Length Contraction

[thomas reid]

In Relativity when something is moving does it become actually physically shorter or does it only appear shorter in the rest frame?

[thomas reid]

The reason I ask is that on the back side of my Sparknotes Physics Study Cards, for "length contraction (Lorentz contraction)" it reads:

"Predicts that objects appear shorter to an observer moving at a constant speed than to an observer at rest ..." [bold added]

I always thought objects became shorter and not just appear as the card suggests.

Is my Sparknotes card wrong?

[beecee]

Briefly every frame of reference is as valid as any other, so yes length contraction does take place..

http://www.askamathematician.com/2011/01/q-why-does-relativistic-length-contraction-lorentz-contraction-happen/

[J.C.MacSwell]

It is shorter in any inertial reference frame that it is moving, along the direction of travel.

In it's own reference frame it's not contracted.

[thomas reid]

Thank you.

I guess Sparknotes could argue that if it is shorter then it also appears shorter as well, and so they are not wrong.

But it is definitely misleading.

[zapatos]

3 hours ago, thomas reid said:

In Relativity when something is moving does it become actually physically shorter or does it only appear shorter in the rest frame?

I don't think it "becomes" shorter though. Its measurement is simply different depending on the FOR. It is not as if an object is constantly changing size depending on who is looking at it.

It is more akin to describing an object's color as gray when viewed under fluorescent light but brown when viewed under incandescent light. Both descriptions are accurate depending on the circumstances when you measure it.

I'm happy to hear rebuttals if I did not accurately describe the situation.

[beecee]

3 hours ago, zapatos said:

I don't think it "becomes" shorter though. Its measurement is simply different depending on the FOR. It is not as if an object is constantly changing size depending on who is looking at it.

It is more akin to describing an object's color as gray when viewed under fluorescent light but brown when viewed under incandescent light. Both descriptions are accurate depending on the circumstances when you measure it.

I'm happy to hear rebuttals if I did not accurately describe the situation.

And actually any object that appears grey under fluoresecent light is grey as you say. Since the colour of any object in the first instant, depends on the nature of the EMR falling on them.  At least that's the way I see it. Length contraction again, in my opinion is real in the frame it is detected in. I did find some references that may help...Like I said, all FoR are as valid as each other. 

 

 

or this which basically states that in the case of muons, one frame sees time dilation, while the other sees length contraction....http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html

 

Edited September 20, 2017 by beecee

[Strange]

To some extent, the answer to this question depends more on what you mean by "appears","physically", "real", etc. It is not just an optical illusion but nothing actually changes in the object that is length contracted.

For example, one of the best examples of length contraction is the fact that when we collide protons in a particle accelerator they are flattened by length contraction. This is seen in the way they bounce off each other; this can only be explained by colliding "disks" rather than spheres. But if you were moving alongside the particles, they would still be spherical.

And, for example, you are currently moving at nearly the speed light relative to something (e.g. the particles in that accelerator, or the muons mentioned before) but you don't feel squashed by that.

[DrKrettin]

I remember as a student having to explain this Gedankenexperiment problem:

Imagine an infinitely large and infinitely thin and infinitely smooth table with a slot in it of length L, and a rod of length L- dL just small enough to fall through it if you placed it over the slot and dropped it. Imagine the rod sliding along its axis towards the slot. When it reaches the slot it will fall through. Now imagine the same at a relativistic speed. An observer on the table will see the rod moving towards him, contracted, and it will fall through the slot. An observer on the rod will see the slot approaching, contracted. But then the slot is smaller than the rod and the rod will not fall through. Clearly an apparent paradox.

Anything happening at very low speeds must also happen at relativistic speeds so it must fall through the slot regardless of speed. Of course I can't remember the maths, but it turns out that even when the observer on the rod sees a contracted slot, the ends of the rod meet the ends of the slot at the same time so it still falls through. 

I'm not sure whether that helps at all. 

 

 

[Strange]

37 minutes ago, DrKrettin said:

I'm not sure whether that helps at all.

Without an explanation of how relativity of simultaneity solves this, I'm not sure it will.

https://en.m.wikipedia.org/wiki/Ladder_paradox

[DrKrettin]

1 minute ago, Strange said:

Without an explanation of how relativity of simultaneity solves this, I'm not sure it will.

