
the person and clock is also circling the center of the Earth FASTER due to
having to travel a longer circumference each day, which has a Time Dilation
effect due to the higher speed. **Hawking (and
the others who have presented such public spectacles) never mention that there
are actually two Relativistic time effects going on, due to both General and
Special Relativity. **Since they never even mention the fact that two
effects are happening, no one ever does the math (presented here) to show that
the two Relativistic time-rate effects happen to exactly counteract each
other! **I expect a lot more of Hawking.**
More than that, ALL modern Physicists (including Hawking) have never yet solved
Einstein's original set of ten Tensor Calculus Differential Equations to discover that
the time-rate effects of General and Special Relativity happen to be opposite.
**They all (wrongly) assume they are the same,
all Time Dilation effects.** Why doesn't someone at least try to do
the math? **And so the "major
conclusion" that Hawking presented in his mountain experiment is simply
not true!** He did a one-day experiment and his results were that the
two (identical) Cesium clocks were then 20 nano-seconds different where he
claimed that "the results confirmed the assumption he had started out
having made." It is a sad aspect of modern science that researchers first
make an assumption and then (selectively) do some experiment which seems to
confirm that they are right!

By the way, the mountain experiments of Hawking and others are essentially just variants on a theme of the failed 1971 Hafele-Keating experiment in the jet airliners. But at least then, four Cesium clocks were used instead of one. A valid such mountain experiment should run for a month or a year rather than just a single day. And it should be repeated by others who do not carry the same pre-conceived assumptions.

Since 2006, I have tried to get NASA or the ESA to include a Cesium
clock in a soft-landing on the Moon. **In 2018, the Japan
Space Agency (JAXA) intends to launch another soft-lander to the surface
of the Moon. Such a simple experiment, where identical Cesium clocks on the
Earth and Moon might be continuously compared, will prove once and for all
whether Einstein was right about his Equivalency Principle and therefore
General Relativity**. My calculations, based on Einstein,
indicate that the Earth clock should count about 10,976 extra ticks every
hour than the identical clock on the Moon, entirely due to the difference in
our gravitational fields on the surface of the Earth and Moon, and on
Einstein's General Relativity and his Equivalency Principle of gravitation
and acceleration. Such a simple and
inexpensive experiment would instantly confirm that Einstein was right and it
would also demonstrate the logical flaws in the popular assumptions regarding
Time Dilation, the Hafele-Keating experiment, the Twins Paradox, alleged
Time Travel, wormholes, and other fields of modern Physics.

Physicists use a fairly simple equation to calculate the Time Dilation effect that occurs during Special Relativity, that is, when there is no acceleration but a relatively high constant velocity. This can be due to either the observed light source moving toward the observer or away from the observer (the Time Dilation effect is the same, either way).

Here is the **Time Dilation formula** factor for time-rate: ß (which is
)
This is the multiplying factor of the rate of time that appears to be
passing to an observer. (c) represents the speed of light and (v) represents the
velocity. If v is in the range of any velocity that we humans are capable of
creating, this factor is extremely minimal. This factor (called ß) was
discovered by Hendrik Lorentz and George FitzGerald around 130 years ago.

Consider the Earth satellite called the ISS (International Space
Station) orbiting at 27,743.8 kilometers per hour, orbiting the Earth every
hour and a half. This is 7.7066 kilometers per second. In this case, we would
have v = 7.7066 and c = 299,792.5 kilometers per second. ß is then **
0.999 999 999 669, which gives us the Time Dilation
proportion effect for the ISS satellite due to Special Relativity**
due to the orbital speed. This is assuming a perfectly circular orbit such
that the speed stayed exactly constant, and an Earth that was perfectly
spherical, none of which is quite precisely true.

So for an observer on the Earth's surface the satellite might seem to
show time passing slightly more slowly than we would measure with our Cesium
(atomic) clocks in a lab on Earth. NASA tried to do this experiment during the
1960s by putting an identical Cesium clock inside an orbiting satellite, and
compared the time with that of their "Standard" Cesium clock in
Washington, DC. **Those experiments were all
failures**, where they always showed greater variation between the
various Cesium clocks than the expected Dilation effect!

You might notice that the apparent difference is really minimal! In an entire year, the two clocks (in the ISS as compared to an atomic clock in a Lab on the surface of the Earth) would only have become different by about 1/100 of a second.

