Time Dilation

[nitsuj]

A body moves at 0.9999 c, in my FoR i have placed two devices one light second distance apart. As the body passes right next to each device it (body or device) flashes a pulse of light. Would it look like this from my FoR?

 

[ghwellsjr]

Yes, after about 7.5 seconds after the first flash.

 

[nitsuj]

I think this is what the body sees from its FoR, (not scaled with first picture, just to illustrate body is in the middle of the light rings).

With the picture in the first post, Im guessing where the line crosses the circles the distance between is 1 light second, which is the distance between the light pulse triggering devices.

This spacing gets smaller towards the area of the body where the circles pretty much are in the same spot (picture in first post).




From my FoR, is the spacing between the cirlces (picture in first post) all of the same interval (as the 0.9999c body would measure, one light second)? I read from Taylor & Wheeler that intervals are invariant.

 

[ghwellsjr]

I think this is what the body sees from its FoR (body is in the middle of the light rings).

Your second image is what it looks like in the body's FoR, but it's not what the body can see. The only way observers can "see" traveling light is to put reflectors at equally-spaced locations with respect to themselves and then all they can tell is the round-trip speed of light measures to be the same for all of them. But they cannot conclude exclusively from any measurement or observation that the light looks like it does in the FoR. Each FoR defines the speed of light to be a constant in that frame which is the reason the two FoR's give a different image.

With the picture in the first post, Im guessing where the line crosses the circles the distance between is 1 light second, which is the distance between the light pulse triggering devices.

No, it's just under 2 light seconds. The flashes occurred 1 second apart so the radii of the circles will have a difference of 1 light second but the difference in the diameters is 2 light seconds.

This spacing gets smaller towards the area of the body where the circles pretty much are in the same spot (picture in first post).

Correct.

From my FoR, is the spacing between the cirlces (picture in first post) all of the same interval (as the 0.9999c body would measure, one light second)? I read from Taylor & Wheeler that intervals are invariant.

The difference in the center points of the two circles is 0.9999 light seconds.

Have you seen my animation that illustrates how two observers with a relative speed of 0.5c will both think they are in the center of an expanding circle of light that was emitted when they were colocated?

https://www.youtube.com/watch?v=dEhvU31YaCw

 

[nitsuj]

Thanks for the replies ghwellsjr

I see that in the first image the distance between the light pulse circles at the bottom is not 1 light second.

But I see it as the distance between the devices 1 light second + the time it takes the body to pass by each device and trigger the light pulses 1.0001 light seconds (1/.9999) so 2.0001 light seconds.

Your animation looks really cool, but I can't tell what the Green and Red circle represent. Im still trying to understand what I see in my single frame image :)

oh wait it looks like the yellow circles that follow each FoR illustrates the transformation and reflects the light pulse back to the observer (so they can measure of course :) The green and red circles are the reflection and show the time dilation (green collapses before red). Very slick

 

[ghwellsjr]

You are right, thanks for correcting my mistake.