kanex
发表文章数: 860
武功等级: 弹指神通
(第六重)
内力值: 343/343
=== My crackpot theory ===
The central issue is that I don’t think the probability interpretation, the operator + Hilbert / Fock space approach, or even the idea of field itself in quantum theories should take any role in a fundamental theory of the universe [but I forget to mention this clearly in any of my email, so Prof. Li became very angry and thought I know nothing about quantum theories]. I will briefly explain the reasons.
The most common interpretation of QFT is: the quantum fields are the only things that matters [in some sense, path integral formalism is more powerful than the canonical approach, for we are able to derive some non-perturbative results from it. But, we shall notice that none of these “topological” solutions are observed. Some people hold the belief that due to some black magic we will get miracles if we know all the non-perturbative features of the theory, but I have to disagree]. It is always said that "particles" are localized Gaussian wave packets of the field [we can map the field to a vector in the Fock space, and have a more “relevant” picture of the particles in the field. But this really does not change anything]. However this is just the principle. We do not need this principle for doing any calculations. And we do not need this principle for making any predictions of the real universe.
I have to say that the only usage of this “principle” is to bring endless confusions.
We just do a functional integral over field histories, and get the only “observable”: the S-matrix [Unfortunately, it is not well-defined when we have the big bang. We do not even know what a vacuum is in that case]. Everything is encoded in it. And, we have huge troubles decoding them. It is very discouraging.
What is worse is that we do not know how to do the integral directly. It is ill-defined from the start. We do a perturbative expansion of the exponential, and get a series. We use funny diagrams to help us remembering the coefficients in the series, and we call them Feynman diagrams. For some deep reason [check john baez’s website. I wont go through it here], Feynman diagrams look superficially close to some “real process”, however it is perfectly legal [and a wide-spread idea] to regard them as merely a tool for doing perturbative calculations and hand-waving arguments.
The integral is still ill-defined because we did not choose the correct measure. We get infinities. Then we have regularization + renormalization. The real mathematics behind them is to replace the Lebesgue measure by Gaussian measure. “Particles” are Gaussian! After all this mess, we finally get some physical results.
Are we satisfied? Is it the end of the story? No.
[to be continue.]
江畔何人初见月`江月何年初照人`
| 发表时间：2005-12-12, 20:10:38 |
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kanex
发表文章数: 860
武功等级: 弹指神通
(第六重)
内力值: 343/343
Re: === My crackpot theory ===
Sorry, I forget to say that we need the idea of particle or creation & annihilation operator to calculate almost everything. It only fails when we want to do something "fundamental". I will try to make this clear...
江畔何人初见月`江月何年初照人`
| 发表时间：2005-12-12, 20:24:11 |
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kanex
发表文章数: 860
武功等级: 弹指神通
(第六重)
内力值: 343/343
Re: === My crackpot theory ===
Please ignore this post.
江畔何人初见月`江月何年初照人`
| 发表时间：2005-12-12, 20:40:37 |
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kanex
发表文章数: 860
武功等级: 弹指神通
(第六重)
内力值: 343/343
Re: === My crackpot theory ===
I have to make it clear that the "theory" I had in my mind and what I said to Dr.Li is almost the opposite: only particles matters. It just happens that I accidentally slip to the field view [which is not correct] because I got something wrong in my brain.
江畔何人初见月`江月何年初照人`
| 发表时间：2005-12-12, 20:51:42 |
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kanex
发表文章数: 860
武功等级: 弹指神通
(第六重)
内力值: 343/343
Re: === My crackpot theory ===
And of course particles should be plane waves instead of wave packets in a relativistic field theory. What a foolish mistake I have made.
江畔何人初见月`江月何年初照人`
| 发表时间：2005-12-12, 21:02:24 |
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