coordinate time and proper time.

morrobay

Quote by Matterwave

Depending on your metric, it's either equal to the proper time, or equal to the squareroot of the negative of the square of the proper time (i.e. [itex]ds=\sqrt{-d\tau^2}[/itex]).

Then if the spacetime interval is timelike it is numerically equal to the proper time.
If the spacetime interval is spacelike then it is numerically equal to the proper distance ?

JDoolin

Quote by salvestrom

I don't see how the number of clocks makes a difference. In the ballistic explosion the central non-moving clock is at the heart of the event, experiencing no velocity-based time dilation giving it a unique quality that none of the others have. In the spatial expansion version, I acknowledge that no clock is unique and infact suggest that all the clocks are synchronised since none of them have an actual velocity.

In the first case I simply put forward that the central clock is actually central, non-moving and not in a gravitational field making it an example of an otherwise hypothetical concept, that cannot be found so easily in our actual universe. But then, I put the same thing forward for the second example, but this time say that all the clocks are representative of the hypothetical coordinate clock.

Unfortunately, I don't feel free to discuss this issue on these forums, due to previous infractions. If you'd like to discuss it further, you can send me a private message, or comment on my blog.

Naty1

Apparently that Wikipedia piece IS rather obtuse ...

I'm not going to pursue interpretating those two paragraphs any further [not worth it] , but I wondered when I read them if their comments were trying to point out that clock times vary within a reference frame dependent on different gravitational potentials....

....a clock located at a solar system barycenter would not measure the coordinate time of the barycentric reference frame, and a clock located at the geocenter would not measure the coordinate time of a geocentric reference frame.....

JDoolin

Quote by JDoolin

Unfortunately, I don't feel free to discuss this issue on these forums, due to previous infractions. If you'd like to discuss it further, you can send me a private message, or comment on my blog.

The main thing I don't want to do is "speculate" on this. However, now that the weekend has come, and I was able to put a good five hours of work into the problem, I can show you the idea without any hand-waving.

Quote by salvestrom

I don't see how the number of clocks makes a difference. In the ballistic explosion the central non-moving clock is at the heart of the event, experiencing no velocity-based time dilation giving it a unique quality that none of the others have. In the spatial expansion version, I acknowledge that no clock is unique and infact suggest that all the clocks are synchronised since none of them have an actual velocity.

In the first case I simply put forward that the central clock is actually central, non-moving and not in a gravitational field making it an example of an otherwise hypothetical concept, that cannot be found so easily in our actual universe. But then, I put the same thing forward for the second example, but this time say that all the clocks are representative of the hypothetical coordinate clock.

Here, I have set up a distribution of 5000 "clocks" and given them each a rapidity in the x-direction between -3 and 3, and a rapidity in the y-direction between -3 and 3. I picked out several random clocks and gave them colors. Here is the explosion from the blue-clock's perspective:

And here is the same explosion from the Yellow clock's perspective:

But the point I wanted to make was, if I had, for instance, selected rapidities in the domain of (-100,100) instead of between (-3,3) then there would hardly be any noticeable difference in the distribution for the selected clocks.

So in fact, I guess I mis-spoke, because it's not the number of clocks that makes a difference, but the width of the rapidity space.

If you'd like to see all 11 perspectives, see here

yuiop

Quote by JDoolin

Each clock would still see roughly the same speed-of-light expanding sphere of clocks no matter where it was, unless it was at one edge of the explosion.

It is my hunch that for a universe worth of clocks similar in size and density to ours, light emitted outwards from clocks near the edge would curve back inwards so that even an observer near the edge would still see an apparent expanding sphere of clocks and would not be aware that they were indeed near the edge of the sphere.

JDoolin

Quote by yuiop

It is my hunch that for a universe worth of clocks similar in size and density to ours, light emitted outwards from clocks near the edge would curve back inwards so that even an observer near the edge would still see an apparent expanding sphere of clocks and would not be aware that they were indeed near the edge of the sphere.

That's why I keep saying the clocks are massless. I was hoping to avoid questions about light "curving," so we could discuss the OP's original question, regarding coordinate time, and proper time.

But, let's say, for instance these 5000 clocks have some negligible mass. There would be a problem at t=0 because they occupy a point, and the negligible masses at zero distance would have an infinite force between them.

But, can you somehow relate what you are saying to the animations; actually it doesn't make any sense to me in regards to the diagrams. How would you see an apparent expanding sphere of clocks if you were at the edge of a flat front? If you look in one direction and see a bunch of clocks moving away, and if you look the other way and see no clocks, how could you avoid being aware that you were near the "edge" of the clocks?

ghwellsjr

Quote by JDoolin

That's why I keep saying the clocks are massless.

There's no such thing as a massless clock. That's why time has no meaning for massless particles like photons. You can only build a clock with massive particles and they cannot travel at the speed of light.

Moataz

I have a simple question. From what I understand about relativity and proper time (I am beginner btw) is that when a clock moves at a huge speed, then it will measure different time than the coordinate time in some other reference frame. So, does that mean it really slows down? as in the difference between its ticks is observed to be slower compared to the other synchronized clocks? For example if I matched my wristwatch against a clock and then traveled at the speed of light then stopped and saw another clock that was already synchronized with the first clock, then I will see that my wristwatch does not match anymore. So it seems to me that what happened is just not a matter of mathematical manipulations but rather a physical reality (wristwatch moving slower) is that true?

Also on wikipedia it says second is 'the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom' but that seems absolute to me?

Also, last question when people say synchronizing two clocks. Does this mean just making sure they have the same reading at the time of checking? or does it mean they have the same pace of ticking? For example if two clocks read 12:00 but one ticks faster does this mean they are not synchronized?

Thank you.

Moataz

Also, my book says that this formula only works in inertial frames.

[tex]\Delta \tau = \int \sqrt[]{1-v^2}dt ; v=speed[/tex]

Bu that does not make sense because v is in terms of t and it is supposed to change over time which means there must be acceleration!?

DrGreg

Quote by Moataz

Also, my book says that this formula only works in inertial frames.

[tex]\Delta \tau = \int \sqrt[]{1-v^2}dt ; v=speed[/tex]

Bu that does not make sense because v is in terms of t and it is supposed to change over time which means there must be acceleration!?

"Inertial frame" means the observer is not accelerating. It doesn't mean that the object being observed can't accelerate.

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Moataz	Also, my book says that this formula only works in inertial frames. [tex]\Delta \tau = \int \sqrt[]{1-v^2}dt ; v=speed[/tex] Bu that does not make sense because v is in terms of t and it is supposed to change over time which means there must be acceleration!?