[Astrogazer (OP)]

Hi,
I’d like clarification on the topic of velocity time dilation please, if anyone can help. 

I start by synchronising three identical atomic clocks in my sitting room. Relative to me sitting at home at ground level watching TV and keeping my eye on my super accurate atomic clock, I know that other clocks at a lower altitude than mine run slower than mine because the Earth’s gravitational field is stronger at lower altitudes than me, and conversely, those clocks at the top of a tower block run quicker than mine because the gravitational field (acceleration field) is not as strong as it is for me.   If these two clocks, the lower one and the higher one, are brought back to my sitting room they would once again run at exactly the same rate as my clock, but they would show different times in accordance with the length of time that they were away, one would be ahead of mine and the other behind mine.   I’m fine with the gravitational effects on clocks.

From now on the thought experiment and discussion is done at precisely the same gravitational field, or the results are modified appropriately to rule out the effects of any different gravitational fields.

Any acceleration, either speeding up or slowing down, causes the atomic clock undergoing this activity to slow down relative to my own in my sitting room. There is no difference on clocks between the acceleration caused by gravity or by rocket motors.

Here is my problem:-
Now I’ve heard from two authoritative sources, Dr. Pamala Gay (Universe Today podcast Astrocast) and Dr. Daniel Whiteson (Daniel and Jorge Explain the Universe)  that the only occasion when velocity can induce time dilation is when the clock accelerates or decelerates.  Both of these will cause time dilation, slowing relative to my clock, regardless of the direction of the acceleration.  I’m fine with that.

But for years it’s been drilled into me that a clock in a spaceship travelling at relativistic velocities relative to me at home, undergoes time dilation.  We have all read that if Alice and Bob are twins and Alice goes on a 10 year high speed space trip when she comes back the Earth Bob is many years older than Alice.   So is this age difference due solely to the four periods of acceleration (speed up, slow down, turn around, speed up, slow down) that Alice underwent?    If Pamala and Daniel are correct, it doesn’t matter how long Alice was away from Earth, only her four periods of acceleration or in other words the top velocity she achieved, not how long she coasted before slowing down.

I posed a triplets thought experiment, and sent it to Daniel, but I don’t think that I got an answer that addressed the crux of my issue.  Here is the triplets paradox:-

Let’s take triplets. Triplet A stays on Earth.   Triple B and C accelerate close to the speed of light over a period of one hour, then triple B immediately decelerates, turns round, accelerates again for one hour, decelerates and arrives back on Earth.    Upon return to Earth, Triple B reads his atomic clock and it reads start time plus 4 hours as expected..   Triple A, reads triple B’s clock and let’s say he reads 10 hours have passed (or whatever you like but it’s more than 4 hours). The clocks are different because of the acceleration undertaken by triple B.

Triple C takes off at exactly the same time as triplet B, accelerates for one hour but instead of immediately decelerating, he decides to turn off the engine and just cruises.   After 20 hours, triple C decelerates, turns round, accelerates over and hour then cruses for 20 hrs, then decelerates over a period of an hour and he is then back on Earth.

So triplet C sees that the following time has passed, 4 hours for acceleration and deceleration, plus 40 hours for the two cruise periods.  44 hours in total.

Triple A reads the clock of triplet C and reads 10 hours (the same as triple B for the acceleration and deceleration period) PLUS 40 hours (covering the two cruise periods) =50 hours.   I believe you said that the during the cruise period of triple C, time for A and C run at the same rate.  Is this correct?

Until just recently I’ve always heard that the longer people are travelling at relativistic speeds, the more the time difference mounts up when they return to Earth.  But from what you said, that is not true.   It’s just the acceleration periods that cause the time dilation, not the high speed cruise times as clocks tick at the same rate as clocks on Earth (let’s forget the effect that Earth’s gravitational field has on slowing the clock on Earth).

Can you clarify this for me please?

Daniel said this :-
‘ When you bring everyone back to Earth so they have the same velocity, the only thing that matters then is how much acceleration they have experienced. So B and C will be the same age relative to A because they've had the same acceleration.’


This tells me that the Earth clocks run at the same speed as clock C during C’s cruise phase.

I posed another question about GPS orbiting satellites to examine this further.  I said that I’ve heard it said that the high altitude of the clocks makes GPS clocks run faster (less gravitational acceleration)  but their speed slows them down so although they do run faster than clocks on Earth, they don’t run as fast as one would expect if only altitude was taken into account.   So this means that their ongoing high speed relative to me on the ground does cause an ongoing time dilation effect and it’s not just the initial launch of the satellites that caused an initial offset.

