Special relativity - please can someone clear this up?

[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?

 

[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.

 

[jcsd]

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?

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 relativity 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?

 

[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.

A path in spacetime is called an interval.

The length of an interval is called its proper time. If you have a clock follow some path, the clock will measure that much time having been elapsed when moved along that path.

This is not really true -- a distant observer will measure a clock as running slowly when it is moving at high relative velocity to the observer. According to the clock, however, everything is just fine.

Imagine Picard is flying along in the Enterprise at 0.9c with respect to the Earth. An observer on the Earth will measure Picard's clock as running slow compared to an identical Earth-bound clock. Picard, however, will see everything on the bridge of the Enterprise as running completely normally, but will measure the Earth-bound clock as running slowly.

If you think about it, it has to be that way... if it weren't, then some cosmic ray particle moving at 0.9c with respect to you somewhere in the depths of space would somehow affect YOUR clock!

- Warren

The longer path ages more, if you measure "length" using the spacetime interval.

Consider the case where the Earth twin stays at home for 10 years according to his own clock. The other twin travels at 80% of light speed, traveling 4 lightyears in 5 years according to the Earth twin, then returns the same way (after an instantaneous deceleration and acceleration back home).

The Earth twin's worldline is a line from (t,x) = (0,0) to (10,0). The traveling twin's worldline consists of two line segments, one from (0,0) to (5,4), the other from (5,4) to (10,0).

The proper time measured by the Earth twin is the spacetime length of his worldline,

$$\tau = \sqrt{{\Delta t}^2-{\Delta x}^2} = \sqrt{(10-0)^2-(0-0)^2} = 10$$

The proper time measured by the traveling twin is the spacetime length of his worldline,

$$\begin{equation*} \begin{split} \tau &= \tau_1+\tau_2 = \sqrt{{\Delta t_1}^2-{\Delta x_1}^2}+ \sqrt{{\Delta t_2}^2-{\Delta x_2}^2} \\ &= \sqrt{(5-0)^2-(4-0)^2}+\sqrt{(10-5)^2-(0-4)^2}\\ &= 3+3 = 6 \end{split} \end{equation*}$$

The traveling twin ages 6 years to the Earth twin's 10 years.

variable speed of light - Physics Help and Math Help - Physics Forums
Address:https://www.physicsforums.com/showthread.php?t=8769&page=1&pp=20[/QUOTE]

 

[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 relativity 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! :)

 

[jcsd]

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?

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 relativity 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 general relativity to resolve the paradox as that can be done using special relativity alone, BUT you need general relativity in order to express the laws of physics in a frame invariant manner.

 

[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, traveling 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?

 

[jcsd]

1. No I'm not saying that 'slow aging' only take place during acceleration. Imagine a spaceship traveling 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.

 

[John_M]

1. No I'm not saying that 'slow aging' only take place during acceleration. Imagine a spaceship traveling 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 changing it's inertial frame while the Earth does not.

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?

 

[jcsd]

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!)

correct.

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?

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

 

[zoobyshoe]

2. I don't really understand zoob's post (Too much maths - I only have a basic knowledge of maths and physics!)

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".

 

[zoobyshoe]

I'm still lost...

Actually, you should be. It shows you're thinking logically through this, and that I forgot to quote one very important thing by Chroot.

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?

Here Chroot explains the "absolute" that you're looking for. (I really should have included this in the post above):

The interval is a very important quantity in relativistic physics because it is invariant. No matter what coordinate system you use, or which observers you consider to be at rest, the interval they will measure for some path $$\Gamma$$ is always the same. The interval is independent of observers and is a fixed quantity for any particular path through spacetime.

- Warren

 

[pmb_phy]

Isn't it the case that this theory simply assumes the Earth is an 'absolute' frame of reference, directly contradicting the relativity principle?

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 in spacetime is called an interval.

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

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

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?

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

 

[zoobyshoe]

Hi Pete,

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

-Zooby

 

[John_M]

correct.

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

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!

Thanks for your help guys!

