This question is from one historical perspective. The question is: how physicists historically found out that one needs quantum fields to describe matter?

Being more detailed. Let us consider the electromagnetic field for a while. Classically this was already a field. Now, if I understood the history correctly, in the days of old quantum theory, when Planck proposed the solution to the blackbody radiation problem in terms of quantized energy levels, and when Einstein did the same to solve the photoelectric effect problem, they were essentialy proposing that light (and hence the electromagnetic waves) could be described in terms of photons.

Since light classicaly was a field it seems to be expected that when this field was properly quantized we would get these particles somehow as proposed by Planck/Einstein. I believe this was done by Heisenberg as soon as he proposed his matrix mechanics.

If I recall, he applied his methods to the electromagnetic field and found a collection of harmonic oscilators, which would be the particles (photons).

Now, it turns out that today we use fields to describe all matter. Some physicist even say that fields are more fundamental than particles altogether.

But other matter (like electrons) classicaly isn't a field like the photon. And in truth, by the historical development of quantum mechanics for the other particles one would expect wave functions instead of fields.

Actualy, it seems Dirac himself proposed his equation as a "wave function equation" rather than a field equation, only later this approach being taken.

So: while the photon is classicaly a field and the historical development pointed towards a particle upon quantization, the quantum field point of view seems quite natural.

But for other matter (like electrons, and all other fundamental particles), how physicists found out, historically, that the field viewpoint was needed? What led physicists to realize one needed to describe all matter with fields, and not just the electromagnetic field?

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  • I don't know the history behind it but I would say Special Relativity. It is within the field description that space and time come in the same footage rather than the point particle description. After all, it's not a coincidence that the same notation is used in SR and in relativistic field theories. This doesn't mean, however, that any field theory is relativistic but it means that a relativistic field theory is always possible to find. – Panos C. Jul 12 at 14:09
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    There are loads of articles about the history of QFT a mere Google away. As I recall Steven Weinberg wrote one that is very interesting reading. (later) aha, I was thinking of this paper. (later still) also this paper. – John Rennie Jul 12 at 15:10

The Wikipedia coverage of the history is pretty spot on, and there is hardly a point in exactly dating the incremental formal developments of the second quantization picture of Dirac, Jordan, Wigner, Pauli, and Heisenberg, etc. QED has served since as a prototype of arbitrary creation and annihilation of matter and antimatter, made possible by relativity, that I suspect you are already aware of.

Here, however, I would wish to emphasize Fermi's 1933 crucial utilization of QFT to do "real physics" (Wigner); particle physics as we understand it even today: he established that the creation, annihilation and transmutation of particles in the weak interaction beta decay could best be described in QFT, specifically through his eponymous quartic fermion interaction. This C N Yang paper is essential reading on the subject. Note link.

A neutron disappears, a proton, electron and neutrino appear, in a calculable framework.The essence of QFT is collective accounting of indefinite numbers of creation and destruction of particles of diverse species, namely second quantization in Fock space: rampant emergence and disappearance of particles/excitations subject to the conservation principles of the particular QFT, here conservation of baryon and lepton numbers, charge, etc. With the above reference, Fermi really opened the conceptual floodgates.

  • "accounting of indefinite numbers of creation/destruction" -- sounds rather like Feynman's Sum over Histories. – Carl Witthoft Jul 13 at 12:15
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    I'm not sure if this is an invitation to clarify... I am only summarizing the effect of Fock space and second quantization: rampant emergence and disappearance of particles/excitations subject to the conservation principles of the QFT. So, in ᵝ decay, conservation of baryon and lepton numbers, charge, etc... An infinity of paths does accommodate that, but it also describes single particle quantum mechanics in a conventional, dull, Hilbert space. – Cosmas Zachos Jul 13 at 13:35

The development of concept of "Field' to describe the events happening around us in connection with various interactions which operated at "action at a distance' has very early beginning.

Faraday and Maxwell created one of history's most telling changes in our physical worldview: the change from particles to fields.

As Albert Einstein put it,“Before Maxwell, Physical Reality …was thought of as consisting in material particles…. Since Maxwell's time, Physical Reality has been thought of as represented by continuous fields, ...and not capable of any mechanical interpretation.

