I What I understand about Time Dilation

[name123]

As I understand it, time dilation can occur under gravity or acceleration, which can be referred to as Gravity Time Dilation and can also appear to be happening when two things are in different frames of reference, which can be referred to as Velocity Time Dilation.

With Gravity Time Dilation, as I understand it there has been objective evidence that there is time dilation under gravity or acceleration.

With Velocity Time Dilation is the evidence here thought to be relative rather than objective?

Imagine for example two space ships were to pass each other. From Spaceship A's perspective, Spaceship B1 might be measured to have passed it at 0.2c in the +ve direction, and from Spaceship B1's perspective, Spaceship A1 might be measured to have passed it at 0.2c in the -ve direction. As I understand it, both would be stating that the clock of the other was going slower than its own clock. It would seem like a logical contradiction for that to objectively be the case, but it could be claimed that there is no objective truth on the matter, and that the truth about the situation is relative.

But supposing that unknown to the people on Spaceship A1 and Spaceship B1, Spaceship A1 was in the same frame of reference as Spaceship A2, and Spaceship B1 was in the same frame of reference as Spaceship B2, and that Spaceship A2 and Spaceship B2 were involved in a twin paradox experiment, where Spaceship B2 had accelerated away from Spaceship A2 and was going to go away and then back again.

As I understand it in the twin paradox experiment the clock on B2 would be thought to be objectively running slower than the clock on A2.

But if that was the case, then would the B1 not be running at the same rate as the B2 clock (whether it was in the same frame of reference as B2's outward journey unaccelerating velocity or B2's inward journey unaccelerating velocity) since they are in the same frame of reference, and likewise A1 be in the same frame of reference as A2. Such that while clock B1 could be thought to be running slower than the clock on A1 from A1's perspective, and the clock A1 could be thought to be running slower than the clock on B1 from B1's perspective, objectively the clock on B1 would be running slower than the clock on A1?

Is there any experiment not involving any Gravity Time Dilation which indicate that Velocity Time Dilation actually happens, rather than just appearing to?

 

[SlowThinker]

Spaceship A1 and Spaceship B1, Spaceship A1 was in the same frame of reference as Spaceship A2, and Spaceship B1 was in the same frame of reference as Spaceship B2, and that Spaceship A2 and Spaceship B2 were involved in a twin paradox experiment, where Spaceship B2 had accelerated away from Spaceship A2 and was going to go away and then back again.

As I understand it in the twin paradox experiment the clock on B2 would be thought to be objectively running slower than the clock on A2.

You may want to clarify what spaceship B2 actually does.
1) It can't be in one reference frame the whole way, because it must change speed at least once to get back to A2.
2) Its clock can't run at the same speed as B1's clock if it's running at different speed.
3) Are all 4 ships on the same line, or is B2 going in some random direction? I hope not because it would complicate things greatly.

In general, the twin paradox is resolved by understanding the discontinuity at the turning point.
Velocity time dilation is verified by muon's decay, which takes much longer for a moving muon compared to a standing or slow one.
There is a way to understand twin paradox through gravitational time dilation, but it's more of an expert exercise and little of an explanation.

 

[PeroK]

Is there any experiment not involving any Gravity Time Dilation which indicate that Velocity Time Dilation actually happens, rather than just appearing to?

The experiments at CERN, for example, show that unstable particles live longer in the lab frame depending on their velocity. The faster they are moving the longer they live, in complete agreement with SR.

SR is 113 years old and very well tested and confirmed.

 

[name123]

You may want to clarify what spaceship B2 actually does.
1) It can't be in one reference frame the whole way, because it must change speed at least once to get back to A2.
2) Its clock can't run at the same speed as B1's clock if it's running at different speed.
3) Are all 4 ships on the same line, or is B2 going in some random direction? I hope not because it would complicate things greatly.

In general, the twin paradox is resolved by understanding the discontinuity at the turning point.
Velocity time dilation is verified by muon's decay, which takes much longer for a moving muon compared to a standing or slow one.
There is a way to understand twin paradox through gravitational time dilation, but it's more of an expert exercise and little of an explanation.

1) B1 It won't be in the same frame of reference as B2 the whole way. But just pick either the frame of reference B2 is in as it leaves or the one it is in as it returns to A2. I don't think it makes a difference which one you pick.
2) It will be at the same velocity as B2. What velocity that would be would depend on whether you pick the point where B2 is leaving A2 or returning to A2.
3) The same line.

 

[name123]

The experiments at CERN, for example, show that unstable particles live longer in the lab frame depending on their velocity. The faster they are moving the longer they live, in complete agreement with SR.

SR is 113 years old and very well tested and confirmed.

In CERN is the particle not going around a circuit, and would that not involve some kind of acceleration (centripetal acceleration?)?

Also like with the A1, B1, A2, B2 example I gave, with A1 and B1 either one could appear to have a slower clock depending on which frame of reference it was measured from. Though given the A2, B2 situation, would the situation of which clock was going slower not have to objectively only be one way?

 

[PeroK]

In CERN is the particle not going around a circuit, and would that not involve some kind of acceleration (centripetal acceleration?)?

Also like with the A1, B1, A2, B2 example I gave, with A1 and B1 either one could appear to have a slower clock depending on which frame of reference it was measured from. Though given the A2, B2 situation, would the situation of which clock was going slower not have to objectively only be one way?

The particles that crash into each other are accelerated but the resulting particles do not.

Also, note that, acceleration does not cause time dilation. Although there are those who would argue that point!

The basic paradox you refer to is explained by The fact that two clocks in relative motion can only pass once, unless one or both of them changes its inertial reference frame. It's changing your inertial reference frame, and with it your simultaneity convention, that is The key to these paradoxes, not acceleration.

 

[PeroK]

@name123 there is a general issue that many students learn about time dilation and length contraction, but not the relativity of simultaneity. These students then present time dilation paradoxes that apparently cannot be explained. And, are often very reluctant to accept that SR includes the relativity of simultaneity, preferring to insist that the paradoxes debunk SR.

There's another thread entitled "resolving observations in two reference frames" that it may be worth looking at, where calculations involving time dilation were inadequate to solve the problem.

 

[name123]

The particles that crash into each other are accelerated but the resulting particles do not.

Also, note that, acceleration does not cause time dilation. Although there are those who would argue that point!

The basic paradox you refer to is explained by The fact that two clocks in relative motion can only pass once, unless one or both of them changes its inertial reference frame. It's changing your inertial reference frame, and with it your simultaneity convention, that is The key to these paradoxes, not acceleration.

So the equivalence between gravity and acceleration doesn't include time dilation?

In the Twin Paradox, I thought that the idea was that when they meet one clock would be slower than the other (the one that accelerated away would be the one that went slower), and that it would be influenced by how long the departing twin traveled away for, and at what velocity. So I was assuming that for A2 and B2, B2's clock would be going slower than A2's both on the outward journey and the return journey. Am I mistaken?

 

[PeroK]

So the equivalence between gravity and acceleration doesn't include time dilation?

This equivalence is not what you think. It's between an accelerating reference frame and a gravitational field.

If you have an accelerating rocket with clocks At the front and rear, then an external observer will measure the time dilation of each clock entirely based on its velocity. The magnitude of the acceleration has no effect, per se.

But, inside the rocket, an observer ( who is accelerating with the rocket) will measure the rear clock time dilated relative to the front clock. This time dilation is equivalent to that where the front clock is higher in a gravitational field.

The greater the acceleration, the greater the equivalent difference in gravitational potential across the rocket.

This is essentially the equivalence principle.

 

[PeroK]

So the equivalence between gravity and acceleration doesn't include time dilation?

In the Twin Paradox, I thought that the idea was that when they meet one clock would be slower than the other (the one that accelerated away would be the one that went slower), and that it would be influenced by how long the departing twin traveled away for, and at what velocity. So I was assuming that for A2 and B2, B2's clock would be going slower than A2's both on the outward journey and the return journey. Am I mistaken?

