Question about Virtual Particles

[mattt]

Advise:

first: study it all in its mathematical rigorous (if possible) formulation (it will take many many long years of hard study).

second: only after that, read popularizations (pop-science books, famous quotes, whatever...) if you like, but now knowing perfectly well what actually lies beneath.If you ever want to (really) understand some of it, never start with pop-books.

So you are asking all of us laymen to stay away from PF?
That's why some of us come here, to ask and to learn from people who know the business, to get them correcting our misconceptions and to grow in our understanding of physics. If you don't like sharing your knowledge with laymen that's fine, but maybe there are others who don't mind.

The problem is that it is not easy trying to explain some things to laymen (or even students). I'll try my best:

We, as humans, have perceptions. We discover some regularities in those perceptions we have. We create abstract concepts, cathegories to treat it, and we discover some relations among them. All our language and thought are made of abstract concepts. Part of it (part of those abstract concepts we create to name and put some order in our perceptions) is what we decide to call "the Physical world".

We discovered (some centuries ago) that another type of abstract concepts (that we also create), called "Mathematics", is amazingly useful (for us) to put order and best understand those other abstract concepts I above called "the Physical World".

So now (and we've been doing this for a while) we use abstract mathematical structures, and then we make a semantic assignment to part (not all, but some) of the mathematical concepts of those mathematical structures, in terms of measurements and observations belonging to what I previously called "the Physical World".

A QFT is a "mathematical structure". I write "mathematical structure", in quotation marks, because actually it is only a rigorously defined mathematical structure in some cases in 1+1 and 2+1 dimensions (and the free case). In the most useful cases (as 3+1 QED or the SM of Fundamental Particles and Interactions) there are very important aspects that still are not clearly or rigorously defined (and it is a source of more confusion, when trying to explain these things).

But imagine for a moment that all these QFTs we use to model (some aspects of) the Physical World, were rigorously defined as a mathematical structure. What is important is those mathematical concepts (called observables) of the mathematical structure that has a semantic assignment (in terms of measurements and observations related to "the physical world").

It is the very model (the mathematical structure + semantic assignment) what tells you what is an observable and what not. Period.

An a model (a mathematical structure + semantic assignment (of some of its mathematical concepts) ) is more useful or less useful (and we humans have our ways to decide about it).

The concepts populary called "Virtual Particles" are not part of the mathematical structure used (and then obviously they are not part of the mathematical concepts that have a semantic assignment).

And you will ask: then what are they (virtual particles) ?

They are some mathematical concepts (some integrals of some kind) that appear in some approximations schemes used to be able to approximate the values of the observables.

An example:

If you have 2 apples and somebody gives you another 2 apples you will have 4 apples. These are abstract concepts used to put names and some order in some perceptions we decide to call "the Physical World".

Then we discover that there is a mathematical structure, called "the whole numbers and the addition of whole numbers" that with some semantic assignment, is very useful to understand these things, so that "2 + 2 = 4" is the use of this mathematical structure to put some order and understanding in that part of "the Physical World" (the apples I have and the apples I will have when someone gives me more apples).

I can use this mathematical structure ( Z , + ) with that semantic assignment even to be able to predict how many apples I will have if I started with 3 apples and then someone gives me 4 more apples.

I use that mathematical structure with that semantic assignment this way: "3 + 4 = 7"

to predict that I will end with 7 apples.

OK, it looks trivial. But imagine that this mathematical structure were so difficult to use (i.e. imagine that it was very very difficult to know how exactly is 3 + 4 under this mathematical structure) that it takes us many years of calculations to know the correct answer. But that there is a mathematical approximation technique that takes way less time. This approximations could be (for example):

3 + 4 = 3 + 3 + 0.5 + 0.25 - 0.13 + 0. 22 - 0.07 + ... ( whatever, it is just an example, and try to imagine that for us humans this way were way easier or took us way less time than just doing 3 + 4 = 7 ).

Then you would find some people saying that "the reason I end up with about 7 apples is because there exist some virtual cuasi-apples, both positive cuasi-apples and negative cuasi-apples, that are "real" because they are used to give a somewhat correct answer".

Does this "explanation" help you in some sense?

 

[PeterDonis]

This vacuum energy you are talking about is the 'dark energy' right?

One theory about dark energy is that it is just a manifestation of the energy in the vacuum. However, this theory does not explain why the current density of dark energy has the magnitude it has; no theory that we currently have does that.

It is said to be 'negative energy' while dark matter, ordinary matter and radiation are 'positive energy'.

No, this is not correct. As ddd123 pointed out, dark energy has negative pressure, but it has positive energy density.

