# The irreducible observer

This question probably verges on pseudo-science and probably sounds like gibberish, so please pardon me. But I'll ask it anyway.

In an ideal lab experiment there is generally a separation between the system to be studied and the apparatus (environment). The two are considered 'unentangled' before the decoherence occurs, right?

However, the environment in itself can also be considered an entangled system (like the previous system) to be observed by humans.

We could then naively conclude that our flesh and form constitutes the true observer.

But all our bodily substance is also coupled to the environment. So who then is the one truly causing the decoherence?

Separate all the entangled material from the human body, what do you get?

What physical structure within us constitutes the eternally unentangled and irreducible observer?

Perhaps my line of thinking is wrong, maybe the entity does not exist outside the Hilbert Space. Then is the the observer entangled with the observed? So would that not mean that the observer can cause his own decoherence?

It might seem like gibberish, but I really don't know what the present status on this question is int the physics community. If there are any papers on the matter please do provide the link. This question nags me all the time.

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It sounds to me like you're wrestling with some of the fundamentally silly aspects of the Copenhagen interpretation. The CI is just silly, which would be more of a problem if it was a physical theory rather than a philosophical interpretation. The CI talks about observers and measurement as if they were different from other physical systems and processes, but they're not. You might be interested in a philosophical paradox about CI, described on p. 4 of Everett's PhD thesis (p. 10 of the pdf): dspace.nacs.uci.edu/handle/10575/1302 –  Ben Crowell Sep 3 '13 at 21:57

Decoherence is the process during which the reduced density matrix for a physical system of interest rapidly converges towards a diagonal form in the "natural" basis due to the physical system's interaction with the environment.

The environment has to have sufficiently strong interactions with the physical system of interest; and it must have a sufficient number of degrees of freedom. These are sufficient conditions for the decoherence to proceed quickly enough. The proof may be given or calculated by tracing over the environmental degrees of freedom.

In none of the derivations of decoherence, one must (or one should) talk about the "identity of an observer". The physical system of interest may be a human being, her muscles, her brain, or other organs of hers. The environmental degrees of freedom whose influence makes another physical system to decohere may also be degrees of freedom located in a human being, such as her atoms or the thermal radiation moving in her stomach. Some degrees' of freedom being an "observer" or not being an "observer" has absolutely no impact on the mechanism of decoherence.

Decoherence isn't a mechanism that divides physical objects to conscious and unconscious ones, that identifies where the "spirit" of any kind is distributed in space. Decoherence is just the gradual loss of coherence, the gradual loss of the information about the relative complex phase between some complex amplitudes in a superposition – equivalently speaking, the decrease of the absolute value of the off-diagonal elements of the density matrix. Decoherence has nothing whatever to do with consciousness.

However, decoherence helps to define which questions may be legitimately asked to quantum mechanics for quantum mechanics to probabilistically answer them (tell us probabilities of different outcomes from a set that has to be consistent and mutually exclusive). Quite typically, good questions or "consistent histories" are those whose microstates decohere from each other so that the density matrix in the final state automatically has vanishing off-diagonal matrix elements between these two states. When it doesn't have, the question "which of the two outcomes is realized" will not satisfy the rules of classical logic. A basis composed of "unnatural" superpositions of Schrödinger's cat's states is the usual example.

But quantum mechanics doesn't constrain "who" is allowed to ask the questions. Anyone can be considered the "owner" of a set of consistent histories. However, if the being or physical object isn't actually able to observe certain degrees of freedom, predictions of such degrees of freedom will be irrelevant for this being or physical object.

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"if the being or physical object isn't actually able to observe certain degrees of freedom, predictions of such degrees of freedom will be irrelevant for this being or physical object."- taking this fact and the fact that the environment always couples to the system on measurement, we can say that if one 'being' were to study the the the entire state of the universe without coupling to it, he would have nothing to discuss. He would see 'a blank space'. Is this a right conclusion? –  dj_mummy Sep 4 '13 at 6:31
So you are saying the measurement is really the absorption of the system's information (dropping off on non-diagonal values in the density matrix). So the rapid diagonalization is the welcoming of new systems into our big 'entangled world' through decoherence. So decoherence is not some consciously caused collapse but the dephasing of the system? That raises further questions: I assume that our globally entangled state today evolved (perhaps unitarily the whole time) from the the Big Bang..... –  dj_mummy Sep 4 '13 at 6:40
Then why are there systems today that we have to couple to our entangled world? If everything in the universe were entangled completely, wouldn't that diagonalize the density matrix completely from the perspective of any component of the physical universe? –  dj_mummy Sep 4 '13 at 6:45
@dj_mummy - concerning your first question: right, an observer is free not to task any questions. It is a natural choice if he doesn't interact with a system. He may still discuss what observers who are coupled and who care may ask and what they find out. ;-) –  Luboš Motl Sep 5 '13 at 15:16
Concerning the second question: not exactly. Decoherence is the decrease of the off-diagonal elements. A measurement is just the act of finding a value of an operator - more generally, answering a question by observation. This is usually an observation of an observable that previously "decohered" but it's not "completely generally" so. –  Luboš Motl Sep 5 '13 at 15:18

There is this interesting gate called the CNOT gate(Which was pointed out to me by Charles Bennett, whose papers I highly recommend). The use of the CNOT gate very nicely illustrates why measurement is not really a problem.

Its take a unknown state(S) that one wishes to be measured, say it is, $\frac{U+D}{\sqrt 2}$.

The initial state of the Recording bit R1 is d.

The Cnot gate is essentially a unitary gate that entangles the Record and the particle. So after a cnot gate is used The state is $\frac{Uu+Dd}{\sqrt 2}$.

Now if you apply the Cnot gate multiple times using several record bits(R2,R3,R4.....) you have something like $\frac{Uuuuuu+Ddddddd}{\sqrt 2}$.

So essentially Measurement is entanglement of the state of the Record to the state of a particle under observation. In this process there is never a breakdown of unitarity.

Any further probing of a record makes further copies of the record, be it an imprint on your consciousness or a computer. Essentially if you look at a record you entangle yourself to the record, and hence inturn the state of the system.

If you want to reverse measurement in someway, you have collect all copies of the record, where ever there are, including any records in your Head, and if you apply the correct unitary evolution operation(by creating the correct physical situation.) then you can restore the original state, But then you CANNOT have any record left of that state any where in the universe. Its always easy to do that when you have CNot gates, But if you have a record in your head or a thermal bath then it is very hard, and practically impossible.

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