Implications of the statement "Acceleration is not relative"

GregAshmore

As a result of the discussion which ensues from this post I hope to understand the implications of this statement: "Acceleration is not relative."

First, I think it will be helpful to establish some context.

Context point 1: I am not an "objector" looking for a paradox, or hoping to catch relativists in a contradiction. I am asking my question in good faith, ready to learn from those who know more than I. (I reserve the right to evaluate responses, as any intellectually honest person must do, but I promise to give a fair and open-minded hearing to all.)

Context point 2: Since my last post, in which I made a dumb mistake in the interpretation of the spacetime diagram (or rather, failed to check my mental image of a pole-in-barn episode against the spacetime diagram), I've worked through the problem in sufficient detail to understand my mistake, and hopefully avoid similar mistakes in future. So, you are not (I hope) wasting your time as you respond to my question. [As a side note, I have not succeeded in forming a mental picture of the "one reality represented by the spacetime diagram", as I had hoped to do. I've come to the conclusion, for now at least, that there is no way to form such a mental image from the spacetime diagram. The Lorentz transformation provides a means of predicting how an episode (collection of events) will be observed in any chosen inertial reference frame. If an extra-frame view of the episode is to be had, it is not going to come from the spacetime diagram by itself.]

Context point 3: Having come to an understanding of the pole-in-barn paradox, I was naturally drawn to consider the last remaining paradox that is unresolved for me. This is the twin paradox. One might say that there are two aspects to the paradox. The first is that the twins would be of different ages when they meet at the end of the episode. That is not really a paradox; it is explained by the notion of proper time, and well illustrated by a spacetime diagram in which the earth is considered to be at rest and the rocket twin is moving. The second aspect of the twin paradox comes about when one considers the rocket twin to be at rest and the earth to be moving. In that case, it is the earth twin who will be younger, a contradiction in that both twins cannot be younger. That paradox I have not resolved, though I have read multiple explanations of it. Yesterday I decided to try again.

I began with Taylor and Wheeler. The twin paradox is dealt with in section 4.6 of Spacetime Physics. The proper time for each twin is calculated, showing the age difference on return of the traveler. Then, the (always rude and unreasonable) objector says, "If there is any justice, if relativity makes any sense at all, it should be equally possible to regard you [the earthbound twin] as the stay-at-home." There follows a detailed explanation that ends with, "notice that the traveler is unique in changing frames, only the traveler suffers the terrible jolt of reversing direction of motion." But this explanation does not address the objection, for the objection is that the rocket twin should be considered at rest. A resting twin cannot reverse motion. The jolt that the resting rocket twin feels must come from some other cause than reversal of motion.

I went to Born, in Einstein's Theory of Relativity. In VI-5, he deals with the objection of the resting rocket twin by asserting that only the rocket twin accelerates. Once again, it seems to me that this objection sidesteps the issue, for by definition the resting rocket twin does not accelerate.

So this morning I searched on this forum, wishing to avoid being the 9,488th person to ask about the twin paradox. I found this thread. Quite quickly I saw what must be at the root of the explanation of the paradox, but which I do not recall ever seeing stated explicitly: "Acceleration is not relative." (This statement was not challenged in the first twelve pages; and anyway I think it merits its own thread.)

I say "at the root of the explanation" because it is the immediate implication of the statement which avoids the paradox: The rocket twin cannot be considered at rest. (More precisely, the rocket twin cannot be considered at rest while he is accelerating. This is implicit in ghwells statement in post #161.)

This statement, to one who began the study of relativity with Einstein's Relativity, is nothing short of shocking. In a religious context (which this is not, of course, but the analogy is too striking to omit mention), this would be tantamount to heresy.

So I went to Einstein's book to see if I had missed something. No, I don't think so. He begins by expressing his desire to bring acceleration into the realm of the principle of relativity. In doing so, his development of the equivalence of inertial and gravitational mass is premised on the example of a man in an accelerating chest who considers himself to be at rest.

I then reread Einstein's own explanation of the twin paradox. Again, the rocket twin is unambiguously at rest when the rocket frame is the reference frame.

It is quite clear to me that Einstein considered acceleration to be relative, and that he considered it perfectly justifiable to consider an observer who accelerates with respect to an inertial frame to be at rest.

I will take a moment here to object to the reason given for the claim that acceleration is not relative. The reason given (post #10 and following) is that acceleration may be independently measured, or felt, without reference to some other frame. But what one measures or feels is force, not acceleration. This distinction, together with the necessary equivalence of inertial mass and gravitational mass in all frames, is the basis for Einstein's claim that an observer in an accelerating frame may consider himself to be at rest in a gravitational field.

What are the broader implications of the statement that acceleration is not relative? Does this mean, as it certainly would appear to mean, that modern relativity is in this very important respect not Einsteinian relativity? Are there other implications as to the meaning of the principle of relativity?

DaleSpam

If you will go back to post #10 you will see that I already discussed this objection in the * comments.

