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Should Fig. 3 not show Earth as moving towards the space craft? If not - why not?

......The curved path is non-inertial and can not be considered to be at rest in any frame.

.... If we are still in Space Twin’s F of R, why are we seeing him as being anything other than stationary?Should Fig. 3 not show Earth as moving towards the space craft? If not - why not?

Yesterday my son asked: Is there any situation in which an outside observer would perceive the twins as ageing at the same rate? My answer (off the cuff, while driving) was: There is, but it would require that the relative speed difference between each twin and the observer be the same. For example, if the observer placed his craft between Earth and the craft in which the twin was travelling, such that, if Earth were regarded as stationary, he was moving away from it at 0.25c, the twin’s craft would be moving away from him at 0.25c. If we now change to the observer’s reference frame, Earth will also be moving away from him at 0.25c. In that case, he should consider that the twins are ageing at the same rate. Thought I'd like to run that past others.

Yesterday my son asked: Is there any situation in which an outside observer would perceive the twins as ageing at the same rate?

So whilst the moving twin might be moving at speed s your observer is moving at 1/2s. That will add relativistic effects to the new observer's journey that merely adds more complexity to the thought experiment.

As jefferyh says, the problem comes with them all coming together to one frame at some stage, choose your frame!

You're answer should have been simply - No! The twins don't age at the same rate as reckoned by observers at rest with respect to the stay at home twin.

In this scenario they don’t come together. We were considering the first of Heumer’s “two cases” in which there is no second meeting.

I’ve just looked back at #4, and I can’t see where I said that the observer was at rest with respect to the stay at home twin. Would it have been clearer if I had used “inertial frame” instead of “reference frame” when referring to the observer?

Is there any situation in which an outside observer would perceive the twins as ageing at the same rate?

Here's a simple proof.

I think Pete may have misread that.

What? Me? Do you know to whom you are talking to? I'm Pete, i.e. PmbPhy! Ask JohnDuffield. He'll explain to you that I never admit that I'm wrong.

So all participants agree that it was space twin who did the out-and-back trip. He's the one with the zigzag lightpath, and he's the one who got time-dilated.

Here's a simple proof. Consider two objects of identical mass at rest next to each twin. Then in all frames of reference at least one of the objects is moving. Then the total momentum of the system consisting of those two particles is non-zero. One can always choose an inertial frame in which the total momentum is zero. In that frame both particles have the same momentum in magnitude and therefore since they have the same mass they have the same speed. Therefore since each object is at rest next to each twin it follows that each twin is moving at the same speed in that frame. If they're moving at the same speed then they're aging at the same rate.

You have had a bit of a hiatus John. Did all that googling take it out of you? BTW whose illustration have you plagiarized this time?

One can identify a reference frame in which each object has the opposite momentum; that is, the absolute value of their momentum is the same but the direction is directly opposite.By the symmetries of special relativity, the time dilation associated with the rest frame of these objects (assuming they have the same rest mass) will be the same relative to this special frame in which they have the opposite momentum.

Jeffrey, as you seem to be active at the moment, may I call your attention to #5 and #8?

I thought: Momentum = mass x velocity. If mass is the same, and they have opposite momentum, they must be moving in opposite directions, relative to each other. Can they be in the same reference frame?

You are assuming there is a return trip. The relativistic equations have to make sense even without a return.

To assume that space twin was moving in any absolute sense because he felt acceleration is unrelativistic thinking.

If Earth and the spacecraft were moving (eg) to the left at 0.5c before take off, then after accelerating, space twin would have to be considered stationary, with Earth moving away at 0.5c as in Huemer’s Fig. 3

In the RF in which Earth is stationary, space twin is perceived as travelling at 0.5c in both the outward and return directions, there is no time dilation.

In the RF in which space twin is stationary, it is Earth that is moving, so why is time dilated (10 years become 8.66 years) in that RF?

We still seem to be saying that because space twin accelerates it is he who is “really moving”.

If Earth were really moving away from the spacecraft, wouldn’t time dilation occur in Earth’s RF?

