# Relative Information and Time Paradox?

## Main Question or Discussion Point

We have a satellite orbiting at a significant amount of the speed of light around the earth.

Hypothetical numbers:

The satellite ages 6 years;
while the;
earth ages 7000 years.

How does the satellite communicate with earth or vice versa? How is information transfer between each frame of reference's time?

Related Special and General Relativity News on Phys.org
Why would this be a paradox?

JesseM

We have a satellite orbiting at a significant amount of the speed of light around the earth.
That's not really possible as the orbital velocity at a given distance depends on the mass of the body being orbited, you'd need something like a black hole for a natural orbit to be a significant fraction of lightspeed...we could imagine the satellite was traveling in a circle using powered flight rather than just orbiting for the sake of your thought-experiment though.
Nano-Passion said:
Hypothetical numbers:

The satellite ages 6 years;
while the;
earth ages 7000 years.

How does the satellite communicate with earth or vice versa? How is information transfer between each frame of reference's time?
Satellite sees the Earth's signals coming in fast forward (if Earth sends a signal once a year, satellite sees them coming in at 7000/6 = 1166.66... per year) while Earth sees satellite signals coming in slow-motion (if satellite sends a signal once a year, Earth sees a new signal only once every 1166.66... years).

That's not really possible as the orbital velocity at a given distance depends on the mass of the body being orbited, you'd need something like a black hole for a natural orbit to be a significant fraction of lightspeed...we could imagine the satellite was traveling in a circle using powered flight rather than just orbiting for the sake of your thought-experiment though.

Satellite sees the Earth's signals coming in fast forward (if Earth sends a signal once a year, satellite sees them coming in at 7000/6 = 1166.66... per year) while Earth sees satellite signals coming in slow-motion (if satellite sends a signal once a year, Earth sees a new signal only once every 1166.66... years).
Forget what they interpret, your telling me that the signal would take longer to travel from the satellite to earth?

JesseM
Forget what they interpret, your telling me that the signal would take longer to travel from the satellite to earth?
No, I'm saying clocks on the satellite would be running slow (in some coordinate system where Earth clocks were running normally) so it would send signals less frequently, for example if observers on the satellite were sending a signal every second according to their own clocks, in the Earth-centered frame they'd only be emitting a new signal once every 1166.66... seconds.

No, I'm saying clocks on the satellite would be running slow (in some coordinate system where Earth clocks were running normally) so it would send signals less frequently, for example if observers on the satellite were sending a signal every second according to their own clocks, in the Earth-centered frame they'd only be emitting a new signal once every 1166.66... seconds.
What would happen if the earth sent a message to this fast moving satellite?

Would the satellite see the signal beat time as slowed.

JesseM
What would happen if the earth sent a message to this fast moving satellite?

Would the satellite see the signal beat time as slowed.

Yes, I did. But, now I am confused.
But, in my thread all the humans suggested if A is moving wrt to B, then B would see A's clock time dilated and vice versa.

So, how do you explain if you are at rest with the satellite frame you would not see the earth's time as time dilated.

Dale
Mentor
Such a "satellite" frame would be non-inertial. The metric is not the Minkowski metric and the time dilation is not symmetric.

JesseM
But, in my thread all the humans suggested if A is moving wrt to B, then B would see A's clock time dilated and vice versa.
Only applies to inertial observers in flat spacetime, you can either model a satellite as traveling a powered circular trajectory in flat spacetime or a free-fall (locally inertial) trajectory in curved spacetime, either way it doesn't qualify.

Such a "satellite" frame would be non-inertial. The metric is not the Minkowski metric and the time dilation is not symmetric.
Oh, that means there is a GR reason for this.

Can you show me the math?

Wait, I found this.
Let us therefore consider the simplest instance of a transformation from an inertial frame, in which the space-time is Minkowskian, to a rotating frame of reference. Thus, ignoring gravitational potentials for the moment, the metric in an inertial frame in cylindrical coordinates is
http://relativity.livingreviews.org/Articles/lrr-2003-1/ [Broken]

I wonder why the heck they apply Minkowski space-time to GPS in the most widely accepted paper on GPS in the mainstream.

I guess they are in error.

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Only applies to inertial observers in flat spacetime, you can either model a satellite as traveling a powered circular trajectory in flat spacetime or a free-fall (locally inertial) trajectory in curved spacetime, either way it doesn't qualify.
In wonder why this is stated.
It is easy to check that both the special relativistic time dilation correction from the speed of the satellite, and the general relativistic gravitational potential correction are much greater than that, so the clocks in the satellites must be corrected appropriately.
http://galileo.phys.virginia.edu/classes/252/general_relativity.html

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion.
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

This does not make time dilation absolute.

JesseM
In wonder why this is stated.
It is easy to check that both the special relativistic time dilation correction from the speed of the satellite, and the general relativistic gravitational potential correction are much greater than that, so the clocks in the satellites must be corrected appropriately.
http://galileo.phys.virginia.edu/classes/252/general_relativity.html

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion.
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html
Both statements are correct, if you think they conflict with what I said you are confused, since you haven't made a specific argument there is no telling where your confusion might lie.

Both statements are correct, if you think they conflict with what I said you are confused, since you haven't made a specific argument there is no telling where your confusion might lie.
OK, so you accepted the mainstream facts I presented. Good. You said the following.

