Non-Perturbative QFT without Virtual Particles

[friend]

Here's a question:

Are "virtual" particle caused by "imaginary" numbers? There are the real and imaginary components to a complex number. And complex numbers are used so you can get interference patterns. For example, in the double split experiment, the wavefunction interfers with itself to cause constructive and destructive peaks and troughs. Could this interference also be explained in terms of virtual particles?

 

[Chalnoth]

Are virtual particles physical?

I don't see any significant distinction between virtual particles and real particles. Real particles are just virtual particles taken to asymptotic infinity. So I see them as being just as physical as real particles.

I know you think that they can't be physical because they only appear in a specific formulation, but that's the case with many things we call physical (such as energy, or the gravitational field).

 

[atyy]

I don't see any significant distinction between virtual particles and real particles. Real particles are just virtual particles taken to asymptotic infinity. So I see them as being just as physical as real particles.

I know you think that they can't be physical because they only appear in a specific formulation, but that's the case with many things we call physical (such as energy, or the gravitational field).

Actually, that's not what I think (my instinct is to say, who cares?). I was just trying to set up an analogy and have people comment on whether the virtual tips were real or not.

In your view, if 15=5+10, the 5 and 10 are not real or physical, even though the 15 is?

 

[Chalnoth]

Actually, that's not what I think (my instinct is to say, who cares?). I was just trying to set up an analogy and have people comment on whether the virtual tips were real or not.

In your view, if 15=5+10, the 5 and 10 are not real or physical, even though the 15 is?

Well, I don't think the analogy works, because none of it's physical. Not in the same way as a particle within QFT is.

 

[atyy]

Well, I don't think the analogy works, because none of it's physical. Not in the same way as a particle within QFT is.

A tip is not physical?

(Actually, my criticism of my analogy might be that everything is too "physical" - I mean $15=$5+$10 -I cannot imagine anything more physical than $5! So my thinking was that although $5 could be a "real" amount paid in another transaction, as far as the $15 tip was concerned, it was "virtual". The example was also meant to show that it was meaningless to ask if the $15 was really $5+$10 or $7+$8.)

 

[Chalnoth]

A tip is not physical?

The actual money is, obviously. But the 15% number is not. Nor does it represent a physical quantity, because its value is relative.

Now, if you had used an actual amount of money as an analogy, then it would make more sense. Because a dollar bill is quite physical.

 

[atyy]

The actual money is, obviously. But the 15% number is not. Nor does it represent a physical quantity, because its value is relative.

Now, if you had used an actual amount of money as an analogy, then it would make more sense. Because a dollar bill is quite physical.

But for any given bill, the 15% tip corresponds to a given dollar amount (ok, maybe I should have said 15%, rounded up to the nearest dollar - or maybe I should have said 17% - a friend of mine said foreigners like me in the US tend to tip too little )

 

[Lapidus]

So can we summarize that there are three views on 'virtual' particles

-they are part of physical reality

-they are just mathematical tools

-it is a matter of taste, physics can't answer, so who cares

Can we perhaps agree on that and by that happily all agree to disagree?

(And yes, I would go for the first!)

 

[rogerl]

So can we summarize that there are three views on 'virtual' particles

-they are part of physical reality

-they are just mathematical tools

-it is a matter of taste, physics can't answer, so who cares

Can we perhaps agree on that and by that happily all agree to disagree?

(And yes, I would go for the first!)

But Arnold Neimaier who is the top Particle Physicist in the world believes it is just mathematical tool so he has to agree with you before the issue is settled. Anyway. I have this question. SUPPOSED virtual particles were really there in the vacuum appearing thanks to Heisenberg Uncertainty Principle where they can borrow the energy from the vacuum and appear in short time. How do we model them by math? Would it differ to our current formulation of them as multivariate integrals or would there be a different formulation?? This is how we can settle the issue by knowing if the math would change if these virtual particles entities are out there versus when they were not.

