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adoion
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also an accelerometer doesn't measure acceleration in free fall only when you stand on the Earth's suface does it do so, you can see that from the link to Wikipedia http://en.wikipedia.org/wiki/Accelerometer
Although calibration is necessary for real devices, for the purpose of thought experiments it is generally a detail which is glossed over. We simply assume ideal measuring devices such as rods, clocks, and accelerometers.adoion said:you would have to calibrate the accelerometers differently in order for both of them to be zero if they accelerate differently, because if you assume that your accelerating RF is actually stationary then you calibrate your accelerometer to read zero in your reference frame, don't you?
Yes. This is why in relativity free-fall frames are inertial and frame attached to the Earth's surface is non-inertial.adoion said:also an accelerometer doesn't measure acceleration in free fall only when you stand on the Earth's suface does it do so, you can see that from the link to Wikipedia http://en.wikipedia.org/wiki/Accelerometer
what I mean is that if you for example take the equivalence principle, take an elevator witch you can think of as the rocket of the traveling twin.DaleSpam said:Although calibration is necessary for real devices, for the purpose of thought experiments it is generally a detail which is glossed over. We simply assume ideal measuring devices. In principle, it is not a bad assumption. If you miscalibrate the accelerometer then you will detect violations of the conservation of momentum which are not accounted for. You will not be able to get experiments to match the known laws of physics. So a miscalibrated accelerometer will be something which is experimentally detectable in the end.
adoion said:what I mean is that if you for example take the equivalence principle, take an elevator witch you can think of as the rocket of the traveling twin.
if the elevator is accelerating with uniform acceleration it acts just like if it were in free fall.
I forgot to mention:stevendaryl said:As DaleSpam said, freefall is considered inertial motion from the point of view of General Relativity, precisely because an accelerometer would show no acceleration.
adoion said:I forgot to mention:
if the elevator (rocket) accelerates under the influence of an gravitational field (at the turnaround) then what would we have ?
an inertial frame that accelerates ??
even from the point of view of special relativity, this has to be a IRF since the laws of stay unchanged in their simplest form.
an accelerometer would measure zero in the above case since the rocket would be in free fall.stevendaryl said:Yes. There are two different notions of "acceleration": coordinate acceleration, and proper acceleration. Coordinate acceleration depends on your coordinate system. For example, the path: (x=0,y=vt) (x=0, y=vt) has zero coordinate acceleration in Cartesian coordinates. But if you switch to polar coordinates: r=x 2 +y 2 − − − − − − √ r = \sqrt{x^2 + y^2}, θ=tan −1 (yx ) \theta = tan^{-1}(\frac{y}{x}), then the coordinate acceleration in terms of r r and θ \theta is nonzero. Proper acceleration is what is measured by an accelerometer, and it is independent of what coordinate system you use.
adoion said:an accelerometer would measure zero in the above case since the rocket would be in free fall.
Yes. And therefore the rockets frame is inertial.adoion said:an accelerometer would measure zero in the above case since the rocket would be in free fall.
adoion said:an accelerometer doesn't measure acceleration in free fall
I had -and still have- an issue with your "retrospective" because I was not thinking about Newtonian mechanics but about special relativistic mechanics with classical "know-how". As a matter of fact, now that I think of it: Einstein even developed GR based on the understanding that SR can handle accelerated frames! But I think that you are right that many people for some time afterward lacked that understanding, if that is what you meant. It's a mystery to me how this original understanding which was rather well explained in papers could have been lost or mixed up for a while.stevendaryl said:You're certainly right, that noninertial frames came up in Newtonian mechanics. So where did the idea that GR was necessary to handle an accelerated reference frame come from?
I think that part of it is the insistence on relativity. [...] Nobody bothered (as far as I know) to try to write Newtonian mechanics in a way that treated all coordinate systems equally. I don't think that the latter was developed until after GR (the Newton-Cartan formulation of Newtonian physics).
It is not a universal IRF. In case you forgot: you can infer my answer (and even infer Einstein's answer), from my earlier reply here:adoion said:I forgot to mention:
if the elevator (rocket) accelerates under the influence of an gravitational field (at the turnaround) then what would we have ? [...]
even from the point of view of special relativity, this has to be a IRF since the laws of stay unchanged in their simplest form.
harrylin said:I had -and still have- an issue with your "retrospective" because I was not thinking about Newtonian mechanics but about special relativistic mechanics with classical "know-how". As a matter of fact, now that I think of it: Einstein even developed GR based on the understanding that SR can handle accelerated frames! But I think that you are right that many people for some time afterward lacked that understanding, if that is what you meant. It's a mystery to me how this original understanding which was rather well explained in papers could have been lost or mixed up for a while.
stevendaryl said:[...]
