Absolutely rotationless reference frames?

[zwierz]

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.

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?

 

[Hiero]

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.

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?

I'm not sure why you say Earth rotates absolutely at that same rate throughout the year... you even said yourself:

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.

 

[Nugatory]

What does your "No" mean?

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.

 

[Dale]

By definition, acceleration is relative to a frame

Not proper acceleration

 

[jbriggs444]

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?

The motion of the Earth about the sun is completely and utterly irrelevant to the rotation rate of the Earth.

 

[Hiero]

The motion of the Earth about the sun is completely and utterly irrelevant to the rotation rate of the Earth.

See I don't understand this statement. Let me try to elaborate my perspective:

Suppose we had a planet tidally locked in an elliptic orbit about the sun (so on the planet there are no days). As the planet is closer to the sun, it will move through a larger angle per time than when it is far from the sun, hence the planet would rotate at a larger angle per time in order to stay tidally locked, correct?

The same effect should remain if the planet isn't tidally locked (say Earth). This is what I'm referring to. I'm actually not sure if you're just saying this rotation is ignorable (2pi radian per year certainly is not much) or if you're saying it literally has no theoretical effect, in which case I would like to know what is wrong with my above understanding.

 

[Hiero]

Actually, I don't see why the effect should remain if it isn't tidally locked, sorry I'm not sure why I kept thinking that.

Edited to add:
It is the assumption that the length of an (apparent) day is fixed which leads to the conclusion that I had in mind (tidal-locking being a special case of this assumption) but of course this assumption is not true for Earth, it is the sidereal day which is constant in length, not the apparent day.

 

[Dale]

it is Mach's perspective that resonates with me.

Unfortunately, insofar as Mach's principle has been developed into something that can be tested experimentally, it seems that the universe does not follow it. Experiment and observations trump philosophy.

 

[Hiero]

Unfortunately, insofar as Mach's principle has been developed into something that can be tested experimentally, it seems that the universe does not follow it. Experiment and observations trump philosophy.

Can you elaborate or refer to such attempts? I had no success in searching it, but I did find this video which has some ideas from this thread. I find the bit at 6:43 in particular to be very interesting.

 

[Drakkith]

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.

Unfortunately it is not. Translational motion is relative, meaning that different frames will measure different rates of motion. A personal walking down the aisle of a train is moving slowly relative to a person sitting down on the train but is moving very quickly to a person on the ground. Rotation is not relative though. ALL frames will agree that a rotating frame is rotating and ALL frames will agree at what rate it is rotating at.

 

[jbriggs444]

Suppose we had a planet tidally locked in an elliptic orbit about the sun (so on the planet there are no days).
As the planet is closer to the sun, it will move through a larger angle per time than when it is far from the sun, hence the planet would rotate at a larger angle per time in order to stay tidally locked, correct?

How much angular acceleration do you think that tidal locking is able to produce in a satellite such as the Earth orbiting a star such as the Sun?

(2pi radian per year certainly is not much)

2 pi radians per year per year would be astromically huge.

 

[Hiero]

Unfortunately it is not. Translational motion is relative, meaning that different frames will measure different rates of motion. A personal walking down the aisle of a train is moving slowly relative to a person sitting down on the train but is moving very quickly to a person on the ground. Rotation is not relative though. ALL frames will agree that a rotating frame is rotating and ALL frames will agree at what rate it is rotating at.

Perhaps my words did not capture my meaning. Really the idea is not just about reference frames and rotation but also about mass. Mach's idea, summarized through my eyes, is that these centrifugal forces (by which we detect rotation of a frame) only arise by virtue of a mass's rotation relative to the greater mass distribution of the universe (as opposed to it's rotation relative to some absolute background space).

In other words, I prefer to think that, if we somehow keep Earth perfectly rotation-less, and then somehow begin rotating the rest of the mass in the universe, that Earth will experience centrifugal forces as if it were rotating.

Obviously this is not a viable experiment, I am just emphasizing that there are two distinct physical principles here (with different predictions) and it is unclear to me why either should be rejected. This is why I'm interested in the experiments that @Dale spoke of.

