Einstein’s clock tower thought experiment question

[MPMin]

If I understand Einstein’s clock tower thought experiment correctly, Einstein saw himself on a train traveling away from a clock that was situated on a clock tower. From Einstein’s perspective, the hands of the receding clock would have appeared to be moving slower, hence, giving the illusion that the clock’s time had slowed down. Is this correct? 
 

If my understanding of the thought experiment is correct, does that also mean that the clock should have red shifted towards the red spectrum as well? 
 

I apologise if I’ve posted this in the incorrect section. My question is a theoretical physics question. 
 

[swansont]

5 hours ago, MPMin said:

If I understand Einstein’s clock tower thought experiment correctly, Einstein saw himself on a train traveling away from a clock that was situated on a clock tower. From Einstein’s perspective, the hands of the receding clock would have appeared to be moving slower, hence, giving the illusion that the clock’s time had slowed down. Is this correct? 
 

No, it was not proposed to be an illusion. The clock ticked slower because time slowed down, owing to relative motion.

 

5 hours ago, MPMin said:

If my understanding of the thought experiment is correct, does that also mean that the clock should have red shifted towards the red spectrum as well? 
 

Sure. It isn’t brought up because it’s irrelevant to the thought problem.

[bangstrom]

On 5/23/2022 at 5:52 AM, swansont said:

No, it was not proposed to be an illusion. The clock ticked slower because time slowed down, owing to relative motion.

 

MPMin’s understanding of the problem is correct. The clock time will appear to slow from Einstein’s perspective and the clock should appear redshifted.

Einstein’s motion away from the clock can not make the clock in the tower tick slower. The clock ticks as normal, but from Einstein’s view the clock does tick slower.

Also, from the perspective of an observer at the clock tower, Einstein’s clock ticks slower. But if Einstein’s clock is actually ticking slower, he should see his clock and the tower either keeping time in sync or running faster.

 

There is an illusion here and no clocks are actually ticking slower. Think about it and guess again.

 

[MPMin]

On 5/23/2022 at 8:52 PM, swansont said:

No, it was not proposed to be an illusion. The clock ticked slower because time slowed down, owing to relative motion.

 

Sure. It isn’t brought up because it’s irrelevant to the thought problem.

Continuing with the thought experiment, if Einstein were to turn around to observe the clock on the tower that the train was heading towards, would the approaching clock on the tower appear to tick slower or faster? 

[swansont]

10 hours ago, bangstrom said:

MPMin’s understanding of the problem is correct. The clock time will appear to slow from Einstein’s perspective and the clock should appear redshifted.

Einstein’s motion away from the clock can not make the clock in the tower tick slower. The clock ticks as normal, but from Einstein’s view the clock does tick slower.

Also, from the perspective of an observer at the clock tower, Einstein’s clock ticks slower. But if Einstein’s clock is actually ticking slower, he should see his clock and the tower either keeping time in sync or running faster.

 

There is an illusion here and no clocks are actually ticking slower. Think about it and guess again.

 

It’s not a guess. In the train’s frame of reference, moving clocks (e.g. the tower clock) run slow, because time runs slow. The tower clock ticks normally in the frame of the tower. There is no valid absolute statement you can make about time and ticking (e.g. “The clock ticks as normal”  or “Einstein’s clock is actually ticking slower” ) since all measurements are relative.

This is well-established physics. There is no illusion here.

If you want to peddle an alternative idea, do it in speculations. 

9 hours ago, MPMin said:

Continuing with the thought experiment, if Einstein were to turn around to observe the clock on the tower that the train was heading towards, would the approaching clock on the tower appear to tick slower or faster? 

Moving clocks tick slower, but you have to distinguish between measurement and observation, because light has a finite travel time.

Janus has made multiple posts that explain this better than I can

one example

https://www.scienceforums.net/topic/120625-are-relativistic-effects-directional/?tab=comments#comment-1123814

 

[Markus Hanke]

17 hours ago, bangstrom said:

There is an illusion here and no clocks are actually ticking slower.

Clocks always tick at the same rate in their own local frames - what changes is their relationship in spacetime. Speaking of clocks ticking “slower” or “faster” is thus meaningless, we can speak only of how two or more clocks are related.

Nonetheless this change in relationship between frames is a real phenomenon that has real, measurable physical consequences; it is not just an ‘illusion’, whatever this even means.

