Debunking the Existence and Duration of Virtual Particles

[Polyrhythmic]

Poly, they are by definition not directly detectable. Hence the name virtual.

And something which is neither directly detectable nor needed for any explanations shouldn't be considered real.

And no perturbation theory mentioned.

Because that was implicitly assumed in the lectures. Feynman diagrams or virtual particles can only be talked about in the context of perturbation theory.

In addition, they are necessary to turn up in the calculations to make the probabilty amplitudes for the measurable states come out right.

This is plain and simply incorrect. The terms required for the correct calculations are there, whether you interpret them as virtual particles is an entirely different question.

 

[Polyrhythmic]

have you done any work on this side of the theory?

I have studied the Dirac equation and and never came across any virtual particles.

 

[Polyrhythmic]

If the energy shift is measured, it is real. End of. Virtual particles are objects which have taken this identity.

That just makes no sense.

 

[Goldstone1]

Goldstone1, this is complete rubbish

Even Dirac himself declared in print that the "sea" and "hole" idea should be abandoned.

(and holes never had anything to do with virtual particles, anyway … holes came in with the Dirac equation in 1928(?), and went out again when virtual particles came in)

hmmm … I'll guess that you've been looking at http://en.wikipedia.org/wiki/Virtual_particles#History" …

Paul Dirac was the first to propose that empty space (a vacuum) can be visualized as consisting of a sea of virtual electron-positron pairs, known as the Dirac sea.​

… this is simply historically wrong …

the Dirac sea was a "sea" of infinitely many electrons, and real positrons were holes in the sea: there were no virtual positrons, and no electron-positron pairs at all

And (for what it's worth) the historical article http://en.wikipedia.org/wiki/Dirac_sea" makes no mention of virtual particles! ​

Well, no... I've not been reading anything of lately. I just recall the class which I took which was an introductory course in QFT and it spoke of the Dirac Sea - it has been replaced, but the general idea of particles being ''embedded'' within the vacuum is still preserved - QFT calls them Virtual particles. I don't know how much into the history you seem to understand, all I know is that QFT predicts virtual particles to be throthing at the subatomic level, and that is all I really wish to know. As for Diracs Equation, I can say that in particle creation, a positron must be created from a virtual entangled particle in the vacuum to the corresponding electron.

 

[Goldstone1]

That just makes no sense.

As Lapidus explains:

''But, as Prof. Susskind explains, or Prof. Randall, or anybody else with some very basic understanding of quantum physics will tell you that the time-uncertainty relation allows undetectable states/ particles to exist for short times. ''

This is what this energy shift is. It is a detectable difference in energy by a quantum which cannot be detected. It is is real though, because it leaves real physical effects in the world.

 

[maverick_starstrider]

Since I assume you are not an expert on non-perturbative quantum field theory that must just be a wild claim.

Why should there be no virtual particles or processes in non-perturbative qft? How do you know?

I don't understand what you're saying. Am I crazy? Virtual particles as a concept and as a calculational tool have absolutely no existence outside of perturbation of quantum field theories in feynman diagrams. In non-perturbative qft the concept of virtual particles simply doesn't exist.

 

[Polyrhythmic]

Well, no... I've not been reading anything of lately. I just recall the class which I took which was an introductory course in QFT and it spoke of the Dirac Sea - it has been replaced, but the general idea of particles being ''embedded'' within the vacuum is still preserved - QFT calls them Virtual particles. I don't know how much into the history you seem to understand, all I know is that QFT predicts virtual particles to be throthing at the subatomic level, and that is all I really wish to know. As for Diracs Equation, I can say that in particle creation, a positron must be created from a virtual entangled particle in the vacuum to the corresponding electron.

If that's what you heard in your QFT course, I can only recommend you to retake it somewhere else.

 

[maverick_starstrider]

As Lapidus explains:

''But, as Prof. Susskind explains, or Prof. Randall, or anybody else with some very basic understanding of quantum physics will tell you that the time-uncertainty relation allows undetectable states/ particles to exist for short times. ''

This is what this energy shift is. It is a detectable difference in energy by a quantum which cannot be detected. It is is real though, because it leaves real physical effects in the world.

There is a world of difference between USING Feynman Diagrams to CALCULATE what the magnitude of the shift and saying that the shift is DUE to the Feynman Diagrams. Once again I keep bringing it back to perturbation in regular QM and you consistently ignore the point. Perturbation is not seen as real QM, why should it be real in QFT?

