Perhaps the question may seem a bit provocative, but it refers to several mathematical and, presently physical facts, pointed out a long time ago:

  1. The Unruh effect suggests that an accelerated observer will contact a different number of real particles than a non-accelerated observer (with respect to a certain pre-established reference frame).
  2. Birrell and Davies (1982) point out a similar ambiguity with respect to the formulation of QFT in curved spacetimes, where the notion of particle would depend on the observer (if I do not misunderstand their statements).
  3. Even in Axiomatic QFT we have statements such as that: Reeh-Schlieder (RS) Theorem entails that the local algebras of AQFT do not contain operators that annihilate the vacuum. Hence if a number operator has the vacuum as an eigenstate, then there are no local number operators. That is perhaps enough to convince most readers that localized particles are not possible in relativistic QFT

Despite the various No Go results for localized particles in relativistic QFT, the interpretation of experiments in high energy physics seems to require a notion of something causing clicks in detectors, and that a “detector” is fairly well localized in some bounded region of spacetime. After thinking about this and the marks that individual electrons seem to leave on phosphorescent screens, my questions are:

  1. Do we really detect individual electrons or causal processes associated with a strongly localized (though not completely localized) electron field?
  2. What would be the "clicks" associated with detections and "marks" left by electrons on phosphorescent screens?

Disclaimer: I understand that I am possibly falling into some kind of semantic trap and that possibly formulated in formal terms my questions could be meaningless in the framework of (axiomatic) QFT, but any informal discussion or clarification could also be useful.


1 Answer 1


If you check my post history you will notice I'm a firm disbeliever on the particle interpretation, which is a spoiler to my answer. Briefly, I see no argument to claim you have a completely localized notion in field theory (at the very worst case, because that would require understanding quantum gravity, which we do not).

Perhaps a way to ease your mind about this is to point out the notion of particle detectors within quantum field theory in curved spacetime. These could be, for example, a simple two-level quantum system interacting with the quantum field. As the detector's state changes from the ground state to the excited state, we can interpret it as having detected a particle. Similarly, changing from the excited state to the ground state can be understood as the emission of a particle. I should also mention that these detector models can be conceived in a fully localized manner (i.e., they follow a single worldline through spacetime).

Nevertheless, this particle point of view is merely an interpretation. You are modeling everything in terms of fields and it is not necessary to think in terms of particles. That is merely a convenience. For example, it might happen that the detector is following a weird trajectory through spacetime that does not allow you to find a Fock space that allows you to get ladder operators corresponding to this notion of particle (disclaimer: I can't give you an explicit example out of the top of my head, so I'm stating this based on intuition and not being able to notice how such a space could be obtained in general).

The marks on screens and clicks on detectors are merely interactions with a quantum field. The fact these interactions can occur in a very local fashion does not really mean there is a fundamental notion of particle, but is an example that, at least in some scenarios, it is useful to think as if particles were real. Similarly, in some scenarios, it is convenient to think as if gravity was force.

Shortly, I see no argument to claim particles are a fundamental entity. Deep down, our best theories describe everything in terms of fields. However, in some particular cases, it is useful to interpret results and phenomena in terms of particles. After all, physics does not describe what the universe is, just what it looks like. Within this line of thought, particles are useful, just not necessary.

For introductory references on particle detectors, you might want to check Sec. 3.3 of Wald's Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics and/or the discussion on my master's thesis (p. 33 onward, see also the references given there).

  • $\begingroup$ Thinking of a bubble chamber, how else to interpret the traces we observe in them, but as real particles But in an accelerated system would we see the same traces? $\endgroup$
    – Davius
    Commented Jul 4, 2023 at 13:34
  • $\begingroup$ @Davius Yes, we would see the same traces, but we would interpret them differently (Chap 2 of my master's thesis describes this things in quite some detail, albeit not with the specific case of the bubble chamber). What matters for the traces to appear is the state of movement of the bubble chamber. However, the interpretation of the experiment depends on the observer $\endgroup$ Commented Jul 4, 2023 at 23:39
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    $\begingroup$ Think of it in special relativity: a given observer sees an electric force, while a different one might see an electric and a magnetic force. Both of them see the very same physical effect, but they attribute different interpretations to it $\endgroup$ Commented Jul 4, 2023 at 23:40

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