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Looking to understand time dilation

by hprog
Tags: dilation, time
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Grimble
#361
Jan4-11, 04:14 AM
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Quote Quote by DaleSpam View Post
Yes, exactly. And since you are measuring the same thing the ratio will be 1 (dimensionless). Similarly, if two clocks measure the same worldline the ratio will be 1.
No, of course I don't mean the SAME circumference, I mean if one were to compare two different circumferences, then one has a ratio; but to compare an entity like a circumference to a diameter, a different entity, then one has the relationship between the two entities, which is not a ratio.
You have had plenty of time to do the spacetime diagram I suggested earlier. How is that coming. Have you finished it yet?
We have one clock that is measuring proper-time along its world-line but how do you define your second clock? Is it the one held by the remote observer? If it is how does it measure the time of a moving body? Or is it just the Lorentz Transformation of the 1st clock's times?

As for the clocks measuring different things; that is the whole point, they are not, they are measuring the same thing (a duration) but in different ways, from different perspectives, which is what relativity is all about! And the ratio between those two measurements is the key to relativity for that is surely how the apparent incompatibility of Einstein's two postulates is resolved. (viz: section 6)
Grimble
#362
Jan4-11, 04:38 AM
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Quote Quote by grav-universe View Post
It doesn't achieve anything one way or the way, only depending upon what we decide is the best way to synchronize clocks. That is all a simultaneity convention is after all, a method by which to synchronize clocks, or a way to determine what a frame's clock settings will be in relation to each other.
I'm afraid I still don't see why anyone would want to synchronise clocks to other than the same time? That is what synchronising clocks means, isn't it, to set them to the same time?
There is no absolute way that clocks must be synchronized, that is the point. For instance, repeating the earlier scenario in a slightly different way, let's say that clocks in frame A are synchronized according to the Einstein simultaneity convention, so that observers in that frame measure light to travel at c in all directions. Now let's say that two observers with some distance between them simultaneously accelerate to a speed v relative to frame A. If the two observers leave their clocks alone, they will no longer measure the speed of light to be the same in each direction between themselves,
???So we have the two observers now in a new FoR, travelling at the same speed with synchronised clocks (showing the same time) at some distance apart, how does this alter their calculation of the speed of light?
but since they have both accelerated simultaneously in the same way to the same speed v, their clocks will read the same according to observers in frame A, and any events that frame A says occur simultaneously, the two observers in their new frame will say the events occur simultaneously as well.

But now let's re-synchronize the clocks of the two observers in their new frame by applying the Einstein simultaneity convention,
But why? They are already sychronised to read the same time and the result of using the Einstein simultaneity convention will be to synchronise them to the same time, how can synchronising them set them to different times???
DaleSpam
#363
Jan4-11, 07:01 AM
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Quote Quote by Grimble View Post
No, of course I don't mean the SAME circumference, I mean if one were to compare two different circumferences, then one has a ratio; but to compare an entity like a circumference to a diameter, a different entity, then one has the relationship between the two entities, which is not a ratio.
Sure it is a ratio. For rectangles it is even called a ratio: the aspect ratio. For circles the ratio is fixed and it is one of the most famous ratios: pi. For right triangles the various ratios are a function of the angle and the ratios are the subject of the trigonometric functions: sin, cos, etc.

Just like all of the above examples, the ratio of two different circumferences is also a dimensionless number. It represents a geometric difference between the two different things being measured, not a conversion between units. Similarly with clocks, they are dilated because geometrically they are measuring the proper time along different world lines.

Quote Quote by Grimble View Post
We have one clock that is measuring proper-time along its world-line but how do you define your second clock? Is it the one held by the remote observer? If it is how does it measure the time of a moving body? Or is it just the Lorentz Transformation of the 1st clock's times?
Don't worry about putting specific clocks on your spacetime diagram. Just draw the coordinate lines t'=0,1,2 and x'=0,1,2 on top of the unprimed frame's coordinate lines t=0,1,2 and x=0,1,2. Use v=0.6c for simplicity
Grimble
#364
Jan5-11, 04:42 PM
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Quote Quote by DaleSpam View Post
Sure it is a ratio. For rectangles it is even called a ratio: the aspect ratio. For circles the ratio is fixed and it is one of the most famous ratios: pi. For right triangles the various ratios are a function of the angle and the ratios are the subject of the trigonometric functions: sin, cos, etc.
If I were to say that an elephant has four legs, that is not the same as saying that everything with four legs is an elephant, is it?
What we are discussing is two measurements of the same distance or the same time.
Those two measurements are different; i.e. contracted or dilated depending upon the perspective of the observers who are performing the measuring.
If two measurements of the same quantity give different values due to the different perspectives of the observers, or due to different ways of measuring then, are they not measuring on different scales?

