Understanding Classical Physics: Frame of Reference

[Dan Andersen]

So I understand that in classical physics, movement only makes sense with reference to another body. So my car moves relative to the surface of the road, for example. But it seems that with acceleration, things appear to be more complicated than that. Let's say we have two objects in space. One is accelerating relative to the other, and as an outside observer, I can't tell which unless I have some kind of objective frame of reference. But the objects can tell, because one of them experiences the acceleration and the other does not. Put in another way, if I spin myself around and around, how can I tell that I'm spinning, and the universe is not? Of course, I can feel centrifugal force acting on my body, so I know it's me; but who is to say that the universe shouldn't be spinning instead? Is there some kind of objective frame of reference that says that something is fixed?

FYI - my physics is limited to college PHYS101, so please keep it simple if you can.

 

[PeterDonis]

Is there some kind of objective frame of reference that says that something is fixed?

No. As you say, acceleration that is actually felt (this is more precisely termed "proper acceleration", although that term is more common in relativity than in Newtonian mechanics) is objective; it doesn't change if you change which body you are defining "motion" in reference to. But motion itself is still relative.

For example, there is nothing to stop you from saying that, if you pirouette on skates, for example, you are "motionless" and the rest of the Universe is spinning around you. This is a perfectly consistent way to describe things. But it doesn't change that fact that, as you pirouette, you feel centrifugal force, while the distant stars that are "spinning around you" do not.

 

[A.T.]

you feel centrifugal force

You don't feel inertial forces. You can use inertial forces to explain the mismatch between the interaction forces, which you actually can feel, and the coordinate acceleration, which you observe in your non inertial frame.

 

[PeterDonis]

You don't feel inertial forces.

Yes, good point, I misspoke. I should have said that, when you pirouette, you feel proper acceleration, while the distant stars that are "spinning" around you do not.

 

[Dan Andersen]

Thanks for the input.
Let me ask a little different way.

I found a wikipedia article that describes the phenomena: http://en.wikipedia.org/wiki/Absolute_rotation

So it seems that Newton said that there was an absolute point of reference to determine rotation: the fixed stars.
Since the stars are fixed, if we rotate relative to them, we are objectively rotating.

But of course, we know now that the stars aren't fixed.

Now Mach's principal (http://en.wikipedia.org/wiki/Mach's_principle) suggests that Newton, though not exactly correct, might have been on to something. Even though the start aren't fixed,
"mass out there influences inertia here"

so, if I'm reading this correctly, the aggregate mass of the universe forms the point of reference.
Is that an accurate understanding of Mach?

Is that a currently accepted scientific position?

 

[PeterDonis]

Newton said that there was an absolute point of reference to determine rotation: the fixed stars.

Yes. But he neglected to explain how that is consistent with the principle of relativity, which says that there is no such thing as absolute motion. Which, of course, is what prompted your question. But if you're thinking that Newton left something out, yes, you're right, he did. (Arguably he had to; physics was just not ready at that time to deal with what he left out. But he knew he was leaving it out; there are passages in his writings where it's pretty clear that he recognized that the picture of physics he was presenting was incomplete.)

How does modern physics answer the question?

First, answering it in the context of modern physics requires relativity, which is technically off topic for this forum (it should be in the relativity forum). So if you want to dig further into what I'm about to say, you should start a new thread in the relativity forum.

The general idea in relativity is that what determines the proper acceleration that an object feels, when it is in a particular state of motion, must be something local, not something distant like the fixed stars. That something local is called the "metric"; at each event in spacetime (i.e., each point in space, at every instant of time), there is a metric that determines, for all possible states of motion of objects passing through that event, which objects feel acceleration (and how much they feel), and which do not. So, for example, the fact that the skater feels acceleration when she pirouettes, while a person standing next to her and not pirouetting does not, is due to the metric at her location in spacetime. (Actually, I'm leaving out an acceleration that they both feel--their weight, due to being on the surface of the Earth instead of out in space. This is the same for both of them, and we're interested here in the difference between them. But it's important to recognize that the weight they both feel, but a rock falling in their vicinity does not, is also due to the metric.)

