[aroberge]

(Apologies to Quantum Field Theorist for the gross simplification below.)

I'm going to assume you know about basic calculus and Taylor series; if not, I'll explain what these are in a subsequent answer if you are interested.

In Quantum Field Theory, we cannot do exact calculations ... only (better and better) approximations. The way we do these calculations is very much similar to doing a Taylor series in Calculus. However, the calculations involved many complicated multi-dimensional integrals

Feynman found out a way to represent these complicated mathematical expressions that occured in those approximate calculations as pictures (known as Feynman diagrams). In these pictures, one could represent (real) particles interacting as lines (straight, curvy, etc., depending on the rules) that end in open space..

As we increased the order of expansion in the approximation (think of powers of the variable in a Taylor series), the terms corresponded to more and more diagrams, each increasing in complexity with the order of expansion.

Well, it turned out that, using the Feynman rules for translating mathematical expressions into parts of a pictures, that lines (straight, curvy) similar to that of "real" particles appeared inside the diagrams; however, these lines were all connected to others and did not end in open space: they do not correspond to any particles that we can measure directly.

However, we can think of these lines as representing "virtual" particles, that we cannot probe directly.

One thing to keep in mind (and that many that mention the "virtual particle" explanations often forget to mention): these diagrams are, in a very strong sense, an artifact of the way we do calculations using the best approximation techniques we know. These are useful computational tools. But individual diagrams should not be thought of as representing an actual precise interaction that is taking place. And virtual particles are just a way to make a connection between what we think we know ("real" particles interacting) and what our approximative way of calculating things give us.

[randomguy1254]

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?

[aroberge]

Let me answer your question first very obliquely. We know that we can represent the sine function near x=0 as the following Taylor series:

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

[randomguy1254]

Very interesting, good analogies and information for me to think about.