Is length contraction (Lorentz transformation) an illusion or real?

[student34]

My textbook (from first year university physics) says that length contraction is actually real. But how can it be real when two different observers can measure two different lengths? For example, if I am in a spaceship going close to the speed of light relative to people on Earth, they will measure my ship longer than I do. How can one object have two different lengths? That goes against basic logic of uniqueness. The only way out of this that I can imagine is that if the universe splits every time objects change their speeds with respect to each other (just like the many worlds interpretation of QM). And then when the objects are at rest with each other the two universe's reconverge, .

The idea that the contraction is an illusion of perspective seems more appealing. Is there a way of claiming that the spaceship actually pivots into another dimension making the ship appear shorter, much like a rod pivoting away from an observer. Or maybe the ship and/or the space around it becomes warped in such a way that the ship appears shorter?

 

[ergospherical]

if I am in a spaceship going close to the speed of light relative to people on Earth, they will measure my ship longer than I do.

Should be the other way around, no? :)

In any case, yes, it is real! Whilst rotations of the coordinate axes in three-dimensional Euclidean space (orthogonal transformations) preserve spatial distances, Lorentz transformations of the coordinate axes in four-dimensional Minkowski space do not preserve spatial distances (not least because the thing that you call "space" changed!).

There's the extra issue of what you'd "see", which is a bit more subtle. For example, Penrose was the first to prove that spheres appear spherical to any observer, due to apparent rotation - in this sense the Lorentz contraction is "invisible"! Nonetheless the actual length (as opposed to apparent length) of a moving sphere is contracted.

 

[PeroK]

The idea that the contraction is an illusion of perspective seems more appealing.

It's not a illusion of perspective. Objects have a proper length, which is the length measured in a frame in which the object is at rest. But, generally, length can only make sense as what is measured (by simultaneous measurements of two ends of an object). And length, by that definition, is frame dependent.

Note that you need to rid yourself of whatever prejudices or preconceptions that cause you to reject that - if you are going to successfully study SR. Studying SR is about changing the way you understand space and time. It's not about reinforcing classical notions of space and time.

 

[hutchphd]

There's the extra issue of what you'd "see", which is a bit more subtle.

This has a nice graphic: https://en.wikipedia.org/wiki/Terrell_rotation

 

[cianfa72]

Objects have a proper length, which is the length measured in a frame in which the object is at rest. But, generally, length can only make sense as what is measured (by simultaneous measurements of two ends of an object). And length, by that definition, is frame dependent.

IMO the point is that every object actually spans a spacetime region (i.e. a spacetime worldtube). We can 'slice' it in different ways, each one defined by the simultaneity convention established by the reference frame used. So you get different answers for the body length depending on the reference frame chosen.

 

[Nugatory]

But how can it be real when two different observers can measure two different lengths?

What you are calling the “length” of an object is the distance between where its ends are at the same time. Because of the relativity of simultaneity (if you are not familiar with this concept, Google for “Einstein train simultaneity” and gnaw on the thought experiment until you understand it - this is probably the most counterintuitive part of relativity but is absolutely essential) the ends aren’t at the same place at the same time for all observers. Thus, the lengths that they’re measuring are between different points in space and there is nothing paradoxical or surprising that they get different results - they’re measuring different things.

Is length contraction (Lorentz transformation) an illusion or real?

This thread title suggests that you have a common (but seriously wrong) misunderstanding: length contraction and the Lorentz transformation are completely different things. The length contraction formula $\Delta L’=\Delta L/\gamma$ is derived from the Lorentz transformation, but there’s a fair bit of algebra involved: basically you have to use the Lorentz transformations to determine where the ends of an object are at the same time in the primed frame given where they are in the unprimed frame.

 

[PeroK]

“Einstein train simultaneity” and gnaw on the thought experiment until you understand it

I would respectfully disagree on this point and advise the OP to avoid this thought experiment at all costs. It's a confusing mess, IMO, and there are far simpler ways to learn about the RoS. E.g. from the first chapter in Morin's book:

https://scholar.harvard.edu/files/david-morin/files/relativity_chap_1.pdf

 

[student34]

Should be the other way around, no? :)

In any case, yes, it is real! Whilst rotations of the coordinate axes in three-dimensional Euclidean space (orthogonal transformations) preserve spatial distances, Lorentz transformations of the coordinate axes in four-dimensional Minkowski space do not preserve spatial distances (not least because the thing that you call "space" changed!).

How can the ship's length of, say, 10m long be true for me, but only have, say, 3m length for observers from Earth? How can one object be two different sizes?

