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/sci/ - Science & Math

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4429673 No.4429673 [Reply] [Original]

Hey /sci/, if speed is relative, then why isn't acceleration relative? Trying to wrap my head around the solution to the twin paradox.

>> No.4429703

Acceleration is relative

>> No.4429711

>>4429703
So this is an incorrect explanation?

mentock.home.mindspring.com/twins.htm

>> No.4429718

relativity motherfucker

Imagine being in a box. You feel a force pushing you to the "ground" of this box.

Are you in a uniform gravitational field or are you accelerating forward? If you looked outside and saw an object go past you, would you still be able to know?

>> No.4429736

A lot of explanations of the twin paradox have claimed that it is necessary to include a treatment of accelerations, or involve General Relativity. Not so.

>> No.4429752

>>4429736
The wikipedia article, at least the section that's readable by someone without a physics degree, uses the acceleration explanation, which to me doesn't make any sense since acceleration is relative and thus one of the twins changing acceleration is still identical to either of them.

>> No.4429753

> A lot of explanations of the twin paradox have claimed that it is necessary to include a treatment of accelerations, or involve General Relativity. Not so.

Actually, you do need a smidgen of something acceleration based (which is general relativity) to explain why, if the twins get back together, they've not both aged more than the other; the acceleration of one of the twins breaks the tie.

>> No.4429757

You should learn to understand relativity in terms of spacetime. The worldline of one twin is a straight path whereas the worldline of the other twin is crooked.

Also it was understood long before Einstein that velocity was relative but not acceleration or rotation. See for example, Newton's bucket.

>> No.4429758

>>4429753
But how is one twin accelerating away and then back not identical to the other doing the same?

>> No.4429765

>>4429757
>but not rotation

There is no such thing as rotation, just objects composed of particles with non-uniform velocities.

>> No.4429771

>>4429753
The quote is correct; you are wrong. You don't need GR. You only need to know that one twin is accelerating. SR handles acceleration just fine. What it does not have is accelerating reference frames, but you really shouldn't think of the arbitrary coordinate systems of GR as accelerating reference frames either.

>> No.4429787

>>4429771
Ah, yes; you treat the acceleration as being instantaneous and therefore negligible for the purposes of relativity. You are right.

But there is still a big difference between the two twins caused by this acceleration; one twin shooting off at 0.5c, stopping and coming back at 0.5c ages differently to one at a steady speed.

>> No.4429804

>>4429771 here,
I think I went too far on the last part. There's nothing particularly wrong with thinking of an arbitrary coordinate system as a reference frame. We even do it in Newtonian mechanics with rotating reference frames. It's just important to remember that they're a very different concept from inertial reference frames. The fact that you can choose an inertial reference frame arbitrarily is a symmetry of nature with an associated conserved quantity. The fact that you can choose a coordinate system arbitrarily is just a reflection of the fact that coordinates don't reality.

>> No.4429836

>>4429787
Can you explain the difference between the two twins, though? From Twin B's perspective it is the stationary twin who is accelerating away and then back.

>> No.4429871

>>4429836
You should stop thinking of reference frames as observer perspectives. That does not work in general.

For one twin, there is an inertial reference frame in which he is stationary the whole time. For the twin that accelerates, there is no such reference frame. There is a reference frame in which he is at rest on the way out, but in that reference frame he will be moving on the way back. And vice versa.

If you use GR-style arbitrary coordinate systems, you can find coordinate systems in which the accelerating guy's (x,y,z) doesn't change, but I wouldn't call such a coordinate system his perspective because there are infinitely many such coordinate systems.

>> No.4429883

>>4429871
My mind is getting slowly blown. What, then, is a reference frame?

>> No.4429899

>>4429871
I'm not getting how the relativity of acceleration fails to mean that one twin moving away and back is identical to the other moving away and back, or both of them moving away and back to a lesser degree. That two people accelerating away from each other both seem to be moving through time more slowly than the other makes sense to me when I think about it in terms of mutual redshifting of emitted light, but it seems to me that in the case of the twin paradox, both twins would see the other as moving more slowly at they separated and then more quickly as they approached.

