Relativity questions

[Ashles]

Okay, I'm trying to get to grips with relativity and I have just about come to terms with the twin paradox.
This states that two twins could exist and one gets into a spaceship and fliues away from the earth then back again incredibly fast and as a result of relitivity the travelling twin would age slower than the twin on earth (he would sort of travel forward in time).

We know that something moving a good proportion of the speed of light compared to something else will experience 'slower time'. The same applies to something in a much stronger gravitational field (although the effects are not related to acceleration which seems massively counter-intuitive to me but apparently this is known fact so fair enough).

So my question is this:
I assume that our solar system is travelling massively fast compared to some of the other stars that we can see in the sky (maybe even a fair proportion of the speed of light), so are we experiencing time dilation with regard to them?
If the Big Bang happened then it is safe to assume that everything started off at the same point, but if we have not currently returned to the same locale as these other stars are we experiencing time dilation?
And if so who is moving faster through time, us or them?
And if we are experiencing the same passage of time why is that if we are moving at massively different speeds relative to each other?

Hope my question makes sense. If not I will try and be clearer.

 

[69dodge]

I assume that our solar system is travelling massively fast compared to some of the other stars that we can see in the sky (maybe even a fair proportion of the speed of light), so are we experiencing time dilation with regard to them?

They think we are.

We think they are.

 

[elgarak]

First question: Yes, that's what should be the case if good ol' Albert was correct. Not sure if this was ever experimentally verified, though.

The other question are a little bit tricky.

It is assumed that the universe is bend in a higher (spatial) dimension. Not easily imaginable, so we have to use an easier picture. Consider the surface of a rubber ball. Blow up the ball, and the surface gets larger.

The 3-dimensional (spatial) universe is like the ball's surface. The center is of course the center of the ball, but lies actually outside of the universe, and cannot be use as a reference for measurements inside of it. Inside the universe (on the ball surface), there's no reference point.

 

[Ashles]

They think we are.

We think they are.

That's what I thought, but it appears that with relativity one body will always be experiencing a faster progress through time than the other.

My problem was that I knew the travelling twin (in the Twin Pardox) would experience faster time than the one on earth, but I thought that the other one would be travelling just as fast relative to the travelling one so why didn't he also experience faster time? Why would he be so much older when the other twin returned to earth?
It seems that it is to do with returning to the inertial state. When the travelling twin returns to earth the difference in time is apparent.

But I am unclear as to what the reality would be while the travelling twin is travelling.

Unless it is actually irrelevant. Is it that we cannot really judge at all what time is being experienced by distant stars (even though we can actually see some of them) until we approach them?

And how the hell did Einstein come up with all of this? It is so counter-intuitive that I cannot fathom how a mind could even conceive of it in the first place.

 

[Ashles]

First question: Yes, that's what should be the case if good ol' Albert was correct. Not sure if this was ever experimentally verified, though.

I thougt relativity was accepted fact.
His equations hold true for everything we have ever observed such as the exact location of GPS satellites, differences in atomic clocks sent into orbit etc.

 

[Just thinking]

Okay, I'm trying to get to grips with relativity and I have just about come to terms with the twin paradox. This states that two twins could exist and one gets into a spaceship and flies away from the earth then back again incredibly fast, and as a result of relitivity the travelling twin would age slower than the twin on earth (he would sort of travel forward in time).

You seem to have the basics down as far as what the twins are doing; the 'Paradox' as it's known, is why is it that only one twin ages normally while one ages very little? According to relativity, each should be able to consider himself at rest and the other doing the moving, so why the difference?

Basically it is because the problem involves not only Special Relativity (systems in inertial frames) but a touch of General Relativity (systems under acceleration). In order for the problem to take place as described, one of the twins, the one in the spaceship, must accelerate to get to his enormous velocity (compared to the one left behind). Then he must turn around somehow (which also involves acceleration) if they are ever to get back together. This makes the experiences for each twin different, as the one left behind experiences no accelerations. Accelerating systems (compared to inertial ones) will have slower running clocks -- hense, the age difference.

We know that something moving a good proportion of the speed of light compared to something else will experience 'slower time'. The same applies to something in a much stronger gravitational field (although the effects are not related to acceleration which seems massively counter-intuitive to me but apparently this is known fact so fair enough).

So my question is this:
I assume that our solar system is travelling massively fast compared to some of the other stars that we can see in the sky (maybe even a fair proportion of the speed of light), so are we experiencing time dilation with regard to them?

In a word, yes. But stars within our own galaxy are not moving fast enough to show much of a relativistic effect. Only when we look at distant galaxies do we start to get decent differences in clocks.

If the Big Bang happened then it is safe to assume that everything started off at the same point, but if we have not currently returned to the same locale as these other stars are we experiencing time dilation?

Again, yes. But we never experience the time dilation the other observers see on us. To us our clocks are always going at the correct rate -- even if we were accelerating.