This change in the conception of Reality is the most profound and the most fruitful that physics has experienced since the time of Newton.

As the preceding quotation shows, Einstein supported a "fields are all there is" view of classical (but not necessarily quantum) physics. He put the final logical touch on classical fields in his 1905 paper proposing the special theory of relativity, where he wrote "The introduction of a 'luminiferous' ether will prove to be superfluous."

For Einstein, there was no material ether to support light waves. Instead, the "medium" for light was space itself. That is, for Einstein, fields are states or conditions of space. This is the modern view. The implication of special relativity (SR) that energy has inertia further reinforces both Einstein's rejection of the ether and the significance of fields. Since fields have energy, they have inertia and should be considered "substance like" themselves rather than simply states of some substance such as ether.

The general theory of relativity (1916) resolves Newton's dilemma concerning the "absurdity" of gravitational action-at-a-distance. According to general relativity, the universe is full of gravitational fields, and physical processes associated with this field occur even in space that is free from matter and EM fields.

Thus by 1915 classical physics described all known forces in terms of fields- -conditions of space--and Einstein expressed dissatisfaction that matter couldn't be described in the same way.

However the real inroads into particle concept and an alternative field description or visualization came in with the advent of Quantum Field Theory.

the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. Major advances in the theory were made in the 1950s, and led to the introduction of quantum electrodynamics (QED). QED was so successful and accurately predictive that efforts were made to apply the same basic concepts for the other forces of nature. By the late 1970s, these efforts successfully utilized gauge theory in the strong nuclear force and weak nuclear force, producing the modern standard model of particle physics.

Let us try to visualise electrons.

Everywhere in space there is a field called the electron field. A physical electron isn’t the field, but rather a localized vibration in the field.

Electrons aren’t the only particles to consist of localized vibrations of a field; all particles do. There is a field for every known particle say a photon, a quark, a gluon field and so on.

Even the recently discovered Higgs boson is like this. The Higgs field interacts with particles and gives them their mass, but it is hard to observe this field directly. Instead, we supply energy to the field in particle collisions and cause it to vibrate. When one says “we’ve discovered the Higgs boson,” you should think “we’ve caused the Higgs field to vibrate and observed the vibrations.”

This idea gives an entirely different view of how the subatomic world works. Spanning all of space are a great variety of different fields that exist everywhere. What we think of as a particle is simply a vibration of its associated field.

This has important consequences on the interaction of particles. For instance, consider a process in which two electrons are fired at one another and get scattered.

In the quasi-classical view of scattering, one electron emits a photon and then recoils. The photon travels to the other electron, which also recoils.

When the photon makes a quark and antiquark pair, the quark field is vibrating while the other two fields have no excitation. Finally, when the quark and antiquark combine to make a gluon, only the gluon field has a vibration.

In the QFT approach, a vibration in the electron field induces a vibration in the photon field. The photon field vibration transports energy and momentum to another electron vibration and is absorbed.

In the well-known process where a photon converts into an electron and an anti-electron, the photon field vibrations are transferred to the electron field and two sets of vibrations are set up—one consistent with an electron vibration and the other consistent with the anti-electron.

This idea of fields and vibrations explains how the universe works at a deep and fundamental level. These fields span all of space. Some fields can “see” other fields while being blind to others.

The photon field can interact with the fields of charged particles but cannot see gluon or neutrino fields. On the other hand, a photon can interact indirectly with the gluon field, first by making quark vibrations which then make gluon vibrations.

Quantum fields are really a mind-bending way of thinking. Everything—and I mean everything—is just a consequence of many infinitely-large fields vibrating.

The entire universe is made of fields playing a vast, subatomic symphony. Physicists are trying to understand the melody.

Reference-

https://arxiv.org/ftp/arxiv/papers/1204/1204.4616.pdf https://en.wikipedia.org/wiki/History_of_quantum_field_theory http://www.pbs.org/wgbh/nova/blogs/physics/2013/08/the-good-vibrations-of-quantum-field-theories/

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