## If spin really did represent particles actual spin...

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quarkcosh1
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### If spin really did represent particles actual spin...

...how fast would they be spinning relative to the speed of light. All the links I could find on this say it would be faster than the speed of light but they don't say how much faster. They just seem to assume this number shouldn't be important since nothing can travel faster than the speed of light. There are some theories though where the speed of light is not the fastest speed. In the context of those theories thats why I think knowing this spin speed would be important. Also I am not sure if this speed is the same for all particles or not.

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### Re: If spin really did represent particles actual spin...

The "spin" quality of particles doesn't represent physical spinning, tho, so your question doesn't make any sense. You're asking a question about some hypothetical universe with completely different laws of physics, so we can provide any answer you want.
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### Re: If spin really did represent particles actual spin...

Well, if spin is physical, then I state that particles are also physically point-masses. And so, no matter how fast a particle spins about its own axis, the whole particle travels exactly 0 times the speed of light or any other speed.

Also, this is very much pseudo-science.

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### Re: If spin really did represent particles actual spin...

It's really difficult to represent fundamental particles as little spheres with a definite radius. Composite particles like protons and neutrons are a bit easier, but not by much. There just isn't a well defined surface to work with.

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### Re: If spin really did represent particles actual spin...

quarkcosh1 wrote:There are some theories though where the speed of light is not the fastest speed. In the context of those theories thats why I think knowing this spin speed would be important.
Those "theories" are likely no more than pseudoscientific nonsense, but even if they weren't, the main reason it's not important to convert spin to a Newtonian angular momentum is because the particles aren't little spinning spheres.

As in, even if a particle had a spin that would hypothetically correspond to a sub-luminal speed, it wouldn't matter because that's not how tiny particles work.
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doogly
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### Re: If spin really did represent particles actual spin...

I mean, but it's not a dumb question.

It's nice to know why people say that this wouldn't work. There is a classical theory of the electron, with the radius as the Thomson scattering length

If you take that, pretend it's a sphere, and its spin angular momentum is hbar/2, and you do
v = hbar/2 / (2/5 m_e r_e)

Which is 160 times c. So since you believe in special relativity, now you have some good reasons to doubt this spinning sphere of charge nonsense, besides just being berated for such ridiculous thinking.

And it is, indeed, truly ridiculous.
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ijuin
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### Re: If spin really did represent particles actual spin...

The problem with having particles literally spin is that they would need to have enough rotational kinetic energy to noticeably affect their apparent mass under SR.

stianhat
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### Re: If spin really did represent particles actual spin...

In addition, if spin was classical - you'd change the symmetry of the electron and with it goes many chemical bonds. And there is a problem with requiring the electron to be a dipole but I see it has been mentioned already.

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### Re: If spin really did represent particles actual spin...

gmalivuk wrote:is because the particles aren't little spinning spheres.
This kind of threw me for a loop - maybe not perfect spheroids, but what then are they? Chaaaaaaaaarges?
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doogly
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### Re: If spin really did represent particles actual spin...

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Jorpho
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### Re: If spin really did represent particles actual spin...

Does it take energy to flip a particle between two entirely degenerate spin-states? I can't seem to recall encountering the question before; usually everyone's only interested in the fact that the states are degenerate and things can be done that make them not-degenerate.

Because then you could model the particle as a sphere (with some kind of definite radius), consider the energy that would be required to rotate that sphere 180° perpendicular to its axis of rotation, and then arrive at a speed of rotation. I guess? But that's probably already close enough to the above calculation.

ijuin
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### Re: If spin really did represent particles actual spin...

It does take energy, because there is still angular momentum, but it is more like how massless photons have momentum.

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### Re: If spin really did represent particles actual spin...

Oh, spin corresponds to/is actual angular momentum?

Thank you. I didn't know that.
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doogly
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### Re: If spin really did represent particles actual spin...

No, it follows the same rules for addition as an angular momentum. That's all.
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### Re: If spin really did represent particles actual spin...

It's a little more like angular momentum than just adding the same way (but not much). Angular momentum as a conserved quantity has to include spin and not just orbital angular momentum.

There are also ways in which it definitely isn't the same as ordinary orbital angular momentum; in particular, when calculating the magnetic moment of an orbiting electron, its spin is about twice as effective as its orbital angular momentum.
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doogly
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### Re: If spin really did represent particles actual spin...

Oh that's true, it doesn't just follow a parallel logic, it adds to regular angular momentum. So the "intrinsic / extrinsic" names for "spin /orbital" can make some sense as well.

Yeah, it's weird.
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### Re: If spin really did represent particles actual spin...

doogly wrote:If you take that, pretend it's a sphere, and its spin angular momentum is hbar/2, and you do
v = hbar/2 / (2/5 m_e r_e)

Which is 160 times c..
That's proper velocity, not coordinate velocity.

I'm not sure I'm doing the math right, but I think that comes out to a coordinate velocity (of the outermost part of the equator) of 0.99998296 c.
A number which, AFAIK, implies nothing.

-Edited for better math
Last edited by Quizatzhaderac on Mon Mar 07, 2016 11:07 pm UTC, edited 2 times in total.
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doogly
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### Re: If spin really did represent particles actual spin...

What math are you doing?
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ijuin
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### Re: If spin really did represent particles actual spin...

doogly wrote:Oh that's true, it doesn't just follow a parallel logic, it adds to regular angular momentum. So the "intrinsic / extrinsic" names for "spin /orbital" can make some sense as well.

Yeah, it's weird.

To elaborate, a particle that has a spin of "1", for example, has one unit of angular momentum--not one unit of angular velocity or one unit of revolutions per second.