Euclid In Jeopardy

Edward Schaefer wrote:
 [Comparing clocks on the MIR Space Station] is a valid test of 
 relativity, and I will therefore conceded the point.  However, do 
 keep in mind that your ideas predict a time difference of 0.  I 
 would therefore consider any difference that cannot be accounted 
 for by the drift of the clocks to be an invalidation of your 
 principle.  Of course, it the result differs substantially from 
 both 0 and 26us/day then we *both* have to review our ideas of 
 reality.

You should both get busy with that review, because you're both wrong.  
The MIR space station is in an orbit about 236 miles (380 km) above 
the Earth's surface, so the theory of relativity predicts that ideal 
clocks on the MIR would show a difference of -24.8 usec per day 
relative to a clock sitting on the surface of the Earth.

Needless to say (or so one would have thought), this issue has 
already been settled experimentally.  Pound and Rebka demonstrated 
to incredible accuracy the relativistic gravitational time dilation 
between the top and bottom of a 22.6 meter tower, and of course 
this is also confirmed by solar and other astronomical observations 
over a wide range of gravitational potentials.  On this basis we 
can say with confidence that a stationary clock located 22,000 miles 
above the North Pole runs +49 usec/day fast compared with a clock 
sitting at the North Pole.  We also know that the GPS satellites, 
which are at that same 22,000 mile gravitational potential, show 
only +43.7 usec per day, so there is a discrepancy of -5.3 usec 
per day.

However, if we compute the predicted relativistic time dilation 
of a GPS satellite taking the orbital *velocity* as well as its 
altitude into account, we find that relativity predicts exactly 
43.7 usec/day, i.e., the discrepant -5.3 usec goes away when 
velocity is included.  Without this velocity effect we have an 
experimental discrepancy that we can't explain.  Thus, anyone 
who claims to base his beliefs on experimental results can hardly 
disagree that an orbiting clock at 22,000 miles runs 5.3 usec/day 
slower than a stationary clock at the same altitude.

The ratio of "clock rates" between a stationary clock at radius
r and an orbiting clock at radius R is simply the square root of
(1 - 3M/R)/(1 - 2M/r), where M is the gravitational radius of the
Earth (0.00443 meters).  All the above predictions are given by this
formula, which has been experimentally verified both on the surface 
of the Earth and in orbit.  There's no rational basis for thinking 
that at some intermediate radius between the Earth's surface and 
the GPS satellites this formula becomes inaccurate (and then 
becomes accurate again higher up).

The 66 Iridium satellites and the 288 Teledesic satellites will 
all be in low earth orbit, at about 435 miles up, so they will 
show about -21.0 usec/day discrepancy relative to a stationary 
clock at the Earth's surface.  Of course, we also have numerous 
particle experiments (which work on the same principle as Cesium 
clocks) at the Earth's surface (0 miles up) confirming the 
differential time lapse of -29.8 usec/day for the orbital 
velocity at the surface to very high precision.

Incidentally, if the MIR clocks were found to consistently and 
repeatably indicate something significantly different than -24.8 
usec/day (let's say they show -23.8, or -25.8, usec/day), then the 
first suspects would be unknown upset effects during the transport, 
oblatenes of the Earth or other gravitational anomalies, and maybe 
the detailed QM workings of the clocks themselves.


Keith Stein wrote:
 The major difference between my view and yours, Mr Swift,
 is that i beleive that such time dilations are only an 
 'APPARENT' effect , and that these GPS time dilations would 
 also disappear if tested with ADJACENT clocks.  Stein's Law
 is that CLOCKS WILL ALWAYS READ THE SAME WHEN BROUGHT 
 TOGETHER.

Nonsense.  Consider three identical clocks on Earth.  Send 
one of them up in a GPS satellite for a year.  (This is not 
hypothetical; it has been done many times.)  During the first 
day it accumulates 44 usec APPARENT excess over the clocks 
on Earth, and over the first year it accumulates 16060 usec 
APPARENT excess over the clocks on Earth.  Now send up the 
second clock to link up with the first in orbit. After one 
day, the first and second satellites will APPARENTLY read 
16104 and 44 usec (respectively) in advance of the clock on 
Earth.  You have agreed to this and experience confirms it.

The question is, how do those two clocks appear to an astronaut 
up there with them?  If I ask him (via the radio) to tell me how 
much difference he sees between those two clocks, how can he 
answer me without contradicting Stein's Law?  

He can't.  Thus, you cannot assert Stein's Law without denying 
even the APPEARANCE of time dilation for GPS satellites, which 
means you have to reject direct experience.


Albro Swift wrote:
 After one day, the first and second satellites APPARENTLY 
 read 16104 and 44 usec (respectively) in advance of the 
 clock on Earth.  You have agreed to this and experience 
 confirms it.

Keith Stein wrote:
 BUT that's my point Mr. Swift, experience does NOT confirm it.
 In fact you can't give a reference to any experiment in which so 
 much as 1 micro second of time dilation has been measured using 
 ADJACENT clocks.

There's an old joke about a group of men in an open field trying 
to hold a ladder vertical while one of them climbs to the top 
with one end of a tape measure.  A stranger comes by and asks 
what they are doing.  "We're trying to see how tall this ladder 
is", one of them answers.  "Well", says the stranger, "wouldn't 
it be easier to just lay it on the ground and measure it?"  The 
man answers "Oh, we already know how LONG it is, but we want to 
know how TALL it is."

The only one of your conditions that you claim has not been 
meet is ADJACENCY.  You conceed that various GPS satellites are 
all at the same altitude (i.e., gravitational potential), and 
that various GPS satellites have the same orbital velocity, so
the only remaining variable is neither gravity (GR) nor speed 
(SR), but simply adjacency (ER).  

The term "ER" refers to Euclidean Relativity, which is the ancient 
notion that entities are invariant under simple translation.  This 
is a very important and fundamental principle, because the entire 
Galaxy is moving, and we are never really in the same place twice.
Thus, if experiments were valid only for the specific point in 
space at which they were performed, then all experiments would be 
worthless.

We have performed multiple GPS experiments, and they differ only 
by translations, i.e., their specific positions in space.  The 
relative velocities and gravitational potentials (and all other 
physical paramaters that we can identify) are identical.  Therefore, 
if your "adjacency" experiment gave results differing from what 
would be inferred from the simple application of ER to existing 
results, then you would have called into question not SR or GR, 
but rather ER.

That would certainly be a profound and significant result (as would 
any result that conflicts with the application of fundamental rational 
principles to empirical data), but it just as certainly would NOT lead 
us back to anything like the classical notion of absolute time.  To 
the contrary, it would force us even further away from classical 
symmetries, into a bizarre realm of anisotropic weirdness that would 
cause Euclid, Galileo, and Newton to spin in their graves, and leave 
you yearning for the good old days of simple and intuitive relativistic 
physics.  A man of your obvious simple-mindedness should get down on 
his knees every day and pray that no experiment will ever show the 
kind of result you are suggesting.