It may be interesting that although all measurable results in quantum theory are in the form of probabilities there is at least one instance where this theory predicts a certain result. If the same measurement is immediately made a second time on a quantum system the second result will be the same as the first with probability 1. In other words the state of the quantum system revealed by the first measurement is confirmed by the second measurement. It may seem odd that the theory predicts the result of the first measurement as a probability distribution of possible results but predicts only a single possible result for the second measurement.
Wojciech Zuruk considers this as a postulate of quantum theory (see his paper quantum Darwinism ). (sorry for the typo in the quote).
Postulate (iii) Immediate repetition of a measurement yields the same outcome starts this task. This is the only uncontroversial measurement postulate (even if it is difficult to approximate in the laboratory): Such repeatability or predictability is behind the very idea of a state.
If we consider that information exchange took place between the quantum system and the measuring device in the first measurement then we might view the probability distribution implied by the wave function as having undergone a Bayesian update on the receipt of new information. We might understand that this new information moved the quantum model to predictive certainty regarding the result of the second measurement.
Of course this certainty is only certain within the terms of quantum theory which is itself falsifiable.
I fail to discern your point, here; sorry. Specifically, I don’t see what makes this more interesting in context than my expectation, within the limits of precision and reliability of my measuring device, that if I (e.g.) measure the mass of a macroscopic object twice I’ll get the same result.
Yes, good point. Classical physics, dealing with macroscopic objects, predicts definite (non-probabilistic) measurement outcomes for both the first and second measurements.
The point I was (poorly) aiming at is that while quantum theory is inherently probabilistic even it sometimes predicts specific results as certainties.
I guess the important point for me is that while theories may predict certainties they are always falsifiable; the theory itself may be wrong.
It may be interesting that although all measurable results in quantum theory are in the form of probabilities there is at least one instance where this theory predicts a certain result. If the same measurement is immediately made a second time on a quantum system the second result will be the same as the first with probability 1. In other words the state of the quantum system revealed by the first measurement is confirmed by the second measurement. It may seem odd that the theory predicts the result of the first measurement as a probability distribution of possible results but predicts only a single possible result for the second measurement.
Wojciech Zuruk considers this as a postulate of quantum theory (see his paper quantum Darwinism ). (sorry for the typo in the quote).
Postulate (iii) Immediate repetition of a measurement yields the same outcome starts this task. This is the only uncontroversial measurement postulate (even if it is difficult to approximate in the laboratory): Such repeatability or predictability is behind the very idea of a state.
If we consider that information exchange took place between the quantum system and the measuring device in the first measurement then we might view the probability distribution implied by the wave function as having undergone a Bayesian update on the receipt of new information. We might understand that this new information moved the quantum model to predictive certainty regarding the result of the second measurement.
Of course this certainty is only certain within the terms of quantum theory which is itself falsifiable.
I fail to discern your point, here; sorry. Specifically, I don’t see what makes this more interesting in context than my expectation, within the limits of precision and reliability of my measuring device, that if I (e.g.) measure the mass of a macroscopic object twice I’ll get the same result.
Yes, good point. Classical physics, dealing with macroscopic objects, predicts definite (non-probabilistic) measurement outcomes for both the first and second measurements.
The point I was (poorly) aiming at is that while quantum theory is inherently probabilistic even it sometimes predicts specific results as certainties.
I guess the important point for me is that while theories may predict certainties they are always falsifiable; the theory itself may be wrong.
Ah, I see. Yes, exactly… the theory may be wrong, or we have made a mistake in applying it or interpreting it, etc.