Lamb Shift

[Higgins]

Here' s a very nice little Wikkipedia article on this shift in the spectrum of the hydrogen atom. Note that this is an effect that can be explained by QED (Quantum Electrodynamics), but not by QM.

Note also the physical explanation is that the effect is caused by the virtual photons of the electromagnetic field, which again is not possible in QM, but only in QED.

http://en.wikipedia.org/wiki/Lamb_shift

[lpetrich]

You have to qualify it to nonrelativistic quantum mechanics. Quantum Electrodynamics is a relativistic theory.

Another such interesting effect is the departure of the electron's magnetic dipole moment from its lowest-order, "Dirac" value, the anomalous magnetic dipole moment (http://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_moment); it is about (1 + 1/900) times greater.

That magnetic dipole moment can be imagined as a result of the electron being charged and spinning; that gives it a built-in electric-current loop.

You might be interested in the various precision tests of QED (http://en.wikipedia.org/wiki/Precision_tests_of_QED); that magnetic moment is one of them.

[Higgins]

You have to qualify it to nonrelativistic quantum mechanics. Quantum Electrodynamics is a relativistic theory.

Another such interesting effect is the departure of the electron's magnetic dipole moment from its lowest-order, "Dirac" value, the anomalous magnetic dipole moment (http://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_moment); it is about (1 + 1/900) times greater.

That magnetic dipole moment can be imagined as a result of the electron being charged and spinning; that gives it a built-in electric-current loop.

You might be interested in the various precision tests of QED (http://en.wikipedia.org/wiki/Precision_tests_of_QED); that magnetic moment is one of them.

Nice stuff. The fact that QM doesn't explicitly incorporate special relativity is something fundamental that I don't often consider. QED (by definition I suppose? At least in Schweber's Book (http://books.google.com/books?id=61n5dE7FJQgC&dq=silvan+schweber&printsec=frontcover&source=web&ots=gT_U059_zF&sig=uz6b3kFvGAC0GgmVL0GowIKVUxc
that's when QED begins: when Dirac comes up with his relativistic versions of the Schoedinger equations,
though Schweber also notes Jordan's field view and its formal results.) is a range of formalisms that explicitly incorporate special relativity as well as being a research tradition and a "theory" (ie an area of work and teaching).

[lpetrich]

Some comments about Newtonian mechanics and special relativity.

Newtonian mechanics features relativity of motion; if you are in a car on a freeway and you are passing a truck, the truck is moving backwards relative to you, and forwards relative to the road. We normally omit what we consider mentioning what something's motion is relative to, because it is usually its environment. But when it is not clear from such a context, we often get more specific, like distinguishing between an airplane's airspeed and groundspeed.

Galileo had done a thought experiment about relativity of motion. Imagine that you are below decks in a ship; how could you tell that you were moving? He proposed that there was no fundamental physical difference between these states, and that insight became part of Newtonian mechanics.

But every object nevertheless "sees" the same time between space-time points. Or does it? A first hint of trouble was with Maxwell's equations of the electric and magnetic fields; they have wave solutions with the waves traveling at a constant speed in a vacuum: c. However, that is contrary to Newtonian mechanics, and that gave physicists a LOT of headaches in the late 19th century. Albert Einstein got the correct solution: special relativity, which modifies Newtonian mechanics to be consistent with Maxwellian electrodynamics. But a side effect is that objects don't all "see" the same time separation between space-time points, any more than they "see" the same space separation between them. It is a VERY tiny difference in familiar circumstances, but at speeds approaching c it can become VERY large.


Back to quantum mechanics. In general, it is non-relativistic; it depends on having some well-defined time coordinate. However, it does not exclude special relativity; including it puts in some rather strong constraints, because time gets mixed up with space.


The result is relativistic quantum field theory; a paradigm that includes quantum electrodynamics and related theories. And QED itself is now recognized to be a subset of a bigger theory, the electroweak theory. Yes, electromagnetic and weak interactions forming parts of a single interaction.

[smoore]

I believe the original calculation only assumed the presence of a random EM field, i.e. a "classical field" (Weldon was the author, I believe). I generalized this to the a positive temperature Lamb shift some years ago using the same technique and the Planck spectral density. Thus, you might say that the Lamb shift doesn't need quantum anything at all, only electrodynamics (which, of course, requires relativity). The same type of calculations have been shown to lead to the Casimir effect. From thereon, the calculations become very hard. In spite of all the mumbo-jumbo about Feynman diagrams etc, QED's real claim to fame is that it gives a concrete algorithm for calculating an (asymptotic?) series of approximations while dealing with the infinities of a point charge. Maxwell couldn't do that.

[dclary]

I can f'ing guarantee that when I came into this thread, my idea of what a lamb was did not match anyone else's here.

[Pthom]

And I was wondering why anyone would need to sift the little fluffy things.