Field Quanta

[jswalsh@ix.netcom.com]

I have recently completed reading "Deep Down Things" by Bruce Schumm.
It it Bruce gives an excellent description of how quanta behave
relative how particles of like charge repel each other. However, there
is no description of how particles of opposite charge attract each
other.

Is the a similar explanation of how particles of opposite charge
attrack each other through such quanta?

jswalsh

[Arnold Neumaier]

jswalsh@ix.netcom.com schrieb:
> I have recently completed reading "Deep Down Things" by Bruce Schumm.
> It it Bruce gives an excellent description of how quanta behave
> relative how particles of like charge repel each other. However, there
> is no description of how particles of opposite charge attract each
> other.
>
> Is the a similar explanation of how particles of opposite charge
> attrack each other through such quanta?

It doesn't work. Exchange particles are ''virtual particles''
- as the name says, purely fictitious objects -, introduced solely
to let the complicated multidimensional integrals arising in quantum
field theory (and abbreviated by Feynamn diagrams) look somewhat
tangible. See the entry ''How real are 'virtual particles'?''
in my theoretical physics FAQ at
http://www.mat.univie.ac.at/~neum/physics-faq.txt

Thus any 'explanations' of what virtual particles do is meaningless.
You could as well ask how the person (virtual image) in the mirror
you are looking manages to move its hand when you lift your hand.


Arnold Neumaier

[Oh No]

Thus spake Arnold Neumaier <Arnold.Neumaier@univie.ac.at>
>jswalsh@ix.netcom.com schrieb:
>> I have recently completed reading "Deep Down Things" by Bruce Schumm.
>> It it Bruce gives an excellent description of how quanta behave
>> relative how particles of like charge repel each other. However, there
>> is no description of how particles of opposite charge attract each
>> other.
>> Is the a similar explanation of how particles of opposite charge
>> attrack each other through such quanta?

Yes. The same description works equally well although it is a little
less obvious.

>
>It doesn't work. Exchange particles are ''virtual particles''
>- as the name says, purely fictitious objects -, introduced solely
>to let the complicated multidimensional integrals arising in quantum
>field theory (and abbreviated by Feynamn diagrams) look somewhat
>tangible. See the entry ''How real are 'virtual particles'?''
>in my theoretical physics FAQ at
> http://www.mat.univie.ac.at/~neum/physics-faq.txt
>
>Thus any 'explanations' of what virtual particles do is meaningless.
>You could as well ask how the person (virtual image) in the mirror
>you are looking manages to move its hand when you lift your hand.
>

This is often asserted as though a definite fact, but it is actually
just a point of view, one to which Feynman himself did not subscribe. He
considered that we should not distinguish between real and virtual
particles.



Regards

--
Charles Francis
substitute charles for NotI to email

[Igor Khavkine]

On 2007-02-08, Oh No <NotI@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Arnold Neumaier <Arnold.Neumaier@univie.ac.at>

>>[...] Exchange particles are ''virtual particles''
>>- as the name says, purely fictitious objects -, introduced solely
>>to let the complicated multidimensional integrals arising in quantum
>>field theory (and abbreviated by Feynamn diagrams) look somewhat
>>tangible. See the entry ''How real are 'virtual particles'?''
>>in my theoretical physics FAQ at
>> http://www.mat.univie.ac.at/~neum/physics-faq.txt
>>
>>Thus any 'explanations' of what virtual particles do is meaningless.
>>You could as well ask how the person (virtual image) in the mirror
>>you are looking manages to move its hand when you lift your hand.
>
> This is often asserted as though a definite fact, but it is actually
> just a point of view, one to which Feynman himself did not subscribe. He
> considered that we should not distinguish between real and virtual
> particles.

There are many points of view and yours maybe one of them, Feynman's may
be another, and mine a third. All of these points of view may be equally
valid and allowed to disagree when discussing physics informally.

However, the same can no longer be said when we leave the informal realm
in favor of the quantitative and scientific one. Then, a physicist, that
considers the question "What is a virtual particle?" in earnest, will
not be able to find a definition that satisfies what is usually mean by
both "virtual" and "particle".

The only definition that I know of that most can agree on is: a "virtual
particle" is an internal line on in a Feynman diagram. Since Feynman
diagrams only lives on paper, then so do virtual particles. A
quantitative treatment of these wiggly lines on papar as "particles" is
truly impossible.

Igor

[ebunn@lfa221051.richmond.edu]

In article <1170698617.093486.250580@a34g2000cwb.googlegroups. com>,
<jswalsh@ix.netcom.com> wrote:
>I have recently completed reading "Deep Down Things" by Bruce Schumm.
>It it Bruce gives an excellent description of how quanta behave
>relative how particles of like charge repel each other. However, there
>is no description of how particles of opposite charge attract each
>other.
>
>Is the a similar explanation of how particles of opposite charge
>attrack each other through such quanta?

Try the Usenet Physics FAQ:

http://math.ucr.edu/home/baez/physics/Quantum/virtual_particles.html

-Ted

--
[E-mail me at name@domain.edu, as opposed to name@machine.domain.edu.]

[Igor Khavkine]

On 2007-02-06, jswalsh@ix.netcom.com <jswalsh@ix.netcom.com> wrote:
> I have recently completed reading "Deep Down Things" by Bruce Schumm.
> It it Bruce gives an excellent description of how quanta behave
> relative how particles of like charge repel each other. However, there
> is no description of how particles of opposite charge attract each
> other.
>
> Is the a similar explanation of how particles of opposite charge
> attrack each other through such quanta?

As Arnold Neumaier already pointed out, it is misleading to think of a
"virtual particle" as some kind of tangible particle that is absorbed
and emitted during interactions. There is however a way of picturing a
kind of intermediary force carrier in the kinds of interactions you have
in mind.

The following picture is purely classical. Consider for example the
electromagnetic field interacting with charged particles. The
electromagnetic field is defined throughout space. Think of a taught
sheet or the surface of water as a lower dimensional example. On the
other hand, particles are localized points in space. As these particles
move, they stretch and produce ripples in the electromagnetic field.
Again, think of objects moving on the sheet or on the surface of a pond.
In either case, they produce ripples or other kinds of waves emanating
from the moving objects. These waves move away from the point particles
at a certain characteristic speed (which happens to be the speed of
light in the EM case). If there are two particles present, then each one
will change its motion when it encounters ripples produced by the other.
In effect, you see the two particles interacting, the motion of one
affects the motion of the other. But what's really happening is that
each particle changes its motion only in response to the changes in the
field around it. However, this field carries information (in the form of
traveling ripples and waves) about the motion of other distant
particles. In this sense, the field is seen as a carrier for the
interaction between these particles.

If you know anything about quantum mechanics and especially quantum
mechanics applied to simple systems such as the harmonic oscillator, you
should know that the energy levels of on oscillator are quantiezed. The
EM field behaves very much like a whole bunch of separate oscillators,
one for each frequency. So the quantum states of the EM field (or rather
of each separate frequency) are also quantized. These quanta are called
photons. Just as the motion of classical particles excites various wave
forms of the EM field, the motion of quantum particles excites various
quantum states of the EM fields. These states contain superpositions of
states with different numbers of photons. Each of these states
contributes to the interaction of charged particles with the field, just
as happens with wave forms in the classical case. Again, this induces an
effective interaction between charged particles mediated by the EM
field.

In a certain (well defined, quantitative) way, the interactions between
charged particles can be represented by drawing Feynman diagrams on a
piece of paper. These diagrams may have different numbers of internal
wavy lines (photon lines). The number of lines corresponds to the number
of photons in a quantum state of the EM field contributing to the
interaction. All such states contribute. It's just the ones with the
fewest number of photons contribute the most. Those are the diagrams
you'd see most often. So, the discrete number of internal photon lines
tells us that we are dealing with a quantized EM field. On the other
hand, the effect of the EM field as a force carrier can be pictures
precisely as in the classical case. A certain wave form produced by one
particle influences the motion of another one.

Hope this helps.

Igor

[Arnold Neumaier]

Oh No schrieb:
> Thus spake Arnold Neumaier <Arnold.Neumaier@univie.ac.at>
>> jswalsh@ix.netcom.com schrieb:
>>> I have recently completed reading "Deep Down Things" by Bruce Schumm.
>>> It it Bruce gives an excellent description of how quanta behave
>>> relative how particles of like charge repel each other. However, there
>>> is no description of how particles of opposite charge attract each
>>> other.
>>> Is the a similar explanation of how particles of opposite charge
>>> attrack each other through such quanta?
>
> Yes. The same description works equally well although it is a little
> less obvious.
>
>> It doesn't work. Exchange particles are ''virtual particles''
>> - as the name says, purely fictitious objects -, introduced solely
>> to let the complicated multidimensional integrals arising in quantum
>> field theory (and abbreviated by Feynamn diagrams) look somewhat
>> tangible. See the entry ''How real are 'virtual particles'?''
>> in my theoretical physics FAQ at
>> http://www.mat.univie.ac.at/~neum/physics-faq.txt
>>
>> Thus any 'explanations' of what virtual particles do is meaningless.
>> You could as well ask how the person (virtual image) in the mirror
>> you are looking manages to move its hand when you lift your hand.
>>
>
> This is often asserted as though a definite fact, but it is actually
> just a point of view,

It is the only correct point of view. There is no way to observe
virtual particles, and the name was chosen to reflect this.

