A Question Concerning Time Dilation

[Elen Sila]

In case you can't read my handwriting, this is what it says.

 

"Satellite orbiting sun at a distance of 10,000 AU. Satellite completes one circuit every 365.25636 days, travelling at 99.35 percent the speed of light, but maintains a constant distance from the earth. Not counting time dilation incurred during transit to this distance, or acceleration to this speed, and reckoning only from the moment the satellite receives a confirming signal from the earth... would the satellite's clocks experience time dilation (relative to the earth)?"

 

NOTE – I'm aware that the satellite couldn't actually be orbiting at that speed and at that distance; Kepler's laws demand that the satellite actually have an orbital period of about one million years. However, this scenario assumes that the satellite is using its engines to maintain a constant speed, and a constant distance from the earth and the sun. It's not technically "orbiting" the sun so much as it is "flying around" it in circles.

Edited August 28, 2011 by Elen Sila

[swansont]

Yes, it would experience time dilation. The clocks would be faster from the gravitational effect (given by GM/rc^2), but this would be small compared to the slowing from the kinetic term, given by gamma.

[IM Egdall]

Elen Sila -- Here's a real world application of your idea you might find interesting: Global Positioning Satellites:

 

GPS receivers compare "time signals received from a number of GPS satellites (usually 6 to 12) in its line of sight." From this, the receiver calculates "its current position and heading." The key here is time signals from the different satellites must be known to an accuracy of 20 to 30 nanoseconds.

 

The two relativity effects which alter the timing of the satellite clocks are:

 

Relative Motion. Atomic clocks on board the satellites run slower than clocks on Earth by about 7 thousand nanoseconds per day. This is due to their motion relative to the Earth (kinematic time dilation per special relativity).

 

Relative Altitude. Satellite atomic clocks run faster than Earth clocks by about 45 thousand nanoseconds per day. This is due their much higher altitude. (gravitational time dilation per general relativity).

 

The two relativity effects produce a net gain of about 45 -7 = 38 thousand nanoseconds per day in the timing of satellite clocks (compared to clocks on the ground). This net gain is huge compared to the 20-30 nanoseconds accuracy GPS needs to work. Thus, if the system ignored the effects of special and general relativity, "a navigational fix from GPS would be false after only 2 minutes. And errors in global positions would continue to accumulate at a rate of about 6 miles (10 kilometers) each day!"

 

So the success of the GPS system in providing locations on Earth (and in airplanes) to accuracies of 5 -10 meters is a continuous verification of Einstein's predictions that time is slowed by both motion and gravity! <BR clear=all> http://www-astronomy.../Unit5/gps.html

Edited August 28, 2011 by IM Egdall

[Elen Sila]

I guess I just don't get time dilation. In order to say "Spacecraft A is moving faster than planet B; therefore spacecraft A is experiencing time slower than planet B," you must have an absolute point of reference from which to determine A's and B's absolute velocities. If you only base time dilation off relative velocity, then an observer onboard spacecraft A would view planet B as moving faster, and thus planet B would be the one experiencing time at a slower rate. They can't both be experiencing time slower than the other; that's a contradiction.

 

The way I've always resolved the contradiction is by imagining that time dilation is simply an illusion, caused by the Doppler effect. If you're moving away from someone at 0.99c, you both observe each other as perceiving time very slowly, because each of your signals from each other are highly red-shifted. However, this means that if you were moving towards someone at 0.99c, then you would both observe each other as perceiving time very quickly, because your signals from each other would be highly blue-shifted; and likewise, if you were maintaining a constant distance from each other, but travelling at different velocities relative to an outside reference point (like the sun in my scenario, or the center of the earth in the GPS scenario), you would not observe time dilation from each other, except in the form of signal delay. And if you travelled very far away from the earth and then returned, the red-shifting during departure and the blue-shifting during return would cancel each other out, and you would still be the same age as your twin on earth.

 

How can both spacecraft A and planet B observe time dilation from the other, if time dilation is NOT simply the Doppler effect?