The resolution to the twin paradox is not simple. There are perhaps hundred threads on here alone.

I prefer a version with no acceleration. Technically, the traveling twin is the one who changes inertial reference frame. That results in what is called differential ageing.

The time dilation itself is symmetric on both the outward and return journeys, but the change of reference frame causes a change in the simultaneity convention.

In any case, acceleration does not directky cause the time dilation to be asymmetric, it's fundamentally the change of reference frame that does that.

 

[Herman Trivilino]

Imagine for example two space ships were to pass each other. From Spaceship A's perspective, Spaceship B1 might be measured to have passed it at 0.2c in the +ve direction, and from Spaceship B1's perspective, Spaceship A1 might be measured to have passed it at 0.2c in the -ve direction. As I understand it, both would be stating that the clock of the other was going slower than its own clock.

This is not a complete way to state the situation. If each had only one clock they would not be able to reach that conclusion. A needs two clocks, separated along the line of relative motion, to be able to determine that B's clock is running slow. But B will not agree that A has synchronized his two clocks correctly, and can attribute A's conclusion to the way A synchronized his two clocks.

Likewise for B.

Until you explore the above and attempt to understand it you will not be able to sort out your misunderstanding. It's the relationship between proper time and coordinate time that first needs to be understand before the symmetry of time dilation can be understood.

It would seem like a logical contradiction for that to objectively be the case, but it could be claimed that there is no objective truth on the matter, and that the truth about the situation is relative.

There is an abundance of evidence indicating that it happens. It only seems like a logical contradiction if you don't understand it.

If it didn't happen, engineers who design particle accelerators would be creating entirely different designs. Likewise for the engineers responsible for maintaining the GPS.

 

[Herman Trivilino]

In the Twin Paradox, I thought that the idea was that when they meet one clock would be slower than the other

No. One clock will show that less proper time has elapsed on it than the other. That's a comparison of two proper times.

Time dilation (what you are calling velocity time dilation) is a comparison of a proper time to a coordinate time, not a comparison of two proper times.

 

[Janus]

As I understand it, time dilation can occur under gravity or acceleration, which can be referred to as Gravity Time Dilation and can also appear to be happening when two things are in different frames of reference, which can be referred to as Velocity Time Dilation.

With Gravity Time Dilation, as I understand it there has been objective evidence that there is time dilation under gravity or acceleration.

With Velocity Time Dilation is the evidence here thought to be relative rather than objective?

Imagine for example two space ships were to pass each other. From Spaceship A's perspective, Spaceship B1 might be measured to have passed it at 0.2c in the +ve direction, and from Spaceship B1's perspective, Spaceship A1 might be measured to have passed it at 0.2c in the -ve direction. As I understand it, both would be stating that the clock of the other was going slower than its own clock. It would seem like a logical contradiction for that to objectively be the case, but it could be claimed that there is no objective truth on the matter, and that the truth about the situation is relative.

But supposing that unknown to the people on Spaceship A1 and Spaceship B1, Spaceship A1 was in the same frame of reference as Spaceship A2, and Spaceship B1 was in the same frame of reference as Spaceship B2, and that Spaceship A2 and Spaceship B2 were involved in a twin paradox experiment, where Spaceship B2 had accelerated away from Spaceship A2 and was going to go away and then back again.

As I understand it in the twin paradox experiment the clock on B2 would be thought to be objectively running slower than the clock on A2.

But if that was the case, then would the B1 not be running at the same rate as the B2 clock (whether it was in the same frame of reference as B2's outward journey unaccelerating velocity or B2's inward journey unaccelerating velocity) since they are in the same frame of reference, and likewise A1 be in the same frame of reference as A2. Such that while clock B1 could be thought to be running slower than the clock on A1 from A1's perspective, and the clock A1 could be thought to be running slower than the clock on B1 from B1's perspective, objectively the clock on B1 would be running slower than the clock on A1?

Is there any experiment not involving any Gravity Time Dilation which indicate that Velocity Time Dilation actually happens, rather than just appearing to?

What you've run into is a common stumbling block for those first learning Relativity. It is the distinction between "time dilation" and "total difference in accumulated time".
Let's change your set up a bit. Let's consider three spaceships A, B and C and the Earth. Spaceship A is traveling away from the Earth at a constant 0.6c(relative to the Earth) and Spaceship B is traveling towards the Earth in the opposite direction at 0.6c. Spaceship C starts at the Earth, travels away at 0.6c, then turns around and returns to the Earth at the same speed (ship C follows the basic twin paradox scenario).
During the outbound leg of ship C:
Earth will measure the clock on ship's A, B and C as ticking 0.8 as fast as its own.
Ship A will measure the clock on Ship C as ticking at the same rate as its own, the Earth clock ticking at a rate of 0.8 and the clock on ship B ticking at a rate of 0.47
Ship B will measure the Earth clock ticking at a rate 0.8 of its own, and the clocks on ships A and C ticking at a rate 0.47 of its own
Ship C will measure Ship A's clock as ticking at the same rate as its own, the Earth clock ticking at a rate of 0.8, and Ship B's clock ticking at a rate of 0.47

During the return leg of ship C:
Earth will still measure the clocks on all three clocks as ticking at a rate of 0.8
Ship A will measure the Ship Clock as ticking at a rate of 0.47, the Earth clock ticking at a rate of 0.8, and Ship B's clock ticking at the same rate as his own.
Ship B will measure the Earth clock as ticking at 0.8, the Ship C clock as ticking at the same rate as his own, and Ship A's clock ticking at 0.47
Ship C will measure ship A's clock as ticking at 0.47, The Earth clock at 0.8 and Ship B's clock ticking at the same rate as his own.

These are all time dilation measurements, or one to one comparisons between tick rates of given clocks at any particular moment.

However, to work out the total accumulated time difference between Earth and Ship C for Ship C entire trip, you have to consider more than just time dilation. There are other relativistic effects that come into play.
For instance, length contraction.

Let's assume that the distance that ship C travels from the Earth before turning around is 0.6 light years. Thus according to the Earth ship C spends 1 year going away and 1 year coming back. But, for ship's A, B and C, for which the Earth has a relative velocity of 0.6c, the same distance is only measured as being 0.48 ly.
Thus during the outbound leg, both Ship A and C will conclude that it took 0.48ly/0.6c = 0.8 years by their clocks to reach the point of turnaround.
and during the Inbound leg, Both Ships B and C will conclude that it took 0.48ly/0.6c = 0.8 years by their clocks to reach the point of turnaround.

Ergo, Ship C will conclude that a total of 1.6 years will have elapsed for it during the trip, which is the same conclusion that the Earth came to.

Its a bit more complicated to work out what ship A concludes for the whole trip.
First, we know that It measures 0.8 years as passing on its own clock and Ship C's clock during the Outbound leg
Second, the Earth clock is measured as ticking off 0.8*0.8 yr = 0.64 yr during this time.
The return leg is a bit more tricky. We have to use relativistic velocity addition to determine that Ship A measures Ship C's relative velocity to be ~0.882c (it was this relative velocity I used to get the 0.47 factor for time dilation I gave above.
This gives a difference of velocity between Earth and Ship C of ~0.28c according to Ship A. We also know that Ship A measures the distance between Earth and the turn around as being 0.48 ly . Thus by Ship A's clock it should take 0.48 ly/ 0.282 c = ~1.7 yrs for Ship to complete the return leg. During which time the Earth clock accumulates 1.7yrs*0.8 1.36 yrs, which when added to the 0.64 yrs it accumulated during the outbound leg of ship C equals a total of 2 yrs which agrees with what the Earth itself measured.
Ship C's clock will accumulate 1.7y*0.47 = 0.8 yrs during the return leg. Added to the 0.8y accumulated during the outbound leg, gives 1.6 yrs total for the trip, agreeing with both the Earth's and Ship C's measurement.

