Accelerations at various distances.

[g_sanguinetti]

Does anyone assert that time runs, faster for object "P", as seen from object "Q", (as opposed to slower) when object "P" accelerates toward (Or would it be away? If it is away, modify the following follow-up question accordingly. ) object "Q"?

If so:
Does anyone assert that the magnitude of such an effect is distance dependent?

If so:
Consider the case of objects "A", "B", and "C", where "A", "B" and "C" start off in the same inertial frame and lay on a straight line and where "A" and "B" are a great distance apart and "C" is near 'B' and where "C" accelerates toward both "A" and "B". There should be no time dilation between "A" and "B" yet there would be different observed times for the "C" by "A" and "B".

Can this be when 'A' and 'B' are both in the same inertial frame?

Thanks,

- George -

 

[Fredrik]

If Q is inertial, then the distance to P and the acceleration of P are both irrelevant. The direction of the velocity is too. Only the speed is relevant. (Assuming that we are only interested in the relative ticking rates).

 

[g_sanguinetti]

If Q is inertial, then the distance to P and the acceleration of P are both irrelevant. The direction of the velocity is too. Only the speed is relevant. (Assuming that we are only interested in the relative ticking rates).

That is what I always thought (and still do, actually); and that is why I started some other threads. Let me direct you this thread, if you read though it you will see that I have come across a contrary opinion that is relied on to evade the time dilation paradoxes as I have presented them: https://www.physicsforums.com/showthread.php?t=183104

 

[JesseM]

That is what I always thought (and still do, actually); and that is why I started some other threads. Let me direct you this thread, if you read though it you will see that I have come across a contrary opinion that is relied on to evade the time dilation paradoxes as I have presented them: https://www.physicsforums.com/showthread.php?t=183104

You are confusing things here, I never said that time runs faster for an accelerating clock as measured by any inertial frame, which is the only type of frame that's normally used in SR. However, if you construct a non-inertial coordinate system where an accelerating observer is at rest (where the normal rules of SR no longer apply--for example, the coordinate speed of light may be something other than c), then in this coordinate system distant clocks may run faster. What I said was:

On the other hand, if you want to analyze things from the perspective of a non-inertial coordinate system where each twin is at rest throughout the entire trip (both before and after accelerating), it depends on the details of how you construct this non-inertial coordinate system (how you define simultaneity at different points in the trip, for example), there isn't really a single set way to do it. I suppose the most natural way would be to construct your non-inertial coordinate system so that its definition of simultaneity and distance at each moment always matches the definitions of the instantaneous inertial rest frame of the ship at that moment, and such that the time coordinate of events along the ship's worldline always matches the proper time of the ship (time according to the ship's own clock). If you do it this way, then in each ship's non-inertial coordinate system the second ship's clock will be running slow during the non-accelerating portions of the first ship's worldline, but will run fast--possibly extraordinarily fast, depending on how quick the acceleration is--during the accelerating portions.

 

[Fredrik]

That is what I always thought (and still do, actually); and that is why I started some other threads. Let me direct you this thread, if you read though it you will see that I have come across a contrary opinion that is relied on to evade the time dilation paradoxes as I have presented them: https://www.physicsforums.com/showthread.php?t=183104

You got some good answers in the other thread. I don't see anything I disagree with there. I haven't examined every word though. What in Jesse's answers do you think disagrees with what I said?

 

[g_sanguinetti]

If Q is inertial, then the distance to P and the acceleration of P are both irrelevant. The direction of the velocity is too. Only the speed is relevant. (Assuming that we are only interested in the relative ticking rates).

"Using the type of coordinate system I describe above, it would have to do with the fact that even though the accelerations are equal on different trips, if the inertial phases of the trips were different lengths than the distance to the second ship during the period when the first ship accelerates will be different on different trips (and vice versa), and the amount that the second ship's clock jumps forward in the first ship's non-inertial coordinate system is a function of distance, a bigger move forward at greater distances."

First off, does everyone agree with the statement made in the bold italics above?

Next the underline statement, unless I am misinterpreting it, is not true simply by the way I set up the experiment - all accelerations are equal and opposite for the two ships.

Also, I can phrase it this way, what I wanted to know initially were two things: 1) Will the same number of back to back muon decays occur in each ship, i.e., will the clocks run the same - choose whatever coordinate system you like - but keep each set of different length journey equal and opposite for the participants.
And I asked: 2) If it is in the acceleration phase that all journeys compensate for the slowing of the clocks how could that occur when the slowing phases were different and the acceleration phases of the same magnitude?

