I An issue with length contraction

[student34]

I have read that length contraction is real and not just an illusion. However, when I compare an object at rest with an observer and the object in motion relative to another observer, I see that instead of there being a real length contraction, there is simply a difference in the part of the object being observed. In other words, the two observers are just looking at two different parts of the object.

To illustrate my issue. This video attempts to explain how length contraction is not an illusion, but it seems to only enforce my issue. Watch starting at 7:05 to 7:20,

The line at an angle is the length of the ship at rest, and the horizontal line (contraction) is the length of the ship as observed in motion.

When we think of the ship as just one large structure extending through time, aren't those lines just depicting different parts of the ship?

Then isn't length contraction similar to saying that a 3d cube, with 1 cm^2 sides, has a length contraction of 1 cm and a rest length of 2^(1/2)L?

 

[malawi_glenn]

We have to be careful with "looks" here, because length contraction is what is being measured, i.e. coordiates position and time.
When we look at objects, we need to account for how the light emitted from the object is traveling to our eyes/detector

 

[Doc Al]

I see that instead of there being a real length contraction, there is simply a difference in the part of the object being observed. In other words, the two observers are just looking at two different parts of the object.

Not sure how you're getting this. Both observers measure the length between the same two points of the object.

 

[PeroK]

In other words, the two observers are just looking at two different parts of the object.

You mean if a football field was moving at $v= \frac {\sqrt 3} 2 c$ in some inertial reference frame, giving a gamma factor of $2$, then an attempt to measure the length of the field between the goalposts atveach end would somehow instead measure the distance from one set of goalposts to the halfway line?

That has got to be nonsense! The observers would measure the distance from goalpost to goalpost.

 

[student34]

Not sure how you're getting this. Both observers measure the length between the same two points of the object.

The points are in different positions in time, causing the difference in length, right?

 

[Doc Al]

The points are in different positions in time, causing the difference in length, right?

To measure the length between two points of a moving object, the observer must measure their positions at the same time. And, yes, the two frames will not agree that the measurements were made at the same time -- that's the relativity of simultaneity. But they certainly measure the same two points on the object.

 

[Motore]

The points are in different positions in time, causing the difference in length, right?

When an object is at rest relative to you, you measure the length from the tip to the end to be $L$. When the same object is moving relative to you, you measure the length from the tip to the end to be $L'$, and $L' < L.$ No more an illusion as the measurement of your monitor right in front of you.

 

[Dale]

You mean if a football field was moving at $v= \frac {\sqrt 3} 2 c$ in some inertial reference frame, giving a gamma factor of $2$, then an attempt to measure the length of the field between the goalposts atveach end would somehow instead measure the distance from one set of goalposts to the halfway line?

That has got to be nonsense! The observers would measure the distance from goalpost to goalpost.

That isn’t too far off from what actually happens though. The difference is that we are looking at 4D objects, so while they are both measuring from goalpost to goalpost in space, in time they are measuring differently. One of them is measuring with time lines straight across the pitch and the other is measuring with time lines diagonally across the pitch.

 

[student34]

I don't know what everyone else is seeing, but I clearly see different points on the "structure" of the ship that is extending through time.

 

[Doc Al]

I don't know what everyone else is seeing, but I clearly see different points on the "structure" of the ship that is extending through time.

Realize that those slanted lines on the diagram represent the positions of the same two points on the object! The two observers disagree on when the measurements were made but not on the points being measured.

 

[Dale]

I have read that length contraction is real and not just an illusion. However, when I compare an object at rest with an observer and the object in motion relative to another observer, I see that instead of there being a real length contraction, there is simply a difference in the part of the object being observed. In other words, the two observers are just looking at two different parts of the object.

I would strongly recommend against using imprecise words like “real”. It is far better to use words with a defined and agreed-upon meaning.

Length contraction is measurable, it is also frame-dependent. Some people will call it real because it is measurable, and some people will call it not-real because it is frame-dependent. But everyone should agree that it is measurable and frame-dependent. So the designation of real or not-real doesn’t convey any information.

 

[PeterDonis]

Length contraction is measurable, it is also frame-dependent.

The term "frame-dependent" can cause confusion here. Actual measurement results are invariants; that means they are not "frame-dependent" in at least a very common usage of that term.

Length contraction as an actual measurement depends on the state of motion of the object relative to the measurement apparatus; in other words, a measurement of the length of an object that is moving relative to the measurement apparatus is represented by a different invariant than a measurement of the length of the same object by measurement apparatus at rest relative to the other.

Each of these different invariants could, in principle, be described using any coordinates you like; for example, you could describe the invariant that represents the measurement of the object's length by an apparatus at rest relative to the object, using coordinates in which the object is moving (and in which the measurement apparatus is also therefore moving). The individual components of things like 4-vectors in the coordinate representation of any invariant are "frame dependent" in the sense of depending on which coordinates you choose; but the invariants themselves are not.

 

[Motore]

I don't know what everyone else is seeing, but I clearly see different points on the "structure" of the ship that is extending through time.

This is what you measure the length of the rocket to be, moving relative to you:

And this is what an observer in the rocket (at rest relative to the rocket) would measure the length to be:

Note that both observers measure the length bewteen the tip and the tail of the rocket at the same time in their rest frames. And those lengths won't be the same.

 

[student34]

Realize that those slanted lines on the diagram represent the positions of the same two points on the object! The two observers disagree on when the measurements were made but not on the points being measured.

If I had 2 parallel strings set up like the worldlines of the endpoints of the ship shown in the video, we would not think that any 2 points on one of the strings are the same point.

 

[Doc Al]

If I had 2 parallel strings set up like the worldlines of the endpoints of the ship shown in the video, we would not think that any 2 points on one of the strings are the same point.

