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Are all fields in the universe we know of quantum fields? Do all fields that exist must be inherently quantum in nature?

How about fields that are yet to be discovered (ie. a new field like Higgs field) , do they all have to be quantum fields?

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    $\begingroup$ We're still trying to make sense of how gravitational fields make sense in quantum terms, but there are good theoretical reasons to think gravity should be just as quantum as any other field. $\endgroup$
    – J.G.
    Aug 19, 2018 at 17:55
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    $\begingroup$ @J.G. - Except that quantum gravity is almost definitely not described by a quantum field theory. There are good theoretical reasons to believe that gravity should be quantized in some way, but it is certain that quantum field theory is not the way to go. $\endgroup$
    – Prahar
    Aug 19, 2018 at 18:00
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    $\begingroup$ @Prahar In its present form, yes; but once we have a more mature understanding of the topic, gravity will be "a quantum field" in some sense, just not the "has a CFT ultraviolet limit" sense. $\endgroup$
    – J.G.
    Aug 19, 2018 at 18:21
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    $\begingroup$ The underlying premise of the question is a field of epistemological landmines, and hence ill-defined: What does it mean for a "field" to "exist"? For instance, many experiments can be explained much better with classical electrodynamics than a hopelessly overcomplicated quantum electrodynamics explanation, but some can't. Does that mean the classical electric field doesn't "exist"? $\endgroup$
    – ACuriousMind
    Aug 19, 2018 at 22:24
  • $\begingroup$ @J.G. That seems more like an answer than a comment. $\endgroup$
    – rob
    Aug 19, 2018 at 22:30

2 Answers 2

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Currently all fundamental fields are quantum, except for gravity. For this reason Quantum Gravity is a hot area of research, but the full Quantum Gravity theory has not been developed yet. Why not?

The challenge is not just technical, but conceptual. On one hand, the Quantum Field Theory cannot consistently co-exist with any classical theory. If the Quantum Field Theory is correct, then gravity must be quantum. On the other hand, gravity cannot be just another quantum field theory, because gravity bends the space and time ("the background"), on which the Quantum Field Theory is based, and this creates unreasonable challenges (time is steady and independent in QFT, but depends on the field and is dynamic in GR) that technically result in non-renormalizability of quantization.

The only logical way to resolve this contradiction is to admit that both theories, General Relativity and Quantum Field Theory, are approximations of another unknown yet theory that in itself is neither General Relativity nor Quantum Field Theory. As mentioned in the comment of @Prahar above, chances are that gravity will be quantized in some way, but Quantum Gravity will not be a standard Quantum Field Theory.

Other possibilities also have not been ruled out, such as that gravity may not have a quantum nature or have a nature that would change our understanding of "quantum" and what exactly we mean by it. Thus the answer to your question is that no one knows yet.

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    $\begingroup$ Many would consider the Higgs field fundamental. Others may still question its existence. Is it really the Higss that makes particles massive? Or is it Quantum Gravity instead? The best answer to your persistent question is that we don't know. What seems to be certain is that the Quantum Field Theory must be modified, but it is unclear if gravity must become quantum or something else completely new, as the quantum physics concept as we know it breaks down at the Planck scale. Perhaps it would help if you clarified what exactly you mean by "quantum" and what the motivation for your question is. $\endgroup$
    – safesphere
    Aug 19, 2018 at 22:23
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    $\begingroup$ The non-compatibility of general relativity with quantum field theory is not inherently "because gravity bends the space and time", it is because of the technical issue of non-renormalizability of the naive quantization of GR. This issue can also happen for other classical theories which in no shape or form bend space and time, so to claim that that aspect of GR is at fault for not being quantizable is ill-supported. $\endgroup$
    – ACuriousMind
    Aug 19, 2018 at 22:26
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    $\begingroup$ @ACuriousMind This is not a graduate question that would benefit from such a level of details. This technical issue is not simply "technical", but comes from the fact that QFT is based on the static (or steady) time while time in GR is dynamic and depends on the field itself, which is just another way of saying that the spacetime is curved (including by the field itself that is defined on this time in the first place). Thus your comment lacks the physical insight. And if another classical field is also non-renormalizabile, it may be for an entirely different reason than gravity. $\endgroup$
    – safesphere
    Aug 19, 2018 at 22:53
  • $\begingroup$ @ACuriousMind What is even being quantized in those "naive" attempts? Some weak-field approximation? $\endgroup$
    – Joker_vD
    Aug 19, 2018 at 23:09
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    $\begingroup$ @parker Because currently gravity is not quantum, we cannot exclude the possibility of discovering other fields that would not be quantum at lest until we learn to quantized them. So no, newly discovered fields don't have to be auantum right away. For example, the field related to the causal properties of time that was reportedly discovered by Kozyrev around 60 years ago was not quantum (search for Kozyrev Causal Mechanics). $\endgroup$
    – safesphere
    Aug 20, 2018 at 15:39
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We believe that fundamentally the universe is quantum mechanical. So we would expect all fundamental fields to be quantum in nature. However that does not mean that all fields are quantum.

The laws of physics depend are scale-dependent (Joseph Conlon gives a very good exposition on this in Why String Theory?). Thus the nature of the field will depend on the scale of the theory/problem. If the scale of the problem lies in the classical domain then the fields of interest will be classical in nature. In principle we can solve such a problem with quantum fields, but in practice it does not quite work that way.

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