Question about length contraction

peterspencers

I am on a spacecraft as it makes a journey between two planets. I use a lightpulse to measure the distance before I set off, I then accelerate to a speed that is close to the speed of light and measure the distance again. I find that the distance when I am stationary (relative to the planets) is much grater than it is when I am moving very fast.

I think I understand the equations for length contraction, but I have a few nagging questions....

Does space 'actually' contract for the fast moving craft, relative to the planet? And is space considered to be a separate entity to matter and energy?

bgq

Hi,
Before special theory of relativity much of things have their own identity which is represented by its properties, but special relativity makes things somehow loses some of their properties. That is distance between two objects is NOT anymore something that is absolute property of two objects the distance in between, but the distance is something that every frame can measure it differently. Referring to your question, you measure a larger distance; but this is not to mean that the distance is larger, other observer may measure it smaller.

haael

The geometrical interpretation of that fact is most closely related to rotation. The spacetime is "rotated" along the axis of the fourth dimension and you see it from a different angle, that's why it looks contracted.

Suppose you have a circle. When you look at it from a different angle, it will look as an ellipse. One dimension is contracted.

Lorentz transformations look strikingly similar to rotations. The difference lies in the measure that they leave unchanged.

When x is an angle, for normal rotations you have: (sin x)^2 + (cos x)^2 = 1
For Lorentz transformations, you have: (sinh x)^2 - (cosh x)^2 = 1
Another approach is to say that normal rotations leave a unit matrix unchanged:
R(x)^(-1) [[1, 0], [0, 1]] R(x) = [[1, 0], [0, 1]]
Lorentz transformations leave the matrix that have one diagonal element negative:
L(x)^(-1) [[-1, 0], [0, 1]] L(x) = [[-1, 0], [0, 1]]

This very fact led to the interpretation of special relativity as a geometry of a 4-dimensional space and to the concept of spacetime.

harrylin

"Space" in one direction is in SR simply the measured length, based on an assumption of simultaneity (Einstein: "rulers" and "clocks"). See if you can follow the elaborations here:

physicsforums.com/showthread.php?p=4016947
physicsforums.com/showthread.php?p=4019235

peterspencers

So from the given replies, firstly, in regards to Bells spaceship paradox. This gets at the heart of my question, is length contraction real enough to break strings? or is it just a perspective issue? With Bells paradox, it all depends on how you accelerate the two ships. Simultaneity would seem to be important, however if the acceleration of the ships was equal then the string will accelerate equally and thus contract equally with the ships as though the string were as much a part of the ship as the ships were! thus the string will not break.
Comparing Bells paradox to the Ehrenfest Paradox, where we have a train with its carriages connected by strings traveling along a circular track. As the track and the train are in two separate reference frames the contraction will only apply to the train, thus the strings will break, as now the strings arn't sufficient to cover the circumference of the track.
If i apply this to my question regarding my ship as it travels between two planets. And now ask how long it takes for the ship to get from planet A to planet B. I would take the speed of my craft, divided by the now contracted length between the two planets.

So this would seem to suggest that the the answer to my question is, 'yes' the length really does contract.

However my limited understanding of Haael's response suggests that length contraction is a phenomenon of perspective?

What is the current definition of 'spacetime'?

peterspencers

Would it be fair to say that space is a creation of time through movement. Movement of information at the speed of light, information in the form of bosons interacting with fermions. Time being cycles of boson interaction through fermions?

pervect

Ummm - I don't think so. Where did you read this? It sounds like a personal theory I hope you're aware of the status of personal theories here at PF....

Earlier you asked

Spacetime is a 4 dimensional manifold.

Manifolds are built from the underlying concept of topological spaces.
Topological spaces are built from the notion of "open balls" or "open sets"

The exact definition of manifolds (and the rest) is somewhat technical, alas. But as an example, the 2d surface of a 3d object would be an example of a 2d object. If you visualize such a curved 2d surface as having "extra dimensions", you'll get 3d and 4d manifolds. That's really just a visual aid, but it may be helpful. A really rigorous treatment of manifolds and topological spaces would be quite long, and I probalby couldn't do it justice in a post, especially as there are a lot of tiny but vital details to "get right".

harrylin

To the contrary! I only linked my two posts there which directly answered your original question and more, here once more:

- Yes, the accelerated observers will, if and after they re-synchronizes their clocks, measure a contracted distance between the planets.

- The stay-at-home observer who uses a reference system in which he is in rest, will measure that the rulers of the accelerated observer have contracted and that he now de-synchronised his clocks ("measurements" depend on system-dependent convention).
In this way the stay-at-home can explain why the accelerated observers measure all unchanged distances as if they are contracted.

However, as explained everywhere in that thread, length contraction is a physical effect: for it to happen to the whole system of ship-string-ship, the string should pull the ships together. And as the string is defined as not strong enough, it must break.

