Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Bill S on 18/03/2015 22:03:41
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Question about Michael Huemer’s spacetime diagrams.
http://home.earthlink.net/~owl232/twinparadox.pdf
In Figure 2 the Earth is considered as stationary; its world line simply follows the vertical time axis.
Space Twin is considered to be in motion relative to the Earth. He moves to the right at 0.5c, then to the left at 0.5c.
In Figure 3 Space Twin is considered to be stationary. His world line starts by following the vertical time axis. The Earth is considered as being in motion relative to Space Twin, so it moves to the left at 0.5c.
The reason that Earth is considered to be moving at 0.5c is that that was the speed of the spacecraft in the first F of R.
At t = 8.66, Space Twin decides to change speed and direction.
Figure 3 then shows Space Twin as being in motion. 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?
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Should Fig. 3 not show Earth as moving towards the space craft? If not - why not?
The way I see it: From the point of view of inertial frames this twin as you know can can consider themselves stationary. So initially the earth appears to move away from the twin.
However, there comes a point where the twin wishes to return to earth. At this point the twin accelerates and is no longer in an inertial frame so is shown as moving. For earth to come back towards the twin would require it to do the accelerating.
From a ST diagram point of view you can only consider yourself stationary if you are in an inertial frame.
Would be interested in how others view it.
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Ultimately you could plot a spacetime diagram in Planck units. The time axis in units of 1 Planck time and the space axis in units of 1 Planck length. Light will always follow a 45 degree path with respect to the origin. Any constant velocity will also describe a straight line path away from the light path. However an acceleration will follow a curved path. The curved path is non-inertial and can not be considered to be at rest in any frame.
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......The curved path is non-inertial and can not be considered to be at rest in any frame.
I did the diagrams for curved path and got a similar result, he spends less time at higher speeds but gets extra dilation from the greater g effect. I must look at your thread on escape velocity, similar problem.
.... 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?
Bill, in the example you quote I think the straight lines are used for simplification, assume instant acceleration to new speed. The important thing is to maintain the same FofR.
While the travelling twin considers himself stationary it is relative to a particular frame he has established, when he accelerates towards earth any movement has to be considered relative to that frame. If having accelerated he then began to view earth as moving towards himself he would have changed his FofR, To retain consistency you would have to draw a new diagram in which this leg of the journey is considered as stationary, but the previous leg as moving.
In other words you have to keep one FofR throughout.
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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.
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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.
They won't be ageing at the same rate to your new observer. To maintain the constant distance the observer must be also moving at a constant velocity. 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.
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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.
I think that should work. relative to the new observer both earth and the other twin are moving in opposite directions at the same speed. I don't think he even needs to be half way except it makes it easier to visualise.
As jefferyh says, the problem comes with them all coming together to one frame at some stage, choose your frame!
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Yesterday my son asked: Is there any situation in which an outside observer would perceive the twins as ageing at the same rate?
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.
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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.
Cast list: Earth twin (ET), observer (O) and space twin (ST)
Imagine a spacetime diagram on which we consider ET as stationary. O is travelling at 0.25c to the right and ST is travelling at 0,5c to the right.
If we designate ST as stationary, then O and ET are travelling to the left at 0.25c and 0.5c respectively.
If we designate O as stationary, ET is moving to the left at 0.25c and ST to the right at 0.25c.
I may have oversimplified this, but I can’t see the additional complication.
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As jefferyh says, the problem comes with them all coming together to one frame at some stage, choose your frame!
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.
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.
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?
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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.
In that case I think it works
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?
I think Pete may have misread that.
Reference frame should be ok, and if they are all up to speed, they are inertial frames (which is what Heumer assumes for simplicity)
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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?
I know. Since your son asked
Is there any situation in which an outside observer would perceive the twins as ageing at the same rate?
I assumed he had a particular frame of reference in his mind and assumed it was the stay at home twin's frame. However I see here that I was wrong. One can always choose a frame of reference in that situation where both twins move at the same speed. In that frame the twins age at the same rate during the period of time when both of them are moving at constant speed, i.e. the traveling twin is not slowing down or speeding up. So the answer really is - Yes!
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.
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Here's a simple proof.
Interesting proof, not sure I would have thought of using that concept.
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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 I'm confused now. Since Colin is clearly 100% correct, what does that say about John? Lol!
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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.
LOL, Pete's wrong about this too. He has admitted to being wrong. He just doesn't do it enough.