Daniel said that while the two clocks, one on Earth and the other orbiting, are at different velocities it’s a symmetric system and it’s only when the travelling clocks come back to Earth that a proper analysis can take place.  So I’m puzzling the following.  Is it the case that while the GPS satellite is orbiting and its radioing its clock’s time down the Earth, that Earth sees an ongoing velocity discrepancy accruing (we are not talking altitude dilation but speed only), that should the satellite be captured and brought back to NASA for analysis, that the GPS clock shows an offset due to the time spent at altitude, plus the launch acceleration and recovery deceleration phase only but not the 20 years of accrued dilation caused by the speed.   Isn’t that a lot of accrued time to loose on the homeward journey?

So on the one hand I’m being told that cruising at high speed doesn’t cause time dilation and on the other that it does.   Which is correct?

Thanks.

[Halc]

I start by synchronising three identical atomic clocks in my sitting room.

Just saying, a clock is a clock, atomic or otherwise. Atomic clocks have the accuracy needed for some experiments, but relativity affects paint peeling just as much as it does any other clock. We assume they all measure time, and you don't need an atomic clock to show that one twin measured half the time of the other.

Relative to me sitting at home at ground level watching TV and keeping my eye on my super accurate atomic clock, I know that other clocks at a lower altitude than mine run slower than mine because the Earth’s gravitational field is stronger at lower altitudes than me, and conversely, those clocks at the top of a tower block run quicker than mine because the gravitational field (acceleration field) is not as strong as it is for me.

It is not the acceleration field that causes this, but rather the gravitational potential field. The rate at which clocks run is a function of potential, not acceleration, so a clock on the surface of Mercury will run much slower than one of the surface of Earth despite you weighing less (lower acceleration field) there.

From now on the thought experiment and discussion is done at precisely the same gravitational field, or the results are modified appropriately to rule out the effects of any different gravitational fields.

That would mean there's no significant gravity at all, yielding flat Minkowski spacetime.

Any acceleration, either speeding up or slowing down, causes the atomic clock undergoing this activity to slow down relative to my own in my sitting room.

No. I can put one clock in a parked car on the equator of Earth and another one accelerating furiously at a linear velocity of 1600 km/hr in some centrifuge at the pole. The one at the pole would accelerate thousands of times as much the one sitting in the parking lot, but when brought together they will still read the same time.  Acceleration doesn't directly cause time dilation. Both clocks are moving at the same speed relative to the inertial frame of Earth and are at the same potential, so they'll not run at different rates.

Here is my problem:-
Now I’ve heard from two authoritative sources, Dr. Pamala Gay (Universe Today podcast Astrocast) and Dr. Daniel Whiteson (Daniel and Jorge Explain the Universe)  that the only occasion when velocity can induce time dilation is when the clock accelerates or decelerates.

Very poorly worded. For one thing, there is no 'decelerate' in physics. It's all acceleration, which is defined in physics as a vector change in velocity. They seem to be using the common language definition where acceleration is a scalar increase in speed relative to an implied frame, and deceleration being a decrease in speed.

One clock X moving relative to another clock Y will be dilated (slower) in the frame of Y. No acceleration is required. Acceleration of one or both is only required to separate them and then bring them back together again.

Both of these will cause time dilation, slowing relative to my clock, regardless of the direction of the acceleration.

This is wrong, as illustrated by example with the centrifuge at the pole.

But for years it’s been drilled into me that a clock in a spaceship travelling at relativistic velocities relative to me at home, undergoes time dilation.  We have all read that if Alice and Bob are twins and Alice goes on a 10 year high speed space trip when she comes back the Earth Bob is many years older than Alice.

So far so good.

So is this age difference due solely to the four periods of acceleration (speed up, slow down, turn around, speed up, slow down) that Alice underwent?

No, because I can do that same series of acceleration without the dilation. There are many 'correct' answers to what exactly causes the dilation, but the primary one (and probably least helpful) is that Alice's worldline between the departure and reunion events has a shorter temporal length than does Bob's.
A more helpful explanation is that relative to any one inertial frame, Alice usually is moving faster and is more dilated.
It can be explained by relativity of simultaneity (something that should never be overlooked), or by moment-of-acceleration which is acceleration time distance, sort of like torque.

If Pamala and Daniel are correct, it doesn’t matter how long Alice was away from Earth, only her four periods of acceleration or in other words the top velocity she achieved, not how long she coasted before slowing down.

They'd be wrong about that. Alice isn't going to be 5 years younger if she does those same accelerations but only goes to Pluto and back.

