nature of an observer
For instance, in the double slit experiment, what is exactly defined as an observer? I remember from somewhere, light is also an observer?
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In terms of experimentation, an "observer" can be generalized to include any device that records an event in way that then touches so many other atoms and particles, such as by radiation or vibrations, that reversing the even becomes statistically nearly impossible (although never completely impossible).
Feynman's example of neutrons sometimes reflecting as waves off of crystals, and sometimes colliding with specific atomic nuclei in that crystal, is a pretty good example. As long as the neutron reflects as a wave, its observed signature in the universe remains highly indeterminate in terms of spatial location. Once it hits that atomic nucleus, however, it immediately does things like giving off radiation, jostling the atom, and changing the local dynamics of he crystal. To preserve causality, every single one of those outgoing effects must be captured and reflected back to the point of origin before the capture event can be reversed. That is, to say the least, and unlikely set of events, so in that case the location of the neutron becomes "detected" and very, very well defined.
Any dense concentration of hot matter in general tends to make a very good "observer" for precisely that reason, since dense hot matter is incredibly messy and fast-acting in terms of how it scatters information and makes it very hard to reverse. Only when dense matter loses some of its many degrees of available information does quantum-type reversibility start to make events ambiguous, with both superfluid helium and the more recent "true" Bose condensates of diffuse metal atoms being a conspicuous examples.
This is also why the traditional portrayal of Schrodinger's cat is actually pretty silly, because when the cat dies it absolutely showers the universe with phonons and radiation and all sorts of mostly-irreversible data. There simply is no quantum superposition in that case, since the hot matter of the cat and its surroundings make the entire event very, very hard to reverse. That's an image that really needs to be phased out.
Electrons in atoms make absolutely terrible observers, simply because they don't have enough state available to them to record anything at all. So they just sit there in their lowest energy states and stay fuzzy. Good thing too, makes all of chemistry possible, that.
I guess the term 'observer' is pretty misleading, and should be avoided. It's better to think of it in terms of measurements.
You start with an arbitrary state vector $\Psi = (1, 1)$*. It's a superposition of the two possibilities 'left slit' $(1,0)$ and 'right slit' $(0,1)$. A measurement is a physical process that projects this into an eigenstate of your observable $\hat O$ - it shaves off all components in a certain base except one. Physically, if you perform the measurement, you get e.g. $(1,0)$, and you can say it went through the left slit. Mathematically, your new vector solves the equation $\hat O \, \left|\Psi'\right\rangle = \lambda \, \left| \Psi' \right \rangle$, that means it is in an eigenstate - it now has a definite value of which-slit-it-went-through.
This is the important thing about quantum mechanical measurements: You don't 'measure' in the usual sense of the word (scan something passively), you manipulate and select (or 'prepare states'). For example, in the Stern-Gerlach experiment, you don't somehow scan the spin of the electrons. You pass them through a magnetic field which brings them in to a spin eigenstate. Then you know, that the ones that go up (or down) now have spin up (or down).
Now, what is the observer here? If you don't want to get metaphysical, it's just somebody who performs the QM measurement.
Personally, I'm always wary of explanations that envolve human conciousness, priviliged observers, etc.. I like my physics to also work on the moon, even when no one is looking :-).
(Also, note that 'observer' might have a different meaning in different parts of physics. In relativity, when you talk about observers you mean different frames of reference (moving at different speeds). You might also encounter it in the discussion of light cones or event horizons. There are some things a certain observer cannot see (because they are outside of his/her light cone, on the wrong side of an event horizon, ...).)
* Note that $\Psi$ is really a function (the wave function). In linear algebra one can treat functions as vectors. One can compose any function (of the kind we need in QM) from base functions, just like one can compose any spatial vector by adding base vectors. Forgive me if this is already clear and trivial to you, but these are really basic things that make QM much less mysterious.
Oh, and sorry if my notation is a bit sloppy. It's more about the general idea.
The mathematician von Neumann who came up with the idea of collapse by measurement discovered the von Neumann chain process in quantum mechanics. Using the concept of entanglement, he showed that the system entangles with the apparatus, and the system-apparatus combination entangles with the first observer, and the system-apparatus-observer combination entangles with another observer further out, etc. This is Wigner's friend. He left out the environment because he didn't appreciate decoherence, but you should also add the environment into the mix. The chain grows with time expanding the bubble of Greenberger-Horne-Zeilinger (GHZ) entanglement. With multiple observers observing from different angles, you can have multiple chains, but all entangled with each other.
Past the point of irreversible decoherence, it doesn't matter where along the chain the collapse happens. From a positivist point of view, the location is unobservable. This is the Heisenberg cut, his movable "Schnitt". Does the von Neumann chain ever end? How far out can you push the "Schnitt"? In the Wigner's friend scenario, you can push the "Schnitt" past a human observer to another observer further out. Wigner, of course, would deny that, claiming you can't even push it past the innermost human observer, but what's so special about humans? What about cats? von Neumann also noted that without a collapse, you end up with a "universal wave function" of the entire universe.
This depends on interpretation of quantum mechanics, but if to take the interpretations with collapse and non-branching universe in their final form, the conclusion is that the observer is a unique special person which has special physical properties, and the only one for whom this theory completely works.
If to take many-worlds or relative interpretations, each person will see himself as the observers, so that their observations will not be consistent with each others.
This is a deep philosophical problem, but the fact that each person should see himself not obeying any universal theory (even if all other people should seem to obey) is an established fact (see here)
An "observer", in this case, is anything that can "see" or observe and remember or record the event. The main point is that the observer can record the event. For example if you where to put this experiment in a chamber filled with gas. The gas would be considered an observer because if you wanted to later look for the path the particle took or, more importantly, which slit it went threw you could because the gas would have recorded it. If you have every herd of Schrodinger's cat, this experiment was used to demonstrate the theory that everything is statistics or probability, until you observe it when it is at that point condensed down into matter. If you where to observe the particle it would at that point be condensed down into matter and act again like a newtonian particle. The key thing is that what ever observes the particle "remembers" it
Whatever an observer is, it is always the case in the universal wavefunction, there is a superposition of the observer existing and not existing. Suppose a specific human is assigned to be the designated observer. That person's conception is probably dependent upon random events like the position of sperms which are sensitive to the outcome of quantum events. At any rate, that person's genetic material as determined by genetic crossover is definitely sensitive to quantum events. And a person's genes determine the chance for survival up till the age where they can be counted as an observer. So, there is a superposition of that person existing or not existing, or in a superposition of different genes. Less controversially, structure formation owes its origin to quantum fluctuations just after the big bang, and the location of clumps of matter determine the potential locations of the observer. That decoherence happens in all of these cases is besides the point. If quantum mechanics is defined with respect to an observer, post-selection for the existence of the observer is unavoidable. Those branches where the observer doesn't exist have to be thrown out.
Questions on the nature of the observer can't be disentangled from the anthropic principle. Maybe Wheeler was right in his participatory universe.
I tried in my own way to answer that here. I was trying to say that in the quantum world reversibility implies information cannot be copied. It can only be moved (i.e. traded). So if something observes something else, it has to remove information from the something else (and replace it with some of its own information). The observer can be as big as an eye, or as small as a photon.
Anything material has the dual aspect of both being matter and a proto-observer (property dualism). An electron orbiting a nucleus in an atom is a proto-observer of the nucleus and the other electrons in it. A thermostat is a proto-observer observing whether the room is "too hot" or "too cold" or "just right". A sufficiently advanced aggregate of proto-observers like a human brain can become an observer. This position is panobserverism. ;)