Understand Virtual Particles in Quantum Gravity

  • Thread starter wolram
  • Start date
In summary, a 'virtual' particle in QFT is an off the mass shell particle. It is introduced due to a specific mathematical method of calculation, called perturbative expansion, and is not related to Heisenberg's uncertainty principle or the idea that a particle can have a different energy for a short time.
  • #1
wolram
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What a virtual particle *is* in theories of quantum gravity.

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

You must understand that a non scientist may want to know how things work, and it is unfair for you guys to use terms like *virtual* without
giving some explanation as to what it means.
 
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  • #2
wolram said:
You must understand that a non scientist may want to know how things work, and it is unfair for you guys to use terms like *virtual* without
giving some explanation as to what it means.

I already told in other thread, I would like understand the psicologocal or semiotical implications of the word "virtual" when used in "virtual particle", because it is probably the most repeated physics question in the internet (check the FAQ of physics in USENET). Not that people asks about particles under Heisenberg uncertainty or about particles in Off-shell Feynman diagrams... they ask about virtual particles.
 
  • #3
I can just about understand Heisenberg uncertainty, but how does this help
in understanding the real world, it is you guys that use these words, i just want to know how they help in understanding the blossoming of the universe.
 
  • #4
Interesting that I found this post on a search for the precise definition of "virtual". Apparently there is a gap between the "popular" notion of virtual and the "scientific" notion.
 
  • #5
Here is a citation from
http://arxiv.org/abs/quant-ph/0609163

Virtual particles?

The calculational tool represented by Feynman diagrams
suggests an often abused picture according to which
``real particles interact by exchanging virtual particles".
Many physicists, especially nonexperts,
take this picture literally, as something that
really and objectively happens in nature. In fact, I have
{\em never} seen
a popular text on particle physics in which this picture was
{\em not} presented as something that really happens.
Therefore, this picture of quantum interactions as processes
in which virtual particles exchange is one of the
most abused myths, not only in quantum physics, but in
physics in general. Indeed, there is a consensus among experts
for foundations of QFT that such a picture should
not be taken literally. The fundamental principles
of quantum theory do not even contain a notion of a
``virtual" state. The notion of a
``virtual particle" originates {\em only} from a
specific mathematical method of calculation, called perturbative
expansion. In fact, perturbative expansion
represented by Feynman diagrams can be introduced even in
{\em classical} physics \cite{thorn,penco}, but nobody
attempts to verbalize these classical Feynman diagrams
in terms of classical ``virtual" processes.
So why such a verbalization is tolerated in quantum physics?
The main reason is the fact that the standard interpretation
of quantum theory does not offer a clear ``canonical" ontological picture
of the actual processes in nature, but only provides
the probabilities for the final results of measurement outcomes.
In the absence of such a ``canonical" picture,
physicists take the liberty to introduce
various auxiliary intuitive pictures that sometimes help them
think about otherwise abstract quantum formalism. Such auxiliary
pictures, by themselves, are not a sin. However, a potential
problem occurs when one forgets why such a picture has been introduced
in the first place and starts to think on it too literally.
 
  • #6
wolram said:
What a virtual particle *is* in theories of quantum gravity.

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

You must understand that a non scientist may want to know how things work, and it is unfair for you guys to use terms like *virtual* without giving some explanation as to what it means.

They will basically tell you that a 'virtual' particle in QFT is off the mass shell

[tex]E^2 - c^2p^2 \neq\ m^2c^4[/tex]

This hasn't anything to do with Heisenberg's uncertainty principle and the
idea that a particle "can have a different Energy for a short time"

On the contrary. The laws of conservation are always observed
exactly in QFT, for each and every vertex. The fact that they are off
the mass shell is simply because the particles are not free solutions but
are interacting. Every real particle which interacts is "off the mass shell"
One could use the terms "free" and "interacting" particles instead of
the terms real and virtual

In more technical terms:

The equation of motion of a virtual electron contains the interaction term
from the photon “it has absorbed” while the equation of motion of a
virtual photon contains the transition current representing the change
of motion of the electron which has emitted the photon. This is the reason
why they are off the mass shell.Regards, Hans
 
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  • #7
Demystifier said:
Here is a citation from
http://arxiv.org/abs/quant-ph/0609163

Virtual particles?

The calculational tool represented by Feynman diagrams
suggests an often abused picture according to which

[...]

However, a potential
problem occurs when one forgets why such a picture has been introduced
in the first place and starts to think on it too literally.

Great text :approve:
 
  • #9
Demystifier said:
However, a potential
problem occurs when one forgets why such a picture has been introduced
in the first place and starts to think on it too literally.

