Consider a magnetized sphere. You levitate it in a magnetic field, then apply an AC field, which causes the spere to begin spinning. You raise the frequency of the magnetic AC filed, to the point where the radial velocity reaches the speed of light-will the mass of the sphere increase?
Yes, the mass will increase, but the radial velocity will never reach the speed of light (otherwise known as c).
It’s fundamentally the same as accelerating something in a straight line.
As the sphere spins faster, it’s apparent mass (from the point of view of the accelerating AC field) will increase, making it harder to accelerate. Assuming the sphere doesn’t disintegrate from the centripetal/centrifugal forces, the apparent mass will keep increasing the closer the radial velocity gets to c. The field will never be strong enough to have the radial velocity actually reach c.
Here’s a simpler version of the OP: Suppose I take a very long stick, and anchor one end of it down somehow. Now I move the midpoint 100,000 miles per second. The far end must be moving 200,000 mps, which is faster than light, right?
NOT.
What about the lectrons in atoms (which already spin); can you spped them up?
Of course, long before your sphere even approaches a measurable increase in mass, the forces holding the molecules of the sphere together will be smaller than the centrifugal force tearing it apart.
Particle spin is fundamentally different from the sort of spinning a Harlem Globetrotter can do with a basketball atop his finger. We call it “spin” but it’s not really the same thing at all; the electrons aren’t spinning in the sense we’re familiar with.
Then… what ARE they doing?
Nobody knows. Really.
I think we need to clear up what we are talking about first. Is suspect that when the laypeople here are talking about electrons spinning they are referring to the electrons orbiting around the nucleus. Yeah?
Well that just doesn’t happen. That idea vanished in the scientific world before you were born, but thanks to bad high school textbooks and bad sci fi it;s still popularly believed. Electrons don’t orbit the nucleus the way planets orbit a sun. Electrons exist around the nucleus. It’s all very quantum, but they don’t really move, they just exist in a probability cloud. The further you get from the nucleus the less chance you have of finding an electron, but they don’t actually orbit the nucleus at all. They just exist simultaneously at all points around the nucleus until the waveform is collapsed somehow, and then they exist ion single point? Make sense? No, it doesn’t make sense tome either, but it works in
practice and the physicists tell use its true. So just accept it.
When the experts like QED use the term electron spin they are referring, rather more correctly, to a property of electrons that defines their interaction with other electrons. Electrons have properties that effect how they interact with other quantum level particles. We give those properties names like spin, angular momentum and so forth because they help us concetpualise the interactions, but the names don’t in any way reflect the physical state of the electron. Electrons are described a shaving spin have spin but they don’t actually spin.
Actually, spin is pretty unambiguously a sort of angular momentum. When you add up all of the angular momentum of a system, you have to include the spin if you want it to be conserved.
Apropos to the OP, given our current bounds on the size of the electron, if you tried to model it as a sphere that’s spinning (in the classical sense) about its axis, you would in fact find that the equator of the electron is moving faster than the speed of light. All this really tells you, though, is that you can’t model an electron as a classical sphere.
QM enjoys playing with our minds. As Chronos says, even though the electron doesn’t actually spin it still has a sort of intrinsic angular momentum that is somewhat similar to a charged particle that actually did spin.
Similarly, in the hydrogen atom the potential equation has what is called a centrifugal term just like the classical equations for satellite motion. In fact it’s this term that causes the potential to have a minimum.
It seems that the quantum world is constantly dangling facts that make us think of the classical world, but then nails us with a gotcha. I suppose this is all a result of the Correspondence Principle, but for God’s sake how can something act so much like it moves but doesn’t. It’s all very frustrating indeed.
Keeve’s observation has been used as the basis for proving that perfectly rigid materials can’t exist. Imagine a light year long rod of it and you start pivoting one end at some reasonable speed chosen so that it were truly rigid the other end would have a speed greater than that of light. Impossible.