What is 'reality' in physics? I’m trying to find a definition of reality that fits with current mainstream physics but avoids any subjectivity (as with the idea that ‘consciousness causes collapse’, or with the ‘many worlds’ idea that the observable universe is just the branch we happen to have ended up in).
My thought was that it is the eigenstates, particularly of electrons in atomic orbitals, that we typically measure, and it is the odd (in quantum mechanical terms) definiteness of their energy which gives form to the world as we know it. So could I define reality like this?
‘Reality’ is a privileged set of eigenstates of the wave functions of charged particles in potential energy wells (i.e. stationary states) evolving stochastically in conformity with certain conditions – probability amplitudes, conservation of momentum and energy, increase in entropy etc. – beginning with the Big Bang.
The thought is that it is this privileged set of eigenstates which constitutes the real world and differentiates what is actual (and so capable of being seen or measured) from what is possible, as represented by the other parts of the wave function. (I think this idea is similar to Heisenberg’s idea of quantum objects as ‘potentia’ – https://arxiv.org/ftp/arxiv/papers/1709/1709.03595.pdf.)
Obviously I know that the wave function is also ‘real’ – I’m not disputing that. But to account for the world as we experience and measure it we seem to need an idea of reality in another more concrete sense – the one actual world from amongst the various possible worlds which exist in superposition in the wave function. Hence the idea that while the wave function is real, the eigenstates we can measure are ‘more real’ (which is why we can measure them). (I find it a basic weakness of the many worlds interpretation that it does not account satisfactorily for the fact that we only experience and measure one world, and the idea that there are many worlds all equally as real as each other contravenes the probabilistic nature of the wave function and the conservation laws it reflects.)
The ‘real’ set of privileged eigenstates interacts with the wave function in both directions: the probability amplitude of the wave function defines the probability of the eigenstates’ stochastic evolution, and the eigenstates define the normalisation framework of the wave function probability amplitudes (i.e. their evolution triggers wave function collapse – this differentiates the idea from Bohm’s hidden variables/pilot wave theory, which denies collapse, as well as suffering from a number of other well-known problems).
Can anyone see any problems with this from a physics point of view? In particular, is there any reason to think that electrons can ‘actually’ be in multiple eigenstates at once? I know that the wave functions of electrons in excited states evolve continuously into lower states reflecting the probability of spontaneous decay, but I also understand that when their states are measured they still give their excited state (until they decay) without affecting the probability evolution, and the quantum Zeno effect doesn’t kick in until measurements become frequent enough to disrupt the wave function evolution itself (see Quantum Zeno effect and unstable particles). This seems to suggest that the 'real' electron and its energy state is empirically distinguishable from the wave function and its probability amplitude.
I should be clear that I'm not trying to propose some new theory here, I'm just trying to understand what reality is from the point of view of current mainstream physics e.g. what Heisenberg meant by characterising quantum phenomena as potentia.
 A: I think your last paragraph is mistaken. If a state $|\mathrm{excited}\rangle$ evolves into $\frac{1}{\sqrt{2}}(|\mathrm{excited}\rangle+|\mathrm{decayed}\rangle)$ and you measure it in $|\mathrm{excited}\rangle$, it is now in state $|\mathrm{excited}\rangle$ and has to evolve all the way back to the decayed state from the beginning. The net rate of decay depends on the measurement frequency, sure, but this always happens! There is every reason to think electrons can be in multiple energy eigenstates at the same time and no reason not to think so.
I'd also say that with an agnostic view of the "many worlds interpretation" (which is, we can have a wavefunction $|\psi\rangle$ or a superposition of many 'universes' $\sum c_i|\psi_i\rangle$ - a totally unobjectionable claim) we can still explain how each of the "universes" evolve, and phenomena like decoherence help explain measurement without the measurement axiom for the most part.
The only definition of "reality" that can be argued is that we're homo sapiens sapiens, we have eyes and ears and hands, we scribble things on paper, and sometimes those things have a bearing on the things that come to us through our eyes/ears/hands. Some of our pen scribblings known as "classical mechanics" are known to not reflect reality, but people still have a very hard time letting go of concepts like "classical information" and "classical state" to the point where people sometimes equate "classical state" with "reality".
The real point being is that physics is empirical and nothing more. Pilot wave theory and the von Neumann "axioms" already exist and give identical predictions. If we say one is correct or "real" and one is incorrect or "not real", we're no longer doing physics, we just have bad or good taste.
A: There are very strong reasons to think that quantum superposition is a real phenomenon.
What you are proposing is a brand of hidden variable theory, that is the idea that there exists some permanently well-defined ("real") state what would be somehow scrambled into invisibility in the QM formalism, while accounting in some unfathomable way for the seeming probabilistic nature of measurement.
Hidden variable theories have being ruled out by numerous experimental verifications of the violation of Bell's inequality. 
