Non-Perturbative QFT without Virtual Particles

[ParticleGrl]

But in QFT, production and detection of particles is _always_ represented by external lines, not by internal ones.

A photon is produced by some particles A, and much later scatters with some particles B. I can calculate this either as two processes-production of a photon by A, and then scattering at B. OR, I can calculate it as scattering of A and B. In the first case, the photon is real, in the second case virtual (though on shell or very nearly on shell).

Also, treating the external lines as real isn't enough to get physically sensible cross-sections. If you treat an external electron, quark, or gluon line as "real" and calculate a renormalized cross section, it will come out divergent (because it not infrared safe).

You have to treat the "real" final states for an electron as an electron+a cloud of soft/virtual photons.

For QCD final states, you have to define jet functions (and be sure they are infrared safe). The real final states are of course hadrons, but even doing perturbative QCD you have to have clouds of partons for the final states.

 

[Haelfix]

The standard Feynman diagrams have no interpretation at all outside a scattering framework. .

Yes, although almost everything in physics can be written in a scattering framework.

Thus if you deny the prepared and detected particles the status of real particles, nothing is left to check the theory for correctness.

Eh? I am saying exactly what Particlegrl just said. When you measure a photon from some atomic process, you can consider it as a scattering event involving some particles of a detector (like electrons in your retina), that causes some chain of events that registers as a click in a detector (like a neuron in your brain). Thus one could loosely say that the photon measured is virtual.

Heurestically speaking, a virtual particle is considered virtual by nature of its very short lifetime. But there, you can make that distinction arbitrarily silly, which is why I mentioned the process of observing 'nearly on shell' light from alpha centauri. The point being, that there is no empirical way (in the language of perturbation theory and scattering theory) to distinguish the concepts. Any way you could envisage would involve a probing particle that alters the original system.

Maybe I'm saying this poorly, its much easier to draw the feynman diagram!

 

[A. Neumaier]

This, to me, is like claiming that the electric field between the plates of a capacitor isn't actually made up of a collection of photons.

In the Coulomb gauge, photons are manifestly absent from this field.
Believing that they are nevertheless present there is like believing that virtual particles are present in classical field theory. But nobody does the latter.

And one could equally say that the virtual particle-free formulations are merely describing the collective behavior of the virtual particles, instead of summing up their individual contributions.

Their individual contributions are infinite and hence physically meaningless.

 

[Chalnoth]

In the Coulomb gauge, photons are manifestly absent from this field.
Believing that they are nevertheless present there is like believing that virtual particles are present in classical field theory. But nobody does the latter.

Well, at least you're consistent.

Their individual contributions are infinite and hence physically meaningless.

That's only because we don't understand what's going on at high energies, though.

 

[A. Neumaier]

A photon is produced by some particles A, and much later scatters with some particles B. I can calculate this either as two processes-production of a photon by A, and then scattering at B. OR, I can calculate it as scattering of A and B. In the first case, the photon is real, in the second case virtual (though on shell or very nearly on shell).

But the results will not be the same.

Also, treating the external lines as real isn't enough to get physically sensible cross-sections. If you treat an external electron, quark, or gluon line as "real" and calculate a renormalized cross section, it will come out divergent (because it not infrared safe).

You have to treat the "real" final states for an electron as an electron+a cloud of soft/virtual photons.

For QCD final states, you have to define jet functions (and be sure they are infrared safe). The real final states are of course hadrons, but even doing perturbative QCD you have to have clouds of partons for the final states.

The real, external electron _is_ the electron dressed with its electromagnetic field, because only these are valid asymptotic states.

Electrons without this field are not gauge invariant, and hence as fictitious as virtual particles. Simile for QCD.

 

[A. Neumaier]

Thus one could loosely say that the photon measured is virtual.

Loosely, one can say everything. I have nothing to say to those content with such a loose view of reality.

 

[A. Neumaier]

That's only because we don't understand what's going on at high energies, though.

No. Renormalization is needed no matter what is going on at high energies.
Even in string theory.

 

[friend]

So if a tree falls in the forest and no one hears it, does that make it a "virtual" tree?

 

[Haelfix]

But the results will not be the same.

What 'results' are you talking about?

 

[ParticleGrl]

But the results will not be the same.

? What is different?

The real, external electron _is_ the electron dressed with its electromagnetic field, because only these are valid asymptotic states.