[MPMin]

14 hours ago, swansont said:

It’s not a guess. In the train’s frame of reference, moving clocks (e.g. the tower clock) run slow, because time runs slow. The tower clock ticks normally in the frame of the tower. There is no valid absolute statement you can make about time and ticking (e.g. “The clock ticks as normal”  or “Einstein’s clock is actually ticking slower” ) since all measurements are relative.

This is well-established physics. There is no illusion here.

If you want to peddle an alternative idea, do it in speculations. 

Moving clocks tick slower, but you have to distinguish between measurement and observation, because light has a finite travel time.

Janus has made multiple posts that explain this better than I can

one example

https://www.scienceforums.net/topic/120625-are-relativistic-effects-directional/?tab=comments#comment-1123814

 

Thank you for the link. I have not yet been able to establish an answer to my query from the other discussions.

Perhaps if i restate the thought experiment and ask questions about that might make it clearer to my understanding.

The thought experiment is as follows: Let’s assume there are two clock towers facing each other along a straight track. All conditions effecting the two clock towers are negligible. Let’s also assume there is a train positioned at one end of the track and lets assume there is an observer at each clock tower and on the train, and the observer on the train also has a clock. Lets also assume that all observers can see all clocks all the of the time. The train will travel from one clock tower to the other, however, before the train leaves, the train is stationary at one end of the track right next to one of the clock towers. Let’s call the point of origin clock tower A and observer A, the destination clock tower B and observer B and the clock on the train clock C and observer C. To be clear, each observer remains in with their respective clocks and while the train is stationary at clock tower A all clock appear to tick at the same rate to all observers.

Let’s assume the train has left clock tower A (point of origin) travelling towards clock tower B (point of destination) and has reached a constant velocity towards clock tower B, the following questions are with reference to this situation.

How does observer A (at point of origin) perceive the ticking rate of clock C (on the train)

How does observer B (at point of destination) perceive the ticking rate of clock C (on the train)

How does observer C (on the train) perceive the ticking rate of clock A (at origin), B (at destination) and C (on the train) just wondering if the observer on the train perceives any difference to the ticking rate of the clock on the train?

Edited for spelling and grammar.

 

 

Edited May 26, 2022 by MPMin

[bangstrom]

On 5/23/2022 at 5:52 AM, swansont said:

No, it was not proposed to be an illusion. The clock ticked slower because time slowed down, owing to relative motion.

Einstein should see the tower clock ticking slower because he sees the ticks arriving slower at his moving location due to the Doppler effect but the clock did not actually tick any slower.  It makes no sense to speak of time as having slowed. The observation of a slower time is real but the actual slowing of time at the tower is an illusion.

As Janus said in the quote you cited, “Do not conflate what a observers visually sees via the light arriving from a source with what that observer would conclude it happening at the source.”

3 hours ago, MPMin said:

Let’s assume the train has left clock tower A (point of origin) travelling towards clock tower B (point of destination) and has reached a constant velocity towards clock tower B, the following questions are with reference to this situation.

How does observer A (at point of origin) perceive the ticking rate of clock C (on the train)

How does observer B (at point of destination) perceive the ticking rate of clock C (on the train)

How does observer C (on the train) perceive the ticking rate of clock A (at origin), B (at destination) and C (on the train) just wondering if the observer on the train perceives any difference to the ticking rate of the clock on the train?

Observer A should see the clock on the train ticking slower.

Observer B should see the approaching clock on the train ticking faster.

Observer C on the train should see the clock at A (the origin) ticking slower. B (at the approaching destination) ticking faster. And C (on the train) should see no difference on his clock.

 

[MPMin]

36 minutes ago, bangstrom said:

Einstein should see the tower clock ticking slower because he sees the ticks arriving slower at his moving location due to the Doppler effect but the clock did not actually tick any slower.  It makes no sense to speak of time as having slowed. The observation of a slower time is real but the actual slowing of time at the tower is an illusion.

As Janus said in the quote you cited, “Do not conflate what a observers visually sees via the light arriving from a source with what that observer would conclude it happening at the source.”

Observer A should see the clock on the train ticking slower.

Observer B should see the approaching clock on the train ticking faster.