Let’s take triplets. Triplet A stays on Earth.   Triple B and C accelerate close to the speed of light

This suggests absolute speeds. Velocity is relative, and so you must specify 'close to the speed of light relative to frame X. The statement is meaningless without it. I'm moving at close to the speed of light relative to some frames right now and it doesn't bother me at all.

over a period of one hour

Again ambiguous without specifying the frame in which this hour is measured. I'm guessing B's proper time here: as measured by B's watch. The description below implies that.

Upon return to Earth, Triple B reads his atomic clock and it reads start time plus 4 hours as expected.   Triple A, reads triple B’s clock and let’s say he reads 10 hours have passed (or whatever you like but it’s more than 4 hours).

If both of them are in each other's presence and looking at the same (B's) clock, then they're not going to read different values. Both A and B read 4 hours on B's clock. A's clock will read more, and they both can read that as well.

The clocks are different because of the acceleration undertaken by triple B.

Not because of that, no. The acceleration is only necessary because without it, B would not have come back to A's presence.

Triple C takes off at exactly the same time as triplet B, accelerates for one hour but instead of immediately decelerating, he decides to turn off the engine and just cruises.   After 20 hours, triple C decelerates, turns round, accelerates over and hour then cruses for 20 hrs, then decelerates over a period of an hour and he is then back on Earth.

So triplet C sees that the following time has passed, 4 hours for acceleration and deceleration, plus 40 hours for the two cruise periods.  44 hours in total.

OK.

Triple A reads the clock of triplet C and reads 10 hours (the same as triple B for the acceleration and deceleration period) PLUS 40 hours (covering the two cruise periods) =50 hours.

No, he reads 44 hours. They're looking at the same clock. They can't see different times.

I believe you said that

Who said? This was your first post ever. Nobody has said anything to you except perhaps Pam and Dan above whom you don't appear to be addressing.

during the cruise period of triple C, time for A and C run at the same rate. Is this correct?

The time rate for any particular clock is frame dependent, and none was specified, so the question is ambiguous. Relative to the inertial frame of either A or C, it’s the other one that’s moving and thus the other clock that runs slow.

Until just recently I’ve always heard that the longer people are travelling at relativistic speeds, the more the time difference mounts up when they return to Earth.

Until recently then, you had it right.

But from what you said, that is not true.

You seem to be replying to a comment made by somebody selling you nonsense.

Daniel said this :-
‘ When you bring everyone back to Earth so they have the same velocity, the only thing that matters then is how much acceleration they have experienced. So B and C will be the same age relative to A because they've had the same acceleration.’

Totally wrong. Daniel doesn’t know his stuff at all. Anybody can put out a podcast. It doesn't make them right.

I posed another question about GPS orbiting satellites to examine this further.  I said that I’ve heard it said that the high altitude of the clocks makes GPS clocks run faster (less gravitational acceleration)  but their speed slows them down so although they do run faster than clocks on Earth, they don’t run as fast as one would expect if only altitude was taken into account.   So this means that their ongoing high speed relative to me on the ground does cause an ongoing time dilation effect and it’s not just the initial launch of the satellites that caused an initial offset.

All correct. The launch has almost zero effect. They’re so high up that the dilation (slowing) due to their slow orbital speed is far less than the speedup from the gravitational potential difference, as you described.

Daniel said that while the two clocks, one on Earth and the other orbiting, are at different velocities it’s a symmetric system and it’s only when the travelling clocks come back to Earth that a proper analysis can take place.

No, there’s plenty of ways to do a proper analysis of their rates while still in orbit since they return to the same relative separations at regular intervals.

So I’m puzzling the following.  Is it the case that while the GPS satellite is orbiting and its radioing its clock’s time down the Earth, that Earth sees an ongoing velocity discrepancy accruing (we are not talking altitude dilation but speed only), that should the satellite be captured and brought back to NASA for analysis, that the GPS clock shows an offset due to the time spent at altitude, plus the launch acceleration and recovery deceleration phase only but not the 20 years of accrued dilation caused by the speed.   Isn’t that a lot of accrued time to loose on the homeward journey?

No latent accrual will take place on this journey of far less than a light second. Daniel is telling you more nonsense I see.

So on the one hand I’m being told that cruising at high speed doesn’t cause time dilation and on the other that it does.

Speed is frame dependent, so I’d reword it as: “Cruising at high speed relative to a given inertial frame causes time dilation relative to that same frame.

Gravitational dilation is less frame dependent. Two clocks at different potentials will objectively run at different rates, all else being equal.

Hope this helps.

[yor_on]

As Halc wrote. I just want to comment on that this one is a divider, it would be nice, at least interesting, if we could restrict a time dilation to accelerations, but I don't see how that could be done. But it still find adherents.

