Modern Physics view of Length Contraction?

1. Feb 8, 2012

meBigGuy

I've been told several times that length contraction is not "real" in the sense of material or its space actually contracting. How does modern physics (by that I mean what is being taught currently) view Bell's spaceship paradox. Will the string break? Why, if length contraction is not real. I also have a hard time with the extended lifetimes of Muons in the atmosphere if, from their point of view, space had not contracted.

2. Feb 8, 2012

Staff: Mentor

It basically comes down to one's definition of "real." Different people have subtly different ideas about what "real" means in this context.

3. Feb 8, 2012

nitsuj

Maybe ask them if time dilation is "real", in the sense that time "really" slows down.

Is what is measured by the observer more "real" then what is measured by the moving (contracted/time dilated) "body"?

Both would agree the string broke.

Last edited: Feb 8, 2012
4. Feb 8, 2012

ghwellsjr

One of the "rules" we use in evaluating the calculations we get from applying Special Relativity is that values that change just because we view the same parameter from different Frames of Reference are not "real" since they are dependent on the arbitrary frame we select. Length contraction is frame dependent (as is time dilation) so we can never say that a given length is "really" contracted as the same length might get shorter in one frame and longer in another.

However, when a rigid object is accelerated so that its speed changes, every frame will say that its length changes. Remember, an acceleration in one frame can be a deceleration in another frame so a length that gets shorter as a result of an acceleration in one frame would get longer as a result of deceleration in another frame. Some frames will say it gets longer, some frames will say it gets shorter. So we can never say that its length "really" contracts, only that its length "really" changes.

When we talk about the acceleration of a rigid object, we usually don't get down to the details of exactly where the force of acceleration is applied, we usually treat the entire object as a single point with its location being specified by a single value and we assume that it will survive the acceleration and not be stressed to the point where we could actually detect any damage as a result of the acceleration. This allows us to describe the object as a single event at any given point in time so that we can easily transform its coordinates into other frames and "calculate" the length contraction without concern for whether a real object will survive the force of acceleration. This, of course, can only happen in thought problems.

However, if we talk about a rigid object being accelerated at more than one point, then we have to specify the object with more than one event and we can no longer ignore the effects of stresses. So if we specify the problem in one frame such that the multiple points of acceleration cause the length to be stressed to the point of fracture (because we say that it cannot survive that stress), then this has nothing to do with viewing the problem from different reference frames as they will all say the same thing.

So the bottom line is that lengths that change as a result of viewing them from different reference frames are not "real" but lengths that change as a result of a rigid object being accelerated are "real".

5. Feb 8, 2012

nitsuj

So acceleration defines what is "real" in this context?

I see no difference in the scenarios between acceleration & inertial in determining if length contraction is "real".

Seems odd to say if the body is accelerating (i.e. every other FoR would agree who is moving) then it is "real". perhaps the process of determining what is "real" is democratic.

Doesn't the string get a vote?

Or is that merely the way physicists describe "real"?

Last edited: Feb 8, 2012
6. Feb 8, 2012

harrylin

Yes you could say that.
If according to measurements with all inertial reference systems a change of length occurs, then there is universal agreement about the reality of that occurrence - even though there is disagreement about the value of that change of length.
The string breaks; isn't that telling?
As already mentioned, "real" isn't a well defined term among physicists.

7. Feb 8, 2012

nitsuj

Yea, that's why I wonder why the definition of "real" is ambiguous in this context.

Anyhoo, no difference if I think length contraction is really a "real" relativistic effect.

Hmmm.... thinking of the string some more, the "at rest" FoR and moving "body" FoR would disagree on the length of the string/distance between ships. i.e. it broke for different reasons, with neither being wrong from a physics perspective.

The string "really" broke because it shrank (at "rest" FoR), the string "really" broke because the distance between ships increased (in motion FoR), I think that's right.

Looks like the only way to argue that it is "real' is to [STRIKE]determine[/STRIKE] assign a preffered/privileged FoR, Earth would get the most votes I'm sure .

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8. Feb 8, 2012

clem

Try http://arxiv.org/abs/0906.1919

9. Feb 8, 2012

ghwellsjr

It's no different than talking about whether a body is at rest or in motion, it's frame dependent. But there is no inertial frame in which an accelerated body can be at rest both before and after the acceleration. So in a frame in which the body ended up at rest, its length gets longer, not shorter. Would you call that length contraction?