But those worldlines aren't "things" like string -- they represent the position of some specific piece of the object as a function of time. Two points on the line are not different parts of the object, just that same part at a different time.

 

[student34]

Note that both observers measure the length bewteen the tip and the tail of the rocket at the same time in their rest frames. And those lengths won't be the same.

But the other end of the ship is in a different time.

 

[Motore]

But the other end of the ship is in a different time.

Not when you measure the length between tip and tail in your rest frame.

 

[student34]

But those worldlines aren't "things" like string -- they represent the position of some specific piece of the object as a function of time. Two points on the line are not different parts of the object, just that same part at a different time.

Then think about it this way. We could have a scenario where the first point of the nose of the ship does not even exist at the time of both observers measuring the ship. For example what if the nose were built really fast after the 2 clocks agreed on time. This would prove that these two points at the nose of the ship are not the same just like 2 separated points on a string are not the same.

 

[student34]

Not when you measure the length between tip and tail in your rest frame.

I meant to say that the 2 separated points in the illustration (at the nose of the ship) are at differing times.

 

[PeterDonis]

We could have a scenario where the first point of the nose of the ship does not even exist at the time of both observers measuring the ship.

There is no single "time at which both observers measure the ship". That is what the relativity of simultaneity means.

In the drawings in post #13, there are three events in spacetime. At the first event (the one on the left in both diagrams), both observers record the spatial position of the rear of the ship.

At the second and third events (the two different dots on the right in the two different diagrams), the two observers respectively record the spatial position of the front of the ship.

Events #1 and #2 happen at the same time according to the observer who sees the rocket as moving.

Events #1 and #3 happen at the same time according to the observer who is on the rocket and at rest relative to it.

In the alternate scenario you propose in the quote above, the nose of the ship is not yet built at event #2, but has just been completed at event #3. In this scenario, the observer who sees the rocket as moving would not be able to measure the rocket's length at the time at which events #1 and #2 happen in his frame, because the rocket's nose would not have been built yet. He would have to wait until the time at which event #3 happens in his frame, and his length measurement would involve event #3, at the nose, and a different event, event #4, at the tail (at whatever point on the tail's worldline was simultaneous with event #3 in his frame).

 

[student34]

There is no single "time at which both observers measure the ship". That is what the relativity of simultaneity means.

In the drawings in post #13, there are three events in spacetime. At the first event (the one on the left in both diagrams), both observers record the spatial position of the rear of the ship.

At the second and third events (the two different dots on the right in the two different diagrams), the two observers respectively record the spatial position of the front of the ship.

Events #1 and #2 happen at the same time according to the observer who sees the rocket as moving.

Events #1 and #3 happen at the same time according to the observer who is on the rocket and at rest relative to it.

In the alternate scenario you propose in the quote above, the nose of the ship is not yet built at event #2, but has just been completed at event #3. In this scenario, the observer who sees the rocket as moving would not be able to measure the rocket's length at the time at which events #1 and #2 happen in his frame, because the rocket's nose would not have been built yet. He would have to wait until the time at which event #3 happens in his frame, and his length measurement would involve event #3, at the nose, and a different event, event #4, at the tail (at whatever point on the tail's worldline was simultaneous with event #3 in his frame).

Ok, I agree, but I do not see how any of this conflicts with what I am saying.

 

[PeterDonis]

I do not see how any of this conflicts with what I am saying.

You said:

at the time of both observers measuring the ship

There is no such time. At the very least, you need to clarify what you meant by the phrase I just quoted, since what it says does conflict with what I posted in post #20--that's why I made that post.

 

[student34]

You said:There is no such time. At the very least, you need to clarify what you meant by the phrase I just quoted, since what it says does conflict with what I posted in post #20--that's why I made that post.

Ok, what I said was not accurate.

The heart of my issue is trying to understand whether or not there really is a length contraction or just a different perspective.

 

[Dale]

The heart of my issue is trying to understand whether or not there really is a length contraction or just a different perspective

Forget this question. It is a meaningless question because it focuses on the meaningless word “really”

 

[Ibix]

Ok, what I said was not accurate.

The heart of my issue is trying to understand whether or not there really is a length contraction or just a different perspective.

There is a measurable length contraction. The underlying reason is that the two frames take different 3d cross sections through the 4d worldtube as "the object, now" and those cross sections have different lengths. Whether you regard that as "really length contraction" or not is up to you. I wouldn't regard "really" as a helpful distinction.

 

[student34]

Forget this question. It is a meaningless question because it focuses on the meaningless word “really”

I still have the problem without the word "really". I will stop using it.

 

[student34]

There is a measurable length contraction. The underlying reason is that the two frames take different 3d cross sections through the 4d worldtube as "the object, now" and those cross sections have different lengths. Whether you regard that as "really length contraction" or not is up to you. I wouldn't regard "really" as a helpful distinction.

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.

 

[russ_watters]

The case of the rocket is a measurement that doesn't appear to have physical implications. That's why people think it is un-physical/an illusion. So perhaps it would useful to look at cases where there are real physical implications, such as with muon decay observations or relativistic space travel?

Or, from a Newtonian perspective: does it matter if different observers measure a car's speed differently - is the difference physically "real"? Well it does matter if it collides with a "stationary" object, in which frame the object was stationary.

 

[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.

Because the terminology predates Minkowski rewriting relativity in terms of geometry. In fact it goes back to Fitzgerald contraction, which was believed to be a compressive effect of the ether when one moved through it. The name has stuck. It's hardly the only infelicitous naming convention in physics - see conventional current, for example.

 

[Dale]

I still have the problem without the word "really". I will stop using it.

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

 

[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.