Question

Suppose there's a radioactive material and a 1/2 quantum probability of detecting it by a Geiger counter. This puts the system in a superposition. Also suppose you are in the same room, and the walls of the room are perfectly decoherence-proof. You observe the Geiger counter and get a definite result. Either it had gone off, or it hadn't. The Copenhagen interpretation tells you the decay or nondecay only became real when it was measured, and the result reached you. Your friend is waiting outside the room. After a very long delay, you open the door, and he observes whether or not you had seen the Geiger counter go off.

He then has the nerve to tell you

There is only one observer, and that's me, not you. You are nothing more than a dull bound state of electrons and protons. Before the door opened, you never had the property of knowing whether the Geiger counter went off. Only when the door opened did you acquire that property.

Unnerving, but you reason, your friend is just like you. Both of you are humans and made up of a bound state of electrons and protons. What applies to you ought to apply to him and vice versa. Or are you special and inherently different from him?

You object that you remember very distinctly whether or not you heard the Geiger counter go off. He counters

Your memory of having known whether or not the Geiger counter went off only came into being when the door opened. Just because you have that memory now does not mean it was real before the door opened.

You object that applying the Copenhagen interpretation to yourself tells you you did have a definite knowledge before the door opened. He counters

It's a meaningless question whether or not you knew the state of the Geiger counter before the door opened and I measured you because there is no way in principle for me to find out. There is no inconsistency here.

Don't all observers have to agree? Both of you agree on your current memory of having had a definite state and that is observable.

Did you have a definite knowledge of the state of the Geiger counter before the door opened? Change the story a little. You haven't opened the door yet, but you know your friend is waiting outside. Do you have a definite knowledge now? You think you do, but does that make it so?

After some further reflection, you realize the present you is a different observer from your past selves. How definite was the past?

Answer 1

The "inner" observer has observed the outcome of the experiment well before the "outer" observer but there is no contradiction whatsoever.

In particular, if the "outer" observer properly defines the projection operator that determines whether the "inner" observer had a well-defined feeling or perception of knowledge (with some allowed error margin for confusion) after he did his measurement, the "outer" observer will find out that indeed, the "inner" observer had a well-defined feeling. So they will surely agree about that. However, the "outer" observer couldn't have predicted which of the outcomes was actually measured by the "inner observer": he can just prove that the "inner" observer had a well-defined perception.

However, the outer observer is allowed - and encouraged - to use quantum mechanics uniformly for all objects, including bound states of protons and electrons that are sometimes called "other people". If he does so, the wave function - encoding the probability amplitudes sufficient to make any future measurements - is uniformly spreading and linear superpositions of macroscopically distinct states are omnipresent as the intermediate states.

This was discussed nicely e.g. in Sidney Coleman's "Quantum Mechanics In Your Face"

http://motls.blogspot.com/2010/11/sidney-coleman-quantum-mechanics-in.html

Let me mention that quite typically, the "inner" observer could be "less reliable" and "less decoherent" than the outer one. So he could "perceive" that some other decohered histories have already disappeared as possibilities, but the interference could get restore later etc. which could ultimately refute the "inner" observer's classical memory. That's why a more reliable, more decohered "outer" observer shouldn't be imagining that the wave function of the observer system collapsed before the measurements are actually done - and/or perceived - by the "outer" observer.

This comment becomes completely obvious if you imagine that the inner observer is just a collection of a small number of atoms that is decohering pretty slowly. Still, some perception of classical outcomes and decoherence may start to emerge. But it's still fuzzy enough for the classical approximation to be inaccurate. It's clear that in such a situation, the outer observer - who is much more reliably "classical" - can't believe the would-be classical concepts used by the "inner" observer because the "outer" observer knows very well that the "inner" observer is just a quantum mechanical system for which the classical approximation is highly imperfect.

I think that the reason why you and others have problems with these simple things is that you still fundamentally refuse to accept that at the fundamental level, the world is quantum mechanical, and that all classical concepts - such as well-defined positions or completely well-defined results of experiments that become "absolute facts" - are just approximate. They are approximate because classical physics is not the way how the world works at the deepest level. If one wants to describe any system totally accurately, he has to use the full quantum mechanical theory where everything is allowed to have a nonzero chance to interfere and "recohere", whether or not other "conscious beings" are parts of this world.

At the same moment, every observer who uses a quantum mechanical description and who wants to convert some observations into "facts" must make sure that the "facts" are mutually decohered or "consistent" histories. Still, everyone should acknowledge that all such facts are always an approximation assuming that decoherence is sufficiently strong to make it de facto impossible for the historical facts to be "reverted" or "retroactively modified" by the future evolution. Quantum, small enough particles do many non-classical things. Quantum tunneling is an example. A small observer's perception that a measurement has become a "fact", but this fact is later "undone" by subsequent recoherence, is another example. That's why one must never assume "too early" that some components of the wave functions have disappeared.

By the way, you also incorrectly suggest that the lab with the inner observer may be "screened against decoherence". This is just a misunderstanding of what decoherence means. Decoherence depends on the separation of the degrees of freedom of the studied system and the environmental degrees of freedom. But that doesn't mean that the "environment" has to be physically separated from the "interesting system". Quite generally, many of the environmental degrees of freedom are geometrically located "inside" the objects we are interested in. The environment is composed of all the useless, "high-entropy" information we're not interested in - surely things like lots of infrared photons traveling through our bodies, reflecting from the walls of the lab, and so on. You may isolate the lab from the external world but you will not stop the fact that it's still valid to describe the phenomena inside the lab by decoherence.

If the "outer" observer knows how to define the degrees of freedom in the lab to the interesting and environmental ones, he will also find out that the different states of the "inner" observer's brain have quickly decohered from each other. That means that for the purpose of all predictions about the "inner" observer only, the quantum probability waves may be replaced - with a good enough accuracy - by a nearly diagonal density matrix. The diagonal entries are the probabilities but again, the "outer" observer is not forced to imagine that the (later unobserved) a priori possible outcomes have seen their density matrix elements collapse to zero. He naturally does it only when he actually makes the measurement at the very end. When the decoherence happens in the middle, and it's reliable enough, it's consistent for the outer observer to assume that one of the results was "already real" after the "inner" observer made his measurement. But the "outer" observer surely doesn't have to assume that such a premature collapse has taken place. Why would he do it? Because of the respect to the "inner" observer as a fellow human with consciousness? No such "respect" exists in science. Science doesn't care whether someone may claim to be an observer - it still allows accurate predictions for any conglomerates of particles