That's a funny variant. See a discussion with the original paper (no train) here:
http://physicsforums.com/showthread.php?t=503462

Do you think that your acceleration contracts the universe??
Confusion about that reigns, even in the literature; and I ascribe that to the erroneous question of asking if it is one or the other. My 2 cts: it's both, as follows from my earlier explanations.
- a change of velocity induces real effects, as proven with clocks; real effects on rulers and clocks necessarily affect measurement systems.
- if your measurement system is affected and you make a new synchronization with those instruments then what you next measure is a phenomenon that is a matter of perspective.

peterspencers

So when the ship accelerates it 'actually' contracts and has its time dilated. But the planets around it don't 'actually' become length contracted and time dilated, they just appear to. And the 'real' length contraction/time dilation only becomes apparent when the craft slows down to the planets reference frame and you compare clocks?

harrylin

No: that is from the perspective of the stay-at-home. From the perspective of the end rest frame of the ship, the ship expands to the un-contracted length and its clocks speed up to the "normal" speed. There is only agreement that real physical things happen. There is no absolute reference frame for us to base absolute statements on such as that something that is in inertial motion is "actually" contracted.
See above: no inertial reference frame is preferred, so that we cannot establish any "absolute frame". The "planet's (rest?) reference frame", if such a thing existed, has no special status (except perhaps for ease of calculation); that is the meaning of the relativity principle.

peterspencers

Ok...but when the passanger onboard the craft returns after a long, high speed flight, he finds that he has actually aged less than the people on the planet. Theifore surely one must conclude that the time dilation 'did' actually happen and it was dependant on the reference frame that experienced acceleration.

harrylin

Quite so... More precisely, that one of the two changes velocity (and not the other) is responsible for the asymmetry in the accumulated clock times when they meet again. That is the so-called "twin paradox" scenario which is currently (for the Nth time ) being discussed here:
http://physicsforums.com/showthread.php?t=642784

Perhaps you want to join the discussion there, if these things are relatively new to you; by now I walked away as it's like a soap opera that I have seen plenty of times, and just as superficial.

nitsuj

Comparatively, yes it does actually contract, but that's just from moving so fast (time slows)... What makes that statement true is comparatively.

How else could spacetime account for the length traveled in reduced time, but with a reduced length as well. So does it actually contract? I guess the word contract implies spacetime physically shrunk, and if that's the question then no it doesn't actually contract.

One of the coolest ways to interpret spacetime is to consider we don't ever measure spacetime it self, it's un-possible. So spacetime itself doesn't contract. If you accept time dilation, just consider contracted length as the other side of the coin. This all helps ensure that causes & Effects happen in the right order




From an observation perspective yes spacetime is separate from the stuff within it. (SR/GR yes, QM maybe not so much)

For me "Bell's Spaceship paradox" demonstrates that contraction/dilation is separate from spacetime itself.

That said whether you call c a "speed limit" for spacetime, or a "speed limit" for the fundamental forces is a matter of taste imo. Bottom line seems to be about how we define/observe spacetime (and most specific the relationship of length/time).

peterspencers

Well... i'm very appreciative of your help, if that makes the mononity any easier to bear :p

I've been back and read through most of the link you posted, in regards to the bells spaceship paradox, and I want to make sure ive understood it by running it past you in this thread, the other thread is way too crowded and alot of people seem to be in dissagreement about a few things.

So basically the string breaks! It breaks because:

So.... does the string break because its a 'relatively' weak object? If we did a thought experiment where there was no string, just one big ship with engines at the front and back (like the lead ship and the following ship), would there be forces of tension in the middle of the craft due to the same reasons that make the string break?

harrylin

I let myself be dragged back into it.
Right - and as a result the ends of the ship will move closer until the engines have stopped and the forces have equilibrated to obtain the contracted length of SR. That is all very theoretical of course; in practice, until the engines stop their forces and perhaps slight differences in "identical" engines will be more important.

peterspencers

ok, and in Bells situation, would the fact that, once the ships have finished accelerating, there is a broken string between them, be evidence that they have physically contracted? What other forces, other than 'actual' atomic contraction, could explain the broken chord?

Also... the quote I lifted from the other thread containing the statement:

Why would the increasing gap become length contracted? I thought space itself remained unchanged?

harrylin

Replied in post #10: I said No. Please try to understand other perspectives. From all inertial frame perspectives the length changes, but differently. From the point of view of the end rest frame the string even de-contracts, and the broken chord is than explained by earlier departure of the front rocket.
Not sure from where you quote it, so I must guess a little. Probably with "Lorentz-contract that increasing distance" was meant "do a Lorentz transformation to the launch pad frame from an accelerating frame". I don't use accelerating frames with shrinking rules, but some others do; with a shrinking ruler (assuming force equilibrium, which is doubtful!), you would measure an increasing distance - that's all. According to the launch pad frame's perspective, the distance is not changing and neither does the string contract, but its equilibrium length contracts so that it is increasingly in a stretched state (ignoring any dynamic effects).