[swansont]

I guess I just don't get time dilation. In order to say "Spacecraft A is moving faster than planet B; therefore spacecraft A is experiencing time slower than planet B," you must have an absolute point of reference from which to determine A's and B's absolute velocities. If you only base time dilation off relative velocity, then an observer onboard spacecraft A would view planet B as moving faster, and thus planet B would be the one experiencing time at a slower rate. They can't both be experiencing time slower than the other; that's a contradiction.

 

The velocities are always measured with respect to each other or some reference frame; there is no absolute motion or absolute rest. You are at rest in your own reference frame, but there isn't any experiment you can do to show that you are at rest while someone else is moving.

 

Both observers measuring each other's time to be slow isn't a problem because they are not in the same frame. There is no "right answer". If they get into the same frame it will require that one of them accelerate, and that can be determined, so you will then have one clock with less elapsed time than the other.

 

The way I've always resolved the contradiction is by imagining that time dilation is simply an illusion, caused by the Doppler effect. If you're moving away from someone at 0.99c, you both observe each other as perceiving time very slowly, because each of your signals from each other are highly red-shifted. However, this means that if you were moving towards someone at 0.99c, then you would both observe each other as perceiving time very quickly, because your signals from each other would be highly blue-shifted; and likewise, if you were maintaining a constant distance from each other, but travelling at different velocities relative to an outside reference point (like the sun in my scenario, or the center of the earth in the GPS scenario), you would not observe time dilation from each other, except in the form of signal delay. And if you travelled very far away from the earth and then returned, the red-shifting during departure and the blue-shifting during return would cancel each other out, and you would still be the same age as your twin on earth.

 

How can both spacecraft A and planet B observe time dilation from the other, if time dilation is NOT simply the Doppler effect?

 

If you look at relativity, the question becomes how can they not? You have to have a preferred frame of reference for it to be true. GPS does work, after all.

[Elen Sila]

Both observers measuring each other's time to be slow isn't a problem because they are not in the same frame. There is no "right answer". If they get into the same frame it will require that one of them accelerate, and that can be determined, so you will then have one clock with less elapsed time than the other.

 

But how close together do they have to be to be considered "in the same reference frame"? If "in the same reference frame" just means "travelling in the same direction, and maintaining the same distance from each other", then the earth and the satellite are in the same reference frame, just as two atomic clocks would be if they were in the same room together. The distance between the earth and the satellite, like the distance between the two atomic clocks, is only significant in that it creates signal delay.

Edited August 28, 2011 by Elen Sila

[Janus]

But how close together do they have to be to be considered "in the same reference frame"? If "in the same reference frame" just means "travelling in the same direction, and maintaining the same distance from each other", then the earth and the satellite are in the same reference frame, just as two atomic clocks would be if they were in the same room together. The distance between the earth and the satellite, like the distance between the two atomic clocks, is only significant in that it creates signal delay.

 

The thing is that they aren't in the same inertial frame. The satellite is in a forced orbit, which puts it in a rotating frame and under constant acceleration (as evidenced by the fact that the ship has to be constantly firing its engines is order to maintain its orbit.)

[Elen Sila]

The thing is that they aren't in the same inertial frame. The satellite is in a forced orbit, which puts it in a rotating frame and under constant acceleration (as evidenced by the fact that the ship has to be constantly firing its engines is order to maintain its orbit.

 

Yeah, I was thinking about that. That's why I decided to create a revised scenario. In case you can't read my handwriting, it reads as follows.

 

"Satellite, orbiting at 74.865 km/s [with respect to the sun], with a semi-major axis of 23685251 kilometers, or 34 solar radii, or 0.1583 AU. Satellite's orbital nodes precess at a rate of about 22.68 degrees per orbit, or one full circuit every 365.25636 days. Earth, orbiting at 29.785 km/s [with respect to the sun], with a semi-major a[x]is of 149598261 kilometers, or 215 solar radii, or 1 AU."

 

We'll say that Mercury's orbit has somehow been altered to provide the gravitational impetus for the satellite to precess at such an outrageously rapid rate, so we don't need to fire the satellite's rockets at all once we've achieved orbit. Regardless of the details however, the satellite is moving about 2.5 times faster than the earth, with respect to the sun, completing one orbit every 23 days, and its orbit is slowly turning so that the earth is always located at the satellite's orbital north pole. The satellite is thus maintaining a constant distance from the earth, despite its outrageous orbital velocity.