 

[atyy]

But Arnold Neimaier who is the top Particle Physicist in the world believes it is just mathematical tool so he has to agree with you before the issue is settled. Anyway. I have this question. SUPPOSED virtual particles were really there in the vacuum appearing thanks to Heisenberg Uncertainty Principle where they can borrow the energy from the vacuum and appear in short time. How do we model them by math? Would it differ to our current formulation of them as multivariate integrals or would there be a different formulation?? This is how we can settle the issue by knowing if the math would change if these virtual particles entities are out there versus when they were not.

I think everyone is agreed that the maths does not change, neither does what the theory predicts about any experimental outcome. The disagreement is only on how to name the maths.

 

[rogerl]

I think everyone is agreed that the maths does not change, neither does what the theory predicts about any experimental outcome. The disagreement is only on how to name the maths.

If the maths do not change supposed virtual particles were really there versus they were not. Then it is possible to assume they exist?? So if the math is the same, We may as well say it is possible that virtual particles were really there in the vacuum appearing thanks to Heisenberg Uncertainty Principle where they can borrow the energy from the vacuum and appear in short time?? But then some folks say Lattice QFT that doesn't use perturbation theory don't require the multivariage integrals. Here supposed the virtual particles were really there, how do you integrate it into Lattice QFT math??

 

[atyy]

If the maths do not change supposed virtual particles were really there versus they were not. Then it is possible to assume they exist?? So if the math is the same, We may as well say it is possible that virtual particles were really there in the vacuum appearing thanks to Heisenberg Uncertainty Principle where they can borrow the energy from the vacuum and appear in short time?? But then some folks say Lattice QFT that doesn't use perturbation theory don't require the multivariage integrals. Here supposed the virtual particles were really there, how do you integrate it into Lattice QFT math??

There are many ways of calculating the same thing.

 

[rogerl]

There are many ways of calculating the same thing.

So how do you use Lattice QFT without perturbation to describe virtual particles (supposed for the sake of arguments these were real in that they could borrow the energy from the vacuum and appear in short time thanks to Heisenberg Uncertainty Principle).

 

[atyy]

So how do you use Lattice QFT without perturbation to describe virtual particles (supposed for the sake of arguments these were real in that they could borrow the energy from the vacuum and appear in short time thanks to Heisenberg Uncertainty Principle).

The point is that there is an underlying theory.

Lattice methods and virtual particles are two different ways of calculating what experimental predictions the underlying theory makes.

As long as both methods proceed correctly from the underlying theory, they will make the same experimental predictions.

 

[rogerl]

The point is that there is an underlying theory.

Lattice methods and virtual particles are two different ways of calculating what experimental predictions the underlying theory makes.

As long as both methods proceed correctly from the underlying theory, they will make the same experimental predictions.

Does this underlying theory involves virtual particles?
If you meant lattice methods don't involve virtual particles and it's true virtual particles are just side effect of our perturbation method. How come they have to propose Supersymmetry to solve the Hierarchy Problem. In Hierarchy Problem, the Higgs can have Planck mass because of quantum contributions. So what they do is propose that the virtual particles of Supersymmetric particles can cancel the very large quantum contributions in the Hierarchy Problem. Why do they have to take drastic measure and radical idea just to get rid of the large contribution if virtual particles are just multivariate integrals. Why didn't they just go to lattice methods to solve it?

 

[Vanadium 50]

But Arnold Neimaier who is the top Particle Physicist in the world

Don't be snotty.

It's clear you have a lot to learn. It would behoove you to be nicer to the people who are spending their time trying to teach you.

 

[rogerl]

Don't be snotty.

It's clear you have a lot to learn. It would behoove you to be nicer to the people who are spending their time trying to teach you.

What. But I really think A. Neumaier is one of the top physicists in the world. Just look at his website with very complex mathematics and he is writing a book. So I'm just admiring him and consider his opinion important because of his multidisciplinary background in mathematics and physics. That's why I'm basing the facts about virtual particles on what he has to say and whether he admit they may still be real in spite of being just multivariate integrals because he is an expert in his department. My latest question on him is how physics have to take radical ideas like Supersymmetry just to deal with the virtual particles problems and why not just propose lattice QFT.

