Inertial and non inertial frames

[bgq]

So you're looking for the reason that makes Newton's laws true in some frames while not true in others?

Yes, that is exactly my point.

 

[Dale]

If so, can you please give me simple clear consistent undebatable answers to the following two simple clear questions?

1) Does the acceleration depend on the frame of reference?

The question is not clear. By "acceleration" do you refer to "coordinate acceleration" or "proper acceleration". Also, since acceleration is a vector are you referring to a dependency of the components, the underlying geometric object, or the norm?

 

[TrickyDicky]

The question is not clear. By "acceleration" do you refer to "coordinate acceleration" or "proper acceleration". Also, since acceleration is a vector are you referring to a dependency of the components, the underlying geometric object, or the norm?

AFAIK, we were discussing "absolute" acceleration, which people here has identified with proper acceleration explaining it away as a "local observable". But that suggests we should call local observables like proper time, "absolute time" which would be both wrong and confusing in a theory that bans absolute time and space. And what seems to bother the OP is that within SR, if the principle of relativity holds, there should not be any absolute motion, and that includes absolute accelerations. Vectorial components in afine spaces surely are frame dependent.


This quote from "Quantum gravity" by Carlo Rovelli might help (or confuse who knows):
"Generalizing relativity. Einstein was impressed by galilean relativity. The velocity of a single object has no meaning;only the velocity of objects with respect to one another is meaningful. Notice that, in a sense, this is a failure of Newton's program of revealing the "true motions". It is a minor, but significant failure. For Einstein, this was the hint that there is something wrong in the Newtonian conceptual scheme.
In spite of its immense empirical success, Newton's idea of an absolute space has something deeply disturbing in it. As Leibniz, Mach, and many others emphasized, space is asort of extrasensorial entity that acts on objects but cannot be acted upon. Einstein was convinced that the idea of such an absolute space was wrong. There can be no absolute space, no "true motion". Only relative motion, and therefore relative acceleration must be physically meaningful. Absolute acceleration should not enter physical equations."

 

[bgq]

AFAIK, we were discussing "absolute" acceleration, which people here has identified with proper acceleration explaining it away as a "local observable". But that suggests we should call local observables like proper time, "absolute time" which would be both wrong and confusing in a theory that bans absolute time and space. And what seems to bother the OP is that within SR, if the principle of relativity holds, there should not be any absolute motion, and that includes absolute accelerations. Vectorial components in afine spaces surely are frame dependent.


This quote from "Quantum gravity" by Carlo Rovelli might help (or confuse who knows):
"Generalizing relativity. Einstein was impressed by galilean relativity. The velocity of a single object has no meaning;only the velocity of objects with respect to one another is meaningful. Notice that, in a sense, this is a failure of Newton's program of revealing the "true motions". It is a minor, but significant failure. For Einstein, this was the hint that there is something wrong in the Newtonian conceptual scheme.
In spite of its immense empirical success, Newton's idea of an absolute space has something deeply disturbing in it. As Leibniz, Mach, and many others emphasized, space is asort of extrasensorial entity that acts on objects but cannot be acted upon. Einstein was convinced that the idea of such an absolute space was wrong. There can be no absolute space, no "true motion". Only relative motion, and therefore relative acceleration must be physically meaningful. Absolute acceleration should not enter physical equations."

It seems that you understand exactly what my point is. Thank you very much for this clarification.

 

[PAllen]

It seems that you understand exactly what my point is. Thank you very much for this clarification.

Key point: What Mach and Einstein sought in an ideal theory is one thing. What was achieved is completely different. Neither SR nor GR meet this criterion at all, which displeased Einstein as he came to realize that GR failed to achieve this Machian goal.

Thus, in discussing interpreting SR, you must accept its axiomatic structure - which includes, by assumption, a family of distinguishable inertial frames.

 

[bgq]

1) Hmm, I think I don't understand clearly the concept of "proper acceleration". Can anyone explain this to me in more details or give me some links? Thanks in advance.

2) I will try to explain my whole point in (as I hope) a very clear simple way: Newton's laws, accelerometer, ... are just ways to identify whether a frame is inertial or not, my question is what in this universe the reason that makes some frames inertial and others not?