 

In this scenario, why would the satellite experience time dilation, IE not be in the same frame of reference, as an observer standing on earth's north pole?

Edited August 29, 2011 by Elen Sila

[DrRocket]

In case you can't read my handwriting, this is what it says.

 

"Satellite orbiting sun at a distance of 10,000 AU. Satellite completes one circuit every 365.25636 days, travelling at 99.35 percent the speed of light, but maintains a constant distance from the earth. Not counting time dilation incurred during transit to this distance, or acceleration to this speed, and reckoning only from the moment the satellite receives a confirming signal from the earth... would the satellite's clocks experience time dilation (relative to the earth)?"

 

NOTE – I'm aware that the satellite couldn't actually be orbiting at that speed and at that distance; Kepler's laws demand that the satellite actually have an orbital period of about one million years. However, this scenario assumes that the satellite is using its engines to maintain a constant speed, and a constant distance from the earth and the sun. It's not technically "orbiting" the sun so much as it is "flying around" it in circles.

 

This is relly a general relativity issue. You are comparing two clocks, one (in an earth orbit) essentially in free fall and another undergoing acceleration to maintain a specified trajectory.

 

Now it is not fair to compare two clocks that are spatially separated, but if you idealize so that the satellite clock leaves the earth and returns later, which can be done with minimal effect, then the satellite clock which follows a non-geodesic path, will record less time than the earth-bound clock which does have a geodesic world line in spacetime.

 

This is essentially the "twin paradox" re-cast.

[Elen Sila]

Now it is not fair to compare two clocks that are spatially separated, but if you idealize so that the satellite clock leaves the earth and returns later, which can be done with minimal effect, then the satellite clock which follows a non-geodesic path, will record less time than the earth-bound clock which does have a geodesic world line in spacetime.

 

Here's what I'm saying. (And this goes for both my original scenario, and the scenario I just posted a few minutes ago.)

 

Upon achieving its orbit, the satellite sends a "requesting response" signal to the earth, and the satellite's clock starts counting. Upon the earth receiving this signal, a "verifying response" signal is sent back towards the satellite, and the earth's clocks start counting. Upon receiving the earth's response, the satellite's clocks stop counting, and beam their recorded time elapsed back to the earth. When the earth receives the satellite's second signal, the earth clocks stop counting, and compare their result to the result the satellite reported.

 

In the first scenario, the one-way signal transit time for an earthbound observer should be 57.75 days, or 115.50 days for a two-way exchange; in the second scenario, the one-way signal transit time should be about 505.2 seconds, or 1010.4 seconds for a two-way exchange.

 

My question is this: would the satellite and the earth count the same amount of time elapsed between receipt of signals?

[DrRocket]

 

My question is this: would the satellite and the earth count the same amount of time elapsed between receipt of signals?

 

 

And per my post above, the answer is "no".

[Elen Sila]

And per my post above, the answer is "no".

 

And as per my previous posts, if the answer is an unqualified "no", then I don't understand relativity theory.

 

Now, I could accept a qualified no. For example, time dilation in the first scenario could be justified in that the craft must be constantly accelerating by firing its engines towards the sun; and the time dilation in the second scenario could be justified in that the craft, while maintaining the same distance to the earth, is not constantly travelling in the same direction. These would be qualified reasons why the satellite and the earth would not share a parallel experience of the passage of time.

 

Let's take a third scenario, much simpler and more topical than my first two. I am living in an observatory located in Ecuador, at zero degrees' latitude. Directly over my head, night and day, there is a geostationary satellite, hovering at an altitude of 35786 kilometers. At any given moment, if you were to draw my straight-line trajectory, and the satellite's straight-line trajectory, the two lines would be parallel; we are travelling in the same direction. Likewise, at any given moment, if you were to measure my distance to the satellite, and compare it to the distance between me and the satellite at any other given moment, the figure would always be the same. That satellite and I are maintaining a constantly equal distance from each other.