 

[Drakkith]

Obviously this is not a viable experiment, I am just emphasizing that there are two distinct physical principles here (with different predictions) and it is unclear to me why either should be rejected. This is why I'm interested in the experiments that @Dale spoke of.

I don't have any experiments for you, but perhaps you should ask yourself why they should be accepted instead of rejected? What reason would we have to accept that the universe is rotating? What does it mean to rotate the entire universe? Are all objects revolving around a central axis somewhere? That's problematic and probably violates the cosmological principle, but I admit I'm not certain.

 

[Hiero]

I don't have any experiments for you, but perhaps you should ask yourself why they should be accepted instead of rejected?

Well I'm not accepting it nor advocating it as a superior choice. I just think it is an idea worthy of consideration, which I personally prefer (and perhaps I will change that preference when I learn more).

What reason would we have to accept that the universe is rotating? What does it mean to rotate the entire universe? Are all objects revolving around a central axis somewhere? That's problematic and probably violates the cosmological principle, but I admit I'm not certain.

I don't mean to say the universe is rotating, just that if it were rotating on the whole, we wouldn't know. See the 4th minute of this video (particularly the point at about 5:00).

What does it mean to rotate the entire universe? Are all objects revolving around a central axis somewhere?

No, I don't mean the whole universe rotating together like some rigid body. Maybe it can be stated like this: 'the frames in which the universe has a net angular momentum of zero are the frames in which no centrifugal forces are felt.' This statement is still very fuzzy to me. Is the angular momentum of the entire universe even calculable (even in theory I mean)? Any time I have to consider "the entire universe" I feel like I've left the realm of physics.

 

[Drakkith]

I don't mean to say the universe is rotating, just that if it were rotating on the whole, we wouldn't know. See the 4th minute of this video (particularly the point at about 5:00).

I don't agree with this video. Specifically the statement that you only know you're rotating because you can reference the entire universe around you. A hypothetical society brought up inside of a very large, rotating, sealed environment would have little trouble developing the same physical laws we have despite the fact that they cannot observe the rest of the universe.

Note that pop-sci videos often present you with nice, pretty pictures and diagrams that make you feel like you understand what they're talking about. This is often not the case. We spend a great deal of time here at PF helping people get past misunderstandings brought on by these videos. You'd be amazed at how much nonsense is spread through these videos and other mediums.

No, I don't mean the whole universe rotating together like some rigid body. Maybe it can be stated like this: 'the frames in which the universe has a net angular momentum of zero are the frames in which no centrifugal forces are felt.' This statement is still very fuzzy to me. Is the angular momentum of the entire universe even calculable (even in theory I mean)?

No, because we cannot see the entire universe and will never be able to. But even if we could, this criteria doesn't work. All frames would measure the same total angular momentum. Besides, now you're talking about the angular momentum of objects within the universe. That may not be the same thing as saying the universe as a whole is rotating. Hence why I asked what it even means to say that the universe is rotating. Without a proper definition or description, is it useful to prefer it over the non-rotating description?

Any time I have to consider "the entire universe" I feel like I've left the realm of physics.

Indeed. It's always problematic to try to make statements about the universe and great care should be taken when doing so.

 

[Hiero]

I don't agree with this video. Specifically the statement that you only know you're rotating because you can reference the entire universe around you. A hypothetical society brought up inside of a very large, rotating, sealed environment would have little trouble developing the same physical laws we have despite the fact that they cannot observe the rest of the universe.

To be honest I'm not sure what you're talking about.

Note that pop-sci videos often present you with nice, pretty pictures and diagrams that make you feel like you understand what they're talking about. This is often not the case. We spend a great deal of time here at PF helping people get past misunderstandings brought on by these videos. You'd be amazed at how much nonsense is spread through these videos and other mediums.

Yes I'm sure, but I found that video after this thread was created. At any rate these ideas are in my mind somehow, so I will contemplate it all the same.

No, because we cannot see the entire universe and will never be able to.

This is a good point, but it could be restricted to the local (observable) universe.

But even if we could, this criteria doesn't work. All frames would measure the same total angular momentum.