Observed particles are always onshell, hence massless for photons,
whereas it is an easy exercise that the virtual photon mediating
electromagnetic interaction of two electrons in the tree approximation
is never onshell.

> one to which Feynman himself did not subscribe. He
> considered that we should not distinguish between real and virtual
> particles.

Please give a reference, not from his writing for laymen, where he often
simplifies things beynd what would be scientifically acceptable, but a
reference in a journal or his textbook.

Arnold Neumaier

[Oh No]

Thus spake Igor Khavkine <igor.kh@gmail.com>
>On 2007-02-08, Oh No <NotI@charlesfrancis.wanadoo.co.uk> wrote:
>> Thus spake Arnold Neumaier <Arnold.Neumaier@univie.ac.at>
>
>>>[...] Exchange particles are ''virtual particles''
>>>- as the name says, purely fictitious objects -, introduced solely
>>>to let the complicated multidimensional integrals arising in quantum
>>>field theory (and abbreviated by Feynamn diagrams) look somewhat
>>>tangible. See the entry ''How real are 'virtual particles'?''
>>>in my theoretical physics FAQ at
>>> http://www.mat.univie.ac.at/~neum/physics-faq.txt
>>>
>>>Thus any 'explanations' of what virtual particles do is meaningless.
>>>You could as well ask how the person (virtual image) in the mirror
>>>you are looking manages to move its hand when you lift your hand.
>>
>> This is often asserted as though a definite fact, but it is actually
>> just a point of view, one to which Feynman himself did not subscribe. He
>> considered that we should not distinguish between real and virtual
>> particles.
>
>There are many points of view and yours maybe one of them, Feynman's may
>be another, and mine a third. All of these points of view may be equally
>valid and allowed to disagree when discussing physics informally.

Indeed. Ultimately a particular view may be shown to be correct, but
that is not the situation at the moment. I merely caution against
adopting a particular view as though it is established fact.

>However, the same can no longer be said when we leave the informal realm
>in favor of the quantitative and scientific one. Then, a physicist, that
>considers the question "What is a virtual particle?" in earnest, will
>not be able to find a definition that satisfies what is usually mean by
>both "virtual" and "particle".

Finding answers to such questions is what I would regard as the object
of scientific research. One should not be too restrictive in this kind
of research. It may well be that what is usually meant by the word
"particle" does not correspond to anything in nature. For example, I
think that many people envisage a particle as a classical object which
has a position in space. But we do also discuss particles as quantum
objects. The usual definition of particle must be revised, but it does
not follow from that that no definition is possible.

>The only definition that I know of that most can agree on is: a "virtual
>particle" is an internal line on in a Feynman diagram. Since Feynman
>diagrams only lives on paper, then so do virtual particles. A
>quantitative treatment of these wiggly lines on papar as "particles" is
>truly impossible.

There I must disagree with you. One should not prejudge the results of
research. If correct definitions are found for terms like "particle" and
the ultraviolet divergence is avoided through the proper use of Wick's
theorem (see Scharf Finite QED), if in addition the Landau Pole is
avoided by a suitable small scale modification to QED (there is more
than one possible, but I use a particularly simple one), and if
critically and most importantly one pays proper heed to Von Neumann,
that quantum superposition is a property of a many valued logic, i.e. it
is a part of a language which one should learn to understand, just as
one needs to learn any language in order to understand what is said in
that language, then it is indeed possible to interpret the wiggly line
as an ontological entity, which one may call a particle, and there is no
need to distinguish this by use of the word virtual. Moreover, Feynman
rules, do give a quantitative treatment. The paper in a Feynman diagram
is another matter. That really does have no physical meaning.

Regards

--
Charles Francis
substitute charles for NotI to email

[Oh No]

Thus spake Arnold Neumaier <Arnold.Neumaier@univie.ac.at>
>Oh No schrieb:

>>> Thus any 'explanations' of what virtual particles do is meaningless.
>>> You could as well ask how the person (virtual image) in the mirror
>>> you are looking manages to move its hand when you lift your hand.
>>>
>>
>> This is often asserted as though a definite fact, but it is actually
>> just a point of view,
>
>It is the only correct point of view.

Please don't substitute dogmatism for logic in scientific argument.

>There is no way to observe
>virtual particles, and the name was chosen to reflect this.

At best this is semantically tautologous and of little worth. At one
time there was no way to observe the far side of the moon. Is it any
more "real" now, simply because we can send a spacecraft to view it? At
worst, it is simply wrong. We can observe the effect of "virtual"
particles, so to suggest they are not real seems a little unreasonable.

>
>Observed particles are always onshell, hence massless for photons,
>whereas it is an easy exercise that the virtual photon mediating
>electromagnetic interaction of two electrons in the tree approximation
>is never onshell.

Again, that is a matter of semantics and definitional truism. Energy is
an empirical quantity and as such is strictly only meaningful in
measurement. Since it is conserved in measurement, it is possible to
define another quantity with the same value at all times. If you use
that quantity for your definition of mass, then of course you find
particles off mass shell. It is equally possible to define mass so that
particles are always on mass shell, in which case you either sacrifice
conservation of energy in interactions, or you sacrifice vector
properties between measurements. By your own argument, since it is
obviously not possible to observe between measurements, your definition
of energy between measurement is "virtual" and not open to empirical
test.

>> one to which Feynman himself did not subscribe. He
>> considered that we should not distinguish between real and virtual
>> particles.
>
>Please give a reference, not from his writing for laymen, where he often
>simplifies things beynd what would be scientifically acceptable, but a
>reference in a journal or his textbook.

You denigrate Feynman. He specifically states that he means his account
in QED to be scientifically correct. Are you calling him a liar for
saying that he sees no reason to distinguish? You may also refer to
Schweber, qed and the men who made it for confirmation that this was
Feynman's view.



Regards

--
Charles Francis
substitute charles for NotI to email

[Arnold Neumaier]

Oh No schrieb:
> Thus spake Arnold Neumaier <Arnold.Neumaier@univie.ac.at>
>> Oh No schrieb:
>
>>>> Thus any 'explanations' of what virtual particles do is meaningless.
>>>> You could as well ask how the person (virtual image) in the mirror
>>>> you are looking manages to move its hand when you lift your hand.
>>>>
>>> This is often asserted as though a definite fact, but it is actually
>>> just a point of view,
>> It is the only correct point of view.
>
> Please don't substitute dogmatism for logic in scientific argument.

I don't write only for you but for all readers of s.p.r.,
who can make their own judgment about the quality of my statements.
Calling my statement dogmatism doesn't diminish its truth.

I gave a scientific argument, which you apparently did not recognize,
and much more can be found in my theoretical physics FAQ at
http://www.mat.univie.ac.at/~neum/physics-faq.txt


>> There is no way to observe
>> virtual particles, and the name was chosen to reflect this.
>
> At best this is semantically tautologous and of little worth.

It reflects the opinion of those who coined the notion.


>> Observed particles are always onshell, hence massless for photons,
>> whereas it is an easy exercise that the virtual photon mediating
>> electromagnetic interaction of two electrons in the tree approximation
>> is never onshell.
>
> Again, that is a matter of semantics and definitional truism.

Yes, it is a matter of semantics (= meaning), which is on my side.
You can bend the words by redefining everything to your taste.
I don't have this choice since I want to represent objective knowledge,
so I use the words according to their best use.


> Energy is an empirical quantity and as such is strictly only meaningful in
> measurement.

Your usage of the word is completely off the mark.
Energy is also a theoretical quantity, and as such is meaningful
and of highest importance in most of theoretical physics.

Virtual particles, on the other hand, are _only_ a theoretical
quantity, without any empirical content.


>>> one to which Feynman himself did not subscribe. He
>>> considered that we should not distinguish between real and virtual
>>> particles.
>> Please give a reference, not from his writing for laymen, where he often
>> simplifies things beynd what would be scientifically acceptable, but a
>> reference in a journal or his textbook.
>
> You denigrate Feynman.

Feynman was a great lecturer and knew how to present science to laymen.
But nobody - not even Feynman - can do this without watering down the
scientific contents. Physics is to a large extent a formal science
just because the formality is necessary to have precise, scientifically
impeccable concepts. When talking to laymen, 'scientifically correct'
means nothing more than 'scientifically correct within the limits
possible in lectures for laymen'.


> He specifically states that he means his account
> in QED to be scientifically correct. Are you calling him a liar for
> saying that he sees no reason to distinguish? You may also refer to
> Schweber, qed and the men who made it for confirmation that this was
> Feynman's view.

If you are correct, you'd find it easy to support your view also from
his journal publications or his textbook. There he talks to collegues
and does not need to use simplified, inaccurate language aimed at
laymen.


Arnold Neumaier

[Oh No]

Thus spake Arnold Neumaier <Arnold.Neumaier@univie.ac.at>
>Oh No schrieb:
>> Thus spake Arnold Neumaier <Arnold.Neumaier@univie.ac.at>
>>> Oh No schrieb:
>>
>>>>> Thus any 'explanations' of what virtual particles do is
>>>>>meaningless.
>>>>> You could as well ask how the person (virtual image) in the mirror
>>>>> you are looking manages to move its hand when you lift your hand.
>>>>>
>>>> This is often asserted as though a definite fact, but it is actually
>>>> just a point of view,
>>> It is the only correct point of view.
>> Please don't substitute dogmatism for logic in scientific argument.
>
>I don't write only for you but for all readers of s.p.r.,
>who can make their own judgment about the quality of my statements.
>Calling my statement dogmatism doesn't diminish its truth.
>
>I gave a scientific argument, which you apparently did not recognize,

I recognised it and refuted it. Did you not recognise that?