But you can't draw this dressed electron as a line in a Feynman diagram. The point I'm trying to make is that all the lines in diagram have an equally dubious claim to being the "real" objects.

Electrons without this field are not gauge invariant, and hence as fictitious as virtual particles. Simile for QCD.

Certainly, I can compute gauge invariant quantities which are not infrared safe. This leads me to believe these are separate issues, though I am open to persuasion. Is there a quick calculation I can do to convince myself otherwise?

 

[strangerep]

But you can't draw this dressed electron as a line in a Feynman diagram.

Yes you can, but the initial formulation of the Hamiltonian must be redone
in terms of these new gauge invariant asymptotic fields. See below.

Certainly, I can compute gauge invariant quantities which are not infrared safe. This leads me to believe these are separate issues, though I am open to persuasion. Is there a quick calculation I can do to convince myself otherwise?

A quick calculation? No. But here's some background (taken from the introduction to
latest version of a paper I've been trying to write for a couple of years now). Please
forgive the remaining embedded latex macros. I hope you can read around them
and follow the symbolic reference citations (which are really the main point of
re-posting this stuff here).

----------------------------------------

Textbook treatments of the infrared (IR) divergences in quantum
electrodynamics (QED) typically introduce a small fictitious photon
mass to regularize the integrals. Allowing this mass to approach zero,
it becomes necessary to sum physically measurable quantities, such as
the cross sections for electron scattering, over all possible
asymptotic states involving an infinite number of soft photons, yielding
the so-called "inclusive" cross section.

The IR divergences are thus dealt with by restricting attention only to these
"IR-safe" quantities such as the inclusive cross section. However, various
authors have expressed dissatisfaction with this state of affairs in which
the cross sections become the objects of primary interest rather than the
S-matrix. The seminal paper of {\sc Chung} \cite{Chu} showed how one may
dress the asymptotic electron states with an operator familiar from the
(Glauber) theory of photon coherent states, thereby eliminating IR divergences
in the S-matrix to all orders for the cases he considered.

In a series of papers, {\sc Kibble} \cite{Kib1,Kib2,Kib3,Kib4}
provided a much more extensive (and more rigorous) development of Chung's
idea, solving the dynamical problem to show that IR divergences are
eliminated by dressing the asymptotic electron states by coherent states
of soft photons. Various separable subspaces are mapped into each other
by the S-matrix, but there is no stable separable subspace that is mapped into itself.

Later, {\sc Kulish \& Faddeev} \cite{KulFad} (``KF'' hereafter) gave a
less cumbersome treatment involving modification of the asymptotic
condition and a new space of asymptotic states which is not only
separable, but also relativistically and gauge invariant. They were
able to derive Chung's formulas without the laborious calculations of
Kibble, yet also obtained a more satisfactory generalization to the
case of arbitrary numbers of charged particles and photons in the
initial and final states.

KF emphasized the role of the nonvanishing interaction of QED at
asymptotic times as the source of the problems.\footnote{The nonvanishing
asymptotic Coulomb interaction had already been investigated in the
nonrelativistic case by {\sc Dollard} \cite{Dol}.}
This inconvenient fact means that QED's asymptotic dynamics is not
governed by the usual free Hamiltonian $H_0$, so perturbative
approaches starting from such free states are singular (a so-called
"discontinuous" perturbation). Standard treatments rely on the
unphysical fiction of adiabatically switching off the interaction, but
KF wished to find a more physically satisfactory operator governing the
asymptotic dynamics.\footnote{ However, {\sc Horan, Lavelle \&
McMullan} \cite{HorLabMcM-1,HorLabMcM-2} claim that the KF method has
problems when applied to theories with 4-point interactions, as it
involves operator convergence. They construct a more general method
based on weak (matrix element) convergence.}

Supplement S4 in {\sc Jauch \& Rohrlich} \cite{JauRoh} gives a useful
textbook presentation of infrared divergences along the above lines.

[...] this solution to the infrared problem [i.e., emphasizing only IR-safe
inclusive cross-sections, etc] is now superseded by a much deeper understanding
of this difficulty. That a full understanding was lacking as late as the early 1960's
can also be seen from the inability until that time to compute a transition
probability AMPLITUDE that is infrared-divergence free. [...]

