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Comment by ISL | Hacker News Reader

An important nitpick: the description of the equivalence principle [1] in the article is incorrect.

A spinning astronaut in a universe without stars can discern whether she or her partner is spinning, particularly if they work together a little.

The astronaut can change her moment of inertia by curling into a ball or spreading out: if the astronauts' relative rotation rate changes, she's rotating. If it doesn't, she's not.

Things are more complicated if they're both rotating, but with mental math and freshman/high-school physics, they'll be able to sort it out completely.

Even in a universe without any external reference, it's possible to place limits on your rotation rate. If a centrifugal force is palpable when extending an appendage, then you're rotating.

[1] https://en.wikipedia.org/wiki/Equivalence_principle

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IANAP, but that argument strikes me as circular - you are presupposing that inertia works the way we are used to in order to figure out which astronaut is rotating.

But imagine two astronauts in empty space and let's turn one upside down stacking them head to head, or helmet to helmet. Now spin one of them around his vertical axis [1].

The situation looks completely symmetric to both of them. Why should the relative speed of rotation change if one of them extends or retracts his limbs but not if the other one does the same thing? What breaks the symmetry of the situation in absence of any other matter in the universe that could be used as a preferred frame of reference for defining spinning versus being at rest?

[1] I am not sure if you could do that, but I tend to say no. One of the astronauts would have to try to spin the other one which should make himself spin in the opposite direction, conservation of angular momentum. Ad hoc it seems like you could establish a preferred frame of reference, a frame of zero angular momentum this way.

As a thought experiment, you can certainly arrange whatever initial conditions you like. We already discarded the rest of the universe, after all.

You're absolutely correct that I'm assuming the current understanding of how inertia works. It would be fascinating if we were to somehow perform the experiment and didn't get the usual result.

Your symmetry argument is excellent and well-stated. I have no complete counter.

To extend the argument: If just one astronaut is in an otherwise empty universe, can she tell whether or not she is spinning at 100 RPM by extending her arms to sense centrifugal force? The usual laws of physics would say that she can. A laser-gyro should work too. I think Mach would guess that she can't.

Because I can't make an empty universe, I don't know how to do the experiment, but it's interesting to ponder.

One astronaut (the spinning one) will detect a centrifugal force, and the other will not.

If the spinning astronaut took a yo-yo out of her pocket, she would observe it accelerates radially away from her. The stationary astronaut's yo-yo would drift freely with no acceleration.

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

The yo-yo is no different than extending and retracting limbs, it presupposes inertia as we know it. Why should the two yo-yos behave differently if the situation is totally symmetric?

I am not sure what point you are trying to make or what you are asserting is being "presupposed". What is described above are the results of an experiment. That's the way physics works; that's what will happen if you do the experiment. No suppositions needed.

The situation is not totally symmetric: The yo-yo behaves differently for the spinning astronaut than it does for the stationary one. That is why the article is wrong; the two situations are measurably different, not equivalent.

You are missing the point. This is not an experimental fact because we have no empty universe at hand to do it. Two cylinders spinning relative to each other around a common axis in otherwise empty three-dimensional Euclidean space are totally symmetric. Or how would you tell which one is spinning? It is as meaningless to speak about the rotation of one of the cylinders as it is meaningless to speak about the velocity of a single object.

Ah, I think I see what you are hung up on.

In newtonian mechanics, the equivalence principle says that any two inertial coordinate frames look "the same". For example, if you have two spaceships heading toward each other, the picture looks "the same" as if you pretend that one spaceship is stationary and the other is moving twice as fast, or vice versa.

This is not true only of geometric relationships, but also for the laws of physics: If you choose to view things in coordinate frame A, and apply the same laws of physics, you will still get the same predicted motion as if you had done the calculation in coordinate frame B. There is no experiment that can tell you which frame is "moving", because you always get the same answer.

With your example of two rotating bodies, it is true that the picture looks geometrically "the same" if we pick a different rotating reference frame. The problem is that the laws of physics do not look "the same" under this transformation. If I choose a coordinate frame where the spinning astronaut is stationary, and I try to predict what will happen using the laws of physics of the original frame, I will get wrong results-- the motion of the yo-yo will look "unphysical" for a stationary system. So when you change between rotating and stationary coordinate frames, the laws of physics change too.

That means I can tell whether I am in an "absolutely rotating" coordinate frame by doing tests to measure the laws of physics (i.e. are there coriolis and centrifugal forces acting on me?), without any reference to some other, external frame.

So the fundamental question is under what circumstances the picture looks "the same". In both cases, geometric relationships are equivalent, but in only one of the cases are the laws of physics also equivalent. The original article lied by saying the laws of physics are the same in the rotating case, and that is simply not true.

Does that make sense?