>and much more can be found in my theoretical physics FAQ at
> http://www.mat.univie.ac.at/~neum/physics-faq.txt
>
>
>>> There is no way to observe
>>> virtual particles, and the name was chosen to reflect this.
>> At best this is semantically tautologous and of little worth.
>
>It reflects the opinion of those who coined the notion.

That is fine. An opinion, which is as I said.

>>> Observed particles are always onshell, hence massless for photons,
>>> whereas it is an easy exercise that the virtual photon mediating
>>> electromagnetic interaction of two electrons in the tree approximation
>>> is never onshell.
>> Again, that is a matter of semantics and definitional truism.
>
>Yes, it is a matter of semantics (= meaning), which is on my side.
>You can bend the words by redefining everything to your taste.
>I don't have this choice since I want to represent objective knowledge,
>so I use the words according to their best use.

I just pointed out that what you had said was only true by definitional
truism. That is not descriptive of objective knowledge.

>> Energy is an empirical quantity and as such is strictly only meaningful in
>> measurement.
>
>Your usage of the word is completely off the mark.
>Energy is also a theoretical quantity, and as such is meaningful
>and of highest importance in most of theoretical physics.

It's importance is the value it has in measurement.

>Virtual particles, on the other hand, are _only_ a theoretical
>quantity, without any empirical content.

So what you are saying is that a number is real real even between
measurements (you disagree with Dirac and Von Neumann btw), whereas
matter is not? How very Pythogorean.

Regards

--
Charles Francis
substitute charles for NotI to email

[Thomas Smid]

On 6 Feb, 23:32, Arnold Neumaier <Arnold.Neuma...@univie.ac.at> wrote:

> Thus any 'explanations' of what virtual particles do is meaningless.
> You could as well ask how the person (virtual image) in the mirror
> you are looking manages to move its hand when you lift your hand.

I don't think this analogon is quite appropriate: the crucial
difference is that the person in the mirror is never going to hit you
i.e. he doesn't have any physical impact whatsoever on the world. The
virtual particle in contrast is supposed to be associated with a very
real and measurable physical force. So in this sense, it appears
somewhat inconsistent to deny the reality of virtual particles.

Anyway, whether real or virtual, there is in my view a conceptual
problem with the idea of field quanta transmitting fundamental forces:
with this model, a fundamental force is effectively reduced to a
macroscopic force due to the interaction of the intermediating field
quanta with the particles, rather than an interaction between the
particles themselves. Not only this, but the concept doesn't actually
achieve what it is supposed to achieve (namely to eliminate the
concept of an action-at-a-distance) because now there is instead to
explain by means of which (very real) force the field quanta transmit
their momentum to the particle. In this respect, the whole concept
seems to be somewhat circular and thus inconsistent.

Thomas

[Igor Khavkine]

On 2007-02-14, Thomas Smid <thomas.smid@gmail.com> wrote:
> On 6 Feb, 23:32, Arnold Neumaier <Arnold.Neuma...@univie.ac.at> wrote:
>
>> Thus any 'explanations' of what virtual particles do is meaningless.
>> You could as well ask how the person (virtual image) in the mirror
>> you are looking manages to move its hand when you lift your hand.
>
> I don't think this analogon is quite appropriate: the crucial
> difference is that the person in the mirror is never going to hit you
> i.e. he doesn't have any physical impact whatsoever on the world. The
> virtual particle in contrast is supposed to be associated with a very
> real and measurable physical force. So in this sense, it appears
> somewhat inconsistent to deny the reality of virtual particles.

The very real and measurable physical force can be quite satisfactorily
described without reference to virtual particles. Hence, whether you
consider virtual particles real has no bearing on the description on
measurements.

> Anyway, whether real or virtual, there is in my view a conceptual
> problem with the idea of field quanta transmitting fundamental forces:
> with this model, a fundamental force is effectively reduced to a
> macroscopic force due to the interaction of the intermediating field
> quanta with the particles, rather than an interaction between the
> particles themselves. Not only this, but the concept doesn't actually
> achieve what it is supposed to achieve (namely to eliminate the
> concept of an action-at-a-distance) because now there is instead to
> explain by means of which (very real) force the field quanta transmit
> their momentum to the particle. In this respect, the whole concept
> seems to be somewhat circular and thus inconsistent.

There's a simple solution to your conceptual problem: do not take the
idea of virtual particles as force carriers too seriously. What you
should take seriously is the fact that particles do not interact
directly (which you call action-at-a-distance), but rather only ineract
locally with a field. In turn (Newton's third law), the field interacts
with the particles, thus carrying information about their motion
(information which travels no faster than light). That's how particles
sense each other. This picture holds both classically and quantum
mechanically, as I explained in a parallel post in this thread.

The partition of momentum between the field and the particles and total
momentum's conservation is a simple consequence of translational
invariance of the theory (Noether's theorem). Since interactions happen
locally, the momentum transfer also happens locally. Again, no
action-at-a-distance necessary and no inconsistency.

Igor

[Igor Khavkine]

On 2007-02-09, Oh No <NotI@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Igor Khavkine <igor.kh@gmail.com>

>>There are many points of view and yours maybe one of them, Feynman's may
>>be another, and mine a third. All of these points of view may be equally
>>valid and allowed to disagree when discussing physics informally.
>
> Indeed. Ultimately a particular view may be shown to be correct, but
> that is not the situation at the moment. I merely caution against
> adopting a particular view as though it is established fact.

Facts and correctness do not mix with informality. You should apply
scruitny to a formal description of QFT, not an informal description of
it.

>>However, the same can no longer be said when we leave the informal realm
>>in favor of the quantitative and scientific one. Then, a physicist, that
>>considers the question "What is a virtual particle?" in earnest, will
>>not be able to find a definition that satisfies what is usually mean by
>>both "virtual" and "particle".
>
> Finding answers to such questions is what I would regard as the object
> of scientific research. One should not be too restrictive in this kind
> of research. It may well be that what is usually meant by the word
> "particle" does not correspond to anything in nature. For example, I
> think that many people envisage a particle as a classical object which
> has a position in space. But we do also discuss particles as quantum
> objects. The usual definition of particle must be revised, but it does
> not follow from that that no definition is possible.

This may be subject of research, but not in physics. In physics, there
already is a definition of particle, both classically and quantum
mechanically. Thus, the statement that a "virtual particle" is not a
particle is formal, true, and has already been given in precise language
in this discussion. You may invent your own definition, but then you're no
longer speaking the same language as other physicists.

> [...] The paper in a Feynman diagram
> is another matter. That really does have no physical meaning.

Good, how about the ink on the paper? One more step and you're almost
there...

Igor

[basically yes]

"Igor Khavkine" <igor.kh@gmail.com> a écrit dans le message de news:
slrnet8sqh.78l.igor.kh@corum.multiverse.ca

> The very real and measurable physical force can be quite satisfactorily
> described without reference to virtual particles.

But the reference to a field is necessary, which amounts to the same.
Actually, a particle is understood as an excitation of a field. Each time
there is a field, a real excitation can exist, which is the case of the
interaction field. Therefore, the virtual particle has some reality. It is
virtual in the sense that the excitation doesn't obey the free field
equation. In particular, the Maxwell operator applied to the field doesn't
yields 0 (for a photon or gluon) as is expected for a massless particle
on-shell. The word "virtual" means "too short lived to be observed", not
anything magic, metaphysical, or "Feynmanian". Feynman's treatment doesn't
add anything new to the physical model.

> Hence, whether you
> consider virtual particles real has no bearing on the description on
> measurements.

Indeed, since it is a mere word. By the same token, that we consider real
particles virtual has no bearing on the description. The issue was, what
(physically) differentiates a real (free) particle from a virtual (mediating
interaction) particle, which I think I have answered, without resorting to
useless abstruse considerations.

[basically yes]

"Igor Khavkine" <igor.kh@gmail.com> a écrit dans le message de news:
slrnet921p.7aq.igor.kh@corum.multiverse.ca

> This may be subject of research, but not in physics. In physics, there
> already is a definition of particle, both classically and quantum
> mechanically.

If a theory is needed in order to define a particle (CM or QM), that means a
particle isn't defined *physically*. Physics isn't textbook physics. This
thread is about interaction, which makes sense even outside of a theory.

> Thus, the statement that a "virtual particle" is not a
> particle is formal, true, and has already been given in precise language
> in this discussion.

Saying that a virtual particle is off-shell means that it isn't a particle?
How can it be off-shell then, if it don't even exist? If a virtual particle
is only an amplitude, so is also a real particle. I see no reason why a
*virtual* particle shouldn't be a particle, how formal and true all that may
be.

> You may invent your own definition, but then you're no longer speaking
> the same language as other physicists.

Do I understand correctly that if the theory of virtual particle should be
falsified by experiment, Nature wouldn't be speaking the same language as
physicists?

