- #1
Hiero
- 322
- 68
So there are no "absolutely motionless" reference frames, but is there a set of reference frames which could be described as "absolutely rotation-less"?
Hiero said:The universe then does "prefer" a set of reference frames?
Hiero said:So the angular velocity of a reference frame (or object) is an absolute quantity?
Hiero said:Am I alone in thinking this is quite a profound idea? I have never heard this point be talked about.
Drakkith said:I don't believe so.Hiero said:The universe then does "prefer" a set of reference frames?
Drakkith said: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?
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.Hiero said:The idea of everything being relative and no inertial reference frame being preferred is a comfortable one;
Hiero said: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).
Hiero said: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.
Hiero said: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.
Hiero said:Are there places/times when the rotation and the orbit of Earth cancel and I'm rotation-less in space?
Hiero said: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)?
If you are sitting still relative to the earth, you are rotating once every sidereal day.Hiero said:What is my rotation right now?
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.Are there places/times when the rotation and the orbit of Earth cancel and I'm rotation-less in space?
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.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)?
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.Hiero said: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).
No inertial frame is preferred over any other inertial frame. Any inertial frame is equally distinguishable from any non inertial frame.Hiero said: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. There is only angular velocity of one reference frame relative another one. Absolute motion and particularly absolute rotation is nonsenseHiero said:So the angular velocity of a reference frame (or object) is an absolute quantity?
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.zwierz said: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 said:No. There is only angular velocity of one reference frame relative another one. Absolute motion and particularly absolute rotation is nonsense
what does notion "inertial" do with pure kinematic notion "rotation"? Ok, give me please definition of "rotating frame"jbriggs444 said:has pointed out, a rotating frame can be distinguished from an inertial frame.
zwierz said:what does notion "inertial" do with pure kinematic notion "rotation"? Ok, give me please definition of "rotating frame"
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.and also give me a definition of angular velocity
So you replaced the word "frame" with the word "object".Nugatory said:A rotating frame is a frame in which some rotating object is at rest
what is a proper acceleration?Nugatory said:by measuring the proper acceleration of each part of that object.
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.zwierz said:S
what is a proper acceleration?
and how do you deduce formula ##\boldsymbol a=\dot{\boldsymbol v}## from this definition ?Nugatory said:Proper acceleration is what an accelerometer measures.
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.zwierz said:and how do you deduce formula ##\boldsymbol a=\dot{\boldsymbol v}## from this definition ?
Are you familiar with accelerometers? Particularly the 6 degree of freedom kind?zwierz said:Ok, give me please definition of "rotating frame"
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.Nugatory said: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,
Proper acceleration is invariant. It is the same no matter what frame of reference you adopt.zwierz said:Exactly. By definition, acceleration is relative to a frame
the thing you are calling "Proper acceleration" is the acceleration relative to an inertial framejbriggs444 said:Proper acceleration is invariant.
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.jbriggs444 said:The Earth rotates at the same rate regardless of whether it is near the sun (January) or far from it (July). Tidal gravity...
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.gmax137 said: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
And it is still invariant.zwierz said:the thing you are calling "Proper acceleration" is the acceleration relative to an inertial frame
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.Hiero said: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?
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.zwierz said:the thing you are calling "Proper acceleration" is the acceleration relative to an inertial frame
What does your "No" mean? So if I calculate acceleration as ##\boldsymbol a=\ddot{\boldsymbol r}## (here ##\boldsymbol r## is a radius-vector of inertial frame )and if I calculate proper acceleration, do I obtain different results?Nugatory said: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.
I am talking about the contribution of angular velocity due to Earth's orbit. The angular velocity of the orbit of Earth varies throughout the year, right? And to find the absolute angular velocity of Earth we would need to consider this contribution?jbriggs444 said: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.
jbriggs444 said: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.
It means that your statement "the thing you are calling 'Proper acceleration' is the acceleration relative to an inertial frame" is incorrect. The proper acceleration is completely independent of any reference frame.zwierz said:What does your "No" mean?
Not proper accelerationzwierz said:By definition, acceleration is relative to a frame
The motion of the Earth about the sun is completely and utterly irrelevant to the rotation rate of the Earth.Hiero said:I am talking about the contribution of angular velocity due to Earth's orbit. The angular velocity of the orbit of Earth varies throughout the year, right?
And to find the absolute angular velocity of Earth we would need to consider this contribution?