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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?

Qmechanic
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Charles Hudgins
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  • Comments are not for extended discussion; this conversation has been moved to chat. – Buzz Oct 02 '22 at 21:02
  • Not all particles are observable in the conventional sense; indeed most are identified by their effects such as gravitational ones. – michael nettleton Oct 04 '22 at 18:36
  • In some sense, "particle" means "the thing you can observe about a quantum field". – DanielSank Oct 05 '22 at 01:07
  • 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.) – Mahir Lokvancic Oct 06 '22 at 10:16
  • @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? – Charles Hudgins Oct 07 '22 at 01:53
  • Re "why do we seem to always observe states with definite particle content:" I doubt this can be answered (reduced to other basic phenomena); it simply is so, something that we observe the way nature works. It could be because "continuous-exchange-of energy/momenta" universe could be unstable (as already indicated by original Planck's insight). Given this backdrop, we developed mathematical tools and structures that seem to incorporate the concept of quanta remarkably well and faithfully, so much so that you can essentially read nature from mathematics. – Mahir Lokvancic Oct 07 '22 at 21:28
  • Re "can't a quantum field be a superposition of states with different particle content...:" Actually, it already is, but it is only the interaction among systems (fields) that manifests itself thru quanta. Again, why the interactions are mediated via quanta (at least "hard" interactions) is basically an axiom of nature, to the best of my understanding of these matters. This is rather similar to the measurement problem in quantum mechanics -- it is simply a postulate (despite some claims from decoherence theories, etc, to the contrary). – Mahir Lokvancic Oct 07 '22 at 21:28

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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.

Greg Martin
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FlatterMann
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  • I am confused. Aren't particles the same as quanta, and is saying we observe quanta not the same as saying we observe particles? What are the quanta of a fermionic field if not fermions, for example? Are fermions not particles? I should mention that I am not familiar with quantum field theories so I'm probably missing the point. But as a layman myself, I don't see how this answer explains the second paragraph of the question. – Hans Wurst Sep 30 '22 at 10:44
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    @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. – FlatterMann Sep 30 '22 at 11:20
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    @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. – Ponder Stibbons Sep 30 '22 at 11:22
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    @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. – FlatterMann Sep 30 '22 at 11:23
  • @FlatterMann This is unrelated to my other comment. I didn't even realize that you're the same user until now. I am sure that your answer is good and your criticism of the commonly used language seems point on. It's just hard to understand for me, who has little knowledge of high energy physics. Its just surprising that the common place language would be so wrong(?). Do you know references that make a point of introducing quanta with a clear distinction to particles? Wikipedia (I know, it's not the best source) certainly does not. – Hans Wurst Sep 30 '22 at 11:50
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    @HansWurst Einstein got the quantum concept in his paper about the photoelectric effect initially right but then he suddenly introduces a completely unnecessary location property for photons (quanta don't have coordinates). He doesn't use this property even once and it is certainly not motivated by the experimental data. Where did this unforced error come from? It came from Einstein's mind, just like the phlogiston and the ether came from the minds of physicists who felt a need to "objectify" properties. Humans like to think in terms of things... even when it is absolutely false to do so. – FlatterMann Sep 30 '22 at 11:58
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    @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". – David S Sep 30 '22 at 22:37
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    @David Can you show me where I was talking about philosophy? I was consistently talking about energy transfer. A source puts energy into a quantum field and a detector takes energy out. There is absolutely no need to get philosophical about any of this. You can even find the engineering parameters for detector sensitivity in the manufacturer's data sheets or the papers of the physicists who are building custom detectors. We are always very careful to specify the minimal energy that can be distinguished from thermodynamic noise and the energy resolution of these devices. – FlatterMann Sep 30 '22 at 23:03
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    What is special about an atom that makes it so that the number of electron quanta is so fixed? Why don’t H atoms have a superposition of electron number states? Why don’t we have a superposition of 0 1 and 2 electron states in the H atom? Maybe interaction with the photon field does cause a little bit of mixing of these states leading to things like the Lamb shift? – Jagerber48 Oct 02 '22 at 20:38
  • @Jagerber48 The number of electrons in an atom is not fixed. That's simply an assumption from chemistry due the low energy regime that won't let us see pair production. In reality the full QFT description of an atom would have to allow for virtual electron-positron pairs even in low order. There is nothing wrong with such approximations (we are doing physics, after all), but they don't reflect all of reality but only certain small corners of it. – FlatterMann Oct 02 '22 at 20:45
  • Still, at low energy integer quanta numbers are overwhelmingly preferred (at least for massive fields?) why is this the case? Why isn’t a 1.5 electron atom stable? – Jagerber48 Oct 02 '22 at 21:04
  • @Jagerber48 Certainly not for photons. The discovery of quantum mechanics starts with a system (Planck radiation) that does not have a well defined number operator. I am simply pointing out that quantum mechanics explains absolutely everything except for gravity, but every time somebody specializes it for one particular purpose they run into the danger to oversimplify it in a really poor way. There is no need for that. Quantum field theory has very complex math but a trivial ontology. It is actually much easier to think of the physics in QFT terms than e.g. in Copenhagen terms. – FlatterMann Oct 02 '22 at 21:11
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    @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. – David S Oct 03 '22 at 16:35
  • @DavidS The observation that physics has made the "objectification" mistake multiple times before with the phlogiston and the ether is merely science history (and as such a fact) and, if you forgive me, maybe amateur psychology. If you are reading the early literature on quantum mechanics carefully, especially Heisenberg and Bohr, then you will also find (or at least I believe so), that these physicists had some mighty good ideas like weak measurement very early on (around 1927-ish), but then they waffled and went back to some not so good ones (like the Heisenberg microscope). – FlatterMann Oct 03 '22 at 19:08
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    This may be a bit of a non-sequitur, but an interesting thing about terminology in physics is the quality described by Lee Smolin (of Canada's Perimeter Institute) as "emergence", in his pop-sci book titled "Time Reborn": Matter may be wet, but particles of it "emerge" from combinations of subatomic objects that aren't. A more subtle example of "emergence", with some experimental support, is Mersini-Houghton's view of time as possibly emerging from quantum entanglement. (I'm using the term "object" in a sense that's not necessarily grammatical.) – Edouard Apr 16 '23 at 11:11
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    @Edouard I agree. Every complex physical phenomenon "emerges" in some more or often less straight forward way from a very small number of microscopic ones. Time is a rather curious one, indeed. The idea of time as an order parameter has been around for a very long time, probably 50 years of more. It was certainly being discussed as that even when I was an undergrad, which is a very long time ago (way before Smolin and Mersini-Houghton). The problem with ideas about microscopic time structure is the absence of evidence. We simply can't seem to get past QFT and its geometric background. – FlatterMann Apr 16 '23 at 11:21
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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.

