"snapdragon31" wrote in message
...
On Jan 30, 4:55 am, "Jeckyl" wrote:
"snapdragon31" wrote in message

...
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

There is nothing to solve

but none of them is a valid solution.

They all predict the same result. Why do you think they are all invalid ..
is it because they all give the same reults which is different to what
you'd
like it to be?

Let me show you why it is a logical problem that has no solution.

It isn't a problem .. its a statement of what would happen.

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

What distances and times are you measuring?

The information we have is:
1. v - velocity of moving twin.
2. x = v * t

3. x' = v * t'

OK .. so we area assuming here that x and t are the distance and duration
the stationary twin S sees the moving twin M travel on the first leg of
the
journey, and that corresponds to a distance of x' and t' that the moving
twin M seems the stationary twin S travel.

4. x' = x * sqrt(1 - v^2/c^2)
5. t' = t * sqrt(1 - v^2/c^2)

Lets just double check that .. LT tells us that (assuming we have that at
t=t'=0 x=x'=0, the corresponding event for (x,t) for S is (x',t') for M,
where
x' = gamma(x - vt)
t' = gamma(t - xv/c^2)
where gamma = 1/sqrt(1-v^2/c^2)
So when M (as seen from S) has gone a distance x = vt, M will be at
(x1',t1') in its own frame of reference
x1' = gamma(vt - vt)
x1' = 0 (as expected .. M has not moved relative to itself)
t1' = gamma(t - vtv/c^2)
t1' = gamma(t(1 - v^2/c^2))
t1' = gamma(t(1 - v^2/c^2))
t1' = t/gamma
and at that time, M will see S as being at (x2',t2')
x2' = -vt1'
x2' = -vt/gamma
x2' = -x/gamma
So that's all fine (other than getting the sign correct there)

I hate equations.

I wonder why?

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

close enough .. and gamma = 10.013

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

Sounds fine so far

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.

The first leg of it .. ie the trip away from S .. yes

So I assume now you are going to look at it all in reverse

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.

What is the difference between 'measured' and 'caclulated' as you see it?

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.

As explained to you before .. you have used the same name x here for two
different values. You are confusing yourself as a result.

In the first case x is how far M travels in time t
In the second case x is how far M travels in time t/gamma

How could you expect them to be equal?- Hide quoted text -

- Show quoted text -

Both case refer to the same journey - the first leg of the journey of
M from Earth to a star 10c away.

The first one does refer to the whole journey .. the second one does not

[snip same thinkg repeated for no good reason]

At the very beginning, we know that the value of x measured by S is
10c

Yes .. it is.

And that is a different thinkg to the x you calculated in the second set of
equations. Which is why it has a different value. Just calling two thing x
does not mean they are the same thing.

so the predicted value of 0.1c must be wrong.

No .. it is a prediction of a different thing .. it is NOT a measurement of
the distance between the S and point 10c away.

Lorentz transformation does not work in this case.

Yes .. it does .. perfectly. You just don't understand how to apply it.

[snip more misunderstanding]

I suggest you look at the pole and barn paradox. That is where you have
(say) a pole 10m long and a barn 5m long with doors at each end .. but if
the pole is moving faster enough, length contraction means that according to
an observer in the bar, the pole is less than 5m long .. which means if the
observer in the barn times it right, when the pole enters one end of the
barn, he can close the front and rear doors at the same time temporarily
trapping the 10m pole in the 5m barn, and then open the doors a fraction of
a second later to let the pole out the other end. YET, as the barn is
moving relative to the pole with the same relative speed, the barn must be
less than 2.5m long according to the pole .. so how can the pole be trapped
wholly within a barn that is more than 4 times shorter than the barn?

When you understand how that can work, that may help you see why you are
having problems understanding your scenario.