Understanding special relativity

[A-wal]

Hello. I thought I understood special relativity very well, but that’s the trouble when you don’t research anything and just here bits and pieces then fill in the gaps yourself. Something was bothering me when it dawned on me that my understanding of it includes an aether and I know the universe shouldn’t. I’m taking a logical wrong turn somewhere and I can’t pin it. I‘ve understood the concept for about four years but thought that time would slow to half rate at half the speed of light because for every action there is an equal and opposite reaction, so the faster you move though space; the slower you move through time, all relative to the speed of light. So your total speed through space-time should remain constant ( C ). So if you move and half the speed of light through space; you move at half the speed of time relative to someone who remain stationary in your original world line. I’m here because I found out that assumption is wrong.

In the twin paradox; you travel around for a bit, very fast and come back visibly younger than your twin. This very much implies an aether. There not both older relative to the other. Maybe they’re separated by the fact that freely moving motion is always relative but acceleration/deceleration isn’t? That still implies an aether. One (the one that ages slower) was moving through space “faster” than the other after all relativistic factors are a taken into account? If not, why not?

Edit: Length changes as well! Space-time as a whole contracts. So is it just length are all three spatial dimensions. In a straight line presumably it would be one dimension but that doesn’t seem to fit very well. In four dimensional space-time in which they are interchangeable, it doesn’t seem right that two dimensions change relative to the rest of the universe and two don’t.

Edit2: Apparently length contraction appears differently for different observers. So if that’s true, both observers measure the same amount of time dilation, that is to say; they both observe the other moving through time slower than themselves, e.g. at half speed while moving at three quarters of light speed (zero from their perspective of course). But they see length contraction differently, so if one sees the space between them as lengthened relative to them, then the other observes contraction of space, again implying an aether as a distinction is made as to which one is actually moving. That doesn‘t ring true. Time and space are merely different aspects of the same thing, like matter/energy, isn’t that the whole point? Why would they behave differently? I’m clearly missing something here.

Edit3(I‘m not rewriting it because it will probably be less clear): With the acceleration/deceleration thing: It should mean there’s no distinction between the two. Acceleration in one direction is deceleration in the opposite direction if there’s no aether. Is that right? If there the same thing because there’s no absolute rest then how can one twin be older than the other? Hold on, there’s no distinction between which of two objects is moving, but if there is a change in their velocity relative to each other then there is a distinction between which one made that change, and that one will be the young twin, right? That means that time is moving at the same rate for both (but not from their perspective because the other is moving away from them both, so each will see the other moving through time slower them themselves) while they are consistently moving away from each other at the same speed and the only real time dilation that accurse is during acceleration/deceleration. It has nothing to do with velocity?

 

[Mentz114]

Yes, you are confused.

Edit: Length changes as well! Space-time as a whole contracts. So is it just length are all three spatial dimensions. In a straight line presumably it would be one dimension but that doesn’t seem to fit very well. In four dimensional space-time in which they are interchangeable, it doesn’t seem right that two dimensions change relative to the rest of the universe and two don’t.

Directions are arbitrarily chosen when you set up a coordinate system. Perceived lengths change along the direction of the relative velocity between the frames.

Acceleration can be felt by the observer who experiences it. In that sense it is absolute. If two observers are in uniform motion and have a constant relative velocity, the situation is symmetric. If one of them fires his rocket engines and accelerates, he will feel it, and the situation is no longer symmetric, because the other observer feels nothing.

But that doesn't let us attribute relativistic effects to acceleration.

There are a lot of threads in this forum discussing these points, you might like to look at some of them.

 

[tiny-tim]

Welcome to PF!

I‘ve understood the concept for about four years but thought that time would slow to half rate at half the speed of light because for every action there is an equal and opposite reaction, so the faster you move though space; the slower you move through time, all relative to the speed of light. So your total speed through space-time should remain constant ( C ).

Hello A-wal! Welcome to PF!

That's a very long question, so I'm only replying to a bt of it.

Yes, your total speed through space-time should remain constant, but that's using Pythagoras' rule: you add them as if they were at right-angles:

if your speed through space is v, then your speed through time is c√(1 - v²/c²), and if you square and add, and then square-root, you get c.

 

[Fredrik]

In the twin paradox; you travel around for a bit, very fast and come back visibly younger than your twin. This very much implies an aether. There not both older relative to the other. Maybe they’re separated by the fact that freely moving motion is always relative but acceleration/deceleration isn’t? That still implies an aether. One (the one that ages slower) was moving through space “faster” than the other after all relativistic factors are a taken into account? If not, why not?

Check out #3 and #142 (page 9) in this thread to see how the twin paradox can be resolved without resorting to assumptions about an aether.

Edit: Length changes as well! Space-time as a whole contracts. So is it just length are all three spatial dimensions. In a straight line presumably it would be one dimension but that doesn’t seem to fit very well. In four dimensional space-time in which they are interchangeable, it doesn’t seem right that two dimensions change relative to the rest of the universe and two don’t.

I'm not sure I understand what your concern is here. The velocity difference between the two inertial frames defines one particular direction, so it would be pretty strange if all directions were affected equally.

Edit2: Apparently length contraction appears differently for different observers. So if that’s true, both observers measure the same amount of time dilation, that is to say; they both observe the other moving through time slower than themselves, e.g. at half speed while moving at three quarters of light speed (zero from their perspective of course). But they see length contraction differently, so if one sees the space between them as lengthened relative to them, then the other observes contraction of space,

The only scenario where two observers observe the same amount of time dilation but different length contractions (when they're looking some other physical system) is when they have the same speed but are moving in different directions. The object they're measuring only contracts in the direction of their motion.