 

[Polyrhythmic]

As Lapidus explains:

''But, as Prof. Susskind explains, or Prof. Randall, or anybody else with some very basic understanding of quantum physics will tell you that the time-uncertainty relation allows undetectable states/ particles to exist for short times. ''

This is what this energy shift is. It is a detectable difference in energy by a quantum which cannot be detected. It is is real though, because it leaves real physical effects in the world.

No. All physical effects you mention can be calculated without assuming that virtual particles have any physical significance.

 

[mattt]

Virtual particles are gauge-dependent: different perturbation schemes use different kind of virtual particles that have nothing to do one to another.

In Lattice QED (or in general, Lattice QFT) you can compute everything (in principle, assuming enough time and superfast computers).

The S-Matrix is what gives the answers of the Theory. The different ways of computing its elements (perturbatively, non-perturbatively) by means of different kind of approximations, are just that, calculations techniques.

 

[dm4b]

I'd love to see a good explanation of this still too.

More generally, what is the mechanism behind the electromagnetic force.

The popular view is two electrons (or some other charged particle) exchanging virtual photons, which mediate the message. But, what is the correct way to view this, without the use of fictitious entities such as virtual particles?

I've never seen this explained well.

Bump. Anybody? ;-)

 

[Polyrhythmic]

Bump. Anybody? ;-)

You can view those interactions as caused by an intrinsic link of the fields, realized by the coupling terms in the lagrangian.

 

[tiny-tim]

… an introductory course in QFT and it spoke of the Dirac Sea - it has been replaced

exactly!

so why are you (still) talking about it?? …

Well I beg to differ... the Dirac sea is a reseviour of negative virtual energy states... have you done any work on this side of the theory?

Decouple the dirac equation into left movers and right movers, and then the theory asks where the positron comes from when it is created. It is effectively a hole in the sea, once a virtual particle. The Dirac Equation does involve the ''mathematical'' concept of virtual particles.

Goldstone1, you've not done any research yourself, so you have to rely on established theories as quoted by others …

the Dirac sea is not an established theory, it is discredited, or in your own words replaced …

do you not see that you cannot use it to support any argument? ​

 

[dm4b]

You can view those interactions as caused by an intrinsic link of the fields, realized by the coupling terms in the lagrangian.

Thanks for the reply Polyrhythmic.

Are you talking about the higher-order terms in a Lagrangian for an Interacting field, as opposed to the Lagrangian for a Free field, which is missing those terms?

Sure, mathematically speaking, "forces" (interactions) arise from terms like that. But, I still don't see how that is a "mechanism". That's math.

Nor, does it give a good visualization of the mechanism behind the force, as does the virtual particle picture.

 

[Polyrhythmic]

Are you talking about the higher-order terms in a Lagrangian for an Interacting field, as opposed to the Lagrangian for a Free field, which is missing those terms?

Yes.

Sure, mathematically speaking, "forces" (interactions) arise from terms like that. But, I still don't see how that is a "mechanism". That's math.

I thought that this answer would be unsatisfying, but I don't have a better one. Maybe somebody does, but as far as I see it, that coupling is the fundamental core of the interaction.
When you think about it, does the Coulomb law provide a better mechanism? It just a mathematical formula, but it predicts the experiment quite well. It also doesn't explain "why" opposite charges attract each other, or in other words, what causes those objects to move.

Nor, does it give a good visualization of the mechanism behind the force, as does the virtual particle picture.

That's not a criterion. Try to visualize curved spacetime. You'll have a hard time, yet it gives great testable predictions. I admit that the virtual particle picture looks nice and plausible at first glance, but once you dig deeper into the theory you see that it is false. A correct explanation that is hard to visualize should be preferred, not a false visualizable one.

 

[maxverywell]

I'm not an expert (I'm still undergrad physics student) but I think that the fact that in non-perturbative QFT there are no virtual particles doesn't mean that they don't exist. As in Coulomb law, there are no virtual particles, but we need them to describe the mechanism of interactions, not just to compute the results of interactions as in non-perturbation QFT, Coulomb law etc. So they are indeed real in the sense that they are responsible for the interactions. This is a matter of how you define the reality and the particles.

 

[Polyrhythmic]

I'm not an expert (I'm still undergrad physics student) but I think that the fact that in non-perturbative QFT there are no virtual particles doesn't mean that they don't exist.