You may be confused by the fact that dark energy causes what is sometimes referred to as "repulsive gravity", i.e., a universe full of dark energy has accelerating expansion, instead of decelerating expansion as would be the case with ordinary matter or radiation or dark matter. This is because the quantity that governs the acceleration/deceleration of the expansion is not the energy density $\rho$, but the quantity $- (\rho + 3p)$, where $p$ is the pressure. For dark energy, at least in the simplest form of a cosmological constant, we have $p = - \rho$, so $\rho + 3p$ is negative and the quantity $- (\rho + 3p)$ is positive, indicating acceleration. For ordinary matter or radiation or dark matter, $- (\rho + 3p)$ is negative and we have deceleration. But $\rho$ itself is positive in both cases.

Hence the cosmological theory which says that both actually have the same total value and cancel each other, so the Universe could have popped up out of nothing.

No, that is not what the theory you refer to says. It says that the negative energy density due to "gravitational potential energy" exactly cancels the positive energy density of everything else, including dark energy. To make this work, you have to adopt a particular definition of "gravitational potential energy", but in a general curved spacetime there is no unique way to define that concept.

Dark Energy isn't the same thing as Vacuum Energy.

I don't think this is correct as a blanket statement; I think it's better to say that we don't know whether or not dark energy is just a manifestation of the energy in the vacuum, or whether it's something else. See above.

 

[Gerinski]

Does this "explanation" help you in some sense?

Yes thanks a lot for the extensive reply. I still miss a more clear answer to the question: "if the observed effects sometimes wrongly attributed to virtual particles are not caused by virtual particles, then what are they caused by?" So far I only got one answer: "they are caused by the quantum field modes".
Which is fine but not too explanatory. It leaves the feeling that we do not know how to express in words the causes for these effects, for if we did there would not be any reason for anybody to invoke the non-existing concept of virtual particles.

 

[Gerinski]

Thanks a lot, that was helpful.

 

[ddd123]

Yes thanks a lot for the extensive reply. I still miss a more clear answer to the question: "if the observed effects sometimes wrongly attributed to virtual particles are not caused by virtual particles, then what are they caused by?" So far I only got one answer: "they are caused by the quantum field modes".
Which is fine but not too explanatory.

We are summing over infinite terms that almost formally resemble real particles, except they violate energy conservation, exhibit divergences (infinities) and are not quantum states by themselves, but the sum is finite and is the real result, which though is not akin to a particle process. If the other more knowledgeable posters agree, an "explanatory" answer would be: real particles are quantum field excitations which become discrete and observable as point-like; these other effects, instead, are quantum field excitations which are a "smeared continuum" instead of a discrete particle. As if, instead of having that one, definite and discrete particle, you smeared that stuff in a continuously variable form. Of course you're not smearing particles in the ordinary sense, but particles come essentially from the same fields that exhibit these modes, so here they are behaving differently (but cannot do something else completely, being the same field) by smearing that stuff like a paste, or a stream of continuously variable modes, instead of throwing it like a bullet of single mode. It's similar to path integrals but here the process themselves vary and not just the paths.

 

[craigi]

Yes thanks a lot for the extensive reply. I still miss a more clear answer to the question: "if the observed effects sometimes wrongly attributed to virtual particles are not caused by virtual particles, then what are they caused by?" So far I only got one answer: "they are caused by the quantum field modes".
Which is fine but not too explanatory. It leaves the feeling that we do not know how to express in words the causes for these effects, for if we did there would not be any reason for anybody to invoke the non-existing concept of virtual particles.

So as we discussed earlier in the thread, there are semantic difficulties with the term virtual particle. The term, originated in pertubative QFT, to describe the effects represented by some of the internal lines in Feynman diagrams. The latter part of the thread has largely been discussing virtual particles in this context and you have been given an analogy as to why the approximation methods used mean that they're not only virtual by definition, but that they must also be ontologically not real.

There is another context in which the term virtual particle is used in the literature, which is to describe the zero point fluctuations of a quantum field. In the most general form of QFT, without pertubation, each point in the field is uncertain in position and momentum, in a similar way to particles are uncertain in position and momentum in Quantum Mechanics. This gives rise to unstable fluctations in the field. We can compare these unstable fluctations to the stable fluctations which are associated with particles. This leads to the commonly mentioned heuristic, which describes vacuum fluctuations as virtual particles popping in and out of existence through out space and time.

 

[PeterDonis]

It leaves the feeling that we do not know how to express in words the causes for these effects

That is correct; the only way to precisely describe these causes is with math. Words aren't adequate because, if you don't already know the math, you don't know what the words are referring to; there's no way to point to anything in your experience and say "we're talking about that", which is how we confirm that we're talking about the same thing when we use words in ordinary conversation.