Note something here. While the Earth measured that it aged 1 year during both legs, this isn't what Ship A measured. Ship A measured that the Earth aged 0.64 years during the outbound leg, and 1.36 years during the return leg. Same total time for the two legs but different leg times.

we can work out the same thing for Ship B and it will also agree as to the total time accumulated by Earth and ship C.

All that;s left is to work out things from Ship C's perspective.

Outbound leg takes 0.8 yrs (due to length contraction) and inbound take the same, for a total trip time of 1.6 years
Earth ages 0.8y*0.8 = 0.64 yrs during outbound leg and the same during the inbound leg for a total of 1.28 yrs.
This however, does not jive with the two years the Earth and the other two ships got for an answer. So what went wrong?

The answer lies in the fact that Ship C had to change its velocity between outbound and return legs. and this is a whole different kettle of fish than when dealing with unchanging velocities. When something is moving at constant speed it is in an inertial frame, But while it is changing velocity, it is in a non-inertial frame. and the rules for dealing with measurements made from within non-inertial frames are different than those for dealing with inertial frames.

For instance, if you are under an acceleration, You will measure clocks in the direction that you are accelerating as running fast, even if they are not moving with respect to you. The further away a clock is, the faster it will run as measured by you. If the clock is moving relative to you, this add an additional factor you need to deal with.

So what this means for ship C is that, as it changes velocity from going away to returning to Earth, it is undergoing an acceleration towards the Earth, and since Earth is quite a distance away in this direction, ship C will measure* the clock on Earth as running fast, and will the Earth clock will accumulate 0.72 yrs during this period, which when added to the 1.28 yrs accumulated during the coasting legs of the trip brings the total accumulated time for the Earth up to the proper 2 years.

Again, while ship C also agrees with everyone else as to the total accumulated time for the Earth, it measures it as having gotten there by a different route.

* It is important here to note that throughout this post, when I use the word "measure", I do not mean "visually perceive". What you would visually see is complicated by things such as aberration, Doppler shift, light propagation delays, etc. (for example, the Earth would measure the Outbound leg of Ship C as taking 1 year, however, an Earth observer wouldn't visually see ship C reach its turnaround point until 1.6 yrs after it left. This is due to the extra time it takes light to travel from that point to the Earth. ) So by "measure", I mean what's left over after we account for these other effects.

 

[russ_watters]

With Gravity Time Dilation, as I understand it there has been objective evidence that there is time dilation under gravity or acceleration.

With Velocity Time Dilation is the evidence here thought to be relative rather than objective?

Both effects are observed simultaneously in GPS satellites.

Is there any experiment not involving any Gravity Time Dilation which indicate that Velocity Time Dilation actually happens, rather than just appearing to?

This is not a reasonable or necessary request. Scientific instruments are so sensitive that the gravity effects are noticeable if you place two clocks on different shelves, so it would be very difficult to do an experiment with no gravitational impact. But you can easily calculate the two effects, to account for them separately.

[experiments with high energy particles notwithstanding -- I prefer ones with real clocks]

 

[Nugatory]

Is there any experiment not involving any Gravity Time Dilation which indicate that Velocity Time Dilation actually happens, rather than just appearing to?

The muon lifetime observations (take a look at the sticky thead at the top of this forum: https://www.physicsforums.com/threads/faq-experimental-basis-of-special-relativity.229034/) show time dilation in the absence of any significant gravitational effect.

However, it's not necessary to do this to confirm the effects of relative velocity.

Back up a moment to a much simpler theory, Newton's law of gravity. What was so special about it? It predicts that if you drop something, it will fall - but people have known that forever, probably even before they were people. Every monkey knows that, and watching my cat play at pushing objects off a shelf, I'm pretty sure that she knows it too. No, the big deal with Newton's laws is that they predict the exact speed and trajectory of the dropped object; we can compare these quantitative predictions with observations and conclude that we really have learned something important about the way the universe works.

Likewise, we can calculate the exact effect of gravitational time dilation and velocity-based time dilation in those situation where both are present. This is a very wide range of very different situations (the things referenced by the FAQ I linked above, and everything mentioned by other posters above) with very different contributions from gravity and velocity - but the results always match. So it is fair to say that both effects are well and thoroughly confirmed even without experiments that isolate each one.

 

[name123]

This equivalence is not what you think. It's between an accelerating reference frame and a gravitational field.

If you have an accelerating rocket with clocks At the front and rear, then an external observer will measure the time dilation of each clock entirely based on its velocity. The magnitude of the acceleration has no effect, per se.

But, inside the rocket, an observer ( who is accelerating with the rocket) will measure the rear clock time dilated relative to the front clock. This time dilation is equivalent to that where the front clock is higher in a gravitational field.

The greater the acceleration, the greater the equivalent difference in gravitational potential across the rocket.

This is essentially the equivalence principle.

So from the outside, the time dilation is as you would expect given the velocities. But the time dilation with respect velocity is normally relative, but with the acceleration it is objective as can be observed from the inside of the rocket (if acceleration stopped and the clocks were bought together, one would have "ticked" less than the other). With CERN, where the particles undergo acceleration due to moving in a circle, can one tell if the time dilation relative or objective?

 

[name123]

What you've run into is a common stumbling block for those first learning Relativity. It is the distinction between "time dilation" and "total difference in accumulated time".
Let's change your set up a bit. Let's consider three spaceships A, B and C and the Earth. Spaceship A is traveling away from the Earth at a constant 0.6c(relative to the Earth) and Spaceship B is traveling towards the Earth in the opposite direction at 0.6c. Spaceship C starts at the Earth, travels away at 0.6c, then turns around and returns to the Earth at the same speed (ship C follows the basic twin paradox scenario).
During the outbound leg of ship C:
Earth will measure the clock on ship's A, B and C as ticking 0.8 as fast as its own.
Ship A will measure the clock on Ship C as ticking at the same rate as its own, the Earth clock ticking at a rate of 0.8 and the clock on ship B ticking at a rate of 0.47
Ship B will measure the Earth clock ticking at a rate 0.8 of its own, and the clocks on ships A and C ticking at a rate 0.47 of its own
Ship C will measure Ship A's clock as ticking at the same rate as its own, the Earth clock ticking at a rate of 0.8, and Ship B's clock ticking at a rate of 0.47

During the return leg of ship C:
Earth will still measure the clocks on all three clocks as ticking at a rate of 0.8
Ship A will measure the Ship Clock as ticking at a rate of 0.47, the Earth clock ticking at a rate of 0.8, and Ship B's clock ticking at the same rate as his own.
Ship B will measure the Earth clock as ticking at 0.8, the Ship C clock as ticking at the same rate as his own, and Ship A's clock ticking at 0.47
Ship C will measure ship A's clock as ticking at 0.47, The Earth clock at 0.8 and Ship B's clock ticking at the same rate as his own.

These are all time dilation measurements, or one to one comparisons between tick rates of given clocks at any particular moment.

However, to work out the total accumulated time difference between Earth and Ship C for Ship C entire trip, you have to consider more than just time dilation. There are other relativistic effects that come into play.
For instance, length contraction.

Let's assume that the distance that ship C travels from the Earth before turning around is 0.6 light years. Thus according to the Earth ship C spends 1 year going away and 1 year coming back. But, for ship's A, B and C, for which the Earth has a relative velocity of 0.6c, the same distance is only measured as being 0.48 ly.
Thus during the outbound leg, both Ship A and C will conclude that it took 0.48ly/0.6c = 0.8 years by their clocks to reach the point of turnaround.
and during the Inbound leg, Both Ships B and C will conclude that it took 0.48ly/0.6c = 0.8 years by their clocks to reach the point of turnaround.

Ergo, Ship C will conclude that a total of 1.6 years will have elapsed for it during the trip, which is the same conclusion that the Earth came to.

