Length contraction of space with multiple reference frames

[ghwellsjr]

I did not address in any event "non-inertial" coordinates, frames, observers,... only relative motion at constant velocity. The previous input was simply irrelevant.
Two simple questions which attract simple answers:
Is it true that the radar method of distance measurement, when comparing the dynamic case where the target object is moving in respect to the observer with the static case where it is at rest, leads to either a shorter or a larger result (as compared to the static case) for the two-way wave propagation time, on the ground that the distance to be covered varies during the propagation itself (as opposed to the static case), the result being shorter if the object moves toward the observer and larger if the object moves away from him/her (Y/N)?

N: It's always shorter in both cases, just like SR determines.

Is it true that SR always predicts a contraction of lengths and distances in the dynamic case as compared to the static case, irrespective of whether the target object moves toward or away from the observer (Y/N)?

Y.

Then we might understand where the discrepancy comes from.

If you would try it, you would find that there is no discrepancy. Or are you going to require me to do it for you?

 

[Sugdub]

N: It's always shorter in both cases, just like SR determines.

Then I wish to understand how this counter-intuitive conclusion is arrived at.

 

[ghwellsjr]

Then I wish to understand how this counter-intuitive conclusion is arrived at.

Your discrepancy is counter-intuitive. How did you arrive at it?

 

[Sugdub]

Your discrepancy is counter-intuitive. How did you arrive at it?

Through formal reasoning: the asymmetry of the conclusion (the bias induced by the relative motion always applies in the same direction, a contraction) can only be logically derived if rooted into an asymmetry in the hypotheses.
However, the set of hypotheses applicable to the radar method of distance measurement does not include any non-symmetrical hypothesis into which the asymmetry of the conclusion could be rooted: the delta to the optical path of the radar wave can either shorten or increase the two-way propagation time, depending on whether the object moves toward or away from the observer during the measurement process. So the conclusion you are targeting is logically impossible.

 

[ghwellsjr]

Through formal reasoning: the asymmetry of the conclusion (the bias induced by the relative motion always applies in the same direction, a contraction) can only be logically derived if rooted into an asymmetry in the hypotheses.
However, the set of hypotheses applicable to the radar method of distance measurement does not include any non-symmetrical hypothesis into which the asymmetry of the conclusion could be rooted: the delta to the optical path of the radar wave can either shorten or increase the two-way propagation time, depending on whether the object moves toward or away from the observer during the measurement process. So the conclusion you are targeting is logically impossible.

But you haven't actually tried it, have you? Of course not or you wouldn't be making these statements.

I challenge you to create a scenario where a distant rod is stationary in an Inertial Reference Frame and show with a spacetime diagram that an observer at rest at location zero measures the correct Proper Length of the rod using two radar signals that are emitted and detected at different times but their midpoint is at the same time.

Then transform the scenario to a high speed and show with another spacetime diagram that a different observer at rest at location zero doing exactly the same measurement will determine that the length of the rod is contracted to the amount determined by Special Relativity as shown in the diagram.

Then repeat by transforming the scenario to the same high speed in the opposite direction.

Can you do that?

 

[Mentz114]

...
I challenge you to create a scenario where a distant rod is stationary in an Inertial Reference Frame and show with a spacetime diagram that an observer at rest at location zero measures the correct Proper Length of the rod using two radar signals that are emitted and detected at different times but their midpoint is at the same time.
...

I don't understand the bit I've bolded. Can you elaborate ? If the rod is comoving with the observer then any radar measurement of the rods length gives the rest length - that is obvious. But I'm having difficulty convincing myself that a receding rod will not measure longer than an approaching one. Although I don't see this as a problem.

 

[PAllen]

I don't understand the bit I've bolded. Can you elaborate ? If the rod is comoving with the observer then any radar measurement of the rods length gives the rest length - that is obvious. But I'm having difficulty convincing myself that a receding rod will not measure longer than an approaching one. Although I don't see this as a problem.

