Is clock become slower or faster

[Amit Shukla]

Hello everyone ,

While studying Special Theory of Relativity , I got stucked with a conceptual problem and need
a satisfying answer desperately . My question is - if there are two observers A and B ...A stays
on the Earth B goes in the empty space with the speed say 0.7c . A will measure that B's clock
runs slowly but what B will measure for A's clock ..will it be slower or faster . What I think , that this situation is symmetrical , B in his reference frame sees A moves with the same speed ,so his clock would also runs slower ... I know this problem points out the Twins Paradox Problem ... and both of them challenges my ability to grasp this subject ...Please anyone with
suitable explanation provide me the solution ...Thanks ..!

 

[Passionflower]

Hello everyone ,

While studying Special Theory of Relativity , I got stucked with a conceptual problem and need
a satisfying answer desperately . My question is - if there are two observers A and B ...A stays
on the Earth B goes in the empty space with the speed say 0.7c . A will measure that B's clock
runs slowly but what B will measure for A's clock ..will it be slower or faster . What I think , that this situation is symmetrical , B in his reference frame sees A moves with the same speed ,so his clock would also runs slower ... I know this problem points out the Twins Paradox Problem ... and both of them challenges my ability to grasp this subject ...Please anyone with
suitable explanation provide me the solution ...Thanks ..!

The situation is actually not symmetrical as B leaves the shared frame of reference by accelerating away from A.

 

[JesseM]

Hello everyone ,

While studying Special Theory of Relativity , I got stucked with a conceptual problem and need
a satisfying answer desperately . My question is - if there are two observers A and B ...A stays
on the Earth B goes in the empty space with the speed say 0.7c . A will measure that B's clock
runs slowly but what B will measure for A's clock ..will it be slower or faster . What I think , that this situation is symmetrical , B in his reference frame sees A moves with the same speed ,so his clock would also runs slower ... I know this problem points out the Twins Paradox Problem ... and both of them challenges my ability to grasp this subject ...Please anyone with
suitable explanation provide me the solution ...Thanks ..!

As long as they both move at constant velocity, it is true that in each one's inertial rest frame the other clock is running slower. It has to do with the relativity of simultaneity: for example, if clock A and B start out at the same location both reading a time of 10 seconds and then they move apart at 0.6c, then in A's rest frame the event of A reading 20 seconds is simultaneous with the event of B reading 18 seconds, but in B's rest frame the event of B reading 18 seconds is instead simultaneous with the event of A reading 16.4 seconds, so each one thinks the other is running at 0.8 normal speed.

You might take a look at the diagrams I gave in this thread showing two rows of clocks moving at constant velocity relative to one another, showing how in each row's rest frame, the clocks in the other row are slowed-down and out-of-sync...

 

[JesseM]

The situation is actually not symmetrical as B leaves the shared frame of reference by accelerating away from A.

This asymmetry doesn't change anything though--it doesn't affect the fact that in the inertial reference frame where B is at rest after acceleration, it is A that is running slower than B. And of course you could always just imagine A and B passing each other at constant velocity rather than B accelerating away from A, the analysis of how each is behaving in the other's rest frame once they start moving apart would be no different.

 

[Passionflower]

This asymmetry doesn't change anything though

It seems that we would have to agree to disagree on this one.

--it doesn't affect the fact that in the inertial reference frame where B is at rest after acceleration, it is A that is running slower than B.

Correct, when there is relative motion each observes the other to run slower, but this effect is simply there due to relative motion. While for differential aging we need to have asymmetrical wordlines.

And of course you could always just imagine A and B passing each other at constant velocity rather than B accelerating away from A, the analysis of how each is behaving in the other's rest frame once they start moving apart would be no different.

Yes, but how is that relevant to the case discussed above, I guess I do not get your point.

If they pass each other at constant velocity the situation is symmetrical, if B accelerates away from A the situation is not symmetrical.

 

[JesseM]

Correct, when there is relative motion each observes the other to run slower, but this effect is simply there due to relative motion. While for differential aging we need to have asymmetrical wordlines.

By "differential aging" you mean when one of them accelerates after they had moved apart for a while and reunited at a single location to compare ages, correct? I didn't think the OP was asking about this, the question was just about two clocks A and B moving apart although it was noted that this problem is related to the Twin Paradox (but in any case you didn't seem to be talking about B accelerating to turn around back towards A as in the twin paradox, since you said 'B leaves the shared frame of reference by accelerating away from A')

Yes, but how is that relevant to the case discussed above, I guess I do not get your point.