Its a bit more complicated to work out what ship A concludes for the whole trip.
First, we know that It measures 0.8 years as passing on its own clock and Ship C's clock during the Outbound leg
Second, the Earth clock is measured as ticking off 0.8*0.8 yr = 0.64 yr during this time.
The return leg is a bit more tricky. We have to use relativistic velocity addition to determine that Ship A measures Ship C's relative velocity to be ~0.882c (it was this relative velocity I used to get the 0.47 factor for time dilation I gave above.
This gives a difference of velocity between Earth and Ship C of ~0.28c according to Ship A. We also know that Ship A measures the distance between Earth and the turn around as being 0.48 ly . Thus by Ship A's clock it should take 0.48 ly/ 0.282 c = ~1.7 yrs for Ship to complete the return leg. During which time the Earth clock accumulates 1.7yrs*0.8 1.36 yrs, which when added to the 0.64 yrs it accumulated during the outbound leg of ship C equals a total of 2 yrs which agrees with what the Earth itself measured.
Ship C's clock will accumulate 1.7y*0.47 = 0.8 yrs during the return leg. Added to the 0.8y accumulated during the outbound leg, gives 1.6 yrs total for the trip, agreeing with both the Earth's and Ship C's measurement.

Note something here. While the Earth measured that it aged 1 year during both legs, this isn't what Ship A measured. Ship A measured that the Earth aged 0.64 years during the outbound leg, and 1.36 years during the return leg. Same total time for the two legs but different leg times.

we can work out the same thing for Ship B and it will also agree as to the total time accumulated by Earth and ship C.

All that;s left is to work out things from Ship C's perspective.

Outbound leg takes 0.8 yrs (due to length contraction) and inbound take the same, for a total trip time of 1.6 years
Earth ages 0.8y*0.8 = 0.64 yrs during outbound leg and the same during the inbound leg for a total of 1.28 yrs.
This however, does not jive with the two years the Earth and the other two ships got for an answer. So what went wrong?

The answer lies in the fact that Ship C had to change its velocity between outbound and return legs. and this is a whole different kettle of fish than when dealing with unchanging velocities. When something is moving at constant speed it is in an inertial frame, But while it is changing velocity, it is in a non-inertial frame. and the rules for dealing with measurements made from within non-inertial frames are different than those for dealing with inertial frames.

For instance, if you are under an acceleration, You will measure clocks in the direction that you are accelerating as running fast, even if they are not moving with respect to you. The further away a clock is, the faster it will run as measured by you. If the clock is moving relative to you, this add an additional factor you need to deal with.

So what this means for ship C is that, as it changes velocity from going away to returning to Earth, it is undergoing an acceleration towards the Earth, and since Earth is quite a distance away in this direction, ship C will measure* the clock on Earth as running fast, and will the Earth clock will accumulate 0.72 yrs during this period, which when added to the 1.28 yrs accumulated during the coasting legs of the trip brings the total accumulated time for the Earth up to the proper 2 years.

Again, while ship C also agrees with everyone else as to the total accumulated time for the Earth, it measures it as having gotten there by a different route.

* It is important here to note that throughout this post, when I use the word "measure", I do not mean "visually perceive". What you would visually see is complicated by things such as aberration, Doppler shift, light propagation delays, etc. (for example, the Earth would measure the Outbound leg of Ship C as taking 1 year, however, an Earth observer wouldn't visually see ship C reach its turnaround point until 1.6 yrs after it left. This is due to the extra time it takes light to travel from that point to the Earth. ) So by "measure", I mean what's left over after we account for these other effects.

So once returned the proper time that has passed for ship C is less than the proper time that has passed for Earth. Its clocks have objectively "ticked" less than those on Earth, regardless of how it appeared to ship C. Not quite clear on how from C's perspective the Earth's clocks suddenly seem to have been ticking faster after all, and not have done 0.8 the amount of "ticks" that had happened on C. If you can explain that, that would be great, if not, it doesn't matter.

But if for ship C its clocks have objectively ticked less than those on Earth's. Then its clock was ticking slower as it had appeared to the observer on Earth.

Given that C's journey consisted of an outward leg, during which it's clocks were in synch with those of A and an inward leg during which it's clocks were in synch with those of B, then can one not conclude that like C the clocks on A and B were objectively ticking slower than those on Earth?

Supposing A goes out along side C, and passes B at the point C turns around, and as B passes A it sets its clock to the time on A's and comes back along side C. If one were to assume almost instantaneous acceleration and deceleration for C, then presumably its clock would be roughly in synch with A's on the outward journey and in synch with B's on the inward journey, and the time on B's, like C's would be less than the clock it passes on Earth as C returns. Unlike C, A and B would be in inertial frames.

 

[name123]

Both effects are observed simultaneously in GPS satellites.

With satellites are they not undergoing acceleration due to a circular orbit around the Earth? If so are you suggesting that if one were to return to Earth that even taking the acceleration and gravity effects into account, there will be another objective effect? If so then how are such effects relative?

 

[russ_watters]

With satellites are they not undergoing acceleration due to a circular orbit around the Earth? If so are you suggesting that if one were to return to Earth that even taking the acceleration and gravity effects into account, there will be another objective effect? If so then how are such effects relative?

You can literally calculate the effects separately. They have different equations. I'm not sure what you mean by "how are such effects relative" though.

This article tells how big each effect is:
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

[note; acceleration is rolled-up with gravity]

 

[name123]

The muon lifetime observations (take a look at the sticky thead at the top of this forum: https://www.physicsforums.com/threads/faq-experimental-basis-of-special-relativity.229034/) show time dilation in the absence of any significant gravitational effect.

However, it's not necessary to do this to confirm the effects of relative velocity.

Back up a moment to a much simpler theory, Newton's law of gravity. What was so special about it? It predicts that if you drop something, it will fall - but people have known that forever, probably even before they were people. Every monkey knows that, and watching my cat play at pushing objects off a shelf, I'm pretty sure that she knows it too. No, the big deal with Newton's laws is that they predict the exact speed and trajectory of the dropped object; we can compare these quantitative predictions with observations and conclude that we really have learned something important about the way the universe works.

Likewise, we can calculate the exact effect of gravitational time dilation and velocity-based time dilation in those situation where both are present. This is a very wide range of very different situations (the things referenced by the FAQ I linked above, and everything mentioned by other posters above) with very different contributions from gravity and velocity - but the results always match. So it is fair to say that both effects are well and thoroughly confirmed even without experiments that isolate each one.

But gravity or acceleration time dilation is objective regarding the slowing of the proper time. But velocity time dilation is supposed to be relative is it not? I have presumed that it is and that there are no objective results regarding the slowing of proper time for velocity time dilation. With the muon experiments are the muons not in a circular orbit, and thus undergoing acceleration?

 

[name123]

You can literally calculate the effects separately. They have different equations. I'm not sure what you mean by "how are such effects relative" though.

This article tells how big each effect is:
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

[note; acceleration is rolled-up with gravity]

In the article it states:
---
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 [2].

Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.
---

It seems as though the velocity was used in the Special Relativity calculation, and the Earth mass in the General Relativity calculation. But the velocity in the case of satellites are not in a straight line. They are in circular orbit. Thus I thought acceleration. And it seems from what the article states, that this was ignored and that the time dilation was calculated as though they were traveling in a straight line, though it seems you disagree. The article doesn't seem to specifically mention that it has been taken into account that the satellites are in circular orbit.

As I understand it with Special Relativity, from the satellites' perspective clocks on Earth should be ticking more slowly (ignoring gravity time dilation effect). I also thought that with Special Relativity the truth of which are ticking more slowly due to velocity time dilation was supposed to be relative. That there was no objective truth about the matter. But from what you seem to be saying is that while it may seem relative, the clocks can be brought together and it can be objectively observed which of the clocks had actually been ticking slower due to the velocity time dilation effect found in Special Relativity. Such that the truth of the matter might have seemed relative, but actually wasn't.