[Igor Khavkine]

On 2007-02-16, basically yes <canceljobs@thesapjobboard.com> wrote:
> "Igor Khavkine" <igor.kh@gmail.com> a écrit dans le message de news:
> slrnet8sqh.78l.igor.kh@corum.multiverse.ca
>
>> The very real and measurable physical force can be quite satisfactorily
>> described without reference to virtual particles.
>
> But the reference to a field is necessary, which amounts to the same.
> Actually, a particle is understood as an excitation of a field. Each time
> there is a field, a real excitation can exist, which is the case of the
> interaction field. Therefore, the virtual particle has some reality. It is
> virtual in the sense that the excitation doesn't obey the free field
> equation. In particular, the Maxwell operator applied to the field doesn't
> yields 0 (for a photon or gluon) as is expected for a massless particle
> on-shell. The word "virtual" means "too short lived to be observed", not
> anything magic, metaphysical, or "Feynmanian". Feynman's treatment doesn't
> add anything new to the physical model.

Can you make these statements precise? I'd like to see this "field" that
doesn't yield 0 under the Maxwell operator. Is it an operator? a state
in the Hilbert space? some function on spacetime? An explicit example
would be really nice.

I've made essentially the same request in my parallel reply. Feel free
to answer in either subthread.

Igor

[Thomas Smid]

On 15 Feb, 14:36, Igor Khavkine <igor...@gmail.com> wrote:
> On 2007-02-14, Thomas Smid <thomas.s...@gmail.com> wrote:
>
> > On 6 Feb, 23:32, Arnold Neumaier <Arnold.Neuma...@univie.ac.at> wrote:
>
> >> Thus any 'explanations' of what virtual particles do is meaningless.
> >> You could as well ask how the person (virtual image) in the mirror
> >> you are looking manages to move its hand when you lift your hand.
>
> > I don't think this analogon is quite appropriate: the crucial
> > difference is that the person in the mirror is never going to hit you
> > i.e. he doesn't have any physical impact whatsoever on the world. The
> > virtual particle in contrast is supposed to be associated with a very
> > real and measurable physical force. So in this sense, it appears
> > somewhat inconsistent to deny the reality of virtual particles.
>
> The very real and measurable physical force can be quite satisfactorily
> described without reference to virtual particles. Hence, whether you
> consider virtual particles real has no bearing on the description on
> measurements.

I was not suggesting to consider virtual particles as real, as this
would be logical contradiction in terms. On the other hand, as
indicated above, keeping virtual particles virtual would mean that one
has a real effect caused by a non-real cause, which I definitely would
not consider a satisfactory situation either. Neither is it in my
opinion acceptable to claim that the cause for this force would only
live on paper in form of some symbols. What would we do without paper,
or if nobody would be there to write down the corresponding symbols?
Would the associated force then cease to exist?
I can't help but think that all these 'explanations' merely try to
verbally cloak the fact that the whole concept is conceptually
inconsistent (in the same sense as some people may claim false
statements to be 'virtually true').


>
> > Anyway, whether real or virtual, there is in my view a conceptual
> > problem with the idea of field quanta transmitting fundamental forces:
> > with this model, a fundamental force is effectively reduced to a
> > macroscopic force due to the interaction of the intermediating field
> > quanta with the particles, rather than an interaction between the
> > particles themselves. Not only this, but the concept doesn't actually
> > achieve what it is supposed to achieve (namely to eliminate the
> > concept of an action-at-a-distance) because now there is instead to
> > explain by means of which (very real) force the field quanta transmit
> > their momentum to the particle. In this respect, the whole concept
> > seems to be somewhat circular and thus inconsistent.
>
> There's a simple solution to your conceptual problem: do not take the
> idea of virtual particles as force carriers too seriously. What you
> should take seriously is the fact that particles do not interact
> directly (which you call action-at-a-distance), but rather only ineract
> locally with a field. In turn (Newton's third law), the field interacts
> with the particles, thus carrying information about their motion
> (information which travels no faster than light). That's how particles
> sense each other. This picture holds both classically and quantum
> mechanically, as I explained in a parallel post in this thread.

Well, the point is that this picture is actually inconsistent with
Newton's third law if the interacting particles are moving relatively
to each other: if one chooses for instance the reference frame such
that one particle is resting, then the field of the latter would be
stationary but that of the other would be moving, so the force exerted
by the resting on the moving particle would have to be calculated
unretarded (i.e. according to the momentary distance d), but the force
exerted by the moving on the resting particle would correspond to the
'retarded' distance d*(1-v/c) (assuming the particles are moving
apart) (see my web page http://www.physicsmyths.org.uk/retard.htm for
a derivation of this), i.e. Newton's third law would not apply
anymore. This is obviously not acceptable as it would mean that the
total momentum of a closed system would not be constant (which means
for instance a perpetuum mobile would be possible). And of course the
fact that the force would depend on the inertial frame would be
conceptually inconsistent with the notion of 'force' in the first
place.


Thomas

[Igor Khavkine]

On 2007-02-18, Thomas Smid <thomas.smid@gmail.com> wrote:
> On 15 Feb, 14:36, Igor Khavkine wrote:

>> The very real and measurable physical force can be quite satisfactorily
>> described without reference to virtual particles. Hence, whether you
>> consider virtual particles real has no bearing on the description on
>> measurements.
>
> I was not suggesting to consider virtual particles as real, as this
> would be logical contradiction in terms. On the other hand, as
> indicated above, keeping virtual particles virtual would mean that one
> has a real effect caused by a non-real cause, which I definitely would
> not consider a satisfactory situation either.

As I was trying to say in my previous post, there is no real effect
associated to virtual particles. They are a metaphor introduced to as a
layman's explanation of QFT calculations. So, keeping them "virtual",
as you say, should be entirely satisfactory, unless you are *only*
interested in the layman's explanation.

> Neither is it in my
> opinion acceptable to claim that the cause for this force would only
> live on paper in form of some symbols. What would we do without paper,
> or if nobody would be there to write down the corresponding symbols?
> Would the associated force then cease to exist?

The point I'm trying to get across is precisely the opposite.
Interactions, say electromagnetic ones, cannot depend on the fact that
we use paper to write down our calculations of them. So, they can't
depend on the symbols that we write down on them either.

> I can't help but think that all these 'explanations' merely try to
> verbally cloak the fact that the whole concept is conceptually
> inconsistent (in the same sense as some people may claim false
> statements to be 'virtually true').

So far, you've only supported your claim of inconsistency by pointing
out that some metaphors used to explain QFT to a general audience are
not terribly clear or precise. That's not terribly surprising, either,
since it is very hard to present a simple explanation while keeping all
the details that are necessary for consistency. If you look at QFT in
technical detail, then "the whole concept" is quite consistent.

If you have looked at QFT at a technical level, but are still confused
by parts of it, now is your opportunity to ask questions to clear up the
confusion.

>> There's a simple solution to your conceptual problem: do not take the
>> idea of virtual particles as force carriers too seriously. What you
>> should take seriously is the fact that particles do not interact
>> directly (which you call action-at-a-distance), but rather only ineract
>> locally with a field. In turn (Newton's third law), the field interacts
>> with the particles, thus carrying information about their motion
>> (information which travels no faster than light). That's how particles
>> sense each other. This picture holds both classically and quantum
>> mechanically, as I explained in a parallel post in this thread.
>
> Well, the point is that this picture is actually inconsistent with
> Newton's third law if the interacting particles are moving relatively
> to each other: if one chooses for instance the reference frame such
> that one particle is resting, then the field of the latter would be
> stationary but that of the other would be moving, so the force exerted
> by the resting on the moving particle would have to be calculated
> unretarded (i.e. according to the momentary distance d), but the force
> exerted by the moving on the resting particle would correspond to the
> 'retarded' distance d*(1-v/c) (assuming the particles are moving
> apart) (see my web page http://www.physicsmyths.org.uk/retard.htm for
> a derivation of this), i.e. Newton's third law would not apply
> anymore. This is obviously not acceptable as it would mean that the
> total momentum of a closed system would not be constant (which means
> for instance a perpetuum mobile would be possible). And of course the
> fact that the force would depend on the inertial frame would be
> conceptually inconsistent with the notion of 'force' in the first
> place.

The "derivation" on your website is wrong. It assumes that particles
interact with each other directly through some sort of
action-at-a-distance potential. As you point out, "momentary distance"
is frame dependent, which means that it has no place in a relativistic
theory. And, it doesn't. Each particle only interacts with the field it
sees around itself. The field then interacts, again only locally, with
the particles. The dynamical equations for the field ensure that
information about the motion of each particle is propagated to all other
ones. A more in depth discussion of the role of a field in carrying
information about the motion of a particle interacting with it can be
found in the recent thread:

news:1167672276.632364.284210@a3g2000cwd.googlegro ups.com
http://groups.google.ca/group/sci.physics.research/browse_frm/thread/dc09192e363ded3f

The thread contains a link to a Java applet visually demonstrating how
the field carries this information.

There is only one field (with dynamical equations of its own), not a
field associated with each particle. The only time when we can consider
the total field composed of a superposition of potentials associated to
individual particles is when the field's equations of motion are linear
(e.g. electromagnetism). This is already not the case for any nonlinear
field theory (phi^4, Yang-Mills, gravity, etc.). Even in the linear
case, the superposition picture is not complete since it does not
account for all possible forms of radation (say, radiation that comes in
from infinity, as opposed to radiation that's produced by accelerated
charges).

Finally, Newton's third law does hold and remarkably well at that.
However, it doesn't hold between particles directly. Rather it holds
for the field-particle pair. In particle mechanics, Newton's third law
states that if system A exerts a force on system B, then system B exerts
an equal and opposite force on system A.

