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My understanding is that, in the context of quantum field theory, particles arise as a computational tool. We perform an expansion in the path integral in some parameter, and the terms in these expansions correspond to Feynman diagrams which can be interpreted as interactions between particles.

My question: if particles are just a computational tool, why does it seem like particles really exist, and not quantum fields? For example, it seems like chemical reactions really do occur through the exchange of discrete particles called electrons. Are states with definite particle number perhaps more probable, more easily observed, or some kind of classical limit?

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – Buzz
    Commented Oct 2, 2022 at 21:02
  • $\begingroup$ Not all particles are observable in the conventional sense; indeed most are identified by their effects such as gravitational ones. $\endgroup$ Commented Oct 4, 2022 at 18:36
  • $\begingroup$ In some sense, "particle" means "the thing you can observe about a quantum field". $\endgroup$
    – DanielSank
    Commented Oct 5, 2022 at 1:07
  • $\begingroup$ Are you phrasing the question in the context of virtual particles or real particles? (My impression about QFT is that it is the former with the implicit interpretation, whereas the latter has a straightforward interpretation with experiment; specific coefficients in the QFT equations correspond to elements of reality that we perceive as quanta.) $\endgroup$ Commented Oct 6, 2022 at 10:16
  • $\begingroup$ @MahirLokvancic Both. My question boils down to: why do we seem to always observe states with definite particle content? Even when we aren't directly making observations, it seems that low energy macroscopic interactions happen as though there is definite particle content. In general, can't a quantum field be a superposition of states with different particle content? Why don't we see that playing out in low energy phenomena? Or, said differently, why isn't it a problem that we barely ever consider states with particle number superposition when describing phenomena? $\endgroup$ Commented Oct 7, 2022 at 1:53

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We don't observe particles, at least not in the sense of the physical definition of a particle (as the physical approximation of the motion of an extended classical body by the motion of its center of mass) or corpuscle (tiny pieces of matter).

What we are observing are quanta. Quanta are combinations of energy, momentum, angular momentum and charges (electric charges, lepton number etc.). These quanta are being irreversibly exchanged between quantum fields and external systems, like the detectors at CERN, for instance.

Quanta are not computational tools. They are the actual physical quantities that we are measuring in detectors and they differ in nothing from the classical energy, momentum, angular momentum and charge concepts.

What trips up many students and laypeople is the fact that quanta are properties and not objects. The "particle" nomenclature is one of the more unfortunate ones in physics. It suggests that quantum fields are made up of atomistic elements. That is not so. A general quantum field state does not have a fixed number of quanta that exist independently of emission and absorption processes. The quanta we emit into a quantum field are in general also not the same as those that we absorb from the quantum field. Both of those simplifications exist only in the most trivial scenarios. In reality what we "emit" and "absorb" depends on the physical properties of the emitter and absorber and the physical interactions in the "free field", just like in non-relativistic quantum mechanics where we have to specify the initial state (and by that the properties of the system that does the "preparation" of the quantum state), the free dynamics and the measurement system (i.e. the specific type of absorber). Only if we have all three components defined do we have a description of a realistic physical system.

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    $\begingroup$ @HansWurst The term "particle" has a well defined meaning in classical physics (it is the name of an approximation). So does the term "quantum" in quantum mechanics (where it denotes irreversible energy, momentum etc. transfers). The two are not synonymous and they are not even remotely related. It is an unfortunate historical artefact that physicists talk about particles when they actually mean quanta. "Fermion" and "boson" denote different field symmetries which are specific to three dimensions. They are not internal properties of tiny objects. $\endgroup$ Commented Sep 30, 2022 at 11:20
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    $\begingroup$ @HansWurst I hope this is close to the real theory and to popular language. An electron is a pattern in the electron field. When electron and positron annihilate, these patterns just fade away. But, this can only happen if, for example, another pattern, called a photon, in a photon field appears. This is because the behavior of these fields is coupled. A discrete amount of a property disappears from one field and appears in another - and that is the quanta transfer. Viewed from our macro level this can seem to be a classic particle. But there is no hard lump transferred. $\endgroup$ Commented Sep 30, 2022 at 11:22
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    $\begingroup$ @HansWurst If you are referring to chemistry.... in chemistry the number of electrons is a constant. That's the reason why we can count them as little blue balls. In nuclear and high energy physics the number of electrons is not constant. Only total charge and lepton number are conserved. $\endgroup$ Commented Sep 30, 2022 at 11:23
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    $\begingroup$ @FlatterMann Seems like you're a little lost in the forest of philosophy. Humans speak of the wind as if it is a thing. To claim a thing isn't a thing is to call it by a different name. Here, particle seems to have adopted the definition of quanta, and can be used interchangeably when discussing the topic in general. The particle is the pareidolia that the layman sees. Though, I'd be interested in what name you call clouds in the sky, as they are not "things" in almost the same way quanta are not "things". $\endgroup$
    – David S
    Commented Sep 30, 2022 at 22:37
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    $\begingroup$ @FlatterMann The edits massively improved the answer. Initially, your answer and supporting comments appeared more of an argument against the word "particle" than to answer the question. You have a clear understanding of multiple independent phenomena that laypeople coalesce into what they call a "particle". A quanta may not have coordinates, but the emitters and absorbers do. Regarding philosophy, you're all over it with things like "Humans like to think in terms of things... even when it is absolutely false to do so." Two interpretations of the quantum world differ mostly in philosophy. $\endgroup$
    – David S
    Commented Oct 3, 2022 at 16:35
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"My understanding is that particles arise as a computational tool."