This may all be written out of some sort of preoccupation that a picture
is taken to literally for your taste or gut feeling , however, the text has
become way to dogmatic for my personal taste.

Your message is:

Those who consider a literal interpretation seriously are likely somewhat
dumb (associate them with non-experts). "Kindly" you grant that they are
not necessary evil though. (no sin). But still you cast doubt that their
viewpoint should be tolerated at all...

There are many physicist who do take the literal interpretation very
seriously. Nobel price winners like Feynman and Veltkamp (edit: Veltman)
For the latter the only thing which really makes sense in QFT is the
diagrammatica.

Interestingly. These people are/were down-to-earth, no nonsense people
in a quest for a non mystical, logical picture of Quantum Mechanics. Such
a picture however does not necessary need to coincide with the most
common primary reactions like QM should be Brownian motion or Bohmian...


Regards, Hans.
 
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  • #10
Hans de Vries said:
This may all be written out of some sort of preoccupation that a picture
is taken to literally for your taste or gut feeling , however, the text has
become way to dogmatic for my personal taste.

Your message is:

Those who consider a literal interpretation seriously are likely somewhat
dumb (associate them with non-experts). "Kindly" you grant that they are
not necessary evil though. (no sin). But still you cast doubt that their
viewpoint should be tolerated at all...

There are many physicist who do take the literal interpretation very
seriously. Nobel price winners like Feynman and Veltkamp. For the
latter the only thing which really makes sense in QFT is the
diagramatica.

Interestingly. These people are/were down-to-earth, no nonsense people
in a quest for a non mystical, logical picture of Quantum Mechanics. Such
a picture however does not necessary need to coincide with the most
common primary reactions like QM should be Brownian motion or Bohmian...


Regards, Hans.

Actually, your previous (and this) answer is the only one with content to it in this thread :approve:

Careful
 
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  • #11
Careful said:
Actually, your previous answer was the only one with some (correct) content to it :approve:

Careful

Oh yeah? Just because you liked that part and not the latest? Strikes me that this thread is getting pretty heavy on the personal theory side. Let us all remember that the great physicists who built field theory up to the level of the standard model were not fools, and may even have understood more deeply than we do. ALL of us!
 
  • #12
selfAdjoint said:
Oh yeah? Just because you liked that part and not the latest? Strikes me that this thread is getting pretty heavy on the personal theory side. Let us all remember that the great physicists who built field theory up to the level of the standard model were not fools, and may even have understood more deeply than we do. ALL of us!

I clearly meant post 6 and 9 written by Hans. There is nothing personal about it, he gives a fairly objective point of view on the issue. I think we misunderstood each other here. Of course I agree with the last post, it is well known that Veltman is quite sceptical towards QFT.
 
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  • #13
if you disagreed you could have said you disagreed instead of the insulting expression you did use.

I don't know why so many savants from Europe think that this kind of trash talk is appropriate in discussing controversial issues.
 
  • #14
selfAdjoint said:
if you disagreed you could have said you disagreed instead of the insulting expression you did use.

I don't know why so many savants from Europe think that this kind of trash talk is appropriate in discussing controversial issues.

The thing is that there is no controversy in what Hans said (and neither is there about this topic), some other comments on this thread were much more insulting (as correctly pointed out by him). By the way, I believe Freidel (?) developped a theory of 2+1 quantum gravity with point particles entirely based upon a fairly ``literal'' interpretation of the Feynman diagrams.
 
  • #15
Careful said:
Of course I agree with the last post, it is well known that Veltkamp is quite sceptical towards QFT.

Martinus Veltman (sorry, my typo) strongly beliefs in Feynman
diagrams (diagrammatica) but is not so impressed by how they
are derived, quote:

Martinus Veltman said:
Here is the most curious situation: The resulting machinery is
far better than the originating theory. There are formalisms that
in the end produce the Feynman rules starting from the basic
ideas of quantum mechanics. However these formalisms have
flaws and defects, and no derivation exist that can be called
satisfactory.


(From the introduction of Diagrammatica, The Path to Feynman
diagrams).

And further, in relation to the discussion on this thread:

Martinus Veltman said:
Feynman rules have a true physics content, and the physicist must understand that.
Regards, Hans
 
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  • #16
IHans, about this explanation, could you be more concrete for instance in the case of electroweak interaction by exchange of a W or Z0 particle? My understanding is that two electrons, or two neutrinos, can interact by exchange of a Z0 even if their kinetic energy is a lot less than the mass of the Z0.


