I am currently attending a course on Quantum Field Theory and I got into thinking how valid these theories are. As the theory attempts to describe reality only far above the Planck (length) scale, this has to be taken into account.

Another problem that occurs is, how can we measure the validity of theory? For example the new particle found at LHC in 2012 has been detected with more than 5 sigma. But such a standard deviation can not be given for a whole theory.

I remember that one my lecturers once said that QED has been validated more than QCD. As both theories describe the same scope of energies, is that a statement one can make? Is there a way to measure the validity of a theory?

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    $\begingroup$ You validate these theories the same way you validate any other theory: by comparing their predictions with experimental reality. In the case of QED, the agreement between the predicted g-2 for electrons is mind boggling (the most precise agreements between theory and experiment going, unless things have changed recently and I didn't notice). Interestingly---and surprisingly to many people---the agreement on the same quantity for muons is not so good, leading many people to speculate about New Physics in the lepton flavor sector. $\endgroup$ – dmckee Jul 15 '13 at 23:53
  • $\begingroup$ Thanks for the answer, that gave me some deeper insight. Is it just a hypothesis, that the predicted g-2 from the standard model muon might differ from the measured one or is there already strong evidence? $\endgroup$ – physicsGuy Jul 16 '13 at 6:33
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    $\begingroup$ Hi Thomas, quantum field theory in the form of QED, QCD, EW theory are expected to work well below the Planck scale not far above it. At or probably even below the Planck scale, quantum gravity effects are expected to kick in which are not necessarily just described by QFT. $\endgroup$ – Dilaton Aug 14 '13 at 22:36

Theories are usually based on many assumptions. Domain of validity is a set of conditions under which this assumptions hold. For example QED/QCD does not take into account gravity - it neglects it. This gives us corresponding domain consisting of all energies at which gravity is much weaker then Strong and EM force.

One usually can ESTIMATE domain of validity by looking into assumptions. But it is also possible to measure this domain by simply finding the conditions in which theory starts to deviate from experiment more then desired.

Ideally each theory has to declare its domain of validity very clearly to avoid any kind of confusion and errors in thinking. This is rather well done in textbooks for mechanics, electricity and quantum mechanics. In field theory it is more tricky since theory is very undeveloped concerning practical applications so deviations from experiment can arise not from the end of validity domain but from the mistakes in complex calculations.

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    $\begingroup$ This is wrong, quantum field theory as for example the standard model of particle physics works very well, it agrees with all measurements so far, so your last paragraph is completely wrong. Physicists interested in beyond the standard model physics rathe think quantum field theory and the standard model work annoyingly well, since any robust signs of new physics persistently refused to show up until now. $\endgroup$ – Dilaton Aug 14 '13 at 22:31
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    $\begingroup$ "deviations from experiment can arise not from the end of validity domain but from the mistakes in complex calculations." This is true in any field and is nothing special to QFT. But when you do the calculations correctly, which people for the most part know how to do, then the standard model is very successful. $\endgroup$ – Michael Brown Aug 15 '13 at 1:10
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    $\begingroup$ "Have any of above WRITERS done anything in QCD?" QCD is well confirmed by now. You understand that it becomes perturbative and well controlled above the confinement scale, and lattice models work well below the confinement scale with quantifiable uncertainties. "I have a feeling that your knowledge is based on wikipedia and monte-carlo generator." Serious? Next time second guess your feelings before saying something like that. The things you are complaining about are common features of any nontrivial theory, quantum or classical. So it is totally unfair to pick on QCD or even QFT. $\endgroup$ – Michael Brown Aug 15 '13 at 14:54
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    $\begingroup$ It is a big jump from saying (reasonably) that "some of the calculations I would like to see done are hard to do accurately" to "[the] theory is very undeveloped concerning practical applications" and "Most of the calculations in QED and QCD are like little experiments on their own." A big and unjustified leap. $\endgroup$ – Michael Brown Aug 15 '13 at 14:56
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    $\begingroup$ QCD is an asymptotically free gauge theory so it is perfectly well behaved at arbitrarily short distances. In fact the standard model (including QCD) makes sense all the way up to the Planck scale. For the first time in decades particle physics doesn't have an obvious scale below the Planck scale where the dominant theory must go wrong. This is not due to any uncertainty in the calculations, but rather the fact that the SM is renormalizable, has no Landau poles below the Planck scale, and includes all the degrees of freedom we know about. (Yes, I remember dark matter...) $\endgroup$ – Michael Brown Aug 15 '13 at 16:20

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