Is rotation absolute or relative?

[Johnny5]

Here is an article at Wolfram about rotation. In the article you will see mention of a rotation matrix.

 

I'd like to discuss this particular article, with a view in mind to answer the question, "is rotation absolute or relative."

 

This is going to help me in my ongoing analysis of precession, and things like Foucalt's pendulum. I am hoping to learn something new, and resolve a hundred or so unanswered questions of mine.

 

The article starts off with what is a very important statement, as regards the mathematical analysis of rotating frames of reference. The article begins:

 

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes.

 

I do not see them as conventions. Something deeper, which involves the very meaning of "inertial reference frame" is going on.

 

There may be some kind of mathematical equivalence between rotating objects in stationary coordinate systems, and stationary objects in rotating coordinate systems, but there is a physical difference.

 

My point is this, I don't think the mathematical treatment brings out the physics of rotation.

 

If you read down into the Wolfram article, which is extremely well written, you will notice the following:

 

Any rotation can be given as a composition of rotations about three axes (Euler's rotation theorem), and thus can be represented by a matrix operating on a vector,

 

Somewhere in the Euler rotation theorem lies a connection to the aerospace concepts of: yaw, pitch, and roll.

[LKL]

Sorry, this may be a little off your main point, but the Wolfram article gave me a massice head-ache...

 

What's the physical difference between "rotating objects in stationary coordinate systems, and stationary objects in rotating coordinate systems"?

 

The only one I can think of is that a rotating coordinate system would have a non-Euclidean geometry.

 

Also, what kind of analysis are you doing of precession, purely mathematical or experimental as well?

[Johnny5]

Sorry, this may be a little off your main point, but the Wolfram article gave me a massice head-ache...

 

It's not necessary to start the thread off with a massive amount of mathematics. I was hoping to slowly move from simple things about rotating frames of reference, to the math. Hopefully we can both avoid headaches, although matrices are not that complicated, but certainly if you aren't familiar with linear algebra, you dont have a chance at understanding rotation explained in terms of matrices. However, and this would be my point, I think anyone can develop an intuitive understanding of rotation, without knowing matrix algebra, which is the reason I started off this paragraph by saying, "it's not necessary..." So don't worry about matrices for now.

 

What's the physical difference between "rotating objects in stationary coordinate systems' date=' and stationary objects in rotating coordinate systems"?

 

The only one I can think of is that a rotating coordinate system would have a non-Euclidean geometry. [/quote']

 

I'm not an expert with non-euclidean geometry, but if you know a bit about that, you can try to show me how it connects.

 

I was thinking more of something like Mach. Suppose nothing in the universe existed, other than a single billiard ball. Make it an eight ball.

 

Now choose a reference frame to analyse the motion in.

 

Suppose you choose a reference frame in which the center of mass of the eight ball is at rest, and furthermore the eight ball isn't spinning. Hence, the number 8 isn't rotating in the frame.

 

Now, suppose that some external force is applied to the eight ball, to get it spinning in the frame, without moving the center of mass.

 

As you can see, Newton's laws of motion weren't violated, and there is now a spinning eight ball. To really make this clear, "There is now an eightball which is spinning in an inertial reference frame."

 

Now, go back to before the external force was applied.

 

The center of mass of the eight ball is at rest in the frame, and the eight ball isn't rotating.

 

Now, add the stars. Thus, we are not ignoring their existence, and Mach talked about this.

 

Now, there are many non-inertial frames we can conceive of, in which the eight ball is spinning... but, and this is the key point, they are non-inertial frames.

 

This takes a bit of explanation, but you have to go into this, otherwise you miss the whole point.

 

Suppose that the number 8 is pointing to the center of galaxy X.

 

Currently, the eight ball isn't spinning, in some frame. Furthermore, let it be the case that there are no external forces acting upon the eightball, so according to Newton/Galileo's first law of motion, the center of mass will be at rest or moving in a straight line at a constant speed, in any inertial reference frame. So imagine a frame in which the CM of the eightball is at rest.

 

Thus, the number eight will continue to face galaxy X, until external forces are applied to it.

 

Mathematically, we can discuss a reference frame which is in orbit about the eight ball.

 

Think of it as if there is a satellite orbiting the eightball. From the satellite reference frame, the number 8 appears to be moving in a circle.

 

Only in reality, it is the satellite in orbit, not a spinning eight ball, because the number 8 is always pointing at galaxy X.

 

If you ignore the existence of the stars, it isn't clear right away, that the satellite frame is a non-inertial frame.

 

But, when you realize that from the satellites point of view, the center of mass of galaxy X is accelerating, in absence of an external force, which violates Newton's third law, it is then you realize the satellite frame is a non-inertial one.

 

So what does this have to do with my question?

 

Well, my question is, "Is rotation absolute or relative?"

 

I am trying to reduce the answer to a problem in binary logic, which amounts to a decision that needs to be made, regarding frames of reference.

 

I am thinking like this:

 

If A is true then "spin is relative."