No I don't think it will. But I remember that we as students used to say that relativity was rather like an erection - the more you thought about it, the harder it got.

[swansont]

7 hours ago, zapatos said:

I don't think it "becomes" shorter though. Its measurement is simply different depending on the FOR. It is not as if an object is constantly changing size depending on who is looking at it.

Right. One is avoiding the notion of a preferred frame where the "true length" can be determined, or the idea that there is a physical effect happening, which crushes an object just by looking at it from a different FOR.

[J.C.MacSwell]

8 hours ago, zapatos said:

I don't think it "becomes" shorter though. Its measurement is simply different depending on the FOR. It is not as if an object is constantly changing size depending on who is looking at it.

It is more akin to describing an object's color as gray when viewed under fluorescent light but brown when viewed under incandescent light. Both descriptions are accurate depending on the circumstances when you measure it.

I'm happy to hear rebuttals if I did not accurately describe the situation.

It depends on what is meant. I would say that if you considered an object in the reference frame in which it is initially at rest, it would "become" shorter as it is accelerated.

[zapatos]

1 hour ago, J.C.MacSwell said:

It depends on what is meant. I would say that if you considered an object in the reference frame in which it is initially at rest, it would "become" shorter as it is accelerated.

If we used "undergo change" (definition used by Merriam-Webster) instead of "become" would you say the object 'changes' as it is accelerated? I've been thinking of it more in terms of the conditions under which we make the measurement are changing, rather than that the object is changing.

Edited September 20, 2017 by zapatos

[thomas reid]

In the "Jouster's Paradox" two jousters with lances of equal lengths when at rest are moving towards one another.

And so in the one inertial frame of reference the one jouster gets knocked over first.

And in the other inertial frame of reference the other jouster gets knocked over first.

And the resolution of the "paradox" is that no body is a perfectly rigid body.  And so after colliding the shortened lance (one or the other depending on which frame of reference is being considered) then stretches out on then knocks over the other jouster.

If this is a correct statement of the Jouster's Paradox then, to me, it seems that length contraction must be real (there must be a real physical contraction of the length of the moving body in the resting body's frame of reference) for the moving jouster to get knocked off first (in the resting frame of reference) before the resting jouster gets knocked off (in the resting frame of reference).

This is why the "appearance" reference on my flash card confused me.

No?

 

 

 

 

 

Edited September 20, 2017 by thomas reid
extra file

[Strange]

I haven't seen this paradox before. It looks quite likely that the explanation, again, is relativity of simultaneity; in other words, each frame of reference has a different view of what "first" means.

[thomas reid]

Yes, relativity of simultaneity is a relevant here.  There are two events: knocking off the left jouster and knocking off the right jouster.  And in one inertial frame of reference the sequence of these two events is left jouster is knocked off first and right jouster is knocked off second, and in the other inertial frame of reference the sequence of events is the right jouster is knocked off first and the left jouster is knocked off second.

But what leads to this difference in sequence of events is "length contraction of the moving body in the direction of its motion."

Or, at least, that is how I learned it.

[studiot]

 

36 minutes ago, thomas reid said:

In the "Jouster's Paradox" two jousters with lances of equal lengths when at rest are moving towards one another.

And so in the one inertial frame of reference the one jouster gets knocked over first.

And in the other inertial frame of reference the other jouster gets knocked over first.

And the resolution of the "paradox" is that no body is a perfectly rigid body.  And so after colliding the shortened lance (one or the other depending on which frame of reference is being considered) then stretches out on then knocks over the other jouster.

If this is a correct statement of the Jouster's Paradox then, to me, it seems that length contraction must be real (there must be a real physical contraction of the length of the moving body in the resting body's frame of reference) for the moving jouster to get knocked off first (in the resting frame of reference) before the resting jouster gets knocked off (in the resting frame of reference).

This is why the "appearance" reference on my flash card confused me.

No?

 

 

 

 

 

 

I think the key to this one is to realise that not only does the each jouster see the approaching lance as shorter than his own but he also sees the distance between himself and the tip of the moving lance to be shorter. That is he sees all distances in the moving frame (considering himself static) shorter along the inter-line.

