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An observable basically is something you can measure. However compared to just any general measurement, an observable has one specific property: If you repeat the measurement without the system changing in between, you get the same result (this is obviously not true for all possible measurement procedures). Such measurement have indeed been experimentally ...


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take a system initially uncorrelated with the environment, with both being in pure states. It interacts with the environment, forming an entangled state. Taking a partial trace over the environment leads to a mixed state matrix for the system with nearly zero off-diagonal entries. The problem is we can reverse both the environment and the system so that the ...


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#What is a wavefunction? A wave function is a mathematical solution of one of the basic quantum mechanical equations: Schrodinger, Klein Gordon, Dirac. By the postulates of quantum mechanics the square of this wavefunction gives the probability of finding the system under study when looking at (x,y,z,t) or (p_x, p_y, p_z,E) or similar four vector spaces. ...


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I am going to answer this in a hurry because the question is on the edge of being closed. Quantum mechanics isn't just about "wavefunctions", it is also about "observables". An observable is something like: energy, position, momentum... i.e. it includes all the properties of classical physics. The wavefunction (or state vector or quantum state) is the ...


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The question you ask is essentially: How to solve the measurement problem? As you can see from that article (although I wouldn't say it's a very good one), there are several approaches to either get a theory where no collapse occurs (thereby rendering the question futile) or to explain the collapse. So far, nothing has been so satisfactory as to be a ...


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I agree in full with Marty Green except the explanations of chemistry in which I was unable to follow so well (that doesn't say that I disagree with them). But, let me put the things in short. The collapse is a phenomenon that is supposed to occur when a quantum object comes in contact with a quantum system. For instance, a quantum particle falls on a ...


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In theory, every example of wavefunction collapse should be explainable through a mechanism of normal time evolution of the wave function. The apparent collapse is only an illusion. People who agree with this idea like to talk about "decoherence", which is a fancy sounding word, but it doesn't really tell you anything. In fact, there is very little interest ...


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Let's say that "decoherence" is that transition from a pure quantum state to a mixed state due to interactions with the environment. (A reasonable definition?) Mixed states are NOT decohered states, they are states where the phases of the wavefunctions are well defined, just not in an eigenstate that will give a unique eigen value at measurement. ...


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I haven't studied this in any detail, so take what I say with a grain of salt. But from summaries I've read, like the essays on decoherence.de, I think that in the Copenhagen interpretation "collapse" would still have to be understood as conceptually distinct from decoherence. I think a way to see this would be by imagining an idealized Schroedinger's-cat ...


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When a particle passes through an ideal pair of slits, it's wave function can be written in the form $$\psi(x) = \alpha\, \psi_1(x) + \beta \,\psi_2(x)$$ where $\psi_{1,2}(x)$ are the wave-functions you would get by closing either slit 2 or slit 1, respectively. We say that the wavefunction is in a coherent superposition. What is coherent about this ...


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Anna's explanation is very illuminating, but here is a shorter one: Assume that we prepare a pair of particles in the entangled state $$\exp(i\theta)\left|A_1\right\rangle\left|B_2\right\rangle + \exp(i\varphi)\left|A_2\right\rangle\left|B_1\right\rangle,$$ where subscript 1 means that the particle follows a trajectory slightly different than the particle ...


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To understand decoherence one must understand coherence. In systems described by wave functions , i.e. sinusoidal distributions (waves) in a variable, coherence means that the waves , if more than one , have a known phase to each other. There is a long article in wiki on coherence. Quantum mechanical solutions of a system of particles are wave functions, ...


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But the way I've seen it be explained, it seems that the reason things collapse is that upon interacting with macroscopic things, the wave function decoheres until there is only one component left. No. That's not the way decoherence works at all. A system $S$ interacts with the environment $E$ with a Hamiltonian that does the following: $$ ...


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Decoherence is not a sufficient explanation for the collapse. Decoherence means that the phases between the components of the wave-function, (when the latter is expanded as a quantum superposition), are destroyed. But WHY in a measurement we get a certain ONE from these components, the decoherence doesn't explain. And what happens with the other components ...


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Your question presupposes that collapse actually occurs. A third observer might view Bob and Alice to be entangled with the system. The combined state lives in a "larger" Hilbert space (I mean in the sense that it is a product space). Now, there are projections of this state into spaces where Alice particle 1 to have gone down path a, Bob particle 2 to have ...



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