Observer C on the train should see the clock at A (the origin) ticking slower. B (at the approaching destination) ticking faster. And C (on the train) should see no difference on his clock.

 

Thank you for your answer. You state that both observers A and C see each other’s respective clocks ticking slower. Is that because they are effectively moving away from each other? Does the apparent slower ticking occur because the photons take longer to reach each observer, and if so, does that mean each observer is seeing fewer photons because they are arriving less frequently due to the Doppler effect, and does that mean that red shifted light is inherently dimmer than the original source?

[bangstrom]

1 hour ago, MPMin said:

 You state that both observers A and C see each other’s respective clocks ticking slower. Is that because they are effectively moving away from each other? Does the apparent slower ticking occur because the photons take longer to reach each observer, and if so, does that mean each observer is seeing fewer photons because they are arriving less frequently due to the Doppler effect, and does that mean that red shifted light is inherently dimmer than the original source?

The classical Doppler effect is the major contributor to the observations. It takes longer for light to reach the train as distances increase so the time between ticks also appears longer.

The light appears dimmer with distance because the light is emitted radially and the train captures less of the emitted light as the emission spreads. This is not a part of the Doppler effect.

The redshifting of light is a Doppler effect at relativistic speeds. It takes longer for an entire wavelength of light to be detected when the receiver is moving away causing the wavelengths appear longer and shifted more towards the red (longer wave) end of the color spectrum. The same happens with sound waves but at vastly slower speeds.

Red shifted light is not necessarily dimmer but it is less energetic than light with shorter wavelengths.

[MPMin]

33 minutes ago, bangstrom said:

The classical Doppler effect is the major contributor to the observations. It takes longer for light to reach the train as distances increase so the time between ticks also appears longer.

The light appears dimmer with distance because the light is emitted radially and the train captures less of the emitted light as the emission spreads. This is not a part of the Doppler effect.

The redshifting of light is a Doppler effect at relativistic speeds. It takes longer for an entire wavelength of light to be detected when the receiver is moving away causing the wavelengths appear longer and shifted more towards the red (longer wave) end of the color spectrum. The same happens with sound waves but at vastly slower speeds.

Red shifted light is not necessarily dimmer but it is less energetic than light with shorter wavelengths.

Does observer C on the train encounter more photons from clock tower B than it does from clock tower A as its heading towards B and away from A?

[swansont]

3 hours ago, bangstrom said:

Einstein should see the tower clock ticking slower because he sees the ticks arriving slower at his moving location due to the Doppler effect but the clock did not actually tick any slower.  It makes no sense to speak of time as having slowed. The observation of a slower time is real but the actual slowing of time at the tower is an illusion.

As Janus said in the quote you cited, “Do not conflate what a observers visually sees via the light arriving from a source with what that observer would conclude it happening at the source.”

Moving clocks actually run slow. Read what else Janus wrote. One effect in play is "Time dilation, which always has the moving source clock tick slow"

Kinematic time dilation has been experimentally confirmed many times. To deny that it happens is ludicrous. If you synchronize two clocks and move one, and then bring it back to the source, it will indicate less time has elapsed. In such a demonstration the clocks would be co-located and at rest when the comparisons are made, so there is no doppler shift to cause confusion. Time dilation is a very real effect.

7 hours ago, MPMin said:

How does observer A (at point of origin) perceive the ticking rate of clock C (on the train)

How does observer B (at point of destination) perceive the ticking rate of clock C (on the train)

How does observer C (on the train) perceive the ticking rate of clock A (at origin), B (at destination) and C (on the train) just wondering if the observer on the train perceives any difference to the ticking rate of the clock on the train?

It's important to define what you mean by perceive. One needs to distinguish between the raw data (what do my eyes see) and the underlying physics (what do I measure), as I mentioned earlier and the explanation I linked to. The doppler shift will make the two not be the same; the changing travel time of the light has an effect. A measurement requires that you remove this confounding effect.

Once the effect of that travel time is factored out, during the trip C will conclude that A and B are running slow. A and B will see C's clock as running slow. When C reaches the destination and stops, next to B, C's clock will have run slow (C has undergone an acceleration, which allows one to distinguish between the effects; they are not symmetrical)

 

31 minutes ago, MPMin said:

Does observer C on the train encounter more photons from clock tower B than it does from clock tower A as its heading towards B and away from A?

