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Author Topic: If I were a sphere spinning really fast would my equator age more slowly....?  (Read 4333 times)

Offline Eric A. Taylor

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Can't fit the question in!

Lets say I'm a sphere, about 10 miles in diameter (about the size of a neutron star) and spinning thousands and thousands of times each second (like a millisecond pulsar) my equator would be moving at close to the speed of light. Would that part of the star age more slowly that the poles? If so what sorts of implications would that imply. Would the poles cool more rapidly than the equator (as seen from someone far away?


 

Offline syhprum

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With a 10 mile radius Neutron star rotating once per millisecond an object on the equator would be moving at 62832 miles per second nowhere near c. 
« Last Edit: 26/08/2010 22:21:32 by syhprum »
 

Offline imatfaal

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With a 10 mile radius Neutron star rotating once per millisecond an object on the equator would be moving at 62832 miles per second nowhere near c. 

Its almost exactly one third the speed of light - quite quick enough for relativistic effects to be apparent and important. 

 

Offline Soul Surfer

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You are thinking wrongly.  Ageing is a process only attributable to living things. At very high velocities particles that decay after a short time can travel further before they decay but that is a statistical process and individual particles just have a fixed probability of decaying in any particular time interval and do not age in that sense.
 

Offline Eric A. Taylor

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You are thinking wrongly.  Ageing is a process only attributable to living things. At very high velocities particles that decay after a short time can travel further before they decay but that is a statistical process and individual particles just have a fixed probability of decaying in any particular time interval and do not age in that sense.

I think you're wrong here. Any physical object that changes it's properties over time is said to age. Stars are a classic example. They are clearly not alive in any way we would define it, yet they have an early mid late and end periods.

A neutron star cools and it's rotation slows over time. What are the consequences of an object that has different temperatures (differences of millions of degrees) very close together?

 

Offline Eric A. Taylor

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With a 10 mile radius Neutron star rotating once per millisecond an object on the equator would be moving at 62832 miles per second nowhere near c. 

If you consider .339 C "nowhere near" light speed....That's closer to C than a car driving down the freeway is to the speed of sound. 70 MPH is about Mach .10. An object moving at .333 C will experience 1 year in 3 of an object that is stationary relative to itself.

 If a neutron star spins just 3000 times a second it's equator is whipping around at about .999 C.

  Well this kinda kills my point. I looked up what the fastest pulsar ever seen. It's PSR J1748-2446ad at 716 Hz. That's really fast but not all that close to 1000 times per second. However surely PSR J1748-2446ad is not the fastest pulsar there is, just the fastest we've seen. Take the fattest person you've ever seen in person. Likely that person is quite over weight, but surly he or she is not the fattest person ever.
 

Offline syhprum

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I must admit .339 c is pretty fast I made the comment before I did the calculation, I never thought of car speeds in terms of Mach numbers (I can just about make mach 0.2 when the cops aren't looking)
 

Offline Eric A. Taylor

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Where? It might be tough in England, much easier in Nevada.
 

Offline mlandri

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Great topic...

You might be interested in the following site: newbielink:http://www.fourmilab.ch/cship/timedial.html [nonactive]. Talks about time dilation and speed. For example, moving at .3c causes time to run about 5% slower compared to an observer at rest.

Sounds like the crux of you question is whether or something at the equator of a spinning body is moving faster than something at its poles. The angular velocity at any point on the sphere will be the same. In other words, it will take the same amount of time to rotate around 360 degrees regardless of your latitude. However, at the equator, you will have a greater linear velocity. This is the case, because radius of the sphere is greater at the equator than closer toward the poles.

You could easily solve your hypothetical question by calculating the difference in linear velocities between a point at the equator and a point close to one of the poles and plugging these values into the equation referenced in the above link. Probably will be big differences and, hence, differences in the flow of time could be large enough to notice. Go for lunch at the equator. Come back to your girl closer to one of the poles only to find that she is, well ..., much more wrinkly than you expected.

However, I'm guessing that this probably would NOT be something that you could extrapolate to a real physical entity such as a rotating neutron star or black hole. Other complicating factors such as gravity, state of matter in super dense objects, wobble, and the such would muck things up. Given that these objects appear to be pretty stable, I suspect that time dilation differences at different latitudes are not too important to their physical evolution.
« Last Edit: 05/09/2010 14:06:22 by mlandri »
 

Offline yor_on

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I think there are Black Holes just as you thought Erik, spinning near light speed. As for the discussion if matter age I will say that it does :) Not that I doubt that it is a non linear process Soulsurfer, and that we only can pinpoint it statistically (probability), but I have a decided feeling that we too are non-linear objects.

As for the discussion of different 'frames' and how they age relative each other, yea, those 'frames of reference' gives me a real big headache considering where one ends and another one starts, and have done so a very long time, and your idea highlight that problem very nicely Eric. But, if spinning near light speed it seems to me that nothing made of matter could stand the tidal forces created by a spherical black hole. I wonder if a neutron star could? Is there any 'normal' matter spinning that fast that will hold together?

But assuming that you were standing far away from such a 'naked' object, and ignoring how it 'keeps together' while it spins, it seems to me that the far observer actually would see different parts age differently fast. That a black hole can spin so fast I see as depending on it being a 'singularity' and not 'matter' as in the ordinary sense.



Rotating at almost the speed of light.
==
Oh, neutronstars only huh?
« Last Edit: 08/09/2010 18:19:39 by yor_on »
 

Offline Eric A. Taylor

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I think black holes are entirely different animals. No one really knows (or likely will ever know and then be in a position to publish in a peer reviewed journal) what is inside a black hole. Even our understanding of physics can't tell us. Likely there is nothing inside. They are quite literally a hole in space-time.
 

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