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My question is not about (pseudo) philosophical debate; it concerns mathematical operations and experimental facts.

What is an observer? What are the conditions required to be qualified of observer, both mathematically and experimentally?

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I guess we'll have to wait for the next season of Fringe to find out... en.wikipedia.org/wiki/… –  dbrane May 14 '11 at 16:18
This is hard to Answer adequately at least because there will be a different Answer for different interpretations of quantum theory. I presume you mean quantum theory? Not that a classical observer is easy to get really straight. My immediate reaction is that you should go to the Stanford Encyclopedia of Philosophy, plato.stanford.edu/contents.html, read a few things that come up when you search for "observer quantum", then ask a more specific Question. –  Peter Morgan May 14 '11 at 16:26
@Peter "no philosophical debate". I know the subject is sensitive. My question accepts the answer "nobody knows". (But I personnally do not guess so; otherwise, how could experiments be done? How could theory be so precise? No matters which interpretation is the correct one, I suppose it can be given at least a few hints.) –  Isaac May 14 '11 at 17:11
Dear @Isaac, "nobody knows" isn't really an accurate answer. It's more correct to say that we do know that there is no unique answer because the question depends on definition and is associated with no operational way to test it. We talk about observers to express the idea that various properties of physical systems may be "perceived" or measured by some objects, but what is exactly needed for an object to be able to measure "something" with a certain "accuracy" depends on the "something" and the "accuracy", as well as all other details. There is no "universal" answer to all such questions. –  Luboš Motl May 14 '11 at 17:20

8 Answers 8

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Observer is a special person (or a system that contains such person) which does not obey the usual laws of quantum mechanics. While it is much easier to define observer from a philosophical point of view, the mathematical answer is that the observer is a system which manifests subjective decoherence when observed. For the definition of subjective decoherence and precise mathematical formulations, refer to this work.

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Sorry, all systems obey the laws of quantum mechanics, whether they're observers or not. –  Luboš Motl Jan 3 '13 at 12:00
@Luboš Motl It has been shown that universally-valid theories are not possible. A theory can be only universally-valid in a relative sense, that is valid for any system, not including observer. See here: homepages.fhv.at/tb/cms/?download=tbDISS.pdf –  Anixx Jan 3 '13 at 15:42
Isn't subjective decoherence the same as quantum entanglement? An electron's up-spin state observes its entangled electron in its down-spin state and vice versa. If an electron could think, if you'd talk to it, it would tell you the other electron always has been in a down-spin state. –  Jan Dvorak Dec 20 '14 at 11:13

Are we talking quantum mechanics? Then I'd say that a "measurement" is any operation that entangles orthogonal states of the system under consideration with orthogonal states of the environment. "Measurement" is the important thing in most formulations of QM. Colloquially speaking, an observer is something that performs measurements.

The only other place in physics I can think of where "observer" shows up is in the oft-used phrase "This is obvious to the casual observer". This is just shorthand for "I can't be bothered to write out the mathematical proof".

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I think this pretty much gets it. The main point would be that "observer" is not a precisely defined concept; there isn't any set of mathematical conditions that something has to be considered an observer, for example. –  David Z May 14 '11 at 20:55
Nice answer. Let me add that a lot of the esoteric fallout from QM is due to people having some wrong ideas about the term "observer", telling you that your consciousness somehow creates the material world. Maybe in more rigorous terms, an observer could be anything that induces decoherence by coupling microscopic quantum states to different states of a macroscopic system. –  Lagerbaer May 14 '11 at 21:32
A nice secret way to promote the logic of decoherence without using the word, +1. ;-) –  Luboš Motl May 15 '11 at 7:48
If you define the observer as "something that performs measurements" and measurement as "any operation that entangles states of the system under consideration with states of the enviroment" you could realize that you need an observer of the observer to say that measurement was really done, this is in the Schrödinger's Cat paradox, it's not enough the operation itself, you need an observer of both things to define an observer, Schrödinger could perfectly realize that a cat is enough for wave colapse(old ugly word) or decoherence, but he put an observer outside the box of his thought experiment. –  HDE May 17 '11 at 18:12

Either the observer is classical or the observer is quantum. If the observer is classical, we are back to the Heisenberg cut of the world into a quantum part and a classical part, and the explanatory gap needs to be bridged in this manifestly dualistic interpretation. If the observer is quantum, then another observer needs to observe the first quantum observer by the tenets of quantum mechanics. Down the road of infinite regress we go.

