Undergrad An issue with length contraction

[PeroK]

Your reply adds to my concern. If what you say is correct, then why is it even called length contraction when there doesn't seem to be any reason for it to be called that.

I suspect that if and when AI manages to understand physics, it will require only a very basic mathematical vocabulary and will not try to understand things in human terms. AI would probably not need the concepts of time dilation, length contraction and simultaneity; or, "worldtubes".

But, as a human being you need to build up your understanding using all manner of intermediate and possibly unnecessary concepts, such as length contraction.

It concerns me that you get sidetracked by all these extraenous ideas and your concerns over terminology seem to be at best pointless. Why not length contraction? How much study time are you proposing to waste musing over that question?

 

[student34]

Without that word I don't see the problem. Can you re-state it?

Is there a length contraction, or is it only a different observation?

 

[Ibix]

Your reply adds to my concern. If what you say is correct, then why is it even called length contraction when there doesn't seem to be any reason for it to be called that.

And another way to look at it is that there is no form of words that exactly captures what length contraction is. So if we changed the name somebody else would be here arguing that the new name isn't right either. That's why we tell people to concentrate on the maths, which is precise. Length contraction is just a label for a section of the maths and some related possible experimental measures.

 

[Ibix]

Is there a length contraction, or is it only a different observation?

This is a false distinction. Length contraction is the phenomenon that the measured length of a moving object is less than that of the same object when it's stationary.

If you mean "is there a compressive stress causing the reduction in length" then the answer is no.

 

[student34]

And another way to look at it is that there is no form of words that exactly captures what length contraction is. So if we changed the name somebody else would be here arguing that the new name isn't right either. That's why we tell people to concentrate on the maths, which is precise. Length contraction is just a label for a section of the maths and some related possible experimental measures.

The reason I started this thread is because I wanted to know if I was interpreting this part of GR incorrectly. It helps me to know what the consensus here is.

 

[Dale]

Is there a length contraction, or is it only a different observation?

Yes to both. Those are not mutually exclusive

 

[student34]

Yes to both. Those are not mutually exclusive

I do not understand how the former is true too. Wouldn't a contraction have to involve the shortening of distance between two events kind of like we would need for any to points on a 2d object? I do not see any changes made between any 2 events anywhere in the example.

 

[PeterDonis]

the shortening of two events

You can't "shorten" events. Events are points in spacetime. They don't even have a "length" to begin with.

"Length contraction" just means that you have spacelike intervals between different pairs of events, that correspond to the "length" of an object according to different observers (because the events in each pair are on the worldlines of the two ends of the object). The spacelike interval between the pair of events corresponding to the length of the object in the frame in which it is moving, is shorter than the spacelike interval between the pair of events corresponding to the length of the object in the frame in which it is at rest.

 

[student34]

You can't "shorten" events. Events are points in spacetime. They don't even have a "length" to begin with.

"Length contraction" just means that you have spacelike intervals between different pairs of events, that correspond to the "length" of an object according to different observers (because the events in each pair are on the worldlines of the two ends of the object). The spacelike interval between the pair of events corresponding to the length of the object in the frame in which it is moving, is shorter than the spacelike interval between the pair of events corresponding to the length of the object in the frame in which it is at rest.

I changed edited my post to what I meant to say.

 

[PeterDonis]

I changed edited my post to what I meant to say.

The edited post isn't any better. You can't "shorten the distance between two events". The distance between two points in spacetime is an invariant. It makes no sense to talk about making it "shorter". Nor does "length contraction" involve any such thing. It involves comparing two different distances (spacetime intervals), between two different pairs of events, just as I described.

 

[student34]

You can't "shorten" events. Events are points in spacetime. They don't even have a "length" to begin with.

"Length contraction" just means that you have spacelike intervals between different pairs of events, that correspond to the "length" of an object according to different observers (because the events in each pair are on the worldlines of the two ends of the object). The spacelike interval between the pair of events corresponding to the length of the object in the frame in which it is moving, is shorter than the spacelike interval between the pair of events corresponding to the length of the object in the frame in which it is at rest.

Yes, the interval is shorter. But that only seems to be a matter of perception.

For example, Bob is observing the distance of one side of a square to be 1 meter, and Alice is observing opposite corners of the square to be 2^(1/2). We wouldn't say that the square contracted. Nothing is changing or contracting.

Furthermore, we wouldn't say that the square is shorter for Bob than it is for Alice. That is trivially incorrect.

 

[PeterDonis]

the interval is shorter. But that only seems to be a matter of perception.

I have no idea what you mean. Spacetime intervals are invariants. All observers agree on them.

For example, Bob is observing the distance of one side of a square to be 1 meter, and Alice is observing opposite corners of the square to be 2^(1/2). We wouldn't say that the square contracted. Nothing is changing or contracting.

That is true. But we also would not say that Alice was measuring a "side" of the square to begin with. We would say she was measuring a "diagonal". And everybody recognizes that the side and the diagonal of a square are different line segments with different lengths.