Do you understand the difference between proper acceleration (the kind of acceleration measured by accelerometers independently of any reference frame) and coordinate acceleration (the kind of acceleration relative to some reference frame)?

GregAshmore

My objection is that accelerometers do not measure acceleration, but force. Force does not imply acceleration--at least, not according to Einstein.

GregAshmore

I should probably mention why I have had difficulty accepting Einstein's explanation of the paradox. In it, the gravitational field is posed as the result of induction from the distant stars. I don't see how a gravitational signal (which as I understand travels at the speed of light) can cause the force felt by the resting rocket traveler. It is true that Einstein first argues that the gravitational field is just as real as kinetic energy, which also "disappears" with the appropriate choice of reference frame. But he does not seem convinced by this explanation, and looks to the massive stars as the source.

DaleSpam

They measure proper acceleration. Proper acceleration does not imply coordinate acceleration.

I get the impression that you may not be familiar with the distinction between the two concepts. Here are some places to start:

http://en.wikipedia.org/wiki/Accelerometer
http://en.wikipedia.org/wiki/Proper_acceleration

PeterDonis

[Edit: I see I didn't type fast enough. However, I still think the following is worth consideration.]

The first thing to do, IMO, is to state it properly (pun intended, as you will see in a moment):

Proper acceleration is not relative. (It is a direct observable.)

Coordinate acceleration is relative. (It depends on the coordinates you adopt.)

This distinction is crucial; it's only a very slight exaggeration to say that every time I've seen someone confused about "acceleration", it's because they're confusing the two types of acceleration given above.

Yes, that's correct, and it's good that you recognize it; if only all the people who have been posting twin paradox threads recently would do so... However, you don't appear to fully understand *why* it is true. See below.

No, this is not correct. The calculation of the two proper times, which is illustrated in a spacetime diagram in which the stay-at-home twin is at rest, as you say, assumes that the stay-at-home twin is at rest in a single inertial frame (the frame in which the diagram is drawn) for the entire scenario. The traveling twin does not satisfy that condition; there is no single inertial frame in which he is at rest for the entire scenario. So you can't run the same argument for the traveling twin.

If you define "motion" as "inertial motion", then this is true. But with this definition of "motion", you *cannot* simply declare by fiat that you are going to consider the rocket twin as being at rest. "Being at rest", on this definition of "motion", is not a convention; it's a physical condition that can be objectively tested--just test whether the observer feels acceleration. The traveling twin does; the stay-at-home twin doesn't. So the stay-at-home twin can be considered to be "at rest", but the traveling twin can't.

Alternatively, you could define "motion" in such a way that you can legitimately say that the traveling twin does not "reverse motion", so he can be considered "at rest" during the entire scenario. But if you do *that*, then you can't simply declare by fiat that the twin who is "at rest" is the one whose proper time is greater. You have defined "at rest" so that it no longer always corresponds to maximal proper time; an observer "at rest" may feel acceleration, and if he does, you will be able to find some other observer who experiences more proper time between two given events than the observer "at rest" does.

Notice that I have basically just re-stated what I said at the start of this post, that proper acceleration is not relative. The traveling twin has a nonzero proper acceleration for at least some portion of his trip; the stay-at-home twin has zero proper acceleration during the entire scenario. That is an invariant physical difference between them.

It does; it comes from his firing the rocket. There's no need to stipulate that his motion "reverses". The fact of his feeling acceleration, where the stay-at-home twin does not, is an objective physical difference between them that doesn't depend on whether or not he "reverses motion".

Here you are, once again, confusing proper acceleration with coordinate acceleration. The "resting" twin does not have any coordinate acceleration; but that doesn't mean he has no proper acceleration. And it's proper acceleration that is relevant for determining elapsed proper time, because proper acceleration is the direct observable.

Again, see my clarification at the start of this post. Which someone probably gave in the thread you linked to; certainly I've given it in plenty of twin paradox threads lately, in more or less the form I've given it here.

This is true if you define "at rest" as "at rest in an inertial frame". Which I believe was the implicit definition of "at rest" that was being used in that thread. The reason it's a common definition is that, as I said above, inertial motion has special properties, physically, because it corresponds to zero proper acceleration and therefore maximal proper time. If you define "at rest" to allow observers with nonzero proper acceleration to be "at rest", as I noted above, you lose that key property.

Note that the man feels acceleration; he feels his own weight and can stand on the "floor" of the chest as he would stand on the Earth's surface. So he has nonzero proper acceleration, and if he is considered to be "at rest" then we have adopted a definition of "at rest" which does not guarantee that "at rest" corresponds to "maximal proper time".

Again, don't confuse coordinate acceleration with proper acceleration. Einstein did consider coordinate acceleration to be relative; the observer who accelerates with respect to an inertial frame has nonzero coordinate acceleration with respect to that inertial frame, but zero coordinate acceleration with respect to his own "rest frame" (which is not an inertial frame). But he has nonzero proper acceleration regardless of which frame you choose; proper acceleration is not relative, and Einstein agreed with that too.