The answer I think I'm getting here is that "time speeding" is distance depend. Does everyone agree that the amount of time speeding that occurs during accelerations is distance depend?

And because of this answer I started the threads "orbital time dilation", which may or may not be pertinent, and of course this thread.

Anyway, I appreciate all input.

Thanks,

- George -

 

[g_sanguinetti]

"If Q is inertial, then the distance to P and the acceleration of P are both irrelevant."

Did you answer a question I didn't ask then? I'm asking about time changes during accelerations at various distances.

 

[JesseM]

"If Q is inertial, then the distance to P and the acceleration of P are both irrelevant."

Did you answer a question I didn't ask then? I'm asking about time changes during accelerations at various distances.

You can talk about accelerating objects without using a non-inertial frame--do you understand the distinction? A frame is just a coordinate system, and an inertial frame is one where if an object has a constant position coordinate, then the object isn't accelerating, in the sense that the object feels no G-forces (one can imagine constructing the coordinate system physically using a grid of non-accelerating rulers and clocks which fill space, so if an event happens next to the 12-meter mark on the x-axis ruler and the clock at that mark reads 5 seconds when the event happens, then the event is assigned coordinates x=12 meters, t=5 seconds). But you can certainly use this coordinate system to assign coordinates to an object which has a changing position coordinate, and also a changing coordinate velocity, i.e. an accelerating object.

 

[g_sanguinetti]

I have no problem with any of that.

And now for the original question. . . ?

Does time speed up in accelerating frames?

Is it distance dependant?

(Time slows in a gravitational field doesn't it? For those interested in trying to answer this thread, don't let answering this side question side track you, please.)

Thanks Again.

 

[JesseM]

I have no problem with any of that.

And now for the original question. . . ?

Does time speed up in accelerating frames?

Is it distance dependant?

If you define the accelerating coordinate system in the way I suggested, where at any given instant the accelerating coordinate system's definition of simultaneity must match that of the object's instantaneous inertial reference frame, then in this type of coordinate system it is possible for other clocks to speed up, and this will depend on their distance from the reference object. What is your objection to this? The argument in your first post was:

Consider the case of objects "A", "B", and "C", where "A", "B" and "C" start off in the same inertial frame and lay on a straight line and where "A" and "B" are a great distance apart and "C" is near 'B' and where "C" accelerates toward both "A" and "B". There should be no time dilation between "A" and "B" yet there would be different observed times for the "C" by "A" and "B".

Can this be when 'A' and 'B' are both in the same inertial frame?

Here you are using the phrase "in the same inertial frame" in an ambiguous way. A and B have the same inertial rest frame, but the frame in which A ticks faster than B would be a non-inertial coordinate system centered on C. Objects are not inherently "in" one frame or another, one can consider the same object from the perspective of any coordinate system, so just as I said above that we can analyze an accelerating object from the perspective of an inertial coordinate system, here we are analyzing the inertially-moving objects A and B from the perspective of a non-inertial coordinate system.

The definition of simultaneity in the non-inertial system is key here. If clocks at A and B were synchronized in the inertial rest frame of A and B, so in this frame when A reads 10 seconds B also reads 10 seconds, that means in the rest frame of an inertial observer D moving towards A and B at a constant speed, A's clock will be ahead of B's, so when B reads 20 seconds A might read 30 seconds. So obviously if we design the non-inertial coordinate system such that its definition of simultaneity always matches that of C's instantaneous inertial rest frame at that moment, then if C starts out at rest relative to A and B when both read 10 seconds in C's instantaneous inertial rest frame, and then C accelerates until its instantaneous inertial rest frame matches that of D, and at that moment in the instantaneous inertial rest frame B reads 20 seconds, then A must have advanced forward to 30 seconds in this time in the non-inertial coordinate system which is defined in this way.

You also said:

Next the underline statement, unless I am misinterpreting it, is not true simply by the way I set up the experiment - all accelerations are equal and opposite for the two ships.

What experiment were you referring to here? The thought-experiment in your original post seemed to be one where A and B remain inertial while C accelerates to move from B's position to A's position, so I don't understand what you mean by "all accelerations are equal and opposite for the two ships".

 

[g_sanguinetti]

Sorry about that last one about equal and opposite accelerations. I was referring to a related but different thread. You can ignore for this thread.

As for the others why look at them from "c's" point of view? I just find it curious that if "A" and "B" are in the same reference frame that "c's" clock would appear different to each dependant and their distance from "c" (given that "c" is accelerating). But this is what you are saying, correct?

Thanks for your patience.