Edited September 20, 2017 by studiot

[thomas reid]

studiot, yeah i get that every moving body length contracts ... but the question is does the person at rest just see those moving bodies contract or is it that they actually do contract for the person at rest?

I bought up the Jousters Paradox because, to me, if it is the case the the moving jouster is knocked off his horse first in the other jouster's rest frame then, to me, this suggest that length contraction is not just a matter of measurement or appearance but rather an actual physical shortening in the rest frame.

That's how I've understood length contraction but, again, my Sparknotes card seems to suggest otherwise and so that's the reason I ask the question I did in this thread.

Thank you.

[swansont]

Somehow I don't trust the explanation has to do with rigidity and stretching out.

This goes through the analysis, but mentions neither

http://iopscience.iop.org/article/10.1088/0031-9120/35/3/306/pdf

The conclusion is it doesn't matter that one hits before the other in either rider's frame

"A would only find out that he had hit B after he found himself hit by B, as the information from his own lance tip would not yet have reached him. "

 

[thomas reid]

Can anyone sign up for iopscience or do i need a dot edu email address?

I can imagine that I'm wrong about the correct resolution for the Jousters "paradox" ... but my question still is: is length contraction physically occurring or simply a matter of measurement and appearance?

Time dilation must be physically real ... right?  Time dilation is not just a matter of measurement and appearance ... right?  So wouldn't the other basic relativistic dynamic, length contraction, also be physically happening?

 

[zapatos]

Yes, time dilation is physically real. Make sure you don't think of things within your frame as being 'real' but then questioning whether or not something in another frame is also real. They are all equally real.

I think the difficulty arises because of the language around whether or not the object 'contracts'; that is, whether or not an object goes through some sort of metamorphosis simply because someone happens to be viewing it from a new frame.

 

[thomas reid]

My understanding (before encountering my Sparknotes card and was caused to question it) of length contraction is that in the rest frame the length of an object does not change and this is a real fact about the physical world, while in another frame of reference where it is in relative motion that same object is contracted in its direction of motion and this is also a real fact about the physical world.  The word "contraction" is part of the phrase "Length Contraction."  I don't know of a better word to use than the language of Relativity itself.

Using your word, would you say that "time dilation" involves a "metamorphosis" of "time" (that is, a slowing down of time)?

My question still is: is length contraction something that is viewed to happen or is it something that happens?

[studiot]

I am sorry I rather scrambled my last post so you missed the main point which was that you don't only have to consider the lance length you must also consider the shrinking empty space between the jousters.

[thomas reid]

I don't want to go too far off topic (I would really like to get my question answered), but I don't think that the space between the jousters does shrink (in the inertial frame of reference of the jouster at rest).

If the moving jouster himself is considered to remain in place (as he moves) relative to the length contraction then the length of the lance contracts towards him and the distance between the jouster at rest and the moving tip of the lance gets longer (in the rest frame), if the midpoint of the lance is considered to remain in place (at it moves) relative to the length contraction then the distance between the jouster at rest and the moving tip also gets longer (in the rest frame), and if the tip of the lance is considered to remain in place (at it moves) relative to the length contraction then the distance between the jouster at rest and the moving tip remains the same (in the rest frame).

This usually isn't an issue when looking at Special Theory of Relativity thought experiments because they simply start out with the two bodies in relative motion and so which way the contraction occurred isn't at issue and we just start out with a body that is contracted in another frame of reference in which it is moving.

Where I have found this is relevant is in Bell's Spaceship Paradox.  (Again, I really don't want to go too far off topic.)  Briefly and generally, Bell's Spaceship Paradox involves a distance that goes through acceleration (a string between to spaceships) and the question is what happens to the string (does it break).  The resolution, in part, (again, briefly and generally) comes down to where force of acceleration occurs.  And what happens is that if, say, the rocket engine is at the midpoint of each spaceship then the front and back of the space ship length contract in to that point (and if the rocket engine it at the front or at the back then the length contraction occurs forward or backwards).  (And, yes, the main part of resolving this paradox is considering whether or not the two space ships take off at the same time from different perspectives.)

---

I think length contraction is physically real in the rest frame.  I think the moving body becomes physically shorter in its direction of motion in the rest frame.  My flash card, however, has caused me to question this belief.  And I guess I came here just looking for some confirmation (or disconfirmation).