Yes. If you are collecting pulses of light as your measurement, it's why the raw data disagree coming from A and B during the trip. But you can't make a conclusion about what the clocks are actually doing of you are excluding data that is in transit. You have to collect all the data to make a valid measurement. If you wait until all the pulses arrive, the time on A and B will agree, as they must.

[bangstrom]

9 hours ago, swansont said:

Moving clocks actually run slow. Read what else Janus wrote. One effect in play is "Time dilation, which always has the moving source clock tick slow"

Janus is right but your answer to the question in the OP was wrong. Here is the question with your reply below.

 

On 5/23/2022 at 5:52 AM, swansont said:

On 5/23/2022 at 12:38 AM, MPMin said:

If I understand Einstein’s clock tower thought experiment correctly, Einstein saw himself on a train traveling away from a clock that was situated on a clock tower. From Einstein’s perspective, the hands of the receding clock would have appeared to be moving slower, hence, giving the illusion that the clock’s time had slowed down. Is this correct? 
 

No, it was not proposed to be an illusion. The clock ticked slower because time slowed down, owing to relative motion.

The correct answer to the question is: Yes, Einstein should see the hands on the tower clock moving slower because of the classical Doppler effect.

Your answer (in the expansion) makes no sense as stated. You may be thinking correctly but it came out all wrong.

If Einstein's clock is running slower, he should see the tower clock running faster than his own but this is the opposite of what he observes. Also, Einstein should see no change to the clock in his own reference frame.

Janus is correct that Einstein's clock is running slower than the tower clock but he added the caveat that you must discount the classical Doppler effect from your observation. Einstein can not observe any relativistic change from his own reference frame but he does observe the Doppler effect where the tower clock appears to be running slower.

 

Edited May 26, 2022 by bangstrom
added (in the expansion)

[swansont]

1 hour ago, bangstrom said:

Janus is right but your answer to the question in the OP was wrong. Here is the question with your reply below.

 

The correct answer to the question is: Yes, Einstein should see the hands on the tower clock moving slower because of the classical Doppler effect.

Your answer (in the expansion) makes no sense as stated. You may be thinking correctly but it came out all wrong.

If Einstein's clock is running slower, he should see the tower clock running faster than his own but this is the opposite of what he observes. Also, Einstein should see no change to the clock in his own reference frame.

Janus is correct that Einstein's clock is running slower than the tower clock but he added the caveat that you must discount the classical Doppler effect from your observation. Einstein can not observe any relativistic change from his own reference frame but he does observe the Doppler effect where the tower clock appears to be running slower.

 

You do not have an adequate understanding of relativity to contribute here.

[bangstrom]

4 hours ago, swansont said:

You do not have an adequate understanding of relativity to contribute here.

I am here to learn.

The question in the OP asked if it is correct that Einstein on a train moving away from the clock tower should see the receding clock running slower? I say, Yes.

The answer you gave “ The clock ticked slower because time slowed down, owing to relative motion.” makes no sense to me as an answer to the question and I understand about time dilation.

First, should Einstein see the tower clock running slower or not?

[zapatos]

2 hours ago, bangstrom said:

First, should Einstein see the tower clock running slower or not?

 

2 hours ago, bangstrom said:

"The clock ticked slower..."

 

Edited May 27, 2022 by zapatos

[MPMin]

Id like to clarify some of the detail in thought experiment I stated.

The intended meaning of ‘perceived’ is ‘as it is seen by the observer’ 

I have also deliberately omitted the acceleration phase of the train and skipped straight to the constant velocity phase to ignore the effects caused by acceleration at this stage of my understanding. 

I am also here to learn, please help me understand the following concepts. With reference to the thought experiment:

While the train maintains it’s constant velocity towards B and away from A, does observer C experience a slower passage of time compared to both observers at A and B?

If time is passing slower for observer C, in that clock C is ticking slower than both Clocks A and B, why doesn’t observer C see clocks A and B ticking faster than clock C?

 

 

 

[Markus Hanke]

4 hours ago, bangstrom said:

The question in the OP asked if it is correct that Einstein on a train moving away from the clock tower should see the receding clock running slower? I say, Yes.

The answer you gave “ The clock ticked slower because time slowed down, owing to relative motion.” makes no sense to me as an answer to the question and I understand about time dilation.