Much earlier, {\sc Dirac} \cite{Dir55} took some initial steps in
constructing a manifestly gauge-invariant electrodynamics. The dressing
operator he obtained is a simplified version of those mentioned above
involving soft-photon coherent states, but he did not
address the IR divergences in this paper. Neither Chung, Kibble, nor
Kulish and Faddeev cite Dirac's paper, and the connection between explicit
gauge invariance and resolution of the IR problem did not emerge
until later. [\att Who was the first to note this??] In 1965 Dirac noted
\cite{Dir65}, \cite{Dir66} that problems in QED arise because the full
gauge-invariant Hamiltonian is typically split into a "free" part $H_0$
and an "interaction" part $H_I$ which are {\it not} separately
gauge-invariant. Indeed, Dirac's original 1955 construction had
resulted in an electron together with its Coulomb field, which is
clearly a more physically correct representation of electrons at
asymptotic times: a physical electron is always accompanied by its
Coulomb field.

More recently, {\sc Bagan, Lavelle, McMullan}
\cite{BagLavMcMul-1}, \cite{BagLavMcMul-2} (``BLM'' hereafter) and other
collaborators\footnote{See also the references in \cite{BagLavMcMul-1}
and \cite{BagLavMcMul-2}.} have developed these ideas further, applying
them to IR divergences in QED, and also QCD in which a different class
of so-called "collinear" IR divergence occurs. (See also the references
therein.) These authors generalized Dirac's construction to the case of
moving charged particles. Their dressed asymptotic fields include the
asymptotic interaction, and they show that the on-shell Green's
functions and S-matrix elements for these charged fields have (to all
orders) the pole structure associated with particle propagation and
scattering.

The purpose of the current paper is to set out some of the calculations
of the above references in a more pedagogically accessible form, with
emphasis on the connection(s) between explicit gauge-invariance of the basic
field (having physically acceptable asymptotic dynamics), and resolution of
IR divergence problems.

[blah, blah, blah ...]

References:

\bibitem{BagLavMcMul-1}
E. Bagan, M. Lavelle, D. McMullan,~\\
"Charges from Dressed Matter: Construction",~\\
(Available as hep-ph/9909257.)

\bibitem{BagLavMcMul-2}
E. Bagan, M. Lavelle, D. McMullan,~\\
"Charges from Dressed Matter: Physics \& Renormalisation",~\\
(Available as hep-ph/9909262.)

\bibitem{Bal} L. Ballentine,
"Quantum Mechanics -- A Modern Development", ~\\
World Scientific, 2008, ISBN 978-981-02-4105-6

\bibitem{Chu}
V. Chung,
"Infrared Divergences in Quantum Electrodynamics", ~\\
Phys. Rev., vol 140, (1965), B1110.
(Reprinted in \cite{KlaSkag}.)

\bibitem{Dir55}
P.A.M. Dirac,
"Gauge-Invariant Formulation of Quantum Electrodynamics",~\\
Can. J. Phys., vol 33, (1955), p. 650.

\bibitem{Dir65}
P.A.M. Dirac,
"Quantum Electrodynamics without Dead Wood",~\\
Phys. Rev., vol 139, (1965), B684-690.

\bibitem{Dir66}
P.A.M. Dirac,
"Lectures on Quantum Field Theory",~\\
Belfer Graduate School of Science, Yeshiva Univ., NY, 1966

\bibitem{Dol}
J. D. Dollard,
"Asymptotic Convergence and the Coulomb Interaction",~\\
J. Math. Phys., vol, 5, no. 6, (1964), 729-738.

\bibitem{HorLabMcM-1}
R. Horan, M. Lavelle, D. McMullan,~\\
"Asymptotic Dynamics in QFT",~\\
Arxiv preprint hep-th/9909044.

\bibitem{HorLabMcM-2}
R. Horan, M. Lavelle, D. McMullan,~\\
"Asymptotic Dynamics in QFT -- When does the coupling switch off?",~\\
Arxiv preprint hep-th/0002206.

\bibitem{Jac}
J. D. Jackson,
"Classical Electrodynamics" (2nd Edition),~\\
Wiley, 1975, ISBN 0-471-43132-X

\bibitem{JauRoh}
Jauch \& Rohrlich
"The Theory of Photons \& Electrons" (2nd Edition),~\\
Springer-Verlag, 1980, ISBN 0387072950.

