- #36
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I never ever use the word "real" or "reality" in this context since it's not well-defined. I mean, what I wrote: If I have prepared a system in a state, of the formDemystifier said:
$$\hat{\rho}=\sum_{\beta} p_{\alpha,\alpha'} |a,\alpha \rangle \langle a,\alpha'|, \quad p_{\alpha,\alpha'}=p_{\alpha',\alpha}, \quad p_{\alpha,\alpha} \geq 0, \quad \sum_{\alpha} p_{\alpha,\alpha}=1$$
where ##|a,\alpha \rangle## is a CONS of eigenstates of the self-adjoint operator ##\hat{A}## with eigenvalue ##a## (labelled with an appropriate set of parameters ##\beta##), then the value of the observable ##A##, represented by the operator ##\hat{A}##, is determined to be ##a##. With any proper measurement, I'll find this value ##a## with certainty (as Born's rule tells you).
Concerning any other observable ##B##, represented by the self-adjoint operator ##\hat{B}## with CONS of eigenstates with eigenvalues ##b##, ##|b,\beta \rangle##, the probability to find the value ##b## when properly measuring ##b## is given by
$$P(b|\hat{\rho})=\sum_{\beta} \langle b,\beta|\hat{\rho}|b,\beta \rangle.$$
That's it. QT doesn't imply more but also nothing less. That's also all you need as interpretation of the formalism in order to describe what's observed in the lab/nature (from the point of view of physicists).
QT is incomplete as we don't have a valid description of the gravitational interaction.