Maybe the scenario you had in mind is one where the observers measure each other rather than some third object? In that case, they always observe the same thing: The other guy is flatter and aging slower than he would be at rest. This might seem like a contradiction but it isn't.

Edit3(I‘m not rewriting it because it will probably be less clear): With the acceleration/deceleration thing: It should mean there’s no distinction between the two. Acceleration in one direction is deceleration in the opposite direction if there’s no aether. Is that right?

Yes, "deceleration" is an unnecessary word. It's all just acceleration, but in different directions. This doesn't really have anything to do with SR. It's the same in non-relativistic mechanics.

Hold on, there’s no distinction between which of two objects is moving, but if there is a change in their velocity relative to each other then there is a distinction between which one made that change, and that one will be the young twin, right?

Yes. That's the difference. The world line of the older twin is a straight line. The world line of the younger twin isn't straight. Straight lines (geodesics) always experience the longest proper time.

...and the only real time dilation that accurse is during acceleration/deceleration. It has nothing to do with velocity?

No, that conclusion is wrong. Check out the posts I mentioned above for a complete explanation (actually two complete explanations) of the twin paradox. Also, check out Kev's #1 and DrGreg's spacetime diagram in #4 in this thread.

 

[A-wal]

Yes, you are confused. Directions are arbitrarily chosen when you set up a coordinate system. Perceived lengths change along the direction of the relative velocity between the frames.

Yea, I was thinking out loud really, like why is it affecting two dimensions, not is it affecting four. I was thinking in terms of definitive separations between the four but I’ve cottoned on to the fact that they’re interchangeable from different frames now. Well, two are. Hmm, time is always one of them. Does that make it more fundamental then the spatial ones? Wouldn’t that contradict the theory? Am I thinking too much? Quite probably.

So if an object was spinning and moving very fast, it would constantly change shape. Cool.

Acceleration can be felt by the observer who experiences it. In that sense it is absolute. If two observers are in uniform motion and have a constant relative velocity, the situation is symmetric. If one of them fires his rocket engines and accelerates, he will feel it, and the situation is no longer symmetric, because the other observer feels nothing.
But that doesn't let us attribute relativistic effects to acceleration.

Why? If the relative velocity is the same for both observers then what else is there that separates them other than which one accelerated/decelerated?

There are a lot of threads in this forum discussing these points, you might like to look at some of them.

If I did that I’d of got more confused. I thought I’d get my head round the theory first. Then I might actually be able to understand what I’m reading in some kind of context. You know, you could just use the actual theories as the front page and lock, or even delete all the forums.


tiny-tim: Thank you mate. What does the 1 represent? A relative version of c? I’m not sure why that equation is so complicated. cv(1 - v2/c2) Why? Could I really take the piss and ask you to please explain it? I don’t think in equations and I know they always seem far less complicated when you understand why.


Fredrik: Cheers.

I'm not sure I understand what your concern is here. The velocity difference between the two inertial frames defines one particular direction, so it would be pretty strange if all directions were affected equally.

It’d be funny though.

The only scenario where two observers observe the same amount of time dilation but different length contractions (when they're looking some other physical system) is when they have the same speed but are moving in different directions. The object they're measuring only contracts in the direction of their motion.

Gocha.

Maybe the scenario you had in mind is one where the observers measure each other rather than some third object? In that case, they always observe the same thing: The other guy is flatter and aging slower than he would be at rest. This might seem like a contradiction but it isn't.

No, that makes perfect sense because they’re moving at the same speed relative to each other.

Yes. That's the difference. The world line of the older twin is a straight line. The world line of the younger twin isn't straight. Straight lines (geodesics) always experience the longest proper time.

That’s exactly what I’m trying to get my head round.

No, that conclusion is wrong. Check out the posts I mentioned above for a complete explanation (actually two complete explanations) of the twin paradox. Also, check out Kev's #1 and DrGreg's spacetime diagram in #4 in this thread.

Right, so velocity is relative and acceleration isn’t, but the amount of time your velocities are different effects the real time dilation once they are in the same frame again? But the effects of time dilation are the same for both observers at constant but different speeds, so it must become real time dilation only through acceleration?

 

[tiny-tim]

tiny-tim: Thank you mate. What does the 1 represent? A relative version of c? I’m not sure why that equation is so complicated. cv(1 - v2/c2) Why? Could I really take the piss and ask you to please explain it? I don’t think in equations and I know they always seem far less complicated when you understand why.

Hi A-wal!

(that "v" is a square-root, of course )

c√(1 - v²/c²) is just another way of writing √(c² - v²).

I wrote the √(1 - v²/c²) part separately because I thought you'd recognise 1/√(1 - v²/c²) as the familiar "gamma", or time dilation, factor.

If t is coordinate time, and s is time on the clock,

then ds/dt = √(c² - v²),

so (dx/dt)² + (ds/dt)² = v² + (c² - v²) = c².

 

[Fredrik]

That’s exactly what I’m trying to get my head round.

(We're talking about the fact that what a clock measures is the proper time of the curve that represents its motion).

It's important to realize that this is a postulate, not a derived result. It's one of the statements that defines the special theory of relativity.

Right, so velocity is relative and acceleration isn’t, but the amount of time your velocities are different effects the real time dilation once they are in the same frame again? But the effects of time dilation are the same for both observers at constant but different speeds, so it must become real time dilation only through acceleration?

They can't meet again unless someone changes his velocity, but if they do I think we have moved beyond simple "time dilation" (which is supposed to be about two events on the time axis of some inertial frame) and should be talking about the proper time of their world lines instead.