 

Now obviously we're separated by 119 milliseconds of light-time (239 milliseconds both ways), so it's not fair to say we're in the same reference frame, per se. Nevertheless, by passing a signal back and forth between us, and comparing our measurements of the passage of time between receipts, we should be able to determine that, all other considerations (such as difference in gravity) ignored, we are experiencing the passage of time at the same rate, and no time dilation is occurring.

 

Now, that's not to say there couldn't be a difference in time perception for gravitational reasons; after all, I'm about 6.6 times closer to the earth's center of mass than the satellite is; so the earth's gravity is pulling on me about 43.7 times harder, by the inverse square law. And it would make sense, if that geostationary satellite were going to be used as a global positioning satellite, to take relativistic time dilation into account, if for that reason only.

 

But, after having accounted for gravitational time dilation, it doesn't seem to me like any time dilation should be incurred due to difference in relative velocity.

Edited August 29, 2011 by Elen Sila

[csmyth3025]

And as per my previous posts, if the answer is an unqualified "no", then I don't understand relativity theory.

The short answer is that you don't understand relativity theory.

 

The long answer - with all the gory calculations - can be found in the Wikipedia article on "Error analysis for the Global Positioning System", specifically the section on "calculation of time dilation" here:

 

http://en.wikipedia....f_time_dilation

 

Although this article relates specifically to GPS satelites, the calculations are also applicable to your scenario.

 

Chris

[Elen Sila]

The short answer is that you don't understand relativity theory.

 

Sigh. I guess not.

 

Alright. A couple miscellaneous questions then.

 

1. Would an atomic clock on the north pole and an atomic clock on the equator run at different speeds (as measured by timings of signal exchanges)?

 

2. Let's say the atomic clock on the north pole is located on a platform that rotates clockwise once every sidereal day, so that the clock is essentially standing still with respect to the center of the earth. Now let's say you have a second atomic clock on an airplane that's flying westward along the equator at an altitude of 10 kilometers and a speed of 1677 kilometers per hour, thus also standing still with respect to the center of the earth. If a system of radio towers is set up to relay signals back and forth between the plane and the outpost at the north pole, and the operators on the plane and at the north pole both compare their measurement of the timings of signal exchanges, will there be a difference in the perception of time between the plane and the pole?

Edited August 29, 2011 by Elen Sila

[IM Egdall]

I guess I just don't get time dilation. In order to say "Spacecraft A is moving faster than planet B; therefore spacecraft A is experiencing time slower than planet B," you must have an absolute point of reference from which to determine A's and B's absolute velocities. If you only base time dilation off relative velocity, then an observer onboard spacecraft A would view planet B as moving faster, and thus planet B would be the one experiencing time at a slower rate. They can't both be experiencing time slower than the other; that's a contradiction.

 

I think a lot of people have this question when they start really thinking about relativity. Let me try to give you an answer. Say stationary Sam is at rest and Moving Mary is moving in uniform motion (constant speed and constant direction). You are correct: from Mary's point-of-view she is at rest and Sam is the one that is moving.

 

So Sam sees Mary's clock running slower than hers because Mary is moving with respect to him. AND Mary sees Sam's clock running slower than hers because she sees Sam moving with respect to her! As looney as this sounds, this is just what special relativity predicts. Time effects are symmetric between Sam and Mary. THERE IS NO ABSOLUTE REFERENCE FRAME.

 

But both watches can't both be running slow compared to the other, can they? To check this, we have to get the two watches side-by-side. And this action resolves the conundrum.

 

Say in order to compare the two watches side-by-side, Mary decides to travel to Sam. To do this, she must change her speed and direction. So she is no longer in uniform motion (more formally no longer in an inertial reference frame). And any change in speed and/or direction is acceleration (in the physics definition.) This acceleration by Mary destroys the symmetry. So because she experiences this acceleration, it is Mary's time which runs slower than Sam's.

 

And when Sam and Mary compare watches side-by-side, they find that yes, Mary's watch has run slower than Sam's.

 

Now I have seen a number of ways to show this, using special or general relativity. The simplest explanation I have found uses general relativity's gravitational time dilation. When Mary slows down and turns around to get back to Sam, she is pressed against her vehicle like gravity. This gravity effect slows her time down.