All: I think the easiest way to think about this subject is to refer to the Simple inference of time dilation due to relative velocity (http://en.wikipedia.org/wiki/Time_dilation#Simple_inference_of_time_dilation_due_to_relative_velocity), which features the parallel-mirror light clock. Note that the Lorentz factor is derived from Pythagoras's theorem, that the elapsed time is the number of reflections, and that the light path length is the same for both twins. Draw their lightpaths in space, and it's all very clear. What's also clear is this: only one of them has felt the accelerations. 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.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2Fa%2Fa5%2FTime-dilation-002.svg%2F400px-Time-dilation-002.svg.png&hash=c7512e7864501d98abc9f6143bbd2e8d)
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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?
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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.
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
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Jeffrey, as you seem to be active at the moment, may I call your attention to #5 and #8?
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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.
It is important to make one thing clear.
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.
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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?
Mr. Duffield's presentation is almost correct, however, as usual he has left out a core feature of relativity theory to which he objects: that there is no true reference frame. The use of the Pythagorean theorem that Mr. Duffield seems to revere is only justified in its use if one assumes that one can make use of a light signal to synchronize any frame of reference relative to stationary clocks (in the form of regular physical systems that can be considered to be synchronized in some fashion). This assumption, at least in standard texts from Einstein's 1905 paper onwards, arises from the assumption that there is not one inertial reference frame in which the laws of physics are correct and the correct presentation of the laws of physics relies on identifying this frame.
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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.
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?
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Returning to Huemer’s Figures 2 and 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?
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Jeffrey, as you seem to be active at the moment, may I call your attention to #5 and #8?
Yes Bill I have noted this. I will come back to you when I have a little more time.
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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?
I'm unclear what you mean by Can they be in the same reference frame? Typically one speaks of two objects as being at rest in frame S, not simply "being" in the same reference frame. Typically I'd interpret that as the observer whose frame of reference is S observes those objects in his frame. It's measurements/observations that one speaks of when they speak of frames of reference.
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You are assuming there is a return trip. The relativistic equations have to make sense even without a return.
They do. If you have two twins passing each other in space, each one sees the other one as time-dilated. But this is no more a paradox than two twins separated by distance saying each one looks smaller than the other.
To assume that space twin was moving in any absolute sense because he felt acceleration is unrelativistic thinking.
It isn't. The two twins could have started off as co-moving twins. The one who feels the acceleration is moving relative to the other.
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
That's unrelativistic thinking.
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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.
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.
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?
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.
We still seem to be saying that because space twin accelerates it is he who is “really moving”.
That's right. He can feel it.
If 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.
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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?
Unless one is using a strange reference frame, every object is in every reference frame. One cannot assign velocity without identifying a reference frame. The rules for assigning reference frames (kinematics) are the rules for how one can consistently assign velocities.
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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.
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.
This is amongst the worst advice one can get if one wants to be able to use and understand special relativity. Reference frames are not "a state of motion", they are the schema of the rules for consistently assigning all possible velocities.
One can "Draw the zigzags in his parallel-mirror light clock clock" for both twins from each of the frame of reference in which the twin is at rest. (Of course, it's ultimately better to simply learn how to do the math rather than draw these out and measure them.)
The original question was, "If we are still in Space Twin’s F of R, why are we seeing him as being anything other than stationary?"
The answer is: people do not own frames of reference. We can identify a frame of reference in which a person is stationary, at least for a time, but that doesn't mean that the person remains stationary relative to that reference frame forever.
If we want to try to construct a reference frame out of the two reference frames in figures 3 and figure 4, that's fair. But we will find that this is not a well formed reference frame. Try plotting the trajectory of the other twin in the new reference frame and you will find discontinuities. This is because one is using an artificial reference frame, not an inertial reference frame.
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.
This is a special position that only Mr. Duffield holds. People are welcome to accept the holy word of Mr. Duffield if they wish.
We still seem to be saying that because space twin accelerates it is he who is “really moving”.
That's right. He can feel it.
As the document by Michael Huemer points out, this is a profoundly anti-relativistic position to take. Again, one is welcome to accept the Church of Einstein (Reformed) that Mr. Duffield offers.
If 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.
This is actually profoundly wrong. First, there is no "really moving away" As Michael Huemer shows, even if we consider the Earth to be in motion the entire time, the time experienced by the twin off Earth is always less than the twin on Earth by exactly the same amount by the event at which they are reunited. Second, 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. Special relativity does not recognize a cobbled together reference frame from two reference frames to be a single, well-formed reference frame.
