Meaning of the word 'particle'

[Qwadratix]

TL;DR Summary

Looking for a resolution of an apparent contradiction on the meaning of the word 'particle'

This is something that's bugged me for a long time and since I don't have any particular expertise in the subject, maybe I'm missing something obvious. But here goes.
I was taught that the term particle in QM is synonymous with quanta. That is, that a particle is the lowest excitation level of a quantum field, a single quantum. As such, my understanding would be that it is essentially an infinite plane wave of fixed frequency propagating in the field.
On the other hand, when it comes to 'actual' particles (which are basically a delta function) the only way you can describe them in wave function terms is as a wave packet of multiple frequencies and wavelengths with a group velocity.

So whenever someone talks about particles I have these two contradictory models in mind, which causes me some confusion.

 

[PeroK]

In QM a localised particle is instantaneously a delta function. Although even that is physically an idealisation of a sharp Gaussian function or something similar.

More generally a particle is described by a wave function, that may be highly non-localized. An electron in a hydrogen atom, for example.

The description in QFT is even more general. In general, the number of particles is not fixed. Technically, the field is typically not in an eigenstate of the particle number operator.

Even though the two mathematical descriptions are different, the QFT description can be approximated by a QM wavefunction in certain circumstances.

 

[pines-demon]

I was taught that the term particle in QM is synonymous with quanta.

Sure... I mean if I was introducing a course on quantum mechanics I would not do this, because in the single-particle/non-relativistic quantum mechanics, quanta refers to the quantization of energy, angular momentum and other properties. However it is due to relativistic quantum field theory that we can see that particles can be interpreted as quanta of a particle field

As such, my understanding would be that it is essentially an infinite plane wave of fixed frequency propagating in the field.

Sure, if you choose that basis. Quanta are basis dependent. For a free particle that works but in most cases that might not be the right basis. You need to choose the basis where the particle number is conserved to talk about quanta (in most cases that is not even possible).

On the other hand, when it comes to 'actual' particles (which are basically a delta function) the only way you can describe them in wave function terms is as a wave packet of multiple frequencies and wavelengths with a group velocity.

So whenever someone talks about particles I have these two contradictory models in mind, which causes me some confusion.

Again I sincerely think that you are mixing qft and non-relativistic terms.

 

[PeterDonis]

the term particle in QM is synonymous with quanta. That is, that a particle is the lowest excitation level of a quantum field

As @pines-demon commented, you are mixing non-relativistic and relativistic models.

In non-relativistic QM, single "particles" and "quanta" are the smallest quantum systems that are modeled. There are no quantum fields in non-relativistic QM.

In relativistic QM, i.e., quantum field theory, "particles" are particular states of quantum fields, but there are many quantum field states that have no particle interpretation, including very common states such as the coherent states emitted by things like lasers.

my understanding would be that it is essentially an infinite plane wave of fixed frequency propagating in the field.

No. In QFT, particles do not "propagate in the field". They are states of the field.

when it comes to 'actual' particles (which are basically a delta function) the only way you can describe them in wave function terms is as a wave packet of multiple frequencies and wavelengths with a group velocity.

No. A delta function is a wave function--just one that you have to be careful how you specify mathematically. (A good discussion is in Ballentine, where he describes the rigged Hilbert space formalism.) The reason wave packets are used is that it is impossible to actually prepare a particle in a delta function state (here we are talking about non-relativistic QM and we are assuming that whatever experiment we are doing is modeled to sufficient accuracy by non-relativistic QM); the best we can do is to prepare a wave packet.

 

[PeterDonis]

So whenever someone talks about particles I have these two contradictory models in mind, which causes me some confusion.

The way to avoid the confusion is to look at whether the someone is talking about non-relativistic QM or relativistic QFT, or more generally what kind of experimental scenario they are talking about and whether it can be modeled well enough by non-relativistic QM or whether it requires QFT to model.

 

[Qwadratix]

The way to avoid the confusion is to look at whether the someone is talking about non-relativistic QM or relativistic QFT, or more generally what kind of experimental scenario they are talking about and whether it can be modeled well enough by non-relativistic QM or whether it requires QFT to model.

I appreciate that these two models are from different disciplines and as such are different. I don't personally have a problem with the distinction.
However, my compliant is that these two models are sufficiently unalike to make the use of the same word a serious breach of the general principle that words need to have clearly defined meanings if they are to be any use in science.

Perhaps I should rephrase my point. the quanta of a field are not localised at any point in space. As has been said, they are states. On the other hand, a particle in the common sense has a location. In effect, these two particles definitions are Fourier images
It just strikes me as an unnecessary and potentially confusing complexity to have this situation, even though (I agree) you can say 'Oh well we're talking about QM, not classical mechanics'.

It's as if zoologists visiting Australia decided to call kangaroos 'dolphins' on a whim.

 

[pines-demon]

I appreciate that these two models are from different disciplines and as such are different. I don't personally have a problem with the distinction.
However, my compliant is that these two models are sufficiently unalike to make the use of the same word a serious breach of the general principle that words need to have clearly defined meanings if they are to be any use in science.

Perhaps I should rephrase my point. the quanta of a field are not localised at any point in space. As has been said, they are states. On the other hand, a particle in the common sense has a location. In effect, these two particles definitions are Fourier images
It just strikes me as an unnecessary and potentially confusing complexity to have this situation, even though (I agree) you can say 'Oh well we're talking about QM, not classical mechanics'.

It's as if zoologists visiting Australia decided to call kangaroos 'dolphins' on a whim.

The thing is that you can work out the semiclassical limits of all these theories and show that when quantum mechanical phenomena can be ignored, particles do behave like classical particles. It is the same for illumination phenomena outside of a lab, you can sometimes talk about light rays (eikonal approximation) instead of light waves.

 

[Nugatory]

However, my compliant is that these two models are sufficiently unalike to make the use of the same word a serious breach of the general principle that words need to have clearly defined meanings if they are to be any use in science.

It's frustrating and annoying, but natural language is always going to depend on the context to resolve this sort of ambiguity. The ambiguity goes away when we look at the math instead of the words, which is why it is often said that "math is the language of physics".

 

[PeroK]

It's as if zoologists visiting Australia decided to call kangaroos 'dolphins' on a whim.

There is the Mahi-Mahi, aka the dolphin-fish; not to be confused with the dolphin (mammal).

https://en.wikipedia.org/wiki/Mahi-mahi