 

[Gerinski]

That is correct; the only way to precisely describe these causes is with math. Words aren't adequate because, if you don't already know the math, you don't know what the words are referring to; there's no way to point to anything in your experience and say "we're talking about that", which is how we confirm that we're talking about the same thing when we use words in ordinary conversation.

That's fine, but whatever the math refers to, it must be something real, a real property of our Universe (at least as real as the other things described by the same math such as fields and particles) for it leads to effects which can not be attributed to any other of those things.

The reply I would have expected right from the beginning would be something like: "what we call virtual particles is a real property of the vacuum but calling it 'particles' is a misnomer, for it is in no way the same as real particles. Some of its mechanisms can be mathematically modeled using analogies with some of the properties from real particles but the analogy with particles stops there. The property of the vacuum we refer to is not and can not be mediated by any 'particle'".

rather than than someone saying that "they are just a mathematical artifact devoid of any real existence". There's a difference between both kinds of statement.

With something like this we would have saved a few posts (not that I mind, on the contrary they were all very interesting to me).

At any rate thanks to everybody for the very informative discussion.

 

[Vanadium 50]

That's fine, but whatever the math refers to, it must be something real, a real property of our Universe (at least as real as the other things described by the same math such as fields and particles) for it leads to effects which can not be attributed to any other of those things.

You keep saying this. It's not true.

 

[craigi]

That's fine, but whatever the math refers to, it must be something real, a real property of our Universe (at least as real as the other things described by the same math such as fields and particles) for it leads to effects which can not be attributed to any other of those things.

The reply I would have expected right from the beginning would be something like: "what we call virtual particles is a real property of the vacuum but calling it 'particles' is a misnomer, for it is in no way the same as real particles. Some of its mechanisms can be mathematically modeled using analogies with some of the properties from real particles but the analogy with particles stops there. The property of the vacuum we refer to is not and can not be mediated by any 'particle'".

rather than than someone saying that "they are just a mathematical artifact devoid of any real existence". There's a difference between both kinds of statement.

With something like this we would have saved a few posts (not that I mind, on the contrary they were all very interesting to me).

At any rate thanks to everybody for the very informative discussion.

They exist in the theories, but not in the phenomena, in that they cannot be directly observed. The '+' operator exists in the theories, but how would be go about observing it? We can write it on a blackboard. Does that make it real? You could argue that it does, but from the perspective of quantum theory, we have to say no.

We may think that we have a good understanding of what real means from everyday language, but it is already an overburdened term in quantum theory. To communicate with clarity, we need to use one of the existing usages.

 

[ddd123]

This gives rise to unstable fluctations in the field. We can compare these unstable fluctations to the stable fluctations which are associated with particles.

What are you referring to specifically with the stable / unstable terms?

 

[Gerinski]

I don't care anymore about the virtual particles.

Do we agree that the vacuum has a property for which we have no good name but which can cause observable effects?

 

[atyy]

The vacuum is just another word for "ground state". It is the state of lowest energy. In most realistic quantum systems, the ground state is difficult to solve for exactly, and is full of interesting properties. Also, we often describe the effects of time-varying interactions with external systems as time-varying perturbations on the ground state. Because most of these effects are too difficult to solve for exactly, we use a wide range of approximations which include "virtual particles". It is not too enlightening to argue whether these things are real or not, but it is more important to know their use as excellent mathematical approximations in quantum mechanics. And yes, the simple answer is the ground state is extremely interesting.

It is a slight abuse of terminology for "ground state", but a celebrated exact "ground state" is the superconducting BCS ground state: http://www.scholarpedia.org/article/Bardeen-Cooper-Schrieffer_theory#Ground_state.

Here are some papers trying to describe either exactly or approximately the ground state in interesting systems.

http://arxiv.org/abs/cond-mat/0108214
Ground states of quantum antiferromagnets in two dimensions
Subir Sachdev, Kwon Park

http://arxiv.org/abs/1010.3745
Geometric phases and competing orders in two dimensions
Liang Fu, Subir Sachdev, Cenke Xu

http://arxiv.org/abs/1308.2229
Ground state phase diagram of the 2d Bose-Hubbard model with anisotropic hopping
Janik Schönmeier-Kromer, Lode Pollet

 

[craigi]

What are you referring to specifically with the stable / unstable terms?

An analogy for the stable fluctuation would be a ripple on the surface of water. An unstable fluctuation is something other than that.

 

[Jilang]

Like a diving beetle?

 

[craigi]

I started a new thread, here:

https://www.physicsforums.com/threads/david-tong-lectures-on-quantum-field-theory.810902/

with resources for David Tong's QFT course. He discusses virtual particles throughout. He teaches from Peskin and Schroeder, which also discusses virtual particles throughout.

