The fact that we can only calculate probabilities for values of physical quantit

Question

The fact that we can only calculate probabilities for values of physical quantities in quantum measurements means that...

A) radiation and matter are not described by mathematical relations between measurements.

B) the probabilities cannot be calculated from mathematical relationships

C) the results of physical measurements bear no relationship to theory

D) the average values of a large number of measurements correspond to the calculated probabilities.

E) the average of the values calculated in a large number of different theories corresponds to the results of a measurement.

Please Explain - I need to understand this for finals

Explanation / Answer

It is D) the average values of a large number of measurements correspond to the calculated probabilities.

one of the remarkable features of the physical world is that randomness is incarnate, irreducible. This is mirrored in quantum theory by the appearance of a quantity, the wave function, which gives us probabilistic information about the properties of a physical system. As a consequence, there enters into quantum theory many of the concepts that had their origins in the analysis of classical probabilitistic processes, such as the average (or expectation) value of some random quantity, and its standard deviation, or uncertainty. These concepts are defined in exactly the same way in the quantum theory as in classical theory of probability and statistics; it is just the origin of the probability in the first place that is unusual

REFER to LINKS:

http://physics.mq.edu.au/~jcresser/Phys201/LectureNotes/ProbabilitiesExpectationValues.pdf

http://sites.stat.psu.edu/~ajw13/stat200/mos/05_probdistr/05_probdistr_print.html

https://onlinecourses.science.psu.edu/stat200/book/export/html/34

https://en.wikipedia.org/wiki/Expected_value

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