
#127
Feb2713, 09:56 AM

P: 43





#128
Feb2713, 09:59 AM

P: 381





#129
Feb2713, 05:06 PM

Sci Advisor
P: 5,307

Anyway, it's irrelevant for decoherence




#130
Feb2813, 12:07 PM

P: 73

Please understand that I do not understand the large majority of scientific jargon on this thread, would it be possible for you to try to explain this as if to someone that is slightly above a layman (I have knowledge of most concepts, just not the mathematics behind them, which I do not understand). Thank you. 



#131
Feb2813, 01:57 PM

Sci Advisor
P: 5,307

Virtual particles in the sense I define them  as internal lines in Feynman diagrams  are a mathematical tool used for an approximation  socalled perturbation theory. Unfortunately most quantum field theories like QED, QCD etc. are very complicated and we do not have the mathematical tools to solve them exactly. But fortunately we have several approximations. Perturbation theory is used for weak coupling, where it makes sense to start with free, noninteracting particles and to add small corrections for interactions. Interestingly this works very well in many cases, especially for scattering experiments (but there are other problems like QCD bound states, e.g. protons, neutrons, ... where this approximation is useless).
If you would have mathematical tools to solve quantum field theories exactly, there would be no reason to introduce perturbation theory, there would be no name for the mathematical artifacts, and we would not have these discussions. Before studying QCD I was working on twodimensional models, fields living on a line = one space dimension + one time dimension. These models a rather simple, a good starting point for beginners. There are exactly solvable models with bound states, there are other approximations, and thefore no reason to use perturbation theory. In QCD there are tools to study nonperturbative aspects, tools like chiral effective theories, lattice gauge theories, ... All these tools do not require Feynman diagrams and therefore  using these tools  there is nothing which we call 'virtual particle'. In addition there are mathematical reasons against perturbation theory. We know that strictly speaking it is illdefined, it is something which does not exist mathematically, but nevertheless it seems to work in a very restricted sense. And there are applications where this illdefined math does produce correct results which agree with experiments (strange, isn't it? we can prove that it does not work, but using it seems to work ...). Now what I am saying is that we can START with a formulation w/o any approximation and w/o virtual particles. Then we have to introduce approximations, but doing this we CREATE several problems, or we apply approximations outside their scope of applicability, so the approximation BREAKS DOWN. Doing this we have mathematical artifacts  virtual particles  but due to the problems we introduce there seems to be no good reason to believe in virtual particles to be more than just limited tools. Does this help? 



#132
Feb2813, 05:25 PM

P: 158

I would not be quick to dismiss something as only a 'mathematical artifact' just because it is part of an approximation. This is an interesting methodological question that deserves careful study. Remember that the number 'e' is a limiting value for many types of series expressions. It's possible that these 'approximating' series do have specific meaning in themselves; the fact that they have a welldefined limit at a specific irrational number does not negate that the series terms might have physical content if the argument of the exponential has physical content. Remember that the perturbative expansion of QFT has as an argument for the exponential the action of the field, which certainly has physical content. It's a leap to say categorically that terms in the expansion of a quantity with physical content do not themselves have physical content. Now of course we have to be careful about what the physical quantities are. In the earlier example of the radioactive atom, the exponential argument is not a field, it's just a number (decay rate). So that comparison was not a good one to the QFT case.
I appreciate the interesting discussion here but I should let you know that I am currently swamped with various obligations and may not be able to check in for a while. Thanks again everyone for your interest. I hope you will visit my website which presents preview material from my book and explores some of the ideas we've discussed here. http://transactionalinterpretation.org Best wishes RK 


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