Posted on 10/25/2004 1:46:25 AM PDT by accipter
Actually, I once had a professor who spent three entire weeks of class proving one theorem (as an undergrad). Well, actually, she acknowledged that she failed to prove the theorem because she had made an error that should have been obvious to all of us (but, alas, it wasn't; apparently, neither was it obvious to her, because she never let go of the secret).
If things show up in the math, they are there physically. When you madulate the amplitude of a sinusiodal wave, you generate other frequecies. Those are the frequencies that show up in a Fourier representation of the wave. In AM radio transmission the sinusiodal wave's amplitude is modulated. If you modulate it with pure sinusiodal tone and observe the frequencies, you'll see the carier f + the tone and the carrier - the tone. Those are the upper and lower sidebands. If the modulation contains a range of frequencies, the upper and lower sidebands are the carrier +/- the mod freqs. Either sideband can be detected and the modulating signal recovered. AM is really frequency modulation. Whenever a sinewave, or a DC signal(f=0) is distorted, other frequencies are created.
"inverse Compton Effect"
Requires extreme conditions. ie. e speeds close to c in a plasma, as around a neutron star, or an accelerator.
"In time, all of the Compton effect will be explained in this way."
What about Compton scattering from a beam of very cold, slow neutrons? QED explains all these things and correspondence principle allows for the clasical theory to hold in a great number of cases, but not in all. QED explains the hydrogen atom to fine detail, whereas EM, or even QM can't. The field's are quantized. That's what the success of QED shows. Photons are reality. The Std Model and QCD likewise are more general and contain both QED and classical EM. Why try to reverse it when classical EM theory doesn't have a prayer to answer the questions and provide the knowledge and understanding the more general theories do?
It is generally a crude but adequate universal modeling system. It won't be as efficient or accurate as algorithmically-finite variants of the universal Solomonoff predictors common in algorithmic information theory, which as a class are provably the optimal form of the broader mathematical concept. Incidentally, anyone selling "AI" who isn't using computational constructs of this latter type are selling nonsense; there have been a number of neat mathematical proofs in the last few years that show that intelligence can only be tractably expressed in this narrow range of computational constructs. Particularly amusing when you consider no AI design attempt has ever used them in the past.
So democrats are born w/o Solomonoff predictors and just max entropy?
Just kidding...
Who knows what causes an eclipse? The Shadow knows, heh, heh, heh....
That's not true. I could just as easily represent a signal with a impulse transform or with wavelets or whatever. Does that mean that the signal is made of impulses or wavelets? Of course not. Don't confuse mathematical representation with physical reality!
When you put that AM signal into a circuit and recover the sidebands, what are you really seeing? The original sine wave hidden inside the signal? Nope, you're seeing the response of the circuit to a given input. You don't even see the original sine wave input because the reconstruction by the filter is not perfect, especially when it comes to the beginning and end of the signal. Filters are resonators and you see the resonance of it which can *appear* to look like the original. Think of a filter as a drum. You hit it with a drumstick. The drum vibrates in response. Did you just see a sine component present in the drumstick? No. The drum simply responded to a stimulus.
Why try to reverse it when classical EM theory doesn't have a prayer to answer the questions and provide the knowledge and understanding the more general theories do?
Classical em + relativity can explain most of the Compton effect right now because its been stripped down to a single wave and single electron. One of the reasons why CEM has difficulty is because it has to explain everything all the time. QM and its extensions only deal with the interaction endpoints and ignores what goes on in between. Even in my CEM explanation of the Compton Effect, I had to ignore all of the transients and focus on the endpoints in order to reach the solution (I simply start with an electron at rest then calculate the double doppler effect at a given speed and equate that to the experimental result). I do have a numerical simulation that gives all the transients.
[Groan ...] Actually, you might go with that for a tag line.
It's morning; you can come back inside now.
placemarker
Evil spirits ... devour moon ... me beat on tom-tom ... sacrifice eagle ... moon return ... all is well.
Someone been hittin' the peace pipe?
Me save moon. But me get no respect. Ugh.
Guilty as charged! I bet you even sang songs.
Ahhhh...... channelling "Fdot" again, I see.
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