# An issue with length contraction

• I
• student34
In summary, 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.## Length contraction is not an illusion.

#### 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?

PeroK
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

topsquark and vanhees71
student34 said:
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.

topsquark and vanhees71
student34 said:
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.

topsquark
Doc Al said:
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?

Dale
student34 said:
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.

topsquark, PeterDonis and PeroK
student34 said:
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.

topsquark
PeroK said:
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.

PeroK
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.

student34 said:
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
student34 said:
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.

nasu, topsquark and PeroK
Dale said:
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.

Dale and topsquark
student34 said:
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.

Doc Al said:
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.

topsquark
student34 said:
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.

Motore said:
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.

PeroK
student34 said:
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.

Doc Al said:
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.

PeroK
Motore said:
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.

student34 said:
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).

topsquark, Dale, Doc Al and 1 other person
PeterDonis said:
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.

student34 said:
I do not see how any of this conflicts with what I am saying.
You said:

student34 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.

phinds, russ_watters and topsquark
PeterDonis said:
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.

student34 said:
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”

topsquark and PeterDonis
student34 said:
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.

Dale and topsquark
Dale said:
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.

Ibix said:
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.

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.

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topsquark
student34 said:
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.

topsquark
student34 said:
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?

topsquark
student34 said:
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?

topsquark
Dale said:
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?

student34 said:
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.

topsquark and robphy
student34 said:
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.

topsquark, Motore and Dale
Ibix said:
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.