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by randomguy1254
3484 days ago
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Thanks! That's an interesting fact about Feynman diagrams. If we had a hypothetical machine which could perform these calculations with infinite precision, would the "virtual particles" disappear from the diagram, or is it impossible to know this? |
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sin(x) ≈ x - x^3 / 6 + x^5 / 120 - ....
With more and more terms, we can can calculate it more and more precisely. Does this means that this function really contains all of these powers of x?
Well, suppose we want to calculate sin(pi/2) (angle in radians, which is required for the Taylor series). We know that it is exactly 1. There are no powers of (pi/2) appearing in "1". The Taylor series gives us a convenient way to calculate the value of the function (technically: inside a radius of convergence), but it is not the same as the function itself.
Now, to give an example from Quantum Field theory: let me quote from a wikipedia page [1]:
_In a perturbative approach to quantum field theory, such interactions may require the calculation of hundreds of Feynman diagrams. In contrast, twistor theory provides an approach in which scattering amplitudes can be computed in a way that yields much simpler expressions._
So, these hundreds of Feynman diagrams would lead us to think of many virtual particles describing an interaction. The Amplituhedron type of calculation is done completely differently, in a way that does not lead one to think of interactions through virtual particles.
Now to answer your question: I do believe that, if we were smart enough to find a way to compute things exactly, "virtual particles" would not appear as intermediate steps of computations. But, then again, to be perfectly honest, the same would likely be of "real" particles which are just a convenient way of thinking of excitations in quantum fields ...
[1] https://en.wikipedia.org/wiki/Amplituhedron