This is a "cart before the horse" statement. Experiments determined that particles existed,( see here a bubble chamber photo of particle tracks) then "computational tools" were found by mathematically wise physisists that could model the interactions of the observed particles.

Quantum fields are analogous to a coordinate system on which with differential operators on the named fields ( electron, neutrino...) one can mathematically model the real world existence and interactions of particles and check the validity of the model by comparing to data.

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    $\begingroup$ I suspect the OP is thinking about infrared virtual photons comprising a macroscopic classical electromagnetic field, and, so, serving as mere computational tools; while looking away from the brutal reality of the (macroscopic!) labs and photomultipliers... My hunch is he is asking about cluster decomposition of QFT and the classical limit without going technical... $\endgroup$ Commented Sep 30, 2022 at 13:52
  • $\begingroup$ Even aside from her large PSE "reputation", I guess it might help to note the fact that anna v has been working at CERN throughout the several years that I've been looking at this site. $\endgroup$
    – Edouard
    Commented Apr 16, 2023 at 11:00
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It isn't true that particles are just computational tools. The SLAC did not, for example, fire computational tools down a 10,000-foot beamline and measure their scattering angles and energies as they interacted with other computational tools ;-).

As commented by others, what we call a particle (in a beamline) is an excitation of a quantum field and in the world we inhabit, it is those particles that are manifest; we learn about the underlying field by the study of its excitations.

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    $\begingroup$ Of course I don't actually think that the SLAC is firing computational tools. My question is more why a quantum field almost always looks like particles to us. My understanding is that there are some predictions of qft that are not purely particle phenomena, and yet it seems that particles are what we usually observe. Why? $\endgroup$ Commented Oct 2, 2022 at 13:13
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    $\begingroup$ @CharlesHudgins the best understood experiments in high energy particle physics are based on particle collisions. It is also possible to probe nonlinear effects of quantum fields, such as instantons. In general this is much more difficult and less well studied $\endgroup$
    – Jojo
    Commented Oct 2, 2022 at 17:29
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The theorists have mathematical rationalizations, but the reality (as Bohr pointed out) is that if your experiment senses fields you observe fields, while if it senses particles, you observe particles. Every radio detects the electromagnetic field, not photons. Waves in any field may be observed to diffract so long as their wavelength is accessible to a diffraction structure. On the other hand, if your experiment tracks particles, you'll observe particles.

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    $\begingroup$ @FlatterMann If you crank down the intensity and have sufficiently sensitive electronics, you may detect single photons with a photodiode. That's physical reality. Charged particles leave tracks. That's physical reality. In physical reality, we often see things that behave like particles. We can capture this in models, but models are not physical reality. $\endgroup$
    – John Doty
    Commented Oct 3, 2022 at 23:28
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    $\begingroup$ I, or better, some of the detectors that I have built have been detecting trillions of photons over the years. All we ever get from a photon is one irreversible energy transfer into a photomultiplier or avalanche diode. One can measure the momentum by using lenses, the energy with a grating and the spin with a polarizer. That's it. High energy particles leave tracks because the matter in the detector acts as a weak measurement system. See Mott's paper "The wave mechanics of alpha-ray tracks" (1929). Tracks are an emergent phenomenon. Single quanta don't have them. $\endgroup$ Commented Oct 4, 2022 at 3:10
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    $\begingroup$ Tracks is what we get when high energy quanta interact weakly with matter. That is not a single quantum phenomenon. It is tens, hundreds, thousands or even billions of individual scattering events, no different from a visible light wave being made up of 10^19 photons per Joule. I don't know what mathematical objects you see in Mott's paper. He talks about the reason why a plane wave becomes a track: because once it is localized somewhere a series of weak scattering event will keep it localized along the momentum vector starting with the first localization. $\endgroup$ Commented Oct 5, 2022 at 4:24
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    $\begingroup$ In the physical world you get tracks only if you have weak interaction between a plane wave and matter. Without the matter you always have a plane wave. These are the facts. I am sorry if you find the facts confusing. That confusion goes away as soon as you start building high energy physics detectors like I did in my active life. Nobody has ever managed to see a track without a matter filled detector and that is exactly what quantum mechanics predicts. $\endgroup$ Commented Oct 5, 2022 at 21:39
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    $\begingroup$ If you want to have an argument for arguments sake please have it with someone in the chat. The comment section is, for all I understand, not to be used that way. $\endgroup$ Commented Oct 5, 2022 at 23:51
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This is more of a side comment, but one way of thinking about quantum field theory is to regard it as a computational tool to compute particle interactions a la Weinberg : see https://arxiv.org/abs/hep-th/9702027 for this viewpoint on QFT. In a nutshell, we construct quantum fields to describe particle interactions obeying certain properties (e.g. Lorentz invariance, unitarity, etc) we expect to be held in realistic systems. Note that other answers in this thread seem to be using quanta as the terminology for particles.

Of course, there are cases in QFT where the concept of a particle doesn’t make sense; the scale-invariant theories or conformal field theories. In such a setting we actually measure correlation functions, as is typical of critical phenomena considered in condensed matter systems.

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