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To chime in on the probabilities issue: they aren’t really probabilities. Probability amplitudes are something we don’t really understand, but it is true that
by randomsearch 9y ago
To chime in on the probabilities issue: they aren’t really probabilities.
Probability amplitudes are something we don’t really understand, but it is true that once we have set a basis for measurement, we can treat the amplitudes with respect to that basis as probabilities (written in complex form).
However, this should not be interpreted as “quantum states are probabilistic mixtures of base states” - changing the measurement basis screws up that intuition. For example, if our new basis has one base vector that is equal to the quantum state we are measuring, suddenly our outcome is certain.
Oh I wish I could explain this better.
- sundarurfriend 9y agoI feel like that explanation almost gets me there, but understanding it is just out of reach. Out of my many questions (for which I should probably seek books and videos), I'll ask this one: > changing the measurement basis screws up that intuition. For example, if our new basis has one base vector that is equal to the quantum state we are measuring, suddenly our outcome is certain. How does one change the measurement basis - is it a mathematical exercise done on paper, or is it an actual physical act? Is this what is meant by collapse of a wave function? Is this what we are doing when we 'measure' Schrodinger's cat at the end of the experiment and suddenly have a certain outcome?
- randomsearch 9y agoDifferent measurement instruments have different bases. But we can also model our quantum system and imagine what would happen if we created a new instrument with any basis we choose. Measurement is indeed wave function collapse - when a quantum state in a superposition (with regards to our measurement basis) is measured and produces a definite answer.