Einstein's paper, which does invoke GR to explain the paradox, is an example of bad pedagogy. There is nothing "GR" about it, except for the fact that Einstein maybe was a little unclear about the distinction between the use of noninertial coordinates and gravity.
This is not the only method of forming a non inertial coordinate systems, and as mentioned before it has its own problems.PhoebeLasa said:using a non-inertial reference frame for the rocket-twin which is formed by piecing together multiple inertial frames that are each momentarily co-moving with the rocket-twin at different instants of his life.
DaleSpam said:This is not the only method of forming a non inertial coordinate systems, and as mentioned before it has its own problems.
PhoebeLasa said:Alternative SR methods that have been proposed don't agree with the standard GR method.
PhoebeLasa said:But the momentary co-moving inertial frames method is the only (SR) method that exactly agrees with the often-cited standard GR method ... both give the result that the rocket-twin says that the home-twin suddenly gets much older during the turnaround. Alternative SR methods that have been proposed don't agree with the standard GR method.
In the present paper we recall the definition of ‘radar time’ (and related ‘radar distance’) and emphasise that this definition applies not just to inertial observers, but to any observer in any spacetime. We then use radar time to derive the hypersurfaces of simultaneity for a class of traveling twins, from the ‘Immediate Turn-around’ case, through the ‘Gradual Turn-around’ case, to the ‘Uniformly Accelerating’ case. (The
‘Immediate Turn-around’ and ‘Uniformly Accelerating’ cases are also discussed in Pauri et al.
We show that in all cases this definition assigns a unique time to any event with which Barbara can send and
receive signals,
and that this assignment is independent of any choice of coordinates. We then demonstrate that brief periods of acceleration have negligible effect on the radar time assigned to distant events, in contrast with the sensitive dependence of the hypersurfaces implied by Figures 1 and 2. By viewing the situation in different coordinates we further demonstrate the coordinate independence of radar time,
and note that there is no observational difference between the interpretations in which the differential aging is ‘due to Barbara’s acceleration’ or ‘due to the gravitational field that Barbara sees because of this acceleration’.
That can't be right. Einstein explains in that very same paper why the twin calculation can hardly be considered paradoxical in SR - at least, it surely wasn't paradoxical for people who correctly understood SR at the time. And Einstein understood rather well how to deal with accelerating frames, as -once more- his "induced gravitational fields" were in fact derived from his calculations with accelerating frames. Working backwards, he did not make any calculation error concerning accelerating frames as far as I can tell, and also according to the Physics FAQ: http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.htmlstevendaryl said:I think it was just a matter of figuring out the right pedagogy. Technically, there were no problems in applying SR to noninertial coordinate systems. The issue was how to "frame" what you were doing. Einstein's paper, which does invoke GR to explain the paradox, is an example of bad pedagogy. There is nothing "GR" about it, except for the fact that Einstein maybe was a little unclear about the distinction between the use of noninertial coordinates and gravity. [..]
harrylin said:That can't be right. Einstein explains in that very same paper why the twin calculation can hardly be considered paradoxical in SR - at least, it surely wasn't paradoxical for people who correctly understood SR at the time. And Einstein understood rather well how to deal with accelerating frames, as -once more- his "induced gravitational fields" were in fact derived from his calculations with accelerating frames
Perhaps many people who did not correctly understand SR, got the wrong impression that GR had to be used for accelerated objects frames and even accelerated objects, because Einstein argued that GR could be used like that?
You can also forego accelerating coordinate systems, and just analyze the time elapsed on an accelerating clock using the coordinates of some inertial frame in which you know the clock's coordinate position and velocity as a function of coordinate time. The trick is to approximate a smoothly-varying path by a polygonal path made up of a bunch of short inertial segments lasting a coordinate time [itex]\Delta t[/itex], that way the time elapsed on the clock on each segment will be [itex]\sqrt{1 - v^2/c^2} \Delta t[/itex], and then you can just add up the clock times on all the segments (using the appropriate v for each segment, which can vary from one to another) to get the total time elapsed on the polygonal path. Then you let the time of each segment become infinitesimal, so the sum becomes an integral and the total time elapsed on a clock with velocity as a function of time v(t) is just [itex]\int \sqrt{1 - v(t)^2/c^2} dt[/itex].Nugatory said:There's a widespread misconception that you need general relativity in situations involving acceleration, but it's just not true; special relativity handles acceleration just fine. You can google for "Rindler coordinates" for one example, and you'll find another example (a clock experiencing uniform circular motion due to the Earth's rotation) in Einstein's original 1905 paper to which ghwellsjr gave you a link above.