If not A then "spin is absolute"

 

That is a very rough beginning.

 

In order to know what I mean, it actually helps to look at the spinning cubes in the wolfram article.

 

Suppose that there is a reference frame connected to the cube. The cube has six sides, and your reference frame has three lines, which define six directions relative to the origin of the frame. Let the origin of the frame be permanently located at the center of mass of the cube, and let the axes of the frame permanently emerge through the center of the face of the six sides, no matter what external forces act upon the cube.

 

So,we have a cube of material, and the rest frame of the cube.

 

We can now speak of the orientation of the cube, relative to other objects in the universe.

 

Now, suppose that in the rest frame of the cube, the trajectory of galaxy X is a circle.

 

Thus, when viewed from the rest frame of the cube, the center of mass of galaxy X is moving in a circle.

 

But, when viewed from a reference frame in which the center of mass of galaxy X is moving in a straight line at a constant speed, it appears that the cube is spinning.

 

So is spin absolute or relative?

 

There is a reference frame in which the cube isn't spinning.

There is a reference frame in which the cube is spinning.

 

Relative motion of things in the universe can be viewed from either frame simultaneously.

 

So to understand my question, there is only one more part.

 

Suppose you are standing on one of the faces of a cubical planet.

 

Your eyes are closed, so you cannot see the stars. They are there, but you cannot see them. You are at rest, in the rest frame of the cube.

 

Now, either the cube is spinning relative to galaxy X, or not, but you cannot see galaxy X, because your eyes are closed.

 

Can you from where you are, tell which is the case?

 

If the answer is no, then spin is relative.

If the answer is yes, then spin is absolute.

 

That's where my question is aimed.

 

I am positive the answer is that spin is absolute, but I'm not sure the best way to begin discussing it mathematically, using Newtonian physics.

 

I think something about coriolis force, should be used. The annoying part is that you can never get a clear answer to this from PhD's in physics. Otherwise i'd have understood this a decade ago.

 

When you ask them about it, all you get is "coriolis force is a fictitious force" and you are left with the idea that they don't understand rotational frames of reference.

 

They seem to know that if an ice skater pulls her arms in, she spins faster, but anyone knows that's true, who watches the sports channel.

 

Anyway, hopefully you get the idea of the question at least.

 

Also' date=' what kind of analysis are you doing of precession, purely mathematical or experimental as well?[/quote']

 

Ultimately, I don't see why not both. I have a firm example in mind though.

 

A toy spinning top, like a dradel.

 

Let me see if i can find an animation.

 

Here is one:

 

Precession animation

[swansont]

You can have relative rotation, i.e. you can measure your rotation with respect to anything you want. From a physics perspective rotation is absolute in that you can do measurements that will tell you if you are rotating or have rotated. There are frames that are not rotating.

[Johnny5]

You can have relative rotation, i.e. you can measure your rotation with respect to anything you want. From a physics perspective rotation is absolute in that you can do measurements that will tell you if you are rotating or have rotated. There are frames that are not rotating.

 

See this is the kind of answer i want to read.

 

By saying that there are frames that aren't rotating, you are saying that rotation is absolute. The formulation of the statement, is as if that is the case.

 

Yes, rotation is absolute.

 

There is a mathematical relativeness to it, but when you are talking reality, it is as you say. I just don't want to be in the minority here, and don't bail on me.

 

For quite some time, I've been trying to develop the logic necessary to discuss rotation as an absolute.

 

There has to be some element which is beyond the mathematical treatment of it.

[LKL]

What are the frames that aren't rotating?

 

I don't know much about non-Euclidean geometry, pretty much all of my knowledge stems from the book "Readable Relativity", so I'll just quote some of the main points concerning rotation. Suppose there's a rotating disc, an observer some distance from it(on the same plane) who regards the disk as rotating about its center axis and an observer on the disc. They both consider the other observer rotating about the center axis and so on. It gets interesting when the guy on the disc draws a circle using the center of the disc as its center and goes on to measure its diameter and circumference. When he's measuring its diameter, the outside observer doesn't find his rule contracting. When he's measuring the circumference, however, the outside observer will see the rule contracting. So, they can't agree even on the value of pi. Therefore the disc-stationed observer will live in a non-Euclidean geometry. I guess this would hint at rotation being absolute, since we can all agree on that under non-rotating circumstances our geometry is strictly Euclidean. I'm not certain that the assumption can be made, though.

 

Regarding experimental analysis of precession, how about a forced-precession device? Something that spins a flywheel while at the same time rotating its axis. Might be fun!

[Johnny5]

Regarding experimental analysis of precession' date=' how about a forced-precession device? Something that spins a flywheel while at the same time rotating its axis. Might be fun![/quote']

 

What exactly is a flywheel? I know your other post talks about it, and I wanted to run through the math, generate the equations.

