Implications of the statement "Acceleration is not relative"

harrylin

Of course it's always possible to be at rest relative to oneself and to define non-inertial reference frames and coordinate systems. However such a reference frame isn't what is implied with "at rest" in the context of SR, which relates the physics to inertial frames: you have remarked that yourself. And saying that something is in rest in a frame in which we define it to be in rest ("the rocket is at rest in its non-inertial frame") is simply meaningless.
Not sure to parse that correctly; some of the text of Langevin that I omitted argues for absolute space. That's a matter of opinion.
Once more, "at rest" in SR normally means at rest in an inertial coordinate system that one chooses as "rest system". In no SR space diagram is the rocket continuously "at rest", because it is moving during part of the voyage no matter which inertial system one chooses as "rest" system.

ghwellsjr

Actually, Event B is of no consequence in the definition of your scenario. As long as we know the rocket's speed and where (or when) it turns around, that defines the end point.

However, I'd like you to consider an issue related to the one you just raised here and that is, how does the rocket know when to turn around? The rocket cannot know from any direct measurement when the Earth has traveled 10 units away in the rocket frame. That distance is the difference between the spacial components of Event B and C which are simultaneous in the Earth frame but which have a distance between them of 16.67 in the rocket frame. Even if the rocket had instant access to the remote information, it would still have to do some calculation if it's based on distance to determine when to fire its rockets.

To me, a much cleaner way to specify the Twin Paradox is to state the Proper Time on the traveler's clock when he should fire the rockets to turn around. This has the advantage that it doesn't require the specification of any reference frame. In fact, it doesn't even require fully specifying any events since we don't care about the spatial component. So if we know how long it takes for the traveler to get to the turnaround point and we know how fast he is traveling, those two parameters fully specify the complete Twin Paradox scenario (assuming of course that he is returning at the same speed he left at). I fully explained this in the thread you linked to in your opening post.

harrylin

Quite so; with the demotion of pseudo gravitational fields one returns to Langevin's argument that acceleration has "absolute" effects that everyone can observe -even for the case that the accelerometer reading remains zero.
One can always choose a coordinate system to be always at rest in; once more, that is meaningless for the physics. However, it is certainly true that proper acceleration (both definitions of it) is quantitatively agreed upon by all. If that's all you wanted to understand, then you have certainly achieved your goal.
That person, if indeed he denies to be changing his state of motion, will have to explain the physical causes for the observed effects; and I mistakenly thought that you were contemplating the different physical explanations that are given in the literature. If and when you come to that point, you may want to read earlier comments and references that were provided in this discussion.

ghwellsjr

T&W never consider non-inertial frames or a frame in which the traveler is at rest, at least not when discussing the Twin Paradox. What they are dismissing is the explanation that I gave in post #23 of the thread you linked to in your OP. I considered three Inertial Reference Frames which included different rest states of the two twins. I attempted to show that any one of them was adequate to explain everything about the scenario, which is pretty much the classic way of explaining the Twin Paradox. But they think they have a better way which involves any observer calculating the spacetime interval between pairs of events. I don't think that helps at all but since they are writing the book, they get to decide when the objectors are happy. But real objectors, like you, remained unhappy.

GregAshmore

True. But no one is claiming that the rocket is at rest in an inertial frame--not even the twin in the rocket. The twin in the rocket feels the unbalanced force of the rocket engine, and he knows (or would know upon reunion) that the twin on earth feels no such force. Even without the formal definitions of inertial and non-inertial, the rocket twin would recognize that his situation is fundamentally different than that of his twin. Fully aware of that difference, he claims that he is at rest throughout the episode.

I don't see how the claim is disproved by pointing out that the rocket changes inertial frames during the firing of the engine. The change of inertial frames only confirms what everyone knows: the rocket is non-inertial. From the earth twin's point of view, the rocket is in an inertial frame, accelerates, and comes to rest in another inertial frame. The rocket twin disagrees with this assessment. He can point to the spacetime diagram (which the earth twin accepts as valid) and show that he remains at rest in his own frame, even while not at rest in any one inertial frame. To prove the rocket twin wrong, it must either be shown that his frame moved with respect to some absolute position marker, or that the laws of dynamics are violated if he does not move. There is no absolute position marker, and the laws of dynamics are not considered in my analysis. [If these statements are wrong, at least they are not bald statements; I've done my homework. ]

GregAshmore

I read that post in its entirety before opening this thread. I didn't catch on to what you were doing because in each of the diagrams the rocket twin is spoken of as moving for part of the trip.