 

Sam, in this example, stays in uniform motion. So he does not experience acceleration. So there are no acceleration/gravity effects on his time. So time does not slow down for Sam, only Mary.

 

If you want a detailed explanation per special relativity, go to my website, marksmoderrnphysics.com and click on Its Relative, Archives, and The Twins Paradox. (Here the effect is explained as a combination of time dilation and the Doppler effect.)

Edited August 29, 2011 by IM Egdall

[swansont]

Sigh. I guess not.

 

Alright. A couple miscellaneous questions then.

 

1. Would an atomic clock on the north pole and an atomic clock on the equator run at different speeds (as measured by timings of signal exchanges)?

 

2. Let's say the atomic clock on the north pole is located on a platform that rotates clockwise once every sidereal day, so that the clock is essentially standing still with respect to the center of the earth. Now let's say you have a second atomic clock on an airplane that's flying westward along the equator at an altitude of 10 kilometers and a speed of 1677 kilometers per hour, thus also standing still with respect to the center of the earth. If a system of radio towers is set up to relay signals back and forth between the plane and the outpost at the north pole, and the operators on the plane and at the north pole both compare their measurement of the timings of signal exchanges, will there be a difference in the perception of time between the plane and the pole?

 

1. No, because the earth is not a rigid sphere. The oblateness causes a change in the gravitational time dilation that cancels the effects of the kinematic dilation, as long as you are on the geoid. This is convenient, because it makes clocks run at the same rate anywhere on the surface of the earth at the geoid — you only have to correct for elevation. Movement or signal exchange gives you a Sagnac term but this is purely geometrical in the earth-centered, earth-fixed frame and is zero for N-S exchanges.

 

2. The plane-bound clock is moving faster than the earth because it has a greater radius and the same angular speed. The speed increase is only a part in 640 of the already-existing part in 10^12 dilation. The clock will run faster by about a part in 10^12 owing to the gravitational time dilation.

[Elen Sila]

Say in order to compare the two watches side-by-side, Mary decides to travel to Sam. To do this, she must change her speed and direction.

 

But they're explicitly not doing that in my scenarios. Nobody is changing speed or direction. They're comparing passage of time by sending signals back and forth and comparing the time intervals they perceive between receipts of the signals.

 

So, Mary sends a signal to Sam, then Sam sends a signal back, then Mary tells Sam how long it took him to respond, from her perspective, then Sam compares this to the time he measured between signals. Thus, they are able to compare passage of time without changing their speed or direction.

[csmyth3025]

But they're explicitly not doing that in my scenarios. Nobody is changing speed or direction. They're comparing passage of time by sending signals back and forth and comparing the time intervals they perceive between receipts of the signals.

 

So, Mary sends a signal to Sam, then Sam sends a signal back, then Mary tells Sam how long it took him to respond, from her perspective, then Sam compares this to the time he measured between signals. Thus, they are able to compare passage of time without changing their speed or direction.

Various military and civilian GPS navigation devices communicate with GPS satelites millions of times each day. The comparison of their clock times is as described in the Wikipedia article on "Error analysis for the Global Positioning System" that I cited earlier.

 

Are you saying that you don't understand time dilation as predicted by relativity theory, or are you expressing your doubt that this effect is real?

 

Chris

[J.C.MacSwell]

The thing is that they aren't in the same inertial frame. The satellite is in a forced orbit, which puts it in a rotating frame and under constant acceleration (as evidenced by the fact that the ship has to be constantly firing its engines is order to maintain its orbit.)

 

I think this can be misunderstood.

 

They are both in an infinite number of inertial frames (as well as other frames). They do not have the same shared rest frame (at least not an inertial one), but are still in existence in each others, even if their inertial rest frames are constantly changing and are not the preferred frame to consider their movements in.

 

I think in strong gravitational fields inertial frames can be only defined locally, so something far enough away might not be able to have a position defined in that frame, but I don't think this applies here (not significantly)

Edited August 30, 2011 by J.C.MacSwell

[Elen Sila]

Are you saying that you don't understand time dilation as predicted by relativity theory, or are you expressing your doubt that this effect is real?