 

[bgq]

Key point: What Mach and Einstein sought in an ideal theory is one thing. What was achieved is completely different. Neither SR nor GR meet this criterion at all, which displeased Einstein as he came to realize that GR failed to achieve this Machian goal.

Thus, in discussing interpreting SR, you must accept its axiomatic structure - which includes, by assumption, a family of distinguishable inertial frames.

So can we say that the theory assumes the existence of preferable frames called inertial frames without discussing the reasons that make such frames exist?

 

[Mentz114]

1) Hmm, I think I don't understand clearly the concept of "proper acceleration". Can anyone explain this to me in more details or give me some links? Thanks in advance.

2) I will try to explain my whole point in (as I hope) a very clear simple way: Newton's laws, accelerometer, ... are just ways to identify whether a frame is inertial or not, my question is what in this universe the reason that makes some frames inertial and others not?

Proper acceleration is the 'a' in F=ma. When an inertial mass is subject to a force there is proper acceleration.

The second question is a bit philosophical but the obvious answer seems to be 'inertia'.

 

[PAllen]

So can we say that the theory assumes the existence of preferable frames called inertial frames without discussing the reasons that make such frames exist?

Correct. So far, no accepted theory of physics provides an answer to why acceleration in an empty universe is detectable and absolute. It is not that scientists haven't tried - just that no attempt so far has led to a successful theory.

 

[DrGreg]

bgq

The following isn't intended to be rigorous but a simplified argument:

1. An inertial particle is defined to be one that moves freely without being influenced by any other forces
2. It's an experimentally observed fact that (in regions where the tidal effects of gravity are negligible) inertial particles move at constant velocity relative to each other. Physics can't really explain why this should be, it's just the way our universe works.
3. We use inertial particles to define inertial frames.
4. Proper acceleration of a particle is acceleration relative to the inertial frame in which it is momentarily at rest. Equivalently it's what an accelerometer measures. Equivalently (for those who understand the terminology) it's the norm of the particle's 4-acceleration vector. It follows from this that inertial particles are those that that have zero proper acceleration.
5. When people talk about "acceleration", you need to be clear whether they mean "proper acceleration", or "relative acceleration" = "coordinate acceleration". Every object has a unique proper acceleration (which any observer can calculate, and all get the same answer, and which the object can measure directly with an attached accelerometer without reference to any frames), but can have multiple coordinate accelerations dependent on who is calculating them.

 

[TrickyDicky]

So far, no accepted theory of physics provides an answer to why acceleration in an empty universe is detectable and absolute. It is not that scientists haven't tried - just that no attempt so far has led to a successful theory.

I think this is the most honest answer that can be given to the OP.

 

[Dale]

And what seems to bother the OP is that within SR, if the principle of relativity holds, there should not be any absolute motion, and that includes absolute accelerations.

This is clearly a misunderstanding of the principle of relativity, which is specific to inertial motion, not arbitrary motion.

 

[Dale]

It seems that you understand exactly what my point is. Thank you very much for this clarification.

Then you clearly misunderstand the principle of relativity in SR. See my comment to TrickyDicky above.

 

[Nugatory]

So can we say that the theory assumes the existence of preferable frames called inertial frames without discussing the reasons that make such frames exist?

I wouldn't say "preferable frames". I think "frames that behave in a particular way" might be a better way of phrasing it.

But with that said, yes, the theory assumes the existence of these frames. Of course we didn't just pull this assumption out of thin air; there is an enormous amount of observation and experience that suggests that the assumption is consistent with the way the world works, therefore is likely to be a good starting point for a useful theory.

 

[TrickyDicky]

This is clearly a misunderstanding of the principle of relativity, which is specific to inertial motion, not arbitrary motion.

Well, that is the special principle of relativity, and there I was thinking of the generalized principle, that includes arbitrary motion.
Anyway, are you saying that since SR postulates don't include arbitrary motion, proper acceleration should not be included in SR?

 

[Dale]

Anyway, are you saying that since SR postulates don't include arbitrary motion, proper acceleration should not be included in SR?

