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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.

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    $\begingroup$ The only thing we know - and ever will be able to know - about our world is what we can sense (see, feel, smell, hear, taste). These may count as subjective measures according to your description. And I agree, they are subjective. But if several people sense the same, then it indicates that this might objectively be reality $\endgroup$
    – Steeven
    Commented Feb 7, 2018 at 15:30
  • $\begingroup$ In physics, reality is what we can measure. Anything else is speculation. $\endgroup$
    – probably_someone
    Commented Feb 7, 2018 at 15:52
  • $\begingroup$ What is 'reality' in general? Can we say any concept in physics is 'reality', or just increasingly accurate representations of what we are capable of detecting? To the best of my knowledge; physics isn't concerned about explaining what reality is; but instead describing phenomenon that appear to be 'real'. Perhaps if you give a more strict definition on what you mean by "reality" your attempts to physically describe it will make more sense. $\endgroup$
    – JMac
    Commented Feb 7, 2018 at 16:06
  • $\begingroup$ @probably_someone, the problem is that it may be necessary to speculate about reality before anything about it can be measured. The more physics has attempted to avoid overtly asserting axioms or concepts, and stick to "only what can be measured", the more they are asserted covertly, or the more meaningless and unintelligible the measurements become. $\endgroup$
    – Steve
    Commented Feb 7, 2018 at 16:13
  • $\begingroup$ @Steve I never said that speculation is in any way unnecessary; in order to actually understand measurements (and thus, understand reality), we must speculate as to their relation to each other, making a model that adequately explains the data we have. But the invention of a new physical theory that better explains measurements does not mean that reality itself has changed. Rather, it means that our understanding of reality (i.e. our understanding of the measurements we make) has changed. $\endgroup$
    – probably_someone
    Commented Feb 7, 2018 at 16:18

2 Answers 2

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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.

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  • $\begingroup$ The problem is, what are these "other universes"? Presumably they cannot be detected, since the moment they come into existence they become inaccessible. Far from being unobjectionable, it's one of the most fanciful and outlandish hypotheses! $\endgroup$
    – Steve
    Commented Feb 7, 2018 at 16:20
  • $\begingroup$ @Steve that misses the point completely. You have a Hilbert space $\mathcal{H}$ and a superposition of states in that Hilbert space $\sum_i c_i |\psi_i\rangle$. That is the claim I'm saying is unobjectionable. $\endgroup$
    – user12029
    Commented Feb 7, 2018 at 16:38
  • $\begingroup$ I took this from here: 'Exponential decay which is interrupted by a measurement is still exponential... This means that if you are working on time-scales where Fermi's rule is applicable, measuring whether that particle has decayed or not will do nothing to the decay rate… Quantum zeno effect happens when you muck up the states in intermediate times, before Fermi's golden rule has a chance to become valid.' physics.stackexchange.com/questions/33232/… $\endgroup$
    – willjones1982
    Commented Feb 8, 2018 at 14:11
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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.

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  • $\begingroup$ I don't doubt that quantum superposition is real. I explain that I mean real in a more concrete sense (i.e. measurable). I agree about hidden variables (I refer to Bohm's theory, though Bell did argue that non-local hidden variables theories are still possible). I'm not proposing some new theory! I'm trying to understand what physics implies about the real world. My question really is whether, given that we always measure electrons to be in one stationary state, even as their wave function moves between them, is there any physical reason not to take these states as the more concrete reality? $\endgroup$
    – willjones1982
    Commented Feb 8, 2018 at 14:34
  • $\begingroup$ The point of my answer is: if those states are "more concrete" then they are hidden variables; else, what does "more concrete" means? $\endgroup$
    – Stéphane Rollandin
    Commented Feb 8, 2018 at 16:08
  • $\begingroup$ As for "I don't doubt that quantum superposition is real": ok, then why do you ask "is there any reason to think that electrons can ‘actually’ be in multiple eigenstates at once"? $\endgroup$
    – Stéphane Rollandin
    Commented Feb 8, 2018 at 16:09
  • $\begingroup$ I don't think they're hidden variables. There's nothing hidden about what we measure. As I say, I'm not trying to propose some new theory just understand what reality means within current physics. My point is that obviously the wave function/quantum superposition is real in some sense, but the pure states we measure must be real in some other 'more concrete' sense if we are to make sense of the fact of measurements. The best illustration is the quantum Zeno effect. This seems to show an evolving quantum superposition but also an actual measurable energy state (reference in next comment). $\endgroup$
    – willjones1982
    Commented Feb 8, 2018 at 17:24
  • $\begingroup$ 'Exponential decay which is interrupted by a measurement is still exponential... This means that if you are working on time-scales where Fermi's rule is applicable, measuring whether that particle has decayed or not will do nothing to the decay rate… Quantum zeno effect happens when you muck up the states in intermediate times, before Fermi's golden rule has a chance to become valid.' physics.stackexchange.com/questions/33232/… $\endgroup$
    – willjones1982
    Commented Feb 8, 2018 at 17:24

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