And if so who is moving faster through time, us or them?

If both are in inertial frames, we will always see their clocks moving slower -- and they will always see ours as moving slower. Who's right? Both.

And if we are experiencing the same passage of time why is that if we are moving at massively different speeds relative to each other?

We're not, as I just described. But the velocities I'm speaking of must be very large, otherwise the time dilations are minimal.

Hope my question makes sense. If not I will try and be clearer.

A common concern, as relativity introduces concepts that are at first counter-intuitive. But after reading through some good books it starts to make more and more sense.

 

[Roboramma]

That's what I thought, but it appears that with relativity one body will always be experiencing a faster progress through time than the other.

I could be wrong (I probably understand this less than you do), but I think it has something to do with who's doing the accelerating.
Like with the Twin Paradox - while he's traveling away at a constant velocity it looks to you that time is going slower for him, but it looks to him like time is going slower for you. However, when he accelerates things change.
So I think that if the other star is moving away from (or toward us) at a constant velocity, the two reference frames are equal - nothing distinguishes ours from theirs. But if one is accelerating there is an inequality that somehow changes the situation.

Those who understand this please show if and where I've completely messed this up.

 

[Just thinking]

... Like with the Twin Paradox - while he's traveling away at a constant velocity it looks to you that time is going slower for him, but it looks to him like time is going slower for you. However, when he accelerates things change.

Yes -- and that's the big issue. Only a system under acceleration can look upon an inertial one and see the inertial system's clocks running faster than their own. And at the same time (well, sort of) have the inertial system's occupants look upon the accelerating system and see their clocks moving slower. It can also happen in reverse depending on whether the accelerating system is accelerating away from or towards the inertial system. This was the confusing part for Einstein as well, so don't feel bad.

 

[Ashles]

Accelerating systems (compared to inertial ones) will have slower running clocks -- hense, the age difference.

I initially thought that it was related to acceleration, but apparently it isn't.
From http://en.wikipedia.org/wiki/Twin_paradox :

Note: it is wrong to think twin paradoxes are simply due to acceleration effects. One needs no acceleration to achieve a twin paradox in flat spacetime (cf. Brans and Stewart). Thus, a twin paradox situation does not always imply acceleration.

If both are in inertial frames, we will always see their clocks moving slower -- and they will always see ours as moving slower. Who's right? Both.

The example that caused me issues with all of this was one I read in Big Bang by Simon Singh.
It involved Alice and Bob. Alice is in a train carriage moving 80% of the speed of light. Bob stands on the station platform. They both wave. As Alice passes Bob he sees her waving incredibly slowly (assumoing he could see her). But the impression I got was that Alice would see Bob waving slowly too. But how could that be if Alice was actually moving faster through time relatove to Bob?

 

[Ashles]

This was the confusing part for Einstein as well, so don't feel bad.

This was really bugging me at work today while I was trying to write management handover notes about a client complaint. It's good to know that Einstein had trouble with it too.

Once again I find the whole concept of relativity easier to accept as a concept than the idea that somebody actually thought of it as a possibility in the first place.

When people refer to Einstein as a genius they generally really aren't getting the half of it are they?

 

[Dilb]

You don't need GR to analyse the twin paradox. The key isn't acceleration as such, it's the fact that the speed is different at different times for the travelling twin (yes, that involves acceleration, but clocks running slower while accelerating isn't the relevant effect).

The biggest thing to understand special reletivity is knowing how to draw Minkowski diagrams. Essentially, an object moving one way has a different sort of time-warping than an object which is moving in the opposite direction, reletive to your stationary frame. When the travelling twin changes direction, there idea of "simultanious" (same time as they see it) warps from going foreward in time as distance increase to going backwards in time as distance increases. The diagram here is much more obvious than this explanation.
http://www.physicsdaily.com/physics/Twin_paradox

Essentially, when the moving twin changes direction, the age of his brother jumps from less than him to greater than him.

 

[Just thinking]

I initially thought that it was related to acceleration, but apparently it isn't.
From http://en.wikipedia.org/wiki/Twin_paradox :

This is seriously misleading as the author compresses the accelerations for the U-turn back home to astonishingly high (read unsurvivable) g-forces. A good deal of time differences occur then -- like one seeing the other's clocks speed up to enormous rates even for a brief instant. Please re-read his notations. "During the U-turn the plane of simultaneity jumps from blue to red and very quickly sweeps a large segment of the lifeline of the resting twin. Suddenly the resting twin "ages" very fast in the reckoning of the traveling twin." I'll give you one guess what is happening during this adjustment. That's right -- immense acceleration.

The example that caused me issues with all of this was one I read in Big Bang by Simon Singh.t involved Alice and Bob. Alice is in a train carriage moving 80% of the speed of light. Bob stands on the station platform. They both wave. As Alice passes Bob he sees her waving incredibly slowly (assumoing he could see her). But the impression I got was that Alice would see Bob waving slowly too. But how could that be if Alice was actually moving faster through time relatove to Bob?

