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**Physics, Astronomy & Cosmology / How does time dilation work?**

« **on:**23/11/2021 22:35:26 »

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.

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.