There is no evidence in other theories because they just arise as a mathematical construct, namely perturbation series expansion.

As in Coulomb law, there are no virtual particles, but we need them to describe the mechanism of interactions, not just to compute the result of interactions as in non-perturbation QFT, Coulomb law etc.

No, we don't.

So they are indeed real in the sense that they are responsible for the interactions.

Your logic is flawed.

This is a matter of how you define the reality and a particles.

Something which has neither experimental evidence nor theoretical backing should not be considered real.

 

[dm4b]

I thought that this answer would be unsatisfying, but I don't have a better one. Maybe somebody does, but as far as I see it, that coupling is the fundamental core of the interaction.

When you think about it, does the Coulomb law provide a better mechanism? It just a mathematical formula, but it predicts the experiment quite well. It also doesn't explain "why" opposite charges attract each other, or in other words, what causes those objects to move.


That's not a criterion. Try to visualize curved spacetime. You'll have a hard time, yet it gives great testable predictions. I admit that the virtual particle picture looks nice and plausible at first glance, but once you dig deeper into the theory you see that it is false. A correct explanation that is hard to visualize should be preferred, not a false visualizable one.

Coulomb's Law in basic EnM (no SR, or QFT, considerations) is almost like magic. Instant and no mechanism. So, I agree, no better. But, the virtual particle picture does make it more appealing.

I actually really like the spacetime curvature picture, which is why I didn't bring it up.

It would be nice if there was something like that for EnM (that's not fictitious, that is)

It could very well be that as we advance further and further in physics, the nice visualizations just aren't available anymore. But, I always had my doubts about that

 

[Vanadium 50]

There seems to be two sides to this debate - on one side are people who have done the actual calculations. On the other are people who are using quotes from popularizations in support of their position. That alone should tell you something.

You can't use the Lamb shift as evidence for virtual particles, since it was calculated a year before anyone had every heard of virtual particles.

 

[maxverywell]

No, we don't.

Why? How do you explain the Coulomb interactions between charged particles or interactions on non-perturbation QFT?

 

[Polyrhythmic]

Why? How do you explain the Coulomb interactions between charged particles or interactions on non-perturbation QFT?

Read one of my last posts, #165.

Besides, virtual particles don't even explain anything in perturbative quantum field theory.

 

[maxverywell]

Read one of my last posts, #165.

So you don't have an answer. Why not to adopt the notion of virtual particles which explains the interactions?

Read one of my last posts, #165.
Besides, virtual particles don't even explain anything in perturbative quantum field theory.

They are the mediators of fundamental interactions.

 

[Polyrhythmic]

So you don't have an answer.

I didn't say that I don't have one. It's just not the answer you would like to hear.

Why not to adopt the notion of virtual particles which explains the interactions?

For reasons that have been discussed to death in this thread.

They are the mediators of fundamental interactions.

Please don't randomly quote popular phrases as if they gave any meaning to your argument. Do some research, study some quantum field theory. Then we can continue ;)

 

[Goldstone1]

exactly!

so why are you (still) talking about it?? …



Goldstone1, you've not done any research yourself, so you have to rely on established theories as quoted by others …

the Dirac sea is not an established theory, it is discredited, or in your own words replaced …

do you not see that you cannot use it to support any argument? ​

I think it is premature to say I have not investigated these claims.

Very well, if you don't want me to use the Dirac Sea, then it's replacement uses the same dynamics, virtual particles in a zero-point energy field.

 

[Goldstone1]

No. All physical effects you mention can be calculated without assuming that virtual particles have any physical significance.

No, I'd say a theory tries to make sense of the physical effects. They are real. And if the theory of virtual particles are correct, then they will almost certainly have a physical significance, again, as they attempt to explain many physical characteristics of many field theories borne from QM.

 

[alxm]

By analogy to Many-Body perturbation theory, what the virtual-particles-are-real advocates seem to be saying here: It's not the case that there's an exact solution to the Schrödinger equation for a polyelectronic atom or molecule, and a perturbation expansion is not merely a mathematical tool to calculate those mathematically-intractable many-body effects.