If both are in inertial frames each will see and measure the other as moving slower through time -- and both are correct. There is no universal time or rate of time.

 

[Alkatran]

I really think anyone who ever has to learn about relativity should go to:

http://casa.colorado.edu/~ajsh/sr/paradox.html

It REALLY clears up the whole thing. Just seeing the tilted circle is eye-opening.

 

[Dilb]

And how the hell did Einstein come up with all of this? It is so counter-intuitive that I cannot fathom how a mind could even conceive of it in the first place.

He made 2 assumptions.
1. All inertial frames are equivilent (this is implied in electromagnetism and physics in general).
2. The speed of light is constant (also implied in EM).

Everything else is just algebra. Lots and lots of algebra. It's actually all fairly obvious if you can just do the math, and ignore the crazy results.

 

[Alkatran]

and don't forget that this was the solution to a problem that had been nagging at physics for a few decades at that point.

If Einstein hadn't discovered it, someone else would of (although perhaps many years later).

 

[Dilb]

and don't forget that this was the solution to a problem that had been nagging at physics for a few decades at that point.

If Einstein hadn't discovered it, someone else would of (although perhaps many years later).

They had the solutions. Other physicists just didn't want to apply them, because it meant abandoning universal time and just seemed crazy. There's a reason they're called Lorentz transformations.

 

[Just thinking]

When people refer to Einstein as a genius they generally really aren't getting the half of it are they?

No -- they aren't.

 

[69dodge]

But I am unclear as to what the reality would be while the travelling twin is travelling.

Unless it is actually irrelevant. Is it that we cannot really judge at all what time is being experienced by distant stars (even though we can actually see some of them) until we approach them?

Yes, that's basically it.

I mean, there's sort of a way to judge, which works pretty well, except that if we judge and they judge, each of us thinks the other's clock is running slow. So there's no "real" way to judge.

 

[epepke]

The example that caused me issues with all of this was one I read in Big Bang by Simon Singh.
It involved Alice and Bob. Alice is in a train carriage moving 80% of the speed of light. Bob stands on the station platform. They both wave. As Alice passes Bob he sees her waving incredibly slowly (assumoing he could see her). But the impression I got was that Alice would see Bob waving slowly too. But how could that be if Alice was actually moving faster through time relatove to Bob?

You're confusing yourself. Don't feel bad; we all go through this phase.

As for acceleration, it is important for the twin "paradox." However, the arguments for acceleration in flat spacetime are not qualitatively different from the ordinary SR arguments. So you have a choice of whether to calculate for the acceleration or just assume that it's instantaneous. It's a lot easier to do the latter.

Yes, when Alice is moving, she will measure Bob's clock as going slowly compared to hers. And Bob will measure Alice's clock as going slowly compared to his.

However, to compare clocks for elapsed time, Alice has to come back. It doesn't do any good to measure elapsed time at a distance, because simultaneity doesn't work at a distance.

Now, to avoid having to talk about acceleration, because the math is hard, we'll assume that Alice jumps from an outbound train to an inbound train going at the same speed. Of course, this would probably squish her, but we'll ignore that. Because the trains are at the same place, simultaneity does work, and so her Timex watch takes a licking but keeps on ticking.

The trick is to understand that there are three reference frames, not two: Bob's frame, the outbound train, and the inbound train. Let's assume that the trains have conductors, and conductors usually carry watches.

Bob measures Alice's clock as going slowly on both the outbound and inbound trips, by the same amount if they're at the same speed relative to him. The outbound conductor measures Alice's clock as going at the normal rate on the outbound trip, but really really slowly on the inbound trip. The inbound conductor measures Alice's clock as going really really slowly on the outbound trip but at the normal rate on the inbound trip.

All three agree that when Alice gets back to Bob, her clock will read less elapsed time.

Back to the OP. It's meaningless to ask who is moving faster through time. There is no absolute standard by which that can be determined, which is one of the reasons that this is called relativity.

 

[epepke]

This is seriously misleading as the author compresses the accelerations for the U-turn back home to astonishingly high (read unsurvivable) g-forces. A good deal of time differences occur then -- like one seeing the other's clocks speed up to enormous rates even for a brief instant. Please re-read his notations. "During the U-turn the plane of simultaneity jumps from blue to red and very quickly sweeps a large segment of the lifeline of the resting twin. Suddenly the resting twin "ages" very fast in the reckoning of the traveling twin." I'll give you one guess what is happening during this adjustment. That's right -- immense acceleration.

That's the hard way of doing it.

But you can still ignore it and have no acceleration at all. Just have Alice hold her watch up to the window. When the inbound train passes, Agnes in the inbound train looks at Alice's watch and synchronizes it to Alices. When Agnes gets back to Bob, her watch will read less elapsed time of exactly the same amount.