It's relevant in the sense that the analysis of what happens in each one's rest frame after they start moving apart is basically identical (exactly identical if the initial acceleration is assumed to be instantaneous). For example, if you know A and B are moving apart at 0.7c, the answer to the question "in B's rest frame, what time does A read when B's clock shows they have been moving apart for 5 years" would be the same regardless of whether B had instantaneously accelerated away from A or if B had just passed A at constant velocity. And the question in the OP was "A will measure that B's clock runs slowly but what B will measure for A's clock ..will it be slower or faster", so it doesn't matter to the question whether B accelerated initially or passed A at constant velocity, either way the answer is "A's clock is running slow in B's rest frame, by exactly the same factor that B's clock is running slow in A's rest frame".

 

[Passionflower]

It's relevant in the sense that the analysis of what happens in each one's rest frame after they start moving apart is basically identical (exactly identical if the initial acceleration is assumed to be instantaneous).

As I wrote before there are some time dilation effects when observers are moving wrt each other. But I totally disagree with the notion that these two cases are identical in any way.

I don't think we would disagree at all on any of the numerical outcomes of cases in SR but it just seems we have some philosophical differences of opinion. That is not a big deal and it is probably not worth discussing.

 

[Aemilius]

Hello everyone ,

While studying Special Theory of Relativity , I got stucked with a conceptual problem and need
a satisfying answer desperately . My question is - if there are two observers A and B ...A stays
on the Earth B goes in the empty space with the speed say 0.7c . A will measure that B's clock
runs slowly but what B will measure for A's clock ..will it be slower or faster . What I think , that this situation is symmetrical , B in his reference frame sees A moves with the same speed ,so his clock would also runs slower ... I know this problem points out the Twins Paradox Problem ... and both of them challenges my ability to grasp this subject ...Please anyone with
suitable explanation provide me the solution ...Thanks ..!

Actually is quite simple: You are comparing values in different coordinates systems. The same thing is if you have two maps: one modern with the north in the top and other very old with the north in the bottom. Both maps depicts two cities, one "above" the other. ¿Which one is really above the other? XD

 

[JesseM]

As I wrote before there are some time dilation effects when observers are moving wrt each other. But I totally disagree with the notion that these two cases are identical in any way.

What two cases do you mean? Presumably one is the case I mentioned where they are both moving inertially forever and just pass each other at some point, but what's the second? Again, are you just talking about a case where the only acceleration is an initial one that starts them moving apart, after which they continue to move apart inertially forever, or are you talking about a case where there is an acceleration after they have been moving apart which allows them to come back together and show differential aging? I was only talking about the initial-acceleration case, not the turnaround-case which is obviously quite different. Hopefully you would agree that in the initial-acceleration case there is no objective frame-independent truth about which is really aging more slowly as they move apart, that different inertial frames disagree about who is aging more slowly and all inertial frames are equally valid, right? And hopefully you would also agree that all numerical statements about what happens afterwards would be the same as if they had just passed each other moving inertially rather than one accelerating instantaneously to begin moving apart? If so, then that's at least two sense in which "these two cases are identical", though obviously they are non-identical in terms of what happened before the two started moving apart (I don't know if that's all you meant by 'I totally disagree with the notion that these two cases are identical in any way' or if you meant something more about their non-identicalness).

 

[Passionflower]

What two cases do you mean? Presumably one is the case I mentioned where they are both moving inertially forever and just pass each other at some point, but what's the second?

The second case is when there is acceleration.

Hopefully you would agree that in the initial-acceleration case there is no objective frame-independent truth about which is really aging more slowly as they move apart.

I don't. If two observers are co-located in the same frame of reference and one accelerates away this observer will age less wrt the inertial observer.

 

[JesseM]

The second case is when there is acceleration.

OK, but my whole question was based on distinguishing between two different cases "when there is acceleration" and asking you to tell me which you were talking about:

Again, are you just talking about a case where the only acceleration is an initial one that starts them moving apart, after which they continue to move apart inertially forever, or are you talking about a case where there is an acceleration after they have been moving apart which allows them to come back together and show differential aging?

As I said, I was only talking about the initial-acceleration case and comparing it to the "passing at constant velocity" case, these two cases are identical in the senses I mentioned.

Hopefully you would agree that in the initial-acceleration case there is no objective frame-independent truth about which is really aging more slowly as they move apart.

I don't. If two observers are co-located in the same frame of reference and one accelerates away this observer will age less wrt the inertial observer.

Obviously objects are not "in" a frame of reference in any literal sense, so I guess "in the same frame of reference" is shorthand for "sharing the same rest frame". If so, then relative to that one specific inertial frame where they were initially at rest, it's true that the one that accelerates will thereafter age more slowly, but see the part in bold about a "frame-independent truth" about who is aging more slowly. The fact that objects share the same rest frame does not obligate us to use that frame to analyze their behavior, you could equally well analyze this situation from the perspective of a different inertial frame where the two observers were initially moving at some nonzero velocity together, then when one accelerated it caused his velocity to become lower relative to this frame, so in this frame he ages more quickly then the inertial observer who continues on at the same higher velocity. You're not arguing that this frame's analysis of the situation is any less correct than the analysis in the inertial observer's rest frame, are you?