Now I’m more confused than usual. I thought: Momentum = mass x velocity. If mass is the same, and they have opposite momentum, they must be moving in opposite directions, relative to each other. Can they be in the same reference frame?

Quote from: Bill S on 28/03/2015 22:21:12In the RF in which Earth is stationary, space twin is perceived as travelling at 0.5c in both the outward and return directions, there is no time dilation.Forget about the reference frame, it's little more than "a state of motion". Space twin suffers time dilation. Draw the zigzags in his parallel-mirror light clock clock.

Space twin experiences 8.66 years while Earth twin experiences 10 years, because elapsed time is merely a cumulative measure of the local motion of light. And the acceleration says who's moved relative to who.

Quote from: Bill S on 28/03/2015 22:21:12We still seem to be saying that because space twin accelerates it is he who is “really moving”.That's right. He can feel it.

Quote from: Bill S on 28/03/2015 22:21:12If Earth were really moving away from the spacecraft, wouldn’t time dilation occur in Earth’s RF?Yes. But Earth isn't, so it doesn't.

The second false resolution I have heard is that it is the Space Twin who will have aged slower, because it was he who had to accelerate in order to get up to his great speed. In STR,” [special theory of relativity] “there is an objective distinction between accelerated and uniform (non-accelerated) motion. So it’s an objective fact that Space Twin underwent acceleration while Earth Twin didn’t.

….in the "twin paradox", the twin not on Earth explicitly changes his state of motion relative to an inertial reference frame. It is that stipulation that does all the work.

One does not need to introduce special effects from acceleration to have different effects from different motions.

Interestingly, given the orbit of the Earth, one could rig up a scenario where the space twin is the one who goes at a constant speed and meets up with the Earth at a later time and finds that there is special relativistic time dilation such that the Earth twin has aged less.

The acceleration just ensures that the space twin returns to the Earth.

Quote from: PhysBangThe acceleration just ensures that the space twin returns to the Earth.If by this you mean that this is the only place where the acceleration comes into play then you're quite incorrect. The acceleration in fact does a great deal more than that. It's very important in fact. In the first place its what breaks the symmetry between the two twins in motion since its the broken symmetry that determines which twin ages more. From the Earth observer's point of view the acceleration distinguishes which twin will be the youngest when brought to rest next to the other twin who never accelerated.In the second place it can be shown that it is the acceleration itself which causes the stay at home twin to age more than the traveling twin as reckoned from the traveling twin's frame of reference. When the traveling twin's frame ship is accelerating he is effectively in a gravitational field. Clocks at different "heights" in the field (i.e. different clocks which are welded in place along the length of the ship) run at different rates as do all clocks in his accelerating frame of reference. Thus when the traveling twin determines that its time to start to slow down so when he gets to his destination he'll be at rest he starts accelerating. The accelerating twin determines that he's in a gravitational field and that the stay at home twin is very high in this gravitational field. As such the stay at home twins wristwatch is now running at a faster rate and this is where the twin starts aging faster than the traveling twin! Most people aren't aware of this fact and its rarely discussed in physics texts. But it one knows general relativity its quite easy to see. But most people never wonder what things appear like from the traveling twins perspective.

1) The acceleration does not cause the symmetry breaking, it's the velocities that do.

This is because we are considering Special Relativity alone.

2) The differing rates of clocks at different heights is an effect from General Relativity which is irrelevant to this scenario. This is because we are considering Special Relativity alone.

Thank you for coming in and repeating the same myths that were pointed out as unhelpful in the document from the OP.

those finer points are irrelevant to the discussion of the twin paradox in the context of Special Relativity alone.

Although most scenarios in Special Relativity are most easily described using inertial frames, there is no reason why these frames absolutely must be used. The Equivalence Principle analysis of the twin paradox simply views the scenario from the frame in which Stella is at rest the whole time. This is not an inertial frame; it's accelerated, so the mathematics is harder. But it can certainly be done. When the mathematics is described fully, what results is that we can treat a uniformly accelerated frame as if it were an inertial frame with the addition of a "uniform pseudo gravitational field". By a "pseudo gravitational field", we mean an apparent field (not a real gravitational field) that acts on all objects proportionately to their mass; by "uniform" we mean that the force felt by each object is independent of its position. This is the basic content of the Equivalence Principle....The Equivalence Principle analysis of the twin paradox does not use any real gravity, and so does not use any General Relativity. ...But it needs to be emphasized that we are not using any actual General Relativity here,...