[Origin]

I just want to comment on that this one is a divider, it would be nice, at least interesting, if we could restrict a time dilation to accelerations,

If you restricted time dilation to acceleration then you would have to ignore time dilation due to velocity.  Why would you do that?  If you did that you would get incorrect answers to most questions involving time dilation.  GPS wouldn't work if you ignored time dilation due to the different inertial frames.

[yor_on]

True, and a good argument as I think. Then we have that classical muon thought experiment in where the reason it can reach so far into earths atmosphere is due to the complementary of time dilation and LorentzFitzGerald contraction, depending on what frame of reference you use. Earth defining it as a 'slower clock' for the muon while the muon defines it as a length contraction of the distance.

But I've had serious arguments with people wanting it to belong solely to accelerations. And there the 'twin experiment' is a often used argument, referring to the 'turnabout' as the reason for a time dilation.

[Janus]

True, and a good argument as I think. Then we have that classical muon thought experiment in where the reason it can reach so far into earths atmosphere is due to the complementary of time dilation and LorentzFitzGerald contraction, depending on what frame of reference you use. Earth defining it as a 'slower clock' for the muon while the muon defines it as a length contraction of the distance.

But I've had serious arguments with people wanting it to belong solely to accelerations. And there the 'twin experiment' is a often used argument, referring to the 'turnabout' as the reason for a time dilation.

People tend to confuse "time dilation" with "total difference in elapsed time"
Time dilation is what you measure happening to a clock that is either moving relative to you or at a different gravitational potential.  Total difference in elapsed time is what you are considering after you bring the clocks back together in twin experiment.
For the "stay at home" twin which never undergoes acceleration, the time difference is entirely due to time dilation caused by the relative motion of their twin, the only effect their twin's acceleration has is to cause the time dilation the stay at home twin measures for their twin to change moment by moment while they accelerate.
For the twin that does undergoes acceleration, things are a bit different. During the outbound and inbound legs, he simply measures* time dilation for his twin based on  their relative velocity. But when he is accelerating he would measure an additional effect.  Clocks in the direction of his acceleration run faster, and the further away, the faster they run. Clocks in the opposite direction run slow (this effect is on top of the time dilation due to relative motion.)

So when he accelerates to come to a rest with his twin and then accelerates back up to speed towards him, he will measure his twin's clock as running very fast. So fast that it more than makes up for the outbound and inbound legs where his measures it as running slow.
When he returns to his twin he will end up arriving at the same answer for the total difference in their elapsed times as his twin does, he'll just conclude that it came about  for different reasons.
And that's the crux of it. While both twins agree at the end about the difference in total elapsed time experience by either, they don't have to agree upon what "caused" the end result, and neither twin's interpretation of events is any more of the "truth" than the other's.

* when I use "measure" here, I don't mean what he directly observes, but what he would determine as what is happening to the other clock after he accounts for light propagation delay.

[hamdani yusuf]

No. I can put one clock in a parked car on the equator of Earth and another one accelerating furiously at a linear velocity of 1600 km/hr in some centrifuge at the pole. The one at the pole would accelerate thousands of times as much the one sitting in the parking lot, but when brought together they will still read the same time.  Acceleration doesn't directly cause time dilation. Both clocks are moving at the same speed relative to the inertial frame of Earth and are at the same potential, so they'll not run at different rates.

What happened to equivalence principle? Wouldn't it mean that we can distinguish between gravitational acceleration and rocket acceleration inside a closed space ship cabin?

[MikeFontenot]

[...]
So when he accelerates to come to a rest with his twin and then accelerates back up to speed towards him, he will measure his twin's clock as running very fast. So fast that it more than makes up for the outbound and inbound legs where his measures it as running slow.
When he returns to his twin he will end up arriving at the same answer for the total difference in their elapsed times as his twin does, he'll just conclude that it came about  for different reasons.
And that's the crux of it. While both twins agree at the end about the difference in total elapsed time experience by either, they don't have to agree upon what "caused" the end result, and neither twin's interpretation of events is any more of the "truth" than the other's.

Very good explanation.  I would just add, to your comment that I've highlighted in red, that the two twins generally don't agree (and don't have to agree) about their respective ages when they are separated.  They obviously MUST agree when they are co-located, and they do.

[alancalverd]

If only. We could reduce its entropy by walking away from a pile of rubble!

[Eternal Student]

Hi.

Thanks for the info on Rindler.  I didn't know time was considered to run backward behind the Rindler horizon.  (Obviously it's not required to resolve or understand the twin paradox but it is interesting).
   

Anybody is free to use any coordinate system they want

     It's important and probably should be added to International law - but what can you do?

Best Wishes.