- George -

 

[JesseM]

As for the others why look at them from "c's" point of view? I just find it curious that if "A" and "B" are in the same reference frame that "c's" clock would appear different to each dependant and their distance from "c" (given that "c" is accelerating). But this is what you are saying, correct?

No, no! The distance-dependent rate of ticking is solely in a non-inertial reference frame, I thought I made that quite clear. Of course in the inertial rest frame of A and B, the rate any clock is ticking (including C's) depends solely on its speed at that moment.

 

[g_sanguinetti]

No, No, back. :-)

What I'm saying is that those in the inertial frames would see those in the accelerated frames' clocks change, though, correct? And that would be speed up if approaching, correct? (Or would it be slow down? :-) )

Now that we have established the general backround for my questions, a series of short questions and short answers may be very productive for me. Please hang in there.

:-)

Thanks Again.

 

[JesseM]

What I'm saying is that those in the inertial frames would see those in the accelerated frames' clocks change, though, correct? And that would be speed up if approaching, correct? (Or would it be slow down? :-) )

Are you talking about what they see visually (which is influenced by the Doppler effect) or what is actually true in their rest frame? In their rest frame the accelerated clock is always running slower than their own, not faster.

 

[g_sanguinetti]

Are you talking about what they see visually (which is influenced by the Doppler effect) or what is actually true in their rest frame? In their rest frame the accelerated clock is always running slower than their own, not faster.

I am primarily interested in what is actually true, however, how it would appear to each other is also very interesting.

The clocks appear to run slower no matter what the direction?

If the clocks always appears to run slower then we have a real paradox, don't we?


Thanks,

- George -

 

[MeJennifer]

I am primarily interested in what is actually true

Only what you can actually measure is true, that is the basic premise of the scientific method. Note that inferences by using a so called plane of simultaneity is not something that is actually physical, it cannot be because such a plane is not causally connected, it is only in the imagination of human beings. See for instance the Andromeda paradox for some of the "absurdities" that arise when insisting on the reality of a plane of simultaneity.

 

[g_sanguinetti]

Physics and Metaphysics, some truisms:
The Universe is no doubt stranger than we can imagine. Paradoxes are clues to where we should direct our thinking. Our models are the state of our understanding. If they do not meet our expectations then either their premises or our expectations need to be modified. If they predict, then maybe it is our expectations that need to change, if they don't, then absolutely their permises must change.

Do you think that the concept of the "plane of simultaneity" is wrong as it is presently conceived?

Thanks for the input.

- George -

 

[JesseM]

I am primarily interested in what is actually true, however, how it would appear to each other is also very interesting.

The clocks appear to run slower no matter what the direction?

Your language is still ambiguous, you really need to specify whether you are talking about what is seen visually, or what is true in terms of the coordinates of a given frame (and if the latter, whether you are asking about an inertial frame or a non-inertial one).

 

[g_sanguinetti]

Your language is still ambiguous, you really need to specify whether you are talking about what is seen visually, or what is true in terms of the coordinates of a given frame (and if the latter, whether you are asking about an inertial frame or a non-inertial one).

I want to know what actually happens.

 

[JesseM]

I want to know what actually happens.

The usual perspective is that there are only objective truths about frame-independent facts such as local events happening at a single location in both space and time (like what two small clocks read at the moment they arrive at the same position), there isn't any objective truth about the spatial distance between two ends of an object, at least not one that any physical experiment can discover. But what you said was "I am primarily interested in what is actually true, however, how it would appear to each other is also very interesting." So, my question was about what exactly you meant by "appear", especially in the case when you then asked "The clocks appear to run slower no matter what the direction?" If you're talking about visual appearance the Doppler effect is relevant (because of the Doppler effect, a clock moving towards you will visually look like it's running faster), if you're talking about what appears to be true in the coordinates of your inertial rest frame the answer is that a moving clock always runs slower than your own (i.e. the gap between the time-coordinates assigned to each tick of the moving clock is larger than the gap between time-coordinates of yours), if you're talking about what appears to be true in a non-inertial coordinate system then in this case a clock which is moving in this system can run either faster or slower.

 

[Fredrik]

"If Q is inertial, then the distance to P and the acceleration of P are both irrelevant."

Did you answer a question I didn't ask then? I'm asking about time changes during accelerations at various distances.

You didn't say that both P and Q were accelerating, so I assumed that Q wasn't.

And now for the original question. . . ?

Does time speed up in accelerating frames?

Is it distance dependant?

