posted
"In GR, time (or more technically, Speed of Light * time) is simply another direction you can travel in, with one restriction - you can only go one way through time (no backwards time travel!)."
I suppose the better question is "how do we measure time?"
To say that "time is a direction" is all good, if I new it was a direction in correlation to something. The only way, I suppose to measure time if not by the speed of light, is by comparison to things that happen, and the rate of experience observers have between the two things.
Since what people observe is going to be different, it therefore means that time is relative to the observer. Correct?
Posts: 9754 | Registered: Jul 2002
| IP: Logged |
posted
Ok, a bit of a question, which should be easy, and I believe I know the answer, but wanted to double check.
Hypothetically:
I created a box with unlimited air supply and pressure, is completely sealed, with no windows, and put a gerbil in it. I take said box into space. I attach a 10 foot pole to the box and swing it around over and over again in a 360 degree spin.
First) is the gerbil experiencing any centrifugal force and being pushed against a wall, or is it free floating. I believe it is free floating.
Second) would time be moving slower for it compared to a gerbil outside staring at the box?
Posts: 9754 | Registered: Jul 2002
| IP: Logged |
posted
I believe it will feel neither centrifugal force (which is an imaginary "convenience" force) nor is it floating. It is subjected to the centripetal force. The box is pushing in on the gerbil.
Space is no different than Earth in this regard. Just like those amusement rides that spin fast, creating forces on you, so would the spinning cardboard box. Now it may depend on the speed of the rotation exactly how much it is feeling, but it's still there, I believe. ---
Probably, but at such a minute level as to be inconsequential.
posted
To answer the question without reference to abstruse arguments that only physicists and pedants care about, yes, the gerbil will feel centrifugal force. And yes, time would slow down for it, but obviously not very much.
That said, really, there is no centrifugal force. Trust me.
Posts: 10645 | Registered: Jul 2004
| IP: Logged |
posted
On a vaguely related note, here's a thought experiment which bothers me a bit. Suppose I have a sphere of unobtainium, which is perfectly reflective on the inside. It is filled with vacuum. Now, using my handwavium drill, I open a tiny hole in the unobtainium, let in some arbitrarily large amount of photons, and close the hole, leaving the unobtainium unchanged except that there are now photons in the cavity. We know that the gravitational mass increases, since I've increased the energy of the system; my question is, what happens to the inertia, both linear and angular? And, given some answer based on the theory of GR, what is the relevant experiment showing this particular result to be correct?
Posts: 10645 | Registered: Jul 2004
| IP: Logged |
posted
Centrifigual Force is in reality the Dark Side of "The Force" so the Hamster in the box would be a Sith Hamster, while the Hamster watching, uninfluenced by the Dark Side, would be a Jedi Hamster.
(Pictures two hamsters with tiny hamster-sized light sabers, battling to the death. Admit it. Light Saber Weilding Hamsters is why you went into physics in the first place.)
Oh, and if you put an infinite amount of atmosphere in a box you would crush the poor hamster into a singularity.
Posts: 11895 | Registered: Apr 2002
| IP: Logged |
quote:Originally posted by King of Men: On a vaguely related note, here's a thought experiment which bothers me a bit. Suppose I have a sphere of unobtainium, which is perfectly reflective on the inside. It is filled with vacuum. Now, using my handwavium drill, I open a tiny hole in the unobtainium, let in some arbitrarily large amount of photons, and close the hole, leaving the unobtainium unchanged except that there are now photons in the cavity. We know that the gravitational mass increases, since I've increased the energy of the system; my question is, what happens to the inertia, both linear and angular? And, given some answer based on the theory of GR, what is the relevant experiment showing this particular result to be correct?
Can the rotation of the sphere "drag" the photons along? In otherwords, if I have a sphere filled with fluid, the fluid begins to spin as I spin the sphere (due to frictional effects, I believe). Would photons get dragged around in the same way?
More generally, what does GR predict about the angular inertia of solid objects? That is, the inertia depends on the mass density and the shape. I can see how GR messes with the mass density, but doesn't SR also predict shape changes (I mean, length contracting/etc must change at least one dimension). So, does the calculation of the moment of inertia depend on ones perspective? (I guess this shouldn't be surprising since everything short of ds^2 is dependent on the observation, this one I've just never thought about before).
For the linear question, I have NO idea. I'm invisioning a photon starting at the back of the sphere moving forward as the sphere moves forward. But relative to the forward edge of the sphere, the photon is moving c, so this is really screwing with my head ;-), Thus, from an outside observor, the sphere should contract a bit in the direct ion of motion, so now we have an ellipse? But I distinctly remember reading something that said that spheres ACTUALLY contract to spheres (though, as usual, I could be wrong)
So, instead of answering, I pose more questions ;-)
As an aside, I'm taking a quantum field theory course. So far, there has been NO physics :-) It's great.
Posts: 168 | Registered: Jul 2006
| IP: Logged |
posted
T_Smith, I think I know what you're getting at. If you put the gerbil in the center of a torus and set that to spinning then it wouldn't feel a force. The gerbil wouldn't be set to moving with the torus and the torus would just cheerfully spin around it. It wouldn't effect the gerbil unless the gerbil made contact with any of the walls, in which case it would start moving with the torus and begin to experience a simulated gravity force. It's hard to explain with out diagrams, so I hope that makes sense.
In the case of a box, well think about it. At first it'd be freefloating, but the wall of the box would quickly smack into it. Once that happened the gerbil would be accelerated with the box and would feel the simulated gravity force (centripedal is the actual force in question there).
Posts: 3295 | Registered: Jun 2004
| IP: Logged |
posted
About the linear inertia, I convinced myself (and another grad student, so maybe there's something to it) that you would get extra inertia from Doppler effects. At any rate, you would get an additional resistance to acceleration. Whether the resistance would be at the correct rate, ie whatever extra energy you pumped in would show up as F=(m+dm)a where dm=dE/c^2, well, that's another matter entirely.
But the angular moment is puzzling me. I suppose you'd have to say that there's enough interaction between the photons and the unobtainium to create a drag, since otherwise you're basically just manipulating the original unobtainium sphere, but I don't know if it makes sense to say that a fluid of photons is rotating.
Basically, though, the whole subject of rotating objects in GR is strictly for experts; I was hoping one would come along. Mere particle physicists should fear to tread here, and I do.
Posts: 10645 | Registered: Jul 2004
| IP: Logged |
Printer-friendly view of this topic
