I understand a virtual particle is not technically a particle, but more of a disturbance in a field. I can't seem to wrap my head around the concept and why it has large implications.
Virtual particles are bookkeeping devices which pop up in QFT due to the superposition principle. See also John Baez' explanation :)
"Virtual particles" is a quite misleading term of a mathematically well defined object, known as the Feynman propagator in relativistic perturbative quantum field theory. Also the idea that Feynman diagrams depict scattering processes as if you could think about them like collisions of miniature billiard balls is quite misleading. One should keep in mind their quantum (field) theoretical meaning.
They depict in a very clever way formulas that allow you to systematically calculate S-matrix elements for scattering processes in quantum field theory. The external lines depict asymptotic free states of the incoming and outgoing particles, usually plane-wave momentum eigenstates (which are distributions rather than functions by the way). These states can be identified as specific kinds of particles (say electrons) hitting a detector with a quite sharp momentum and can be counted to get measure a cross section for some process of interest (e.g., elastic electron-electron scattering), which is evaluated in QFT using the S-matrix elements which are written cleverly in terms of Feynman diagrams.
The internal lines stand for propagators. These do not symbolized particles that can somehow be detected in the above sense with real-world detectors. They are just mathematical objects used to evaluate the matrix elements.
To really understand elementary particles you have to study quantum field theory and see how the Feynman rules are derived and which meaning the physical quantities have you can define from them. The Feynman diagrams should be seen as a very clever symbolism to write down complicated formulae rather than pictures of what's going on in real-world scattering processes.
I often use the following analogy. Suppose you have 1 apple. Then you can writeBear with me, I'm only an undergraduate physics student. I think my biggest area of misunderstanding how they can have negative momentum?
I often use the following analogy. Suppose you have 1 apple. Then you can write
1 apple = 2 apples + (-1 apple)
But both 2 apples and -1 apple are virtual apples, the only real thing here is 1 apple. The virtual apples are nothing but a computational tool. Does it help?
Virtual particles are not even a disturbance in a field. They are nothing but a computational tool, not much different from the apples on the right-hand side in the post above.I understand a virtual particle is not technically a particle, but more of a disturbance in a field.
SeeI understand what you are saying, but could you give me an example of where this would happen?
In QFT a "real particle" could be associated with a state in a Hilbert space; technically a "virtual particle" is not a Hilbert space state but an integrated bunch of propagatorsBear with me, I'm only an undergraduate physics student. I think my biggest area of misunderstanding how they can have negative momentum?
that's itVirtual particles arise as mathematical excitations if 'perturbation theory' is used in a calculation.
They have no physical reality, which is why they are called 'virtual'.
If perturbation theory is not used, there are usually no virtual particles.