Assuming that the dynamical equations that govern systems A and B come
from a variational principle (a Lagrangiam formulation), this law is a
simple consequence. Namely, from the equations of motion of system A, we
can find its Lagrangian, which contains a term describing its
interaction with system B, call this the A-B term. The same can be done
if the roles of A and B are interchanged, and the B-A term is obtained.
However, since the equations of motion of A and B come jointly from the
same Lagrangian, then the A-B and B-A terms are one and the same. In
this form, Newton's third law can be generalized as follows: if we know
how system A acts on system B, then we know how system B acts on A. Here
A or B are no longer restricted to particle systems, they could also
represent fields.

Consider a particle that feels a force proportional to the gradient of a
field. Then the above exercise tells us that the same particle will act
as a point source for the field, with the previous constant of
proportionality now representing its charge.

Incidentally, Newton's second law is instrumental in showing
conservation of total linear momentum. The above discussion demonstrates
that in a field-particle system, momentum is only transfered locally
from field to particle and vice versa.

Igor

[Arnold Neumaier]

Thomas Smid schrieb:
> On 6 Feb, 23:32, Arnold Neumaier <Arnold.Neuma...@univie.ac.at> wrote:
>
>> Thus any 'explanations' of what virtual particles do is meaningless.
>> You could as well ask how the person (virtual image) in the mirror
>> you are looking manages to move its hand when you lift your hand.
>
> I don't think this analogon is quite appropriate: the crucial
> difference is that the person in the mirror is never going to hit you
> i.e. he doesn't have any physical impact whatsoever on the world. The
> virtual particle in contrast is supposed to be associated with a very
> real and measurable physical force. So in this sense, it appears
> somewhat inconsistent to deny the reality of virtual particles.

No. The force is the expectation of a force operator, and has nothing to
do with virtual particles, except very indirectly. About as much as the
terms in a power series for sin x have to do with the resulting angle...
For details of this analogy, see the entry ''How real are 'virtual
particles'?'' in my theoretical physics FAQ at
http://www.mat.univie.ac.at/~neum/physics-faq.txt
One should not mix up some calculational tool with the concept for whose
computation it is used.

Arnold Neumaier

[Oh No]

Thus spake Igor Khavkine <igor.kh@gmail.com>
>On 2007-02-09, Oh No <NotI@charlesfrancis.wanadoo.co.uk> wrote:
>> Thus spake Igor Khavkine <igor.kh@gmail.com>
>
>>>There are many points of view and yours maybe one of them, Feynman's may
>>>be another, and mine a third. All of these points of view may be equally
>>>valid and allowed to disagree when discussing physics informally.
>>
>> Indeed. Ultimately a particular view may be shown to be correct, but
>> that is not the situation at the moment. I merely caution against
>> adopting a particular view as though it is established fact.
>
>Facts and correctness do not mix with informality. You should apply
>scruitny to a formal description of QFT, not an informal description of
>it.

Indeed. That is why I have given a formal description of qed in

gr-qc/0605127
A Treatment of Quantum Electrodynamics as a Model of Interactions
between Sizeless Particles in Relational Quantum Gravity

I admit that, although historically I did this first, it did not hold up
as a truly rigorous treatment without first giving a formal treatment of
quantum theory from first principles. This has been given in

gr-qc/0508077
A Relational Quantum Theory Incorporating Gravity

which I have just updated, after improving a number of treatments, in
particular I have completed a formal derivation of the affine connection
in the classical limit, and clarified the proof of Schwarzschild (which
is used to show the EFE, not the other way about).

>>>However, the same can no longer be said when we leave the informal realm
>>>in favor of the quantitative and scientific one. Then, a physicist, that
>>>considers the question "What is a virtual particle?" in earnest, will
>>>not be able to find a definition that satisfies what is usually mean by
>>>both "virtual" and "particle".
>>
>> Finding answers to such questions is what I would regard as the object
>> of scientific research. One should not be too restrictive in this kind
>> of research. It may well be that what is usually meant by the word
>> "particle" does not correspond to anything in nature. For example, I
>> think that many people envisage a particle as a classical object which
>> has a position in space. But we do also discuss particles as quantum
>> objects. The usual definition of particle must be revised, but it does
>> not follow from that that no definition is possible.
>
>This may be subject of research, but not in physics. In physics, there
>already is a definition of particle, both classically and quantum
>mechanically.

That is not possible, since it would require a definition of reality,
and there isn't one and I doubt there can be. We may assume reality, but
we may not define it. There may be a formal definition of a mathematical
abstraction called a particle. That is not physics, it is mathematics.
Physics studies what the particle actually is, not simply what proceeds
from definitions which may or may not well represent it.

>Thus, the statement that a "virtual particle" is not a
>particle is formal, true, and has already been given in precise language
>in this discussion.

I have never seen such a definition, and certainly not within this
discussion - oh, unless you mean the one about it being off mass shell.
I accept that, but I have pointed out that it is a misleading
definition. There is another one, that there is no probability amplitude
for the observation of a virtual particle. But that is misleading too.
Just because a particle cannot be observed, it does not follow that it
is not real.

>You may invent your own definition, but then you're no
>longer speaking the same language as other physicists.

I would like to speak a language which describes nature. That is what
physics is, or should be, about. Then the definitions should be
determined by nature, not by physicists. Step one is understanding what
Von Neumann was saying about Hilbert Space being a formal language. That
is the language we must learn to speak if we are going to understand
physics. As far as I can tell, physicists, by and large, ignore Von
Neumann, in which case they will not speak a language in which physics
can be understood. In that case, you are right, I will not be speaking
the same language as them.
>
>> [...] The paper in a Feynman diagram
>> is another matter. That really does have no physical meaning.
>
>Good, how about the ink on the paper?

:-)

>One more step and you're almost
>there...

No, you don't get it. I already know what physicists say about
particles, fields, and Feynman diagrams, and have done for approaching
thirty years. While there is a realist interpretation in which
fundamental entities may be described as particles, and in which space-
time is not fundamental, there is no such fundamental realist
interpretation of fields.

Regards

--
Charles Francis
substitute charles for NotI to email

[Igor Khavkine]

On Feb 16, 5:19 pm, basically yes <cancelj...@thesapjobboard.com>
wrote:
> "Igor Khavkine" <igor...@gmail.com> a =E9crit dans le message de news:
> slrnet921p.7aq.igor...@corum.multiverse.ca

> If a theory is needed in order to define a particle (CM or QM), that mean=
s a
> particle isn't defined *physically*. Physics isn't textbook physics. Th=
is
> thread is about interaction, which makes sense even outside of a theory.

Since virtual particles are by definition not measurable, then they
are
definitely not defined *physically*. What is normally understood by a
particle is necessarily tied to measurements and hence physical.

> > Thus, the statement that a "virtual particle" is not a
> > particle is formal, true, and has already been given in precise language
> > in this discussion.
>
> Saying that a virtual particle is off-shell means that it isn't a particl=
e?
> How can it be off-shell then, if it don't even exist? If a virtual parti=
cle
> is only an amplitude, so is also a real particle. I see no reason why a
> *virtual* particle shouldn't be a particle, how formal and true all that =
may
> be.

Then, please, take your quantum theory of choice, maybe QED or maybe
just single particle QM, and construct a state (that's an element of
the theory's Hilbert space of states) representing a "virtual
particle".
Just to for definiteness, please use the Heisenberg picture for states
and operators (if you can't, please explain why). If you wish, I can
do
the same for a particle and we can compare.

> Do I understand correctly that if the theory of virtual particle should be
> falsified by experiment, Nature wouldn't be speaking the same language as
> physicists?

As far as I know, nature doesn't speak any language, physicists do. So
I can't make anything of that part of your question. But since the
concept of virtual particles is only used in prosaic explanations of
QFT to laymen, there's no theory that actually depends on it. In that
sense it is not falsifiable.

Igor

[basically yes]

>> But the reference to a field is necessary, which amounts to the same.
>> Actually, a particle is understood as an excitation of a field. Each
>> time there is a field, a real excitation can exist, which is the case of
>> the interaction field. Therefore, the virtual particle has some
>> reality. It is virtual in the sense that the excitation doesn't obey
>> the free field equation. In particular, the Maxwell operator applied to
>> the field doesn't yields 0 (for a photon or gluon) as is expected for a
>> massless particle on-shell. The word "virtual" means "too short lived
>> to be observed", not anything magic, metaphysical, or "Feynmanian".
>> Feynman's treatment doesn't add anything new to the physical model.

"Igor Khavkine" <igor.kh@gmail.com> a écrit dans le message de news:
slrnetcs63.8l7.igor.kh@corum.multiverse.ca

> Can you make these statements precise? I'd like to see this "field" that
> doesn't yield 0 under the Maxwell operator. Is it an operator? a state
> in the Hilbert space? some function on spacetime? An explicit example
> would be really nice.

Let's take the example of the electromagnetic interaction. The field is, to
one's choice, the electromagnetic tensor or the 4-potential, or in second
quantization the imaginary field on which the corresponding operators act
in the Heisenberg representation. The first quantization is simpler for the
explanation. The Maxwell operator is the one that applied to the field
gives the Maxwell equations. For a free field, its action yields 0, and
would be m x field if the mass were not 0. For a field mediating an
interaction, it is a function of the currents of the interacting particles,
and is not 0 as if the mass weren't 0. The concept of photon is different
from the one of the free case, yet the electromagnetic field is the same
with the same law of motion.

