What is wrong with the following proof: Theorem Quark transformation is impossible. Proof: Assume a quark can transform. A particular quark exists: top and this transforms into an anti-b quark while emitting a W-. Then the intermediate state exists: t-anti-b-W- / t-W-anti-b. This is impossible since a t quark is a fundamental particle. Similar reasoning holds for the other qaurks and antiquarks. Alternatively this is circumventable by assuming there is no intermediate state: the t exists and the next instant (one planck time) the W- and anti-b exists. Then there is no causal link between the t and anti-b so the reaction couldn't have happened. QED.
This sounds like another case of Zeno's Paradox. If everything is instant, and there's nothing between, then nothing can ever happen to anything, anywhere. Here's an idea to chew on: Quarks, though fundamental, do interact with other particles (neutrinos, for example). A particle interaction can lead to a quark transformation without an intermediate stage. Here's another idea to chew on: What you are grappling with is a very broad problem that strikes at the very heart of the incompatibility between QM and GR. If discrete particles of zero size interact, you get infinities. That's where string theory come in. Fundamental particles are comprised of 1-dimensional strings, whose interacting cross sections make these impossible transitions possible.
I don't think I'll get away with believing quark transformations being impossible. But quark transformations violate Quark Conservation, which I think holds.
The causal link is that the weak interaction created a W- boson, simultaneously changing the top quark into an anti-bottom.
Why should there not be a transitional state, just as there is during the absorption of a photon by an electron in an atom? In that case, one uses the time-dependent form of the Schrödinger equation to model the change from one electron orbital state to another over a finite (though very short) period of time, under the perturbing influence of the electric vector of the photon's wave. Nobody contends it is instantaneous. No doubt the QM of quark interactions will be a lot less well developed, since it is very hard to do experiments that get at the underlying process, but that does not mean such processes do not occur.
I had started using the same example - a photon being absorbed by an electron and jumping to an excited state, but I realized that's not the same thing as a particle changing into another particle, so I didn't complete it. But I agree with you - in QM, everything is mediated by particles. No reason why one quark couldn't change into another by absorbing or emitting a particle.
I don't see what is wrong with the analogy. A photon is a particle constituted by a disturbance in the EM field, whereas other particles are disturbances in other fields. At all events, none of these interactions between QM entities is modelled as instantaneous, which was really my point. Things evolve into other things via a transitional process that can in principle be described mathematically.
There's nothing in between says the Feynman diagram. It also says the reaction happens instantaneously.
Can you show me a source for your claim that the processes depicted in a Feynman diagram occur instantaneously? I think you have made this up and that it is not true.
It looks more or less like this (time goes left-right, space goes up-down): ……………..._______>W- t >_____| ……………..|_______<anti-b just with the up-down line contracted into a vertex and the dots deleted.
There is a law of conservation of mechanical energy. In the quark transformation process mechanical energy is destroyed and a different kind of mechanical energy is created.
I know what a Feynman diagram looks like. My point is that the diagram on its own says nothing about the time taken for the changes depicted to take place. So where do you get this idea that the changes must be instantaneous? Other quantum interactions e.g. those between electrons and phtons, are not. So what makes you think that these processes are?
Don't know if this will help: "the top quark has a very short lifetime".....bottom of page 2 Top quark pair decays......Figure 3 http://mafija.fmf.uni-lj.si/seminar/files/2011_2012/Seminar_-_Top_Quark-1.pdf
There is an error in my posts: "anti-b" must be replaced by "b". Feynman diagrams are for counting the number of ways an interaction can happen so I don't think it is accurate in the time taken for an interaction. All interactions should take a finite time to happen because space must do a computation first.