Anyway we are not here to discuss semantics. We are concerned with relativity, Special Relativity
Now in respect of the apparent incompatability ofthis two postulates, Einstein said in sections 4 6 that
*In view of this dilemma there appears to be nothing else for it than to abandon either the principle of relativity or the simple law of the propagation of light*in vacuo.
and indeed he goes on to say in section 6
At this juncture the theory of relativity entered the arena. As a result of an analysis of the physical conceptions of time and space, it became evident that*in reality there is not the least incompatibility between the principle of relativity and the law of propagation of light,*and that by systematically holding fast to both these laws a logically rigid theory could be arrived at.*
So can you explain HOW he does that, using the moving light clock thought experiment?
For it seems to me that only changing the scale of a measurement achieves this. Maybe that is where I am becoming confused.
JesseM
#365
Jan5-11, 04:53 PM
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Quote Quote by Grimble View Post
I'm afraid I still don't see why anyone would want to synchronise clocks to other than the same time? That is what synchronising clocks means, isn't it, to set them to the same time?
How are you going to define "same time"? Each observer synchronizes their own clocks using the assumption that light signals travel at the same speed in all directions relative to themselves, and the result is that according to each observer's definition of simultaneity, the clocks of the other observer are out-of-sync. If I think my clocks are synchronized and I use my clocks to determine that your clocks are out-of-sync, but you think your clocks are synchronized and you use your clocks to determine that my clocks are out-of-sync, how do you propose to settle the matter? Remember that if we construct our own coordinate systems using clocks synchronized this way, the laws of physics will obey exactly the same equations in both coordinate systems, which means any experiment I do with an apparatus at rest in my frame will give the same result if you do the same experiment with the same apparatus at rest in your frame.

Relativity doesn't rule out the notion that there is some metaphysical truth about simultaneity, so that only one observer's clocks are "really" synchronized. But only God could no that truth--according to relativity, there is no experimental way to show that the laws of physics "prefer" one frame, they are all exactly equivalent as far as empirical experiments go so there can be no experimental basis for judging one frame's definition of simultaneity to be "correct" and another's to be "incorrect".
DaleSpam
#366
Jan5-11, 10:13 PM
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Quote Quote by Grimble View Post
What we are discussing is two measurements of the same distance or the same time.
No, we are not. I have explained this several times already. Please finish the spacetime diagram I suggested. Then you can see geometrically what I am saying.

Quote Quote by Grimble View Post
For it seems to me that only changing the scale of a measurement achieves this. Maybe that is where I am becoming confused.
I think that the problem is more that you have not made any substantial effort to understand the many good explanations you have been given already. Your confusion is therefore likely to remain.
Grimble
#367
Jan6-11, 10:03 AM
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Quote Quote by JesseM View Post
How are you going to define "same time"? Each observer synchronizes their own clocks using the assumption that light signals travel at the same speed in all directions relative to themselves, and the result is that according to each observer's definition of simultaneity, the clocks of the other observer are out-of-sync. If I think my clocks are synchronized and I use my clocks to determine that your clocks are out-of-sync, but you think your clocks are synchronized and you use your clocks to determine that my clocks are out-of-sync, how do you propose to settle the matter? Remember that if we construct our own coordinate systems using clocks synchronized this way, the laws of physics will obey exactly the same equations in both coordinate systems, which means any experiment I do with an apparatus at rest in my frame will give the same result if you do the same experiment with the same apparatus at rest in your frame.