Now as to the string, if you set it up in a frame such that it breaks because it wants to contract but the accelerating spaceships won't let it contact, there are other frames in which it wants to expand, but it still breaks because the forward spaceship takes off before the rear one.

10. Feb 8, 2012

nitsuj

Yea I eventually came to a simular conclusion, see my above post. #7.

The arrogance of my FoR is tough to shake sometimes lol.

Last edited: Feb 8, 2012
11. Feb 8, 2012

ghwellsjr

The earth is not an inertial frame so it doesn't qualify. Besides, we're talking Special Relativity where we ignore gravity and there is no such place in the universe where that qualifies. I prefer to educate people about Special Relativity. It is really a very simple concept with very easy math that anyone can understand who takes a small bit of effort.

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12. Feb 8, 2012

ghwellsjr

Your FoR is not inertial either.

13. Feb 8, 2012

nitsuj

Yea to your point I'm idealizing.

And Im suprised you missed my point regarding a preffered FoR, oh wait you didn't you just split hairs/introduced some specifics into the idealized scenario.

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14. Feb 8, 2012

ghwellsjr

Do you mean this comment?

15. Feb 8, 2012

nitsuj

yea that one; It is really a very simple concept with very easy math that anyone can understand who takes a small bit of effort.

It seems to imply something

16. Feb 8, 2012

ghwellsjr

Special Relativity is very simple to understand, especially if you learn it from Einstein in his 1905 paper. What makes it so difficult is that many people have so many misconceptions about it that they have to first unlearn and then relearn.

17. Feb 8, 2012

nitsuj

Well, the comment couldn't be anymore subjective.

18. Feb 8, 2012

meBigGuy

Clem, the Franklin paper described the concept of 4 dimensional rotation, which is sort of how I have always thought of it (I aways thought of it as a "spatial distortion" that is inherent in the fabric of space). It's clear to me that the length of moving bodies actually change in the reference frame. It is not an "apparent" change. I'm still not exactly clear as to why the string breaks immediately though. I'll have to read it more carefully, as I pretty much skimmed it. I actually expected him to say it wouldn't break. Thanks for that one.

People age differenty in the direction of acceleration, so lengths change also. I need to work through it.

19. Feb 9, 2012

ghwellsjr

Aging occurs without regard to direction.

20. Feb 10, 2012

meBigGuy

Aging occurs without acceleration or relative motion also. Seems to come along with existance. Sometimes considering the context goes a long ways.

I was saying that identically accelerated objects age differently in the direction of acceleration.

21. Feb 11, 2012

ghwellsjr

And I was saying "Aging occurs without regard to direction."

22. Feb 11, 2012

pervect

Staff Emeritus
As has been noted, "real" isn't a well defined term. One element often associated with reality is "observer independent" or "frame independent" quantites. These are quantites that have the same value no matter what frame of reference one is in.

It is tempting, but probably overly ambitious, to say that quantites that depend on the observer aren't real.

For example, by this definition kinetic and total energies in Newtonian mechanics wouldn't be "real", because it's observer dependent. If you look at a closed, isolated system in Newtonian mechanics all observers will agree that energy of the closed system conserved, but different observers will give different values to this conserved energy - because the kinetic energy of an object depends on the observer, and the kinetic energy is part of the total energy.

The concept of distance, and the concept of "now", were, before relativity, both regarded as being observer independent. Post-relativity, both the concept of distance and the concept of "now" are regarded as being dependent on the observer, though the observer dependence only becomes obvious at high velocities.

You may occasionally see remarks trying to summarize this that say "distance isn't real" and "now is an illusion", but that's rather over-ambitious, much like saying that energy isn't real because different observers don't agree on it's value. It's more helpful to say that "distance is observer dependent" and "now is observer dependent".

The good news is that there is an observer independent quantity in relativity. This is known as the Lorentz interval. So if you like to think of observer independent quantities as "really real", you can think of the Lorentz interval as being "really real".

23. Feb 11, 2012

clem

What is your definition of "the length of moving bodies"?

24. Feb 11, 2012

nitsuj

Pretty sure meBigGuy is referring to comparative aging. with the observations being symmetric how is this "regardless of direction"?

25. Feb 11, 2012

nitsuj

Maybe the same hurdle I had, assuming a preferred/privileged FoR.

Although his/her statement is qualified with "it's clear to me". So there's how he/she defines it.