 

Confusion as to how it can be real (albeit recognition that it is), and profound desire to one day meet a professor or layperson who can explain it to me in terms I understand. This desire manifests in the form of visiting science forums to ask people hypothetical scenarios, in the hopes that someone's explanation of one or more of them might be the explanation that finally gets my understanding to "click".

 

Basically, I can understand time dilation as an effect of acceleration, or of being in a gravitational field. That would be some sort of absolute, physical effect. What I can't understand is time dilation as a mere product of being in different reference frames (except as a Doppler effect) – in particular, when you can compare reference frames that are in uniform circular motion, using the signal-timing method I've described in this thread. The signal-timing method I've described should allow for comparison of time passage without needing to change reference frames; and what, logically, it should show, is that, minus gravitational or accelerative effects, time dilation does not occur between people just because they're in different frames.

 

Obviously, that's not what actually happens. And I recognize that, but don't understand it.

 

I imagine any one of you could probably explain it to me if we were in person; I tend to be a pretty visual thinker (hence the uploaded diagrams). I'm trying my hardest to glean understanding from your responses, but I'm still just drawing a blank – hence, why I keep asking different hypothetical questions. Sorry if I'm wasting everyone's time.

Edited August 30, 2011 by Elen Sila

[IM Egdall]

But they're explicitly not doing that in my scenarios. Nobody is changing speed or direction. They're comparing passage of time by sending signals back and forth and comparing the time intervals they perceive between receipts of the signals.

 

So, Mary sends a signal to Sam, then Sam sends a signal back, then Mary tells Sam how long it took him to respond, from her perspective, then Sam compares this to the time he measured between signals. Thus, they are able to compare passage of time without changing their speed or direction.

 

 

OK, assume Sam and Mary are in uniform motion with respect to each other, and they send timing signals to each other. From Sam's timing signals, Mary concludes his time is running slower. And from Mary's timing signals, Sam concludes that her time is running slower. As long as there is no change in speed or direction (no acceleration), both Sam and Mary observe the same thing -- symmetry is maintained.

 

There are two effects to take into account here: time dilation and the Doppler Effect. Again, I recommend you please read my article on the Twins Paradox to see the details. Click on:

 

http://www.marksmodernphysics.com/ and then click on Its Relative, then Archives, then The Twins Paradox.

Edited August 30, 2011 by IM Egdall

[Elen Sila]

OK, assume Sam and Mary are in uniform motion with respect to each other, and they send timing signals to each other. From Sam's timing signals, Mary concludes his time is running slower. And from Mary's timing signals, Sam concludes that her time is running slower.

 

You don't seem to be understanding the scenario I've set up.

 

Mary, upon achieving geostationary orbit, sends the following message to Sam, directly below her on the equator. "Dear Sam. My atomic clock will start running the moment I send this message. Please start your atomic clock the moment you receive this message."

 

Sam, upon receiving this message, sends the following message back. "Dear Mary. Message received! My atomic clock will start running the moment I send this message. Please stop your atomic clock the moment you receive this message."

 

Mary, upon receiving Sam's response, sends the following message back. "Dear Sam. Thanks! My atomic clock recorded that X milliseconds passed between my sending my message and my receiving your response. Please stop your atomic clock the moment you receive this message."

 

Sam, upon receiving Mary's response, sends the following message. "Dear Mary. Good work! My atomic clock recorded that Y milliseconds passed between my receiving your first message and my receiving your last message. See you when you get back to earth!"

 

If X is less than Y, then Y cannot be less than X. One of them must be perceiving time faster or slower than the other, or else they must not be experiencing time dilation.

Edited August 30, 2011 by Elen Sila

[csmyth3025]

You don't seem to be understanding the scenario I've set up.

 

Mary, upon achieving geostationary orbit, sends the following message to Sam, directly below her on the equator. "Dear Sam. My atomic clock will start running the moment I send this message. Please start your atomic clock the moment you receive this message."

 

Sam, upon receiving this message, sends the following message back. "Dear Mary. Message received! My atomic clock will start running the moment I send this message. Please stop your atomic clock the moment you receive this message."

