Events for frame changing clocks

[Dale]

Ok, if any single inertial frame can explain everything then pick up S and/or S' and please explain me my original post. The requirement is there should not be any duplicating and skipping events.

In S first A accelerates then B accelerates then C accelerates. Each red and the cooresponding green dots are simultaneous in S.

No events are duplicated nor skipped.

 

[Mentz114]

The requirement is there should not be any duplicating and skipping events.

Obviously, if we send two light beams, one in each direction, from any point on any of the worldlines, then every other WL will receive news of the event in some (finite) time, and once only. So no event can possibly be missed or duplicated by realistic observers on those WLs.

I believe the duplicating and skipping events is due to an incorrect use of the LT, ignoring signal spped and making incorrect assumptions about events lying on LoS, which are naturally not causally connected.

Incorporating the finite signal speed, for instance by using the times and locations assigned by a radar-observer ( Dolby & Gull's method) any hint of this weirdness disappears. Causality rules.

After you answer all my questions in bold, I would like you to explain to me the "new method for defining LoS", please.

This refers to the Dolby&Gull paper, the link is in a Dalespam post earlier http://arxiv.org/abs/gr-qc/0104077

 

[ghwellsjr]

Ok, if any single inertial frame can explain everything then pick up S and/or S' and please explain me my original post. The requirement is there should not be any duplicating and skipping events.

Did you read post #44 where I said that yuiop already provided this for you and you rejected it? Look at post #7 where he drew it from the point of view of the S frame. Do you want something more?

 

[yuiop]

Ok, if any single inertial frame can explain everything then pick up S and/or S' and please explain me my original post. The requirement is there should not be any duplicating and skipping events.

If it helps, sketch the paths in your OP diagram on the first applet on this web page:

http://www.reagenix.com/personal/sci/space_time/test.html

Now label some events using the right mouse button and then move the slider at the top left or right. Moving the slider is the same as changing to a new reference frame. Notice that in any reference frame, none of the labelled events get skipped or duplicated. Does that answer your question?

 

[ghwellsjr]

Ok, if any single inertial frame can explain everything then pick up S and/or S' and please explain me my original post. The requirement is there should not be any duplicating and skipping events.

OK. I have taken the diagram from your original post and put co-ordinates on it that seemed reasonable to me. I'm assuming that c=1 so the vertical axis is time in seconds and the horizontal axis is the x-position in light-seconds. The co-ordinates are shown as [t,x]. I show the co-ordinates for the three events where each clock changes speed and for each of the four red events and each of the four green events.

All these co-ordinates are for the S frame:

Notice that the green and red events are paired in that each pair is simultaneous in the S frame as depicted by the three horizontal lines. (I could have drawn four more lines going through each pair of simultaneous events but I didn't do it since you didn't do it.)

Now, the exact same diagram but with all the co-ordinates transformed to the S' frame which I am assuming is moving at a speed of 0.4c with respect to the S frame:

Now you can see that the red and green pairs are not simultaneous in the S' frame but the three speed-changing events are since they all occur at time zero. Also note that the four red events are at the same location in the S' frame, meaning that they occur at different times but at the same location in the S' frame.

But notice that the co-ordinates are not aligned with the axes so I have redrawn the diagram so that the S' frame is aligned and the S frame is skewed but otherwise, this is exactly the same information that is contained in the previous image:

Now it is really obvious that the three speed changing events are simultaneous since in addition to their time co-ordinates all being zero, the events are on the same horizontal line.

It is also obvious that the four red events all occur at the same location in the S' frame since they are on a vertical line (and their position co-ordinates are the same) and that the four green events are not at the same location.

Finally, it is obvious that the pairs of green-red events that were simultaneous in the S frame are not simultaneous in the S' frame since they are not on a horizontal line of simultaneity. The LoS from the S frame are now shown skewed.

Notice that no events have disappeared or are duplicated in any of the diagrams.

 

[mananvpanchal]

If it helps, sketch the paths in your OP diagram on the first applet on this web page:

Thanks, I have been trying to find something like this from long.

 

[mananvpanchal]

George

Great work. I appreciate it. But, I know that we can define all the events in any co-ordinate system.

By the way, third diagram doesn't show contracted length between clocks.

First two diagram shows proper length in S frame at same time is greater than contracted length in S frame at same time.
Please, see the distance between A and C clocks at first LoS of S frame and at second LoS of S. The distance at first LoS is shorter than the distance at second LoS.

But, in third diagram proper length in S' frame at same time is equal to contracted length in S' frame at same time.
Please, draw two horizontal LoS of S' frame, one above spatial axis and other below spatial axis. You would see that both distance is same at both LoS of S' frame.

 

[ghwellsjr]

George

Great work. I appreciate it. But, I know that we can define all the events in any co-ordinate system.

Then why did you start this thread?

By the way, third diagram doesn't show contracted length between clocks.

That's because I just inverted your drawing instead of re-drawing it from scratch. Just go by the values of the co-ordinates and assume the diagram is to a different scale. The point of the drawing is only to show that no events disappear and no events are duplicated, a point which you now claim you knew all along.

First two diagram shows proper length in S frame at same time is greater than contracted length in S frame at same time.
Please, see the distance between A and C clocks at first LoS of S frame and at second LoS of S. The distance at first LoS is shorter than the distance at second LoS.

Yes, because in the S frame, the A clock starts moving toward the C clock before the C clock starts its motion so the distance between the A and C clocks gets smaller. It goes from 200 light-seconds to 168 light-seconds. (I didn't show the event that would make this clear, because you didn't show that event either and I didn't think this exercise was about proper lengths, only about lines of simultaneity and about the disappearance or duplication of events in different frames.)

But, in third diagram proper length in S' frame at same time is equal to contracted length in S' frame at same time.
Please, draw two horizontal LoS of S' frame, one above spatial axis and other below spatial axis. You would see that both distance is same at both LoS of S' frame.

Yes, because in the S' frame, the clocks all change their speeds simultaneously and so their distance apart remains a constant 183.3 light-seconds, both before and after the change in speed.

But why are you now pointing out the differences in proper lengths according to different frames when the whole point of this thread had to do with duplicated or disappearing events?