 

[russ_watters]

Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.
---

It seems as though the velocity was used in the Special Relativity calculation, and the Earth mass in the General Relativity calculation. But the velocity in the case of satellites are not in a straight line. They are in circular orbit. Thus I thought acceleration. And it seems from what the article states, that this was ignored and that the time dilation was calculated as though they were traveling in a straight line, though it seems you disagree. The article doesn't seem to specifically mention that it has been taken into account that the satellites are in circular orbit.

It isn't ignored, it's in there. Gravity and acceleration are related, so gravitational time dilation while in orbit has it's own equation:

https://en.m.wikipedia.org/wiki/Gravitational_time_dilation

As I understand it with Special Relativity, from the satellites' perspective clocks on Earth should be ticking more slowly (ignoring gravity time dilation effect). I also thought that with Special Relativity the truth of which are ticking more slowly due to velocity time dilation was supposed to be relative. That there was no objective truth about the matter. But from what you seem to be saying is that while it may seem relative, the clocks can be brought together and it can be objectively observed which of the clocks had actually been ticking slower due to the velocity time dilation effect found in Special Relativity. Such that the truth of the matter might have seemed relative, but actually wasn't.

Right. If the activities of the observers are not identical/symmetrical, then there is an objective difference that can be used to tell which clock is faster/slower.

 

[Nugatory]

But gravity or acceleration time dilation is objective regarding the slowing of the proper time. But velocity time dilation is supposed to be relative is it not? I have presumed that it is and that there are no objective results regarding the slowing of proper time for velocity time dilation.

It is relative ("frame-dependent" would be a much better way of saying it), but that does not preclude objective experimental results. Different observers moving at different speeds relative to one another will measure different lifetimes for the muon (or whatever other phenomenon we're considering), but the lifetime that any given observer will measure is an objective quantity that we can calculate from what we know of that observer's speed relative to the muon. We can, if necessary, describe the lifetime without any reference to the rate of time - we can note where the hands of a clock are pointing when the muon is created and where they are pointing when the muon decays.

With the muon experiments are the muon's not in a circular orbit, and thus undergoing acceleration?

Not. They are shooting pretty much straight down from the sky above us. They're in free fall so not accelerating, and gravitational effects are well and thoroughly negligible (affects their speed by maybe one part in one billion - but don't take my word for it, calculate for yourself!). We see similar situations when particles are coasting after being created in a collision.

 

[name123]

It isn't ignored, it's in there. Gravity and acceleration are related, so gravitational time dilation while in orbit has it's own equation:

https://en.m.wikipedia.org/wiki/Gravitational_time_dilation

I understand that, what I meant was that I had presumed they had not taken it into account in their calculations. That they had used the special relativity equations for the velocity time dilation, and had used the general relativity equations with a 0 velocity just to calculate the amount of time dilation that would have been expected given the gravity. One reason (apart from the way it was written) is that I would have thought if you used the General Relativity equations, and had included the velocity of the circular orbit, then you would have come to the correct answer. There would be no need to then calculate the special case equation and modify the answer from the General Relativity equation.

Right. If the activities of the observers are not identical/symmetrical, then there is an objective difference that can be used to tell which is faster/slower.

So there would be experiments to show that despite velocity time dilation appearing relative, actually it isn't. One would be shown to be correct and the other wrong.

 

[jartsa]

[note; acceleration is rolled-up with gravity]

Acceleration of a clock has no effect on the ticking rate of said clock. That is called the "clock hypothesis".

 

[name123]

It is relative ("frame-dependent" would be a much better way of saying it), but that does not preclude objective experimental results. Different observers moving at different speeds relative to one another will measure different lifetimes for the muon (or whatever other phenomenon we're considering), but the lifetime that any given observer will measure is an objective quantity that we can calculate from what we know of that observer's speed relative to the muon. We can, if necessary, describe the lifetime without any reference to the rate of time - we can note where the hands of a clock are pointing when the muon is created and where they are pointing when the muon decays.

But if things are frame dependent then will not observers in those different frames disagree about what the other person's clock time was relative to their own? I thought for example that each would consider the other's clock to tick slower than their own. So if observer A and observer B were in different frames of reference, and A were to observe the creation of the muon and its destruction and measure it on a clock in its frame of reference to take X seconds, then it could claim that the time that it lasted according to B's clock was longer, where as B would claim that the time on A's clock measured the life of the muon to be longer. So how could they agree what the times were on each other's clocks were when the muon was created and the muon was destroyed?

Not. They are shooting pretty much straight down from the sky above us. They're in free fall so not accelerating, and gravitational effects are well and thoroughly negligible (affects their speed by maybe one part in one billion - but don't take my word for it, calculate for yourself!). We see similar situations when particles are coasting after being created in a collision.

From the link on the page that you referred mentioned it did sound as though the muons were in a circular orbit in the experiments.

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html
---
Bailey et al., “Measurements of relativistic time dilation for positive and negative muons in a circular orbit,” Nature 268 (July 28, 1977) pg 301.Bailey et al., Nuclear Physics B 150 pg 1–79 (1979).

They stored muons in a storage ring and measured their lifetime. When combined with measurements of the muon lifetime at rest this becomes a highly relativistic twin scenario (v ~0.9994 c), for which the stored muons are the traveling twin and return to a given point in the lab every few microseconds. Muon lifetime at rest: Meyer et al., Physical Review 132, pg 2693; Balandin et al., JETP 40, pg 811 (1974); Bardin et al., Physics Letters 137B, pg 135 (1984). Also a test of the clock hypotheses (below).
---

 

[PeterDonis]

With Gravity Time Dilation, as I understand it there has been objective evidence that there is time dilation under gravity or acceleration.

Gravitational time dilation depends on position within the gravitational field, not on acceleration.

With satellites are they not undergoing acceleration due to a circular orbit around the Earth?

No; satellites are in free fall orbits, with zero proper acceleration. But in any case, acceleration is irrelevant to gravitational time dilation--see above.

 

[PeterDonis]

From the link on the page that you referred mentioned it did sound as though the muons were in a circular orbit in the experiments.

There are actually two different experimental tests with muons. One is muons in storage rings, described in the references you mention. The other is muons created high in the Earth's atmosphere by cosmic rays, and measured when they reach the Earth's surface. See, for example:

https://en.wikipedia.org/wiki/Muon#Muon_sources

http://physicsopenlab.org/2016/01/10/cosmic-muons-decay/

These are the muons @Nugatory was talking about; the key is, as he said, that these muons are moving in straight lines in free fall.

 

[russ_watters]

...I would have thought if you used the General Relativity equations, and had included the velocity of the circular orbit...

The General Relativity equation does not include a velocity term. Please look at the wiki link posted.

So there would be experiments to show that despite velocity time dilation appearing relative, actually it isn't. One would be shown to be correct and the other wrong.

I'm not sure I would use the words "relative", "correct", and "wrong" in the way you did. I would say the time dilation is relative (edit: better term provided: frame dependent), it's just not symmetrical if the situation isn't symmetrical. And nothing needs to be wrong with any of this as long as it is calculated correctly!

 

[name123]

Gravitational time dilation depends on position within the gravitational field, not on acceleration.

Would an observer in an accelerating rocket not notice a clock at the front of the rocket going faster than at the rear, as one might if the rocket were standing up on an object which had an appropriate gravitational field?

No; satellites are in free fall orbits, with zero proper acceleration. But in any case, acceleration is irrelevant to gravitational time dilation--see above.

So it is not the case that the velocity of the satellite going in a circular orbit creates an acceleration equal to the acceleration of gravity in an opposite direction to counter balance it, so that if the velocity were 0 the satellite would fall to the Earth, and if it were considerably greater than its orbit velocity it would leave orbit and go off into space?

 

[PeterDonis]

Would an observer in an accelerating rocket not notice a clock at the front of the rocket going faster than at the rear

Yes, but that's because the front of the rocket is higher up in the "gravitational field" produced by the rocket's acceleration. It's not because of the acceleration itself (since the difference in clock rates will be present even if the acceleration is the same in the front and the rear).

