I What is the difference between virtual and real particles in string theory?

[Souhardya Nandi]

I am reading a bit about them. However, I feel that there is not much difference between them except for the life span. Can you please help me understand the distinction ? Can this be explained on basis of string theory ? Please elaborate.

 

[PeterDonis]

I am reading a bit about them.

What books/papers are you reading?

Can you please help me understand the distinction ?

This question is too broad for a useful discussion. The PF search feature will turn up numerous threads on this topic (in the Quantum Physics forum--please note I have moved this thread there since it is a much better fit). Also there are a number of PF Insights articles on virtual particles. You will be much better able to frame a more specific question if you take some time to work through this material first.

 

[Souhardya Nandi]

What books/papers are you reading?
This question is too broad for a useful discussion. The PF search feature will turn up numerous threads on this topic (in the Quantum Physics forum--please note I have moved this thread there since it is a much better fit). Also there are a number of PF Insights articles on virtual particles. You will be much better able to frame a more specific question if you take some time to work through this material first.

Can you please provide link to a useful PF Insights article ?

 

[vanhees71]

https://www.physicsforums.com/insights/physics-virtual-particles/
https://www.physicsforums.com/insights/misconceptions-virtual-particles/

 

[kimbyd]

Virtual particles stem from quantum scattering theory. Scattering theory uses quantum mechanics to describe what happens when two (or more) particles approach one another from infinity, interact in some way, and then two (or more, possibly different) particles escape to infinity.

There is no currently-known way to solve the equations involved in the process above exactly. So an approximation is used. The approximation goes by the name of "perturbation theory". The idea is to break up the equation which describes the solution into a bunch of smaller pieces which can be solved. Then, adding up those smaller pieces gives an answer.

The interesting bit is that when you start writing down those small pieces, they look like individual particle interactions: an electron/positron pair being destroyed and creating a photon, a photon splitting into a quark/anti-quark pair, etc. But not exactly like individual particle interactions. These apparent particles have many of the properties of real particles, but the relationship between their energy and momentum doesn't make sense for a real particle (it implies that the square of their mass should be negative).

This whole mathematical construction of breaking up the interaction into pieces looks like a description of a mess of possible virtual particle interactions that occur and create the final result when summed together. But there isn't any reason to believe that this mathematical description actually physically describes anything that actually occurs. It is possible (perhaps even likely) that it's just a mathematical trick that happens to look like the creation/destruction of a bunch of virtual particles. There's no way to really be sure unless we can find an exact solution for these interactions.

 

[vanhees71]

Indeed, and of course another ingeneous idea was by Feynman to invent his famous Feynman diagrams. However, one should be aware that they do NOT depict anything going on in nature. The suggestion of the diagrams that quanta are on a worldline in Minkowski diagrams (which are behind the intuitive idea of Feynman diagrams) is highly misleading. E.g., photons, i.e., the quanta of the electromagnetic field do not even have a position observable! So Feynman diagrams should be read as a very efficient notation for the formulas which let you easily organize the evaluation of S-matrix elements (whose square with the appropriate treatment of the energy-momentum conserving $\delta$ distributions let you calculate measurable quantities like cross sections for a given scattering process). The diagram technique has also enabled a lot of other formal progress, most notably the issue of renormalization. E.g., one of the most important results of perturbative renormalization theory, solving the issue of overlapping divergences is the Zimmermann forest formula that summarizes in a very clear way the mathematical results of Bogoliubov, Parasiuk, Hepp, and Zimmermann (BPHZ).

 

[PeterDonis]

The suggestion of the diagrams that quanta are on a worldline in Minkowski diagrams (which are behind the intuitive idea of Feynman diagrams) is highly misleading.

I agree; I've always thought that, if one insists on interpreting the diagrams as diagrams, they were much better interpreted as being in momentum space, not position space. But even that has limitations.

 

[kimbyd]

Indeed, and of course another ingeneous idea was by Feynman to invent his famous Feynman diagrams. However, one should be aware that they do NOT depict anything going on in nature.

Yup. The Feynman diagrams are a graphical representation of the individual pieces that make up the perturbative expansion. They are useful in intuitively grasping how the calculations are done, but are not necessary to do so and may not describe anything that actually happens.

And even if they do (approximately) describe something that actually happens, it most definitely isn't as simple as the creation/destruction of virtual particles.