Rather, the perturbation series is reality. The way electrons really work is that this many-body problem (which of course exists classically as well), is a force mediated by a bunch of undetectable-but-real 'virtual' interactions (although this concept has absolutely no meaning in the absence of any electrons). Even though you're dealing a non-relativistic, 'standard' QM in the Coulomb gauge, where the coulomb interaction is instantaneous, it really occurs through these 'virtual' interactions. Electrons first interact in pairs, then in triplets, and so forth, and not all at once, because that's what the perturbation series looks like.

I can even draw illustrative diagrams - Goldstone diagrams, according to certain rules, whose topology will tell me what the terms of my series look like:

This 'explains' these 'virtual interactions', since it gives a visual picture of what's going on, physically - it's not just some abstract graph illustrating the mathematics involved. The reason we 'know' this, is because many-body perturbation theory works. It gives the correct result for the true, interacting, system of electrons. It's far from the only way of arriving at the correct result, though. In fact, it's only an approximate method and quite often, it's not the most accurate one. It hasn't predicted anything that can't be predicted by any other method. But - the argument seems to go - it must be describing objective reality because it does work, and how else would you visualize or describe the 'many-body force'?

But why stop there? That's just one example. How about quasi-particles? Or any of the hundreds of other cases in physics where a difficult problem can be made tractable by re-casting it in terms of some fictional-but-easier-to-describe system? Does it make physical sense to say that every periodic function is actually a superposition of plane waves because it can be described that way, mathematically? Or sticking with PT, if you know your stuff, you know that perturbation theory can be applied just as well to classical physics - You can even http://arxiv.org/abs/hep-th/0605061" there as well!

So here's what I'm asking: Do all perturbation expansions describe "real" things? The consequences of that would be absurd and without precedent. But if they don't, why should they enjoy a special status in QFT? The fact that perturbation theory works at describing real-and-observable quantities isn't an argument. Saying you need virtual particles to "explain" things is circular logic - if they're real something is not a full explanation unless they include them. Stating that "X said so." most certainly isn't an argument.

Nobody's denying there are notable physicists who really do believe in the "reality" of virtual particles. It's unfortunate that they assert that opinion as if it were uncontested physical fact in their popular-scientific writings, when it's neither uncontested, nor a matter of actual physics. Worse, they often invoke spurious arguments, such as the Lamb shift or Casimir effect, as 'proof' of their position. And so we have a bunch of people here under the false impression that this is actually physical fact, regurgitating these fallacies and basically appealing to authority. This is stupid. If you're going to debate a philosophical standpoint, you should at least know that you're doing so. And you should present real arguments relevant to the actual debate on the topic, rather than simplistic popular-scientific statements.

http://www.springerlink.com/content/51r27u20u354mh5n/" is an article (from a philosophy of science journal, as it should be) giving an overview of some of the serious arguments for and against virtual particles. The points raised by the virtual-particles-are-real advocates in this thread are notably absent.

 

[byron178]

[...]

so you are saying they are real?

 

[maverick_starstrider]

so you are saying they are real?

Dude, are you just trolling? He just spent like 3 paragraphs explaining why it makes no sense to say they're real.

 

[Lapidus]

There seems to be two sides to this debate - on one side are people who have done the actual calculations. On the other are people who are using quotes from popularizations in support of their position. That alone should tell you something.

You can't use the Lamb shift as evidence for virtual particles, since it was calculated a year before anyone had every heard of virtual particles.

Vanadium 50 can you answer https://www.physicsforums.com/showpost.php?p=3368854&postcount=144"?

Since I assume you belong to the camp who has done the actual calculations, I'm thrilled to here from you.

Please don't randomly quote popular phrases as if they gave any meaning to your argument. Do some research, study some quantum field theory. Then we can continue ;)

Maybe maxverywell was not quoting popular books, but things learned from Jackson "Electrodynamics", perhaps from page 3 of this very book where can be read "The concept of E and B are classical notions. It can be thought of as the classical limit of quantum mechanical description in terms of real and virtual photons."

Or maybe he was quoting from the Nobel laureate and one of the most respected man in field theory, Frank Wilczek:

"..the association of forces and interactions with particle exchange. When Maxwell completed the equations of electrodynamics, he found that they supported source-free electromagnetic waves. The classical electric and magnetic fields thus took on a life of their own. Electric and magnetic forces between charged particles are explained as due to one particle acting as a source for electric and magnetic fields, which then influence others. With the correspondence of fields and particles, as it arises in quantum field theory, Maxwell’s discovery corresponds to the existence of photons, and the generation of forces by intermediary fields corresponds to the exchange of virtual photons. The association of forces (or, more generally, interactions) with exchange of particles is a general feature
of quantum field theory."http://arxiv.org/abs/hep-th/9803075" , page 3.

