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Well, I am pleasantly proven wrong, thanks! Yes, I was thinking of general relativity, you are correct.
Are you saying that the particles are oscillating in reaction to your hand bouncing the mesh, like a handful of marbles on a bed bouncing around? What constitutes a "hand push" in the real world? A high energy collision like at the LHC? Or day to day interactions between objects?
This is very fascinating, although I can't help but see a similarity between the two canvases. Is that just because they are both so complex that we need simple analogies to try and wrap our heads around the concepts?
No, the analogy is more that the oscillations are themselves the particles.
The addition of energy into a system would be this hand push. The fact that the particles themselves exist means that they are oscillations in this mesh (with some energy/frequency). Interactions with other particles can add or remove energy.
Definitely these canvas metaphor are just conveniences. Also, I got it from Zee’s “Quantum Field Theory in a Nutshell” which is a standard graduate or advanced undergrad level book on QFT.