Personal Topic

[Moronium]

Ashby is widely recognized expert regarding the GPS.  This paper tells you more than you'd ever want to know about the GPS and how it works, and has lots of math for those who love math.  I'm just quoting pertinent excerpts.

 

Relativity in the Global Positioning System

 

Neil Ashby, Living Reviews in Relativity December 2003, 6:1

 

The Global Positioning System (GPS) uses accurate, stable atomic clocks in satellites and on the ground to provide world-wide position and time determination. These clocks have gravitational and motional frequency shifts which are so large that, without carefully accounting for numerous relativistic effects, the system would not work.

 

The purpose of this article is to explain how relativistic effects are accounted for in the GPS. Although clock velocities are small and gravitational fields are weak near the earth, they give rise to significant relativistic effects. These effects include first- and second-order Doppler frequency shifts of clocks due to their relative motion, gravitational frequency shifts, and the Sagnac effect due to earth’s rotation. If such effects are not accounted for properly, unacceptably large errors in GPS navigation and time transfer will result.

 

Almost all users of GPS are at fixed locations on the rotating earth, or else are moving very slowly over earth’s surface. This led to an early design decision to broadcast the satellite ephemerides in a model earth-centered, earth-fixed, reference frame (ECEF frame), in which the model earth rotates about a fixed axis with a defined rotation rate...

 

Although the ECEF frame is of primary interest for navigation, many physical processes (such as electromagnetic wave propagation) are simpler to describe in an inertial reference frame. Certainly, inertial reference frames are needed to express Eqs. (1), whereas it would lead to serious error to assert Eqs. (1) in the ECEF frame.

 

The time transformation t = t′ in Eqs. (3) is deceivingly simple. It means that in the rotating frame the time variable t′ is really determined in the underlying inertial frame. It is an example of coordinate time.

 

Now consider a process in which observers in the rotating frame attempt to use Einstein synchronization to establish a network of synchronized clocks...Observers fixed on the earth, who were unaware of earth rotation, would use just ƒ dσ′/c for synchronizing their clock network. Observers at rest in the underlying inertial frame would say that this leads to significant path-dependent inconsistencies, which are proportional to the projected area encompassed by the path.

 

Synchronization is thus performed in the underlying inertial frame in which self-consistency can be achieved.... For atomic clocks in satellites, it is most convenient to consider the motions as they would be observed in the Earth-Centered Inertial (ECI) Frame.  Then the Sagnac effect becomes irrelevant...For the GPS it means that synchronization of the entire system of ground-based and orbiting atomic clocks is performed in the local inertial frame, or ECI coordinate system.

 

 

https://link.springer.com/article/10.12942/lrr-2003-1

 

Anyone who understands that, and who also understands the basic premises of SR (who I've yet to run across in this forum) would immediately understand that the GPS system rejects SR and adopts a Preferred Frame Theory of relativistic motion, with the ECI serving as the preferred frame.

 

SR simply will not work in the "real world."

 

A PFT treats all motion, simultaneity, and time as absolute, not relative.  It has to, for the GPS to be a viable practical system.  Although SR cannot be used, the Lorentz transformations can and are, of course.  The GPS abandons SR's formulation of the LR, and implements them in the way Lorentz designed them. This of course means that the speed of light is not constant in every inertial frame.  The speed of light is variable in GR, too, of course.

Edited March 5, 2019 by Moronium

[Moronium]

Now consider a process in which observers in the rotating frame attempt to use Einstein synchronization to establish a network of synchronized clocks...Observers fixed on the earth, who were unaware of earth rotation, would use just ƒ dσ′/c for synchronizing their clock network. Observers at rest in the underlying inertial frame would say that this leads to significant path-dependent inconsistencies, which are proportional to the projected area encompassed by the path.Synchronization is thus performed in the underlying inertial frame in which self-consistency can be achieved. (From the paper cited above)

 

 

The GPS abandons SR's formulation of the LR, and implements them in the way Lorentz designed them. This of course means that the speed of light is not constant in every inertial frame.  The speed of light is variable in GR, too, of course. (From my post above)

 

 

In the GPS, using a PFT, the speed of light is "constant" (isotropic) in only one frame, i.e., the preferred frame (the ECI in this case). In other frames of reference, the speed of light will vary depending on direction.  Einstein synchronization, as used in SR, assumes that the synchronization is being done in a non-moving frame, and hence is inappropriate for any frame of reference (whether moving at a uniform speed or not), other than the preferred one.   External synchronization is used in a PFT, which results in a variable speed of light in frames other than the preferred one.