So it is not the case that the velocity of the satellite going in a circular orbit creates an acceleration equal to the acceleration of gravity in an opposite direction to counter balance it, so that if the velocity were 0 the satellite would fall to the Earth, and if it were considerably greater than its orbit velocity it would leave orbit and go off into space?

Both of these "accelerations" are coordinate accelerations and depend on your choice of coordinates. Note that I said proper acceleration in my quote: that is the acceleration that you actually feel and measure with an accelerometer, and it is also the kind that the equivalence principle is talking about. A satellite in orbit feels no acceleration.

 

[name123]

Both of these "accelerations" are coordinate accelerations and depend on your choice of coordinates. Note that I said proper acceleration in my quote: that is the acceleration that you actually feel and measure with an accelerometer, and it is also the kind that the equivalence principle is talking about. A satellite in orbit feels no acceleration.

Ok, thanks.

 

[name123]

The General Relativity equation does not include a velocity term. Please look at the wiki link posted.

Thanks I had overlooked the part below.

I'm not sure I would use the words "relative", "correct", and "wrong" in the way you did. I would say the time dilation is relative (edit: better term provided: frame dependent), it's just not symmetrical if the situation isn't symmetrical. And nothing needs to be wrong with any of this as long as it is calculated correctly!

I assume with 2 satellites in free fall orbit at the same velocity and altitude but in opposite directions around a sufficiently large glass sphere, that they would observe each other's clocks to be going slower than their own (due to velocity time dilation), and also to observe a clock on the Sphere to be going slower than they would expect given gravity time dilation alone. The situation would be symmetrical for both of the orbiting satellites would it not?

Though presumably each time they pass each other they would notice that their clocks are actually the same, and that would be further confirmed when they are brought to the surface of sphere, where they would further notice that the clock on the sphere had actually been going faster than they would have expected given gravity time dilation alone. So they would notice a distinction between the appearance of time dilation which is relative, and the actual difference in the rate their clocks ticked.

 

[jartsa]

Would an observer in an accelerating rocket not notice a clock at the front of the rocket going faster than at the rear, as one might if the rocket were standing up on an object which had an appropriate gravitational field?

An inertial observer might say that the observer in the accelerating rocket gets fooled into thinking that the clock at the front of the rocket is going faster than the clock at the rear of the rocket by the way that light travels between the rear and the front.

So this is very "relative".If in an accelerating rocket a clock is moved next to another clock, then everyone must agree about the rate difference and the difference of the readings of the two clocks. So now the inertial observer must agree with the observer inside the rocket. So the two observers must agree that a front clock has ticked faster than a former rear clock that was at some time moved from the rear to the front.

So this is "absolute".

 

[PeterDonis]

With 2 satellites orbiting at the same velocity opposite ways around a sufficiently large glass sphere would observe each other's clocks to be going slower than their own,

Based on measurements over a period of time much shorter than one orbit, yes.

Though presumably each time they pass each other they would notice that their clocks are actually the same

Yes.

that would be further confirmed when they are brought to the surface of sphere, where they would further notice that the clock on the sphere had actually been going faster than they would have expected given gravity time dilation alone

No. Assuming the clock on the sphere is at rest on the sphere, it would have been going exactly as fast as gravity time dilation predicts. And faster than the clocks on the satellites (that is, if the satellites were both launched from rest on the sphere, made a bunch of orbits, and then came back and landed at rest on the sphere, the clock that stayed at rest on the sphere the whole time would show more elapsed time).

So they would notice a distinction between the appearance of time dilation which is relative, and the actual difference in the rate their clocks ticked.

Yes.

 

[name123]

An inertial observer might say that the observer in the accelerating rocket gets fooled into thinking that the clock at the front of the rocket is going faster than the clock at the rear of the rocket by the way that light travels between the rear and the front.

So this is very "relative".If in an accelerating rocket a clock is moved next to another clock, then everyone must agree about the rate difference and the difference of the readings of the two clocks. So now the inertial observer must agree with the observer inside the rocket. So the two observers must agree that a front clock has ticked faster than a former rear clock that was at some time moved from the rear to the front.

So this is "absolute".

So the truth of the situation would not be relative, the inertial observer would have initially been wrong.

 

[name123]

No. Assuming the clock on the sphere is at rest on the sphere, it would have been going exactly as fast as gravity time dilation predicts. And faster than the clocks on the satellites (that is, if the satellites were both launched from rest on the sphere, made a bunch of orbits, and then came back and landed at rest on the sphere, the clock that stayed at rest on the sphere the whole time would show more elapsed time).

But it would not be at rest from the satellites' frame of reference would it? I would have thought that the satellites would have thought it was going slower than gravity time dilation would predict, because they would also observe velocity time dilation. When they returned to the sphere though, they would notice that they were wrong about the velocity time dilation of the sphere clock, and that it was actually their clocks that had being going slower due to velocity time dilation. So that the while they had been correct on how much time the sphere clock had lost due to gravity time dilation, they were wrong about how much they thought it was losing to velocity time dilation, actually it had gained.

 

[Janus]

So once returned the proper time that has passed for ship C is less than the proper time that has passed for Earth. Its clocks have objectively "ticked" less than those on Earth, regardless of how it appeared to ship C. Not quite clear on how from C's perspective the Earth's clocks suddenly seem to have been ticking faster after all, and not have done 0.8 the amount of "ticks" that had happened on C. If you can explain that, that would be great, if not, it doesn't matter.

It's not that The Earth's clock "seem to be ticking fast after all"., It's that by C's measurement, the Earth clocks ran really fast during the short time C was under acceleration And ran slow the rest of the time.

But if for ship C its clocks have objectively ticked less than those on Earth's. Then its clock was ticking slower as it had appeared to the observer on Earth.

As far as C is concerned, it's clock only ticked slow relative to the Earth clock during the period it was under acceleration, during the rest of the time it ran faster.

Given that C's journey consisted of an outward leg, during which it's clocks were in synch with those of A and an inward leg during which it's clocks were in synch with those of B, then can one not conclude that like C the clocks on A and B were objectively ticking slower than those on Earth?

No. As measured by the Earth, the clocks on A, B and C all run slow at the same rate while C is cruising. There will be a short period (for our purposes we will treat is as being infinitesimally short) where C when from cruising speed to zero speed and back up to cruising speed, during which time C's clock rate varied between running slow and running at the same rate as the Earth clock.)
As measured by clock A, the Earth clocks always ran slow by a fixed rate, and the clock on C ran at the same rate as theirs for part of the trip and ran really slow (even slower than Earth's clocks) for the rest of the trip

For B, Earth's clocks ran slow at the same rate for the whole time, and C's clock ran really slow for the first part of the trip then ran at the same rate as theirs for the rest of the trip.
For C the Earth clock ran slow during the outbound leg, ran extremely fast during turnaround, and then ran slow again during the return trip.
So while everyone agrees as to what the respective time it is on Earth and on C's clock when they meet up again, they don't agree as to exactly how this came about.
And there is no objective way to say what really happened. In other words, each of these views of what happened during the course of the trip is just as valid as any other. You can't ever say that one clock "actually" ran fast or slow compared to another at any given point of the trip.

Supposing A goes out along side C, and passes B at the point C turns around, and as B passes A it sets its clock to the time on A's and comes back along side C. If one were to assume almost instantaneous acceleration and deceleration for C, then presumably its clock would be roughly in synch with A's on the outward journey and in synch with B's on the inward journey, and the time on B's, like C's would be less than the clock it passes on Earth as C returns. Unlike C, A and B would be in inertial frames.

Now I have to bring the third "leg" of Special Relativity into play, The Relativity of Simultaneity. In a nutshell, it means that events that are simultaneous in one frame, are not going to be simultaneous for another frame in motion with respect to the first frame, if the events are separated along the line of relative motion.

