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Answer by Ponder Stibbons for In neutrino absorption, what is it really that absorbs the neutrino?

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It could be said that in proton + neutrino = neutron + electron, an up quark in the proton is converted to a down quark in the neutron, using up 2.2 Mev. But also leaving us short on 1 electron charge. Another 0.5 Mev gives us the electron which also collects the charge. In this sense, the energy of the neutrino is distributed to both of the products of the particle interaction. But, the proton could also have had kinetic energy that it brings to the reaction. It is not possible, on the current theory, to track explicitly the energy that was originally in the proton or the neutrino and see where it went after the reaction, and that question might have no meaning. Energy is not particles, it is more just a number that is conserved. Compute it before and compute it after, it is the same.

The same question could be asked of a collection of pulleys and weights. Two weights move down and two weights move up. But, the theory does not say where the energy of the original two weights went, only that the total over all the weights is unchanged.

Addendum:

If one insists on having an energy operator and applying it to the fields, then one has an energy density, and coupling this with a momentum operator, an energy flux. In principle one could then follow the stream lines of the energy flow and determine in a sense, by putting a surface around a region and calling it the neutrino, where the energy had gone. In this case, I would expect that it depends on the details of the geometry of the specific interaction.

Compare with the idea of lowering one weight first and raising one at the same time, and then lowering the second weight and raising the second in the previous example. Arguably, in this case the 1st lowered weight energy went to the 1st raised weight. But this conclusion depends on the details of the particular instance of the reaction.


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