In the spacetime case, however, each observer, Alice and Bob, considers the interval they are measuring to be the "length" of the object. And since the "length" measured by one is shorter than the "length" measured by the other, the term "length contraction" is used. It is probably not the best term to describe the physics, but it's the term that's in all the literature so we're stuck with it.

Furthermore, we wouldn't say that the square is shorter for Bob than it is for Alice. That is trivially incorrect.

Of course, because we all recognize that the side of a square is shorter than its diagonal. Our intuitions on this are fine.

Our intuitions also, however, tell us that the "length" of an object should not depend on whether it is moving relative to us or not. Yet relativity tells us that it does. That is why "length contraction" is counterintuitive: because our intuitions are not fine in this case.

We could "fix" this "problem" by requiring another word to be used to describe measuring what we now call the "length" of an object if the object is moving relative to us. But changing the words we use wouldn't change the physics at all.

 

[Dale]

Is there a length contraction

A measurement of the length of an object involves measuring the distance between two ends of the object at the same time. Since two people in relative motion disagree on “at the same time” they disagree on the length of a given object. This is length contraction

Bob is observing the distance of one side of a square to be 1 meter, and Alice is observing opposite corners of the square to be 2^(1/2). We wouldn't say that the square contracted. Nothing is changing or contracting.

And yet it is a fact that there are holes that the square can fit through straight on that it cannot fit through diagonally.

Regarding the terminology. There is nothing we can do about that.

 

[student34]

Our intuitions also, however, tell us that the "length" of an object should not depend on whether it is moving relative to us or not. Yet relativity tells us that it does. That is why "length contraction" is counterintuitive: because our intuitions are not fine in this case.

Keeping in mind the diagonal/square analogy, and with all due respect, your statement about an object's length dependence seems to be deceptive and grows counterintuition unnecessarily. Maybe we should use "perceived length" or something like that?

 

[Dale]

Maybe we should use "perceived length" or something like that?

The terminology is not going to change, so that is not worth the angst. However, do you believe that the longer length across the diagonal of a square vs the side of a square is a matter of perception? Equivalently, if you are trying to fit a sofa through a doorway, is it a matter of perception if it doesn’t fit diagonally?

 

[PeterDonis]

your statement about an object's length dependence seems to be deceptive

Only if you refuse to actually look at the physics (i.e., the mathematical description, which is exact and unambiguous) and expect the ordinary language description to be enough. But it never is. Not for any area of physics. Ordinary language is never enough; you always need to look at the mathematical description if you want an exact, unambiguous description of the physics.

Maybe we should use "perceived length" or something like that?

Good luck persuading everyone who writes scientific papers on relativity. Not to mention having to go back and revise all of the past publications.

Also, you are ignoring the reason why the word "length" is used in ordinary language for both measurements: because, according to our intuitions, both measurements are measurements of the length of the object. Our intuitions are of course wrong in believing that the length measured by both measurements should be the same, since they aren't, but you can't fix wrong intuitions by finding better ordinary language descriptions. You fix them by learning the math.

 

[student34]

The terminology is not going to change, so that is not worth the angst. However, do you believe that the longer length across the diagonal of a square vs the side of a square is a matter of perception? Equivalently, if you are trying to fit a sofa through a doorway, is it a matter of perception if it doesn’t fit diagonally?

You are just changing the orientation. The couch itself does not contract.

 

[student34]

Only if you refuse to actually look at the physics (i.e., the mathematical description, which is exact and unambiguous) and expect the ordinary language description to be enough. But it never is. Not for any area of physics. Ordinary language is never enough; you always need to look at the mathematical description if you want an exact, unambiguous description of the physics.Good luck persuading everyone who writes scientific papers on relativity. Not to mention having to go back and revise all of the past publications.

Also, you are ignoring the reason why the word "length" is used in ordinary language for both measurements: because, according to our intuitions, both measurements are measurements of the length of the object. Our intuitions are of course wrong in believing that the length measured by both measurements should be the same, since they aren't, but you can't fix wrong intuitions by finding better ordinary language descriptions. You fix them by learning the math.

I want to understand all of this; I don't just want to know it.

 

[Dale]

You are just changing the orientation. The couch itself does not contract.

Nevertheless, the difference in length is not a matter of perception, is it?

 

[Dale]

Also, you are ignoring the reason why the word "length" is used in ordinary language for both measurements: because, according to our intuitions, both measurements are measurements of the length of the object.

@student34 this is a key point. See also my description of the measurement of length in post 43. It is what we normally think of as length.

 

[PeterDonis]

I want to understand all of this; I don't just want to know it.

Understand what?

If you mean understand the physics involved in what is called in vague ordinary language "length contraction", I think what has been posted in this thread already should be more than enough.

If you mean understand why people adopt vague ordinary language terms that don't always convey the actual physics very well, that's way off topic for this forum; it's a question of human psychology and sociology, not physics.

