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Underground > Laboratory >

Relativity - WTF?

14:37 / 06.09.04

Relativity fascinates me but, and I'm sure many will agree, it is incredibly confusing.

At the moment I'm trying to work my way through the Twin Paradox.

For the sake of tradition I'll use Alice and Bob. Alice stays on the Earth, Bob flies of accelerating to the speed of light.

Ok. I have a problem with the fact that you can't consider Bob to be stationary in the spaceship and Alice to be accelerating of at the speed of light. I've read that it is because you have to consider Bob as being in an inertial frame of reference.

So does this mean that the time dialation comes from the acceleration then and not the actual speed? Once you are travelling at 0.99c does the time dialation stop increasing as Bob is no longer feeling like he is accelerating?

Help me!!!

11:06 / 07.09.04

As far as I understand it Bob's acceleration destroys the symmetry of the situation.

John Baez has some excellent stuff on this here

21:41 / 18.09.04

But if object A is accelerating from object B then can it not be said that, from Object B's perspective it (Object B) is accelerating from Object A and not the other way around?

10:52 / 19.09.04

No. All inertial systems are equivalent. But when we are talking about non intertial systems (when there is acceleration), there's no such equivalence. In inertial systems, gravity appears, light bends...
Special relativity show us that you cannot tell of you are moving or no in an non inertial system. But in General Relativity you indeed can tell if you are accelerated or no.

15:43 / 19.09.04

How can you tell if you're accelerating or if it's everything around you that's accelerating in the oppositte direction? That's what I don't understand.

16:46 / 19.09.04

Experiments. For example: if you have a device that emits light at a fixed frecuency, the frecuency you're going to measure would be different if you are accelerated.

00:47 / 20.09.04

And if you had a device that emitted light at a fixed frecuency and it was you you who was accelerating then everybody who was standing "still" would be measuring different frequencies as you accelerated.

12:20 / 20.09.04

Ok, but,

1. We are accelerating at 9.8m/s

2. If that only applies to accelerating bodies then surely time dilation is dependent on acceleration and not velocity. Therefore, once you.ve reached 0.99c you are not accelerationg anymore.

16:35 / 20.09.04

But if object A is accelerating from object B then can it not be said that, from Object B's perspective it (Object B) is accelerating from Object A and not the other way around?

it's still not symmetric: Bob feels a force when he accelerates his rocket, Alice back on Earth is in free-fall (for the purposes of this argument) and does not feel that force. From the point of view of general relativity you could regard that force as a gravitational field and that is what produces the clock-skew.

01:54 / 21.09.04

But I can counter that by saying that the "force" that is felt is the force of things moving away from you.

09:14 / 21.09.04

Is it easier to think of mass-energy and space-time.

The mass of the earth causes an imprint in space time. This always stays constant and causes time to run fractionally slower.

Someone accelerating of in a rocket will gradually make a greater and greater deformation in space time as it requires more energy to propel it. This will, in turn, cause time to slow.

I'm sure I am massively oversimplifiying this.

02:42 / 22.09.04

So what you people are saying is that time fuck ups only occur during acceleration?

I would have to disagree. I think time fuck ups happen when the velocities of two objects are assymetrical. The only time that happens is during trajectories that resemble orbiting. The GPS satellites, btw, are a great example of the time fuck ups at work since the time fuck ups have to be factored in in order for one's location to be determined.

Then again, that might have something to do with acceleration. But it's late and I'm not seeing it now.

10:36 / 23.09.04

Well the GPS satellites are at the top of a gravity-well and hence their clocks run faster than clocks on earth: this is a general reletivity effect and both sets of clocks agree that the earth-bound clocks are running slow.

There is also a special relativity effect whereby if two observers are moving with constant velocity wrt each other each sees the other's clock as slow.

22:32 / 23.09.04

Top of the gravity well? Explain.

Also, are the two observers moving away from each other or in the same direction? If the former then how can they possibly observe each other's clocks?

10:39 / 24.09.04

I believe the gravity well is used to describe the behaviour of space-time.

It's the old, "Imagine space-time is like a rubber sheet. When you place a mass on the surface, the sheet deforms into a well-like shape".

So the closer you are to mass the more you feel gravity's effect and the further down the well you are.

GPS satelites will be high up the well as they are a great distance from the Earth.

There is a really interesting (and expensive!) Scientific America available at the moment all about Einstein. Regarding GPS satelites, the magazine states that time actually runs 38microseconds a day slower on the GPS satelites than they do on Earth.

10:41 / 24.09.04

That's 38 microseconds a day.

I really should preview my replys...

13:48 / 24.09.04

explanation of the gravity/acceleration clock phenomenon here
( pix/no math

)

Also, are the two observers moving away from each other or in the same direction? If the former then how can they possibly observe each other's clocks?

The observers can communicate by exchanging light pulses.

14:46 / 24.09.04

Thanks DI.

However, it doesn't really answer my first question.

Does anyone know if my explanation using space-time is correct or am I just pissing in the wind.

Baez's site (which is excellent) explains the phenomenom as such,

NB. Stella is in the rocket, Terence is on Earth.

We'll pick a frame of reference in which Stella is at rest the whole time! When she ignites her thrusters for the Turnaround, she is forced to assume that a uniform "gravitational" field suddenly permeates the universe; the field exactly cancels the force of her thrusters, so she stays motionless.

Not so Terence. The field causes him to accelerate, but he feels nothing new since he's in free-fall (or rather the Earth as a whole is). There's an enormous potential difference between him and Stella: remember, he's light-years from Stella, in a uniform "gravitational" field! Stella's at the bottom of the well, he's at the top (or they would be, if the well weren't bottomless and topless). So by uniform "gravitational" time dilation, he ages years during Stella's Turnaround.

Help!!!???