We are getting closer. You are essentially saying that we can have geometrically indistinguishable states that are physically different. We can have an astronaut with a yo-yo hanging down and one with a yo-yo extending straight away while the world otherwise looks exactly the same to both of them. Both astronauts have to go through the same change in angular velocity just in opposite directions to get to the same state as the other one but one would see the yo-yo dropping down while the other one will see it rising. How does that make sense? What is so special about the one coordinate frame without centrifugal forces? With respect to what is the astronaut not rotating? Note that nothing looks unphysical here, just different but without any obvious thing that justifies the difference. And I am definitely not trying to say I am right and you are wrong, it just doesn't look consistent to me to have centrifugal forces in an empty universe.

The short answer (i.e. without teaching all of Phys 101 in this comment) is that physics treats linear motion differently from curved motion. Objects that are moving in a straight line will continue moving in a straight line unless acted upon by a force. An inertial coordinate frame is by definition one where this holds true.

We can define "absolute rotation" as rotation relative to that coordinate frame. We will not have any trouble agreeing on who is rotating and who is not, because only one coordinate frame will observe perfectly inertial movement, and all the others will measure some coriolis and centrifugal forces.

See this video for better intuition: https://www.youtube.com/watch?v=_36MiCUS1ro

Introducing a probe body does not really solve the problem, it still does not explain what picks one frame of reference over the other. Why does the force free motion of the probe body appear straight for on astronaut but not the other one? I am pretty sure this entire topic is not nearly as straightforward as you suggest, otherwise there would be no debate about Machian views and so on. I will have a look at the papers referenced here [1], they seem to touch a couple of interesting and related points.

[1] http://physics.stackexchange.com/questions/1048/what-if-the-...

I do not really see what the "problem" is. One can easily define a unique (up to translation) "rotation-free" coordinate system that all observers will agree on, without any reference to "fixed stars" or the rest of the universe.

Centrifugal force in a rotating frame is an inevitable consequence of a universe in which conservation of momentum exists. Conservation of momentum is an inevitable consequence (by Noether's theorem) of a universe in which translational symmetry exists (i.e. the laws of motion are not different at some displacement dx). By all observations, all three of those properties hold for appropriate choices of frame.

You cannot suppose a universe with both translational symmetry and symmetry under rotational movement; the two are in conflict. If conservation of momentum holds in some coordinate frame, then it will not hold in coordinate frames that are rotating relatively to it.

If you suppose a universe where a "rotating" reference frame is the one where conservation of momentum holds, then I would be forced to ask "rotating relative to what, if not an inertial frame?" And the inhabitants of such a universe would still certainly find it meaningful to label that frame as "inertial" and define rotation as relative to it.

If you are asking how we tell rotating and non-rotating reference frames apart, the answer is trivial-- non-rotating reference frames obey inertia and rotating frames do not; and there is no ambiguity or disagreement between observers. If you are asking why there exists an inertial reference frame at all, the answer is that this arises from translational symmetry. If you are asking why the universe has chosen a particular coordinate frame to be "non-rotating" over any other, the question seems rather meaningless, because it does not make sense to define rotation except with respect to an inertial frame.

Right now I am again convinced that there is no problem, but I have gone back and forth between it makes sense and it makes no sense a couple of times. I probably never looked at it with enough rigour and got things overlooked or confused. But thanks for your effort and I will also read through "Mach's principle and a relativistic theory of gravitation" which I came across yesterday during this discussion, maybe I will finally reach a state of lasting non-confusion.

This is something that's always bothered me with inertia actually. You have to measure rotation against a frame of reference right?

The way I frame the problem is generally by imagining a gyroscope (say, a spinning bike wheel) somewhere in the universe far away from any galaxy or massive body. Relative to which frame of reference will it maintain orientation?

Wouldn't that be explained by the next paragraph?

> The distinction between the two astronauts makes sense only when you reintroduce the rest of the universe. In the classic interpretation of general relativity, then, inertia exists only because you can measure it against the entire cosmic gravitational field.

This seems like a case of a spherical cow[1], the thought experiment is simplified down to only these two astronauts. No fabric of space around them, and so no inertia.

Perhaps it would have been less confusing if the thought experiment had used two normal people floating in nothingness? The presence of spacesuits makes it seem like they exist within some sort of reasonable environment.

[1] https://en.wikipedia.org/wiki/Spherical_cow

The "reintroduction of the rest of the universe" is a euphemistic introduction of the general idea of Mach's Principle [1]. Such an idea is certainly possible, and physically interesting, but nobody's yet figured out how to test it. A well-motivated and compelling experiment to test Mach's Principle would be worthwhile and a lot of fun.

The current, locally-determined, laws of physics would produce the same outcomes for our rotating astronauts with or without the presence of anything else in the universe.

[1] https://en.wikipedia.org/wiki/Mach%27s_principle

Yes, that part of the article was muddled. It first says the one spinning is dizzy ... and then goes on to explain that will not be able to figure out which that is without stars. How does that make sense?

Hardly a "nitpick". That's a glaring error.

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