 

[Dale]

If you mean understand why people adopt vague ordinary language terms that don't always convey the actual physics very well, that's way off topic for this forum; it's a question of human psychology and sociology, not physics.

And history too.

 

[student34]

Nevertheless, the difference in length is not a matter of perception, is it?

No, but you/GR seem to be saying such a thing.

A more precise analogy is if I walk from in front of the couch to the side where it is say 1 meter wide, I shouldn't say that the couch contracted from x meters to 1 meter.

 

[student34]

Understand what?

If you mean understand the physics involved in what is called in vague ordinary language "length contraction", I think what has been posted in this thread already should be more than enough.

If you mean understand why people adopt vague ordinary language terms that don't always convey the actual physics very well, that's way off topic for this forum; it's a question of human psychology and sociology, not physics.

Ok, I agree, the thread has run its course as far as I am concerned. I just wanted to know if I was misinterpreting something about length contraction. Now I don't think I am.

 

[student34]

And history too.

Probably philosophy and linguistics too.

 

[PeterDonis]

you/GR seem to be saying such a thing.

No, we aren't. See below.

A more precise analogy is if I walk from in front of the couch to the side where it is say 1 meter wide, I shouldn't say that the couch contracted from x meters to 1 meter.

You wouldn't say that, but that's because you are talking about the couch's size along two different spatial directions, and we have different words for the couch's size along different spatial directions. You would say that the couch is, say, x meters long by 1 meter wide. Or x meters along a diagonal and 1 meter wide.

In the case of length contraction, we don't have different ordinary language words for the two different spacelike intervals. We use the same ordinary language word, "length", for both of them, because our ordinary language does not recognize time as a separate dimension, the way we recognize the two spatial dimensions of the couch or the square as separate dimensions. Our ordinary language only sees that in both cases we are measuring "length" along a single spatial direction, the $x$ direction. But that's just a limitation of our vague ordinary language.

Once we look beneath the vague ordinary language at the actual math and physics (geometry), we see the same thing in both cases: we have two different line segments, between two different pairs of points, that have different lengths. There is no "matter of perception": it's just straightforward geometry in both cases.

 

[PeterDonis]

I just wanted to know if I was misinterpreting something about length contraction. Now I don't think I am.

I'm not so sure. See my post #56 just now.

 

[Dale]

No, but you/GR seem to be saying such a thing.

A more precise analogy is if I walk from in front of the couch to the side where it is say 1 meter wide, I shouldn't say that the couch contracted from x meters to 1 meter.

The terminology is what it is. Contraction may not be the best word, but it is the word used to describe the measurements I described above. Those measurements are not just perception. They describe the measured geometry of physical objects.

If we could easily change bad terminology then we wouldn’t still have relativistic mass.

 

[renormalize]

So perhaps it would useful to look at cases where there are real physical implications, such as with muon decay observations...?

student34 should carefully ponder this physical example of length contraction (and time dilation):

Cosmic rays are known to strike the upper atmosphere at $\sim15000\mathrm{m}$ altitude, producing downward-directed muons traveling at nearly the speed-of-light $c$. Since muons at rest have a mean lifetime of $\overline{\tau}=2.2\mathrm{\mu s}$, their maximum travel distance in that time is only $c\overline{\tau}=660\mathrm{m}$. This is much less than the distance to the ground, yet, due to relativity, these muons are readily detected at the Earth's surface.

In the muon's rest frame, the Earth is seen to approach at nearly $c$ with the depth of its atmosphere foreshortened (length-contracted) by a factor of $1/\gamma$, where $\gamma\approx21$. This is thin enough that the muon easily reaches the ground before decaying, in agreement with experiment. (See the left illustration below, where the depth of the atmosphere is symbolized by the height of the mountain.)

Alternatively, at rest on Earth we observe the "internal clock" of the muon to be slowed-down by time-dilation, increasing its apparent lifetime $\overline{\tau}$ by the same $\gamma$-factor of $\sim21$. This gives the muon ample time to reach the surface, again just as experimentally observed. (See the right illustration below.)

I leave it to the OP and the philosophers to debate whether this contraction of atmospheric-depth or dilation of half-life (depending on the reference frame) is "actual" or "apparent", but operationally both effects certainly seem "real" to me.

(Martin Bauer on Twitter)

 

[Ibix]

Maybe we should use "perceived length" or something like that?

Just to illustrate how silly worrying about terminology is, measure the length of something. Now measure it again. Now remember that you advanced in time between those two measurements, so you did not measure the same thing, but rather the intervals between two different pairs of events. So why are you calling them "the" length? They're different measurements even if the answers are the same, so shouldn't you also be agitating not to use the word length at all? We should always talk about the cross section of a worldtube measured at 08:49:23 on October 12th 2022 and the one measured three seconds later, and never the length.

This is why in physical sciences we reason in maths. "The" length is imprecise, let alone length contraction, and this will always be the case whatever term you try to introduce.