Relativity doesn't rule out the notion that there is some metaphysical truth about simultaneity, so that only one observer's clocks are "really" synchronized. But only God could no that truth--according to relativity, there is no experimental way to show that the laws of physics "prefer" one frame, they are all exactly equivalent as far as empirical experiments go so there can be no experimental basis for judging one frame's definition of simultaneity to be "correct" and another's to be "incorrect".
Then you deny Einstein's notion of simultaneity, two events occurring 'at the same time' as set out here?
DaleSpam
#368
Jan6-11, 10:11 AM
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Quote Quote by Grimble View Post
Then you deny Einstein's notion of simultaneity, two events occurring 'at the same time' as set out here?
Don't be silly, comments like this to someone of JesseM's knowledge are not productive at all. JesseM understands the Einstein synchronization convention quite well. You are admittedly confused on the matter, but seem to be unwilling to learn despite the large amount of good information provided.
JesseM
#369
Jan6-11, 04:54 PM
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Quote Quote by Grimble View Post
Then you deny Einstein's notion of simultaneity, two events occurring 'at the same time' as set out here?
This part of my comment was clearly assuming Einstein's definition: "Each observer synchronizes their own clocks using the assumption that light signals travel at the same speed in all directions relative to themselves, and the result is that according to each observer's definition of simultaneity, the clocks of the other observer are out-of-sync."

Do you not understand that Einstein's definition is based on the assumption that each frame defines "simultaneity" using light signals, making the assumption that all light signals travel at the same speed relative to that frame? He says this in the section you quote:
After thinking the matter over for some time you then offer the following suggestion with which to test simultaneity. By measuring along the rails, the connecting line AB should be measured up and an observer placed at the mid-point M of the distance AB. This observer should be supplied with an arrangement (e.g. two mirrors inclined at 90) which allows him visually to observe both places A and B at the same time. If the observer perceives the two flashes of lightning at the same time, then they are simultaneous.
Obviously if we assumed the light from A did not travel at the same speed as the light from B in the observer's frame, then the fact that the light reached him at the same time would not mean the flashes were simultaneous.

But the in the very next section Einstein makes clear that if observers in different frames all assume light travels at a constant speed relative to themselves, then they will disagree about whether a given pair of events (like the lightning strikes in his example) are simultaneous, which is equivalent to my comment that if each frame synchronizes their own clocks using light-signals, each frame will say the other frame's clocks are out-of-sync. Did you read this part of Einstein's text?
Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.
Do you understand that Einstein's definition of "same time" is frame-dependent, i.e. a pair of events that occur at the "same time" in one frame occurred at "different times" in other frames?

If you have trouble following Einstein's example, you might also consider this one. According to Einstein's definition, two clocks in my frame are "synchronized" in my frame (i.e. they always show a given reading, say 3:00, simultaneously) if, whenever I set off a flash of light at the exact midpoint between the two clocks, both clocks are showing the same reading at the moment the light from the flash reaches them. But now suppose I am on a rocket (with the clocks at the front and back of the rocket) being observed by someone in a different frame who defines simultaneity by assuming light travels at the same speed in all directions relative to himself. If he sees the rocket traveling forward, then after the flash is set off at the middle of the rocket he will see the clock at the back moving towards the position (in his frame) where the flash was set off, while the clock at the front is moving away from that position, so if he assumes the light travels at the same speed in both directions, he must conclude the light reaches the back clock before it reaches the front clock. But I have set my clocks to both show the same reading (say, 3:00) at the instant the light from the flash hits them, so in the observer's frame the clock at the back shows a reading of 3:00 before the clock at the front shows a reading of 3:00, and thus in his frame my two clocks are out-of-sync. Of course as I said, the effect is totally symmetrical, since if he synchronizes his own clocks under the assumption that light travels at a constant speed relative to himself, then in my frame (using my definition of simultaneity) his clocks will be out-of-sync.

So do you understand that according to Einstein's definition, each frame has their own definition of simultaneity and clock synchronization which different frames disagree about, and there is no physical basis to judge one frame's opinion as more "correct" than any other's? If so please read my comment again more carefully and tell me if you disagree with any specific part of it:

How are you going to define "same time"? Each observer synchronizes their own clocks using the assumption that light signals travel at the same speed in all directions relative to themselves, and the result is that according to each observer's definition of simultaneity, the clocks of the other observer are out-of-sync. If I think my clocks are synchronized and I use my clocks to determine that your clocks are out-of-sync, but you think your clocks are synchronized and you use your clocks to determine that my clocks are out-of-sync, how do you propose to settle the matter? Remember that if we construct our own coordinate systems using clocks synchronized this way, the laws of physics will obey exactly the same equations in both coordinate systems, which means any experiment I do with an apparatus at rest in my frame will give the same result if you do the same experiment with the same apparatus at rest in your frame.