Textbooks on relativity theory do discuss the proper way to combine reference frames and the limits that one has to bear in mind when one does so.
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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.
Huemer goes on to point out that acceleration cannot be the explanation, because special relativity does not deal with acceleration, and the explanation is contained in special relativity.
….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.
Is it me, or is there a dichotomy here?
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One does not need to introduce special effects from acceleration to have different effects from different motions.
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One does not need to introduce special effects from acceleration to have different effects from different motions.
Could you say a bit more about that, please. Every time I think I've got it a "what if" finds it's way in.
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All the factors that indicate what the time coordinate will read depend on velocity alone. Acceleration changes velocity, yes, but it doesn't in itself enter into the determination of the relativistic effect in this case. Only the trajectory in inertial reference frames matters. If we accept that the stay-at-home twin is in an inertial reference frame, then we cannot find one single inertial reference frame to describe the path of the other twin.
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Thanks PhysBang, OK so far, I think.
Would the next step be to say that we cannot accept that space twin is in an inertial frame (throughout) because we know she accelerates, relative to Earth?
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That would be fair to say, but all that really matters is the velocity (in this case velocities) of the twin in space. Assuming that we can assign to the Earth a constant velocity (at least roughly), then we can't also do this for the space twin because we know this space twin does not have a constant velocity over the course of the scenario. This way, we can have the Earth going at whatever constant speed we would like and then plot the path of the space twin.
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. Of course, then the questions might be whether or not this is negligible, whether or not it is swamped by gravitational effects and so on, but an interesting exercise nonetheless.
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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.
An interesting exercise. Could you do it without space twin having to accelerate away from Earth in the first place?
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Well, yes, you just do it with twin clocks that just happen to be synchronize the first time the pass by each other.
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Got it, thanks.
We start with the assertion by authors of pop sci books that it is space twin’s acceleration, relative to Earth, that is responsible for her being younger. Then we examine Huemer’s contention that this is wrong, and that the age difference could be calculated, and assigned, within special relativity, without recourse to acceleration. Finally we reason that, although acceleration is not essential for the calculations, it is necessary in the matter of deciding which twin would be younger in the end. Should we round off with a few lines from Gilbert and Sullivan’s Mikado?
And I am right,
And you are right,
And all is right as right can be!
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But the acceleration itself does nothing. All the time dilation occurs due to the difference in velocity while the space twin is moving away from the Earth. The acceleration just ensures that the space twin returns to the Earth.
We could do the same scenario with three clocks. One is on Earth and the other passes by and happens to be showing the same time when it passes by. Then, later, a third clock passes by the second clock on its way to Earth, again, happening to show the same time as this second clock at the moment it passes by. Then when the third clock gets to the Earth, we have three otherwise identical clocks that we might naively imagine to show the same time that are out of sync by exactly how much we would calculate based on SR. Nothing in the scenario accelerates.
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Thanks folks, this has been a great learning/thinking thread.
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The 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.
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Just when I thought I was sorting the terrible twins out in my head, the discussion takes another twist. Then I remembered something Sachs said in the Haifa Lectures that I had not resolved, so I'm going to have to think a bit more and probably ask more questions.
Like I said: Good thread!
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The 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.
That causes confusion.
1) The acceleration does not cause the symmetry breaking, it's the velocities that do. That is what the example with the three clocks shows, since the calculations for the three clocks that do not undergo acceleration come out to the same time dilation as the twin scenario with a rocket. 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.
That repeats the same myths that were pointed out as unhelpful in the document from the OP.
Edit: Please keep it civil - mod.
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The 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.
Now that is the kind of answer that I like. That is why it is called relativity after all. There must be many things like this that people normally don't consider and they are hard to track down unless you know the right text to read or the right person to ask. I just wish people would listen to the finer points that you make. If they were paying attention they would pick up some real gems.
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It's too bad those finer points are irrelevant to the discussion of the twin paradox in the context of Special Relativity alone.
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1) 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.
This 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.
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
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.
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.
Thank you for coming in and repeating the same myths that were pointed out as unhelpful in the document from the OP.
There's no myth here. 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 they can read all about this in that text which is online here - http://bookos-z1.org/book/2065579/30320e
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.
Edit: Please keep it civil - mod.
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those finer points are irrelevant to the discussion of the twin paradox in the context of Special Relativity alone.
Jeff was very happy with it.
