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It's commonly said that the existence of antiparticles “saves causality”. How? [duplicate]

The way I've always thought about is something like this: If measurements of space and time are essentially indeterminate (indeterminacy principle), then an entity "traveling at less than the speed of ...
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the causality and the anti-particles

How can I quantitatively and qualitatively understand the fact that there is a relevence between the existence of anti-particles and the causality?