Relativity doesn't rule out the notion that there is some metaphysical truth about simultaneity, so that only one observer's clocks are "really" synchronized. But only God could no that truth--according to relativity, there is no experimental way to show that the laws of physics "prefer" one frame, they are all exactly equivalent as far as empirical experiments go so there can be no experimental basis for judging one frame's definition of simultaneity to be "correct" and another's to be "incorrect".
Grimble
#370
Jan7-11, 03:30 AM
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Quote Quote by DaleSpam View Post
Don't be silly, comments like this to someone of JesseM's knowledge are not productive at all. JesseM understands the Einstein synchronization convention quite well. You are admittedly confused on the matter, but seem to be unwilling to learn despite the large amount of good information provided.
I apologise, that comment was not helpful.

I will draw some diagrams.

It may take me a day or two but I will be back. Thank you.
Grimble
#371
Jan12-11, 08:41 AM
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Quote Quote by JesseM View Post
Relativity doesn't rule out the notion that there is some metaphysical truth about simultaneity, so that only one observer's clocks are "really" synchronized. But only God could no that truth--according to relativity, there is no experimental way to show that the laws of physics "prefer" one frame, they are all exactly equivalent as far as empirical experiments go so there can be no experimental basis for judging one frame's definition of simultaneity to be "correct" and another's to be "incorrect".
Thank you Jesse I have never seen it explained better. I do see where I was getting confused by still thinking there was some specific reality.
Would I be right in saying that it isn't so much that light always travels at the same speed in vacuo where ever it travels, but that it is seen to travel at the same speed, in vacuo from whichever frame (perspective) it is viewed from.?

PS will show my diagrams soon.
harrylin
#372
Jan12-11, 11:41 AM
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Quote Quote by Grimble View Post
Thank you Jesse I have never seen it explained better. I do see where I was getting confused by still thinking there was some specific reality.
Would I be right in saying that it isn't so much that light always travels at the same speed in vacuo where ever it travels, but that it is seen to travel at the same speed, in vacuo from whichever frame (perspective) it is viewed from.?

PS will show my diagrams soon.
Quite. The first statement ("it isn't so much..") may be a statement about invisible physical reality, while SRT only makes statements about observables. Your second statement ("but..") corresponds to SRT's light principle, if with "whichever frame" you mean whichever standard "frame". In that context Einstein's formulation of 1907 may also be useful here:

"We [...] assume that the clocks can be adjusted in such a way that
the propagation velocity of every light ray in vacuum - measured by
means of these clocks - becomes everywhere equal to a universal
constant c, provided that the coordinate system is not accelerated."

Note that in GRT that isn't exactly valid anymore.
invain2
#373
Feb3-11, 05:12 PM
P: 1
Quote Quote by hprog View Post
Hi, I am learning SR and I need help to get the idea of relativity with two clocks.

Yet I can understand that two different frames of reference can each one claim to be at rest, since this is just a logical argument.
But I am not getting the point how they can each claim the other ones clock is the one who slows down, after all this is physical question and it is like two people arguing whether the earth is flat or round in which case only one can be right.

To show an example of what bothers me, lets say that I and another person have synchronized clocks.
Now when it is 12:00 on both of our clocks this person takes off in a linear motion and will never return.
so when my clock will show 5:00, then if the other person is the one who moves then his clock will show 4:00, and if I am the one who moves then the other person's clock will show 6:00.
So the person's clock can be either 4:00 or 6:00 but not both, yet we don't know what it is, but this is like if we don't know if the earth is flat or not and it is a physical question, and can have only one answer, even if we don't know what the answer is.

It is clear to me that I am missing something, so what is it?
I believe that, assuming he keeps moving at the speed of light, it will stay 12:00 for him according to Einstein's theory.
JesseM
#374
Feb3-11, 08:29 PM
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P: 8,470
Quote Quote by invain2 View Post
I believe that, assuming he keeps moving at the speed of light, it will stay 12:00 for him according to Einstein's theory.
hprog didn't say anything about the clock "moving at the speed of light", it would just be impossible for an object with mass like a clock to do so in relativity.


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