This is a distinction without a difference, because in order to make this claim, you have to define "force" in such a way that only "proper force" (force that corresponds to nonzero proper acceleration) is defined as a force. So gravity is *not* a force on this definition; a person at rest on Earth's surface, for example, does *not* feel the "force of gravity"; he feels the force of the Earth's surface pushing up on him. A person who only moves under the "force of gravity", such as an observer in orbit about the Earth, feels *no* force; he is moving inertially, in free fall, weightless. Similarly, the traveling twin feels the force of his rocket engine pushing on him, whereas the stay-at-home twin never feels any force at all. Just substitute "feels force" for "feels acceleration" in everything I said above and all my arguments still go through just fine.

It means you have to pay attention to the crucial distinction between proper acceleration (or "feeling force", if you like that term better) and coordinate acceleration (which may or may not correspond to a felt force). The latter is relative; the former is not.

No. The distinction was always there in relativity, and Einstein was well aware of it.

Only that, once again, the difference between inertial and non-inertial motion (feeling no force vs. feeling a force, in the terms you appear to prefer) is an observable, invariant physical difference; it's not relative.

GregAshmore

I will read them. The premise of Einstein's approach, as I understand it, is that there is no acceleration at all in the reference frame of the resting rocket twin--proper or otherwise.

PeterDonis

No, that's not the premise. There is no coordinate acceleration, but there is proper acceleration. You can't make proper acceleration disappear by changing frames; it's an invariant. Einstein knew that.

DaleSpam

[Now it is my turn to not type fast enough ]

I am not sure when the term "proper acceleration" was coined, but it is safe to say that if Einstein made such a premise then he was refering to coordinate acceleration.

Proper acceleration is the measurement on an accelerometer, so it is necessarily a frame invariant quantity. All coordinates will agree on the reading on an accelerometer even though they may not agree that the reading represents (coordinate) acceleration.

Perhaps you can see the parallel between proper time and coordinate time. Proper time is the measurement on a clock, so it is necessarily a frame invariant quantity. All coordinates will agree on the reading on a clock even though they may not agree that the reading represents (coordinate) time.

GregAshmore

This is an inference.

Again, the bold text is an inference. Einstein interprets the behavior of the instrument in two ways. Observed from the inertial reference frame, it is indeed acceleration that causes the displacement and counteracting force. Observed from the non-inertial frame, it is a gravitational field and the forcible restraint from acceleration that displaces the mechanism. There is no acceleration in the non-inertial frame, according to Einstein's interpretation.


The bold text is contrary to Einstein's explicit statement that there is no gravitational field in the inertial frame. What does not exist in the frame cannot act on the observer in the frame. He explicitly and repeatedly states that the gravitational field exists only in the non-inertial frame. I'm not saying that I agree or disagree with his interpretation; just that this is his interpretation.

Nugatory

All it means is that Einstein was sometimes careless about distinguishing between coordinate and proper acceleration when it was clear from the context which was intended.... And there's no broader implication beyond that. Coordinate acceleration is relative and can be produced without applying any force, simply by choosing non-inertial coordinates. Proper acceleration is not relative, doesn't depend on the coordinates, and happens if and only if a force is applied.

You are right that it is force rather than acceleration that we measure directly, but if we have net force we can infer (proper) acceleration; we don't get one without the other.

Alain2.7183

The Wikipedia page on the twin paradox, in the section on the "viewpoint of the traveling twin", explains the use of "gravitational time dilation" (via the "equivalence principle") to resolve the paradox from the traveler's viewpoint. The result is that, according to the traveler, the home twin's age increases a lot during the traveler's turnaround, enough to more than make up for the home twin's slower aging when the traveler isn't turning around. They also show how to get that same result, by using accelerated motion instead of a fictitious gravitational field.

Nugatory

Those are ways of calculating the differential aging in the traveler's coordinate time. They do not change the coordinate-independent facts: the traveler follows a path of shorter proper time; the traveler clearly is not inertial for his entire journey.

PeterDonis

This is a matter of terminology, not physics. The acceleration--or force, if you prefer--that is felt by the mechanism is the same regardless of which frame you use. That's the physics. Similarly, in the twin paradox, the traveling twin feels a force; the stay-at-home twin does not. That's a physical difference, and it's there regardless of which frame you use to describe the scenario.

DaleSpam

I would call it a definition, but your manner makes me curious. What is wrong with inference? It seems like you are using it as a perjorative, but I don't understand why.

Therefore, the proper acceleration is frame invariant.

There is no coordinate acceleration in the non inertial frame.

ghwellsjr

What statement of mine are you referring to in post #161?

stevendaryl

Why do you say that? Conceptually, you could think of an accelerometer as just a box with a metal ball in the center held in place by springs. When you accelerate the box, the position of the ball within the box is altered. By measuring the position of the ball, you can determine the acceleration of the box.