In second quantization, and using a perturbative method, all that is
represented by different processes with different numbers of photons, which
superpose coherently. It's a mere scripture, where the idea of path dear to
Feynman appears manifestly, but the basic theory is still quantized fields
with interaction terms.

[basically yes]

J'ai écrit:

>> If a theory is needed in order to define a particle (CM or QM), that
>> means a particle isn't defined *physically*. Physics isn't textbook
>> physics. This thread is about interaction, which makes sense even
>> outside of a theory.

"Igor Khavkine" <igor.kh@gmail.com> a écrit dans le message de news:
1171682149.526384.311610@q2g2000cwa.googlegroups.c om

> Since virtual particles are by definition not measurable, then they
> are
> definitely not defined *physically*. What is normally understood by a
> particle is necessarily tied to measurements and hence physical.

I'm a bit confused as what you mean by the definition of a particle. If it
isn't defined in CM and in QM, and in any other theory, how is it? If it is
by measurement, is it a track in a Wilson chamber, a click in a Geiger
counter, radiation pressure, or similar things? How do we then know that
all those facts are linked to one another and to the concept of particle, if
not through a theory?

A particle is never observed directly, just like a virtual particle, that is
only observed through its effect on the interacting particles. Every
concepts we handle are part of a theory, and without a theory, all what we
observe is only a collection of meaningless events.

>> Saying that a virtual particle is off-shell means that it isn't a
>> particle? How can it be off-shell then, if it don't even exist? If a
>> virtual particle is only an amplitude, so is also a real particle. I
>> see no reason why a *virtual* particle shouldn't be a particle, how
>> formal and true all that may be.

> Then, please, take your quantum theory of choice, maybe QED or maybe
> just single particle QM, and construct a state (that's an element of
> the theory's Hilbert space of states) representing a "virtual
> particle".

A quantum of a solution of the Maxwell equation in the presence of charges.

> Just to for definiteness, please use the Heisenberg picture for states
> and operators (if you can't, please explain why). If you wish, I can
> do the same for a particle and we can compare.

A quantum of a solution of the free Maxwell equation.

Now, how can I measure the complete wavefunction of a single electron?

>> Do I understand correctly that if the theory of virtual particle should
>> be falsified by experiment, Nature wouldn't be speaking the same
>> language as physicists?

> As far as I know, nature doesn't speak any language, physicists do. So
> I can't make anything of that part of your question. But since the
> concept of virtual particles is only used in prosaic explanations of
> QFT to laymen, there's no theory that actually depends on it. In that
> sense it is not falsifiable.

Confusion coming back. The virtual particle would be an explanation of a
*theory*, it depends on that theory, which is falsifiable. In short, QFT,
QED and QCD are falsifiable. I think that is what was meant.

[Igor Khavkine]

On 2007-02-20, basically yes <canceljobs@thesapjobboard.com> wrote:

> Let's take the example of the electromagnetic interaction. The field is, to
> one's choice, the electromagnetic tensor or the 4-potential, or in second
> quantization the imaginary field on which the corresponding operators act
> in the Heisenberg representation. The first quantization is simpler for the
> explanation. The Maxwell operator is the one that applied to the field
> gives the Maxwell equations. For a free field, its action yields 0, and
> would be m x field if the mass were not 0. For a field mediating an
> interaction, it is a function of the currents of the interacting particles,
> and is not 0 as if the mass weren't 0. The concept of photon is different
> from the one of the free case, yet the electromagnetic field is the same
> with the same law of motion.

I'm confused by your example. Let F denote the Faraday tensor. When
there are no charges present, it obey's Maxwell's equations:

div F = 0,
div *F = 0 (here *F is the Hodge dual tensor).

In the presence of charges it obeys a different equation:

div F = j (where j is the charge current),
div *F = 0.

These equations work for both in the case when F is a classical field
and when it (as well as j) is a Heisenberg operator in a quantized
theory.

It is true that in the presence of matter j != 0, so the two sets of
equations are not equivalent. But I fail to see where you would insert
the word "virtual" here. That was my question: what mathematical object
in quantum theory do you pin the word "virtual" on?

Igor

[Arnold Neumaier]

basically yes schrieb:
> J'ai écrit:
>
>>> If a theory is needed in order to define a particle (CM or QM), that
>>> means a particle isn't defined *physically*. Physics isn't textbook
>>> physics. This thread is about interaction, which makes sense even
>>> outside of a theory.
>
> "Igor Khavkine" <igor.kh@gmail.com> a écrit dans le message de news:
> 1171682149.526384.311610@q2g2000cwa.googlegroups.c om
>
>> Since virtual particles are by definition not measurable, then they
>> are
>> definitely not defined *physically*. What is normally understood by a
>> particle is necessarily tied to measurements and hence physical.
>
> I'm a bit confused as what you mean by the definition of a particle.

He just took your explanation of what it means for something to be
defined *physically* (namely that no theory is needed), and showed that
you contradict yourself.

In fact, almost everything in physics needs a lot of theory to be
defined, since most experiments don't make sense without an accompanying
teory that tells what the raw data obtained mean and how they are to be
processed to get the measurement values.



> If it
> isn't defined in CM and in QM, and in any other theory, how is it? If it is
> by measurement, is it a track in a Wilson chamber, a click in a Geiger
> counter, radiation pressure, or similar things? How do we then know that
> all those facts are linked to one another and to the concept of particle, if
> not through a theory?

True, but this sounds quite the opposite to your above assertion that
''If a theory is needed in order to define a particle (CM or QM),
that means a particle isn't defined *physically*.''
If you want a consistent discussion, commit yourself to a consistent
set of assertions.


Arnold Neumaier

[Cl.Massé]

J'ai écrit:

>> Let's take the example of the electromagnetic interaction. The field
>> is, to one's choice, the electromagnetic tensor or the 4-potential, or
>> in second quantization the imaginary field on which the corresponding
>> operators act in the Heisenberg representation. The first quantization
>> is simpler for the explanation. The Maxwell operator is the one that
>> applied to the field gives the Maxwell equations. For a free field, its
>> action yields 0, and would be m x field if the mass were not 0. For a
>> field mediating an interaction, it is a function of the currents of the
>> interacting particles, and is not 0 as if the mass weren't 0. The
>> concept of photon is different from the one of the free case, yet the
>> electromagnetic field is the same with the same law of motion.

"Igor Khavkine" <igor.kh@gmail.com> a écrit dans le message de news:
slrnetntmf.lu2.igor.kh@corum.multiverse.ca

> I'm confused by your example. Let F denote the Faraday tensor. When
> there are no charges present, it obey's Maxwell's equations:
>
> div F = 0,
> div *F = 0 (here *F is the Hodge dual tensor).
>
> In the presence of charges it obeys a different equation:
>
> div F = j (where j is the charge current),
> div *F = 0.
>
> These equations work for both in the case when F is a classical field
> and when it (as well as j) is a Heisenberg operator in a quantized
> theory.
>
> It is true that in the presence of matter j != 0, so the two sets of
> equations are not equivalent. But I fail to see where you would insert
> the word "virtual" here. That was my question: what mathematical object
> in quantum theory do you pin the word "virtual" on?

A real photon is a free photon. A virtual photon is a photon mediating an
interaction. From that it is straightforward that a real particle is one in
a space without particles, that is with second term = 0. While a virtual
particle is one in space were there is at least two particle, and is emitted
by them, that is with second term != 0.

It seems startling they are so similar, being both a plain electromagnetic
field. But that is a consequence of decades of use of Feynman's view and
of insisting on their difference. Feynman's diagrams are but calculational
trick enabling to tackle QFT, nothing more, nothing less.

Let's imagine an accelerator that sends electrons one at a time, and a
coaxial coil around the beam. The electron in the beam interact with the
ones in the coil by photon exchange (the discussion is the same in principle
if there is only one electron in the coil.) But an alternative description
is that the moving electron creates a varying (electro)magnetic field that
yields a force on the coil electrons. That field is quite real, but is made
of virtual photons.

The effect can be measured with a voltmeter at the terminals of the coil,
but the field can also be measured by a Hall probe inside the coil. Of
course, both methods amount to the same, but the modified motion of the
electrons in the probe creates a field that is subtracted from the initial
field, and the reading of the voltmeter decreases. What happened is that
the probe intercepted some photons. Therefore they exist and are
observable, safe that they no longer mediate interaction between the beam
and the coil electrons since they have been absorbed. Yet, if the photons
were real, they would have the same fate.

On the other hand, if the wave functions of the interacting electrons don't
overlap, there is a region where the current is zero, and the photons are
free. Are they real or virtual there? Granted, it's a little confusing,
but we only have to conclude that it isn't that clean cut.

"Virtual" takes all its sense in the case of W or Z exchange, since the
bosons are very short lived. But that's quite another story.

[basically yes]

"Igor Khavkine" igor.kh@gmail.com> a écrit dans le message de news:
1171682149.526384.311610@q2g2000cwa.googlegroups.c om

>>> Since virtual particles are by definition not measurable, then they
>>> are
>>> definitely not defined *physically*. What is normally understood by a
>>> particle is necessarily tied to measurements and hence physical.

J'ai écrit:

>> I'm a bit confused as what you mean by the definition of a particle.

"Arnold Neumaier" <Arnold.Neumaier@univie.ac.at> a écrit dans le message de
news: 45DD9F0A.6040700@univie.ac.at

> He just took your explanation of what it means for something to be
> defined *physically* (namely that no theory is needed), and showed that
> you contradict yourself.