 

[pmb_phy]

Hi Pete,

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

-Zooby

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

Pete

 

[selfAdjoint]

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:

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

 

[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?

 

[pmb_phy]

Interval is a geometric, not a coordinate fact, and thus will have the same value in every inertial frame.

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

Pete

 

[zoobyshoe]

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

OK.

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

 

[Janus]

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!

Assuming that Twin B returns to Earth, this happens, according to Twin B, during that phase of the trip when he stops and turns around to return to the Earth. During this turn around period he will see twin A aging very fast. Enought so that it more than compensates for the fact that he sees Twin A age slower during the rest of the trip. How much faster B sees A age depends both on how quickly he does the turn around and how far he is from Twin A when he does it.

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??

No, there is no 'true' frame of reference. Each Twin measures a certain sequence of events, but they both agree on the end result. Twin A always sees Twin B as aging slower, While Twin B sees Twin A age slow during part of the time and fast for part of the time. Both sets of observations are equally valid and you cannot say that one or the other is the "correct" one.

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


Thanks for your help guys!

The triangle are the greek letter "delta", it stands for "change in".

Thus if a plane is flying at an altitude of A= 2000 ft and climbs to an altitude of A= 3000 ft, then

$$\Delta A=1000ft$$

 

[pmb_phy]

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."

No, because there may be more than one inertial observers which are not in the same inertial frame.

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?

No. Its possible that the acceleratio of turnaround occurs in a very short time and the ship travels at constant speed otherwise.

Pete

 

[Nenad]

the way time knows who is moving and who isn't is simple. It is because of the acceleration. The twin in the spaceship has to accelerate in order to fly off into space. Both twions look at one another and both twins see that the other twins time is running slower than theirs. But once the twin in the spaceship comes back, he sees that he is wrong and he has aged less than his brother. So youre right, it is during step 3) that the twin on the spaceship has his time slow down and age less.

 

[jcsd]

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!

Thanks for your help guys!

4) is where the change takes place but it's worth noting that instantaneous acceleration is unphhysical, tho' it helps to illustarte what is happening.

 

[John_M]

"the way time knows who is moving and who isn't is simple. It is because of the acceleration. The twin in the spaceship has to accelerate in order to fly off into space. Both twions look at one another and both twins see that the other twins time is running slower than theirs. But once the twin in the spaceship comes back, he sees that he is wrong and he has aged less than his brother. So youre right, it is during step 3) that the twin on the spaceship has his time slow down and age less."

I'm sure your post contradicts what some of the other people on here have been saying...

 

[John_M]

Let me update my list a bit.

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 turns round and heads back towards Earth.
5. The same as (3) but Twin B is moving in the opposite direction relative to Twin A.
6. Twin B reverts to Twin A's frame of reference.
7. Twin B has aged slower than Twin A.

Next question. If the key elements producing the end result (asymmetrical ageing) are not points (3) or (5), then surely this is not a question of special relativity at all, since acceleration is outside the scope of that theory?

(If they are points (3) and (5) as Nenad seems to be suggesting - surely you have big problems with the relativity principle?)

Quote from pmb_phy:

"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."

Doesn't this statement imply that the twin paradox is outside the scope of special relativity?

 

[selfAdjoint]

Let me update my list a bit.

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 turns round and heads back towards Earth.
5. The same as (3) but Twin B is moving in the opposite direction relative to Twin A.
6. Twin B reverts to Twin A's frame of reference.
7. Twin B has aged slower than Twin A.

Next question. If the key elements producing the end result (asymmetrical ageing) are not points (3) or (5), then surely this is not a question of special relativity at all, since acceleration is outside the scope of that theory?

(If they are points (3) and (5) as Nenad seems to be suggesting - surely you have big problems with the relativity principle?)

Quote from pmb_phy:

"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."

Doesn't this statement imply that the twin paradox is outside the scope of special relativity?

It is false that acceleration is outside of relativity. The fact that a curved timelike worldline has lower proper time than a straight one arises exactly from the relativistic definition of the interval, so that the "Pythagoras Theorem" of relativity is the difference of two squares instead of the sum.