What helped me was to realize that in the typical two-frame spacetime diagram, the world line of an inertial particle shows the particle both as moving and at rest. It is moving in one frame, and at rest in the other frame. Thus, the one spacetime diagram actually shows the case I wanted to see-the case in which the rocket twin considers himself at rest. The symmetrical diagram (which is invalid) is not needed.

GregAshmore

It would be of consequence for the person who mistakenly believes that because either object can be the one that appears to turn around, the spacetime diagram can be drawn with either object having the bent worldline. Event B is where the Earth would turn around. I chose to show at this juncture that the Earth cannot change inertial frames because it experiences no unbalanced force; because it is inertial.

It is a cleaner solution. Yet even now I feel the [vestigial] reflexive urge to tune it out because it says the rocket twin "travels", "turn[s] around", "return[s]". The doubter has been told that in relativity the rocket has the same right to be at rest as the Earth has. Language of motion applied to the rocket speaks so loudly that it drowns out the perfectly valid point that is being made.

For perspective, I have read two or three explanations of the twin paradox to my 30+ son. He has some technical training, has a job that requires him to evaluate contractual language. He had exactly my reaction, without me making any comment.

DaleSpam

The two definitions are equivalent. The Smoot definition basically just pushes the use of accelerometers one step further. Instead of reading the proper acceleration directly off the accelerometer, you define an inertial frame by strapping accelerometers to your clocks and rods, ensuring that they read 0, and then reading the proper acceleration off the clocks and rods.

DaleSpam

Which he can do quite easily simply by stating the laws of physics in a covariant form and then using any coordinates where his state of motion does not change.

harrylin

The physical meaning of "in rest" is very well clarified in Einstein's 1918 paper.
Once more, that is true for Einstein's example and completely wrong (even in two ways) for Langevin's example. "At rest" in the sense that you adopt here only makes sense in the way Einstein elaborates - and that isn't SR.
For a last time, as we've been here twice before: everyone can always claim to be at rest in his own frame; such a statement cannot be disproved. You could just as well state that you're in your own world. That's physically meaningless.

harrylin

I prefer his definition as he doesn't confound a displacement with a force; and it does make a difference when using it in SR, due to the different definition of "inertial frame" in SR.

my_wan

What has been repeated here is that either object CANNOT be the one that appears to turn around because all observers MUST agree on which one accelerated, just as the one that accelerated is also the only one to experience a g force as a result.

You are confusing Einstein's term, most probably with respect to the explanation given for the principle of equivalence. IF every agrees on what happened, even if not to what degree, we are by definition talking about an absolute, not relative event. The relative terms of that absolute involve only the quantitative value associated with it. That is the point we are trying to make with the distinction between coordinate acceleration and proper acceleration.

harrylin

As I suspect that you also don't copy Einstein's physical explanation, I'm curious to know which physical explanation that you found in the literature you fancy for the moving and faster aging Earth with a stationary rocket (let's stay away from personal ideas). How can the firing of the rocket engine move the rest of the universe while keeping the rocket's state of motion unaffected?

DaleSpam

Any way you can determine if your frame is inertial or not is a way of determining your proper acceleration, i.e. it is an accelerometer. You cannot get away from using accelerometers.

harrylin

We have discussed that before, and I found that your definition of "inertial frame" is at odds with that of classical mechanics wrt which SR is defined; as a matter of fact, it's already at odds with Einstein's 1905 paper and Langevin's 1911 paper. So, let's agree to disagree; but if you even disagree to agree to disagree, then I'll just add some links to earlier discussions later, as IMHO everything has been said already.

ADDENDUM: see
http://physicsforums.com/showthread.php?p=4117808
In post #190 I provided three operational ways with which such reference frames can be defined/determined.
See also post #200 there and a 4th defintion (by Einstein) in post #264:
http://physicsforums.com/showpost.ph...&postcount=264

DaleSpam

The phrase "appears to turn around" (emphasis added) seems to refer to coordinate acceleration, in which case it would not be true that all observers must agree on it. If you intended the statement to refer to proper acceleration then it is a little confusing.

I think that GregAshmore understands the distinction between coordinate and proper acceleration, so I think that the rest is just miscommunication about which "flavor" of acceleration is being discussed at any one moment.

DaleSpam

Some links would help. I don't remember that discussion.