Hans de Vries said:
They will basically tell you that a 'virtual' particle in QFT is off the mass shell

[tex]E^2 - c^2p^2 \neq\ m^2c^4[/tex]

This hasn't anything to do with Heisenberg's uncertainty principle and the
idea that a particle "can have a different Energy for a short time"

On the contrary. The laws of conservation are always observed
exactly in QFT, for each and every vertex. The fact that they are off
the mass shell is simply because the particles are not free solutions but
are interacting. Every real particle which interacts is "off the mass shell"
One could use the terms "free" and "interacting" particles instead of
the terms real and virtual

In more technical terms:

The equation of motion of a virtual electron contains the interaction term
from the photon “it has absorbed” while the equation of motion of a
virtual photon contains the transition current representing the change
of motion of the electron which has emitted the photon. This is the reason
why they are off the mass shell.


Regards, Hans
 
  • #17
arivero said:
IHans, about this explanation, could you be more concrete for instance in the case of electroweak interaction by exchange of a W or Z0 particle? My understanding is that two electrons, or two neutrinos, can interact by exchange of a Z0 even if their kinetic energy is a lot less than the mass of the Z0.

Good remark. For neutral weak processes there are vertices where a
neutrino emits a Z. (Like in Griffiths 2.4). Now consider conservation
of momentum and energy at the vertex if the Z has its usual mass
of 91 GeV...


Regards, Hans.
 
  • #18
Hans de Vries said:
Martinus Veltman (sorry, my typo) strongly beliefs in Feynman diagrams (diagrammatica) but is not so impressed by how they are derived, quote

Thanks for the note. I feel great sympathy for that point of view and will look around for Veltman's writings.

Okay, I've ordered a copy of Veltman's introduction to QFT through Feynman diagrams:
http://www.abebooks.com/servlet/SearchResults?&isbn=0521456924&nsa=1

A great Veltman article:

Perturbation Theory and Relative Space
Martinus Veltman, 2006
The validity of non-perturbative methods is questioned. The concept of relative space is introduced.
http://arxiv.org/abs/hep-ph/9404358

By the way, I've just added a section to my book on the elementary particles that has to do with the concept that Feynman diagrams are more fundamental than the Lagrangian. It's section 7.6:
http://www.brannenworks.com/dmaa.pdf

Carl
 
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  • #19
Hans de Vries said:
Martinus Veltman (sorry, my typo) strongly beliefs in Feynman
diagrams (diagrammatica) but is not so impressed by how they
are derived, quote:

Nah, I should have noticed it, the only excuse I have is that it was late in the evening (and I must have thought about ice skating or so):blushing:
 
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  • #20
Here is a citation from
http://arxiv.org/abs/quant-ph/0609163

Virtual particles?

The calculational tool represented by Feynman diagrams
suggests an often abused picture according to which
``real particles interact by exchanging virtual particles".
...

Unfortunately I'm such a non-expert who takes it too literally.

To describe the interaction of two unaccelerated charges on each other ( a conservative static force field) we need the concept of virtual particles. Unless we believe in forces-at-distance.

What am I missing?
 
  • #21
Ratzinger said:
Unfortunately I'm such a non-expert who takes it too literally.

To describe the interaction of two unaccelerated charges on each other ( a conservative static force field) we need the concept of virtual particles. Unless we believe in forces-at-distance.

What am I missing?


Well, Descartes made exactly that argument in introducing his vortices, which you can read about in histories of science. And Newton abolished them in favor of his derived but not motivated inverse square law ("Hypothese non fingo", one translation of which might be "Motivation? Who needs motivation!"). And then the continental physicists dismissed Principia as "spooky action at a distance" and deprived themselves thereby of the modern physics of the universe for a generation.

So the answer is not a simple or obvious one, but we do have to think all around the question with our reasoning minds, not just where our mind's eye can "see".
 
  • #22
Ratzinger said:
Unfortunately I'm such a non-expert who takes it too literally.

To describe the interaction of two unaccelerated charges on each other ( a conservative static force field) we need the concept of virtual particles. Unless we believe in forces-at-distance.

What am I missing?


Well, Descartes made exactly that argument in introducing his vortices, which you can read about in histories of science. And Newton abolished them in favor of his derived but not motivated inverse square law ("Hypothese non fingo" he said,, one translation of which might be "Motivation? Who needs motivation!"). And then the continental physicists dismissed Principia as "spooky action at a distance" and deprived themselves thereby of the modern physics of the universe for a generation.

So the answer is not a simple or obvious one, but we do have to think all around the question with our reasoning minds, not just where our mind's eye can "see".
 
