On Jan 29, 10:40*pm, "Jeckyl" wrote:
"snapdragon31" wrote in message

...





On Jan 29, 8:54 pm, Randy Poe wrote:
On Jan 29, 8:14 pm, HW@....(Dr. Henri Wilson) wrote:

According to relativists, GPS clocks GAIN 38us per day on the ground
clock.
That is due to two components, 45us for gravity and -7us for relative
speed.

Accordingly, an observer (OO) in GPS orbit would see the GC LOSING 52us
per
day.

After one year, the OO would calculate that the OC was about 19ms ahead
of the
GC.
However, the GO would calculate that his GC was only 13ms behind.

What happens when the clocks are reunited?
Who is right?

Two people drive different routes from city A to
city B. When they are reunited, one odometer reads
220 km and the other reads 230 km. Which one is
right?
According to relativity, both odometer readings are wrong. *They do
not represent the true distance of the routes travelled because of the
length contraction effect.

It was an anlogy only .. derr .. to illustrate that taking different paths
in space gives you different elapsed distances .. and that similarly
different paths in space time can give you different elapsed times. *And
there is no such thing as 'true distance' in any case.

According to Newton's law, both odometer readings are right.

Just as in SR, both clocks are right in the so-called twins paradox. *They
are simply measuring different quantities.

The GPS clock paradox is a variation of the twin paradox, so no valid
solution.

Why not .. the so-called twins paradox is well explained by relativity by a
number of methods (all giving the same results) .. why do you think there is
no 'solution'? *Why do you even think there is something there that needs
solving?- Hide quoted text -

- Show quoted text -

Yes, there are tons of solutions to the twin paradox but none of them
is a valid solution.
Let me show you why it is a logical problem that has no solution.
Assuming that Lorentz transformation can predict the time and distance
of the other frame.
Let v = velocity of the moving twin M
x = distance measured by stationary twin S
t = time measured by twin S
x' = distance measured by twin M
t' = time measured by twin M

The information we have is:
1. v - velocity of moving twin.
2. x = v * t
3. x' = v * t'
4. x' = x * sqrt(1 - v^2/c^2)
5. t' = t * sqrt(1 - v^2/c^2)

I hate equations. Let me convert them into numbers.
Let v = 0.995c and x = 10c both v and x can be measured accurately
1/gamma = sqrt(1 - 0.995^2) = 0.1
From the point of view of twin S.
Eq 2. t = x / v = 10c / 0.995c = 10.05 years
Eq 4. x' = x * sqrt(1 - 0.995^2) = x * 0.1 = c
Eq 5. t' = t * 0.1 = 1.005 years (Calculated)
x' = c and
v * t' = 0.995c * 10.05 = c
Eq 3. x' = v * t' = c

Using Lorentz transformation the calculated time twin M used is 1.005
years.
So far so good if the time measured by twin M is 1.005 years for the
whole journey.

1'. v - velocity of moving twin (S).
2'. x' = v * t'
3'. x = v * t
4'. x = x' * sqrt(1 - v^2/c^2)
5'. t = t' * sqrt(1 - v^2/c^2)

Assuming that the measured time is the same as the calculated time =
1.005 year.
From twin M's point of view:
v = 0.995c Velocity of twin S and it can be measured by accurately
t' = 1.005 years (measured)
Eq 2'. x' = 0.995c * 1.005 = c
Eq 4'. x = x' * 0.1 = c * 0.1 = 0.1c (Calculated)
Eq 5'. t = t1 * 0.1 = 0.1005 year
x = 0.1c and v * t = 0.995c * 0.1005 = 0.1c
Eq 3'. x = v * t = 0.1c

So far there is still no problem as long as the calculated x and the
measured x are the same. Unfortunately, the calculated x = 0.1c and
the measured x = 10c.
As a conclusion, Lorentz transformation is not valid at least in one
situation.

Please note that 'stationary' and 'moving' are relative.