Special relativity -- 2 parallel space ships & time perception....

[Josh S Thompson]

If two people are in in space ships traveling next to each other at the same speed and they are going close to the speed of light they see each other expiriencing time more slowly. Why does this happen?

 

[Maxila]

They don't see each others time going more slowly. They only see time going more slowly to an observer for which they have a relative velocity (since they are going the same speed there is no relative velocity between them and their clocks tick at the same rate). As to why they would see time go more slowly to an observer for which they had a relative velocity, Relativity does not offer much explanation beyond time rates are different between observers with relative velocity and/or a different gravitational field.

 

[phinds]

As to why they would see time go more slowly to an observer for which they had a relative velocity, Relativity does not offer much explanation ...

I disagree. The cause of time dilation in SR is very simple and can be shown with a simple diagram.

Here's one of hundreds that are available on the internet. This shouldn't even need any explanation.

 

[Maxila]

I disagree. The cause of time dilation in SR is very simple and can be shown with a simple diagram.

Here's one of hundreds that are available on the internet. This shouldn't even need any explanation.

View attachment 87248

I disagree for two reasons, it doesn't offer any clues as why one sees gravitational time dilation, and that diagram would not be applicable to a case where each observer is on the same vector as could be seen in http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muon.html

 

[PeterDonis]

The cause of time dilation in SR is very simple and can be shown with a simple diagram.

This may be a little too simple. What is moving along the arrows? Are you trying to show a light clock?

t doesn't offer any clues as why one sees gravitational time dilation

That's because gravitational time dilation is a different phenomenon; it doesn't work the same as time dilation in SR, and you have to understand it separately.

that diagram would not be applicable to a case where each observer is on the same vector

What does "on the same vector" mean?

 

[Josh S Thompson]

I thought time dilation for special relativity was all about the difference in the two objects speed, then, in order to not break the speed of light time slows down.

But why would time slow down if the distance between the space ships is not changing,

 

[Maxila]

What does "on the same vector" mean?

Observer A at point 1, Observer B at point 2

 

[phinds]

This may be a little too simple. What is moving along the arrows? Are you trying to show a light clock?

This is the classic example of an astranaut in a space-ship shining a light perpendicular to the motion of the ship to a mirror on the floor and having it go down and come back up in a straight line. But to an observer for whom the ship is moving, the light beam is taking a "V" path, which has to be longer and since the speed of light can't be different only the time can be different, thus time dilation.

 

[PeroK]

Observer A at point 1, Observer B at point 2

It's difficult to see how two points could fail to be on the same vector!

Also, the same time dilation would apply to any other observer at rest with respect to an observer at point 1. So, the location of the observer is not important, only the relative velocity.

 

[PeterDonis]

why would time slow down if the distance between the space ships is not changing

It wouldn't. If the distance between the ships is not changing, then they are not moving relative to each other, so they don't see each other as time dilated. Maxila already pointed this out in post #2.

 

[PeterDonis]

Observer A at point 1, Observer B at point 2

I don't see how this is relevant to what we're discussing. You can always draw an arrow between two points. So what?

 

[PeterDonis]

This is the classic example of an astranaut in a space-ship shining a light perpendicular to the motion of the ship to a mirror on the floor and having it go down and come back up in a straight line. But to an observer for whom the ship is moving, the light beam is taking a "V" path, which has to be longer and since the speed of light can't be different only the time can be different, thus time dilation.

In other words, it's a light clock.

 

[phinds]

In other words, it's a light clock.

Didn't know it by that name, but sounds reasonable.

 

[Maxila]

I don't see how this is relevant to what we're discussing. You can always draw an arrow between two points. So what?

You seem to be missing, or not understood the context to which it was made. If rereading what the comment was in reply too doesn't clear it up, please feel free to then ask me for clarification.

 

[Dale]

I re-read it in context including the hyperphysics link. I also don't see the relevance. You can always draw a vector between two points.

 

[Maxila]

I re-read it in context including the hyperphysics link. I also don't see the relevance. You can always draw a vector between two points.

First, I agree with Peter that the diagram phinds posted is an oversimplification of time dilation. In my reply regrading phinds diagram I said, "that diagram would not be applicable to a case where each observer is on the same vector". Peter later replied he didn't know what I meant by that and I linked the picture of a vector with two points and noted them as observers at each point.

This was meant to illustrate to phinds, that the diagram showing a longer light path as an explanation of time dilation, is not applicable to a case where the relative velocity between observers and the light path are all on the same vector.

 

[Dale]

This was meant to illustrate to phinds, that the diagram showing a longer light path as an explanation of time dilation, is not applicable to a case where the relative velocity between observers and the light path are all on the same vector.

Yes. The illustration only works for the situation where the relative velocity is perpendicular to the light path in the frame where the clock is at rest. Since you can always posit a clock in such an orientation the result is general even if the illustration is not.

 

[PeterDonis]

This was meant to illustrate to phinds, that the diagram showing a longer light path as an explanation of time dilation, is not applicable to a case where the relative velocity between observers and the light path are all on the same vector.

Ah, I see. Yes, you're right, phinds' diagram doesn't cover that case. However, if you analyze that case, under the assumption that the speed of light is constant, it also turns out to show time dilation in the amount predicted by the SR formula. In fact, it's instructive to put both light beams (parallel and perpendicular to the direction of motion) in the same scenario, and verify that, if the distances in both directions are the same in the rest frame of the clock, so the two beams coincide on their return, they will also coincide on their return when viewed in a frame in which the clock is moving (parallel to one beam path and perpendicular to the other).