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An important nitpick: the description of the equivalence principle [1] in the article is incorrect. A spinning astronaut in a universe without stars can discer

by ISL 11y ago

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 https://en.wikipedia.org/wiki/Equivalence_principle

kipple 11y ago
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 https://en.wikipedia.org/wiki/Spherical_cow
- ISL 11y ago
  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 https://en.wikipedia.org/wiki/Mach%27s_principle
simias 11y ago
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?
danbruc 11y ago
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.
- ISL 11y ago
  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.
- tbabb 11y ago
  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 https://en.wikipedia.org/wiki/Bucket_argument
tbabb 11y ago
Hardly a "nitpick". That's a glaring error.
shasta 11y ago
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?

by ISL 11y ago

kipple 11y ago

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 https://en.wikipedia.org/wiki/Spherical_cow

ISL 11y ago
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 https://en.wikipedia.org/wiki/Mach%27s_principle

simias 11y ago

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?

danbruc 11y ago

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.

ISL 11y ago
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.
tbabb 11y ago
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 https://en.wikipedia.org/wiki/Bucket_argument

tbabb 11y ago

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

shasta 11y ago

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?