 

To illustrate, a PFT will find that light takes less time to travel from NY to SF than it does from SF to NY.  SR, which is based on relative rather than absolute motion, would say the travel time is the same since NY and SF never move relative to each other.  But SR is wrong.  The GPS finds a difference of 28 nanoseconds. depending on direction.

Edited March 18, 2019 by Moronium

[A-wal]

SR does not claim that the "moving clock" runs slowly. The only inertial motion in SR is relative motion. The clocks are simply in motion relative to each other. You're again inserting an ether and claiming SR contradicts itself when it actually only contradicts the notion of a preferred frame. Give it a rest dumb dumb.

It's amusing to see you make such claims, with such absolute certainty, when the only thing you're proving is that you don't even have an elementary understanding of what you're talking about.

 

The chain of "reasoning" which you're resorting to here (and everywhere else) is this:

 

1.  SR has been conclusively proven to be absolutely correct

 

2.  Therefore it cannot, and does not, make any kind of contradictory claims.

 

3.  If it makes any claim that does seem to contradict another of it's tenets, well, then.....

 

4.  Simply deny that it makes both claims.

 

5. Q.E.D.

SR doesn't make any kind of contradictory claims simply because it never contradicts itself, it has nothing to do with it being proven. The only way you can pathetically attempt to claim it does contradict itself is to shoehorn in a preferred frame and say "there, see!". SR doesn't use a preferred frame so it's an invalid (and more than a little funny) attempt to fabricate a contradiction where none exists.

 

The only reason the eath twin's watch ends up ahead is because the other twin accelerated and the Earth twin didn't. Pay attention dumb dumb.

Completely wrong, as usual, A-wal.  Acceleration has nothing to due with time dilation caused by motion.  The reason his watch is slower is that he was moving faster, absolutely, not relatively.

 

In this case he wouldn't have been moving faster if he had not accelerated, true, but that is just an accidental circumstance.  Acceleration does not "cause" his time dilation.  You might just as well say that the only reason his watch is slower is because he was wearing a green spacesuit.  It's irrelevant, even if true.

You're (whether intentionally or accidentally) mixing up time dilation caused by relative motion with the difference on their watches when they meet back up.

 

When they're in inertial motion relative to each other each one is time dilated and length contracted from the frame of the other. When one of them changes frames (accelerates) it cause the other one's watch to speed up from the frame of the one that accelerates, putting their own watch behind the other one when they meet back up.

 

I've explained this to you over and over again and it's extremely obvious that there is no contradiction so your refusal to except it only reflects on your own irrationality, do you really think it in any way refutes SR? :)

[Moronium]

". SR doesn't use a preferred frame so it's an invalid (and more than a little funny) attempt to fabricate a contradiction where none exists.

 

Thanks for proving my point.

[Moronium]

 

 

You're (whether intentionally or accidentally) mixing up time dilation caused by relative motion with the difference on their watches when they meet back up.

 

When they're in inertial motion relative to each other each one is time dilated and length contracted from the frame of the other. When one of them changes frames (accelerates) it cause the other one's watch to speed up from the frame of the one that accelerates, putting their own watch behind the other one when they meet back up.

 

I've explained this to you over and over again and it's extremely obvious that there is no contradiction so your refusal to except it only reflects on your own irrationality, do you really think it in any way refutes SR? :)

 

You've explained nothing whatsoever.  Explain this:  How can you get an absolute answer from a relative theory? You can't.  In the twin paradox the motion of the space twin is treated as absolute.  Which it is.

Edited March 17, 2019 by Moronium

[Moronium]

You're (whether intentionally or accidentally) mixing up time dilation caused by relative motion with the difference on their watches when they meet back up.

 

 

What's the difference?  Explain that.

[A-wal]

You've explained nothing whatsoever.  Explain this:  How can you get an absolute answer from a relative theory? You can't.