The Hafele-Keating experiment, which had Cesium clocks inside conventional airliners, actually had slower speeds (around 900 k/h) than our example of a person standing at the Equator, so we will pass on adding those calculations here, although any reader could easily do the math, to see why that NASA experiment failed so dreadfully.

Such experiments did seem to detect slight differences in the rate of
time of the Cesium clocks, but the expected Dilation differences were so small
that they never exceeded experimental errors! There were two reasons for that.
One is that even though Cesium clocks are extremely accurate and reliable,
trying to consistently find a difference of less than one part per billion of
time is near the limit to the capability of such atomic clocks. **
The other reason was that NASA seemed to be ignorant
of the continuous effects of General Relativity.**

In October 1971, NASA installed sets of four Cesium clocks in two passenger
airplanes, and sent one of the airplanes westward around the Earth while the
other airplane was sent eastward. This experiment was considered very
significant, and the **Hafele-Keating**
experiment is still cited as being something important. However, that
experiment was really just a sad joke, demonstrating amazing ignorance! The
most prominent actual experimental result might have been the significant
variation between the set of four allegedly identical Cesium clocks on each
aircraft! Given the speed of passenger airliners, the (expected) effect of
Time Dilation would have only been around 1/50,000 of a second in a year. And
yet the experimental results of the Hafele-Keating experiment showed
experimental errors between the individual Cesium clocks which were far greater
than what they hoped to find. **The 1971 NASA
experiment was a total failure!**

**The other reason is actually far more
important**. In order for a satellite (or an airliner) to
orbit, it must constantly radially accelerate due to the pull of Earth's gravity, to
create the curved circular orbital path. You do this when you try to drive
around a tight circle, and you feel an acceleration which seems to be pushing
you sideways in the seat. **We call it
centripetal acceleration**. Einstein had showed that an entirely
different set of Relativity equations are necessary for when accelerations are
present, which he called General Relativity. The Special Relativity equations
are mathematically simple. The General Relativity equations are horrifically
complicated. Einstein presented a set of ten complex Tensor Calculus
Differential equations, which must be simultaneously solved to get an answer.
So far, in a hundred years of countless mathematicians and physicists trying to
solve those Tensor Calculus equations, no one yet has solved them!

Einstein died in 1955. Around 1960, various groups of physicists decided that they were free to apply speculative assumptions to simplify Einstein's equations, and then they could solve their simplified problem. Unfortunately, the various groups of mathematicians and physicists had made different assumptions (none of which were solidly based on logic!) and so they each got different answers! There is a strong likelihood that ALL of those resulting answers are wrong!

We want to go back to that orbiting ISS satellite and its Cesium clock, to now try to examine the time-rate effects of the centripetal orbital acceleration, which is the time-rate effect of General Relativity.

Here is the factor called the **Equivalency
Principle** in physics.
(c) represents the speed of light, 299,792.458 km/s^{2}. (a)
represents the local acceleration due to a gravitational field or other source
of acceleration. And (d) represents a distance, which is the orbital radius
distance in that gravitational field.

Note that the Equivalency Principle is a dimensionless parameter,
[m/s^{2}] * [m] / [m^{2}/s^{2}]

It is also true that both the acceleration and the distance happen to be Vector quantities, but both are always along the exact same direction, and so their Vector Product is the same as for Scalar numbers, so their Vector nature is irrelevant here.

The ISS satellite is at 342.2 km altitude plus 6378 km Earth radius or
6720.2 km from the Earth's center and the gravitational acceleration it is
subjected to is around 8.827 meters/sec^{2}. This results in the
Equivalency Factor for the ISS being 1 + 0.000 000 000 330

This then results in the (perceived) **General
Relativity time-rate effect on the ISS (as seen from the Earth's surface as)
being 1.000 000 000 330 **(this is more than 1.0000 so therefore it is
a time-rate speeding effect).

I find it fascinating
that for the ISS in a circular orbit, the Time Dilation factor for the ISS due
to the speed is **0.999 999 999 669**,
while the Time Speeding factor due to the acceleration, per General Relativity
is **1.000 000 000 330**

These two time-rate Relativistic effects are both constantly in effect so the two time-rate factors have to be multiplied and they have opposite time-rate effects to each other, where their product is incredibly close to experimentally being exactly 1.000 000 000 net time-rate effect!