\bibitem{Kib1}
T.W.B. Kibble, ~\\
"Coherent Soft-Photon States \& Infrared Divergences. I. Classical Currents",~\\
J. Math. Phys., vol 9, no. 2, (1968), p. 315.

\bibitem{Kib2}
T.W.B. Kibble, ~\\
"Coherent Soft-Photon States \& Infrared Divergences. II.
Mass-Shell Singularities of Green's Functions",~\\
Phys. Rev., vol 173, no. 5, (1968), p. 1527.

\bibitem{Kib3}
T.W.B. Kibble, ~\\
"Coherent Soft-Photon States \& Infrared Divergences.
III. Asymptotic States and Reduction Formulas.",~\\
Phys. Rev., vol 174, no. 5, (1968), p. 1882.

\bibitem{Kib4}
T.W.B. Kibble, ~\\
"Coherent Soft-Photon States \& Infrared Divergences.
IV. The Scattering Operator.",~\\
Phys. Rev., vol 175, no. 5, (1968), p. 1624.

\bibitem{KlaSkag}
J. R. Klauder \& B. Skagerstam, ~\\
"Coherent States -- Applications in Physics \& Mathematical Physics",~\\
World Scientific, 1985, ISBN 9971-966-52-2

\bibitem{KulFad}
P.P. Kulish \& L.D. Faddeev, ~\\
"Asymptotic Conditions and Infrared Divergences in Quantum Electrodynamics",~\\
Theor. Math. Phys., vol 4, (1970), p. 745

\bibitem{PesSch}
M.E. Peskin \& D.V. Schroeder,
"An Introduction to Quantum Field Theory",~\\
Perseus Books, 1995, ISBN 0-201-50397-2

---- (End -----

 

[meopemuk]

strangerep,

I am very interested in reading your paper when it is completed. I was reading Chung, Kibble, Kulish & Faddeev, but so far I was not able to get a consistent picture out of this. I need a detailed and pedagogical introduction. Hopefully, I will find it in your work. My goal is to understand how this approach allows to eliminate infrared divergences in QED loop integrals for scattering amplitudes with charged particles. I am especially interested in the vertex loop integral.

You've mentioned a book by Jauch & Rohrlich. Is it good as an introduction to infrared divergences?

Thanks.
Eugene.

 

[strangerep]

I am very interested in reading your paper when it is completed.

My current estimate is that it might be ready by the year 3000AD. :-(

I was reading Chung, Kibble, Kulish & Faddeev, but so far I was not able
to get a consistent picture out of this.

I know what you mean. I don't know of any paper that gives a comprehensive
consistent picture yet. One kinda has to piece it together. Have you tried looking
through all the more recent papers of Lavelle, McMullan, et al? (I.e., not
just those which I mentioned.) They provide some extra pieces of the puzzle.

I need a detailed and pedagogical introduction.
Hopefully, I will find it in your work.

Alas, I have not yet found it in my work. :-)

But I keep trying.

My goal is to understand how this approach allows to eliminate infrared
divergences in QED loop integrals for scattering amplitudes with charged
particles. I am especially interested in the vertex loop integral.

Have you tried working through Chung's old paper in detail? It's a bit
tedious to follow, and the print quality is not too good.

You've mentioned a book by Jauch & Rohrlich. Is it good as an
introduction to infrared divergences?

It's now a rather old book, but I get the impression it was quite
well-regarded in its day. I only have a copy of supplement S4 from
the 2nd edition, but I looked through some of the whole book a
while back. I think supplement S4 is worth reading because it
summarizes the new understanding pretty well for how it was at
that time. But it necessarily points out some remaining open
problems such as:

The [asymptotic] states defined in this [new] way and S-operators
[...] permit the definition and explicit computation of an S-matrix.
Perturbation calculations have verified that this S-matrix is indeed
free of IR divergences. In fact, a set of Feynman rules has been
developed taking account of the modified mass-shell behaviour [...].
A carefully prescribed order of limits is here necessary. However,
for practical calculations this method does not at the present time
seem to offer advantages over the older perturbation techniques [...]

What has not been achieved so far is a rigorous derivation of these
results which would include a consistent treatment of the
renormalization terms, a general proof of the unitarity of the new
S-matrix and a nonperturbative proof of the absence of IR divergences.
It is obvious that the present treatment of the IR problem comes
as an afterthought. The coherent state space is not introduced into
the theory from the beginning. Nor is the necessary IR renormalization
carried through and shown to be consistent with UV renormalization.

