Rapidly rotating wire

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Goemon
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Re: Rapidly rotating wire

Postby Goemon » Sat Jan 31, 2009 6:36 pm UTC

An observer who's accelerating in empty space and an observer who's in a gravitational field see identical time dilation effects in their immediate vicinity. But at farther and farther distances, the rate of time dilation varies more and more. You can tell the difference between gravitation and acceleration if you do experiments over a large enough area.

The upshot of all this is that there's a big difference between spacetime that's been curved by gravitation, and empty spacetime. In empty, flat spacetime, it's always possible to find a reference frame where all the clocks AT REST with respect to the frame tick at the same rate indefinitely - no time dilation anywhere. An observer or reference frame that accelerates in empty space will see clocks in different places ticking at different rates, but this time dilation is an artifact of the acceleration. It's not a property of the spacetime, it's caused by acceleration and felt only by the person who's accelerating - it doesn't affect others who are in uniform motion.

A true gravitational field, on the other hand, affects everyone. There's no possible trajectory you can take, with or without rocket engines, that will make the time dilation disappear. The time dilation IS a property of spacetime, and you can't get away from it.

By taking measurements over a large enough area, you can determine whether the time dilation is intrinsic to the spacetime, or an artifact of your motion.
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Re: Rapidly rotating wire

Postby Charlie! » Sat Jan 31, 2009 8:01 pm UTC

Goemon wrote:An observer who's accelerating in empty space and an observer who's in a gravitational field see identical time dilation effects in their immediate vicinity. But at farther and farther distances, the rate of time dilation varies more and more. You can tell the difference between gravitation and acceleration if you do experiments over a large enough area.

The upshot of all this is that there's a big difference between spacetime that's been curved by gravitation, and empty spacetime. In empty, flat spacetime, it's always possible to find a reference frame where all the clocks AT REST with respect to the frame tick at the same rate indefinitely - no time dilation anywhere. An observer or reference frame that accelerates in empty space will see clocks in different places ticking at different rates, but this time dilation is an artifact of the acceleration. It's not a property of the spacetime, it's caused by acceleration and felt only by the person who's accelerating - it doesn't affect others who are in uniform motion.

A true gravitational field, on the other hand, affects everyone. There's no possible trajectory you can take, with or without rocket engines, that will make the time dilation disappear. The time dilation IS a property of spacetime, and you can't get away from it.

By taking measurements over a large enough area, you can determine whether the time dilation is intrinsic to the spacetime, or an artifact of your motion.

Look, do you or do you not agree that a stationary observer will observe someone accelerating to have a different rate of passage through time? Yes, acceleration can affect some objects without affecting others, that's nice, but are you claiming that they don't' experience time dilation?
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Re: Rapidly rotating wire

Postby Goemon » Sun Feb 01, 2009 5:48 am UTC

In flat spacetime, time dilation is a function of one thing: velocity. Acceleration doesn't matter.

If you see one person moving at 0.995c with zero acceleration, and another moving at 0.995c who's accelerating at 100g's, then they have the exact same time dilation (about 10).

Of course, if you wait long enough, the person accelerating at 100g's will end up with a different velocity, which will result in different time dilation.

Not sure if we're saying the same thing or not...
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Re: Rapidly rotating wire

Postby Charlie! » Mon Feb 02, 2009 8:54 am UTC

We're not.

Bullet point number 1.

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Re: Rapidly rotating wire

Postby Goemon » Wed Feb 04, 2009 4:03 am UTC

I assume you're referring to this:

Wikipedia wrote:According to General Relativity, gravitational time dilation is copresent with the existence of an accelerated reference frame.


I interpret that to mean what I said earlier: a twin who's accelerating in flat spacetime sees time dilation that's locally equivalent to gravitation (but differs from gravitation over larger distances). His inertial twin standing a few feet away sees no time dilation occuring due to gravity/aceleration.
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Charlie!
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Re: Rapidly rotating wire

Postby Charlie! » Wed Feb 04, 2009 6:35 am UTC

Goemon wrote:I assume you're referring to this:

Wikipedia wrote:According to General Relativity, gravitational time dilation is copresent with the existence of an accelerated reference frame.


I interpret that to mean what I said earlier: a twin who's accelerating in flat spacetime sees time dilation that's locally equivalent to gravitation (but differs from gravitation over larger distances). His inertial twin standing a few feet away sees no time dilation occuring due to gravity/aceleration.

You are incorrect. I'm unsure what I can do here aside from continuous links to this article. Perhaps quotes would help?

wikipedia wrote:It can also be manifested by any other kind of accelerated reference frame such as an accelerating dragster or space shuttle. Spinning objects such as merry-go-rounds and ferris wheels are subjected to gravitational time dilation as an effect of their angular spin.