**Please note that this is a
mathematical proof that the two Relativistic time-rate effects exactly cancel
each other out (for the person on the ISS), within any conceivable error
factor.**

We might try to claim that the passengers on the ISS do not detect any
acceleration and so we could claim that they were in an**
**Inertial Rest Frame of Reference.

Since the ISS passengers do not feel any acceleration, and they
therefore feel that they are in an Inertial Rest Frame of Reference, what do
they see when they look down at Earth? They would see the surface of the Earth
constantly zooming past their (apparently, to their, stationary) satellite. **
By all the laws of science, they would see an apparent
Time Dilation effect where everyone on Earth would seem to be living and moving
slower than they would in their spacecraft!**

**The Earthbound scientists and their
Cesium clocks would detect the apparent Time Dilation time-rate effect on the
ISS satellite and its occupants and its clock. **

**Simultaneously, the scientists on
board the ISS and their Cesium clock would detect the apparent Time Dilation
time-rate effect on the Earth's surface and its billions of occupants and its
Cesium clocks!**

**If there were not any acceleration
due to the orbiting or the rotation of the Earth then, yes, they actually could
both see the others as apparently living more slowly than they live!**
That sounds impossible but it is certainly possible. Special Relativity and
its effects are only for straight line flight, no acceleration, where the
duration of an encounter would necessarily be rather brief.

**For a satellite, which is orbiting
and therefore constantly accelerating, that is not possible**.
In fact, this reasoning proves that the time effects of General Relativity is
opposite that of Special Relativity, and the calculations done above for a man
standing at the Equator and for a satellite even show that the two opposing
time effects exactly cancel each other out. Because of the two time-rate
effects, and the fact that they are opposite, the satellite and its passengers
could orbit for as long as desired without becoming older or younger than
"twin brothers left on Earth!"

That is, for the ISS, the SR Dilation time-rate effect of speed of **
0.999 999 999 669** times the GR Speeding
time-rate effect of acceleration of **1.000 000
000 330** is exactly unity!

We already showed the math that for a person at the Equator of the
Earth, the SR Dilation time-rate effect of speed of **
0.999 999 999 998 796 560** times the GR Speeding time-rate
effect of acceleration of **1.000 000 000 001
203 440** is exactly **1.000 000 000 000 000 000** within experimental
measurement error!

NASA has sent the ISS into a higher orbit recently, so the numbers cited here from NASA are now out-of-date.

Reference was made to the **Twins
Paradox story** of around 1962, which is similar to the example
mentioned above. The Twins Paradox is (wrongly) similar in that it **
assumes no acceleration and therefore, no General
Relativity**, in order for the Time Dilation effect to seem to be
accurate and correct. **There were two huge logical errors in the setup of that
story.** The really obvious one is that they only considered their story from
the rest frame of a non-accelerating Earth. The Earth brother would see the
spaceship brother appear to be aging more slowly than him. But they overlooked
an important fact that Einstein made clear, that anyone in an inertial
rest-frame can equally look at the Universe! **They
overlooked that everything can be looked at from the rest frame of the
non-accelerating spaceship**. Per Einstein's Special Relativity and
Time Dilation, he would certainly see the earthbound brother appear to be aging
more slowly than himself. Both of these situations would be occurring
simultaneously! **They both would see their
twin brother as aging more slowly than him! **Relativity has some peculiar
aspects to it, and this is one of them!

The second huge logical error is that **the
Twins Paradox story totally ignores the fact that there has to be massive
acceleration and deceleration occurring during much, most of such a trip**.
Given any acceleration rate that humans could survive, the process of getting
up to any velocity close to the speed of light, takes a long time, many months,
and then many months of deceleration to slow down to an Inertial Rest Frame of
Reference on any destination planet. The analysis above shows that the effect
of all that acceleration is substantial and it is opposite the Time Dilation
effect which does famously appear to occur during the "coasting"
(Special Relativity) part of the trip. A very thorough examination of all the
true effects show that the Time Speeding effects during the acceleration and
deceleration exactly cancel out the Time Dilation effects of the well known
Time Dilation time-rate effect during the coasting phase. **
Any such entire trip (beginning from and ending in the
same Inertial Rest Frame of Reference) necessarily has no time paradox at all!
**A thorough presentation of that analysis is at http://mb-soft.com/public2/twinspar.html
*The Twins Paradox is Wrong*

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