Two Physics Questions

Posted by jns on January 18, 2006

Angry Professor at “A Gentleman’s C” asked two questions that caught my attention:

• Is there a difference between an electromagnetic field and an electromagnetic wave?
• Why does the addition of particle detectors in the two-slit experiment cause the collapse of the wavefunction?

Good, physics type questions. Naturally I started thinking about answers. I was finally provoked to write the answers down, though, through irritation. My irritation was at the willingness of the people in her comments to provide “answers” who didn’t really understand at all what they were talking about. It reminded me of my early days with Usenet newsgroups when (and this is still prevalent, of course) person A would ask a question and persons B-ZY would say that, although the didn’t know anything about the subject and had no idea about the answer, they’d be happy to offer their ill-informed opinions anyway. Person ZZ would invariably point out to person A that person A should really be interested in an entirely different question and was wasting time asking this one.

So, on the off chance that anyone might be intereted, here are my answers as I wrote them in Angry’s comments:

EM fields and EM waves are really two distinct, but intimately related concepts. A field in general is just a mathematical concept that assigns numbers to every point in space. They may be scalar fields or M-dimensional vector fields, continuous or not, static or time varying. Hydrodynamic fields specify a fluid’s velocity throughout space. EM fields specify the EM force as a function of spatial variables and time.

Stationary electric charges are the sources of static electric fields. Electric currents (steadily flowing electric charge) are the sources of magnetic fields. This connection between E and M is why they’re called EM fields. EM fields are completely described by Maxwell’s equations: four, first-order partial differential equations.

EM waves are time-dependent, propagating disturbances in the EM field, if you want to think of them that way. Propagating means that they travel in some direction and carry energy in the direction of travel. They are created by accelerating electric charges and are solutions of the second-order, partial differential equation, the “wave equation”, which is impicit in Maxwell’s equations. In modern thought, EM waves are identified with photons (just as “gravitons” are identified with the waves that presumably propagate through gravitational fields when masses accelerate).

The results of the double-slit experiment have nothing to do with interactions with photons from the detectors — this is some sort of mistaken impression [that was mentioned in the original question, but I cut it out]. It is an entirely quantum-identified effect. In short, the surprising result was that with one slit there was no interference effect; with two slits there was. This was thought to demonstrate the unequivocal wave-nature of light because how could a particle “know” which slit to go through? Waves, having spatial extent, can sense the presence of the second slit, provided the spacing of the slits is near the wavelength of the waves. The experiment was first done with light, but it can also be done with particles with suitable “slits”.

The answer to the conundrum from quatum mechanics is that the “particle” is really a “probability wave” that can sense both slits when they are present. According to the “Copenhagen Interpretation” of QM, the probability wavefunction has physical reality while the “particle” it represents has none until the act of observation, which instantaneously “collapses” the wavefunction and localizes the particle (in accordance with Heisenberg’s Uncertainty Principle) due to the act of detection itself. However, this result has nothing to do with the nature of the detector, and certainly nothing to do with interacting photons.

The Copenhagen Interpretation is not part of QM; the mathematical formalism works fine without it. It is, indeed, an interpretation of physical processes, and not everyone who uses QM believe the CI. It is claimed as the source of all those new-age ideas about how our minds alter the universe by “observing it”, ideas that demonstrate more clearly a lack of understanding of QM than an understanding of the universe.

Feeling a Little Derivative

Posted by jns on January 11, 2006

I knew a mathematician who had a recurrent dream. He dreamt that he was a partial derivative.

[Jeremy Bernstein, A Theory for Everything (Singer-Verlag, New York, 1996), p. 263.]

This quotation no doubt tells you more about me than I expect, but when I read it I found it terribly funny. I also have the strong conviction that it’s saying “partial derivative” that makes it so funny; “He dreamt he was a derivative” barely provokes a smile. I doubt, though, that it would be at all funny to someone who has no idea what a partial derivative is.