Posted: Sep 26, 2011 9:09 am
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"?
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!
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?
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.
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.
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?
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 ?
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.
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.
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.