 

[vanhees71]

I agree; I've always thought that, if one insists on interpreting the diagrams as diagrams, they were much better interpreted as being in momentum space, not position space. But even that has limitations.

Yes, and indeed it was a famous debate between Feynman and Bohr about this point at the Shelter Island conference (see Schweber, QED and the Men who Made It). Bohr didn't like the hand-wavy interpretation as if the diagrams could be interpreted as particle trajectories in Minkowski space (worldlines). Of course, one problem was, that at the time, Feynman had no clear mathematical derivation of his rules but got it right by a lot of intuition. Schwinger was the opposite case: He had a cumbersome formal scheme without intuitive tools like Feynman's diagrams. To the surprise of the participants of the conference they however got precisely the same results. Finally the issue was clarified by Dyson, who gave a derivation for Feynman's ingenious diagrams from the (operator) QFT formalism, pretty much as it is still done today in all textbooks on QFT. Of course, a lot is simplified today by Feynman's other great achievement, i.e., the formulation of QFT in terms of functional integrals (in this case it's not literary a path integral as you can formulate for non-relativistic QT, see Feynman&Hibbs or Kleinert, but a functional integral over field configurations).

 

[Haelfix]

I agree; I've always thought that, if one insists on interpreting the diagrams as diagrams, they were much better interpreted as being in momentum space, not position space. But even that has limitations.

Its rarely done in textbooks, but its actually instructive to try your hand at writing down Feynman diagrams in position space. Some of the singularity structure of the theory is more readily apparent in that context even if calculations become unwieldy. That actually has some applications when people generalize to string theory.

Anyway, there is a sense in which a finite amount of individual diagrams are representative of the real physics. It has been understood for a long time that at least many QFTs diverge like an asymptotic series, which means that after a finite amount of loops, the approximation breaks down and the series ceases to converge. Therefore the approximation is better if it is truncated at that order, which leaves a finite amount of diagrams as being 'the whole thing', whereas the full resummation is likely infinite. It's up to you if you then wish to use that as a heuristic for how you picture physics.

I would say the real problem occurs when you start trying to use the heuristic for strongly coupled non Abelian theories. But well, that's a different story.

 

[bhobba]

Yes, and indeed it was a famous debate between Feynman and Bohr about this point at the Shelter Island conference (see Schweber, QED and the Men who Made It). Bohr didn't like the hand-wavy interpretation as if the diagrams could be interpreted as particle trajectories in Minkowski space (worldlines). Of course, one problem was, that at the time, Feynman had no clear mathematical derivation of his rules but got it right by a lot of intuition. Schwinger was the opposite case: He had a cumbersome formal scheme without intuitive tools like Feynman's diagrams. To the surprise of the participants of the conference they however got precisely the same results. Finally the issue was clarified by Dyson, who gave a derivation for Feynman's ingenious diagrams from the (operator) QFT formalism, pretty much as it is still done today in all textbooks on QFT. Of course, a lot is simplified today by Feynman's other great achievement, i.e., the formulation of QFT in terms of functional integrals (in this case it's not literary a path integral as you can formulate for non-relativistic QT, see Feynman&Hibbs or Kleinert, but a functional integral over field configurations).

Bohr thought Feynman hand-wavy - oh the irony, the irony.

For those that don't know it being clear was not one of Bohr's traits - great physicist he undoubtedly was.

Another interesting aside was when Dyson was presenting his findings, Feynman was in the audience at the back. He of course, being a friend of Dyson's, already knew it so wasn't interested in the content. He simply sat down the back, keeping everyone near him in stitches with jokes. At the end he said - your in Doc - being an obvious reference to the fact Dyson did not like the Phd system and never got one. But with work like that he could have easily applied for, and got, the even higher award DSc - Doctor of Science. But he simply couldn't be bothered, or maybe disliked even that. - who knows:
http://www.itsokaytobesmart.com/post/84141275467/freeman-dyson-rebel-without-a-phd

This is the type of thing Feynman would have loved - he would have enjoyed saying - hey buddy even I know that and I don't even have a PhD. I think Feynman envied Dyson a bit in that regard.

I also love:
We should try to introduce our children to science today as a rebellion against poverty and ugliness and militarism and economic injustice.

True - but the clarity of thought science engenders just might help solve those problems as well.

Thanks
Bill