 

Mary, upon receiving Sam's response, sends the following message back. "Dear Sam. Thanks! My atomic clock recorded that X milliseconds passed between my sending my message and my receiving your response. Please stop your atomic clock the moment you receive this message."

 

Sam, upon receiving Mary's response, sends the following message. "Dear Mary. Good work! My atomic clock recorded that Y milliseconds passed between my receiving your first message and my receiving your last message. See you when you get back to earth!"

 

If X is less than Y, then Y cannot be less than X. One of them must be perceiving time faster or slower than the other, or else they must not be experiencing time dilation.

Because Mary is in Geostationary orbit the following applies:

 

According to the theory of relativity, due to their constant movement and height relative to the Earth-centered, non-rotating approximately inertial reference frame, the clocks on the satellites are affected by their speed. Special relativity predicts that the frequency of the atomic clocks moving at GPS orbital speeds will tick more slowly than stationary ground clocks by a factor of , or result in a delay of about 7 μs/day, where the orbital velocity is v = 4 km/s, and c = the speed of light. The time dilation effect has been measured and verified using the GPS.

 

The effect of gravitational frequency shift on the GPS due to general relativity is that a clock closer to a massive object will be slower than a clock farther away. Applied to the GPS, the receivers are much closer to Earth than the satellites, causing the GPS clocks to be faster by a factor of 5×10^(-10), or about 45.9 μs/day. This gravitational frequency shift is noticeable.

 

When combining the time dilation and gravitational frequency shift, the discrepancy is about 38 microseconds per day

(ref. http://en.wikipedia....eral_relativity )

 

Keep in mind that GPS satellites are placed so that the orbit Earth twice per day at an altitude of about 20,184 km above the surface of the Earth. A geostationary orbit, by definition, orbits the Earth exactly once per day (it stays over the same spot on Earth all the time) and thus has a higher orbital altitude of about 35,786 km above the surface of the Earth.

 

Lets say for the sake of argument that Mary is on a GPS satellite when she transmits her message to Sam and it takes Sam 8.64 seconds to transmit his message back to Mary. This just happens to be 1/10,000 of a day. When they compare their times Mary will find that her clock shows 38 microseconds/10,000, or 3.8 picoseconds more on her clock than Sam. Mary's clock runs faster than Sam's because of the combined effect of both Special Relativity and General Relativity.

 

If Mary is actually in geostationary orbit this effect will be even greater because she will be orbiting above the surface of the earth at greater distance and her orbital velocity will therefore be less than it is on the GPS satellite. Thus the Special Relativistic effect of slowing down Mary's clock relative to Sam's will be less. Also, she will be in a weaker gravitational field. Thus, the General Relativistic effect causing her clock to run faster than Sam's will be more pronounced.

 

Chris

[swansont]

If X is less than Y, then Y cannot be less than X. One of them must be perceiving time faster or slower than the other, or else they must not be experiencing time dilation.

The symmetric condition is for inertial reference frames. Orbits and rotations involve accelerations, even if you were to do this without gravity. You cannot tell who is moving if the velocity is constant (inertial frame), but you can tell who is accelerating (non-inertial).

[Elen Sila]

If Mary is actually in geostationary orbit this effect will be even greater because she will be orbiting above the surface of the earth at greater distance and her orbital velocity will therefore be less than it is on the GPS satellite. Thus the Special Relativistic effect of slowing down Mary's clock relative to Sam's will be less. Also, she will be in a weaker gravitational field. Thus, the General Relativistic effect causing her clock to run faster than Sam's will be more pronounced.

 

So, even if they account for the gravitational time dilation effect, there will still be velocity-based time dilation, even though Sam and Mary are stationary relative to each other?

 

The symmetric condition is for inertial reference frames. Orbits and rotations involve accelerations, even if you were to do this without gravity. You cannot tell who is moving if the velocity is constant (inertial frame), but you can tell who is accelerating (non-inertial).

 

See, that makes sense to me. If the remaining time dilation in the Sam-Mary scenario, once gravitational difference has been accounted for, is due only to acceleration, then it makes sense.

Edited August 31, 2011 by Elen Sila