anna v
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    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... – Cosmas Zachos Sep 30 '22 at 13:52
  • 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. – Edouard Apr 16 '23 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.

niels nielsen
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    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? – Charles Hudgins Oct 02 '22 at 13:13
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    @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 – Jojo Oct 02 '22 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.

John Doty
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  • There are no experiments that "sense" particles. In physics a "particle" is defined as the approximation of the motion of an extended classical body by the motion of its center of mass. What we call "particle" in high energy physics (for historical reasons) is a combination of energy, momentum, angular momentum and charges. Textbooks are not doing a particularly good job of pointing that out, but if you read the documentation of high energy physics detectors, then it should become clear what physicists are measuring with these devices. – FlatterMann Oct 02 '22 at 22:56
  • @FlatterMann Any photoelectric detector senses photons. That's what you actually see in an experiment. – John Doty Oct 02 '22 at 23:25
  • A photon is an irreversible energy transfer from an electromagnetic field to an external system. You are welcome to look at a solar panel, if you like. It is an energy converter. Electromagnetic energy comes in and electromagnetic energy goes out, just not at the same frequency. – FlatterMann Oct 03 '22 at 03:31
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    @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. – John Doty Oct 03 '22 at 23:28
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    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. – FlatterMann Oct 04 '22 at 03:10
  • @FlatterMann Tracks are what we get in experiments. From a mathematical point of view, they emerge from from an axiomatic treatment of mathematical objects. But mathematical objects are not real: they are the product of human imagination. Mott showed that certain mathematical objects may successfully model the observations, but the observations are the real, fundamental thing for physics. – John Doty Oct 04 '22 at 13:34
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    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. – FlatterMann Oct 05 '22 at 04:24
  • @FlatterMannYou are confusing models with the actual physical world. Consider gravity. Galileo did experiments and came up with an acceleration-based model of gravity. Newton devised a force-based model. Einstein devised a geometry-based model. But all three models capture Galileo's experimental results. The phenomena of physics are the stable foundation, while models change. You are claiming that your model drives the phenomena, but in reality, it's the opposite. Your model was crafted to reproduce the phenomena. – John Doty Oct 05 '22 at 14:59
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    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. – FlatterMann Oct 05 '22 at 21:39
  • @FlatterMann Yes, that abstraction captures what we see in reality: it was designed to do so. It remains an abstraction: a product of human imagination. – John Doty Oct 05 '22 at 22:26
  • @FlatterMann Yes, nobody has ever managed to see a track without a track detector. You don't need quantum mechanics to predict that. – John Doty Oct 05 '22 at 22:28
  • @FlatterMann Plane wave? What does a track detector see if the incoming energy isn't in the form of a plane wave? – John Doty Oct 05 '22 at 22:37
  • @FlatterMann Classical models predict no track when the interaction of the incoming particle with the detector medium is strong, so this is hardly a unique prediction of quantum models. – John Doty Oct 05 '22 at 22:44
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    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. – FlatterMann Oct 05 '22 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.

Dexter Kim
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