 

[student34]

What you are calling the “length” of an object is the distance between where its ends are at the same time. Because of the relativity of simultaneity (if you are not familiar with this concept, Google for “Einstein train simultaneity” and gnaw on the thought experiment until you understand it - this is probably the most counterintuitive part of relativity but is absolutely essential) the ends aren’t at the same place at the same time for all observers. Thus, the lengths that they’re measuring are between different points in space and there is nothing paradoxical or surprising that they get different results - they’re measuring different things.

This thread title suggests that you have a common (but seriously wrong) misunderstanding: length contraction and the Lorentz transformation are completely different things. The length contraction formula $\Delta L’=\Delta L/\gamma$ is derived from the Lorentz transformation, but there’s a fair bit of algebra involved: basically you have to use the Lorentz transformations to determine where the ends of an object are at the same time in the primed frame given where they are in the unprimed frame.

My thread is about whether or not length contraction is an illusion. This response seems to suggest that the length contraction is an illusion.

As you seem to elude to, the observers are measuring the ends of the ship at different times. So the measurement from Earth is not a true comparison as the measurement on the ship. I cannot go outside and measure one end of my car at t1 and then move my car, and then measure the other end at t2 and say that's the measurement of the car. A person in my car would not get the same measurement in seemingly the same way as with the ship.

 

[Nugatory]

I would respectfully disagree on this point and advise the OP to avoid this thought experiment at all costs. It's a confusing mess, IMO, and there are far simpler ways to learn about the RoS.

That’s fair…. There’s more than one way to learn the concept

 

[PeroK]

How can the ship's length of, say, 10m long be true for me, but only have, say, 3m length for observers from Earth? How can one object be two different sizes?

Why not?

 

[student34]

It's not a illusion of perspective. Objects have a proper length, which is the length measured in a frame in which the object is at rest. But, generally, length can only make sense as what is measured (by simultaneous measurements of two ends of an object). And length, by that definition, is frame dependent.

Note that you need to rid yourself of whatever prejudices or preconceptions that cause you to reject that - if you are going to successfully study SR. Studying SR is about changing the way you understand space and time. It's not about reinforcing classical notions of space and time.

Why not?

It is a contradiction. The observers must not be measuring the same property while argeeing on all relevant points of reference.

 

[FactChecker]

How can the ship's length of, say, 10m long be true for me, but only have, say, 3m length for observers from Earth? How can one object be two different sizes?

Remember that the ends of the ship are not measured by both observers at the same place at the same time. They are moving very fast in opposite directions versus each other. If I consider myself "stationary" and observe what is happening on the ship from one second to the next, the ship has traveled very far in that second and I have to compare lengths, processes, and clocks at far distances. So how my clocks are synchronized at great distances is very critical. A person on the ship has a similar situation but is traveling in the opposite relative direction. So we are not talking about the same clocks or locations at all. That is why we both believe that the other has a slower clock (and physical processes) and shorter distances. The length of the ship is determined by the position of the ends AT THE SAME TIME. But we can not agree on what is "the same time".

 

[PeroK]

It is a contradiction. The observers must not be measuring the same property while argeeing on all relevant points of reference.

Are you a physics student?

 

[Nugatory]

This response seems to suggest that the length contraction is an illusion.

You’re using the word “illusion” in the sense of being not real, which just leads to the question of exactly what it is real here. Here are two statements:
A) The nose of a passing spaceship (for definiteness, moving at .8c) was exactly lined up with a stationary clock at exactly noon. Also at noon the tail of the spaceship was exactly lined up with another stationary clock 80 meters away.
B) On the spaceship we stretched a tape measure from nose to tail and it measured 100 meters.

There’s no room for illusion here - both of those statements are real facts about real clocks, spaceships, and tape measures. That’s what it means to say that length contraction is “real” (and almost certainly what your textbook author meant).

Now, you may choose to say that the 80 meter measurement is not a “real” length, that it is an “illusion”…. But why? What, other than your lifetime of experience with speeds too small to expose relativistic effects, makes fact A less “real” than fact B?

 

[PeterDonis]

It is a contradiction.

No, it isn't, it just shows that this...

The observers must not be measuring the same property

...is the case. "Length as measured by observer A" and "length as measured by observer B", if A and B are in relative motion, are different properties of the object. That is what relativity is telling you.

 

[PeterDonis]

while argeeing on all relevant points of reference.

No, the observers do not agree on "all relevant points of reference". They disagree on simultaneity: that means they disagree on which measurements of the ends of the rod take place at the same time. That is why "length" as measured by each observer is a different property.