 

[atyy]

Does this underlying theory involves virtual particles?
If you meant lattice methods don't involve virtual particles and it's true virtual particles are just side effect of our perturbation method. How come they have to propose Supersymmetry to solve the Hierarchy Problem. In Hierarchy Problem, the Higgs can have Planck mass because of quantum contributions. So what they do is propose that the virtual particles of Supersymmetric particles can cancel the very large quantum contributions in the Hierarchy Problem. Why do they have to take drastic measure and radical idea just to get rid of the large contribution if virtual particles are just multivariate integrals. Why didn't they just go to lattice methods to solve it?

That's an interesting question. I don't know. My understanding is that the underlying theory is given by special relativity, quantum mechanics, Wilsonian renormalization, and the standard model Lagrangian. I would guess that the fine tuning problem is a heuristic argument based on Wilsonian renormalization, so it should have a counterpart in a lattice language.

Also, is there such a thing as non-perturbative QED? Unless a QFT is asymptotically free or safe, isn't it by definition only perturbatively defined? According to http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVC-47319XP-1C5&_user=108429&_coverDate=03%2F09%2F1992&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_acct=C000059713&_version=1&_urlVersion=0&_userid=108429&md5=02d57ae15e181b9774e884147a99780a&searchtype=a , QED is likely not asymptotically safe. The only question then is how we choose to name the terms in a particular perturbation expansion.

 

[A. Neumaier]

Also, is there such a thing as non-perturbative QED? Unless a QFT is asymptotically free or safe, isn't it by definition only perturbatively defined? According to http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVC-47319XP-1C5&_user=108429&_coverDate=03%2F09%2F1992&_rdoc=1&_fmt=high&_orig=gateway&_origin=gateway&_sort=d&_docanchor=&view=c&_acct=C000059713&_version=1&_urlVersion=0&_userid=108429&md5=02d57ae15e181b9774e884147a99780a&searchtype=a , QED is likely not asymptotically safe.

This problem is completely open, and the opinion of the physics community on this is divided. Most theorist think that QED does not exist as a nonperturbative theory, but they have no hard arguments - the renormalization group argument leading to the Landau pole and the lack of nontrivial fixed points is itself of a perturbative nature.

To settle the case, one would either need a nonperturbative construction for QED, or better foundations for QFT so that one can make the notion of ''some theory not existing'' more precise.

 

[A. Neumaier]

What. But I really think A. Neumaier is one of the top physicists in the world. Just look at his website with very complex mathematics and he is writing a book. So I'm just admiring him and consider his opinion important because of his multidisciplinary background in mathematics and physics.

My multidisciplinary background in mathematics and physics doesn't make me a top physicist. Only 10% of my publications are in physics, and none is in quantum field theory. moreover, all my highly cited papers are in mathematics, not in physics.

 

[rogerl]

This problem is completely open, and the opinion of the physics community on this is divided. Most theorist think that QED does not exist as a nonperturbative theory, but they have no hard arguments - the renormalization group argument leading to the Landau pole and the lack of nontrivial fixed points is itself of a perturbative nature.

To settle the case, one would either need a nonperturbative construction for QED, or better foundations for QFT so that one can make the notion of ''some theory not existing'' more precise.

If you say lattice methods don't involve virtual particles and it's true virtual particles are just side effect of our perturbation method. How come they have to propose Supersymmetry to solve the Hierarchy Problem?? In Hierarchy Problem, the Higgs can have Planck mass because of quantum contributions. So what they do is propose that the virtual particles of Supersymmetric particles can cancel the very large quantum contributions in the Hierarchy Problem. Why do they have to take drastic measure and radical idea just to get rid of the large contribution if virtual particles are just multivariate integrals. Why didn't they just go to lattice methods to solve it?

Unless it's possible virtual particles were really fundamental entities in the vacuum.