Abstract - In the standard formulation of the twin paradox an accelerated twin considers himself as at rest and his brother as moving. Hence, when formulating the twin paradox, one uses the general principle of relativity, i.e. that accelerated and rotational motion is relative. The significance of perfect inertial dragging for the validity of the principle of relativity is made clear. Three new results are reviewed in the discussion. A cosmic time effect which cannot be reduced to the gravitational or the kinematical time dilation. Perfect dragging in an exact solution of Einstein's field equations describing flat spacetime inside a shell with Kerr spacetime outside it. An extended model of Minkowski spacetime in order to avoid introducing absolute acceleration and rotation through the asymptotic emptiness of the Kerr spacetime.

Quote from: PhysBang1) The acceleration does not cause the symmetry breaking, it's the velocities that do.Incorrect. The worldline of the traveling twin absolutely must not be a straight line in the spacetime diagram. Therefore the worldline must not be straight meaning that the traveling twin is accelerating. The twin could start out moving at constant speed and synchronize his clock with a traveler whose going towards Earth and then the two twins can compare clocks again when they pass by. That's one way of looking at it. But if that worldline represents an ideal clock which can instantaneously change directions without changing speed then it's still accelerating.

Quote from: PhysBangThis is because we are considering Special Relativity alone.Your education in physics appears to have led you to believe there is one and only one way to look at problems such as this. The following reasons are why you're wrong in this instance.

1) In the first place the term special relativity as it is used by the majority of relativists today is that of physics in flat spacetime and not merely because the observer is accelerating. Had you extended your education to general relativity you wouldn't be ignorant of this fact.

2) The only reason only SR was being considered alone was because the OP was unaware that traveling twin's point of view can be analyzed using general relativity. However most relativists would still consider this a problem in special relativity

Quote from: PhysBang2) The differing rates of clocks at different heights is an effect from General Relativity which is irrelevant to this scenario. This is because we are considering Special Relativity alone.Another error based on the common misconception that in modern physics (i.e. what is in current use by contemporary relativists) general relativity is defined as physics in curved spacetime, not about accelerating frames of reference.

I wasn't talking about merely clocks. I was talking about actual physical twins, i.e. I wrote ..it is the acceleration itself which causes the stay at home twin to age more than the traveling twin... Such twins can't accelerate instantaneously. And I was explaining the scenario from the accelerating twins perspective.

This problem is treated exactly as I just explained to you in the text Cosmological Physics by John A. Peacock, pages 7-8. For the rest of the posters here other than you who don't have such a closed mind they can read all about this in that text which is online here - ...sorry, you cannot view external links. To see them, please REGISTER or LOGIN

Oyvin Gron, another well-known GR expert also treats this in the same way as I just described. It was either published or he used the notes to teach his students. I'll post it when I contact the author and get a copy again.

there are other ways of looking at scenarios other than the ones that you know about.

AbstractThe twin paradox is intimately related to the principle of relativity. Two twins A and B meet,travel away from each other and meet again. From the point of view of A, B is the traveller.Thus, A predicts B to be younger than A herself, and vice versa. Both cannot be correct. Thespecial relativistic solution is to say that if one of the twins, say A, was inertial during theseparation, she will be the older one. Since the principle of relativity is not valid foraccelerated motion according to the special theory of relativity B cannot consider herself as atrest permanently because she must accelerate in order to return to her sister. A generalrelativistic solution is to say that due to the principle of equivalence B can consider herself asat rest, but she must invoke the gravitational change of time in order to predict correctly theage of A during their separation. However one may argue that the fact that B is younger than Ashows that B was accelerated, not A, and hence the principle of relativity is not valid foraccelerated motion in the general theory of relativity either. I here argue that perfect inertialdragging may save the principle of relativity, and that this requires a new model of theMinkowski spacetime where the cosmic mass is represented by a massive shell with radiusequal to its own Schwarzschild radius.