Poly, you advice students to find a better/ other explanation than the standard texbook explanation of how quantum physical forces are mediated. And when asked what that should possible be, you say the interaction term in the classical Lagragian does. Thanks Poly. Maybe you are the one who should spend a little less on internet boards teaching physics and hit a bit more the textbooks...

Again, virtual photons have nothing originally to do with any calculation mechanism. They are allowed by quantum mechanics and are by no physical law or theory forbidden. They explain physically how interactions are locally mediated.

That they are not directly measurable and not real in the classical sense is part of their definition. But so are all the intermediate states in the double slit experiment. But these umeasurable intermediate states must be included (explicitly or implicitly) in the calcualtions of measurable outcomes. Because of that many or even most physicists say they part of physical reality.

And that's that.

 

[Polyrhythmic]

Poly, you advice students to find a better/ other explanation than the standard texbook explanation of how quantum physical forces are mediated. And when asked what that should possible be, you say the interaction term in the classical Lagragian does. Thanks Poly. Maybe you are the one who should spend a little less on internet boards teaching physics and hit a bit more the textbooks...

I didn't say anything about the classical Lagrangian. It's not my fault that all those textbook answers are somehow misleading/false. I only believe in arguments, not in blind quotes. Even a nobel laureate can have misconceptions about certain things, that doesn't make him a bad physicist.

Again, virtual photons have nothing originally to do with any calculation mechanism.

You are the one who should hit textbooks, this is simply a false statement. The calculation mechanism (perturbation theory) is the only reason why they ever came up.

 

[Polyrhythmic]

[...], then it's replacement uses the same dynamics, virtual particles in a zero-point energy field.

What? This doesn't make sense.

 

[Polyrhythmic]

No, I'd say a theory tries to make sense of the physical effects. They are real. And if the theory of virtual particles are correct, then they will almost certainly have a physical significance, again, as they attempt to explain many physical characteristics of many field theories borne from QM.

There is no such thing as a theory of virtual particles. Virtual particles may make sense in the half-educated way you view them, but that doesn't change the fact that they are not of physical significance.

 

[dm4b]

What does String Theory say as far as the "mechanism" behind a force? Does it shed any light on the whole virtual particle as a force-mediator topic?

Here's a crazy idea (totally made up in my head just now,so obviously I'm not giving it much credence)

Although not a perturbation series, a Fourier Series is another infinite series whose terms DO have a type of physical significance when applied to say a violin string. They represent different harmonics.

Well, they say each particle in nature is a certain frequency of vibration or energy state of strings. The Universe is a musical symphomy of sorts.

Wouldn't it be cool if virtual particles turned out to represent the "harmonics" of a string?

 

[Polyrhythmic]

What does String Theory say as far as the "mechanism" behind a force? Does it shed any light on the whole virtual particle as a force-mediator topic?

In string theory, there are also graphs comparable to Feynman diagrams coming from a perturbation series expansion. The difference is that those lines are now sheets, since particles are no longer zero-dimensional objects.

Although not a perturbation series, a Fourier Series is another infinite series whose terms DO have a type of physical significance when applied to say a violin string. They represent different harmonics.

That comes from the very nature of the Fourier expansion, its terms represent harmonic function, which in the case of a violin string have an actual physical interpretation.

Well, they say each particle in nature is a certain frequency of vibration or energy state of strings. The Universe is a musical symphomy of sorts.

Wouldn't it be cool if virtual particles turned out to represent the "harmonics" of a string?

That doesn't make sense. The different excitations of the string actually tell us which particle the string represents. This is even before we attempt to calculate interactions by perturbation series expansion.

 

[Goldstone1]

This has become a horrible argument among many posters.

I would like to say that there is nothing wrong with the idea of virtual particles, and if they are real, then the energy lamb shift certainly gives them something real to measure. If you don't want to call them virtual particles, then so be it. But most scientists will agree virtuals particles are a very good tool, even if they are not physically real.

 

[Polyrhythmic]

I would like to say that there is nothing wrong with the idea of virtual particles, and if they are real, then the energy lamb shift certainly gives them something real to measure.