 

[student34]

Are you a physics student?

I took first year physics which had a couple of units in SR. But I do not think this is a very complicated issue. We are taking about 3 spatial dimensions plus 1 time dimension.

The ship has one true size in 3 spatial dimensions in any given instant in time or "slice" in the universe. There simply cannot be two different lengths of the ship at any given instant.

This contraction must be an illusion due to time.

 

[Nugatory]

My thread is about whether or not length contraction is an illusion.

There is a very fascinating thought experiment, Bell’s Spaceship Paradox. It’s a bit challenging (you absolutely must understand relativity of simultaneity to take it on, and when it was first proposed it tripped up a number of competent professional physicists) but worth looking up and working through.

Jumping ahead to the conclusion: if we accelerate a string so that as its speed increases its length becomes increasingly contracted, while we hold the endpoints fixed…. The string will be stretched and eventually break. If that’s not a “real” contraction I don’t know what is.

(But there’s a lot more to this thought experiment. Especially important is to how we explain the string breaking when we describe the experiment from a frame in which the string is at rest…. So work through it for yourself, you’ll be glad you put in the effort)

 

[ergospherical]

It is a contradiction. The observers must not be measuring the same property while argeeing on all relevant points of reference.

There are certain so-called "Lorentz-invariant" properties of a system, e.g. its mass, its charge, etc. which don't depend on reference system... but the length of a body is not such a property (it is really nothing but the difference between two space coordinates at a common time in some reference system).

The ship has one true size in 3 spatial dimensions in any given instant in time or "slice" in the universe. There simply cannot be two different lengths of the ship at any given instant.

This contraction must be an illusion due to time.

Don't forget though that different inertial observers foliate the universe into different sets of spatial slices! the relativity of simultaneity! There are multiple valid ways of slicing the universe at any given moment.

[Mentors’ note: A portion of this post has been translated into language that will be useful in a B-level thread]

 

[phyzguy]

How can the ship's length of, say, 10m long be true for me, but only have, say, 3m length for observers from Earth? How can one object be two different sizes?

If I'm driving down the highway at 60 MPH, I see the objects in my car all as motionless. Someone driving the other direction at 60 MPH sees the things in my car moving at 120 MPH. How can one object have two different speeds?

 

[student34]

You’re using the word “illusion” in the sense of being not real, which just leads to the question of exactly what it is real here. Here are two statements:
A) The nose of a passing spaceship (for definiteness, moving at .8c) was exactly lined up with a stationary clock at exactly noon. Also at noon the tail of the spaceship was exactly lined up with another stationary clock 80 meters away.
B) On the spaceship we stretched a tape measure from nose to tail and it measured 100 meters.

There’s no room for illusion here - both of those statements are real facts about real clocks, spaceships, and tape measures. That’s what it means to say that length contraction is “real” (and almost certainly what your textbook author meant).

Now, you may choose to say that the 80 meter measurement is not a “real” length, that it is an “illusion”…. But why? What, other than your lifetime of experience with speeds too small to expose relativistic effects, makes fact A less “real” than fact B?

So objectively speaking, is the ship 80m long or 100m long? It can not be both because there is only one ship with one size.

 

[phyzguy]

So objectively speaking, is the ship 80m long or 100m long? It can not be both because there is only one ship with one size.

You keep saying this, but it is simply false. The length of the ship is observer dependent. Until you accept this and ask how it can be the case, you will make no progress.

 

[PeterDonis]

The ship has one true size in 3 spatial dimensions in any given instant in time or "slice" in the universe. There simply cannot be two different lengths of the ship at any given instant.

there is only one ship with one size.

Sorry, but these statements are wrong. They would be true if Newtonian physics were exactly right, but it isn't. In relativity it is wrong.

If you are not going to listen to the answers we give you, there is no point in continuing the thread. Thread closed.

 

[Nugatory]

So objectively speaking, is the ship 80m long or 100m long?

Neither. The objective facts are the ones I stated in post #15 above. No statement about the length can be “objective” in the sense that you mean because length is a frame-dependent property just like the speeds that @phyzguy mentioned in post #21.

It can not be both because there is only one ship with one size.

It is true that there is one ship. It is not true that it has one size, any more than the objects in phyzguy’s car have one speed. The only difference between the frame-dependent speeds in phyzguy’s example and the frame-dependent lengths in mine is that one effect is apparent even at speeds that we are familiar with, while the other is only big enough to notice at relativistic speeds.