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

 

[PeterDonis]

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.

While I sympathize with your feelings here, scientific terminology has never met this standard and never will. The only real recourse if a scientist wants to be strictly accurate is to state whatever they are trying to state using math, not words--or at least to use words that specify which particular model they are using. So, for example, using the term "non-relativistic particle" if one is using non-relativistic QM, or "particle state of a quantum field" (or "Fock state" if the context is such that that more technical term will be understood) if one is using QFT.

a particle in the common sense has a location.

But even in non-relativistic QM, this is no longer true (a particle has a wave function, which in any actual scenario will never be an eigenstate of position), so this interpretation of "particle" does not work for either of the models under discussion.

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

No, actually, it's not. The term "particle" comes from (a) pre-QM physics, where the concept was more straightforward, and which is perfectly suitable for everyday use, and (b) loads and loads of experiments in which discrete thingies are detected for which "particle" is the most obvious term, and was therefore the term everybody used.

Then, as is common in science, everybody started finding out about all the complexities lurking beneath the simple stuff above, and had to account for them in scientific models, so that the common term "particle" ceased to have a simple, straightforward, single referent in the models. But the reasons for still using the term "particle" that I described above had not gone away, so the term continued to be used, and people just had to invent other terms to describe things in the models when greater clarity was required.

In other words, none of this happened "on a whim" and your analogy does not at all capture what actually happened and why.

 

[Nugatory]

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

There is a reason why zoologists use neither the word "kangaroo" nor "dolphin", at least when they're doing serious zoology talk. They'll call these animals "Osphranter rufus" and "Tursiops truncatus" and there is zero possibility of assigning the same name to completely different animals.

Same thing with physics, except that when we're serious about physics we use math (because that's the language of physics) instead of Latin (which is the language of taxonomy).

 

[PeterDonis]

whenever someone talks about particles I have these two contradictory models in mind

A good suggestion for dealing with this would be to recognize that, as my post #10 implies, the word "particle" does not have a single well-defined referent in our scientific models any more, and so it should not be taken as referring to any of those models. Instead, it should be taken as referring to the discrete thingies that we detect in experiments, which is a model-independent meaning that still holds good.