 

[A. Neumaier]

If you say lattice methods don't involve virtual particles and it's true virtual particles are just side effect of our perturbation method. How come they have to propose Supersymmetry to solve the Hierarchy Problem?? .

The hierarchy problem is not linked to virtual particles. It is the problem of how to avoid fine-tuning in the coupling constants in order to reproduce vastly different scales observed phenomenologically. http://en.wikipedia.org/wiki/Hierarchy_problem

As everywhere, virtual particles enter the picture only when discussing the problem in perturbation theory, looking at particular diagrams.

 

[rogerl]

The hierarchy problem is not linked to virtual particles. It is the problem of how to avoid fine-tuning in the coupling constants in order to reproduce vastly different scales observed phenomenologically. http://en.wikipedia.org/wiki/Hierarchy_problem

As everywhere, virtual particles enter the picture only when discussing the problem in perturbation theory, looking at particular diagrams.

But Lisa Randall said it has everything to do with virtual particles. Page 252 of Warped Passages states:

"The problem for the hierarchy is that the contribution to the Higgs particle's mass from virtual particles with extremely high mass will be about as big as the Planck scale mass, which is ten million billion times greater than the Higgs particle mass we want - the one that will give the right weak scale mass and elementary particle masses"

page 265:

"In a supersymmetric theory, the virtual Standard Model particles aren't the only virtual particles that contributes to the Higgs particle's mass. Virtual superpartners do, too. And because of the remarkable properties of supersymmetry, the two kinds of contributions always add up to zero. The quantum contributions of virtual fermions and bosons to the Higgs particle's mass are related so precisely that the large contributions made by either bosons or fermions individually are guaranteed to cancel each other out. The value of the fermion's contribution is negative and exactly cancels the bosons' contribution."

You see. Randall said virtual particles have everything to do with it.

Virtual particles is the heart and soul of particle physicists. Are you 100% certain they don't really exist? By exist is meant they could borrow the energy from the vacuum and appear in very short time thanks to Heisenberg Uncertainty Principle.. this distinguishes it from pure mathematic artifacts.

 

[A. Neumaier]

You see. Randall said virtual particles have everything to do with it.

Virtual particles is the heart and soul of particle physicists.

Only in as far as perturbation theory (including individual Feynman diagrams) is taken for reality. I have higher standards for existence. Figurative talk does not yet make things real.

Are you 100% certain they don't really exist? By exist is meant they could borrow the energy from the vacuum and appear in very short time thanks to Heisenberg Uncertainty Principle.. this distinguishes it from pure mathematic artifacts.

These properties are wishful thinking, associated to virtual particle to make them sound intelligible.

But nobody ever has written down equations for how a virtual particle could borrow energy from the vacuum, and in which sense it exists for a short time. This would require to have a dynamical entity associated with virtual particles that changes in time according to some evolution equation such as Schroedinger's.

The existence of virtual particles is therefore no more than virtual. Real particles have a state and a dynamical law that virtual particles lack.

 

[alxm]

But Lisa Randall said it has everything to do with virtual particles. Page 252 of Warped Passages states:

That's a popular-scientific book. There are many popular-scientific books which describe virtual particles as if they're real things. I don't know if they're necessarily taking an ontological position with it. It can also be just a more interesting way of visualizing or describing a perturbation calculation. Saying you're adding up a bunch of terms doesn't sound as fun as interpreting those terms as virtual particle contributions and so on. But nothing you quoted there actually said virtual particles were "real" or spoke of them as if they were more than mathematical abstractions. It talks about "virtual particle contributions", which means the contribution from that term in the perturbation series.

Nobody's disputing you can describe those terms as virtual particle contributions. But that in-itself doesn't make them real. Since I just mentioned it in another thread, you have Goldstone and Hugenholtz diagrams in many-body perturbation theory. In those diagrams the vertices are graphical representations of the contributions to the perturbation series from various electron-pair interactions. But as far as I know, nobody's yet decided to interpret that as meaning electrons actually interact two-at-a-time.