In principle this is true, but unfortunately there is nothing which indicates that they are real.

But most scientists will agree virtuals particles are a very good tool, even if they are not physically real.

You have just captured the essence: they are tool!

 

[Goldstone1]

In principle this is true, but unfortunately there is nothing which indicates that they are real.



You have just captured the essence: they are tool!

You say it is a mathematical tool. How does singling out the virtual particle as a mathematical tool, any different to the very fact that the entire of QM is a mathematical tool. You do realize that we have never observed a particle directly. At this level, it's all about probabilities. And when you come to understand how important probability theory is for a wave function for instance, you will find that the wave function gives virtual particles a very possible existence - in fact, quantum theory predicts them.

So not believing they are there is a matter of choice. There can be no absolutes here.

 

[Polyrhythmic]

You say it is a mathematical tool. How does singling out the virtual particle as a mathematical tool, any different to the very fact that the entire of QM is a mathematical tool. You do realize that we have never observed a particle directly. At this level, it's all about probabilities. And when you come to understand how important probability theory is for a wave function for instance, you will find that the wave function gives virtual particles a very possible existence - in fact, quantum theory predicts them.

So not believing they are there is a matter of choice. There can be no absolutes here.

True, you can also view the wave function as a tool. There is much room for interpretation, but one thing is certain: the wave function plays a central role and we couldn't do any physics without it. This is not true for virtual particles. They arise as a (false) interpretation of a certain tool (perturbation theory), they are in no way a central element of the theory, they are simply not required.

Also your statement that quantum theory predicts them is plainly wrong. Could you give any reference on this?

 

[Goldstone1]

True, you can also view the wave function as a tool. There is much room for interpretation, but one thing is certain: the wave function plays a central role and we couldn't do any physics without it. This is not true for virtual particles. They arise as a (false) interpretation of a certain tool (perturbation theory), they are in no way a central element of the theory, they are simply not required.

Also your statement that quantum theory predicts them is plainly wrong. Could you give any reference on this?

As far as I am aware, so please correct me, when Casimir was in talks with his tutor, they discussed that as you enclose the plates, the wave lengths of photons become more compact... so I am basing this on history, if I can cite this, I will... So basically Casimir knew that quantum theory predicted this phenomenon. And low and behold, it did predict their existence.

 

[mattt]

You can use perturbations techniques in Classical Field Theory if you want, with its own kind of "virtual particles" there. Are you going to say then that the classical dynamics of fields are "mediated" by "its own kind of virtual particles"?

 

[Lapidus]

In quantum mechanics the uncertainty principle tells us that the energy can fluctuate wildly over a small interval of time. According to special relativity, energy can be converted into mass and vice versa. With quantum mechanics and special relativity, the wildly fluctuating energy can metamorphose into mass, that is, into new particles not previously present.

That is the core story of relativistic quantum field theory.

It has not one bit to do with any calculation scheme.

Please, and I ask probably for the tenth time, what forbids 'virtual' states from happening?

And yes, while we at it, how can we do without them, i.e. how are interactions mediated in a relativistic quantum physics theory?

 

[Polyrhythmic]

As far as I am aware, so please correct me, when Casimir was in talks with his tutor, they discussed that as you enclose the plates, the wave lengths of photons become more compact... so I am basing this on history, if I can cite this, I will... So basically Casimir knew that quantum theory predicted this phenomenon. And low and behold, it did predict their existence.

All you have to do in order to calculate the Casimir force is to take a look at the ground state energy in second quantization, both between the plates and free. Between the plates, the modes have to obey different boundary conditions than in the free case. From this energy difference you can directly derive the force. There, no virtual particles needed.

 

[Goldstone1]

You can use perturbations techniques in Classical Field Theory if you want, with its own kind of "virtual particles" there. Are you going to say then that the classical dynamics of fields are "mediated" by "its own kind of virtual particles"?

I think your queery is a matter of interpretation rather than empiracal fact.

 

[Goldstone1]

All you have to do in order to calculate the Casimir force is to take a look at the ground state energy in second quantization, both between the plates and free. Between the plates, the modes have to obey different boundary conditions than in the free case. From this energy difference you can directly derive the force. There, no virtual particles needed.

I think I am failing to show you that the particles where predicted first before their verification in a casimir force. Casimir had a thought-experiment which involves vacuum energy, and it required virtual particles. Beside, Lapidus says it best for an arguement.