I don't think I'll have time to write more on this this weekend, but Synge, in his 1960 GR book proves the following:

- Radar simultaneity and distance exactly reproduces standard Minkowski coordinates for any inertial observer in flat spacetime (the simultaneity part is trivial, since that is the simultaneity definition used by Einstein; the substance is that proper distances computed along the simultaneity surfaces match radar distances)
- For non-inertial observers in SR and any observer in GR, radar coordinates converge to Fermi-Normal coordinates as the spacetime region under consideration shrinks.

 

[ghwellsjr]

...
I challenge you to create a scenario where a distant rod is stationary in an Inertial Reference Frame and show with a spacetime diagram that an observer at rest at location zero measures the correct Proper Length of the rod using two radar signals that are emitted and detected at different times but their midpoint is at the same time.
...

I don't understand the bit I've bolded. Can you elaborate ? If the rod is comoving with the observer then any radar measurement of the rods length gives the rest length - that is obvious.

Yes, in this first scenario, it is not necessary when the two measurements are made (just like picking any two events to determine Proper Length), but I wanted to establish the correct procedure for Sugdub to use in the next two scenarios.

But I'm having difficulty convincing myself that a receding rod will not measure longer than an approaching one. Although I don't see this as a problem.

Seeing is believing. Hopefully, Sugdub will produce the three spacetime diagrams that will convince you. It would be a serious problem if it didn't work out as Sugdub is claiming.

 

[PAllen]

I don't think I'll have time to write more on this this weekend, but Synge, in his 1960 GR book proves the following:

- Radar simultaneity and distance exactly reproduces standard Minkowski coordinates for any inertial observer in flat spacetime (the simultaneity part is trivial, since that is the simultaneity definition used by Einstein; the substance is that proper distances computed along the simultaneity surfaces match radar distances)
- For non-inertial observers in SR and any observer in GR, radar coordinates converge to Fermi-Normal coordinates as the spacetime region under consideration shrinks.

I see a fairly trivial proof that this must be so (the flat spacetime conclusion). Consider some inertial observer constructs Minkowski coordinates. Some event is labeled (x,t). What coordinates would this same observer assign use radar convention? The time would be the same, since radar is the simultaneity convention for Minkowski coordinates. The distance would be c*(1/2 round trip light time). Suppose this isn't the same as x. Then 2x/c does not give the round trip light travel time to event at x from the origin. This violates the axioms used to construct Minkowski coordinates (speed of light is isotropically c in Minkowski coordinates). Thus radar coordinates are identical to Minkowski coordinates for inertial observers. Then all measurements made on a coordinate basis must be the same (e.g. length measured as proper distance at a given time in said coordinates).

 

[phyti]

Only measurements show relativistic effects. There are no physical phenomena associated with them.

How do you explain the time difference of two identically functioning clocks, after separating and rejoining as in the ‘twin’ case, with measurement?

Why does the fast moving a-naut think the universe contracts in his direction of motion?

 

[phyti]

Part of what you're implying is that measurements that involve relativistic effects are not *true* measurements, but that true measurements could be arrived at by subtracting or otherwise removing relativistic effects from the equation, so to speak.

This is contrary to everything I've learned since joining these forums, and while I don't have the chops to dispute in a more technically, I believe it's erroneous.

What you say I am implying is your lack of understanding what was said.
The truth of measurements depends on the interpretation.
If you took a picture of an extremely fast moving rod, approaching on a path that is offset to one side, it would appear longer than a copy you have. The light from the far end has to leave before the light from the near end so as to arrive at the camera simultaneously. This involves a correction for the object motion, but is not a relativistic effect.

Why does the fast moving a-naut think the universe contracts in his direction of motion?

 

[phyti]

If I find the relativistic effect that your clock is moving slower than mine, and you find the relativistic effect that my clock is moving slower than yours, then these are not "true" effects in the sense of being coordinate-independent or frame-independent. They are not like rest-mass is, the same for all observers.

Doppler effect depends on the relative speed of emitter and detector. Since there is only one speed for both, whether converging or diverging, why do you think the effect is not real?

 

[1977ub]

Doppler effect depends on the relative speed of emitter and detector. Since there is only one speed for both, whether converging or diverging, why do you think the effect is not real?

I wasn't speaking of a Doppler effect. Also I don't believe I used the term "real."

