# Special relativity - please can someone clear this up?

1. Jul 31, 2004

### John_M

I don't think this is an original point - but it seems an obvious problem with the idea of time dilation for which I haven't heard a satisfactory answer. I don't have any knowledge of physics beyond GCSE (low level high school) so keep it simple please!

The 'twin paradox'. I'm sure everyone's familiar with it. One twin stays on earth, the other flies off somewhere at high speed and returns. Moving clocks run slow and therefore the twin in the spaceship has not aged as much as the twin who's stayed on Earth.

Isn't it the case that this theory simply assumes the Earth is an 'absolute' frame of reference, directly contradicting the relativity principle? Why can't you say that the twin on Earth is moving, the twin in the spaceship is still, and that the Earth twin's clock should therefore 'run slow'? How can you make the general statement that 'moving clocks run slow' without violating the relativity principle - whether something is moving or not depends on your frame of reference?

2. Jul 31, 2004

### Planetary Nebula

It isn't based merely on saying that "moving clocks run slow", but on working out the whole roundtrip problem, considering the times from the standpoints of both reference frames. In the end, both twins agree about the difference in total time of the trip and which twin has logged the most time. The relativity principle isn't violated either. But the case needs to be closely argued.

3. Jul 31, 2004

### jcsd

No, it doesn't consider the Earth as an absolute frame of refernce, BUT there's an importnat difference between the two refrence frames: the refrence frame on the Earth is an inertial refernce frame, but the refernce frame of the spaceship is non-inertial (i.e. it accelerates). The principle of relativty only applies to inertial reference frames.

You shouldn't make the statement 'moving clocks run slow', as it may not be true: i.e. moving relatuive to what? in which frame of rest frame doe sit run slow?

4. Jul 31, 2004

### zoobyshoe

John,

Here are two quotes from another thread in which the twin paradox was finally explained to me in a way that made sense. The key to my understanding was the concept of the space-time interval. The space-time interval for one twin is not symetrical to that for the other.

variable speed of light - Physics Help and Math Help - Physics Forums

5. Jul 31, 2004

### John_M

"No, it doesn't consider the Earth as an absolute frame of refernce, BUT there's an importnat difference between the two refrence frames: the refrence frame on the Earth is an inertial refernce frame, but the refernce frame of the spaceship is non-inertial (i.e. it accelerates). The principle of relativty only applies to inertial reference frames."

I don't see this. Why can't you say that the spaceship is inertial reference frame, relative to which the Earth is accelerating? Doesn't your answer just restate the same problem?

I agree with your point about 'moving clocks run slow' - but that was exactly my question - I'm trying to get to grips with SR and a good deal of the internet is covered in the phrase! :)

6. Jul 31, 2004

### jcsd

You can't say this in Newtonian physics and you can't say this in special relativity, as I said before the principle of relativity specifically only applies to inertial frames of refernbce not accelerating frames of refernce and there is a definite difference between the two.

The keypoint is in special relativty the laws of physics look different in accelerated frames of refreence than they do in inertial refrence frames, hence the need for general relativity.

edited for typing errors and to clarify:

what I mean by "hence the need for general relativity", is NOT that you need genral relativity to resolve the paradox as that can be done using special relativty alone, BUT you need general relativty in order to express the laws of physics in a frame invariant manner.

Last edited: Jul 31, 2004
7. Jul 31, 2004

### John_M

jcsd...

OK, I remember something about this. Coffee sloshing all over you when you're accelerating etc. But...two questions.

1. The principle of relativity still applies to inertial reference frames. So - assuming you believe that the space-twin ages slower - are you saying that any process of 'slower ageing' taking place on the space-twin's clock occurs only when he is accelerating?

2. I don't really understand zoob's post (Too much maths - I only have a basic knowledge of maths and physics!) But it seems to offer a different explanation to the problem than yours does. It specifically avoids the problem of acceleration/ deceleration:

"The other twin travels at 80% of light speed, travelling 4 lightyears in 5 years according to the Earth twin, then returns the same way (after an instantaneous deceleration and acceleration back home)."

Do you agree with zoob's post?

8. Jul 31, 2004

### jcsd

1. No I'm not saying that 'slow aging' only take place during acceleration. Imagine a spaceship travelling past the Earth at a constant velocity; a clock on the spaceship will appeared to be running slow to someone on the Earth, but it's important to note that there is still symmetry as a clock on the Earth will appear to be running slow to somoen on the Earth.

2) I agree with zoob's post, notice the spaceship is chaning it's inertial frame while the Earth does not.

9. Jul 31, 2004

### John_M

I'm still lost...

With reference to point (1) - A clock on the spaceship will appear to be running slow to someone on the Earth but a clock on the Earth will appear to be running slow to someone on the (I assume you mean 'spaceship' here!)

This is exactly my problem. If there are no absolute frames of reference, what possible reason could there be for saying that, when the frames of reference are synchronised, one particular twin will have aged faster than the other?

