Length and Distance Contraction

[albroun]

hi

Just wondering if someone can clarify for me whether it is merely the length of a moving object that appears contracted to a stationary observer, or whether it is also the distance between the moving object and other objects in its direction of motion that appears contracted. Or is the distance contraction (between the moving object and other objects in its direction of motion) only experienced by the moving observer (in the moving object) in his/her direction of motion? I have read numerous books on relativity and this issue always seems to be left rather fuzzy for some reason.

Many thanks for an answer. BTW I have no maths - am just an interested layperson who has read countless books on relativity, but still confused!

PS - having looked at a few other threads I am still a bit hazy, but it seems that I am confusing actual contraction with visual appearance contraction - my question is really about whether the distance is actually contracted in the direction of motion, and from which reference frame is this so - the stationary observer, or the observer who is moving with the object?

 

[ghwellsjr]

Every non-accelerating observer measures everything else that is stationary with respect to himself normally. Everything that is moving with respect to himself is length contracted along the direction of motion and time dilated.

 

[albroun]

OK so here is a paradox that occurred to me.

Suppose we have a stationary observer measuring the distance between two spacecraft and a star.

Spacecraft A is moving at a constant velocity of 0.01c. Meanwhile Spacecraft B, moving at a constant velocity of 0.99c goes to overtake A, whilst running very close alongside A.

Let us call the point at which the two spacecraft are aligned X.

To our observer, the distance between point X and the star will be both considerably contracted and hardly contracted at all!

Have I misunderstood something here?

 

[ghwellsjr]

You haven't said, but I think you mean, that the star is stationary with respect to me. Therefore, I never see it's distance from any other point in space as contracted. X is just a point in space stationary to me that is defined as the conjunction of the two spacecraft , but X isn't moving with either spacecraft .

 

[albroun]

Yes I assume that the star is stationary with respect to me the observer, and the spacecraft are both heading there.

However, if the distance between a moving object (A or B in the above example) and a stationary object (star) towards which it (A or B) is heading (moving and stationary with respect to me) is contracted, then surely there is some kind of paradox here?

Basically if moving objects can actually shrink the space between themselves and objects in their direction of motion to differing degrees according to their different velocities (from the standpoint of a stationary observer), then a given region of space can be shrunk to differing degrees at the same time, which seems paradoxical?

 

[ghwellsjr]

That's why in Special Relativity it's important to stick with one Frame of Reference at a time since both time and space are relative.

 

[albroun]

Does that mean there is no paradox?

 

[Naty1]

Basically if moving objects can actually shrink the space between themselves and objects in their direction of motion to differing degrees according to their different velocities (from the standpoint of a stationary observer), then a given region of space can be shrunk to differing degrees at the same time, which seems paradoxical?

This is incorrect...that statement IS paradoxical because such length contraction is NOT from the standpoint (reference frame) of a stationary observer. Length contraction is obsevered only from the moving objects themselves...say how far they have to travel to a common point, for example...Observers on two fast but different speed moving objects do not agree on that distance...an outside stationary observer sees a third distance, but the same distance for each moving object.

 

[ghwellsjr]

Does that mean there is no paradox?

Yes, that is what it means.

Virtually all so-called paradoxes in Special Relativity are a result of taking "parameters" from two different Frames of Reference and assuming that they both apply at the same time.

 

[GrayGhost]

Basically if moving objects can actually shrink the space between themselves and objects in their direction of motion to differing degrees according to their different velocities (from the standpoint of a stationary observer), then a given region of space can be shrunk to differing degrees at the same time, which seems paradoxical?

Well, it sure does seem paradoxical at first. However, it "only seems" that way. In fact, no paradox exists. It is most definitely counter intuitive wrt everyday experience, this much is certain. But then, I suppose that depends on whether you wash cars everyday versus working everyday at the LHC super collider :)

You said "a given region of space can be shrunk to differing degrees at the same time". It's not as though the space you record has differing lengths at-once. What differs are the measures of space made by different observers who move relatively. It's a frame-to-frame differential, not a within-frame differential. If you assume yourself at rest with the star, you only record moving bodies length contracted, and cannot measure space as A or B do. The measure of space (and time) is personal per POV.

GrayGhost

 

[ghwellsjr]

If you assume yourself at rest with the star, you only record moving bodies length contracted, and cannot measure space as A or B do.

True, but you can calculate what A or B will measure using the Lorentz Transform.

 

[A.T.]

Many thanks for an answer. BTW I have no maths - am just an interested layperson who has read countless books on relativity, but still confused!

I recently found this quite nice animation:

 

[albroun]

You said "a given region of space can be shrunk to differing degrees at the same time". It's not as though the space you record has differing lengths at-once. What differs are the measures of space made by different observers who move relatively. It's a frame-to-frame differential, not a within-frame differential.

Does this mean that question as to whether space is ACTUALLY contracted, or only APPEARS to be contracted has no meaning, in that the distinction between actuality and what is measured breaks down (as it does, arguably, within quantum physics)?

 

[pervect]

How would you test for the difference experimentally? That should provide a clue whether you're talking about science (if its testable), or philosophy.

 

[GrayGhost]

Does this mean that question as to whether space is ACTUALLY contracted, or only APPEARS to be contracted has no meaning, in that the distinction between actuality and what is measured breaks down (as it does, arguably, within quantum physics)?

Well, QM is based upon probability, relativity is not. Luminal contractions are theoretically measurable, assuming the technology is sufficient. IF you can measure it, then I see it as a physical effect. Yet, no body ever changes in and of itself simply because moving others take their measurements of it. That is, proper values are invariant. Whether the contraction is real or not, depends on how you define the word real, and there seems to be a lot of disagreement between folks on how to do that. That's where philosophy enters. I might argue that contractions are real, while a body never changes in length in and of itself. Another will argue that measured contractions are not real, because a body never changes in length in and of itself. We may go back and forth on this forever, or at least until black holes and all matter decays :)

GrayGhost

 

[abbott287]

Well, QM is based upon probability, relativity is not. Luminal contractions are theoretically measurable, assuming the technology is sufficient. IF you can measure it, then I see it as a physical effect. Yet, no body ever changes in and of itself simply because moving others take their measurements of it. That is, proper values are invariant. Whether the contraction is real or not, depends on how you define the word real, and there seems to be a lot of disagreement between folks on how to do that. That's where philosophy enters. I might argue that contractions are real, while a body never changes in length in and of itself. Another will argue that measured contractions are not real, because a body never changes in length in and of itself. We may go back and forth on this forever, or at least until black holes and all matter decays :)

GrayGhost

I always thought it was just an illusion, and relativity basically was as a whole. But the slowing down of clocks, and someone aging at a slower rate seems to show its not an illusion at all.

 

[GrayGhost]

I always thought it was just an illusion, and relativity basically was as a whole. But the slowing down of clocks, and someone aging at a slower rate seems to show its not an illusion at all.

Yes abbott287, that's how I see it. While no one ever discerns a change in his own clock rate, even if accelerating, his rate of time varies "relative to" the rate of time experienced other observers. This frame-to-frame time-rate-differential is as real as it gets. If it were not, then the twin who departs and later returns to Earth would not be younger than his twin who remained on Earth ... and particle accelerators would not have revealed what they have to date.

GrayGhost