As long as the concept of an observer can't be made mathematically precise and unambiguous, the measurement problem will never be solved.

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J von Neumann in Mathematical foundations of quantum mechanics (eg Princeton 1955, 1996), Chapter IV.1 explained idea of "observer" and I think it is appropriate introduction (and not only for the history of the problem). For more recent discussion and more references it is possible to see, eg: M. Schlosshauer, Decoherence, the measurement problem, and interpretations of quantum mechanics, Rev. Mod. Phys. (2005), etc, etc.

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There are Copenhagen idealists out there who insist the wavefunction or density state lies entirely in the subjective mind of the observer. There is no objective reality out there except in the mind of the observer.

Let me tell them whatever the contents of the conscious mind, the contents are classical information about an alleged world out there. At best, the contents of consciousness can only pick out POVM elements from some predetermined POVM. Where in Nature is the information contained in the wavefunction or density state or path integral or some other beable stored? Certainly not in the contents of consciousness themselves. If such information are stored nowhere, how does Nature manage to keep track of what it is supposed to do and get the sampling probabilities for the POVM right? But if such information are stored elsewhere, then there is an element of reality outside the conscious mind of the observer.

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You may have answered my question, but I do not see where. Could you be clearer? –  Isaac Jan 2 '12 at 17:18

While my previous answer is entirely valid, the same can be explained using more traditional terminology.

To be simple, observer is a physical system that is capable of triggering collapse of the wave function once it comes into a contact with a quantum system.

Which system can trigger wave function collapse is only determined experimentally. But what is known for sure is that any system that is in thermodynamic contact with the observer (or is not thoroughly isolated from it) also can trigger the wave function collapse.

It is experimentally determined that the Earth's environment and atmosphere are capable of triggering the wave function collapse, which means that they are also in thermodynamic contact with the observer.

On the other hand in well isolated and cooled interior of D-Wave Systems' Orion quantum computer the collapse of wave function does not happen unless a contact with the exterior is made intentionally which allows to perform quantum computations which could not be made otherwise.

This hints that there is no observer inside this well-isolated box. By gradually expanding such box and putting more and more matter inside it it is possible in principle to find the actual point that acts as an observer and triggers the collapse.

This is not practically possible unfortunately, because any living organism cannot exist at such low temperatures which are needed for through isolation and its high level of entropy will make any action on it virtually irreversible thus not allowing to test whether the collapse actually happened.

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I prefer a variant of Anonymous Coward's answer given above, by leaving out the environment. I would say that an observer is a system that interacts with the systems it observes by entangling orthogonal states of the systems under consideration with orthogonal states of itself and possibly other systems.

So, I don't bring in the baggage of an environment here, but the possibility of that is included by mentioning "other systems". The fundamental point is that an observer is capable of extracting information from a system. A simple example is the CNOT gate which in the |0>,|1> basis acts on two qubits by applying the NOT operation on the second qubit if the first qubit is |1> and acts as the identity otherwise. This means that when the second qubit in initialized in the |0> state, it can "measure" the first qubit. The observer is thus the CNOT gate, the second qubit is its record of the observation it has made.

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I'd say, "observer" is an arbitrary entity which converts quantum information into classical. Classical information is, roughly, anything that can be duplicated without distortion and transmitted. The need for classicality is anthropic: we are conditioned by evolution to share information for survival and to value "rational thought" whose main defining characteristic is that it can be repeated.

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