Absolutely rotationless reference frames?

[Hiero]

So there are no "absolutely motionless" reference frames, but is there a set of reference frames which could be described as "absolutely rotation-less"?

 

[Drakkith]

I believe so. As far as I know, rotation is frame-invariant. If you measure yourself as rotating, then you are indeed rotating. If you measuring yourself as not rotating, then you are not.

 

[Hiero]

The universe then does "prefer" a set of reference frames?
So the angular velocity of a reference frame (or object) is an absolute quantity?

Am I alone in thinking this is quite a profound idea? I have never heard this point be talked about.

 

[Drakkith]

The universe then does "prefer" a set of reference frames?

I don't believe so.

So the angular velocity of a reference frame (or object) is an absolute quantity?

That is my understanding, though I don't know any of the details on how to show this.

Am I alone in thinking this is quite a profound idea? I have never heard this point be talked about.

I find it about as profound as the fact that there are no preferred inertial frames. Why should one be more profound than the other or more profound than any other physical law?

 

[Hiero]

The universe then does "prefer" a set of reference frames?

I don't believe so.

Well I mean how some classical physicists thought about there being an 'absolute reference frame' ("the ether") but found it not to be the case. Well instead of there being a single absolute reference frame ("the ether"), you are telling me there is a set of them (the rotation-less ones).

I can't help but see it as "the ether" but with regards to rotation as opposed to translation.

I find it about as profound as the fact that there are no preferred inertial frames. Why should one be more profound than the other or more profound than any other physical law?

I suppose by "profound" what I really mean is that the idea doesn't sit right with me. The idea of everything being relative and no inertial reference frame being preferred is a comfortable one; the idea of certain frames having some absoluteness to them is almost unsettling.

 

[Bandersnatch]

The idea of everything being relative and no inertial reference frame being preferred is a comfortable one;

Focus on the word 'inertial' here. Rotating frames are not inertial. That's all. Non-rotating frames are as profound as any other kind of non-accelerating ones.

 

[Drakkith]

Well instead of there being a single absolute reference frame ("the ether"), you are telling me there is a set of them (the rotation-less ones).

No, I'm telling you that rotation is invariant. This does not mean that rotating frames are equivalent to an "absolute" or "preferred" inertial reference frame. One of the key things with an absolute inertial frame is that certain physical laws don't hold in another frame. For example, one of the possible consequences is that the speed of light would not be the same in all directions if you were moving with respect to this absolute inertial frame.

I suppose by "profound" what I really mean is that the idea doesn't sit right with me. The idea of everything being relative and no inertial reference frame being preferred is a comfortable one; the idea of certain frames having some absoluteness to them is almost unsettling.

Why? There are plenty of things that are not relative. Mass (invariant), rotation, acceleration, and others.

 

[Hiero]

So angular velocity, as a vector, is an absolute quantity of an object. I just want to make sure I understand this correctly. I suppose all I'm technically saying is there are set of frames which lack any centrifugal forces.

I've just never thought about this very much. It makes me wonder things like;
What is my rotation right now?
Are there places/times when the rotation and the orbit of Earth cancel and I'm rotation-less in space?
Are objects (say on my table) then exerting different tensions to balance centrifugal forces at different times/places (say now compared to a different part of Earth's orbit about the Sun)?

 

[Drakkith]

So angular velocity, as a vector, is an absolute quantity of an object. I just want to make sure I understand this correctly. I suppose all I'm technically saying is there are set of frames which lack any centrifugal forces.

As far as I know, that's right.

Are there places/times when the rotation and the orbit of Earth cancel and I'm rotation-less in space?

Are objects (say on my table) then exerting different tensions to balance centrifugal forces at different times/places (say now compared to a different part of Earth's orbit about the Sun)?

Honestly, I'm not sure how to treat objects in free-fall.

 

[jbriggs444]

What is my rotation right now?

If you are sitting still relative to the earth, you are rotating once every sidereal day.

In the context of Newtonian mechanics, you are also accelerating in a complicated path due to continental drift, the tides, the jack hammer next door, the Earth's rotation about its axis, its orbit around the Sun, the Sun's motion within the milky way, etc, etc.

Are there places/times when the rotation and the orbit of Earth cancel and I'm rotation-less in space?

If, instead of sitting in a chair, you stand on a turntable aligned with the Earth's axis and turn at a rate of once every 23 hours, 56 minutes and a few seconds in a direction opposite the Earth's rotation then you will be free of rotation.