I’m having difficulty gauging your understanding, based on what is written here.

Are you thinking that (kinematic) time dilation is merely an optical effect, and produces no measurable physical consequences other than what an observer can visually see?

On 5/26/2022 at 10:19 AM, MPMin said:

How does observer A (at point of origin) perceive the ticking rate of clock C (on the train)

He perceives it as dilated (‘slowed’), because they are in relative motion with respect to one another.

On 5/26/2022 at 10:19 AM, MPMin said:

How does observer B (at point of destination) perceive the ticking rate of clock C (on the train)

He also perceives it as dilated, because they are likewise in relative motion. In the formula for kinematic time dilation, the relative speed appears squared, so its relative sign (moving towards or away) is irrelevant.

On 5/26/2022 at 10:19 AM, MPMin said:

How does observer C (on the train) perceive the ticking rate of clock A (at origin), B (at destination) and C (on the train)

He perceives both A and B to be dilated (slower), because he finds himself in relative motion with respect to both those frames. He perceives his own watch at C to be ticking normally (no dilation), because there is no relative motion between himself and his watch. They are in the same frame.

On 5/26/2022 at 10:19 AM, MPMin said:

just wondering if the observer on the train perceives any difference to the ticking rate of the clock on the train?

No, because he’s in the same frame as that clock, so there is no relative motion. Kinematic time dilation arises due to relative motion between frames.

1 hour ago, MPMin said:

While the train maintains it’s constant velocity towards B and away from A, does observer C experience a slower passage of time compared to both observers at A and B?

Observer C himself notices nothing special - his own clock ticks at 1 second per second from his own point of view (no relative motion). However, he sees both A and B going slower - and conversely both A and B see C ticking slower from their own vantage points. That’s because in the frame of the train, both A and B are in motion whereas the train appears stationary; whereas in frames A and B, the train in frame C is in motion, whereas A/B are stationary. In both cases, the respective observer sees the other clock to be in motion, and thus dilated. The observers just trade places.

1 hour ago, MPMin said:

If time is passing slower for observer C, in that clock C is ticking slower than both Clocks A and B, why doesn’t observer C see clocks A and B ticking faster than clock C?

Because kinematic time dilation isn’t something absolute that ‘happens’ locally to a clock - it is a relationship between frames/clocks. 

Think about it - from the vantage point A, the train is in relative motion with some constant speed v, whereas A itself appears stationary. From vantage point of the train on the other hand, frame A is in relative motion with that same speed, whereas the train appears stationary. In both cases the relationship between the frames is the same one - relative motion at speed v - so they both see the same thing, namely the other frame’s clock being dilated. This is also exactly what the mathematics tell you. The relationship between frames is the same one irrespective of which frame you find yourself in - there’s the same relative motion (v is always the same), thus in each case the clock that’s seen to be moving is dilated with respect to the observer, and never appears to be speeding up; you’re plugging the same v into the same formula to obtain time dilation, no matter which frame you are in.

All observers are of course right, even if they don’t agree - but only in their own local frames. This is why measurements of time are not absolute, but depend on which frame they are performed in. This is quite a paradigm shift as compared to our own non-relativistic experience of the world, so it is quite understandable that it seems confusing or even paradoxical at first.

You might wonder whether there are quantities that are not frame-dependent, meaning all observers agree on them, irrespective of relative motion; the answer is yes, but to find them you need to account for both time and space simultaneously. Time dilation always goes hand-in-hand with length contraction, and vice versa. Note that what we are discussing here are kinematic effects - if you add gravity, things become more complicated still.

So the main points are: 

1. Kinematic time dilation is a relationship between clocks (frames), and not something that ‘happens’ locally to a clock. It’s meaningless to say that a single clock is dilated. Nonetheless, this relationship is real (it’s a geometric rotation in spacetime, as it turns out), and thus produces real physical consequences; it’s not just on optical ‘illusion’ based on what you might visually see (though of course optics are affected by this too, so there are corresponding visual effects).

2. Motion is also a relationship between frames, and not an absolute property of an object. 

3. Measurements of time or space on their own are observer-dependent. 

Hopefully this helps.

Edited May 27, 2022 by Markus Hanke

[bangstrom]

1 hour ago, Markus Hanke said:

I’m having difficulty gauging your understanding, based on what is written here.