As an example. Imagine that we put a clock at the turn around point, that has been synchronized with the Earth clock according Earth's and the turn around point's frame. For C and A, when the clock on Earth reads 0, the clock at the turnaround already reads 0.36 yrs. For ship B, when the clock at the turn around reads 0, the clock on Earth already reads 0.36 yr. Thus for ship's A and C, when A leaves Earth at time 0, the clock at turn around reads 0.36 yr, and in the time it takes (0.8 yr by A and C's clocks) this clock runs at a rate of 0.8 and accumulates 0.64 yr to read 1 yr, while their own clocks read 0.8 yr.
Ship B is just passing the turnaround at this moment, and takes the reading of 0.8 yr onto its own clock. For him, it will also be 1 yr at the turnaround clock, but it will be 1.36 yrs at the Earth clock. He will continue on towards Earth, adding another 0.8 yr to his clock, while the Earth clock runs slow and accumulates 0.64y. His clock will read 1.6 yr and the Earth clock will read 2 yrs upon his arrival.

Note that according to ships A and C, when they reach the turnaround point and the clock there reads 1 yr, the Earth clock at that moment only reads 0.64 years, while according to B, when it passes ship A at the turnaround point, the Earth clock already read 1.36 yr. Relativity of Simultaneity in action. For Ships A and C, the events of the Earth clock reading 0.64 and the turnaround clock reading 1 yrs are simultaneous. But for ship B, they are not, for him the simultaneous events are the turnaround clock reading 1yr and the Earth clock reading 1.36 yr.

Unfortunately, when people first start learning about SR, they usually start with time dilation. The problem is that SR only really makes sense if you also include length contraction and the relativity of simultaneity. And of the three, I really think that the relativity of simultaneity should be the one you start with. Once you grasp this idea, the other two fall into place very easily.

 

[jartsa]

So the truth of the situation would not be relative, the inertial observer would have initially been wrong.

Well, the inertial observer says that moving the clock from the rear to the front caused the clock to (velocity) time dilate.

 

[PeterDonis]

So the truth of the situation would not be relative, the inertial observer would have initially been wrong.

No, not wrong, just talking about a different thing.
w.
Suppose the two satellites are just passing each other. By exchanging light signals as they pass, they can confirm that each of them sees the other's clock running slow. But by comparing their total elapsed time from the last time they passed to this time (i.e., over one complete orbit), they can also confirm that their elapsed times per complete orbit are the same. Both of these observations are perfectly "true"; they're just observations of different things.

it would not be at rest from the satellites' frame of reference would it?

The two satellites do not have a "frame of reference" in which they are both at rest while they are orbiting. And neither of the satellites' "frames of reference" work the same as a frame of reference in special relativity, or the same as the "frame of reference" of the clock at rest on the sphere. See below.

I would have thought that the satellites would have thought it was going slower than gravity time dilation would predict, because they would also observe velocity time dilation.

In the satellites' frames of reference (either one), there is no well-defined "gravity time dilation". One way to see this is via the equivalence principle: the satellites are in free fall, feeling no acceleration, so there is no "acceleration time dilation" in their frames. And by the EP, there is thus no "gravitational time dilation" in their frames either, because there is no "gravitational field". If an observer on the satellite releases an object, it doesn't fall; it floats right next to the observer.

By contrast, in the frame of the clock at rest on the sphere, there is a "gravitational field" and there is gravity time dilation, because the clock feels acceleration--and if an observer next to the clock releases an object, it falls.

The only useful concept of "gravity time dilation" that the satellites can use is the same one as the clock at rest on the sphere uses, and according to that concept, the clock at rest on the sphere is ticking at exactly the rate that "gravity time dilation" predicts.

 

[Janus]

But gravity or acceleration time dilation is objective regarding the slowing of the proper time. But velocity time dilation is supposed to be relative is it not? I have presumed that it is and that there are no objective results regarding the slowing of proper time for velocity time dilation. With the muon experiments are the muons not in a circular orbit, and thus undergoing acceleration?

For gravitational time dilation, there is some objectivity, If I place a clock higher in a gravity well it will tick slower than a lower one, and both clocks will agree.
But for acceleration, this only holds if both clocks are undergoing the same acceleration. Then the "lead" clock will run slower than the "trailing" clock.
However, if only one clock is accelerating, then this objectivity can go out the window.
If you You are accelerating away from me, I will measure your clock as running slow as a result of your velocity with respect to me at any given instant. Your acceleration only counts in that it is what changes the velocity.
However, you will measure my clock as running doubly slow. In part because of the increasing velocity between us and in part due to my position relative to you due to your acceleration and the magnitude of your acceleration.
If you were accelerating towards me, I still would only measure your clock as running slow due to velocity, but what you would measure for my clock would be a combination of running slow due to relative velocity and running fast due to the distance between us and the magnitude of you acceleration. Whether this results in net increase or decrease in my clock rate according to you depends on the exact parameters of the scenario.

 

[name123]

Given that C's journey consisted of an outward leg, during which it's clocks were in synch with those of A and an inward leg during which it's clocks were in synch with those of B, then can one not conclude that like C the clocks on A and B were objectively ticking slower than those on Earth?

No. As measured by the Earth, the clocks on A, B and C all run slow at the same rate while C is cruising. There will be a short period (for our purposes we will treat is as being infinitesimally short) where C when from cruising speed to zero speed and back up to cruising speed, during which time C's clock rate varied between running slow and running at the same rate as the Earth clock.)
As measured by clock A, the Earth clocks always ran slow by a fixed rate, and the clock on C ran at the same rate as theirs for part of the trip and ran really slow (even slower than Earth's clocks) for the rest of the trip

But as I also wrote:

Supposing A goes out along side C, and passes B at the point C turns around, and as B passes A it sets its clock to the time on A's and comes back along side C. If one were to assume almost instantaneous acceleration and deceleration for C, then presumably its clock would be roughly in synch with A's on the outward journey and in synch with B's on the inward journey, and the time on B's, like C's would be less than the clock it passes on Earth as C returns. Unlike C, A and B would be in inertial frames.

So if A's clock ticks are roughly in synch with C's on the outward journey (and then continue at the same rate) and B's clock ticks are roughly in synch with C's on the inward journey (and then continue at the same rate) then the amount of "ticks" on C's clock would be roughly equal to the amount A's clock ticked on the outward journey and the amount B's ticked on the inward journey. And since this is less than the clock ticked on Earth, why would it be wrong to conclude that like C the clocks on A and B were objectively ticking slower than those on Earth?

In another conversation another scenario was considered, one in which there are 2 satellites in free fall orbit at the same velocity and altitude but in opposite directions around a sufficiently large glass sphere. They would observe each other's clocks to be going slower than their own (due to velocity time dilation) but when pass each other again they would observe that actually the clock measurements were objectively the same. So while there relative observations were different (when they both observed the other's clock to be going slower), they are able to objectively tell that those observations were did not imply that the other's clock was actually going slower. So while I can understand that A would think the clock on Earth was running slow, given that is was in synch with C's and C's was found to be have objectively ran slower than that on Earth, then I am not sure why you think it would be wrong to conclude that A's was running slower also.

 

[russ_watters]

I assume with 2 satellites in free fall orbit at the same velocity and altitude but in opposite directions around a sufficiently large glass sphere, that they would observe each other's clocks to be going slower than their own (due to velocity time dilation)...

The situation would be symmetrical for both of the orbiting satellites would it not?

Yes. Please note that in orbit, half the time they are approaching each other and half the time they are moving apart. So the time dilation wrt each other oscillates around zero.

...and also to observe a clock on the Sphere to be going slower than they would expect given gravity time dilation alone.

No: Their acceleration means that they and the ground station are not doing similar things. Objectively, the satellite "knows" its clock is the slow one.

So they would notice a distinction between the appearance of time dilation which is relative, and the actual difference in the rate their clocks ticked.

No, the science works if they use it correctly. If it didn't, GPS would not work.

 

[name123]

The two satellites do not have a "frame of reference" in which they are both at rest while they are orbiting. And neither of the satellites' "frames of reference" work the same as a frame of reference in special relativity, or the same as the "frame of reference" of the clock at rest on the sphere. See below.

