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-   -   2 questions - virtual particles and quarks? (http://www.physicsforums.com/showthread.php?t=402864)

rasp May12-10 06:59 PM

2 questions - virtual particles and quarks?
 
1) In non-mathmatical terms, please correct my description of vitual particles...

a) virtual particles are real but too small to be observed directly. i.e. their dimensions are within Plank's values and subject to Heisenberg's uncertainty principles.
b) virtual particles are real mathematically in that their presense satisfies the theory but like individual quarks they do not exist individually and independently and cannot be observed.
c) virtual particles are real and their role can be deduced by their effect on other elementary particles.

2) How do those in the know explain the concept that the quark is considered an elementary particle which doesn't exist independently? It seems to me frought with contradiction, analogous to a number system in which the number 1 is not defined.

ansgar May13-10 02:09 AM

Re: 2 questions - virtual particles and quarks?
 
non of them are correct

virtual particles are only a calculation artefact due to perturbation theory. if we could calculate scattering amplitudes etc without perturbation theory, we would not need them.

physics is independent on which way we choose to calculate things

chrispb May13-10 07:10 AM

Re: 2 questions - virtual particles and quarks?
 
Electric fields are made up of virtual photons.

humanino May13-10 07:24 AM

Re: 2 questions - virtual particles and quarks?
 
Quote:

Quote by chrispb (Post 2715480)
Electric fields are made up of virtual photons.

Sure, that's why Faraday and Maxwell could not understand electric fields.

ansgar May13-10 09:46 AM

Re: 2 questions - virtual particles and quarks?
 
Quote:

Quote by chrispb (Post 2715480)
Electric fields are made up of virtual photons.

are they? how do you know that? from perturbation theory?

tom.stoer May13-10 03:45 PM

Re: 2 questions - virtual particles and quarks?
 
Quote:

Quote by ansgar (Post 2715318)
virtual particles are only a calculation artefact due to perturbation theory. if we could calculate scattering amplitudes etc without perturbation theory, we would not need them.

Exactly. This becomes clear if one quantizes a theory non-perturbatively (unfortunately this is not always possible). The formalism is completely different and does not use virtual particles (free propagators) at all.

Btw.: mathematically a virtual particle is not a single particle but "a rule how to integrate over an infinite number of particles".

rasp May14-10 03:40 PM

Re: 2 questions - virtual particles and quarks?
 
Can you clear up my confusion about the single quark?

Quote:

Quote by rasp (Post 2714956)
that the quark is considered an elementary particle which doesn't exist independently? It seems to me frought with contradiction, analogous to a number system in which the number 1 is defined but doesn't exist.

thanks for the answers on virtual particles

humanino May14-10 04:04 PM

Re: 2 questions - virtual particles and quarks?
 
There are many difficulties associated with "Well identified non-flying objects" as Dokgarbagezer once called them.

Now the way you describe it makes it difficult to answer specifically. I could argue that nothing really "exists independently". Until an interaction has occurred, the evolution operator (or S matrix) reduces to identity operator in a mixed basis.

Can you exhibit a specific contradiction you encounter with the concept of confined particle ?

guerom00 May14-10 04:06 PM

Re: 2 questions - virtual particles and quarks?
 
Quote:

Quote by chrispb (Post 2715480)
Electric fields are made up of virtual photons.

Hmmm… :biggrin:

Virtual particles are associated with fluctuating quantities. The well known example are virtual photons from the EM vacuum : the vacuum state of the electromagnetic field contains, as its name state, zero photon. 0 is an eigenvalue of the number operator (a^+ a) i.e. (a^+ a) |0> = 0 |0>. Problem : the vacuum state |0> is _not_ an eigenstate of the operator (a^+ a)^2. So, to recap, the mean value of the number of photon in the vacuum state is 0 <N>=0 _but_ the mean value of the square of the number of photon is not zero <N^2>≠0. That means its variance is not zero therefore this quantity fluctuates.
Long story short : it means that in the vacuum state |0>, the number of photon (as well as the electric field, the magnetic field, etc…) fluctuate around its mean value which is zero.
What does that mean : You have an EM vacuum. It contains _a mean value_ of zero photon. It means that from time to time, it will contains 1 or 2 or 3, etc… photons. Those photons arising from the mere fluctuations of the number of _real_ photons (which is zero in the vacuum state) are those virtual photons.
For all intented purposes, virtual particles are merely particles which exists for a limited time before dissapearing. :smile:

ansgar May14-10 04:59 PM

Re: 2 questions - virtual particles and quarks?
 