What do you mean? Angular momentum is a quantity which depends on the coordinates with which it is measure with respect to. It depends not only on the location but also rotation of the coordinates, right? In other words, coordinate frames which are rotating with respect to each other will measure different angular momentum of the same object, right? So then I'm simply proposing that those frames which give zero angular momentum of the observable universe also give zero centrifugal force (i.e. are said to be absolutely rotation-less).
I am sure something is wrong with my statement, but in my mind it is how I understand mach's principle.

Besides, now you're talking about the angular momentum of objects within the universe.

Well of course. Like I said, it's not just about rotating frames, it's also about the mass distribution. Rotating mass gives angular momentum, hence angular momentum captures both aspects.

That may not be the same thing as saying the universe as a whole is rotating.

I just want to be clear; I don't mean 'if the universe as a whole is rotating', I mean 'if the universe on the whole is rotating,' i.e. there is a net angular momentum.
For example, the angular momentum of Earth would contribute to the angular momentum of the universe, even though the Earth is not rotating about some universally central axis.

Without a proper definition or description, is it useful to prefer it over the non-rotating description?

Oh it's certainly not useful in any respect. I do not prefer it as a physicist I prefer it as a human being. As a physicist I seek a more precise formulation, which I do not seem to be making progress towards.

 

[Dale]

Can you elaborate or refer to such attempts?

Here is a decent introduction of what I am referring to:

http://www.scholarpedia.org/article/Jordan-Brans-Dicke_Theory

 

[Drakkith]

To be honest I'm not sure what you're talking about.

Just think of the experiments we have done here on Earth to show that it's rotating. A simple experiment is to create a large pendulum and watch as it precesses over time.

To start, a small experiment can be done in which a pendulum is mounted on a rotatable base and rotated. Assign a frame of reference (which includes a coordinate system) to the base of the pendulum such that no point of the base moving. The pendulum's path in this coordinate system, the arc it makes as it move, changes over time, the result of the precession of the pendulum. This indicates that the frame of reference is rotating and all other frames of reference will agree with that.

Now, if the world isn't rotating, a large pendulum, whose base is stationary with respect to the ground, shouldn't have any precession. The arc the pendulum follows should remain the same over time. But if the world is indeed rotating, then the pendulum will precess, indicating that the ground itself is rotating as is everything attached to the ground. It doesn't matter if the scientists performing the experiments can see the rest of the universe or not.

Interestingly, this is similar to a scenario used by Einstein. He posited that an observer, unable to observe anything other than the room he was in, would not be able to tell if he was on the ground or if he was on an accelerating spaceship since all physical laws would be the same in either frame. See here: https://en.wikipedia.org/wiki/Introduction_to_general_relativity#Gravity_and_acceleration

Yes I'm sure, but I found that video after this thread was created. At any rate these ideas are in my mind somehow, so I will contemplate it all the same.

Honestly I wouldn't expect you to stop.

This is a good point, but it could be restricted to the local (observable) universe.

Sure, but that doesn't get you anywhere. See below.

What do you mean? Angular momentum is a quantity which depends on the coordinates with which it is measure with respect to. It depends not only on the location but also rotation of the coordinates, right? In other words, coordinate frames which are rotating with respect to each other will measure different angular momentum of the same object, right? So then I'm simply proposing that those frames which give zero angular momentum of the observable universe also give zero centrifugal force (i.e. are said to be absolutely rotation-less).
I am sure something is wrong with my statement, but in my mind it is how I understand mach's principle.

No, angular momentum is frame invariant. Imagine two frames which are rotating about the same axis at the same rate. Even though no points in either frame are moving with respect to each other, experiments can be done to show that the frames are rotating and measure how much angular momentum they have.

I just want to be clear; I don't mean 'if the universe as a whole is rotating', I mean 'if the universe on the whole is rotating,' i.e. there is a net angular momentum.
For example, the angular momentum of Earth would contribute to the angular momentum of the universe, even though the Earth is not rotating about some universally central axis.

We can already observe matter rotating about some axis. We can talk about the net angular momentum of whole regions of space. But, to me, this says nothing about whether the universe is rotating. It only says something about the distribution of matter within the universe and how it is moving. This doesn't seem to match up with the usual uses of the phrase "rotating universe" that I've seen, but perhaps I haven't looked into this topic enough.

