3 ms·

Perhaps a better way to say it is that particles are not longer small balls of dirt [1], but a mathematical construction that is useful to generate an infinite

Perhaps a better way to say it is that particles are not longer small balls of dirt [1], but a mathematical construction that is useful to generate an infinite serie [2] to calculate the results. Since in some conditions these mathematical tricks behave very similar to small balls of dirt, we reused the word "particle" and even the names we used when we thought they were small balls of dirt. [11] We probably never thought they were made of dirt, and in any case the magnetic moment is the double of the value of the small ball of dirt model. [2] That has so many infinites that would make a mathematician cry.

cjfd 2y ago
Note that particles are not just for perturbation theory. There is a particle whenever there exists a particle annihilation/creation field configuration. A proton is a particle so writing down its creation/annihilation field configuration is in theory possible, though maybe not in practice. Another point is that infinities do not necessarily make mathematicians cry. Abraham Robinson is quite pleased with them. It seems a possible hypothesis that at least some QFT are mathematically well-defined using non-standard analysis. Where 'some QFT' at least renormalizable and perhaps also asymptotically free. I don't know enough about it to know how the Haag theorem, mentioned in another comment impacts this.
- nine_k 2y ago
  Another analogy (flawed as any of them). Sports teams "exist" in a sense. They meet one another in well-defined interactions, called matches, and such an interaction can be described as if teams were well-defined atomic entities, producing a score. But a sports team is not atomic, not a "final reality" entity. A sports team can pass through one gate, or through several gates, when entering a stadium. From a doctor's perspective, the team "does not exist", a doctor only operates in terms of individual players' organisms.

cjfd 2y ago

Note that particles are not just for perturbation theory. There is a particle whenever there exists a particle annihilation/creation field configuration. A proton is a particle so writing down its creation/annihilation field configuration is in theory possible, though maybe not in practice. Another point is that infinities do not necessarily make mathematicians cry. Abraham Robinson is quite pleased with them. It seems a possible hypothesis that at least some QFT are mathematically well-defined using non-standard analysis. Where 'some QFT' at least renormalizable and perhaps also asymptotically free. I don't know enough about it to know how the Haag theorem, mentioned in another comment impacts this.

nine_k 2y ago
Another analogy (flawed as any of them). Sports teams "exist" in a sense. They meet one another in well-defined interactions, called matches, and such an interaction can be described as if teams were well-defined atomic entities, producing a score. But a sports team is not atomic, not a "final reality" entity. A sports team can pass through one gate, or through several gates, when entering a stadium. From a doctor's perspective, the team "does not exist", a doctor only operates in terms of individual players' organisms.