  • #23
CarlB said:
Thanks for the note. I feel great sympathy for that point of view and will look around for Veltman's writings.

Okay, I've ordered a copy of Veltman's introduction to QFT through Feynman diagrams:
http://www.abebooks.com/servlet/SearchResults?&isbn=0521456924&nsa=1

Me too. Should be there when I get home from this visit. Willing to compare notes.
A great Veltman article:

Perturbation Theory and Relative Space
Martinus Veltman, 2006
The validity of non-perturbative methods is questioned. The concept of relative space is introduced.
http://arxiv.org/abs/hep-ph/9404358

Wonderful! Like a cold shower! No final answers, any more than anyone else has, but a thoroughgoing view from an unfamiliar direction.
By the way, I've just added a section to my book on the elementary particles that has to do with the concept that Feynman diagrams are more fundamental than the Lagrangian. It's section 7.6:
http://www.brannenworks.com/dmaa.pdf

Carl

I'll take a look at it as soon as I get a little more free time. You wouldn't think being a retired grandpa would be so time-consuming!
 
  • #25
Hans de Vries said:
Good remark. For neutral weak processes there are vertices where a
neutrino emits a Z. (Like in Griffiths 2.4). Now consider conservation
of momentum and energy at the vertex if the Z has its usual mass
of 91 GeV...
.

Do you claim it is always preserved? I do not see it; should we put down the equations, at the risk of killing the thread? It is a hell of dirac delta functions.
 
  • #26
arivero said:
Do you claim it is always preserved? I do not see it; should we put down the equations, at the risk of killing the thread? It is a hell of dirac delta functions.

Why don't you settle the issue between you in PM and report back here on the results?
 
  • #27
selfAdjoint said:
Why don't you settle the issue between you in PM and report back here on the results?
Because it is not a bilateral issue? Or because it is not a so disgusting thing to be done in public. It is amazing that nowadays sex between consenting adults can be public, but math between consenting adults is still a tabu!

I could point out some verbal, no math, arguments, as to ask about tunneling in a path integral formulation on quantum mechanics. I was visualising beta decay as a tunneling process if you wish. But we are going nowhere if we do not draw the equations. On the other side, I did yesterday for a question in the other subforum and the result is that the thread has gone dead.
 
  • #28
arivero said:
Because it is not a bilateral issue? Or because it is not a so disgusting thing to be done in public. It is amazing that nowadays sex between consenting adults can be public, but math between consenting adults is still a tabu!

I could point out some verbal, no math, arguments, as to ask about tunneling in a path integral formulation on quantum mechanics. I was visualising beta decay as a tunneling process if you wish. But we are going nowhere if we do not draw the equations. On the other side, I did yesterday for a question in the other subforum and the result is that the thread has gone dead.

I was only asking because you seemed hesitant to post the math, and you closed the other thread just after a long exposition. So apparently YOU, not I, have some problem here. Maybe your snark is really directed at someone else?
 
  • #29
selfAdjoint said:
I was only asking because you seemed hesitant to post the math, and you closed the other thread just after a long exposition. So apparently YOU, not I, have some problem here. Maybe your snark is really directed at someone else?

really I am not directing any snark at anyone! I am now hesitant to post math because after doing that in the other thread nobody answered anymore (so the technical word is killed more than closed. The thread is open). And I left two dangling questions (the proton eigenfunction and the antisymmetry of the colour part) I was expecting someone could answer better than myself.
 
  • #30
arivero said:
Do you claim it is always preserved? I do not see it; should we put down the equations, at the risk of killing the thread? It is a hell of dirac delta functions.

Four momentum conservation at the vertex should be general. Look for
instance at Halzen and Martin (Quarks & Leptons) chapter 6. They include
massive spin 1 photons in the Feynman rules although they don't touch
on Yang Mills interactions here.

A way to sneak in arbitrary large virtual masses into a vertex is to
have a very high mass virtual particle going in and out (the
virtual particle and its antiparticle) . They cancel each other out for
momentum conservation. Two of those become a loop then of course.


Regards, Hans.
 
  • #31
arivero said:
Diagrammatica (a pun on the older CERN preprint 'Diagrammar'?) is hard to read.

I really love his popular (non-technical) book from 2003:

Facts and Mysteries in Elementary Particle Physics
https://www.amazon.com/dp/981238149X/?tag=pfamazon01-20

This is a "should have" book.


Regards, Hans.
 
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  • #32
arivero said:
Do you claim it is always preserved? I do not see it; should we put down the equations, at the risk of killing the thread? It is a hell of dirac delta functions.