I don't think so. My point of view is that a particle isn't defined
(physically) without a theory, and that it is also true for a virtual
particle, hence no conceptual difference. Of course, what is understood
(theoretically) by particle is necessarily tied to measurements (that's the
essence of physics), but through hypothesis that may or may not lead to
complete agreement with experimental data, that is, textbook physics.

The confusion between reality and theory is widespread. It is not because a
theory describes correctly reality that the concepts in the theory are real,
they rather are mind tools that proved very fruitful. Now, some phenomena
exhibit a discrete nature, for instance clicks of a Geiger counter. That
leads to the idea of particle, in analogy to a macroscopic particle, but not
directly to the necessity of using the particle concept. In few words, not
to the reality of the particle.

>> If it
>> isn't defined in CM and in QM, and in any other theory, how is it? If
>> it is by measurement, is it a track in a Wilson chamber, a click in a
>> Geiger counter, radiation pressure, or similar things? How do we then
>> know that all those facts are linked to one another and to the concept
>> of particle, if not through a theory?

> True, but this sounds quite the opposite to your above assertion that
> ''If a theory is needed in order to define a particle (CM or QM),
> that means a particle isn't defined *physically*.''

Obviously not. The conclusion (and the word *physically*) in the second
quote doesn't appear in the first one, whatever what "sounds" what. I
suggest you better analyse my writing and hunt for your hidden assumptions.

> If you want a consistent discussion, commit yourself to a consistent
> set of assertions.

I hope you better understand my point of view now.

[Igor Khavkine]

On 2007-02-24, Cl.Massé <retour@contactprospect.com> wrote:

> Let's imagine an accelerator that sends electrons one at a time, and a
> coaxial coil around the beam. The electron in the beam interact with the
> ones in the coil by photon exchange (the discussion is the same in principle
> if there is only one electron in the coil.) But an alternative description
> is that the moving electron creates a varying (electro)magnetic field that
> yields a force on the coil electrons. That field is quite real, but is made
> of virtual photons.

In the formalism of quantum field theory, you have the Fock space
(including both EM and electron states) and the field operators (again,
representing both the EM and electron fields). These are the tools at
your disposal. Now, can you make your statement that "[that field] is
made of virtual photons" mathematically precise? At the same time, it
would help if you could do the same for the case when the word "virtual"
is removed.

Igor

[basically yes]

Cl.Massé a écrit:

>> Let's imagine an accelerator that sends electrons one at a time, and a
>> coaxial coil around the beam. The electron in the beam interact with the
>> ones in the coil by photon exchange (the discussion is the same in
>> principle if there is only one electron in the coil.) But an
>> alternative description is that the moving electron creates a varying
>> (electro)magnetic field that yields a force on the coil electrons. That
>> field is quite real, but is made of virtual photons.

"Igor Khavkine" <igor.kh@gmail.com> a écrit dans le message de news:
slrneu51gv.if.igor.kh@corum.multiverse.ca

> In the formalism of quantum field theory, you have the Fock space
> (including both EM and electron states) and the field operators (again,
> representing both the EM and electron fields). These are the tools at
> your disposal. Now, can you make your statement that "[that field] is
> made of virtual photons" mathematically precise?

No, because two different formulations are used, one classical and one
quantic. They both describe the same phenomenon, that's why the loose term
"is made of" is used.

Mathematically, the situation is analogous to a particle in a harmonic
potential well, but at every point in space-time. The classical formulation
merely says that the particle has an oscillatory motion, which is analogous
to the oscillating field strength. The quantic formulation says that the
state of the particle is expressed as a linear combination of states of well
defined, equidistant (discrete) energy. For a fields, those states are
multi-photons states, and they span the Fock space. Like the position of
the particle, the field strength is no longer determined, but there is a
probability law for its value. The field operator is analogous to the
position operator, the proper values being the possible values of the field
strength.

In the case of the interaction between two free electrons, the field is in
fact described by a superposition of photon states of different energies.

> At the same time, it would help if you could do the same for the case when
> the word "virtual" is removed.

Virtual or real doesn't change the basic theory, be it classical or quantic,
apart from quantic corrections. It is only linked to the particular
physical situation.

[Igor Khavkine]

On 2007-02-27, basically yes <canceljobs@thesapjobboard.com> wrote:
> "Igor Khavkine" <igor.kh@gmail.com> a =C3=A9crit dans le message de new=
s:
> slrneu51gv.if.igor.kh@corum.multiverse.ca
>
>> In the formalism of quantum field theory, you have the Fock space
>> (including both EM and electron states) and the field operators (again=
,
>> representing both the EM and electron fields). These are the tools at
>> your disposal. Now, can you make your statement that "[that field] is
>> made of virtual photons" mathematically precise?
>
> No, because two different formulations are used, one classical and one
> quantic. They both describe the same phenomenon, that's why the loose =
term
> "is made of" is used.

I don't see any conflict here, especially since we are not discussing
classical fields. Everything in QED is mathematically describable in
terms of Fock states and field operators. If you believe that some
objects in QED deserve the name "virtual", then you should spell out
precisely what they are. Until then, the usage of that word remains
informal and any debate as to the reality or measurability of "virtual"
objects or their effects is moot.

Igor
=2E

[basically yes]

"Igor Khavkine" <igor.kh@gmail.com> a écrit dans le message de news:
slrneub2si.a7g.igor.kh@corum.multiverse.ca

> Everything in QED is mathematically describable in
> terms of Fock states and field operators. If you believe that some
> objects in QED deserve the name "virtual", then you should spell out
> precisely what they are.

Yes, and you should ask that to those who stressed a so-called different
meaning to "virtual", including yourself:
> > Thus, the statement that a "virtual particle" is not a particle is
formal, true, and has already been given in precise language in this
discussion. < <

Both in classical and quantum theory, there is no qualitative difference at
all. A particle is defined as an excitation of a quantum field in any case,
whether it is symbolized by an internal line or not.

> Until then, the usage of that word remains
> informal and any debate as to the reality or measurability of "virtual"
> objects or their effects is moot.

I couldn't have concluded better. That demonstrates the utility of thinking
by oneself, rather than using ready-to-think stuff.

[Igor Khavkine]

On 2007-03-02, basically yes <canceljobs@thesapjobboard.com> wrote:
> "Igor Khavkine" <igor.kh@gmail.com> a crit dans le message de news:
> slrneub2si.a7g.igor.kh@corum.multiverse.ca
>
>> Everything in QED is mathematically describable in
>> terms of Fock states and field operators. If you believe that some
>> objects in QED deserve the name "virtual", then you should spell out
>> precisely what they are.
>
> Yes, and you should ask that to those who stressed a so-called different
> meaning to "virtual", including yourself:
>> > Thus, the statement that a "virtual particle" is not a particle is
> formal, true, and has already been given in precise language in this
> discussion. < <

Take a single Feynman diagram in momentum space. Each external leg is
labeled by a 4-momentum, say, p. If p^2 = -m^2, where m is the mass of
the excitation it is associated with, then that particular leg is said
to be "on shell". If this equality does not hold, this leg is said tobe
"off shell" OR is said to represent a "virtual particle".
Also, if there is an internal line in the diagram, it is
labelled by a 4-momentum, which generically is not on shell. This
internal line is said to represent "virtual particle exchange".

These are the only places where one encounters the term "virtual
particle" in a non-poetic context. Now you know what I mean by this
term. I, however, am still puzzled by how you use it.

On the other hand. I can take a Fock state, take it to be an eigenstate
of the number operator for some kind of excitation, with eigenvalue,
say, n. Then I can point to this state, say |psi> and call this a "state
with n particles". Then I can ask and answer various questions about
these particles.

Q: What's their total momentum?
A: <psi|P|psi>, where P is the total momentum operator.

Q: What is their total angular momentum?
A: <psi|L|psi>, where L is the angular momentum operator.

Q: What is their charge density distribution?
A: <psi|rho|psi>, where rho is the charge density operator.

Q: What is the probability that these particles will decay into
another set of m particles?
A: |<phi|psi>|^2, where |phi> is the state representing the other
set of m particles.

And so on and so forth. Since there is no state associated with the
objects that get the attribute "virtual", I can't answer any of these
questions for them. Simply put, the "virtual" ones are not particles.

Igor

[basically yes]

"Igor Khavkine" <igor.kh@gmail.com> a écrit dans le message de news:
slrneui0np.4nc.igor.kh@corum.multiverse.ca

> Take a single Feynman diagram in momentum space. Each external leg is
> labeled by a 4-momentum, say, p. If p^2 = -m^2, where m is the mass of
> the excitation it is associated with, then that particular leg is said
> to be "on shell". If this equality does not hold, this leg is said to be
> "off shell" OR is said to represent a "virtual particle".
> Also, if there is an internal line in the diagram, it is
> labelled by a 4-momentum, which generically is not on shell. This
> internal line is said to represent "virtual particle exchange".
>
> These are the only places where one encounters the term "virtual
> particle" in a non-poetic context. Now you know what I mean by this
> term. I, however, am still puzzled by how you use it.

It's a mere definition, in a diagram that is but a representation of a
mathematical term, which in turn represents a configuration of fields.
I explained what happen as QED describes it. There is no fundamental
difference, both can be represented by a quantum field, the difference
is the "state" of that field, in relation to its equation of motion.
Various basis can be used to write it, none of them has a priviledged
status. The Fock states and the Feynman diagrams are but one of them.