Are you thinking that (kinematic) time dilation is merely an optical effect, and produces no measurable physical consequences other than what an observer can visually see?

I see the time dilation as genuine and not merely optical and it works both ways.

An observer at the tower sees Einstein’s moving clock as running slower due to kinematic time dilation and, likewise, Einstein sees the the tower clock as running slower since he sees the clock tower as moving away from his position.

So Einstein sees the tower clock running slower as a SR effect but the most evident change is the Newtonian Doppler effect.

[MPMin]

1 hour ago, Markus Hanke said:

I’m having difficulty gauging your understanding, based on what is written here.

Are you thinking that (kinematic) time dilation is merely an optical effect, and produces no measurable physical consequences other than what an observer can visually see?

He perceives it as dilated (‘slowed’), because they are in relative motion with respect to one another.

He also perceives it as dilated, because they are likewise in relative motion. In the formula for kinematic time dilation, the relative speed appears squared, so its relative sign (moving towards or away) is irrelevant.

He perceives both A and B to be dilated (slower), because he finds himself in relative motion with respect to both those frames. He perceives his own watch at C to be ticking normally (no dilation), because there is no relative motion between himself and his watch. They are in the same frame.

No, because he’s in the same frame as that clock, so there is no relative motion. Kinematic time dilation arises due to relative motion between frames.

Observer C himself notices nothing special - his own clock ticks at 1 second per second from his own point of view (no relative motion). However, he sees both A and B going slower - and conversely both A and B see C ticking slower from their own vantage points. That’s because in the frame of the train, both A and B are in motion whereas the train appears stationary; whereas in frames A and B, the train in frame C is in motion, whereas A/B are stationary. In both cases, the respective observer sees the other clock to be in motion, and thus dilated. The observers just trade places.

Because kinematic time dilation isn’t something absolute that ‘happens’ locally to a clock - it is a relationship between frames/clocks. 

Think about it - from the vantage point A, the train is in relative motion with some constant speed v, whereas A itself appears stationary. From vantage point of the train on the other hand, frame A is in relative motion with that same speed, whereas the train appears stationary. In both cases the relationship between the frames is the same one - relative motion at speed v - so they both see the same thing, namely the other frame’s clock being dilated. This is also exactly what the mathematics tell you. The relationship between frames is the same one irrespective of which frame you find yourself in - there’s the same relative motion (v is always the same), thus in each case the clock that’s seen to be moving is dilated with respect to the observer, and never appears to be speeding up; you’re plugging the same v into the same formula to obtain time dilation, no matter which frame you are in.

All observers are of course right, even if they don’t agree - but only in their own local frames. This is why measurements of time are not absolute, but depend on which frame they are performed in. This is quite a paradigm shift as compared to our own non-relativistic experience of the world, so it is quite understandable that it seems confusing or even paradoxical at first.

You might wonder whether there are quantities that are not frame-dependent, meaning all observers agree on them, irrespective of relative motion; the answer is yes, but to find them you need to account for both time and space simultaneously. Time dilation always goes hand-in-hand with length contraction, and vice versa. Note that what we are discussing here are kinematic effects - if you add gravity, things become more complicated still.

So the main points are: 

1. Kinematic time dilation is a relationship between clocks (frames), and not something that ‘happens’ locally to a clock. It’s meaningless to say that a single clock is dilated. Nonetheless, this relationship is real (it’s a geometric rotation in spacetime, as it turns out), and thus produces real physical consequences; it’s not just on optical ‘illusion’ based on what you might visually see (though of course optics are affected by this too, so there are corresponding visual effects).

2. Motion is also a relationship between frames, and not an absolute property of an object. 

3. Measurements of time or space on their own are observer-dependent. 

Hopefully this helps.

Thank you for your in-depth reply.

I think I am understanding the relativistic relationships between A and C in that they are both effectively moving away from each other and it doesn’t matter that C is moving from A to B, as far as C is concerned, A is effectively moving away from C just as C is moving away from A therefore the effect is the same to both A and C observers. The same relativistic relationship thus exists between B and C except they are moving towards each other. 

If all three clocks were synchronised before C departed from A, would they all still be synchronised when C arrives at B? I think I can safely assume that A and B would have remained synchronised.