10. Jul 31, 2004

### jcsd

correct.

Because frames one of the twins has changed his frame of refrence while the other one has not, the symmetry is broken.

11. Jul 31, 2004

### zoobyshoe

It is much less hairy than it looks. I, too, know hardly any math, but those equations actually involve only very basic algebra, and basic algebra is just slightly fancy basic math. You just need to know what the variables stand for, and to be able to handle the square/square root button on your calculator. There's no calculus or anything like that here.

The stay at home twin has only one world line because he doesn't go anywhere. The rocket twin has two worldlines: one for the trip out, one for the trip back.

Ambitwistor's main point is that the stay at home twin ends up experiencing 10 years to the traveling twin's 6 years.

Stuff like the triangle symbol shouldn't scare you off. It just stands for "the change in" or "the difference between".

12. Jul 31, 2004

### zoobyshoe

Actually, you should be. It shows you're thinking logically through this, and that I forgot to quote one very important thing by Chroot.
Here Chroot explains the "absolute" that you're looking for. (I really should have included this in the post above):

13. Jul 31, 2004

### pmb_phy

No. Why would you think it implies that? Choose a particular inertial frame of reference. Call that frame S. Now let there be a spacestation and a spaceship each at rest in frame S, each of which are at location A. Suppose now there are two twins. One twin is in the ship and other other in the station. The ship now starts to acclerate. The people in the ship feel the ship accelerating and know that they are not at rest in any inertial frame of reference. However the people in the spacestation are always in an inertial frame. There is a broken symnmetry here which identifies one observer as the traveling twin. When the ship returns the twin inside the ship is younger than the person in the spacestation. This does not single out one inertial frame over the other since there is only one inertial frame in what I've just described, and that's the frame in which the spacestation is a rest.

A path is spacetime is called a worldline. An interval is the $$\Delta s$$ (or to some the $$(\Delta s)^2$$) in the expression

$$(\Delta s)^2 = c^2 (\Delta x)^2 - (\Delta x)^2 - (\Delta y)^2 - (\Delta z)^2$$

Because if the ship leaves point A and comes back to point A then it must have turned around. During that time the ship was in a non-inertial frame.

Pete

Last edited: Jul 31, 2004
14. Jul 31, 2004

### zoobyshoe

Hi Pete,

Terminology confusion, I guess. Would the two word term spacetime interval be synonymous with the term worldline?

-Zooby

15. Jul 31, 2004

### John_M

I'm sorry but it still isn't clear to me! So this is what happens in the twin experiment:

1. Twins A and B are in the same frame of reference.
2. Twin B changes his frame of reference (flying off)
3. The twins are now in a different inertial frame of reference. From A's perspective B's clock is running slower and therefore B ages slower. From B's perspective A's clock is running slower and therefore A ages slower.
4. Twin B reverts to Twin A's frame of reference.
5. Twin B has aged slower than Twin A.

Where, in this sequence of events, has the process of B ageing slower than A taken place? Surely not during point (3) - otherwise you're violating the relativity principle!

Are you suggesting something along the lines of 'because B has changed his frame of reference whereas A has not, B's frame of reference is the 'true' frame of reference?' Or something like that??

zoobyshoe...I'll have another look at those equations...I still find the triangles rather scary though!

16. Jul 31, 2004

### pmb_phy

No. "Interval" is a general expession. "Spacetime interval" refers to an interval in spacetime.

Pete

17. Jul 31, 2004

Staff Emeritus
The interval is the spacetime "distance" between two points, quotes because it includes time as well as space distance. Interval is a geometric, not a coordinate fact, and thus will have the same value in every inertial frame. The name for this is Lorentz invariant, or since it's a number, Lorentz scalar. The square of the interval is (in one signiture) $$-c^2(t_1-t_2)^2 + (x_1-x_2)^2 + (y_1-y_2)^2 + (z_1-z_2)^2$$

Along a world line, each differential element is a differential interval:

$$ds^2 = -cdt^2 + dx^2 + dy^2 = dz^2$$.

18. Jul 31, 2004

### John_M

pmb_phy

"There is a broken symnmetry here which identifies one observer as the traveling twin."

This is similar to what jcsd was saying. Do you mean the following by it:

"Since Twin B has accelerated whereas Twin A has not, it is possible to state in absolute terms that B is moving whereas A is still."

Another point. You say the following:

"This does not single out one inertial frame over the other since there is only one inertial frame in what I've just described, and that's the frame in which the spacestation is a rest."

Right. So in your twin experiment, is it correct to state that B's spaceship, on its voyage, never moves at constant speed - and does not therefore constitute an inertial frame of reference at any point?

19. Jul 31, 2004

### pmb_phy

The interval has the same value in all spacetime coordinate systems, not just those which correspond to inertial ones.

Pete

20. Jul 31, 2004

### zoobyshoe

OK.

In Ambitwistors post the symbol $$\tau$$ is "tau", correct? And stands for "worldline"?? Or?