>> No.4429903

>>4429883
Anything (whether real or imaginary) moving at less than the speed of light can be arbitrarily chosen to be at rest at a particular moment. Making that choose is picking a reference frame. But once you've made the choice, you have to stick with it throughout your analysis. If the thing you chose to be at rest at time t accelerates, you have to treat it as moving now.

In the geometric perspective, to choose a reference frame is to choose the direction of your time axis. Choose the time axis parallel to the worldline of some object, and that object will have constant (x,y,z) coordinates. It will be at rest. At least up to the point where the worldline bends (the time when the object accelerates).

>> No.4429918

>>4429903
What I'm not getting is how one twin accelerating back toward the other breaks the symmetry of the system. With only two entities in this spacetime, it seems that their observations will always be exact duplicates, no matter what happens.

>> No.4429945

>>4429918
Twin A goes about his life in zero gee and nothing of interest happens, other than watching twin B rush past him when B leaves, and rush past him when B returns.

Twin B's experiences are exactly the same as twin A's with the exception of a short, sudden period of acceleration in the middle.

We choose Twin A's reference frame because it's less complicated than B's pair of reference frames.

Without this period of acceleration, twin A and twin B can never meet up again in a flat spacetime, and must rely on lightspeed communications to infer each others age, and each calculates the other to be older* than themselves. In this scenario, they are in fact identical.

*: It might be younger, I can't remember.

>> No.4429955

>>4429899
There's no such thing as "relativity of acceleration." Either something has a nonzero proper acceleration, or it doesn't. You can measure it. Just carry a ball or something with you on the spaceship, and if the ball appears to accelerate when you let go of it, you have a nonzero proper acceleration.

>> No.4429962

>>4429945
But it's exactly the same. You're thinking of acceleration as being "pushed" by another object, in such a way as the entity could tell it was being accelerated. I'm talking about uniform acceleration of every point particle in the body of Twin B.

>> No.4429963

>>4429962
Things don't accelerate unless you push them.

>> No.4429969

>>4429963
Gravity. Even aside from that, you could "push" every single unit of twin B in precisely the same way so that there would be no empirical way for B to tell he was accelerating.

>> No.4429980

Acceleration IS relative. Proper velocity and proper acceleration are both rank 1 tensors that transform in the expected manner.

>> No.4429987

>>4429969
>Gravity.
Then you do need GR. In GR, freely falling things have zero proper acceleration.

>Even aside from that, you could "push" every single unit of twin B in precisely the same way so that there would be no empirical way for B to tell he was accelerating.
Or you could put his brain in a vat, but that has nothing to do with physics.

>> No.4429998

>>4429980
Sure, but the magnitude of proper acceleration is a scalar which is either zero or it isn't. The magnitude of four-velocity is a scalar too, but it's identically 1.

>> No.4430028

>>4429987
I can see you're not familiar with the Least Convenient World method. Fine. Suppose this experiment takes place at such a time as quantum effects give twin B a velocity proximal to C, and later give it a velocity proximal to C in the opposite direction, both apropos of nothing.

>> No.4430040

>>4430028
You're missing the point of the "brain in a vat" comment. Just because you set things up so that the guy can't possibly tell whether he has a proper acceleration, doesn't mean that the situation where he does and where he doesn't are identical.

>> No.4430052

>>4430040
Ok, so what's the difference between him accelerating and the other accelerating?

>> No.4430061

>>4430052
That is the difference. One is accelerating and the other isn't.

>> No.4430069

>>4430061
Why do half the people in the thread say acceleration is relative and the other half, including you, say it isn't?

>> No.4430088

>>4430069
Largely semantic differences; several of the people who said acceleration is relative seem to know what they're talking about.

To be precise, it is the magnitude of proper four-acceleration that is absolute.