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When we look at at a relativistic collision like compton scattering or decay of the Higgs particle, we treat the colliding particles literally as particles following a definite trajectory and scattering with some definite angle. These collisions are treated using relativistic conservation of energy and momentum.

But in quantum mechanics, particles are described by their state vector in the Hilbert space, and do not collapse to be localized particles unless their positions are measured. My question is then: how can we treat these collisions like they are billiard balls, when in reality the particles are wavefunctions and only measurement should result in particles being observed?

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  • $\begingroup$ "do not collapse to be particles unless their positions are measured" There is no such thing as collapse. $\endgroup$ – my2cts Dec 15 '19 at 9:30
  • $\begingroup$ What do you mean? @my2cts en.wikipedia.org/wiki/Wave_function_collapse $\endgroup$ – SRS Jan 1 at 17:38
  • $\begingroup$ Using energy-momentum conservation does not mean that particles are moving in a definite trajectory. $\endgroup$ – SRS Jan 1 at 17:39
  • $\begingroup$ @SRS There is no such thing as wave function collapse as a process, unlike what is suggested in the wikipedia article. The article also does not stress that the collapse concept is interpretation related and does not place it in a broader context. Personally I prefer the ensemble interpretation over CI. $\endgroup$ – my2cts Jan 1 at 17:55
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how can we treat these collisions like they are billiard balls,

They are not treated as billiard balls. In scattering theory, all the mathematics is based on co-variance to Lorenz transformations. The incoming and outgoing are wavefunctions,

Because the solutions have to be Lorenz covariant by construction one is able to use energy and momentum and angular momentum conservation for simple cases, as in the decay of a single particle, or conservation of energy and momentum in individual interactions.

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