Quote:

Quote by guerom00 (Post 2717531)
Hmmm… :biggrin:

Virtual particles are associated with fluctuating quantities. The well known example are virtual photons from the EM vacuum : the vacuum state of the electromagnetic field contains, as its name state, zero photon. 0 is an eigenvalue of the number operator (a^+ a) i.e. (a^+ a) |0> = 0 |0>. Problem : the vacuum state |0> is _not_ an eigenstate of the operator (a^+ a)^2. So, to recap, the mean value of the number of photon in the vacuum state is 0 <N>=0 _but_ the mean value of the square of the number of photon is not zero <N^2>≠0. That means its variance is not zero therefore this quantity fluctuates.
Long story short : it means that in the vacuum state |0>, the number of photon (as well as the electric field, the magnetic field, etc…) fluctuate around its mean value which is zero.
What does that mean : You have an EM vacuum. It contains _a mean value_ of zero photon. It means that from time to time, it will contains 1 or 2 or 3, etc… photons. Those photons arising from the mere fluctuations of the number of _real_ photons (which is zero in the vacuum state) are those virtual photons.
For all intented purposes, virtual particles are merely particles which exists for a limited time before dissapearing. :smile:

according to perturbation theory yes

guerom00 May14-10 05:38 PM

Re: 2 questions - virtual particles and quarks?
 
Virtual particles have nothing to do with perturbation theory. As I've said, they merely are the manifestation of fluctuating eigenvalues of the particle number operator. :smile:

ansgar May15-10 02:22 AM

Re: 2 questions - virtual particles and quarks?
 
Quote:

Quote by guerom00 (Post 2717640)
Virtual particles have nothing to do with perturbation theory. As I've said, they merely are the manifestation of fluctuating eigenvalues of the particle number operator. :smile:

show please

guerom00 May15-10 10:58 AM

Re: 2 questions - virtual particles and quarks?
 
Show what ?
You are thinking of the virtual particles used in the Feynman diagrams I guess… Those are different things; those are indeed purely mathematical artifacts. :smile:

ansgar May15-10 11:00 AM

Re: 2 questions - virtual particles and quarks?
 
Quote:

Quote by guerom00 (Post 2718453)
Show what ?
You are thinking of the virtual particles used in the Feynman diagrams I guess… Those are different things; those are indeed purely mathematical artifacts. :smile:

can you show this fluctuations of the eigenvalues for the number operator?

humanino May15-10 11:35 AM

Re: 2 questions - virtual particles and quarks?
 
Quote:

Quote by ansgar (Post 2718454)
can you show this fluctuations of the eigenvalues for the number operator?

Non-perturbatively of course...

guerom00 May15-10 12:09 PM

Re: 2 questions - virtual particles and quarks?
 
It does not commute with the Hamiltonian I guess.
This is a very general idea : each time you have an eigenvalue of whatever operator, you have to ask yourself whether this eigenvalue will fluctuate or not. One way is to see whether it commutes with the Hamiltonian or calculate its variance.

ansgar May15-10 12:22 PM

Re: 2 questions - virtual particles and quarks?
 
Quote:

Quote by guerom00 (Post 2718534)
It does not commute with the Hamiltonian I guess.
This is a very general idea : each time you have an eigenvalue of whatever operator, you have to ask yourself whether this eigenvalue will fluctuate or not. One way is to see whether it commutes with the Hamiltonian or calculate its variance.

you GUESS??

I can show you that the particle number operator indeed commutes with the hamiltonian, that is a basic exersisce in canonical quantization of fields...

humanino May15-10 12:29 PM

Re: 2 questions - virtual particles and quarks?
 
Maybe I misunderstand, it seems to me I only know how to define the number operator perturbatively. Say on the lattice, I have a field configuration, if I want to define an occupation number, I need to decompose the field into appropriate modes, and I will claim I know the occupation of each mode once my decomposition (in some sense) approximates the configuration well enough. But the number operator is not necessary a priori on the lattice, neither is it defined non-perturbatively. For instance, I can get arbitrary high mode if I request arbitrary high precision.


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