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I have seen discusstions of this types before: there is a question about photons or virtual particles or vaccuum, etc. And there is usually a good and clear explanation from the point of view of Quantum Field Theory (QFT). It is usually final and mostly accepted answer.

But it is sometimes happen, that someone mentions the fact that the Standard Model (SM) gives only approximated predictions. Physicists need a perturbation theory to make predictions for collider experments and that results in some uncertainties. Espectially when ineraction constant is not very small so the series converges slowly.

As I understand the logic of this arguments - that approximate nature of SM preditions somehow undermines the basics of QFT. So the answer to the initial question (about photons or virtual particles or vaccum, etc) is said to be not based on a strictly experimentaly proven theory.

But I cannot see how one makes this logical connection between the statements about SM and about QFT. I suspect that this step is flawed, but I can be mistaken. Do you think there is such connection?

JamalS
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Tziolkovski
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    If having only approximate solutions undermined the physical theory that would make anyone who studies fluid mechanics rather sad! – John Rennie Feb 03 '15 at 19:14

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First: Scientific theories are never proven, only not falsified. Repeat that until it sinks in.

Now, for the actual content of the question: That we only have perturbative ways to compute the S-matrix/scattering amplitudes for the Standard Model is not a reason to doubt its validity. Almost no physical system, apart from toy models, can be solved exactly, there are, for almost every real world situation, approximations involved.

Think of the humble pendulum - even for this silly mass hanging from a string, you almost always will assume the string to be massless and $\sin(\phi) = \phi$ for small angles. This does not mean that the physical description of classical mechanics underlying this is "invalid" (well, it is, since we know of quantum theories, but that is not because the pendulum is not described exactly).

Almost all complicated systems have to be approached perturbatively - start from the simple model you know exactly (most often the harmonic oscillator, which is also the starting point for naive QFT perturbation in a sense), and see what happens if you add (small) complications. This doesn't mean our description of these systems is flawed, it means the real world is damned complicated.

ACuriousMind
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  • I love your first statement! They write "a given theory is proven" so often! Apart from perturbative (analytical) methods, there are numerical also. Even solved exactly, SM remains an incomplete theory, - it does not include some other things. – Vladimir Kalitvianski Feb 03 '15 at 20:04
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QTF is pretty messed up, although many physicists won't probably agree with this. The current methods are good enough to predict outcomes of experiments, but they are quite dubious from a mathematical point of view. Consider Dirac's interaction picture for instance, which is usually invoked by many physicists around the world to predict the outcome of an high energy experiment or to verify that such results are comparable to the known theory. Only problem is that the interaction picture doesn't exists, even for a free scalar field with no interaction at all! (cf Haag's theorem). This fact is usually swept under the carpet, and therefore the ill-defined interaction picture is still broadly used to compute stuff.

Phoenix87
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    Well, as an explanation of sorts of why physicists think this way, a physically valid theory only needs to make verifiably correct predictions. Everything else is secondary. In particular, mathematical validity is not required. Existence (in the mathematical sense), not required. Technically it doesn't even have to be based on math at all, although good luck finding a way to make verifiably correct predictions without involving math in some capacity... anyway, sweeping mathematical inconsistencies under the rug is in some sense an intentional choice, not a denial of a problem. – David Z Feb 04 '15 at 01:46
  • http://physics.stackexchange.com/questions/3983/haags-theorem-and-practical-qft-computations – Mitchell Porter Feb 04 '15 at 01:46
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    Though I agree that the mathematical ill-definedness is aesthetically troubling, and that we should strive to seek a rigorous theory of nature (both from an aesthetic and and epistemic viewpoint), this does not invalidate QFT as a highly accurate and predictive scientific theory for all practical purposes. Just think of how long people did "classical mechanics" without a rigorous notion of calculus! The predictive power of classical mechanics hinges not on the rigor of infinitesimals, and the predictive power of QFT is not dependent on the rigor of the interaction picture. – ACuriousMind Feb 04 '15 at 13:54