This is supported by the general theory of relativity due to the equivalence principle that states that all accelerated reference frames possess a gravitational field. According to general relativity, inertial mass and gravitational mass are the same. Not all gravitational fields are "curved" or "spherical"; some are flat as in the case of an accelerating dragster or space shuttle. Any kind of g-load contributes to gravitational time dilation.
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Re: Rapidly rotating wire

Postby doogly » Wed Feb 04, 2009 6:59 am UTC

Charlie! wrote:
wikipedia wrote:Not all gravitational fields are "curved" or "spherical"; some are flat as in the case of an accelerating dragster or space shuttle. Any kind of g-load contributes to gravitational time dilation.


This is incorrect. Now is a good time to stop getting your GR from wiki; they must have let the noobs edit things. All gravitational fields are cause curvature. That is what gravity *means* in general relativity.
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Re: Rapidly rotating wire

Postby Charlie! » Wed Feb 04, 2009 9:32 pm UTC

doogly wrote:
Charlie! wrote:
wikipedia wrote:Not all gravitational fields are "curved" or "spherical"; some are flat as in the case of an accelerating dragster or space shuttle. Any kind of g-load contributes to gravitational time dilation.


This is incorrect. Now is a good time to stop getting your GR from wiki; they must have let the noobs edit things. All gravitational fields are cause curvature. That is what gravity *means* in general relativity.

:roll: Did they say "cause curvature of space" or did they say "are 'curved' or 'spherical?'" To me, it seems quite reasonable that apparent gravitational fields that have no space dependence (like for an accelerating dragster) could have the "curves" or "spheres" of equal acceleration (or those related to the kind of symmetry the field possesses) no longer be curved at all.

Of course, if you find the word "curved" to be bad or misleading, you could always change that and lower the risk of that bit being misinterpreted.
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Re: Rapidly rotating wire

Postby doogly » Wed Feb 04, 2009 9:53 pm UTC

To me, "curved" means you can calculate the Reimann Tensor and get an answer other than zero. Constant acceleration as in the case of a dragster isn't an apparent gravitational field - if you checked the curvature, you would find that there is none, and correctly conclude that you are not near any masses that are gravitying you.
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Re: Rapidly rotating wire

Postby IHOPancake » Thu Feb 05, 2009 12:47 am UTC

ThinkerEmeritus wrote: Now if you want a really good puzzle: what is holding the positive ions in circular motion? The overall electric field is the wrong sign. Note you can't get out of the puzzle by reversing the electric field, because then I will ask you what is keeping the electrons in circular motion.


Most likely, nothing. The centripetal force required to constrain the wire will be greater than the tensile strength of the wire, causing it to break.
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Re: Rapidly rotating wire

Postby cspirou » Thu Feb 05, 2009 1:22 am UTC

Are we completely ignoring that this would radiate energy and slow down?

Are we also assuming that one end is "magically" fixed in space or is it somehow rotating around a center of mass?

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Re: Rapidly rotating wire

Postby Goemon » Fri Feb 06, 2009 12:45 am UTC

cspirou wrote:Are we completely ignoring that this would radiate energy and slow down?


Only if it has an unbalanced charge distribution - which I don't think would be the case.

cspirou wrote:Are we also assuming that one end is "magically" fixed in space or is it somehow rotating around a center of mass?


The magic one.
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Re: Rapidly rotating wire

Postby ThinkerEmeritus » Fri Feb 06, 2009 1:40 am UTC

Goemon wrote:
cspirou wrote:Are we completely ignoring that this would radiate energy and slow down?


Only if it has an unbalanced charge distribution - which I don't think would be the case.



It has to have an unbalanced charge distribution to keep the conduction electrons in the wire. The electron density must get greater as you go out the wire, so that the larger number of collisions (higher pressure) in the denser electron gas or a net electric field holds the electrons in circular motion. Most likely both are present, especially in circular motion.

Edit: Jesse Beams at the University of Virginia actually did an experiment that showed that there are electric fields near a rotated metal, and that the fields are of approximately the size necessary to keep the metal's ions in circular motion. Thus the conduction electrons have to be supported by the pressure of the electron gas. This was at nonrelativistic speeds, of course.

Also don't forget IHOPancake's remark that there isn't enough tensile force to prevent the wire from snapping. We can ignore these things in order to discuss interesting conceptual issues, but we can't do any such experiment. The effects we are ignoring are at least as big as the ones we are interested in.
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