 

[mattt]

For example:

A=\int_0^1 e^{-x^2}dx

A is a real number perfectly defined (because every continuous function is Riemann-integrable in a compact interval).

We may get to know the first n decimal digits of this number (using one approximation method or another) or we may not know it, but THAT only tells about our knowledge (of the decimal digits of that number). That real number is perfectly defined whether we may know its digits or not.

Imagine we can prove that the following infinite sum 1+a-ab+abc-abcd+... is a good approximation to the number A.

It would be very weird to say "the real number A is what it is because of the numbers a,b,c,d...".


NO, the real number A=\int_0^1 e^{-x^2}dx is perfectly defined, whether we may approximate its value one way or another, or not.


Now, a QFT define a S-Matrix. Its elements (numbers) are perfectly defined (if that QFT can be defined to begin with). Those numbers are the theoretical predictions that that QFT produce (whether we may get to know them in one way or another, or not).

Using perturbation techniques to approximate those numbers is one way for us to get to know them (at least its first decimal digits), but there are other approximation (non-perturbative) techniques to obtain the same goal. But again, that only speak about our knowledge of those numbers, whereas those numbers are perfectly defined (by the mathematical structure of the theory) with or without our knowledge of its decimal digits.

 

[alxm]

I think I am failing to show you that the particles where predicted first before their verification in a casimir force. Casimir had a thought-experiment which involves vacuum energy, and it required virtual particles.

You're making stuff up. And not for the first time in this thread.

First off, Casimir was not first to predict the Casimir effect. Wheeler did, in 1941 (meeting abstract in Phys Rev, v59, p928). Casimir was the first to calculate that effect. He did so without using Feynman diagrams or making any references whatsoever to virtual particles.

Second, calculating the Casimir effect does not require perturbation theory, much less interpreting that perturbation expansion as a representation of a real process.

Third, there's no 'vacuum energy' involved here. The Casimir effect is the same thing as the London dispersion force. It's defined to be the deviation from the ordinary London force once the quantized and relativistic field effects are taken into account. It's a QED effect by definition. It 'proves' that the electromagnetic field is indeed quantized. It does not prove, in any way, that the virtual excitations of that field used in certain QED calculations are any more real than the fictional excitations used, for instance, to calculate a many-body system.

 

[Goldstone1]

You're making stuff up. And not for the first time in this thread.

First off, Casimir was not first to predict the Casimir effect. Wheeler did, in 1941 (meeting abstract in Phys Rev, v59, p928). Casimir was the first to calculate that effect. He did so without using Feynman diagrams or making any references whatsoever to virtual particles.

Second, calculating the Casimir effect does not require perturbation theory, much less interpreting that perturbation expansion as a representation of a real process.

Third, there's no 'vacuum energy' involved here. The Casimir effect is the same thing as the London dispersion force. It's defined to be the deviation from the ordinary London force once the quantized and relativistic field effects are taken into account. It's a QED effect by definition. It 'proves' that the electromagnetic field is indeed quantized. It does not prove, in any way, that the virtual excitations of that field used in certain QED calculations are any more real than the fictional excitations used, for instance, to calculate a many-body system.

If my information at the beginning was incorrect, I apologize.

However, there is vacuum energy involved in the Casimir Effect. It directly involves the zero-point energy field, so I don't know how one could not talk of a vacuum energy.

 

[Goldstone1]

And I don't think I mentioned perturbation theory as such... did I? My memory is not great.

 

[maverick_starstrider]

And I don't think I mentioned perturbation theory as such... did I? My memory is not great.

Virtual particles are perturbation theory. That's what they are. I feel like you have no ground on to discuss such a thing if you don't even know what a Wick Contraction is. Virtual particles and QFT perturbation theory are the same thing. Virtual particles is not a concept separate from perturbation they ARE the perturbations. They exist solely in the scheme of drawing stick figures to figure out the next largest perturbative correction to a field theory integral.

 

[Goldstone1]

Virtual particles are perturbation theory. That's what they are. I feel like you have no ground on to discuss such a thing if you don't even know what a Wick Contraction is. Virtual particles and QFT perturbation theory are the same thing. Virtual particles is not a concept separate from perturbation they ARE the perturbations. They exist solely in the scheme of drawing stick figures to figure out the next largest perturbative correction to a field theory integral.

Yes, I suppose virtual particles are perturbations of energy.