 

I don't know much about non-Euclidean geometry, pretty much all of my knowledge stems from the book "Readable Relativity", so I'll just quote some of the main points concerning rotation. Suppose there's a rotating disc, an observer some distance from it(on the same plane) who regards the disk as rotating about its center axis and an observer on the disc. They both consider the other observer rotating about the center axis and so on. It gets interesting when the guy on the disc draws a circle using the center of the disc as its center and goes on to measure its diameter and circumference. When he's measuring its diameter, the outside observer doesn't find his rule contracting. When he's measuring the circumference, however, the outside observer will see the rule contracting. So, they can't agree even on the value of pi.

 

This is what I want to think about. Agreement on the value of pi for example.

 

I want to have access to a thorough knowledge of rotation.

[Johnny5]

Regarding experimental analysis of precession' date=' how about a forced-precession device? Something that spins a flywheel while at the same time rotating its axis. Might be fun![/quote']

 

Like a flywheel in an engine?

 

A heavy disc of metal attached to the rear of the crankshaft. It smoothes the firing impulses of the engine and keeps the crankshaft turning during periods when no firing takes place. The starter also engages the flywheel to start the engine. Figure 16 The flywheel is mounted to the rear of the crankshaft source

 

Flywheel

[bascule]

Rotation is possible within the absolute spacetime metric. Something spinning in an otherwise empty universe is still spinning, regardless of if there's any non-spinning matter to compare to. As interesting as Mach's ideas were, they were wrong.

[LKL]

How do you know if that something is spinning or not? What kind of measurements would need to be carried out?

 

I don't know if what I quoted earlier about the non-Euclidean geometry in rotating coordinate systems applies to the "satellite orbiting the 8-ball"- system, since now gravity is causing the acceleration. Differing values of pi should still arise, but there are other differences to the situation. For one, the satellite can't determine whether he's orbiting the 8-ball under its gravitational pull or whether he's in the proximity of a spinning 8-ball with no gravitational field at all. In both cases, an observer inside the satellite would find himself seemingly weightless. In the rotating disc- example, the observer on the disc would find what appears to be his weight related to the distance from the center of the disc. A definite difference here.

 

Yes, by a flywheel I mean just a heavy disc of metal with an axel hole in the center.

I = 0.5*m*((radius of the flywheel)^2 + (radius of the axel hole)^2). If you had a flywheel with the axel mounted on the inside rim of a larger wheel, you'd have forced precession by rotating the larger wheel while the flywheel inside it is spinning.

[Spyman]

To determine if the 8-ball is rotating or the satellite is revolving I guess inertia must be involved someway.

 

What if the guy in the satellite fires a bullet at the 8-ball ?

 

When the bullet hits the surface that guy takes a snapshot of it.

 

Will the angle of the bullet be different in the two cases ?

 

Will the angle of the hole created through the 8-ball be different ?

 

Depending of the size of the 8-ball will the bullet even hit it, in the case where the satellite is revolving and aiming straight towards the 8-ball ?

[swansont]

How do you know if that something is spinning or not? What

 

 

If Newton's laws or special relativity are seen to hold, you are not in an accelerating frame. Specific applications to do this for rotations include the Foucalt pendulum and the Sagnac interferometer.

[Johnny5]

If Newton's laws or special relativity are seen to hold, you are not in an accelerating frame. Specific applications to do this for rotations include the Foucalt pendulum and the Sagnac interferometer.

 

SR totally aside, because I don't want to get into that with you here, do you regard an 'accelerating frame' as 100% equivalent to one in which inertial forces are being felt?

 

Forgive that, if it's not totally clear.

 

As for the Foucalt pendulum, I have yet to understand the experiment.

 

I need to understand gyroscopic motion, i know that much.

 

I read that Foucalt is actually the one who first developed a gyroscope, and was using it, in conjunction with his giant pendulum, to draw inferences about the earth's rotation.

 

Let me see if i can find the pictures I was looking at, of some very old gyroscopes:

 

Here are a few pictures of some old gyroscopes, and a brief article on Foucault: Gyroscopes

[bascule]

How do you know if that something is spinning or not? What kind of measurements would need to be carried out?

 

Intertia is the telltale sign of rotational motion. If "empty space" is truly permeated with a "Higgs ocean" which resists change in velocity, then if you were an astronaut lying against the wall of a cylinder spinning in an otherwise empty universe, you would still feel the inertial effects of "centrifugal force" pinning you against the wall as the cylinder spins (within the absolute spacetime metric, or relative to the "Higgs ocean" if you prefer to think of it that way)

 

Wow, did I just say it was both absolute and relative? I think we'll have to wait for the LHC to observe the Higgs boson to really find out...

[swansont]

As for the Foucalt pendulum' date=' I have yet to understand the experiment.

[/quote']

 

 

The earth rotates underneath the pendulum bob, which only feels a force in the plane of the gravity and tension vectors, but nothing perpendicular to that.

[Johnny5]

The earth rotates underneath the pendulum bob, which only feels a force in the plane of the gravity and tension vectors, but nothing perpendicular to that.

 

Thank you Dr. Swanson

 

Kind regards