Posted: Sep 29, 2011 7:40 am
zaybu wrote:twistor59 wrote:
A model is just something that allows us to make predictions. In this case, the prediction is about the behaviour of the outgoing particles in response to the incoming particles. Its connection with the physical world is through the in-states and out-states, nothing else.
We can say the same about spin. We never see it, just a beam of electrons that separates into two in a Stern-Gerlach experiment. Are you saying that spin is not a reality, just a mathematical gimmick? How about the W's and Z bosons, those also aren't directly observed? What about the gluons and quarks, none of these "particles" are directly observed, are they also mathematical "gimmick"? Why bother pursuing the Higgs boson, since it would be just another mathematical "gimmick"?
You, not me, introduced the word "gimmick", which implies a trivialization. I've used "calculational device".
No, spin is a property of real particles, which we can measure in the laboratory. I repeat: real particles are represented in the In and Out states of the scattering process. They are the ONLY things which are measurable. The virtual particles in the perturbation expansion cannot be measured. What can be measured is the scattering cross section given, to a very good approximation, by summing the contributions of the diagrams at successively increasing order. What cannot be measured are the individual contributions to the cross section.
Feynman in an interview with Charles Weiner:
Feynman: I probably made diagrams to help me think about perturbation expressions. It was probably not any specific invention but just a sort of shorthand with which I was helping myself think, which gradually developed into specific rules for some diagrams.
Weiner: For helping you think physically ? In other words, you wher seeing in physical-
Feynman: No, mathematical expressions. Mathematical expressions. A diagram to help write down the mathematical expressions.
zaybu wrote:
Einstein's E=mc2 also comes from an approximation. We nevertheless see that as something describing a real phenomenon. Most of the stuff we get from theory were reached through approximations. Very, very few results were ever obtained through an exact solution, and science would be the poorer if we demand that only exact solutions are valid.
The fact is: each of the Feynman diagrams requires a precise formulation base on the number of straight lines, vertices, wiggling lines, incoming and outcoming lines. If those interactions don't represent the real McCoy, I wonder what does, certainly not the wave model!zaybu wrote:twistor59 wrote:
The point I'm trying to make is that If we had a model that we could solve exactly, the word "virtual particle" would never have existed. If we could find a way of solving for S in terms of the incoming and outgoing momenta and spins
Are you saying that E=mc2 doesn't reflect reality because it comes from an approximation?
I'm saying that the output of the calculation (the scattering cross section) connects with what can be measured, but that there is no reason to suppose that the "internals" of the calculation do. In fact they most definitely cannot.
zaybu wrote:twistor59 wrote:
Just because the approximation method is very good, it doesn't mean that the ingredients in the approximation method are physically real.
In this case, the calculation is based on the precision of how the interaction takes place, which assumes the exchange of particles in a very specific way.
No, "assumes the exchange of particles" is an interpretation of the mathematics. The calculation is based on the perturbation expansion involving the QED vertex terms ΨbarγμΨAμ and the free particle electron and photon propagators.
zaybu wrote:twistor59 wrote:
If you want to, you can do classical mechanics as an approximation using feynman diagrams. If the physical world were classical, would this imply that that the elements of the approximation would have any physical basis ? No, because we know that we can solve the equations exactly in some cases, or use a variety of different approximation techniques.
There is a similarity between perturbation in classical physics and in QFT, but the two are very far apart.
For instance, we use the Hamiltonian in both Classical physics and QFT, but they represent altogether different things. In QFT, H is an operator on the the Hilbert states. It is also the operator that appears in the time evolution operator, making unitarity one of the fundamental requisite of QM. None of that is to be found in classical physics. There are similarities, but also differences.
That's not relevant to the argument. I presented the classical mechanics argument to counter your stance that just because an approximation gives highly accurate results, the internals of the approximation must have some basis in reality.
Give me a square integrable function and I can expand it in terms of sinusoids, or if I feel so inclined, I can expand it in Walsh functions. Which is the "real" one ? They're just different ways to do the approximation.
zaybu wrote:
Each order has a smaller and smaller probability to happen. It doesn't mean that they don't happen. Remember QM, and by extension QFT, is a theory about probabilities from the start. Are we to say that then, being just probabilities, it doesn't describe reality?twistor59 wrote:No indeed, the probabilities represent the best that can be stated about the system, even in principle. (I'm not a hidden variables person).
Do you see what I'm saying though ? In this perturbation scheme, which works very well, to get the full answer you'd have to add ALL orders:
The answer = (diagrams of order α2) + (diagrams of order α4) + .......
Do you see the problem ?zaybu wrote:
The mathematics is always based on a model. When Einstein predicted that light from a star would deflect as it passes near the sun, he based that calculations on a model: that space-time is curved. Do we ever observe this curvature? No, we don't, what we do see is that light does bend, and so we accept the model as such.
Do we ever observe this curvature ? Yes of course, we can measure the components of the metric tensor, which uniquely determine the curvature. We just need rods and clocks. The curvature is thus a measurable quantity. Virtual particles are not, even in principle, measurable. For this reason, I am reluctant to attach terms such as "real" or "physical" to them.
zaybu wrote:
Each term in the perturbation series is based on a model: that particles are exchanged -- in QED, it is the photons; in QCD, it is the gluons; in the electro-weak theory, the W's and Z bosons. And this model is the best there is to explain what's going on. It's not just a fluke or a mathematical gimmick. The evidence supporting that model is overwhelming.
Again - I never introduced the word "fluke" or "gimmick" to the conversation. QED perturbation theory is a model par excellence. However it only makes contact with measurements though the in and out states. You can't, with any certainty, ascribe elements of reality to the internals of the calculation, although this helps with visualization and, as Feynman says, organizing the mathematics. It also helps sell books with popularizations of physics.
zaybu wrote:
It turns out that this approximation method gives an insight into nature better than any other mathematical "gimmick". Besides, no one has ever solved that equation exactly, perhaps that is an indication that the approximation method is the only real deal, and looking for an exact solution is like chasing ghosts.
Ah well, this is an interesting question. QED currently is currently formulated as a perturbative theory from the outset. But even if we were to say that it can only be formulated perturbatively (i.e. no non-perturbative formulation will ever be found), there is a problem:
Scattering amplitude = (contributions from diagrams of order α2) + (contributions from diagrams of order α4) +....
To get the "true" answer, we have to add the contributions of diagrams of all orders. Unfortunately that appears to give infinity.