As written in the other topic, imagine a theoretical universe with only two particles. They are touching and have equal mass.
It seems to me that motion could still exist in this universe, in the form of rotation. I think they would have to rotate at the same velocity, or the masses would not be equal. If I have two touching marbles rotating about a shared axis at the same speed, then from the perspective of a person on the surface of the marble, there is no movement. But if the axis of rotation is not shared, if say the marbles are turning in opposite directions, wouldn’t we have relative motion?
Furthermore don’t spheres slightly flatten when spinning? So if the two particles are spinning about different axes, they will appear to be two different shapes, and from the difference we can infer the existence of rotational motion.
I’m sure I’m missing something here, but particles are not spheres. Even atoms are not spheres. And “particles” don’t just sit anywhere and don’t touch like marbles do. If they are in motion they are waves rather than have particle-like qualities. Nor do they “spin.” That’s a measurement of angular momentum, nothing like a top.
Maybe you can simplify the wave function in such a toy universe, but I’m confused by the setup.
In the first instance, I’m not sure there’s any built-in distinction between a rotating system and a stationary one. (because: rotating relative to what ?) But in the second instance, with each sphere rotating around its own axis, that would sure seem to qualify as motion. But is there an unstated reason why this would be surprising, or would contradict any previous assertion to the contrary?
Maybe taking particle too much from a QM point of view. A particle in this setup clearly isn’t a fundamental particle, but rather a notional object - described as a marble.
This begins a range of difficulties in the setup. If the objects are not fundamental - ie not point objects - there are really more than two of them. They have constituent parts. Two extended objects is probably enough to be able to define a lot of motion, but you could still run into problems with Mach’s Principle. Rotation of the objects as a pair remains an interesting question. Since they are touching we can’t use any change in distance between them to detect forces. (maybe, gravitational attraction may also mean they deform, again they are not basic particles if they can, they are extended objects, and have another level of physical properties - such as elastic modulus. So the toy universe becomes less and less toy at every step. One needs to identify when new properties are being added, and be careful with the implications.)
Mach’s Principle comes into play if they do bulge. If they bulge there is inertia and rotation. Having two extended object may be enough to allow Mach to work, unless you define the axis of rotation as being through the point they touch, and they rotate in the same direction. Then I think you have a problem. Mach would suggest that there cannot be any rotation, and they won’t bulge.
The problem is of course that we can’t create such systems, nor can we suggest they can exist in any form. But exploring the limits is interesting and revealing.
Why? If you can’t measure it, or its effects, does it exist? This is part of what Mach was driving at. He felt that there needed to be some external structure in the universe against which the rotation occurred. Newton believed there was an intrinsic coordinate system. Einstein said there wasn’t. Einstein was a big Mach enthusiast, and felt that Mach’s Principle (of which he coined the name) was an important aspect of the nature of things. There isn’t any consensus, but these thought experiments are interesting.
Einstein felt that rotation against the background of the star filled universe was what gave an object rotational inertia. No external universe, no rotational inertia. In the limit, does having even one object to rotate relative to change the nature of your universe?
The bottom line is, we don’t know if Mach’s principle is true, because to test it, we would need a universe containing nothing but a rotating object. And we don’t have any such universes lying about.
Of course, if we’re talking about extended objects like marbles, made up of many, many atoms, then there are all sorts of motions we can talk about, since the atoms are moving relative to each other.
The idea of a particle being anything other than a physical object with a defined position+mass+shape (usually sphere) is, as of yet, beyond my comprehension.
By “spin” I meant rotation about an axis, not something from Quantum theory.
You all are talking way over my head. (That was intended as a compliment.) Here’s my dumbed-down version of the question.
Suppose the only thing in the universe is one normal sphere. Not an atom, but a regulation ball of some kind, perhaps a basketball. There is nothing else in the universe that it might be rotating relative to, so it is impossible to tell whether it is rotating or not.
(Francis_Vaughan’s use of the word “bulge” made me think of the following:)
But if it is rotating relative to itself, then one would think that the horizontal diameter would be longer than the diameter along the axis of rotation. But I suspect that this too would be useless, because it’s not possible to properly measure distances if one set of endpoints is moving (the points along the equator) and the other endpoints are not (the poles). In other words, relativistic effects would cancel out any difference, and the ball will always appear spherical, whether it really is or not (whatever “really” might mean in this context).
I’ve often wondered about that. So although linear motion and speed is relative, rotational is not? That means, in other words, that although there’s no “center of the universe”, there is innately such a thing as “that direction” such that one could be said to be rotating and not standing motionless even if one were the only object in the universe?
Nah, you can get a significant equatorial bulge from quite modest rotational speeds, where the relativistic effects would be negligible. The difficulty is that Mach’s principle says that you might not get a bulge at all.
If the only three objects were yourself, a spring scale, and some ideal rotating planet, wouldn’t you still be able to measure different weights for yourself at the equator versus the poles? With a rotating reference frame (since your only reference is the rotating planet) you would experience centrifugal force, which lightens your weight a little.
Within the realm of theoretical physics I assume we, the theorists, are free to measure weight without putting a physical scale in the universe. If I’m right that cuts the limit down to two objects.
To put in another way, if you grew up in a sealed opaque box with just some simple physics apparatus to keep you entertained, you could discover that there are inertial frames and non-inertial reference frames just by noticing that in some reference frames have centrifugal force, and some don’t. Then if your box suddenly disappears and you can look outside (and get given some good telescopes) you would discover that the distant galaxies are overall non-rotating with respect to your previously-discovered inertial reference frames.
It would seem like a big coincidence that you could detect something about the overall motion of distant matter without just some local experiments without being able to see any of the outside universe, and reasonable to imagine that the overall motion of distant matter causes the result of the local experiments.
If rotation was relative, would there not be a valid reference frame in which the earth is stationary, and the rest of the universe is whirling around it, at quite impossible speed?
If I understand correctly, there are such reference frames, and they may be convenient for certain calculations (and absurdly inconvenient for others). General relativity (again, if I understand correctly) requires that the speed of light be the maximum speed locally, so the fact that in an earth-centered co-rotating frame it appears that Alpha Centaurus is whizzing about multiples of the speed of light is not a big deal. We would have to deal with the mysterious force that is causing the Earth to bulge, but locally that could be explained by a gravitational field, and would produce exactly the same predictions that would be produced in a non-rotating reference frame that doesn’t have the stars whirling madly.
No, that’s basically it: One can use such a reference frame, but it’s hideously ugly and unnecessarily complicated for a system that’s interstellar in scope. If forced to use one, basically the way to cope with it is to transform in all but name back to an inertial frame.
OK, but does it not become apparent somewhere along that process that something is not right?
I mean, not only the fact that distant objects are going faster than reality permits, but the fact they are describing curved paths around our now-stationary position, with nothing to make them do that.
There is a difference between a reference frame and an inertial reference frame.
Reference frames can be anything, are not special, and have weird physics depending on the frame (I.e. Centrifugal force, Coriolis force, etc…) ,
Inertial reference frames are ones that are not accelerating. They are special because (ignoring QM and relativity) newtons laws hold. (i.e. if you hold a scale with no other forces acting on it, the force will register zero force).
It is very clear if you are not in an inertial reference frame, because a scale with no other forces acting on it will still measure a force.
Rotation is a type of acceleration, therefore rotating frames are not inertial. If you had a universe with just one planet in it you could measure the speed of rotation of that planet (e.g. with a scale to measure centrifugal force). Imagine you’re on a merri-go-round, you can still tell if you are spinning or not even if your eyes are blindfolded.