In the situation that B is observing C coming towards B, both C and B observe each other’s respective clocks ticking slower than their own respective clocks. However, if there is a discrepancy in the synchronisation between C and B when C arrives at B, how does this discrepancy occur when the moving clocks appear to tick slower to each observer than each of the observer’s respective clocks?

To exaggerate the question, imagine that all clocks are synched before C departs from A, and imagine that from B’s perspective, it takes C 1 minute move from A to B, and C happens to move at 50% of the speed of light for the whole trip. Would that mean that when C arrives at B that clock B would be 30 seconds ahead of clock C? And if so, how is it that clock B ticked 30 seconds more than clock C when observer C had been observing clock B to be ticking slower than his own clock at C?

Edited May 27, 2022 by MPMin

[bangstrom]

1 hour ago, Markus Hanke said:

He perceives both A and B to be dilated (slower), because he finds himself in relative motion with respect to both those frames.

He may calculate B's clock to be slower because of time dilation but his perception should be that B's clock is running faster because of the Doppler effect.

11 minutes ago, MPMin said:

To exaggerate the the question, imagine that all clock are synched before C departs from A, and imagine that from B’s perspective, it takes C 1 minute move from A to B, and C happens to move at 50% of the speed of light for the whole trip. Would that mean that when C arrives at B that clock B would be 30 seconds ahead of clock C? And if so, how is that clock B ticked 30 more seconds than C when C had been observing clock B to be ticking slower than C?

Acceleration in velocity slows time exactly as acceleration in a gravitational field slows time so clock C should be running behind A and B as you explained.

[swansont]

5 hours ago, MPMin said:

While the train maintains it’s constant velocity towards B and away from A, does observer C experience a slower passage of time compared to both observers at A and B?

C sees their own clock as ticking at a normal rate. They will measure A and B to be running slow. But since we are talking about light pulses, the pulses coming from A will be spaced out and those from B bunched up. This changes what is seen vs what is happening with the clocks

5 hours ago, MPMin said:

If time is passing slower for observer C, in that clock C is ticking slower than both Clocks A and B, why doesn’t observer C see clocks A and B ticking faster than clock C?

Since the motion is at constant velocity, you can't say who is moving. Time is passing slower for observer C, as measured by A and B. You can't make a blanket statement about time passing slower - it has to be measured in some frame of reference, because time is relative to the frame of reference. Every observer measures moving clocks as running slow. To C, A and B are moving, so C will measure those clocks to be running slow.

5 hours ago, Markus Hanke said:

1. Kinematic time dilation is a relationship between clocks (frames), and not something that ‘happens’ locally to a clock. It’s meaningless to say that a single clock is dilated. Nonetheless, this relationship is real (it’s a geometric rotation in spacetime, as it turns out), and thus produces real physical consequences; it’s not just on optical ‘illusion’ based on what you might visually see (though of course optics are affected by this too, so there are corresponding visual effects).

I'll add that time dilation happens to time in that frame, and that the clocks are measuring the passage of time in that frame.

(Also that nothing is physically happening to the clocks is because this is not a mechanical effect)

[Markus Hanke]

21 hours ago, MPMin said:

If all three clocks were synchronised before C departed from A, would they all still be synchronised when C arrives at B?

No, C will show less elapsed time at the moment of reading his clock as it passes B, since it has been in constant relative motion with respect to B throughout (we assume there was no starting or stopping).

21 hours ago, MPMin said:

I think I can safely assume that A and B would have remained synchronised.

Yes, correct.

21 hours ago, MPMin said:

However, if there is a discrepancy in the synchronisation between C and B when C arrives at B, how does this discrepancy occur when the moving clocks appear to tick slower to each observer than each of the observer’s respective clocks?

That’s because observers C and A/B don’t agree on the distance between A and B - a phenomenon called length contraction, which goes hand in hand with time dilation. Also, there’s a difference between total elapsed time, and instantaneous “tick rate”. The train C reckons that the distant clocks A/B run slower, but he also reckons that the distance A-B is shorter as measured in his frame, so it takes less time on his own train clock (C) to reach B, than it does on B’s clock. So what this means is that yes, B is dilated as reckoned in frame C (just as C is dilated in B) - but the distance A-B is also longer in frame B than it is as seen from C (because A is stationary with respect to B, but neither A nor B are stationary with respect to C). So, when the train arrives, then, as seen from the train C, clock B had to have been measuring out a longer distance at a slower tick rate (remember that speed of light is the same in both frames!), meaning it has to have accumulated more total time than C - even though it was seen as dilated at each instant, just as C was dilated as seen from B. A proper analysis of this will need to reference relativity of simultaneity at each point of the journey, but rest assured that everything works out as self-consistent. In the end, they both agree that total time in C is less than B.