Cancelling your acceleration is trickier and depends on how you account for gravity. In the Newtonian model, you have to identify all gravitating masses, determine the local acceleration of gravity and apply enough counter-balancing force to negate it. In the model of General relativity, gravity is not a force, free fall trajectories are unaccelerated and all you have to do is jump up in the air.

Are objects (say on my table) then exerting different tensions to balance centrifugal forces at different times/places (say now compared to a different part of Earth's orbit about the Sun)?

The Earth rotates at the same rate regardless of whether it is near the sun (January) or far from it (July). Tidal gravity from the Sun theoretically causes stresses in an object on a table on Earth. And those stresses would change slightly based on the distance to the sun. But you'd have to do some monumentally precise work to verify this with experiment. Tidal gravity from the sun most certainly produces measurable stresses in the Earth. The obvious measurable result is the phenomena of spring and neap tides.

I am not certain whether the variation in the Earth's orbital distance from the sun produces measurable seasonal variations in the differential between spring and neap tides.

 

[Dale]

Well I mean how some classical physicists thought about there being an 'absolute reference frame' ("the ether") but found it not to be the case. Well instead of there being a single absolute reference frame ("the ether"), you are telling me there is a set of them (the rotation-less ones).

Yes, these frames are called "inertial" to identify their physically special character. Note that inertial frames do not have any kind of acceleration including rotation, linear acceleration, expansion, etc. So rotation is just one of many forms of non inertial motion which is absolutely identifiable.

I suppose by "profound" what I really mean is that the idea doesn't sit right with me. The idea of everything being relative and no inertial reference frame being preferred is a comfortable one; the idea of certain frames having some absoluteness to them is almost unsettling.

No inertial frame is preferred over any other inertial frame. Any inertial frame is equally distinguishable from any non inertial frame.

I am not sure that we can help how you feel about this stuff, but we can help explain it.

 

[zwierz]

So the angular velocity of a reference frame (or object) is an absolute quantity?

No. There is only angular velocity of one reference frame relative another one. Absolute motion and particularly absolute rotation is nonsense

 

[jbriggs444]

No. There is only angular velocity of one reference frame relative another one. Absolute motion and particularly absolute rotation is nonsense

As @Dale has pointed out, a rotating frame can be distinguished from an inertial frame. It is not a relative measurement. It is "absolute" in the relevant sense.

 

[Dale]

No. There is only angular velocity of one reference frame relative another one. Absolute motion and particularly absolute rotation is nonsense

Rotation can be measured without reference to another reference frame. It is not relative, it is invariant.

 

[zwierz]

has pointed out, a rotating frame can be distinguished from an inertial frame.

what does notion "inertial" do with pure kinematic notion "rotation"? Ok, give me please definition of "rotating frame"

 

[zwierz]

and also give me a definition of angular velocity

 

[Nugatory]

what does notion "inertial" do with pure kinematic notion "rotation"? Ok, give me please definition of "rotating frame"

and also give me a definition of angular velocity

A rotating frame is a frame in which some rotating object is at rest, in the sense that the spatial coordinates assigned by that frame to all parts of that object remain constant.

A rotating object can be recognized in an absolute sense, without relying on any reference frame, by measuring the proper acceleration of each part of that object.

The angular velocity is a parameter that relates the proper acceleration of any given part of the rotating object to its distance from the point of the object that experiences zero proper acceleration.

 

[zwierz]

A rotating frame is a frame in which some rotating object is at rest

So you replaced the word "frame" with the word "object".
Then what is "rotating object"?

by measuring the proper acceleration of each part of that object.

what is a proper acceleration?

 

[Nugatory]

S
what is a proper acceleration?

Proper acceleration is what an accelerometer measures. Because an accelerometer measurement yields the same result in all frames, we don't need any concept of reference frame to talk about proper acceleration.

We can then use measurements of proper acceleration at various points on an object to determine whether the object is rotating, again without any concept of reference frame. That's what Drakkith was getting at above when he said that rotation is frame-invariant.

Now that we have a frame-independent way of determining whether an object is rotating (that is, making a statement about the proper acceleration at various parts of the object) we can consider various reference frames. Some of these have the property that the spatial coordinates of each point on the object are constant, and others do not. By convention we call the ones that do have this property "rotating frames".

 

[gmax137]

To the OP, I too see this as a "profound" subject. At least, it caught my attention when I first came across these ideas.

