Sunday, January 15, 2006
I would like to know.
Subscribe to:
Post Comments (Atom)
skip to main |
skip to sidebar
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? The demo at this site seems to say (the text is truncated) that the particles generated by the detectors interact with the particles being measured. I never heard this explanation before.
The world needs ditch-diggers, too.
About Me
- Angry Professor
- I am a tenured faculty member at a large state university. My teaching efforts primarily consist of delivering statistics lectures to social science majors. These experiences have colored my perspective somewhat.
Disclaimer
This blog is 100% FERPA compliant. It is a work of fiction. Any resemblance to any persons, living or dead, is purely coincidental. The Angry Professor is the creation of Mr. Norrell, who lives in Guam with four rhesus monkeys and a gecko. He has never taught at a university.
Links Everyone Should Have
Reading Assignments
-
-
9 months ago
-
15 years ago
-
10 years ago
-
-
16 years ago
-
9 years ago
-
1 year ago
-
11 years ago
-
7 years ago
-
13 years ago
-
-
9 years ago
-
11 years ago
-
-
-
14 years ago
-
4 years ago
-
16 years ago
-
13 years ago
-
8 years ago
-
-
9 hours ago
-
-
-
7 years ago
-
12 years ago
-
16 years ago
-
11 years ago
-
11 years ago
-
14 years ago
Blog Archive
-
▼
2006
(102)
-
▼
January
(14)
- In which I am greatly amused.
- Go figure.
- The Wingnut Declaration.
- Why I hate my daughter's favorite movie.
- The worst idea to come out of the 20th century.
- Female ginkgos should be banned.
- Overheard in the coffee shop.
- Sometimes crawling into a hole is the only thing t...
- I would like to know.
- I have nothing to complain about.
- A cry for help.
- I know what I should do, I just don't want to.
- On Kinkos, etc.
- I was just getting started.
-
▼
January
(14)
7 comments:
As to the field vs. wave question, I used to tell me students to think in terms of a water analogy. "Is the ocean a body of water or just a bunch of waves?" As I understand it, the short answer is that it is both. A field with a waveform.
I don't know anything about the problems with the experiment in the second part of your question. Related to the uncertainty principle, perhaps.
the addition of particle detectors in the two-slit experiment
Hmmm. My understanding of the two-slit experiment is that it's done with light. The "detector" is simply your eyes and a screen onto which the light is projected. One can also do the experiment with electrons and a phosphor screen, and get the same result.
The stuff about photons hitting particles has more to do with Heisenberg uncertainty. Heisenberg's original paper is actually quite readable and available in "The Discoveries: Great Breakthroughs in 20th - Century Science" by Lightman, with excellent commentary.
I think I'm one of the few people that doesn't care for the Feynman lectures. I find his "proof by thought experiment" irritating in a way that's hard to articulate. It's like they're little stories to convince us that the universe operates as it does. But they're often confusing, and if you go back over it later and don't do it exactly right, you come to the wrong conclusion. Maybe this is just how physicists think (I've known several, and they're an odd breed).
From the page Jimmy cites (which is an excellent summary):
We place a light bulb behind the slits and look to see what is going on...We will see a small flash of light when an electron passes through the slits
Umm...we will? This is precisely my beef with Feynman's thought experiments. He's using a macro effect (surfaces reflect light) applied to a quantum scale. There might be some other way to detect electrons while minimally interfering in their trajectory, but it ain't a teeny lightbulb!
Thanks all - this helped a lot. I like the hydrodynamic explanation of waves and fields. And while I will never understand it at a deep level, I now have a better grip on the two-slit experiment.
An electromagnetic wave is a subset of electromagnetic fields.
Specifically, it is the component of the field that is a solution of the D'Alembertian and has some form f(x-v*t) + g(x+v*t).
Any given electromagnetic field can be decomposed into a wave field and a non-wave field (the latter may be static or time variant). Either component may be zero or non-zero, and in general the decomposition is frame dependent.
Not going to touch the two slit experiment, this margin is too narrow for my brilliant insight
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. 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.
Thank you, steinn and jeff.
Post a Comment