 

[quantumdude]

OK.

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

It stands for proper time.

 

[Janus]

Let me update my list a bit.

1. Twins A and B are in the same frame of reference.

A and B measure each other aging as the same rate as themselves

2. Twin B changes his frame of reference (flying off)

A and B each see each others aging gradually begin to slow down. B however sees A age a little bit slower than A sees B age.(addition slowing seen be B is caused by the fact that he is accelerating away from A)

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.

Okay.

4. Twin B turns round and heads back towards Earth.

A sees B's aging gradually speed up until it matches his again as B slows to a stop before he starts his return journey. He then sees B's aging gradually slow down again as B accelerates back up to speed on the return trip.
B sees A's aging speed up to much faster than his own during the whole of the turn around manuver.

5. The same as (3) but Twin B is moving in the opposite direction relative to Twin A.

okay

6. Twin B reverts to Twin A's frame of reference.

A and B each see each other's aging gradually speed up until they both age at the same rate, in a reversal of stage 1.

7. Twin B has aged slower than Twin A.

Yes, since A always either sees B age more slowly than or the same as himself and B during stage 4 sees A age greatly (more than enough to make up for stages 3 and 5)

Next question. If the key elements producing the end result (asymmetrical ageing) are not points (3) or (5), then surely this is not a question of special relativity at all, since acceleration is outside the scope of that theory?

acceleration is not outside the scope of SR.

 

[zoobyshoe]

It stands for proper time.

Wow. Interesting. So the "worldline" is, in effect, what, something like the "proper spacetime."?

 

[John_M]

acceleration is not outside the scope of SR.

there are a few misleading websites suggesting it is...oh well.

 

[jcsd]

there are a few misleading websites suggesting it is...oh well.

It's a common fallacy, but thionk of it this way: speical relativity wouldn't be much of a kinematic theory if it couldn't deal with acceleration!

 

[pmb_phy]

It's a common fallacy, but thionk of it this way: speical relativity wouldn't be much of a kinematic theory if it couldn't deal with acceleration!

He's right. SR can handle accelerating particles. It just doesn't handle accelerating frames.

For the motion of a uniformly accelerating particle see

http://www.geocities.com/physics_world/sr/uniform_accel.htm

Pete

 

[jcsd]

I can't see why you would say it can't handle acclerated frames, for example we can use SR to find the proper time of an accelerated observer (which you have in on your own website). Just because the principle of relativity does not hold true in accelerated frames and the laws of physics that hold true for inertial frames of reference do not hold true in accelrated frames of refernce and must be modified does not mean that SR cannot handle them.

I suppose the difference between inertial and non-inertial frames of reference is the same difference as viewing Minkowskian spacetime in rectangular coordinates and viewing it in some other orthogonal curvilinear coordinate system.

 

[pmb_phy]

I can't see why you would say it can't handle acclerated frames, for example we can use SR to find the proper time of an accelerated observer (which you have in on your own website). Just because the principle of relativity does not hold true in accelerated frames and the laws of physics that hold true for inertial frames of reference do not hold true in accelrated frames of refernce and must be modified does not mean that SR cannot handle them.

I suppose the difference between inertial and non-inertial frames of reference is the same difference as viewing Minkowskian spacetime in rectangular coordinates and viewing it in some other orthogonal curvilinear coordinate system.

The principle or relativity states that the laws of physics are the same in all inertial coordinate systems. Since that is alll you know then you can't go beyond that and into non-inertial frames. Going from one inertial frame to another requires transformations in the Lorentz group. I guess it took Einstein a while to figure out how to transform to non-inertial frames or that he didn't know how/if the laws of physics could take on tensor form and thus be valid in all frames/coordinate systems. Then when he figured it out he called it the principle of general covariance and called the theory which included this principle the general theory of relativity. It was at that time when he postulated that the laws of physics must take on tensor form and thus hold in all coordinate systems.

Pete