Posted on 03/12/2003 9:21:09 AM PST by gomaaa
Totally off topic, but I suspect schizophrenia is a rather simple disorder structurally -- an inability to turn off what would otherwise be a normal dream state. Perhaps at heart it is a sleep disorder.
True, but there is a lot of evidence that people can be taught to live with bad feelings, and that as their lives improve, the bad feelings diminish. this is the school of therapy that says change the behavior first and the feelings will follow.
It is the only effective treatment for phobias, and it works really well.
In order to talk about it's shape, you would have to localize it, compress it to a single point. That's not allowed by the Heisenberg Uncertainty principle.
You don't even need to compress it to a point. Just an equation of the overall shape would be fine.
I used to work in a lab with a femtosecond pulse laser system. A pulse of about 25 femtoseconds (1fs = 10^-13 seconds) is spread out over a distance of less than a millimeter.
Cool stuff. What was the application? I've read quite a bit about photoconducting antennas and their applications. Even done a few simulations of it using my TLM program.
I think you're describing a photon scattering off an electron here, though I'm not quite certain. The problem is, you're asking for a classical response to a question that ONLY Quantum Mechanics will answer. For one thing, it is IMPOSSIBLE for a photon to scatter off an electron without having the elctron respond.
Classical em handles scattering fine until you get to extremely short wavelengths. Also, I guess my original scattering post was unclear. It would have been more clear to say an "initially stationary electron". Of course, the electron is free to move in response to the incident wave. My whole point was to show that an incident wave accelerates a point electron in such a way that the scattered wave cancels the incident wave at exactly the classical electron radius. It's weird that this radius can be calculated in several (seemingly) unrelated ways.
If they are indistinguishable, why did you describe one as a "free electron" and the other as a "bound electron"???
Let me repeat. Why would a stationary electron reflect e.m. waves?
Good grief. I said "a unit step em wave hits a stationary point electron". Stationary, as in not moving, v(t=0) = 0. The whole point of that paragraph was to describe how the electron accelerates in response to the incident wave and how the resulting reflected/scattered wave behaved.
The important question for society is, if some individuals cannot -- due to objectively verifiable brain disorders -- control their behavior, can we allow them freedom, even if they have not yet committed a serious crime? Right now the courts are mixed on this, as they should be, because there is no objective way of predicting threats. But it is a problem.
Oh, jeez. I have identical twin brothers. One lives in Ireland. One lives in England.
Look, guy, I was hoping to be able to explain something to you. You're pretending to be stupid as a rock, or you're not pretending; either way, it's not going to work, so let's give it up, OK?
Ok. One last thing, I would like an answer to my "great philosopher" question. I'm curious.
The way to describe a light pulse is an equation for the Electric field that solves the wave equation. This can have an incredible variety of forms, all depending on the situation. The most familiar form would be a combination of sin & cos waves, like E=Asin(kx-wt)+Bcos(kx-wt). Alternatively you could use complex exponentials. It gets more complicated when you bring the polarization of the pulse into it, since the numbers A & B can be complex. This isn't generally thought of as an individual photon, though, but a bunch of innumerable photons. (Not really innumerable, but a LOT.) I'm not sure this really answers your question, though.
Classical em handles scattering fine until you get to extremely short wavelengths. Also, I guess my original scattering post was unclear. It would have been more clear to say an "initially stationary electron". Of course, the electron is free to move in response to the incident wave. My whole point was to show that an incident wave accelerates a point electron in such a way that the scattered wave cancels the incident wave at exactly the classical electron radius. It's weird that this radius can be calculated in several (seemingly) unrelated ways.
Ah-ha! You're referring to Thomson scattering. Now I think we're on the same page. This is pretty cool. It's been a while since I've looked at this stuff, so this was a good review for me.
http://hep01.s.chiba-u.ac.jp/lecture/radiation/node1.html
I also found it in Classical Electrodynamis by Jackson(p.694), and I think he does a slightly better job of it.
So the incident wave accelerates the electron, which then emits radiation, as you suggest. The resulting scattering cross section (the "size" of the particle which the incoming wave "sees" and therefor scatters off of) is SigmaT at the bottom of the link I gave. It just so happens to include the classical elctron radius as a factor in the result. As you pointed out, this is also obtained by calculating what volume you would need to cram an electron's charge into to get a potential energy the same as an electron's rest mass. This is really wierd, seeing as how electrons don't really have radii according to QM. There's a nice discussion of this on:
http://www.rsystem.org/rs/satz/elecur.htm
The electron radius gives the correct scale and units for the Thomson cross section, but isn't the exact value. It is useful, but not an actual physical thing. Another way to show that this couldn't be real is to think that if the electron were a small, spinning sphere of this radius, (we can measure it's 'spin') the parts of the electron on the outer rim of the sphere (the equator if you will) would have to be moving faster than the speed of light. Thus neither the radius of the electron, nor it's spin are classical concepts and can only be understood quanutm mechanically.
Cool stuff. What was the application? I've read quite a bit about photoconducting antennas and their applications. Even done a few simulations of it using my TLM program.
Fs lasers have very interesting interactions with matter. They're so fast that they can be used as a strobe light of sorts to measure ultrafast phenomena like the motions of electrons in solids or in atoms & molecules. It can also be used to study the processes of chemical reactions the same way, as they unfold! Lots of cool applications. I'm just more interested in smashing atoms into each other at rediculous speeds.
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