Maybe I am misinterpreting the issue (in which case I apologize!) but four-momentum is indeed always conserved at all vertices in Feynman diagrams. Always. This forces internal lines to be off-shell.

But I am probably missing the point of the discussion, in which case, again, I apologize!

Regards

Patrick
 
  • #33
arivero said:
IHans, about this explanation, could you be more concrete for instance in the case of electroweak interaction by exchange of a W or Z0 particle? My understanding is that two electrons, or two neutrinos, can interact by exchange of a Z0 even if their kinetic energy is a lot less than the mass of the Z0.

Yes they can. There is no limit on their kinetic energies in order to exchange a Z_0 (or anything else that they couple to). It only means that if the Z_0 exchanged will be very off-shell.

Patrick
 
  • #34
Hans de Vries said:
A way to sneak in arbitrary large virtual masses into a vertex is to
have a very high mass virtual particle going in and out (the
virtual particle and its antiparticle) . They cancel each other out for
momentum conservation. Two of those become a loop then of course.

Yep, I see the mechanism. You start on shell having one [tex]E, p[/tex] with [tex]E^2-p^2=m^2[/tex], then it divides to [tex](E_a,p_a), (E_b,p_b)[/tex] and because of the dirac deltas in the vertex you can tell that its sum equals the initial [tex](E,p)[/tex]. Then your onshell tells that [tex](E_a+E_b)^2-(p_a+p_b)^2=m^2[/tex]. and as the quantities [tex]E_a^2-p_a^2[/tex] and [tex]E_b^2-p_b^2[/tex] do not need to coincide with the respective masses [tex]m_a, m_b[/tex] it is said that these quantities, or the corresponding particles, are off-shell or "virtual".

My first little point is that the diagram is built with the dirac deltas and complete freedom to violate Energy-momentun conservation, then you integrate them out in your very first step in order to reduce the number of integrals you need to calculate. I could devise for instance a regularisation of these deltas, do the calculation (ahem) of the integrals, and finally to remove the regularisation so that energy-momentum preservation is imposed at the very end of the process.

The other point is if even after imposing the energy preservation we can claim that the off-shell particles are related to Heisenberg uncertainty. This is, if the probability of propagating a particle of mass [tex]m_a[/tex] and offshell 4-momentum [tex](E_a,p_a)[/tex] is related via uncertainty to a "most probable" interval [tex](\Delta t_a, \Delta x_a)[/tex]. I think it is so because for an on shell particle such interval is infinite (you can go as far as you wish for so much time as you wish).
 
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  • #35
Another possibility, within QFT, is along nrqed's remark that the Z or W is very
off-shell (E<<m). The difference should be due to the Weak interaction
then. This is where things become indeed more complicated to write down
mathematically.

For the Beta decay you were probably thinking about we get according
to "Diagrammatica, Apendix E" :

The vertex function for u --> W-, d Veltman gives:

[tex]ig\frac{1}{2\sqrt{2}} \gamma^\mu(1+\gamma^5)V_{ud}[/tex]

So, there's the chiralty selection and the the Vud which denotes the factor
from the Cabibbo-Kobayashi-Maskawa matrix. The propagator for W is
given by:

[tex]\frac{\delta_{\mu\nu}}{p^2+M^2-i\epsilon}[/tex]

So, well, this still hides the complexity. But the interaction term should
be the product of the u-quark spinor plane wave with the W-plane wave
where W- is:

[tex] W^-\ =\ \frac{1}{\sqrt{2}}\left(A^\mu_1-iA^\mu_2 \right)[/tex]

(Weinberg 21.3.13, Volume 2) Where A is from the Yang Mills field. The
interaction can be found in the Yang Mills equivalent of the normal
covariant derivative:

[tex] \def\pds{\kern+0.1em /\kern-0.55em \partial}
\def\lts#1{\kern+0.1em /\kern-0.65em #1}
\lts{D}_\mu \ \equiv\ \pds_\mu - ie\kern+0.25em /\kern-0.75em A_\mu[/tex]

Which in the Electroweak case becomes:

[tex] \def\pds{\kern+0.1em /\kern-0.55em \partial}
\def\lts#1{\kern+0.1em /\kern-0.65em #1}
\left( \pds_\mu - i\kern+0.25em /\kern-0.75em {\vec A}_\mu \cdot {\vec t}_L\right) u[/tex]

Which can be read from the YM Lagrangian (Weinberg 21.3.11) where
t is the isospin. The real task is now to establish if this interaction can
be enough to mostly cancel the rest-mass energy...:blushing:


Regards, Hans
 
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