The contrast between Newton's Bucket and Mach's principle. I'm not sure there is any way to settle the difference, since we cannot do experiments in and otherwise empty universe. Maybe someone here who understands general relativity can say how the ideas work out in that context?

https://en.wikipedia.org/wiki/Bucket_argument

https://en.wikipedia.org/wiki/Mach's_principle

 

[zwierz]

Proper acceleration is what an accelerometer measures.

and how do you deduce formula $\boldsymbol a=\dot{\boldsymbol v}$ from this definition ?

 

[Nugatory]

and how do you deduce formula $\boldsymbol a=\dot{\boldsymbol v}$ from this definition ?

You don't. That's the definition (note that it is a definition, not something that we deduce) of coordinate acceleration, which is an altogether different (and frame-dependent) thing.

Because coordinate acceleration is frame-dependent, if you search hard enough you will always be able to find an inertial frame in which the coordinate acceleration at a point is at least momentarily equal to the proper acceleration... and that can tempt you into thinking that the two are more tightly related than they are.

 

[Dale]

Ok, give me please definition of "rotating frame"

Are you familiar with accelerometers? Particularly the 6 degree of freedom kind?

A rotating reference frame (loosely) is one where 6DF accelerometers at rest show 0 linear proper acceleration but nonzero rotation.

 

[zwierz]

You don't. That's the definition (note that it is a definition, not something that we deduce) of coordinate acceleration, which is an altogether different (and frame-dependent) thing.

Because coordinate acceleration is frame-dependent,

Exactly. By definition, acceleration is relative to a frame and the same is true for angular velocity. Yes, there is a class of frames such that the accelerometer shows the same results relative to all the frames from this class, so called inertial frames. But it is a physical phenomenon. Let us do not mix up physical phenomena and mathematical (kinematical) definitions.

 

[jbriggs444]

Exactly. By definition, acceleration is relative to a frame

Proper acceleration is invariant. It is the same no matter what frame of reference you adopt.

 

[zwierz]

Proper acceleration is invariant.

the thing you are calling "Proper acceleration" is the acceleration relative to an inertial frame

 

[Hiero]

The Earth rotates at the same rate regardless of whether it is near the sun (January) or far from it (July). Tidal gravity...

I'm not concerned with tidal effects. What I was referring to is the change in angular speed of the Earth about the Sun; wouldn't this change the angular velocity of objects on my table thus causing different centrifugal effects? And yes I realize this effect would be very small and unmeasurable I'm just curious as to if I understand correctly, but I think I do now. Thank you for your detailed response, jbriggs.

To the OP, I too see this as a "profound" subject. At least, it caught my attention when I first came across these ideas.

The contrast between Newton's Bucket and Mach's principle. I'm not sure there is any way to settle the difference, since we cannot do experiments in and otherwise empty universe. Maybe someone here who understands general relativity can say how the ideas work out in that context?

https://en.wikipedia.org/wiki/Bucket_argument

https://en.wikipedia.org/wiki/Mach's_principle

Thank you, I feel like you hit the nail on the head as far as what is bothering me: it is Mach's perspective that resonates with me. I know it makes no operational difference, so perhaps my gripe was not really in the spirit of physics, but I would just prefer to think all motion is ultimately relative.

An example of why I prefer that perspective:
What if we spun the entire universe, (whatever that means,) would everything feel centrifugal forces? Even though the stars would appear "fixed" still?
(The above question is rhetorical and not well posed, it's not meant to be answered, it's meant to explain why absolute rotation is an uncomfortable notion for me.)

Anyway thank you for the links, I feel better knowing about Mach's idea.

 

[jbriggs444]

the thing you are calling "Proper acceleration" is the acceleration relative to an inertial frame

And it is still invariant.

 

[jbriggs444]

I'm not concerned with tidal effects. What I was referring to is the change in angular speed of the Earth about the Sun; wouldn't this change the angular velocity of objects on my table thus causing different centrifugal effects?

The Earth rotates at the same rate, once every 23 hours, 56 minutes and a few seconds (in the "absolute" sense that you originally had in mind) regardless of how fast it is revolving around the sun.

 

[Nugatory]

the thing you are calling "Proper acceleration" is the acceleration relative to an inertial frame

No. Proper acceleration is the deviation between the worldline of the object in question and a geodesic tangent to that worldline. This definition has nothing to do with any frame, whether inertial or not.