 

[Passionflower]

As I said, I was only talking about the initial-acceleration case and comparing it to the "passing at constant velocity" case, these two cases are identical in the senses I mentioned.

Yes, I know what you are saying but I am saying they are completely different. One underwent acceleration while the other did not. The wordlines are fundamentally different.

You're not arguing that this frame's analysis of the situation is any less correct than the analysis in the inertial observer's rest frame, are you?

As you can see I wrote wrt the inertial frame. So in others words A and B are co-located with zero relative velocity, B accelerates away from A thus B's clock wrt A's clock will run slower. This may change in the future, perhaps A will accelerate, or B will accelerate again, who knows.

It is like this, if two men, A and B have no money and A wins the lottery we can clearly say that A is richer than B, but, who knows, perhaps next week B might lose it all gambling his fortune and B gets a day job, etc. We can only base our understanding on what is given. And I am not talking about men C, D, E or F. I am simply comparing A and B, just like the poster does by the way.

 

[JesseM]

Yes, I know what you are saying but I am saying they are completely different. One underwent acceleration while the other did not. The wordlines are fundamentally different.

But they are not different in the two specific senses I mentioned--in both cases it is a frame-dependent question as to who is aging slower, and in both cases all numerical questions about what happens to them after they have started moving apart will have identical answers. Do you agree that they are identical in these specific senses? As I said in my earlier post, "obviously they are non-identical in terms of what happened before the two started moving apart (I don't know if that's all you meant by 'I totally disagree with the notion that these two cases are identical in any way' or if you meant something more about their non-identicalness)."

As you can see I wrote wrt the inertial frame.

Yes, but it was part of your explanation for why you didn't agree with my statement "Hopefully you would agree that in the initial-acceleration case there is no objective frame-independent truth about which is really aging more slowly as they move apart." Do you still stand by the claim that you don't agree with that statement, or does highlighting the bolded part show you why an argument about what's true in a single frame does not work as a reason for disagreeing with my claim that there is no frame-independent truth about who is aging slower? If you still disagree with my statement, please explain carefully why you think there is an "objective frame-independent truth" about who is aging slower.

This may change in the future, perhaps A will accelerate, or B will accelerate again, who knows.

I am specifically asking you to consider a situation where after they begin moving apart, they continue to move inertially forever. This is a thought-experiment so we can impose whatever physical conditions we like.

It is like this, if two men, A and B have no money and A wins the lottery we can clearly say that A is richer than B

I don't see how this works as an analogy, as there is nothing analogous to the notion that velocity and rate of aging are both frame-dependent (we don't have different 'frames' that disagree about who is richer). A better analogy might be if two men were standing at the same position and then one took a few steps in one direction, and we asked which man had a greater x-coordinate after they were no longer at the same position--obviously this depend on how we oriented our x and y axes on the ground, it doesn't have any objective answer that's independent of our arbitrary choice of how to label points on the ground with x and y coordinates.

And I am not talking about men C, D, E or F.

Nor am I talking about a different pair of observers, I'm just talking about analyzing the same physical pair from the perspective of different inertial frames, all of which are equally valid in SR regardless of what physical objects are being analyzed (do you disagree with that? Do you think the fact that they started out at rest relative to one another makes the perspective of their mutual rest frame more valid somehow than the perspective of a frame where they are both initially in motion?)

I am simply comparing A and B, just like the poster does by the way.

Yes, and so am I. The OP didn't say anything about wanting to analyze A and B from the perspective of any single specific frame though, in fact the question was clearly about the "symmetry" that can be seen when we analyze the situation from the perspective of different inertial frames:

My question is - if there are two observers A and B ...A stays on the Earth B goes in the empty space with the speed say 0.7c . A will measure that B's clock runs slowly [i.e., in A's rest frame B's clock runs slowly] but what B will measure for A's clock ..will it be slower or faster . What I think , that this situation is symmetrical , B in his reference frame sees A moves with the same speed ,so his clock would also runs slower [i.e., in B's rest frame A's clock runs slowly]

 

[Passionflower]

You know Jesse I understand your position, and perhaps you understand mine as well, although you might think it is invalid. But I think we can honestly say we will not work it out. We won't get at the end where either you or I say "oh yes, I see now you are right I was all wrong".

Are you aware of the 'teaching a pig how to sing' saying? If so then if it satisfies you I can be the pig. ;)

Go ahead and teach it is similar and then spend another 100 postings explaining that the twin paradox is not a paradox. You reap what you sow. :)

 

[JesseM]

You know Jesse I understand your position, and perhaps you understand mine as well, although you might think it is invalid.