Give it a go. Some of the mathematics may be unfamiliar, but you might be able to pick up enough from the lectures to satisfy yourself, until you've had chance to learn the prerequisites. At least, it should give you an idea of the maths that you'll need to learn.

 

[Alex299792458]

I just came and I skipped the whole forum so if this was already said then tell me. I read somewhere on hyperphysics.com that a virtual particle can exist for 10^-23 seconds so even though it's a very short period of time is it true that they can exist even if the duration is so infinitesimal?

 

[craigi]

I just came and I skipped the whole forum so if this was already said then tell me. I read somewhere on hyperphysics.com that a virtual particle can exist for 10^-23 seconds so even though it's a very short period of time is it true that they can exist even if the duration is so infinitesimal?

You should read the thread, but briefly, what you have read there is based upon a commonly used heuristic. It might get you through undergrad exams, but the full explanation is more involved.

 

[mattt]

Yes thanks a lot for the extensive reply. I still miss a more clear answer to the question: "if the observed effects sometimes wrongly attributed to virtual particles are not caused by virtual particles, then what are they caused by?" So far I only got one answer: "they are caused by the quantum field modes".
Which is fine but not too explanatory. It leaves the feeling that we do not know how to express in words the causes for these effects, for if we did there would not be any reason for anybody to invoke the non-existing concept of virtual particles.

What you call "observed effects" is what I called "(values of) observables" (post # 151).

Remember, you have a mathematical structure plus a semantic assignment (of some of its mathematical concepts, it terms of measurements and observations belonging to "the Physical World", which is in itself another set of abstract concepts).

The value of the observables is given by the mathematical structure + semantic assignment. It is just that.

Maybe in the simple example about the apples you may see it better.

The part of "the Physical World" our model is useful for: "the number of apples I start with, and the number of apples I end up with, after someone gives me more apples".

The model (mathematical structure + semantic assignment) :

Mathematical Structure: (Z,+).
Semantic Assignment: "the number of apples I start with and the number of apples I end up with, are represented by elements of the Z set (set of whole numbers), and the way to connect these two values (initial number, final number) of this observable, is by means of the Z addition (addition of whole numbers), adding a number (representing the amount of apples someone gives me) to the initial number".

Now everything is set and clear. I can use this model (mathematical structure + semantic assignment) to predict some things about that part of "the Physical World", this way:

We work inside the mathematical structure----> "3 + 4 = 7" and then we use the semantic assingment---> "If I start with three apples and then someone gives me four apples, then I end up with seven apples".

I think it is clear how this all works (you just have some part of what I called "the Physical World" we are now interested in, you have a mathematical structure and you have a semantic assignment connecting some of the mathematical concepts (of that mathematical structure) to some of the abstract concepts that belong to that part of the Physical World).

That is all there is. This is what we do.

Strictly speaking, the question "but what is the "real" cause I end up with seven apples when I start with three apples and someone gives me four more apples?" doesn't even make sense!

It is simply that inside the mathematical structure, the mathematical concepts are related in some ways, and in particular those we call "the observables" (those that have an interpretation by means of the semantic assignment) and its possible values, are related, are related because of the structure (the mathematical structure), so if you want you could say "the observables have these values in this case and these other values in that other case, because that is the way they behave inside that mathematical structure we are using".

Or in the examples with the apples: What is the cause (I end up with seven apples) ?

It is just that "3 + 4 = 7" in that mathematical structure, and we are using that mathematical structure plus that semantic assignment to say things about that part of the Physical World.

Look how in this example, to "answer" that "question", I don't even have to mention anything about 0.5, 0.25, -0.13, 0.22, -0.07...(the positive and negative "cuasi-apples) :-)The case of the Virtual Particles in QFT is, in essence, just the same thing.

 

[Gerinski]

That's all very fine, but many people (including scientists I'm pretty sure) prefer understanding than simply knowing. And in some cases the understanding has predated the development of the mathematical model (I believe that was the case with Einstein and GR). Regardless the very respectable "shut up and calculate" approach, more than a few scientists have spent much time trying to understand why things behave the way they do, even in the quantum world. There's nothing inherently wrong in asking the question. If the answer is simply "we can predict the outcome of the experiments but we don't know why" that's also fine, but refraining from asking the question in the first place because we have a mathematical model which works is kind of resigning from the possibility to understand.

 

[Alex299792458]

Sometimes I prefer just knowing but it feels so weird to explain it to other people and you don't understand it yourself so when they ask you a question you can't answer because you only know the facts not the truth and reason behind it. So that's why I started understanding.

 

[Dale]

I don't care anymore about the virtual particles.

Then it seems like a good time to close the thread "Question about Virtual Particles"