Of course, one should keep in mind that the above was written pre-1980,
and lots more work has been done since then.

J&R also give some more references beyond those I mentioned, including
some important papers by Zwanziger.

I find the last part of J&R's remark above interesting -- the bit suggesting
that the coherent state space should be introduced at the beginning. I
interpret this to mean that the Hamiltonian, etc, should be re-expressed
in terms of the physical gauge-invariant asymptotic fields which are what
Chung and subsequent authors derived. I.e., such that the resulting
re-expressed Hamiltonian no longer has a pesky residual interaction part
at asymptotic times. (This was also mentioned by J&R above.)

(If you're unable get the J&R book easily in your locality, send me a PM.)

 

[atyy]

In some cases, don't Fourier expansions have physical meaning? I am thinking of musical notes, consisting of separate harmonics.

So, sometimes terms in a series can have actual physical meaning.

Maybe, in QFT, we stumbled across something with physical meaning, because of our need for an approximate solution to interacting fields. Then again, maybe we didn't.

Seems like the jury is still out on the issue, although not actually leaning in favor of virtual particles?

The terms in a Fourier expansion have physical meaning only because the detector we use (the cochlea) can do that decomposition. If there wasn't such a detector, the Fourier expansion wouldn't have any more or less physical meaning than say a Taylor expansion (ie. it's not really a Fourier series and not a Taylor series). So if we can do the calculation in two ways with and without virtual particles and the detector doesn't know the difference, then we can't say which way of doing it is more or less real.

 

[meopemuk]

(If you're unable get the J&R book easily in your locality, send me a PM.)

Unfortunately, even amazon.com does not carry a copy of the 1980 edition of this book for sale. But I can read (though, not download) the whole text at

http://www.scribd.com/doc/45506278/Jauch-rohrlich-The-Theory-of-Photons-and-Electrons-1980

At first sight Appendix S4 looks interesting, but rather short on details. Will do second sight tomorrow.

Eugene.

 

[A. Neumaier]

Jauch & Rohrlich, Supplement S4, p528

What has not been achieved so far is a rigorous derivation of these
results which would include a consistent treatment of the
renormalization terms, a general proof of the unitarity of the new
S-matrix and a nonperturbative proof of the absence of IR divergences.

This has been achieved in the mean time. See, e.g.,
O. Steinmann,
Perturbative quantum electrodynamics and axiomatic field theory,
Springer, Berlin 2000.

 

[rogerl]

The terms in a Fourier expansion have physical meaning only because the detector we use (the cochlea) can do that decomposition. If there wasn't such a detector, the Fourier expansion wouldn't have any more or less physical meaning than say a Taylor expansion (ie. it's not really a Fourier series and not a Taylor series). So if we can do the calculation in two ways with and without virtual particles and the detector doesn't know the difference, then we can't say which way of doing it is more or less real.

You mean the terms in a Fourier expansion is like the multivariate integrals in QFT? In the former case, we have cochlea that can do the decomposition as you mentioned. In the latter case, we don't have detectors. So you are saying that if we can have detectors. There is possibility that virtual particles are as real as music? Sometimes I wonder if what we experience as feelings are simply the virtual particles (especially virtual photons) in our body. I guess we only have virtual photons in our body and not anything else, isn't it? Or do we have the full fledge garden variety virtual particles in our body too?

 

[atyy]

You mean the terms in a Fourier expansion is like the multivariate integrals in QFT? In the former case, we have cochlea that can do the decomposition as you mentioned. In the latter case, we don't have detectors. So you are saying that if we can have detectors. There is possibility that virtual particles are as real as music? Sometimes I wonder if what we experience as feelings are simply the virtual particles (especially virtual photons) in our body. I guess we only have virtual photons in our body and not anything else, isn't it? Or do we have the full fledge garden variety virtual particles in our body too?

In a certain country, people always tip the waiter 15% of the bill.

Some people claim the tip is composed of two virtual tips 5% + 10%.

The virtual tips are almost like real tips except they are never paid to the waiter.

Are the virtual tips "real" in any sense?

 

[Chalnoth]

In a certain country, people always tip the waiter 15% of the bill.

Some people claim the tip is composed of two virtual tips 5% + 10%.

The virtual tips are almost like real tips except they are never paid to the waiter.