No, I didn't say that. I don't think that I said anything remotely close to that.

 

[haael]

My three euro-cents to this topic.

Inertial and non-inertial coordinate frames in SR are different in the thing that the latter are curvilinear! That's all.

Transformation between two inertial frames in SR always maps straight lines into straight lines. Transformation between inertial and non-inertial frame always maps straight time-like line into a curved one.

Acceleration of a frame is its internal property and one does not need any other frame to check it. Acceleration is a change of speed with time. In SR time is one of the dimensions. "Speed" of a frame is an angle between time and space base vectors of the frame. Acceleration is change of that angle with time. That means, the angle between the base vectors is not constant. Back in the terms of speed, a frame is accelerating if it has different speed at some moment compared to its own speed a moment before. The speed of a frame is compared to the speed of the very same frame at a different moment. We don't need any other frame to check it.

Inertial frames of reference are the frames that use straight lines as the time axis. The transformations of frames with different speed (boosts) change the straight lines into other straight lines of different direction. There is no preferred direction in SR, so this is a symmetry. On the other hand, transformations with frames of a different acceleration map straight time-like lines into curved ones. There is no symmetry in SR that requires straight and curved lines to be equivalent, so there is an absolute acceleration.

In GR, the concept of "straight" is replaced with a concept of "geodesic". A geodesic may be straight or may be not and that is an objective fact (one of the axioms in fact). If a particle is moving along a geodesic, it feels no acceleration. If a geodesic happens to be a straight line, a particle is not affected by any force at all. If a geodesic is not a straight line and a particle is moving along it, then it is free-falling due to gravitational force, but can not feel it. If a particle is moving along a non-straight non-geodesic line, then it feels non-gravitational acceleration. Finally, if a particle is moving along a straight but non-geodesic line, then it means that it is opposing gravity. This is often called hovering, but it need not be - for example humans standing on Earth surface are a case of that situation. We are not free-falling, but instead we are a subject to a force that exactly balances gravity.

So, in GR:
1. straight geodesic lines - no acceleration at all
2. non-straight geodesic lines - gravitational acceleration (free fall)
3. straight non-geodesic lines - force cancelling gravity
4. non-straight non-geodesic lines - unbalanced non-gravitational acceleration

In SR every geodesic is straight, so we have to consider only cases 1 and 4.

 

[TrickyDicky]

No, I didn't say that. I don't think that I said anything remotely close to that.

So explain what you mean then, if you claim that relativity doesn't handle arbitrary motion, I take it you mean it is specific to inertial frames, but at the same type you claim you didn't mean by that that it can't deal with absolute acceleration, IOW arbitrary motion. Please clarify.

 

[TrickyDicky]

Inertial and non-inertial coordinate frames in SR are different in the thing that the latter are curvilinear! That's all.

That is coordinate acceleration, but here it is proper acceleration that is the issue.

 

[haael]

That is coordinate acceleration, but here it is proper acceleration that is the issue.

A particle is properly accelerating if it is moving along a curved path. The curvature of a line is an objective fact, so there is an absolute acceleration.

 

[Mentz114]

A particle is properly accelerating if it is moving along a curved path. The curvature of a line is an objective fact, so there is an absolute acceleration.

Good point. You don't need to compare a curve to a straight line to tell it is curved.

 

[TrickyDicky]

A particle is properly accelerating if it is moving along a curved path. The curvature of a line is an objective fact, so there is an absolute acceleration.

Sure, but you were talking about SR and curvilinear coordinates, and that is what I responded to. Don't confuse coordinates with physical observables, that is a very common thing around here.

 

[Mentz114]

Sure, but you were talking about SR and curvilinear coordinates, and that is what I responded to. Don't confuse coordinates with physical observables, that is a very common thing around here.

Proper acceleration is a tensor and cannot be transformed away.

 

[A.T.]

AFAIK, we were discussing "absolute" acceleration, which people here has identified with proper acceleration explaining it away as a "local observable". But that suggests we should call local observables like proper time, "absolute time" which would be both wrong and confusing in a theory that bans absolute time and space.