The whole idea of an accelerating frame is kind of tricky. What you have to understand is that the "point of view" of the accelerating observer isn't a well-defined concept in general. The only case I know where there's a "natural" way to associate a specific coordinate system with the accelerating observer is when the acceleration is constant. The one thing that's always well-defined is the time coordinate on the observer's world line. His clock will always show the result of the integral of $\sqrt{-g_{\mu\nu}dx^\mu dx^\nu}$, so it's natural to use that as the time coordinate, but the assignment of a time coordinate to events that aren't on the world line is more or less arbitrary.

The clocks appear to run slower no matter what the direction?

If the clocks always appears to run slower then we have a real paradox, don't we?

I haven't followed the whole conversation between you and JesseM, but this looks like a question that's answered in just about every thread about the twin paradox. Have you read any of those?

 

[g_sanguinetti]

Honestly, I'm trying to pin the explanation down step by step. I haven't been happy with the explanations (Haven't read all of them - I may step-up the level of my own diligence due to a rekindled interest, however.) that I ever gotten anywhere.

Here is one more step.
If possible let's look at the problem, for now, soley from the point of view of the interial frames, call them "xxx - the inertial frames". In fact lets, also for now, hold to simple non-explanatory answers, too - sort of like the game "20 questions".
(Hey, saves everyone work. ;-) )

Do the clocks of accelerating bodies always speed up when approaching "xxx - the inertial frames"?

a) Yes b) No c) Maybe d) I don't know e) Who cares?
f) All of the preceding g) None of the preceding


Next step: Do the clocks of accelerating bodies always slow down when receding from "xxx - the inertial frames"?

a) Yes b) No c) Maybe d) I don't know e) Who cares?
f) All of the preceding g) None of the preceding

Step three: Is it always distance dependent? Or is it always distance independant?

a) Yes b) No c) Maybe d) I don't know e) Who cares?
f) All of the preceding g) None of the preceding

I'm sorry for the draconian methods but this is slippery stuff
I hope we all have a sense of humor.
And I hope everyone chimes in.

Thanks a whole lot.



- George -

 

[g_sanguinetti]

The usual perspective is that there are only objective truths about frame-independent facts such as local events happening at a single location in both space and time (like what two small clocks read at the moment they arrive at the same position), there isn't any objective truth about the spatial distance between two ends of an object, at least not one that any physical experiment can discover. But what you said was "I am primarily interested in what is actually true, however, how it would appear to each other is also very interesting." So, my question was about what exactly you meant by "appear", especially in the case when you then asked "The clocks appear to run slower no matter what the direction?" If you're talking about visual appearance the Doppler effect is relevant (because of the Doppler effect, a clock moving towards you will visually look like it's running faster), if you're talking about what appears to be true in the coordinates of your inertial rest frame the answer is that a moving clock always runs slower than your own (i.e. the gap between the time-coordinates assigned to each tick of the moving clock is larger than the gap between time-coordinates of yours), if you're talking about what appears to be true in a non-inertial coordinate system then in this case a clock which is moving in this system can run either faster or slower.

(I actually responded to Fredrik's latest post before I read this one - I'll let my repsonse to Fredik's post stand for any intrepid gallant warriors who care to play my question and answer game.)

I like this well stated response, JesseM - on top of that, I find it quite interesting because it nibbles at the the nature of science itself.

"if you're talking about what appears to be true in a non-inertial coordinate system then in this case a clock which is moving in this system can run either faster or slower."

Always faster when approaching;
always slower when receding, correct?
And always distance dependant, correct?

Thanks,

- George -

 

[g_sanguinetti]

The usual perspective is that there are only objective truths about frame-independent facts such as local events happening at a single location in both space and time (like what two small clocks read at the moment they arrive at the same position), there isn't any objective truth about the spatial distance between two ends of an object, at least not one that any physical experiment can discover. But what you said was "I am primarily interested in what is actually true, however, how it would appear to each other is also very interesting." So, my question was about what exactly you meant by "appear", especially in the case when you then asked "The clocks appear to run slower no matter what the direction?" If you're talking about visual appearance the Doppler effect is relevant (because of the Doppler effect, a clock moving towards you will visually look like it's running faster), if you're talking about what appears to be true in the coordinates of your inertial rest frame the answer is that a moving clock always runs slower than your own (i.e. the gap between the time-coordinates assigned to each tick of the moving clock is larger than the gap between time-coordinates of yours), if you're talking about what appears to be true in a non-inertial coordinate system then in this case a clock which is moving in this system can run either faster or slower.

(I actually responded to Fredrik's latest post before I read this one - I'll let my repsonse to Fredik's post stand for any intrepid gallant warriors who care to play my question and answer game.)

I like this well stated response, JesseM - on top of that, I find it quite interesting because it nibbles at the nature of truth and science.

