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Our best descriptions of the microscopic world, that satisfy many fundamental requirements (as we know them today), are field theories.

Is there something fundamental about field interactions, or are they simply one tool that is flexible enough to offer a good description of fundamental physics?

I'm not asking whether the standard model is complete, but rather how unique our current framework is. If for example advanced life elsewhere has a mathematical description of fundamental physics - is it a field theory, or possibly a completely different approach?

anon01
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3 Answers3

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Comments to the question (v2):

  1. There are various speculations that spacetime (and fields on spacetime) are not fundamental concepts/objects but rather emerging/effective properties of an underlying theory of everything (ToE) yet to be discovered. See e.g. many talks online by Nima Arkani-Hamed, who often stresses this point.

  2. A popular candidate for the ToE is string theory (ST) rather than quantum field theory (QFT). [Strictly speaking, ST is a non-linear sigma model (NL$\Sigma$M) on a 2D world-sheet rather than spacetime, and hence a field theory (FT) in that sense.] There are efforts to develop a second quantized version of ST known as string field theory (SFT).

  3. A related issue is: if a FT does exist, does it have a Lagrangian formulation? See e.g. this Phys.SE post and links therein.

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Qmechanic
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Why we use QFT? Locality, firstly. There is no initely fast propagation of information. For this you got to have some field through which signal spreads at speeds less or equal to speed of light. On the pther hand, STofR and QM imply that number of particles is not conserved. Ordinary QM can not reproduce this fact but QFT can. So QFT is just quantization of classical field. Also, in Lagrangian formalism thery is manifestly inariant to Lorentz transformations. Is there some other theory, better than QFT? I dont know. Also, QFT somewhat resolves wave particle duality introduced by QM.

Žarko Tomičić
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Not only is there a room for an alternative approach, one will have to be found because neither of the two existing ones is overall consistent. The standard model as we know it is supposed to be a perturbative approximation to a yet unknown master theory. The most popular particle interpretation of it is in terms of a Fock space that actually involves no fields, and has particle configurations and creation/annihilation operators instead. It is good enough for perturbative computations with Feynman diagrams, but can't work non-perturbatively because as Malament showed no position operator can be defined even in free QFT. No positions - no particles.

It was originally thought that the field, a.k.a. wavefunctional, interpretation can escape this problem because it can make do with non-point localization operators. Instead of particle configurations it describes QFT states as superpositions of classical fields (the wavefunctionals), and observables as operator-valued fields. This is analogous to the Schrodinger interpretation of quantum mechanics. However, since the wavefunctional space is mathematically equivalent to the Fock space, it can't work either. More explicitly the problem is the following. On one hand, spacetime symmetries are supposed to produce physically equivalent descriptions. On the other hand, rotations of so-called coherent states produce unitarily inequivalent representations in the wavefunctional space, so "equivalent" states have physically inequivalent field content. See Baker's Against Field Interpretations of Quantum Field Theories.

The plurality of unification schemes show how non-unique the current framework might be. String theory alone offers vastly different reinterpretations of it, while loop quantum gravity tries to preserve at least some flavor of the field interpretation.

Conifold
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