This thread is NOT about special relativity, it's about the twin paradox. And the twin paradox takes place in this instance in flat spacetime and the physics of flat spacetime IS what special relativity is about. That's how the term is understood by authorities and experts on the subject. Some, such as myself, still use it otherwise. But it was only about SR because the OP only knew of it in SR. When I showed the OP how to describe this from the traveling twins point of view he was happy about it as was Jeff. The description I posted is in the modern relativity literature.
The UseNet Physics FAQ also explains it in the same that the I did. The author of the FAQ uses the term General Relativity the same way that the GR community uses it. See: http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html
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,...
Underline is mine. PhysBang worries too much about semantics and whether this is called special relativity or general relativity. In any case my point was merely to describe things from another point of view, just as the FAQ explains! :)
The FAQ explains in the lower part of the page about how the meaning of the terms SR and GR changed.
A friend of mine is an expert in GR who is widely published in his field. His name is Oyvind Gron from the University of Oslo.
http://www.mn.uio.no/fysikk/personer/vit/ogron/ (I couldn't find the English version this morning)
The paper he wrote is
The twin paradox and the principle of relativity located at http://arxiv.org/abs/1002.4154
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.
This is an example of someone who also uses GR to refer to acceleration of an observer in flat spacetime as a problem in GR.
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1) 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.
Please go back and read the actual document that the OP is discussing.
The question here is why does SR have an apparent violation of an assumed symmetry here. The answer is the specific velocities involved. If we consider two twins, then we have to introduce acceleration in order to change the velocity of one twin. However, the acceleration doesn't enter in to any SR calculation. We can replicate everything of importance in this scenario by replacing the twins with clocks that happen to pass by one another and happen to be synchronized when they pass by. This removes all acceleration from the scenario but preserves the difference in time dilation between clocks.
This 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.
The reason that I look at this in one way is because that is the way it was laid out in the OP. The question asked in the document in question is how to properly explain the scenario without recourse to General Relativity.
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.
I don't think that statement makes sense; you appear to have made at least one typo in your haste to insult me.
Regardless of the fact that we can consider Special Relativity to be a limiting case of General Relativity, if one sticks to the limiting case, then one sticks to the limiting case.
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
I again suggest that you read the document cited in the original post, where it is quite clear that the author is addressing a popular but unhelpful myth that the resolution of this "paradox" lies in General Relativity. This is also addressed in Bernard Schutz's relativity text, where he also points out that the scenario is purely a feature of Special Relativity alone and is entirely consistent within SR.
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.
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.
You just reiterated my point that the difference in clock heights is a feature of GR. I said nothing about acceleration.
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.
I was using a standard shortcut to talk of clock rates rather than relative time dilation.
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 - http://bookos-z1.org/book/2065579/30320e
I find it odd that you would attempt to prove your point through a citation that you assume is blocked to me in some way.
As Peacock writes, "The so-called paradox lies in the broken symmetry between the twins. There are various
resolutions of this puzzle, but these generally refuse to meet the problem head-on by analysing things from B’s point of view." Indeed, these resolutions generally refuse to do so because in the SR context alone, where is no "B's point of view" in the physical sense that there is no inertial reference frame in which B is at rest. This point is important because the paradox is presented as a supposed failure of the consistency of SR, so a resolution needs to show that SR remains consistent.
Peacock shows that using the ideas of GR, one can produce a calculation that recovers the time dilation from a system of coordinates that GR can use. However, this cannot be viewed as a resolution of the "paradox" that demonstrates the internal consistency of Special Relativity.
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.
I am not surprised that someone might ask students to, as an exercise, run through the scenario in the context of GR. It is an exercise in Ohanion & Ruffini, since in GR, unlike in SR, one can create a system of coordinates in which the space twin is at rest in which one can work out the correct relative time dilation between the two twins. This fact is noted by Ohanion & Ruffini.
there are other ways of looking at scenarios other than the ones that you know about.
I thank you for pointing out that people might not know that when I speak of differing clock rates, that I am speaking of relative time dilation.
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It saddens me to see some acerbity making its way into a thread that has, so far, been so valuable. Let's try a slight change of perspective to see if it will restore harmony.
The following is a quote from the Haifa Lectures (Sachs):
“If, for example, the time change in the description of any process in nature is a physical change in aging, then when a twin sister space pilot goes on a round trip journey from her sister at home, she would age less than her sister during the journey, from the perspective of the stay-at-home sister. But from the perspective of the traveling sister, it is the stay-at-home sister who making the round trip journey and the stay-at-home sister would be younger than her pilot sister after the completion of the round trip journey! Thus, with this interpretation, it would have to be concluded that when the traveling sister returns from her round trip, she would be both older and younger than her sister. This is called the “twin paradox”. The error in this conclusion is the faulty interpretation of the time measure as an objective physical change instead of a subjective scale change, when transforming to different reference frames!”