"if you're talking about what appears to be true in a non-inertial coordinate system then in this case a clock which is moving in this system can run either faster or slower."

Always faster when approaching;
always slower when receding, correct?
And always distance dependant, correct?


Now this all should be analogous to what happens in a gravitational field, i.e., "Equivalency", correct?. (No need to get too in depth with your response to this one.)

Thanks,

- George -

 

[Fredrik]

Do the clocks of accelerating bodies always speed up when approaching "xxx - the inertial frames"?

a) Yes b) No c) Maybe d) I don't know e) Who cares?
f) All of the preceding g) None of the preceding

I think the answer is probably a). The reason I can't answer with certainty is that you haven't defined what it means to "approach" an inertial frame. What I can say with certainty is this: 1. The time axis of an inertial frame is (by definition) a geodesic. 2. Geodesics are (by definition) curves that maximize a proper time integral. 3. Proper time is (by postulate) what you measure with a clock.

 

[g_sanguinetti]

I think the answer is probably a). The reason I can't answer with certainty is that you haven't defined what it means to "approach" an inertial frame. What I can say with certainty is this: 1. The time axis of an inertial frame is (by definition) a geodesic. 2. Geodesics are (by definition) curves that maximize a proper time integral. 3. Proper time is (by postulate) what you measure with a clock.

Thanks for your reply.

It probably would had been better for me to say "get closer and closer to objects that are in an inertial frame" instead of approach . . . .

Now is this phenomenon always distance dependant - always changing the rate of time passage in direct proportion to the distance the objects are away from each other? . . .

 

[Fredrik]

OK, I thought you meant something completely different. The answer is b). The ticking rate of the other clock depends only on its speed in the inertial frame, not on its acceleration or on the direction of its velocity.

This discussion seems to be heading towards the standard mistake in the twin "paradox", so I'll include my standard answer here (posted several times before):

http://web.comhem.se/~u87325397/Twins.PNG

I'm calling the twin on Earth "A" and the twin in the rocket "B".
Blue lines: Events that are simultaneous in the rocket's frame when it's moving away from Earth.
Red lines: Events that are simultaneous in the rocket's frame when it's moving back towards Earth.
Cyan (light blue) lines: Events that are simultaneous in Earth's frame.
Dotted lines: World lines of light rays.
Vertical line in the upper half: The world line of the position (in Earth's frame) where the rocket turns around.
Green curves in the lower half: Curves of constant -t^2+x^2. Points on the two world lines that touch the same green curve have experienced the same time since the rocket left Earth.
Green curves in the upper half: Curves of constant -(t-20)^2+(x-16)^2. Points on the two world lines that touch the same green curve have experienced the same time since the rocket turned around.

From A's point of view B is aging at 60% of A's aging rate. From B's point of view A is aging at 60% of B's aging rate. The reason this isn't a paradox is that the moment before B turns around, he's in a frame where A has aged 7.2 years, and the moment after he's turned around, he's in a frame where A has aged 32.8 years.

(I'm going to bed now, so I won't be answering questions for at least 8 hours, but maybe JesseM or someone else will).

 

[Fredrik]

"if you're talking about what appears to be true in a non-inertial coordinate system then in this case a clock which is moving in this system can run either faster or slower."

Always faster when approaching;
always slower when receding, correct?
And always distance dependant, correct?

I didn't see this post yesterday...weird. Your question here is difficult to answer, but not just because it would take some math to find the correct answer. The problem is (as I said before) that there's no obvious way to assign a time coordinate to events that aren't on the accelerating observer's world line. That makes it difficult to even define what it means for one clock to tick faster (or slower, or at the same rate) as another.

 

[MeJennifer]

That makes it difficult to even define what it means for one clock to tick faster (or slower, or at the same rate) as another.

I suppose I do not see the problem. Clearly an accelerating observer who observes a distant beacon that produces a clock signal can measure the rate of this distant clock according to his local clock.

 

[JesseM]

I suppose I do not see the problem. Clearly an accelerating observer who observes a distant beacon that produces a clock signal can measure the rate of this distant clock according to his local clock.

I believe Fredrik is talking about defining simultaneity in a non-inertial coordinate system where the accelerating observer is at rest (which, assuming coordinate time along the observer's worldline matched his own clock time, would allow you to define how fast distant clocks are ticking in this coordinate system), not about the rate that signals from a distant clock are reaching the observer (just like the time dilation of moving clocks in inertial coordinate systems is different from the rate that signals from the moving clock reach the inertial observer, which is influenced by the Doppler effect).