 

[Hiero]

No, angular momentum is frame invariant.

This isn't how I understand angular momentum. In my eyes, it is simply defined as the sum of the cross product of position and momentum for all mass elements in the system. If we change frames (maybe change the location of the origin, maybe have the new frame move at a constant speed relative to the old, maybe give the frame a constant rotational speed) then we will generally find different angular momenta for the same system, because the position and momentum vectors will change with the frames.

Perhaps you're speaking of general relativity's definition of angular momentum (if that's a thing) or something else I know nothing of, but that is my basic understanding of the topic.

 

[Drakkith]

This isn't how I understand angular momentum. In my eyes, it is simply defined as the sum of the cross product of position and momentum for all mass elements in the system. If we change frames (maybe change the location of the origin, maybe have the new frame move at a constant speed relative to the old, maybe give the frame a constant rotational speed) then we will generally find different angular momenta for the same system, because the position and momentum vectors will change with the frames.

Hmmm. I admit this is getting a bit outside my area of expertise, so I think I'll have to let someone else answer that.

Perhaps you're speaking of general relativity's definition of angular momentum (if that's a thing) or something else I know nothing of, but that is my basic understanding of the topic.

I wasn't, but you did inspire me to look up more information on the topic and it seems that angular momentum isn't always conserved in curved spacetime. So that's probably important if you want to talk about angular momentum in cosmological scales.

 

[gmax137]

I just came across this thread
https://www.physicsforums.com/threads/inertia-and-machs-principle.916815/#post-5779364
that may be of interest to the OP.

 

[Buckethead]

No, angular momentum is frame invariant. Imagine two frames which are rotating about the same axis at the same rate. Even though no points in either frame are moving with respect to each other, experiments can be done to show that the frames are rotating and measure how much angular momentum they have.

Please don't forget about frame dragging. If an object is not exhibiting proper acceleration and is in a frame that is experiencing frame dragging and is also separated by an object (on the same rotational axis as above) such that the second object's frame is not being dragged, then it is possible that both objects can be rotating relative to each other while neither is experiencing proper acceleration.

 

[facenian]

This isn't how I understand angular momentum. In my eyes, it is simply defined as the sum of the cross product of position and momentum for all mass elements in the system. If we change frames (maybe change the location of the origin, maybe have the new frame move at a constant speed relative to the old, maybe give the frame a constant rotational speed) then we will generally find different angular momenta for the same system, because the position and momentum vectors will change with the frames.

You are right. It is easy to check that, when applying a Galilean transformation, the angular momentum defined with respect to a certain frame is not invariant when passing to another reference system that is moving with respect to the first one.

With regard to the initial question space and time in Newtonian mechanics are absolute concepts. In particular space is said to be absolute in a very particuar and philosophically uneasy manner because, althoug relative constant motion can not be detected with respect absolute space, acceletation and consecuently rotational motion can and this is precisely what gives meaning to absolute space. Newton was very soon criticized for this defect in his theory.
On the other hand, although Special Relativity overthrew Newton's absolute time ,it did not change the concept of absolute space.

 

[Dale]

@facenian If you take a blank sheet of paper and draw a straight line and a curved line then you can say that the straight line is straight and the curved line is curved without placing any coordinates on the paper. There is no "absolute vertical" nor "absolute horizontal" implied by the fact that the curved and straight lines are distinguishable.

 

[facenian]

@Dale I'm not sure if I have understood you point. Absolute space in the Newtonian sense does not mean that there is an absolute vertical or horizontal direction neither it means that straight lines are diferent from curved lines only because the existence of absolute space. The problem resides with motion itself because from a kinematical point of view only relative motion is meaningful and this is so even in Newtonian mechanics "but only" for a certain class of rectilinear motion which determines the class of inertial frames. The problem stems from the words "but only". It Is this fact that gives rise to "Absolute Space" because rectilinear acceleration(and rotation) with respect to absolute space can be dectected without reference to any other frame(or body) with respect to which motion is measured.