 

[Mentz114]

Only measurements show relativistic effects. There are no physical phenomena associated with them.

Hmm. I don't know what I meant when I wrote that. Let me try again

1. Time dilation and length contraction appear when measurements are made by me of times and lengths in a moving frame.

2. What I mean by 'physical' in this context, is things that are not coordinate dependent like the LC and TD above.

How do you explain the time difference of two identically functioning clocks, after separating and rejoining as in the ‘twin’ case, with measurement?

Nobody can 'explain' this. SR asserts that clocks show elapsed times that are equal to the proper-lengths of their worldlines. This is a coordinate independent effect. Not to be confused with TD and LC.

Why does the fast moving a-naut think the universe contracts in his direction of motion?

He would be wrong if he thought that. It is a coordinate effect of the relative velocity he has wrt the other objects.

 

[Mentz114]

Yes, in this first scenario, it is not necessary when the two measurements are made (just like picking any two events to determine Proper Length), but I wanted to establish the correct procedure for Sugdub to use in the next two scenarios.

Seeing is believing. Hopefully, Sugdub will produce the three spacetime diagrams that will convince you. It would be a serious problem if it didn't work out as Sugdub is claiming.

OK, thanks. I wait for pictures.

I see a fairly trivial proof that this must be so (the flat spacetime conclusion). Consider some inertial observer constructs Minkowski coordinates. Some event is labeled (x,t). What coordinates would this same observer assign use radar convention? The time would be the same, since radar is the simultaneity convention for Minkowski coordinates. The distance would be c*(1/2 round trip light time). Suppose this isn't the same as x. Then 2x/c does not give the round trip light travel time to event at x from the origin. This violates the axioms used to construct Minkowski coordinates (speed of light is isotropically c in Minkowski coordinates). Thus radar coordinates are identical to Minkowski coordinates for inertial observers. Then all measurements made on a coordinate basis must be the same (e.g. length measured as proper distance at a given time in said coordinates).

I'll have to think about this. Thanks. ( Got any pictures ? )

 

[Dale]

Nobody can 'explain' this. SR asserts that clocks show elapsed times that are equal to the proper-lengths of their worldlines.

I know what you mean, but I wouldn't go quite this far. You can in fact explain the elapsed time on a clock in terms of the two postulates of SR. I.e. time dilation is a derived result.

What we cannot explain in SR is why the postulates are correct, that is simply asserted by the theory.

 

[1977ub]

Why does the fast moving a-naut think the universe contracts in his direction of motion?

1) on the initial level of pure optics, he experiences all kinds of distortions, such as Penrole-Terrell effect which turn sides of moving bodies around.

2) on the the next level - inertial frames, he finds that times and lengths along the direction of motion come out contracted as compared with when at rest wrt them.

3) if he understands SR, he doesn't "think" that anything has contracted.

 

[Mentz114]

I know what you mean, but I wouldn't go quite this far. You can in fact explain the elapsed time on a clock in terms of the two postulates of SR. I.e. time dilation is a derived result.

What we cannot explain in SR is why the postulates are correct, that is simply asserted by the theory.

Noted.

I see a fairly trivial proof that this must be so (the flat spacetime conclusion). Consider some inertial observer constructs Minkowski coordinates. Some event is labeled (x,t). What coordinates would this same observer assign use radar convention? The time would be the same, since radar is the simultaneity convention for Minkowski coordinates. The distance would be c*(1/2 round trip light time). Suppose this isn't the same as x. Then 2x/c does not give the round trip light travel time to event at x from the origin. This violates the axioms used to construct Minkowski coordinates (speed of light is isotropically c in Minkowski coordinates). Thus radar coordinates are identical to Minkowski coordinates for inertial observers. Then all measurements made on a coordinate basis must be the same (e.g. length measured as proper distance at a given time in said coordinates).

Are you saying that using the radar metric of Dolby&Gull, distant measurements show the γ-factor of SR ? As opposed to the naive method where length ( and wavelength) transform like Doppler ?

 

[Dale]

This thread seems to be degenerating into a discussion about "true" and "real". Closed pending moderation.