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Can particles actually pop out from vacuum and annihilate each other? Or is it just a mathematical trick?

ATR
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There are no perfect Euclidean spheres in reality, yet we use them as models for things in physics. Mathematical objects are the products of human imagination. They are not real. Every application of mathematics to physics is a "trick".

Carefully selected mathematical objects sometimes prove to be excellent representations of reality. But the reality lies in physics experiments and observations, not in the mathematics. The math of vacuum fluctuations has been checked by experiments like the Lamb-Retherford experiment, and found to be a good match to reality.

Nothing in your physics textbook actually happens: it's all models. Want reality? Go do experiments.

John Doty
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