Hot answers tagged wavefunction-collapse
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What you describe in your question is the "Copenhagen interpretation" of quantum mechanics. There are more nuanced views of this nowadays that don't treat "measurements" quite so asymmetrically, see e.g. sources that talk about decoherence.
I recommend watching the classic lecture "Quantum Mechanics in your face" by Sidney Coleman for a nice take on this ...
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Interactions merely involve a correlation developing. For example, if an electron is put through a Stern-Gerlach apparatus, a correlation develops between the distance travelled in the x direction and the distance deviated in the y direction. It is reversible. The measurement which occurs when the particle hits the photographic plate is irreversible. It ...
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Dear Jack, there is no physical phenomenon that could be called the collapse. The collapse of the wave function, as first emphasized by Werner Heisenberg and then many others, is just the event when we learn something about a physical property of a physical system. When we learn that Osama bin Laden is located in a building in Pakistan, his wave function - ...
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There are currently two different accounts that give a larger picture of what happens when a quantum system is measured.
One of them is the fact that many random interactions between the system (which might be a 1-body or N-body quantum system) and the environment (which is considered for most purposes a pseudo-classical system with infinite degrees of ...
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Assuming that the incoming "first" particle is prepared in a pure state, interaction with another particle does seem necessary. Such an interaction might simply be the spontaneous emission of a photon or other particle by the original incoming particle, however.
Most importantly, such an interaction is not itself sufficient. For a measurement event to ...
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An observation is an act by which one finds some information – the value of a physical observable (quantity). Observables are associated with linear Hermitian operators.
The previous sentences tautologically imply that an observation is what "collapses" the wave function. The "collapse" of the wave function isn't a material process in any classical sense ...
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I'll start with the second one. $\int\phi^\ast\psi\,\mathrm{d}x$ is, as Chris says in the comments, the scalar (or dot) product of $\phi$ and $\psi$. In the Dirac notation, it is written as $\langle\phi|\psi\rangle$ and it gives the overlap of the two wavefunctions. In other words, it gives the probability amplitude (i.e., what you call square root of ...
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Unitary operators are operators that satisfy some conditions. Among other things, they have to be linear:
http://en.wikipedia.org/wiki/Unitary_operator
The operation (or "an operation") that maps any $\psi(x)$ to $\delta(x-x_0)$ where $x_0$ is the random position resulting from a measurement can't be associated with any linear operator. It's easy to ...
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Answer
Rigorous adherence to the liturgical rituals of the "Church of the Larger Hilbert Space" is feasible in principle yet exponentially inefficient in practice.
Exercise
One way to answer this question is by reference to a feasible numerical computation.
So fire-up MatLab; specify the dynamical system as (say) $n\sim 10$ interacting qubits; specify ...
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The collapse of the wavefunction is generally attributed to decoherence. This is time asymmetric in the same way the second law of thermodynamics is time asymmetric. I suppose it's theoretically possible for a wavefunction to uncollapse, but this is like saying it's theoretically possible for a broken egg to reassemble itself.
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I'll take a stab at this though my answer may be incomplete / fuzzy:
The double slit experiment demonstrates wave-particle duality, not entanglement. It shows that a "particle" can interfere with itself, demonstrating that it really acts as a wave in this instance.
Entanglement is correlation of measurements of particles (most commonly) that were generated ...
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An electron, indeed any particle, is neither a particle nor a wave. Describing the electron as a particle is a mathematical model that works well in some circumstances while describing it as a wave is a different mathematical model that works well in other circumstances. When you choose to do some calculation of the electron's behaviour that treats it either ...
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Let me take a slightly more "pop science" approach to this than Luboš, though I'm basically saying the same thing.
Suppose you have some system in a superposition of states: a spin in a mix of up/down states is probably the simplest example. If we "measure" the spin by allowing some other particle to interact with it we end up with our original spin and the ...