Where I need some clarification is in the distinction between objective physical and subjective scale change.
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It turned out that paper I mentioned has been published. The complete reference is
The twin paradox and the principle of relativity by Øyvind Grøn, Physica Scripta. 87 (2013) 035004
Abstract
The 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. The
special relativistic solution is to say that if one of the twins, say A, was inertial during the
separation, she will be the older one. Since the principle of relativity is not valid for
accelerated motion according to the special theory of relativity B cannot consider herself as at
rest permanently because she must accelerate in order to return to her sister. A general
relativistic solution is to say that due to the principle of equivalence B can consider herself as
at rest, but she must invoke the gravitational change of time in order to predict correctly the
age of A during their separation. However one may argue that the fact that B is younger than A
shows that B was accelerated, not A, and hence the principle of relativity is not valid for
accelerated motion in the general theory of relativity either. I here argue that perfect inertial
dragging may save the principle of relativity, and that this requires a new model of the
Minkowski spacetime where the cosmic mass is represented by a massive shell with radius
equal to its own Schwarzschild radius.
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In the hope of stirring some thoughts on #47, let's try some possible definitions.
Objective: Governed by, or relating to, factors external to the specific case/object.
Subjective: Governed by, or relating to, factors that may not pertain to anything external to the specific case/object.
Scale: (in this sense): A proportion used in determining dimensional relationships.
Thus:
An “objective physical change” is one that comes about as a result of external factors and is imposed on the physical structure/nature of the object in question.
A subjective change is one that is dependent on the nature of the effected object, and may have no significance beyond that.
A subjective scale change is one that is dependent on the nature of the object, but effects only spatial or temporal values pertaining to that object.
What would this imply about the “interpretation of the time measure ……. when transforming to different reference frames!”?
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I here argue that perfect inertial dragging may save the principle of relativity, and that this requires a new model of the Minkowski spacetime where the cosmic mass is represented by a massive shell with radius
equal to its own Schwarzschild radius.
Could someone translate this into lay-speak, please?
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I here argue that perfect inertial dragging may save the principle of relativity, and that this requires a new model of the Minkowski spacetime where the cosmic mass is represented by a massive shell with radius
equal to its own Schwarzschild radius.
Could someone translate this into lay-speak, please?
I would like it worded better too. Is inertial dragging related to the dragging of inertial frames for instance? Or something entirely different? What is the Schwarzschild radius of the cosmic mass? Isn't that infinite by definition?
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I wondered if reading the whole paper would help, but I was left with the impression that Grøn was serious when he indicated that it was an exercise in the understanding of GR, rather than a look at the twins.
Perhaps a combination of Richard Wolfson’s “…the straightest path for a free-float observer in spacetime is also the path on which the time between two events is the greatest”, and Michael Huemer’s insistence “…that there is no reference frame in which Space Twin is at rest throughout the story…” is all we really need, apart from a word of wisdom on #47 [:)].
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Could someone translate this into lay-speak, please?
I would like it worded better too. Is inertial dragging related to the dragging of inertial frames for instance? Or something entirely different? What is the Schwarzschild radius of the cosmic mass? Isn't that infinite by definition?
I sent the author your questions and he replied as follows
"Inertial dragging" is the same as "dragging of inertial frames".
I talk of the cosmic mass inside the horizon, and that is finite
I doubt that satisfies your question so perhaps you have a follow up.
You should go to my forum. I'll ask him to join and answer directly.
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Could someone translate this into lay-speak, please?
I would like it worded better too. Is inertial dragging related to the dragging of inertial frames for instance? Or something entirely different? What is the Schwarzschild radius of the cosmic mass? Isn't that infinite by definition?
I sent the author your questions and he replied as follows
"Inertial dragging" is the same as "dragging of inertial frames".
I talk of the cosmic mass inside the horizon, and that is finite
I doubt that satisfies your question so perhaps you have a follow up.
You should go to my forum. I'll ask him to join and answer directly.
That answers my questions Pete. I don't want to bug the author so I am happy with what he says.
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Everything does exist at the same time under present-dynamism only.
You should post this under New Theories. Either copy it there or ask one of the moderators to move it for you.