Satellite sees the Earth's signals coming in fast forward (if Earth sends a signal once a year, satellite sees them coming in at 7000/6 = 1166.66... per year) while Earth sees satellite signals coming in slow-motion (if satellite sends a signal once a year, Earth sees a new signal only once every 1166.66... years).

Now, you all claim time dilation is reciprocal. Yet, the non flat-earth lab of GPS does not show this.

Can you explain that? Before, you claimed it was because of GR framing. Of course, my correct and accepted mainstream links showed SR is used for time dilation in GPS.

So, we need to see reciprocal time dilation as predicted by SR and I am not seeing it in the factual lab of GPS. I wonder why.

JesseM
Now, you all claim time dilation is reciprocal.
No I didn't, read post 10 again.
chinglu1998 said:
Before, you claimed it was because of GR framing.
Nope, I didn't say that was the only way of thinking about the problem, read post 10 again.
chinglu1998 said:
Of course, my correct and accepted mainstream links showed SR is used for time dilation in GPS.
Nope, they don't say SR alone can be used to get the correct slowdown.

No I didn't, read post 10 again.

Nope, I didn't say that was the only way of thinking about the problem, read post 10 again.

Nope, they don't say SR alone can be used to get the correct slowdown.
OK, let me make sure I understand your non-mainstream position. Are you claiming there exists a frame (GPS satellite) in which if you are at rest with the satellite and the moving earth frame will not be time dilated in your calculations? In fact, I can show you the control center in Colorado syncs the satellite clocks and time dilation does not apply when at rest with the satellite as a mathematical assumption in GPS.

I want to make sure I understand this from you.

Next, what other slowdowns occur in GPS as you claim?

JesseM
OK, let me make sure I understand your non-mainstream position. Are you claiming there exists a frame (GPS satellite) in which if you are at rest with the satellite and the moving earth frame will not be time dilated in your calculations?
If you want to come up with a coordinate system where the satellite is at rest you can do so, but it will not be an inertial one, so conclusions from SR inertial frames (like: clocks which are moving in a given frame always run slow in that frame) don't necessarily apply. Depending on how you choose the coordinate system the Earth clocks may be consistently running fast or varying between running slower and faster, but either way the Earth clocks should elapse more time in total over a complete orbit than the satellite clock.
chinglu1998 said:
In fact, I can show you the control center in Colorado syncs the satellite clocks and time dilation does not apply when at rest with the satellite as a mathematical assumption in GPS.
This would appear to have precisely nothing to do with the question of what would be true in a frame where the satellite is at rest. As you already know, GPS calculations use an Earth-centered frame, not a satellite-centered one.

If you want to come up with a coordinate system where the satellite is at rest you can do so, but it will not be an inertial one, so conclusions from SR inertial frames (like: clocks which are moving in a given frame always run slow in that frame) don't necessarily apply. Depending on how you choose the coordinate system the Earth clocks may be consistently running fast or varying between running slower and faster, but either way the Earth clocks should elapse more time in total over a complete orbit than the satellite clock.

This would appear to have precisely nothing to do with the question of what would be true in a frame where the satellite is at rest. As you already know, GPS calculations use an Earth-centered frame, not a satellite-centered one.
As you already know, GPS calculations use an Earth-centered frame, not a satellite-centered one.

Time for education.

The satellite message contains its ECEF coordinates at light emission. The receiver get this mesaage from a collection of satellites.

When folks say synchronization occurs in ECI, this is confusing. Light travels "synchronized" in ECI. That means if you have a frame in ECI, light measures c in all directions. It does not in ECEF, the MMX frame.

Now, the unit must "sync" to ECI to triangulate. That means, it must correct the light travel times and apply the sagnac correction to the time of light travel based on the direction of the satellite. So, why "sync" to ECI. Because that is the only frame known to humans in which light is measured c in all directions and that is therefore dependable.

But, this does not relieve you of your responsibility to prove reciprocal time dilation.

JesseM
As you already know, GPS calculations use an Earth-centered frame, not a satellite-centered one.

Time for education.

The satellite message contains its ECEF coordinates at light emission. The receiver get this mesaage from a collection of satellites.

When folks say synchronization occurs in ECI, this is confusing. Light travels "synchronized" in ECI. That means if you have a frame in ECI, light measures c in all directions. It does not in ECEF, the MMX frame.

Now, the unit must "sync" to ECI to triangulate. That means, it must correct the light travel times and apply the sagnac correction to the time of light travel based on the direction of the satellite. So, why "sync" to ECI. Because that is the only frame known to humans in which light is measured c in all directions and that is therefore dependable.
Hmm, looks like this is just a pointless digression which has nothing to do with showing any error in what I said.
chinglu1998 said:
But, this does not relieve you of your responsibility to prove reciprocal time dilation.
I didn't argue for reciprocal time dilation, I explicitly said you can't expect it in non-inertial frames.

Dale
Mentor
This does not make time dilation absolute.
Correct, time dilation is relative, so you always have to specify the frame, eg "clock X is time dilated wrt the rotating frame".

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I wonder why chinglu1998 got banned 0_o

So the satellite would be sending in a much lower rate of signals compared to earth but the overall number of signals it would all equal out in relative time... hmm interesting.

I wonder if it is really that simple or there is more to its' transmission of signals and its flight between both events.