In other words, both observers C and B agree that at the moment of C’s passing by B, the clock C shows less total elapsed time - but they disagree on the reason why that is so. B will say it’s because clock C ran slower, whereas C says it’s because the distance A-B was shorter and thus it took less time to cross it. But both agree on the physical outcome - which is the crucial bit.

Take careful note of the highlighted bit - comparing the clocks needs to happen at a single instant, when the clocks pass by one another at negligible spatial distance, or else you’d need to account for light travel time as well.

A real-world example of just such a scenario is atmospheric muons. These are short-lived, very fast moving particles that are produced just outside the earth’s atmosphere. Without relativity they don’t live long enough to have sufficient time to reach the Earth’s surface. But they do, we detect them. Why? Because of relativity. In the frame of the earth, the muon moves very fast, so it’s associated clock ticks slower (=it lives for longer), and thus reaches the surface in time before it decays. In the frame of the muon, earth’s atmosphere is length-contracted, so it has to cross a shorter distance, and thus lives long enough to reach the surface. Both observers agree on the outcome (=no paradoxes), but they disagree on the reason. This is exactly analogous to your train experiment.

23 hours ago, bangstrom said:

I see the time dilation as genuine and not merely optical and it works both ways.

An observer at the tower sees Einstein’s moving clock as running slower due to kinematic time dilation and, likewise, Einstein sees the the tower clock as running slower since he sees the clock tower as moving away from his position.

Ok, agreed 👍

[MPMin]

Thank you all for your contributions.

I think I’m still not understanding the relationship between C and B where C is approaching B with reference to A.  It’s been noted that observer C sees clock B to be running slower than clock C while travelling towards B with reference to A. However, when both observer C and clock C arrive at clock B, All observers agree that clock C is behind clock B even though observer C saw clock B behind clock C until they arrived at B. It would seem that observer C sees clock B running behind clock C, but as soon as they arrive at B, Clock B must suddenly show the time being ahead of C. Is this correct, or am I missing something?

[Markus Hanke]

15 hours ago, MPMin said:

It would seem that observer C sees clock B running behind clock C

It’s not that simple. In frame C, the instantaneous tick rate of B is dilated, whereas the distance A-B appears longer for frame B than frame C. We have thus far only concerned ourselves with the final result of the experiment (C accumulating less time than B in total) - if you want to analyse what C visually sees on clock B at every moment of the journey, then things become complicated, because C and B do not share a common notion of simultaneity while there is a spatial separation between them. So you would have to account for relativity of simultaneity as well, and the analysis will lead you to the relativistic Doppler effect.

15 hours ago, MPMin said:

Clock B must suddenly show the time being ahead of C. Is this correct, or am I missing something?

In actual fact, what you visually see is that the hands on the distant clock advance faster as compared to your own clock - that’s because these intervals “tick out” a total spatial distance that’s different from yours.

The key issue here is that there’s a difference between instantaneous tick rate, and total accumulated time - the instantaneous tick rate of B is dilated with respect to C, but you’re not sharing the same notion of simultaneity, so if you integrate those small infinitesimals, you end up with longer intervals, and thus more overall time passed as seen by you.

It’s like the distant clock projects pictures of itself at you at a steady rate of 1 frame per time unit - but because you are moving towards the clock at high speed, you are encountering each picture at less than one time unit in your own frame, and there will be more of those pictures in total. This is why it visually looks like it’s running fast. But if you were to compare each picture individually to your own clock, using some appropriate concept of relativity of simultaneity, you’d find the instantaneous readings to be dilated with respect to you. The overall times are different, because the overall distance A-B is also different between these frames.

I’m sorry I don’t know how to explain it better - this is neither intuitive nor particularly simple, despite the quite basic scenario. The devil is in the details. Nonetheless, once the maths are done correctly (also not as simple as it might at first seem!), they are found to correspond to what we actually find in the real world.