Tom Mattson

Too bad. The universe isn't known a priori. It is the nature of scientific reductionism to explain things in terms of other, unexplained things. There is no paradox. A paradox occurs when, for some statement X, it is possible to derive both X and ~X from a theory. With SR, it is not possible to do that for any statement X. They are different, but why would I tell you about a mechanism that I do not even believe exists, or see a need for? Moot point, because they are different. Yes, SR does have a connection to physical reality. Its postulates have been experimentally verified, and the consequences of those postulates describe spacetime locally very well.

Well...that's right! But it doesn't imply a frame of absolute rest. The rate of vibration of a physical object doesn't become different in different frames. It simply is different in different frames. There is no mechanism necessary because nothing whatsoever is happening to the clock. Good thing SR doesn't do that then!

Geez, calm down! No one owes you an answer, and we all have real lives that sometimes get in the way of making 20 posts a day. Well except for Johnny, apparently.

I define "crime" as "that which is against the law, and more serious than a violation" (aka: "a misdemeanor or a felony" aka: "transgressions of the law which are tried in criminal court"). Since there's a misdemeanor statute against adultery in Florida, adultery is a crime in Florida. How on Earth should I know? Ask them. It ain't my opinion, it's a fact. To raise the point that there was an avenue open to the Schindlers that could have prevented the action of the Federal government on their behalf.

No' date=' I want to see the Schindler family do something through conventional legal means, rather than getting the Federal government involved. What I've described is feasible, and I wonder why it wasn't done. Well it is a crime, your personal opinion notwithstanding.

No, I do too. I read an article once (can't find the citation, but I'll look for it) that Michael Schiavo stands to lose a substantial inheritance if he gets divorced. That would certainly constitute a motive. But Schiavo has started a whole family with another woman in the last 15 years. In my opinion, he shouldn't be allowed to have his cake and eat it too. The Schindler family may not be able to force a divorce, but they can certainly file a criminal complaint, because adultery is a crime in Florida. They can and should use the threat of jail time as leverage. http://www.sodomy.org/laws/florida/cohabitation.html

Which Lorentz tensor? A Lorentz tensor is anything that transforms as a tensor under a Lorentz transformation.

You already said it: A dipole is 2 poles' date=' which we call north and south. Well if you have Griffiths, then surely you can find out what a B field is with a minimum of trouble. Griffiths is the best book out there at the undergraduate level.

There's nothing strange about it. It's just another magnetic dipole.

Says who? Then consult an EM book. The interaction of a magnetic dipole moment mwith a uniform static B field is well-known. The torque is T=mXB. Not that it's necessary to invoke QED here' date=' but the magnetic force is just an aspect of the EM force, which is mediated by virtual photons. But as I said, there's no need to go to QED when looking at field strengths that are as large as those that are typically used in this sort of experiment. This is actually backwards. We set the divergence of the magnetic field equal to zero because no monopoles have been observed, not the other way around. If a monopole were found, a source term would be added to the RHS of that equation.

You've just answered your own question.

Anyone who has studied classical EM theory understands what a magnetic field is. There is: A magnetic field.

Yes, I do regard it as knowledge. It is a well-confirmed prediction of a deductively valid scientific theory. You guessed right.

That does not preclude its occurance, of course. It would be, if you knew more QM. That's not what electron spin is. Its spin is not analogous to anything classical, such as a spinning top. The spin of the electron is just an intrinsic quantity of angular momentum that the electron is born with.

We are indeed. If you turn a spin-1/2 particle through a complete revolution' date=' its physical state changes in just the way I described. A ket is not a solid object, but the spin-1/2 particle it describes is.

No' date=' it's not an operator. A spinor is an eigenvector of the Pauli spin matrices. Eye of the beholder, and all that. I think it's beautiful. True. Not true in general. That is only the case for spin-1/2 particles. For spin-1 particles, a 2p rotation gets you right back to "ket". It is. Take any object in your house. Now rotate it through 360 degrees, and see if you don't get back to where you started. That's right for lepton, but not for fermion. Quarks are fermions, and they are subject to both nuclear forces.

That's a good start. Yes.

You don't derive it, it's just an arbitrary vector. The vectors |+> and |-> are defined as follows: s3|+>=(1/2)|+> s3|->=(-1/2)|-> where s3 is the 3rd Pauli spin matrix. |+> and |-> are the only eigenstates available, so an arbitrary spin state can be expressed as a linear combination of them, which is what I did.

I'll edit this once LaTeX is fixed, but for now here it is in regular font. To rotate a state vector about a unit normal vector n by an angle f you have to use the rotation operator, which is: D(n,f)=exp(-in.Sf/(h-bar)) where S is the spin operator. Take a state vector for an arbitrary spin-1/2 particle: |a>=c+|+>+c-|-> and let D act on it. For concreteness, let n=k and let f=2p. D(k,2p)=exp(-2piSz)|a> D(k,2p)=exp(-2piSz)c+|+>+exp(-2piSz)c-|-> D(k,2p)=exp(-ip)c+|+>+exp(+ip)c-|-> D(k,2p)=-c+|+>-c-|-> D(k,2p)=-|a> The state vector picks up a negative sign, which is equivalent to a phase change of p radians.

That's where the randomness shows up.

I really couldn't care less about your assertion.