So one cannot use the special relativity equations considering one to be at rest to establish the velocity time dilation that they will observe?

No, not wrong, just talking about a different thing.
w.
Suppose the two satellites are just passing each other. By exchanging light signals as they pass, they can confirm that each of them sees the other's clock running slow. But by comparing their total elapsed time from the last time they passed to this time (i.e., over one complete orbit), they can also confirm that their elapsed times per complete orbit are the same. Both of these observations are perfectly "true"; they're just observations of different things.

It would be true what they experienced, but it wouldn't be true that they actually did observe the other's clock going slower, because it didn't go slower. They would pass each other twice per complete orbit, and their clocks would be the same at the other side also.

In the satellites' frames of reference (either one), there is no well-defined "gravity time dilation". One way to see this is via the equivalence principle: the satellites are in free fall, feeling no acceleration, so there is no "acceleration time dilation" in their frames. And by the EP, there is thus no "gravitational time dilation" in their frames either, because there is no "gravitational field". If an observer on the satellite releases an object, it doesn't fall; it floats right next to the observer.

By contrast, in the frame of the clock at rest on the sphere, there is a "gravitational field" and there is gravity time dilation, because the clock feels acceleration--and if an observer next to the clock releases an object, it falls.

The only useful concept of "gravity time dilation" that the satellites can use is the same one as the clock at rest on the sphere uses, and according to that concept, the clock at rest on the sphere is ticking at exactly the rate that "gravity time dilation" predicts.

The observers on the satellites could know the mass of the sphere, and thus how much gravity time dilation they would expect for the clock on it. Would they not also experience the velocity time dilation effect so experience the sphere clock going even slower than they would have expected given gravity time dilation alone?

If so then my point was that when they return to the sphere they would notice that rather than the sphere clock going slower than theirs due to velocity time dilation, it was theirs' going slower, and so the sphere clock would appear to have gone faster than they would have expected given gravity time dilation alone.

 

[name123]

Yes. Please note that in orbit, half the time they are approaching each other and half the time they are moving apart. So the time dilation wrt each other oscillates around zero.

But with special relativity wouldn't the other satellite's clock appear to be going slower whether it is coming towards it or going away?

No: Their acceleration means that they and the ground station are not doing similar things. Objectively, the satellite "knows" its clock is the slow one.

They aren't doing similar things, but would the satellite not observe the clock on the sphere to be going slower than it would expect simply because of gravitational time dilation, because would an observer on the satellite not observe a velocity time dilation effect?

No, the science works if they use it correctly. If it didn't, GPS would not work.

I wasn't suggesting that the science didn't work, I just thought that the adjustment for the GPS would take into account which clock was objectively going slower.

 

[Nugatory]

So one cannot use the special relativity equations considering one to be at rest to establish the velocity time dilation that they will observe?

The special relativity equations that you are thinking of can only be used in a local inertial frame (although if there were no gravity, the situation you find in most intro textbooks, "local" would extend out to infinity).

Extreme care is required when applying them in any other situation. Before you even try to take on the complexities of gravitational time dilation you should try to understand the Twin Paradox, as your counter-orbiting satellites are just a variation of that classic problem. Start with http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

But with special relativity wouldn't the other satellite's clock appear to be going slower whether it is coming towards it or going away?

What you SEE is the clock running slow when it is moving away from you,and running fast when it is moving away. This is the Doppler effect, described in that link above. You only realize that the other clock is running consistently slow relative to yours when you correct for the time that it took for light to make it from the clock to your eye; if the clock is one light-second away from you the time you SEE is what it read one second ago when the light started towards you.

 

[name123]

The special relativity equations that you are thinking of can only be used in a local inertial frame (although if there were no gravity, the situation you find in most intro textbooks, "local" would extend out to infinity).

Extreme care is required when applying them in any other situation. Before you even try to take on the complexities of gravitational time dilation you should try to understand the Twin Paradox, as your counter-orbiting satellites are just a variation of that classic problem. Start with http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

The twin paradox involves a turnaround, and accelerations etc., and an actual time difference when the clocks reunite. Here though there is no actual time difference when the clocks meet. The situation is symmetrical for both satellites, the situation is not symmetrical in the twin paradox.

What you SEE is the clock running slow when it is moving away from you,and running fast when it is moving away. This is the Doppler effect, described in that link above. You only realize that the other clock is running consistently slow relative to yours when you correct for the time that it took for light to make it from the clock to your eye; if the clock is one light-second away from you the time you SEE is what it read one second ago when the light started towards you.

But neither's clock was running slow when compared to the other's (each time they pass they can notice the same time has passed on each of their clocks). Even though when observing each other bounce torch beams off their mirrored ceilings they might assume the other's clock is running slower.

 

[PeterDonis]

So one cannot use the special relativity equations considering one to be at rest to establish the velocity time dilation that they will observe?

No, because special relativity only applies in flat spacetime, i.e., in the absence of gravitating masses. Here there is a gravitating mass present so spacetime is not flat.

(If spacetime were flat, two objects both in free fall could only meet once. So the fact that the two satellites, both in free fall, meet multiple times is enough to show that spacetime cannot be flat.)

They would pass each other twice per complete orbit, and their clocks would be the same at the other side also.

Yes, that's true, but it's also true that, while passing each other both times, they are in relative motion, and so each would see the other to have velocity time dilation.

The observers on the satellites could know the mass of the sphere, and thus how much gravity time dilation they would expect for the clock on it.

Yes, but this is using the "gravity time dilation" of the clock on the sphere. It is not using any concept of "gravity time dilation" that applies in the satellites' own frames.

Would they not also experience the velocity time dilation effect so experience the sphere clock going even slower than they would have expected given gravity time dilation alone?

No, because the "gravity time dilation" they are calculating doesn't apply in the satellites' own frames, as above, but the velocity time dilation is relative to the satellites' own frames. So there's no way to combine the two as you are describing.

 

[Nugatory]

The twin paradox involves a turnaround, and accelerations etc., and an actual time difference when the clocks reunite. Here though there is no actual time difference when the clocks meet. The situation is symmetrical for both satellites, the situation is not symmetrical in the twin paradox.

It's still a twin paradox situation, because it maintains the apparent paradox...

But neither's clock was running slow when compared to the other's (each time they pass they can notice the same time has passed on each of their clocks). Even though when observing each other bounce torch beams off their mirrored ceilings they might assume the other's clock is running slower.

Both correctly find that the other clock is running slower than theirs always, just as with the classic version of the twin paradox. In the classic paradox, the traveller is surprised to find that the Earth twin ends up older even though the Earth twin's clock was running slower throughout; here each satellite bserver is surprised to find that the twin on the other satellite has aged equally even though their clock was running slower for the entire time of separation. And the resolution is the same in both cases: the difference in clock rate (time dilation) does not lead to apparently obvious conclusion about the total elapsed time.

 

[russ_watters]

But with special relativity wouldn't the other satellite's clock appear to be going slower whether it is coming towards it or going away?

No, moving apart the other's clock appears slow and back together it appears to speed up(as someone else noted, this is more than just time dilation).

They aren't doing similar things, but would the satellite not observe the clock on the sphere to be going slower than it would expect simply because of gravitational time dilation, because would an observer on the satellite not observe a velocity time dilation effect?

Yes, sorry, I missed the switch to GR there.

I wasn't suggesting that the science didn't work, I just thought that the adjustment for the GPS would take into account which clock was objectively going slower.

I guess I'm not following, but what you said before appears to contain contradictions:

I assume with 2 satellites in free fall orbit at the same velocity and altitude but in opposite directions around a sufficiently large glass sphere, that they would observe each other's clocks to be going slower than their own...

Though presumably each time they pass each other they would notice that their clocks are actually the same...

So they would notice a distinction between the appearance of time dilation which is relative, and the actual difference in the rate their clocks ticked.

How can you "notice" something different from what you "observe"?