So, having reduced the question of "what defines rotation?" to the question of "why does the pirouetting skater feel acceleration while a non-pirouetting person does not?", and answered that question with "because of the metric", the next obvious question is, "why is the metric what it is?" In General Relativity, the answer to that question is called the Einstein Field Equation: it links the metric to the matter and energy that is present in spacetime. So ultimately, what determines "rotation"--and in general what determines which states of motion feel what acceleration--is the matter and energy in the universe, acting on spacetime through the Einstein Field Equation.

So in a sense, Newton was right when he said the "fixed stars" determine rotation. The overall metric of the universe is determined by the overall distribution of matter and energy in it, and that distribution is basically symmetrical about the Earth and the solar system. If you work out the implications of that using the equations of GR, you will find that the prediction is that the "non-rotating" state--the one that feels no acceleration due to rotation--is the one that is not rotating relative to the "fixed stars". But the GR picture of why this happens is much less problematic than Newton's picture.

 

[Dale]

Hi Dan, welcome to PF!

Now Mach's principal (http://en.wikipedia.org/wiki/Mach's_principle) suggests that Newton, though not exactly correct, might have been on to something. Even though the start aren't fixed,
"mass out there influences inertia here"

so, if I'm reading this correctly, the aggregate mass of the universe forms the point of reference.
Is that an accurate understanding of Mach?

I would second what Peter said above, but in addition I would like to directly address the question about Mach.

Mach's principle is intuitively quite appealing, but is not rigorously defined so that everyone agrees what it means physically. GR is usually considered non-Machian, but agrees with the data better than more Mach-compatible alternatives. So, Machs principle itself is suspect, as appealing as it is, it is not clearly compatible with reality.

Peter, please chime in if you think I am overstating this.

 

[PeterDonis]

Mach's principle is intuitively quite appealing, but is not rigorously defined so that everyone agrees what it means physically.

I think this is a very important point. GR is, as you say, considered "non-Machian", but it still embodies a lot of what Mach seemed to be wanting when he talked about his principle. Having the metric be determined through the Einstein Field Equation basically amounts to having "mass there govern inertia here". (For a book-length dissertation on this, see Cuifolini and Wheeler's Gravitation and Inertia.)

The problem is that, while I said that the Einstein Field Equation links the metric to the presence of matter and energy, that's not all that's required to obtain a solution. You also need to make additional assumptions to pin down a unique spacetime. For example, when I said that if no matter and energy is present, as in SR, spacetime is flat Minkowski spacetime, what I actually should have said is that if no matter and energy is present anywhere in spacetime, and if we assume that spacetime is nonsingular everywhere and has topology ##\mathbb{R}^4##, then spacetime is flat Minkowski spacetime. If we drop those additional assumptions, there are other solutions of the EFE that also have no matter or energy anywhere (these are called "vacuum" solutions, and include the familiar Kerr-Newman "black hole" spacetimes).

The need to make those additional assumptions to pin down a unique solution is part of why GR is considered "non-Machian"--the Machian purists believe that a Machian theory would be one where no additional assumptions are needed beyond specifying the matter and energy content. But is that "really" required by Mach's principle? There is no full agreement on the answer to questions like that, so not everybody really agrees on what "Mach's principle" means.

 

[Dan Andersen]

Thanks All! These were spectacular answers.
I'm surprised to see that this seemingly simple question wasn't definitively settled centuries ago.
I expected to find a purely classical straight-forward explanation to the phenomena,
but the answer is much more interesting than I anticipated.

I still don't have a full grasp of the problem, or the solution, but I'm light years ahead of where I was a couple days ago.

 

[A.T.]

I'm surprised to see that this seemingly simple question wasn't definitively settled centuries ago.

It might never be settled, because we cannot remove / manipulate the rest of the universe, to see how it affects local inertia here.

 

[Nugatory]

... but the answer is much more interesting than I anticipated.

That's why people never get tired of studying this stuff!

The only thing I could add to the answers above is that you might try googling for "Galilean relativity" and "non-inertial classical frame" for more detailed discussions.