It is neither wrong nor confusing. In this context "absolute vs. relative" just means "frame invariant vs. frame dependent". Proper time intervals are "frame invariant" or "absolute". The notion that "everything is relative in Relativity" is a very common misconception. In fact Einstein originally wanted to call it "theory of invariants", to put the emphasis on the "absolute" quantities.

 

[bgq]

Thank you all for your replies, they are very helpful.

 

[TrickyDicky]

It is neither wrong nor confusing. In this context "absolute vs. relative" just means "frame invariant vs. frame dependent". Proper time intervals are "frame invariant" or "absolute".

It might have been not the best example to make my point, that's true, but what I considered wrong was saying time is absolute in SR and I maintain it. That is not the same as saying that the proper time interval is frame invariant which is of course right.

The notion that "everything is relative in Relativity" is a very common misconception. In fact Einstein originally wanted to call it "theory of invariants", to put the emphasis on the "absolute" quantities.

Nonody here has claimed that "everything is relative".

 

[harrylin]

[..] when we say accelerating (and so non inertial), we mean accelerating with respect to a certain frame (According to both classical and special relativity). What is this frame?
According to the classical theory, the answer is very clear: It is the absolute rest frame, but in SR it seems (to me) that there is something missing. It is not the issue how to test whether a frame is inertial or not, I know the whole story of this, but the issue is what initially makes some frames inertial and the others not? If we say that non inertial frames are those that are accelerating, this has no meaning unless we specify with respect to what frame.

I think that you are using the argument of Newton ("rotating bucket"), enhanced by arguments of Langevin (radiation, "twin paradox")¹. Indeed, quite some early relativists took the stationary ether model for granted despite the fact that it plays no direct role in the equations - the issue being that it can interpreted as playing an indirect role. Later many relativists replaced this by the block universe interpretation². Welcome to the "family of the knowing".

1. https://www.physicsforums.com/showthread.php?p=4111027
2. https://www.physicsforums.com/showthread.php?t=583606

 

[TrickyDicky]

Proper acceleration is a tensor and cannot be transformed away.

It is actually a vector but I don't know what you mean.

 

[Mentz114]

It is actually a vector but I don't know what you mean.

For example, we can find the acceleration of a comoving frame field by calculating U^β∇_αU_β. This is manifestly a tensor, so its components can't all be reduced to zero by a coordinate transformation.

But you know this so why the question ?

 

[bgq]

Thank you very much Harrylin, the links are interesting.

 

[TrickyDicky]

For example, we can find the acceleration of a comoving frame field by calculating U^β∇_αU_β. This is manifestly a tensor, so its components can't all be reduced to zero by a coordinate transformation.

But you know this so why the question ?

I can't see the relation of what you are posting with what is being discussed in the thread.

 

[PAllen]

For example, we can find the acceleration of a comoving frame field by calculating U^β∇_αU_β. This is manifestly a tensor, so its components can't all be reduced to zero by a coordinate transformation.

But you know this so why the question ?

I always think of proper acceleration as the absolute derivative by proper time of the 4-velocity. This is clearly a 4-vector defined on a path.

 

[Mentz114]

I can't see the relation of what you are posting with what is being discussed in the thread.

You started it. Your interventions are generally cryptic and unintelligible to me so I'll leave you to it.

 

[Mentz114]

I always think of proper acceleration as the absolute derivative by proper time of the 4-velocity. This is clearly a 4-vector defined on a path.

Yes this is so. But I did state clearly I was talking about a vector field, a congruence. I have never found a case where one is satisfied and the other not. I'm not smart enough to work out when it will happen.

 

[PAllen]

Yes this is so. But I did state clearly I was talking about a vector field, a congruence. I have never found a case where one is satisfied and the other not. I'm not smart enough to work out when it will happen.

There is a theorem that restricting a field (covariant) gradient to a path, versus the absolute derivative along a path, will always produce the same result. This was discussed in a recent thread here. I don't have a chance now to find it. Conceptually, if I am talking about particle, I think of absolute derivative on a path. If thinking of a congruence, then a gradient makes sense.