Rovelli & others, in Relational Quantum Mechanics (RQM) take the simple ontological picture of the Copenhagen Picture and relativise it. This is what I was suggesting in this question, though I was looking for a specific mathematical treatment.

In the Copenhagen Picture a distinction is made between the microscopic observed system, taken to be quantum mechanical; and the macroscopic observer which is classical.

They argue that this 'mixed' picture is 'klutzy' for three reasons.

  1. That reality shouldn't arbitrarily divide between a quantum mechanical microscopic system and a classical macroscopic one. Physical Reality should be quantum mechanical all the way through. (I say Physical as this is the reality probed by Physics, that is susceptible to Physicalism. I do not mean by this is the only way of theorising reality).

  2. Observers shouldn't be characterized by human beings operating classical macroscopic apparatus, but by interactions between observer & observed - and the observer need not be macroscopic, classical or animate. An electron can observe a proton, for example.

  3. Interactions are going on all the time. A proper description should take into all interactions. That is rather than consider a system of observer & observed; one should consider a single system, which is then divided into observer & observed; and one should consider all possible divisions. These should be consistent. Also reflexive - division A can observe division B, but also division B can observe division A. Simple Transitivity doesn't hold - though if A can observe B, and B can observe C; then A ought to Observe C. Though I suspect its mendable with enough ingenuity.

(The removal of animate or conscious observers also removes one of conceptual mystifications in the interpretations of QM that has seeped into popular culture that somehow consciousness is implicated in QM. This however doesn't negate a Kantian separation of reality into phenomena & noumena since the theoretical physical description of reality is not immediate to the Sensability and is mediated instrumentally).

Rovelli insists that a measurement is always done between an observer and an observed; hence both must be mentioned. One cannot say the 'momentum of a particle is such-and-such', but that the 'momentum of the particle is such-and such for this observer'.

In a broad sense Rovelli has applied Einsteins insight about the 'relativity' of observation. In fact this goes further back to Galileo about the relativity of rest & velocity. Also Leibniz, Huygens & Descartes about the relational conception of space & time. Though interestingly Newton broke with this to develop his physics - he proscribed absolute space & time; and he did this on pragmatic grounds - it made his theory work; he understood the justice of the philosophical arguments but the mathematics of his day - including calculs - wasn't upto such a subtle view.

One can then argue that it is 'meaningless' to speak of the momentum of the universe as a whole, for who or what is there to observe it.

One could say that the universe observes itself; but this possibility is ruled out by Breuer. In fact, he shows that there is information about the whole universe that is impossible to access by any observer, even in principle.

What is the ontological status of information that is permanently inaccessible by any conceivable physical observer?

  • I do not know the answer, but a companion question might be "What is the ontological status of "truths" of theorems in ZFC that are undecidable ". I realize that that math and physics are different domains, but one may be able to transport some of the insights from the philosophy of math to this. Dec 31, 2013 at 23:25
  • Well, there are some answers that lead to more questions here. A theorem is undecidable when it has a model where it can be proved, and others where it cannot. One could attach a measure describing what proportion of the models is the theorem provable. One then gets a 'measure' of truth, rather than a simple true/false dichotomy. Alternatively, if the underlying logic is paraconsistent then all theorems are decidable. Dec 31, 2013 at 23:36
  • it does sound rather like Russells paradox - where you cannot have the universal set; here you might not be possible to have a universal description; and I think that this is Rovellis solution - any description is always partial. Also Breuer was led by Godel to his theorem Dec 31, 2013 at 23:41
  • 1
    Can you provide a citation/reference for Breuer's result? I suspect a rather trivial locality issue.
    – Rex Kerr
    Jan 1, 2014 at 21:05
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    @kerr: its at 'Breuer, T., 1993, “The impossibility of accurate state self-measurements”, Philosophy of Science, 62: 197-214'. The ref comes from the SEP article on RQM. Jan 2, 2014 at 0:16

2 Answers 2


Let me answer by recasting things in terms of truth and knowledge rather than information and accessibility.

There simply must be some truths that will remain permanently unknown. There's a somewhat difficult argument in epistemic logic known as the paradox of knowability that shows this to be the case. For more information, see the SEP article.

Basically, it turns out that the assumption that all truths are in principle knowable collapses into the (obviously) false statement that all truths are in fact known. Hence, we know there must be truths which cannot be known.


Who knows what the best definition for information is, but at the very least we should be able to agree that information is carried by the existence of objects and how they stand in relation to one another. It is also reasonable that to say some object exists only if it is observable. In other words, if "something" lies outside of our capabilities to observe it, we should not consider it to exist at all. This is a working criterion for a definition of existence. Conversely, if "something" does not exist it cannot convey to us any information.

I would say then that information that lies outside of any capacity to observe it is not information at all, for by definition it cannot be correspond to something that exists.

  • +1 to offset the inappropriate IMO downvote. I disagree though: there's plenty of information than needs to be considered for practical reasons, although it's unobservable, i.e. quantum states.
    – Michael
    Jan 2, 2014 at 6:10
  • @Michael Would you elaborate on what sorts of information regarding quantum states you consider to be unobservable?
    – user5132
    Jan 2, 2014 at 6:38
  • These ones, for example.
    – Michael
    Jan 3, 2014 at 3:35

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