> On the other hand. I can take a Fock state, take it to be an eigenstate
> of the number operator for some kind of excitation, with eigenvalue,
> say, n. Then I can point to this state, say |psi> and call this a "state
> with n particles". Then I can ask and answer various questions about
> these particles.
>
> Q: What's their total momentum?
> A: <psi|P|psi>, where P is the total momentum operator.
>
> Q: What is their total angular momentum?
> A: <psi|L|psi>, where L is the angular momentum operator.
>
> Q: What is their charge density distribution?
> A: <psi|rho|psi>, where rho is the charge density operator.
>
> Q: What is the probability that these particles will decay into
> another set of m particles?
> A: |<phi|psi>|^2, where |phi> is the state representing the other
> set of m particles.
>
> And so on and so forth. Since there is no state associated with the
> objects that get the attribute "virtual", I can't answer any of these
> questions for them. Simply put, the "virtual" ones are not particles.

I really don't see why. If the square of the energy minus square of the
linear momentum isn't zero, the photon is off-shell, then by definition
virtual:
<psi|E|psi>^2 - <psi|P|psi>^2 != 0 <=> the photon is off-shell or
virtual. The Feynman diagrams represent the electrons wave function and
the electromagnetic field as well, therefore their is a state for both.

That description is the classical one. With quantum fields, a particles
is still an excitation of a field, whatever the value of the observables
of the field. Mathematically:

<A>(x,t) = <Psi(x,t)|A|Psi(x,t)>
n(x,t) = <Psi(x,t)|a^+(x,t) a(x,t)|Psi(x,t)>

As the Feynman diagrams are for plane waves, the corresponding electron
wave functions fill all the space, and there is a current everywhere so
that the photons are everywhere off-shell. But in real situation, we
have to take a superposition of them. Then, contrary to the diagrams,
there may be a region of space where the current is zero. The
electromagnetic field isn't zero though, and the photons are on-shell
there. All that means that an on-shell photon can be written as a
coherent superposition of off-shell photons! That's the case of a
photon from the sun to earth. So, that idea of "virtual" particle is
unnecessary /enculage de mouche/.

Getting a good insight is a more worthwhile task than nitpicking and
copying out books. Fed up of that discussion. I did my homework, do
yours.

[Igor Khavkine]

Followup-to: fr.sci.physique

On 2007-03-07, basically yes <canceljobs@thesapjobboard.com> wrote:
> "Igor Khavkine" <igor.kh@gmail.com> a crit dans le message de news:
> slrneui0np.4nc.igor.kh@corum.multiverse.ca
>
>> Take a single Feynman diagram in momentum space. Each external leg is
>> labeled by a 4-momentum, say, p. If p^2 = -m^2, where m is the mass of
>> the excitation it is associated with, then that particular leg is said
>> to be "on shell". If this equality does not hold, this leg is said to be
>> "off shell" OR is said to represent a "virtual particle".
>> Also, if there is an internal line in the diagram, it is
>> labelled by a 4-momentum, which generically is not on shell. This
>> internal line is said to represent "virtual particle exchange".
>>
>> These are the only places where one encounters the term "virtual
>> particle" in a non-poetic context. Now you know what I mean by this
>> term. I, however, am still puzzled by how you use it.
>
> It's a mere definition, in a diagram that is but a representation of a
> mathematical term, which in turn represents a configuration of fields.
> I explained what happen as QED describes it. There is no fundamental
> difference, both can be represented by a quantum field, the difference
> is the "state" of that field, in relation to its equation of motion.
> Various basis can be used to write it, none of them has a priviledged
> status. The Fock states and the Feynman diagrams are but one of them.

Fock states are vectors in a Hilbert space, Feynman diagrams are not.
How can they be the same? The meaning of the rest of the paragraph still
eludes me.

>> On the other hand. I can take a Fock state, take it to be an eigenstate
>> of the number operator for some kind of excitation, with eigenvalue,
>> say, n. Then I can point to this state, say |psi> and call this a "state
>> with n particles". Then I can ask and answer various questions about
>> these particles.
>>
>> Q: What's their total momentum?
>> A: <psi|P|psi>, where P is the total momentum operator.
>>
>> Q: What is their total angular momentum?
>> A: <psi|L|psi>, where L is the angular momentum operator.
>>
>> Q: What is their charge density distribution?
>> A: <psi|rho|psi>, where rho is the charge density operator.
>>
>> Q: What is the probability that these particles will decay into
>> another set of m particles?
>> A: |<phi|psi>|^2, where |phi> is the state representing the other
>> set of m particles.
>>
>> And so on and so forth. Since there is no state associated with the
>> objects that get the attribute "virtual", I can't answer any of these
>> questions for them. Simply put, the "virtual" ones are not particles.
>
> I really don't see why. If the square of the energy minus square of the
> linear momentum isn't zero, the photon is off-shell, then by definition
> virtual:
> <psi|E|psi>^2 - <psi|P|psi>^2 != 0 <=> the photon is off-shell or
> virtual. The Feynman diagrams represent the electrons wave function and
> the electromagnetic field as well, therefore their is a state for both.

Ah, and what is the mysterious |psi> that appears in your formulas? Can
you give an explicit example that you will call "virtual"? You use <E>^2
- <P>^2 and not <E^2 - P^2>. I'm sure there is a reason. Also, I was
not aware that Feynman diagrams represent wave functions. How so?

>
> That description is the classical one. With quantum fields, a particles
> is still an excitation of a field, whatever the value of the observables
> of the field. Mathematically:
>
> <A>(x,t) = <Psi(x,t)|A|Psi(x,t)>
> n(x,t) = <Psi(x,t)|a^+(x,t) a(x,t)|Psi(x,t)>

You probably mean

<A(x,t)> = <Psi|A(x,t)|Psi>
n(x,t) = <Psi|a^+(x,t) a(x,t)|Psi>

Heisenberg states don't have position of time dependence.

> As the Feynman diagrams are for plane waves, the corresponding electron
> wave functions fill all the space, and there is a current everywhere so
> that the photons are everywhere off-shell. But in real situation, we
> have to take a superposition of them. Then, contrary to the diagrams,
> there may be a region of space where the current is zero. The
> electromagnetic field isn't zero though, and the photons are on-shell
> there. All that means that an on-shell photon can be written as a
> coherent superposition of off-shell photons! That's the case of a
> photon from the sun to earth.

Can you write an example of an on-shell photon as a superposition of
off-shell photons? I'm somewhat puzzled by this statement and by much of
the rest of this paragraph.

> So, that idea of "virtual" particle is unnecessary /enculage de mouche/.

Very true.

> Getting a good insight is a more worthwhile task than nitpicking and
> copying out books. Fed up of that discussion. I did my homework, do
> yours.

Different isights for different people. However, I'm still missing
insight into whether you actually use the term "virtual" in a way that
is not merely poetic, and along with it an isight into why this thread
started. If you want to continue, you might want to take advantage of
the Followup-To.

Igor

[basically yes]

Follow-up to: sci.physics.bigot

"Igor Khavkine" <igor.kh@gmail.com> a écrit dans le message de news:
slrneuv3et.lt2.igor.kh@corum.multiverse.ca

> Followup-to: fr.sci.physique

Ah, new case of discrimination.

> Fock states are vectors in a Hilbert space, Feynman diagrams are not.
> How can they be the same?

They both are basis, but not of the same thing. The Fock states are a basis
of the quantized fields. The Feynman diagrams are the basis of the
transition matrix. Those basis aren't the only ones, QED can be written in
many different mathematical formulations.

> Ah, and what is the mysterious |psi> that appears in your formulas?

It is your psi, and you didn't make it explicit.

> Can you give an explicit example that you will call "virtual"? You use
> <E>^2 - <P>^2 and not <E^2 - P^2>. I'm sure there is a reason.

Yes, as you psi is an unknown animal, according to the case one or the other
should be taken. The Fock states are usually written with occupation
numbers, not as a wave function of space-time.

> Also, I was not aware that Feynman diagrams represent wave functions. How
> so?

A leg labelled p represent the wave function u.e{ip.x - (m^2-p^2)t} and so
on. The diagram itself represent a transition coefficient for given
incoming and outcoming plane waves and a given photon occupation number, and
consequently correspond to a given electromagnetic field. But that's
textbook physics, why do you ask?

> You probably mean
>
> <A(x,t)> = <Psi|A(x,t)|Psi>
> n(x,t) = <Psi|a^+(x,t) a(x,t)|Psi>

No

> Heisenberg states don't have position of time dependence.

"Heisenberg states" has no meaning. You probably mean Heisenberg matrices.
I used the Schrödinger representation. Second quantization introduces a
formal wave function Psi of A or F or whenever field is used at every
space-time point.

> Can you write an example of an on-shell photon as a superposition of
> off-shell photons? I'm somewhat puzzled by this statement and by much of
> the rest of this paragraph.

I already did my homework. All that is standard textbook physics.

> Different isights for different people. However, I'm still missing
> insight into whether you actually use the term "virtual" in a way that
> is not merely poetic, and along with it an isight into why this thread
> started. If you want to continue, you might want to take advantage of
> the Followup-To.

I'm not sensitive to contempt, as it mostly comes from less intelligent
people who are physiologically unable to understand what I think. It says
much more about you than about me. You can't see the top of my head, so you
can only suppose I'm bald.