You can't get an absolute answer from a relative model, you have to specify a frame to get an answer.

 

You're trying to claim that because SR doesn't give an absolute answer it's contradicting itself but that's absurd.

 

In the twin paradox the motion of the space twin is treated as absolute.  Which it is.

Not true. The inertial motion of both twins is never absolute. This is one of the most basic aspects of the model and if your still getting stuck on this point then maybe you're just not capable (or willing) to understand.

 

What's the difference?  Explain that.

One is caused by relative inertial motion. The other is caused by one of them changing frames.

[Moronium]

You've explained nothing whatsoever.  Explain this:  How can you get an absolute answer from a relative theory? You can't.  In the twin paradox the motion of the space twin is treated as absolute.  Which it is.

 

 

If the relative simultaneity; all frames are equivalent; time dilation is reciprocal; and "all motion is relative" premises of SR were true, then each twin would come back younger than the other.

 

Since that is impossible, SR suddenly abandons all those premises and "resolves" the twin paradox accordingly.

[A-wal]

If the relative simultaneity; all frames are equivalent; time dilation is reciprocal; and "all motion is relative" premises of SR were true, then each twin would come back younger than the other.

 

Since that is impossible, SR suddenly abandons all those premises and "resolves" the twin paradox accordingly.

Only one of them changes frames and that's what causes the difference in their age when they meet back up. If the both change frames together so they mirror each other the whole time then they will be the same age when they meet back up, each will see the other's watch running slowly while they're in relative motion and then running fast when they're accelerating.

Edited March 17, 2019 by A-wal

[Moronium]

You're (whether intentionally or accidentally) mixing up time dilation caused by relative motion with the difference on their watches when they meet back up.

 

One is caused by relative inertial motion. The other is caused by one of them changing frames.

 

 

Completely wrong.  Changing frames has no physical effect on anything.  So-called "time dilation," which is more aptly labelled "clock retardation," IS "the difference on their watches when they meet back up."  

 

There aren't even two different things to talk about or contrast.  Which  (non-existent) thing is caused by "changing frames," do you think?

Edited March 17, 2019 by Moronium

[Moronium]

Only one of them changes frames and that's what causes the difference in their age when they meet back up. If the both change frames together so they mirror each other the whole time then they will be the same age when they meet back up, each will see the other's watch running slowly while they're in relative motion and then running fast when they're accelerating.

 

 

Of course only one of them changes frames, but that's certainly not "why" their age is different.

 

Only one changes frames because only one is really moving.  According to SR it is the moving clock which will run slow.  That is the space twin's clock.

 

He changes frames because he is moving, and changing frames is merely an incidental circumstance which plays NO part in explaining why one is younger than the other.

Edited March 17, 2019 by Moronium

[Moronium]

You're trying to claim that because SR doesn't give an absolute answer it's contradicting itself but that's absurd.

 

 

As usual, you completely misunderstand.  I'm NOT saying SR doesn't give an absolute answer.  I"m saying it DOES give an absolute answer (contrary to it's own premises).  It has to.

 

One IS younger than the other as absolute matter.  That is not a question, the answer to which is"frame dependent" (relative).  It is frame independent (absolute).  The motion of the space twin is treated as absolute, which it is.

 

In short, SR is forced to repudiate itself in order to get the right answer.

Edited March 17, 2019 by Moronium

[Moronium]

Only one changes frames because only one is really moving.  According to SR it is the moving clock which will run slow.  That is the space twin's clock.

 

 

Put another way, as between the two, the earth twin is treated as being at rest (and remaining at rest) while the space twin moves.  This establishes the earth frame as the preferred frame.  It is the earth's frame which gives the right answer.  That alone is enough reason to "prefer" it. To the extent that the space twin "thinks" that the earth clock is running slower than his own, he is just WRONG.  There is nothing "reciprocal" about it.

Edited March 17, 2019 by Moronium

[A-wal]

Completely wrong.  Changing frames has no physical effect on anything.  So-called "time dilation," which is more aptly labelled "clock retardation," IS "the difference on their watches when they meet back up."  

 

There aren't even two different things.  Which  (non-existent) thing is caused by "changing frames," do you think?