(note that the factor he gives is the result of a first-order approximation to the fully accurate formula [itex]t\sqrt{1 - v^2/c^2}[/itex])It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.
If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the traveled clock on its arrival at A will be [itex]\frac{1}{2} tv^2/c^2[/itex] second slow.
I see that you disagree with his argument; and for reasons different from yours, so do I. :)stevendaryl said:My point, as I said, is that the calculation has nothing really to do with GR [..] He's using SR in noninertial coordinates.
harrylin said:I see that you disagree with his argument.
Once more (and with this last repetition I end my discussion about this side topic): that is your main disagreement with Einstein. He admitted that " it is certainly correct that from the point of view of the general theory of relativity we can just as well use coordinate system K' as coordinate system K " , and the rest of that paper is his argument in defence of that position against critics.stevendaryl said:No, I don't disagree with his argument. I disagree that his argument involves General Relativity. [..].
harrylin said:He admitted that " it is certainly correct that from the point of view of the general theory of relativity we can just as well use coordinate system K' as coordinate system K " , and the rest of that paper is his argument in defence of that position against critics.
Einstein clarified that if one would make the mistake to consider the accelerating system K' as a valid "rest" system from the point of view of SR, in which only Galilean reference systems such as K are equivalent, one would create a twin paradox in SR. That has now been explained on this forum many times, even in this thread. The point from which you distracted is the fact that Einstein and his contemporaries knew very well how to handle acceleration in SR.stevendaryl said:I agree that it is correct from the point of view of GR, but it's ALSO correct from the point of view of SR.
harrylin said:Einstein clarified that if one would make the mistake to consider K' as a valid "rest" system from the point of view of SR, in which only Galilean reference systems such as K are equivalent, one would create a twin paradox in SR.
stevendaryl said:Yes, the equations do not have the same form in a non-inertial coordinate system. But that's a fact about SR. The derivation that Einstein gave is an SR derivation. Of course, it's valid in GR, as well, but there is nothing specifically GR about it.
His derivation is an SR derivation, because he did not make use of any of the differences between SR and GR.
K' is invalid as "rest frame" in SR. Despite our differing disagreements with Einstein, we agreed a long time ago on the point that I made, which is that Einstein and others understood acceleration in SR. It was not in "retrospect" that General Relativity was not needed to calculate the twin problem. Einstein never suggested that GR would be needed for the calculation. However, from my discussion with you I now slightly change my hypothesis about how that misunderstanding may have come about. For it now seems plausible to me that many people may have misunderstood Einstein's arguments in his papers from 1916-1918 that GR could be used for accelerated frames and even accelerated objects, so that they misconstrued that according to Einstein GR had to be used. And that's all that I will hypothesize about that. :)stevendaryl said:Yes, the equations do not have the same form in a non-inertial coordinate system. But that's a fact about SR. The derivation that Einstein gave is an SR derivation. Of course, it's valid in GR, as well, but there is nothing specifically GR about it.
His derivation is an SR derivation, because he did not make use of any of the differences between SR and GR.
harrylin said:K' is invalid as "rest frame" in SR.
Einstein certainly agreed with that. I promised to leave our disagreement about the issue that you next brought up, as it is irrelevant for my clarification that obviously this was not "retrospectively" understood - instead it was understood right from the start.stevendaryl said:SR as a theory of physics is not about rest frames. That's a way to talk about SR, and a way to derive the Lorentz transformations, but as a theory of physics, it makes claims about the behavior of clocks and rods and light signals and so forth. Those claims can be expressed in any coordinates you like. The fact that they were originally derived for inertial reference frames is irrelevant [..] There is nothing about using K' that requires going beyond SR.
harrylin said:Einstein certainly agreed with that. I promised to leave our disagreement about the issue that you next brought up, as it is irrelevant for my clarification that obviously this was not "retrospectively" understood - instead it was understood right from the start.
stevendaryl said:I know, I'm not arguing about that. I'm arguing about something else related to GR/SR and the twin paradox, which is the idea that somehow SR says that the traveling twin isn't in a "valid rest frame" while GR says otherwise. That doesn't make any sense. If Einstein said that, then that was very misleading of him.
OK. :)stevendaryl said:I know, I'm not arguing about that.
It is misleading to pretend that there is no difference at all between 1916 GR and modern GR... In a nutshell:I'm arguing about something else related to GR/SR and the twin paradox, which is the idea that somehow SR says that the traveling twin isn't in a "valid rest frame" while GR says otherwise. That doesn't make any sense. If Einstein said that, then that was very misleading of him.