Are the virtual tips "real" in any sense?

The difference is that those 5% and 10% components don't have the same properties as other objects we consider to be real.

 

[rogerl]

Guys. If virtual particles were just side effect of the calculation method, how come in the so called Hierarchy Problem of Particle Physics. The virtual particles can seemingly independently affect the main players? See for example:

http://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model

"Hierarchy problem The standard model introduces particle masses through a process known as spontaneous symmetry breaking caused by the Higgs field. Within the standard model, the mass of the Higgs gets some very large quantum corrections due to the presence of virtual particles (mostly virtual top quarks). These corrections are much larger than the actual mass of the Higgs. This means that the bare mass parameter of the Higgs in the standard model must be fine tuned in such a way that almost completely cancels the quantum corrections. This level of fine tuning is deemed unnatural by many theorists."

----------------------

They even have to propose "RS1" where 2 branes occur with 5th dimension in the bulk to explain or solve the Hierarchy Problem. How can mere multivariate integrals seemingly independently and very strongly influence the primary field if these are just side effects?
How come they don't propose Lattice QFT to solve it? Instead they have to take radical measures such as RS1 or even Supersymmetry to tame the Hierarchy Problem?

 

[A. Neumaier]

I guess we only have virtual photons in our body and not anything else, isn't it?

Our body is composed not of virtual photons but of matter fields of various kinds, well described by non-Newtonian hydromechanics and elasticity theory.

 

[A. Neumaier]

? What is different?

Considering a scattering process as a sequence of two means working with the squared S-matrix in place of the S-matrix. But the S-matrix is not idempotent.

But you can't draw this dressed electron as a line in a Feynman diagram.

Of course, one can. One just needs to set up the perturbation theory differently, perturbing around the correct asymptotic description.

_Any_ sort of perturbation theory produces its associated Feynman diagrams. But the properties of the associated virtual particles vary wildly with the scheme chosen. For example, the virtual particles in covariant perturbation theory and those in light-front parturbation theory have nothing in common - except the existence of a graphical way of writing the terms.

 

[atyy]

Guys. If virtual particles were just side effect of the calculation method, how come in the so called Hierarchy Problem of Particle Physics. The virtual particles can seemingly independently affect the main players? See for example:

http://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model

"Hierarchy problem The standard model introduces particle masses through a process known as spontaneous symmetry breaking caused by the Higgs field. Within the standard model, the mass of the Higgs gets some very large quantum corrections due to the presence of virtual particles (mostly virtual top quarks). These corrections are much larger than the actual mass of the Higgs. This means that the bare mass parameter of the Higgs in the standard model must be fine tuned in such a way that almost completely cancels the quantum corrections. This level of fine tuning is deemed unnatural by many theorists."

Back to the restaurant analogy.

There is the menu price.

The menu price receives large "quantum" corrections from the 15% tip.

The 15% tip consists of 5% and 10% virtual tips.

Hence the menu price receives large "quantum" corrections from the virtual tips.

In this restaurant, if your bill comes out to exactly $37.49, you get a 15% discount.

Many customers are observed to pay a final amount close to the menu price of their food.

Thus it seems that their bills must have been exactly $37.49 to almost completely cancel out the quantum corrections from the "virtual tips".

This level of fine tuning of the menu price is deemed unnatural by many theorists.

 

[Chalnoth]

Back to the restaurant analogy.

There is the menu price.

The menu price receives large "quantum" corrections from the 15% tip.

The 15% tip consists of 5% and 10% virtual tips.

Hence the menu price receives large "quantum" corrections from the virtual tips.

In this restaurant, if your bill comes out to exactly $37.49, you get a 15% discount.

Many customers are observed to pay a final amount close to the menu price of their food.

Thus it seems that their bills must have been exactly $37.49 to almost completely cancel out the quantum corrections from the "virtual tips".

This level of fine tuning of the menu price is deemed unnatural by many theorists.

Once again, the restaurant analogy doesn't work because the components bear no relation whatsoever to anything physical.

Virtual particles, on the other hand, have all of the properties of real particles except the relationship between energy and momentum.

 

[atyy]

Once again, the restaurant analogy doesn't work because the components bear no relation whatsoever to anything physical.

Virtual particles, on the other hand, have all of the properties of real particles except the relationship between energy and momentum.

Are virtual particles physical?

 

[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.