 

[Lapidus]

Lisa Randall has more to say about 'virtual' particles in her book

Virtual particles, a consequence of quantum mechanics, are strange, ghostly twins of actual particles. They pop in and out of existence, lasting only the barest moment. Virtual particles have the same interactions and the same charges as physical particles, but they have energies that look wrong. For example, a particle moving very fast clearly carries a lot of energy. A virtual particle, on the other hand, can have enormous speed but no energy. In fact, virtual particles can have any energy that is different from the energy carried by the corresponding true physical particle. If it had the same energy, it would be a real particle, not a virtual one.

Virtual particles are a strange feature of quantum field theory that you have to include to make the right predictions.

So how can these apparently impossible particles exist? A virtual particle with its borrowed energy could not exist were it not for the uncertainty principle, which allows particles to have the wrong energy so long as they do so for such a short time that it would never be measured.

The uncertainty principle tells us that it would take infinitely long to measure energy (or mass) with infinite precision, and that the longer a particle lasts, the more accurate our measurement of its energy can be. But if the particle is short-lived and its energy cannot possibly be determined with infinite precision, the energy can temporarily deviate from that of a true long-lived particle. In fact, because of the uncertainty principle, particles will do whatever they can get away with for as long as they can. Virtual particles have no scruples and misbehave whenever no one is watching.

You can think of the vacuum as a reservoir of energy—virtual particles are particles that emerge from the vacuum, temporarily borrowing some of its energy. They exist only fleetingly and then disappear back into the vacuum, taking with them the energy they borrowed. That energy might return to its place of origin, or it might be transferred to
particles in some other location.

The quantum mechanical vacuum is a busy place. Even though the vacuum is by definition empty, quantum effects give rise to a teeming sea of virtual particles and antiparticles that appear and disappear— even though no stable, long-lasting particles are present. All particle-antiparticle pairs can in principle be produced, albeit only for very short visits, too short to be seen directly. But however brief their existence, we care about virtual particles because
they nonetheless leave their imprint on the interactions of long-lived particles.

Virtual particles have measurable consequences because they influence the interactions of the real physical particles that enter and leave an interaction region. During its brief span of its existence, a virtual particle can travel between real particles before disappearing and repaying its energy debt to the vacuum. Virtual particles thereby act as intermediaries that influence the interactions of long-lived stable particles.

 

[alxm]

Well, I suppose that settles whether or not she considers them 'real' or not.
Nevertheless, it's still an opinion/interpretation rather than hard physical fact. I'm also doubtful it represents popular opinion among physicists.
(not that I think Randall is speaking for anyone other than herself, although I haven't read the book, so.. )

 

[Lapidus]

Nevertheless, it's still an opinion/interpretation rather than hard physical fact. I'm also doubtful it represents popular opinion among physicists.

Not sure about the popular opinion among physicists on this. Maybe we should take a poll!

 

[A. Neumaier]

Virtual particles, a consequence of quantum mechanics, are strange, ghostly twins of actual particles. They pop in and out of existence, lasting only the barest moment. Virtual particles have the same interactions and the same charges as physical particles, but they have energies that look wrong. For example, a particle moving very fast clearly carries a lot of energy. A virtual particle, on the other hand, can have enormous speed but no energy.

You can think of the vacuum as a reservoir of energy—virtual particles are particles that emerge from the vacuum, temporarily borrowing some of its energy. They exist only fleetingly and then disappear back into the vacuum, taking with them the energy they borrowed. That energy might return to its place of origin, or it might be transferred to
particles in some other location.

The quantum mechanical vacuum is a busy place. Even though the vacuum is by definition empty, quantum effects give rise to a teeming sea of virtual particles and antiparticles that appear and disappear

Look in the literature at a proof of any of these statements, or even a more precise description of what is meant with them, and you won't find anything. This sort of discourse is good for story-telling, but for nothing else.

 

[Vanadium 50]

I think one needs to distinguish between a popularization and a textbook.