No, I honestly don't, the questions I asked were an attempt to try to understand your meaning better (for example, I really am confused about whether you think one inertial frame's perspective is more valid than any other's in this scenario). But if you'd prefer to drop it that's OK with me.

Go ahead and teach it is similar and then spend another 100 postings explaining that the twin paradox is not a paradox. You reap what you sow. :)

The asymmetry in who accelerates initially is irrelevant to understanding the twin paradox, since after all it is always the twin that turns around that is younger when they reunite, the question of which of the two twins accelerated initially makes no difference at all (the twin that turns around after they have been moving apart for some time could easily be different from the twin that accelerated initially).

 

[Passionflower]

since after all it is always the twin that turns around that is younger when they reunite

I fear this is going nowhere but out of curiosity how do you envision an inertial observer turning around?

 

[JesseM]

Go ahead and teach it is similar and then spend another 100 postings explaining that the twin paradox is not a paradox. You reap what you sow. :)

The asymmetry in who accelerates initially is irrelevant to understanding the twin paradox, since after all it is always the twin that turns around that is younger when they reunite, the question of which of the two twins accelerated initially makes no difference at all (the twin that turns around after they have been moving apart for some time could easily be different from the twin that accelerated initially).

I fear this is going nowhere but out of curiosity how do you envision an inertial observer turning around?

I never said the observer who turns around in this twin paradox scenario would be "inertial" (this is a different scenario than the one I had been discussing previously, where the two twins just moved apart forever rather than reuniting as in the twin paradox). My point is just that the question of who accelerates initially is completely irrelevant to determining who has aged less when they reunite, which is the central question in the "twin paradox". If A accelerates initially but B accelerates to turn around after they've been moving apart for a while, then the answer is exactly the same as if B had accelerated initially and then accelerated a second time to turn around; in both cases B will be younger than A by the same amount. So, highlighting the "asymmetry" in the initial acceleration is only going to leave people more confused if you're trying to explain the twin paradox, since this asymmetry is completely unrelated to the asymmetry of one twin being younger when they reunite.

 

[Passionflower]

If A accelerates initially but B accelerates to turn around after they've been moving apart for a while, then the answer is exactly the same as if B had accelerated initially and then accelerated a second time to turn around; in both cases B will be younger than A by the same amount.

That is yet another scenario.

Based on what we are given, e.g. B accelerates away from A we can say that B's clock runs slower wrt A's clock. Introducing all kind of ad hoc scenarios is exactly what I wanted to demonstrate with men A and B and their money, but I fear you don't (want to) understand that.

All right let me stop here because this will get nowhere, just give your response and please do not take it personally if I refrain from replying.

 

[JesseM]

That is yet another scenario.

I only introduced it because you seemed to be claiming that the asymmetry in the original scenario was somehow relevant to the twin paradox (a separate scenario) with your comment "Go ahead and teach it is similar and then spend another 100 postings explaining that the twin paradox is not a paradox. You reap what you sow." If you don't want to talk about other scenarios besides the one given, don't bring them up! The original scenario is not the twin paradox because it says nothing about one accelerating to turn around so that they can reunite at a common location.

Based on what we are given, e.g. B accelerates away from A we can say that B's clock runs slower wrt A's clock.

Nonsense, the fact that B accelerates away from A is a physical fact, it doesn't tell us what frame we must analyze the problem with, if you think that physical facts can somehow force us to use a certain frame you have a fundamental misunderstanding of SR. If all we are given is that B accelerates away from A, we are free to analyze this scenario with any frame we want, including one where A and B were initially moving with nonzero velocity and then B came to rest after accelerating. That is consistent with what was given, it isn't a new scenario.

Introducing all kind of ad hoc scenarios is exactly what I wanted to demonstrate with men A and B and their money, but I fear you don't (want to) understand that.

Do you really not understand the difference between frame-independent physical facts about a physical scenario and frame-dependent descriptions of the scenario?? Hint: money is not frame-dependent, but velocity and rate of aging are. A single physical scenario can be analyzed from anyone of an infinite number of equally valid inertial frames, these aren't "all kinds of ad hoc scenarios", it's the same physical scenario regardless of what frame you choose to label the coordinates of events with. And the original post did not say anything about wanting to analyze things only from the perspective of one frame, as I pointed out earlier the wording of the OP pretty clearly suggested that the whole idea was to look at the "symmetry" when we analyze the same scenario from the perspective of two different frames:

My question is - if there are two observers A and B ...A stays on the Earth B goes in the empty space with the speed say 0.7c . A will measure that B's clock runs slowly [i.e., in A's rest frame B's clock runs slowly] but what B will measure for A's clock ..will it be slower or faster . What I think , that this situation is symmetrical , B in his reference frame sees A moves with the same speed ,so his clock would also runs slower [i.e., in B's rest frame A's clock runs slowly]