Of course they are two different things.

 

While they are in inertial motion relative to each other each one is time dilated from the perspective of the other.

 

When one of them changes frames the other watch is running fast from the frame of the accelerating observer and this is what causes the other observers watch to be ahead of their own when they're back in the same frame.

 

Of course only one of them changes frames, but that's certainly not "why" their age is different.

It's the only reason why their age is different.

 

Only one changes frames because only one is really moving.  According to SR it is the moving clock which will run slow.  That is the space twin's clock.

They're in motion relative to each other while they're inertial. Each one is time dilated and length contracted from the perspective of the other frame because each one is in motion from the perspective of the other frame.

 

He changes frames because he is moving, and changing frames is merely an incidental circumstance which plays NO part in explaining why one is younger than the other.

It's not incidental. The one that changes frames is the one who ends up younger. As I said, if they both change frames to mirror each other then they're the same age when they're back in the same frame.

 

As usual, you completely misunderstand.  I'm NOT saying SR doesn't give an absolute answer.  I"m saying it DOES give an absolute answer (contrary to it's own premises).  It has to.

No it doesn't. SR only ever gives frame dependent answers. Once they're back in the same frame then they agree about the amount of time that's passed for each of them because a frame dependent answer and an absolute answer is the same thing in this case, because they're in the same frame.

 

One IS younger than the other as absolute matter.

Only if one changes frames and the other doesn't, or if one changes frames more than the other to be precise. As I said, if they both change frames to mirror each other then they're the same age wen they're back in the same frame.

 

That is not "frame dependent" (relative), it is frame independent (absolute).  The motion of the space twin is treated as absolute, which it is.

The inertial motion of the two is relative. If they both change frames to mirror each other then they're the same age when they're back in the same frame.

 

In short, SR is forced to repudiate itself in order to get the right answer.

Don't be silly, it does no such thing.

[A-wal]

Put another way, as between the two, the earth twin is treated as being at rest (and remaining at rest) while the space twin moves.  This establishes the earth frame as the preferred frame.  It is the earth's frame which gives the right answer.  To the extent that the space twin "thinks" that the earth clock is running slower than his own, he is just WRONG.  There is nothing "reciprocal" about it.

The Earth twin is in motion relative to the space twin and so is time dilated and length contracted from the frame of the space twin.

 

The space twin is in motion relative to the Earth twin and so is time dilated and length contracted from the frame of the Earth twin.

 

The space twin changes frames (at least three times) causing the Earth twin's watch to speed up while the space twin is accelerating and creating the difference in elapsed time when they're back on Earth (the total speed up of the Earth twin from the space twin's perspective when the space twin is accelerating is greater than the total slow down of the Earth twin's watch while the space twin is inertial).

Edited March 17, 2019 by A-wal

[Moronium]

The Earth twin is in motion relative to the space twin and so is time dilated and length contracted from the frame of the space twin.

 

What are you even trying to say here?  Whose time in dilated?  Certainly not the earth twin's.  He is not "in motion," he is treated as being at rest.  I agree that, per SR, the space twin is FORCED to claim that he is at rest, but he is WRONG.  He aint.

[Moronium]

The Earth twin is in motion relative to the space twin and so is time dilated and length contracted from the frame of the space twin.

 

The space twin is in motion relative to the Earth twin and so is time dilated and length contracted from the frame of the Earth twin.

 

The space twin changes frames (at least three times) causing the Earth twin's watch to speed up while the space twin is accelerating and creating the difference in elapsed time when they're back on Earth (the total speed up of the Earth twin from the space twin's perspective when the space twin is accelerating is greater than the total slow down of the Earth twin's watch while the space twin is inertial).

 

If you understood SR at all, then you would know that "changing frames" has nothing to do with anything, as I've told you.  According to the mathematically-formulated lorentz transformations, it is the moving clock which will run slow.  Those transformations say nothing about "changing frames, nor should they.  It is irrelevant.  Motion is what causes the difference.

 

The point is the same no matter how much you talk about non sequiturs like changing frames.  One twin is younger, one is older.  The "resolution" gives you an absolute answer, not a relative one,.

Edited March 17, 2019 by Moronium