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As suggested in the answer above, in general, decoherence increases the entropy associated with a quantum system and as such has the same type of time-reversal asymmetry that appears in thermodynamics. The question, however, is also concerned with how an "uncollapse" would look like. Here I want to illustrate how this can be done in principle.
The net ...
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In terms of quantum field theory, an electron is an elementary excitation of the electron field, in a similar way as a water wavelet is an excitation of a water surface. There is a slight difference, though, as excitations of a quantum field are quantized, hence come in discrete bunches (1,2,3,... electrons) describing their size, while water wavelets are ...
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An often good on-line source for the interpretation of quantum theory is the Stanford Encyclopedia of Philosophy, which has a page on "collapse theories".
There is a lot of literature on whether one needs collapse if one takes the wave function seriously, as opposed to the mainline Physicist's approach of taking a more empiricist view, as outlined well by ...
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"Collapse the waveform" is a loaded term, that would not be agreed to by all physicists. There are a great many "no-collapse" interpretations out there in which there is no special role for measurement that directly alters the wavefunction. There are also collapse-type interpretations in which the collapse happens more or less spontaneously, as in Roger ...
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I have been looking at what is available of the book online, and believe that you are right that the Postulate 3 is (in a sense discussed below) weaker than the usual QM Projection Postulate.
Firstly there are some notational issues here. The $M_m$ are a family of operators, called Measurement Operators, indexed by $m$ which is a label for the outcome ...
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Much of how you answer this question comes down to your view of the wavefunction or state. If you think that the quantum state is a state of reality (that is, an ontic state), then you must either reproduce the predictions of orthodox (Copenhagen) QM without the measurement postulate or you must explain why nature provides two forms of evolution. The former ...
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No, as what counts as a collapse depends on how you separate your system from the environment.
Note that detecting photons is not a collapse of the photon wave function in von Neumann's sense, as the photon is afterwards not in a position eigenstate, but completely disappeared.
However, for certain simple systems, collapses (quantum jumps into eigenstates) ...
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In the following answer I am going to refer to the unitary evolution of a quantum state vector (basically Schrodinger's Equation which provide the rate of change with respect to time of the quantum state or wave function) as $\mathbf{U}$. I am going to refer to the state vector reduction (collapse of the wave function) as $\mathbf{R}$. It is important to ...
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I think the main issue here is that you're attempting to think about a system in isolation -- the energy states of an electron subject to the electrostatic potential created by the positively charged nucleus -- and trying to understand the measurement based on this system. This is hopeless, as the measurement is not a part of this system.
Your first big ...
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In principle everything exists in a superposition of states. However everything interacts with it's environment, and this collapses the superposition through a mechanism called decoherence. In the particular case of Schrodinger's cat there is a brief discussion of this here. Also search this site for decoherence as there have been lots of questions about it.
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Jherico, I see that you are keen in finding answers to your questions, or putting your views across for a debate, and this is really good. This is what science is all about. I think your questions deserve attention and proper debate.
Here is an effort from my side to help dilute some of the misunderstanding through the comments section of this forum.
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Much has been covered in these answers, but one aspect has been left out.
The actual physics going on in any measurement process includes amplification. Feynman thought this was significant. Here is a perhaps little-known quotation of his:
We and our measuring instruments are part of nature and so are, in principle, described by an amplitude function ...
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It is the case that all measurements proceed via the exploitation of the natural interactions that we understand theoretically. But once the measurement is completed and the result in hand, the QM analysis of the subsequent evolution of just those systems that yielded that particular result can no longer employ the original state function (which allows for ...
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It is not a weaker form. The book quotes "index m refers to the measurement outcome". As Lubos wrote, the classical measurement outcome could be anything physical, which is not the focus of the postulate, so basically if $\mu(m)$ is a classical measurement outcome and $m$ is your corresponding index then it is implicit that $\mu$ is a mapping
$\mu ...
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As I understand it, when physicists talk about something behaving both like a particle and a wave, what they mean is that it has momentum like a particle, but its position is determined probabilistically by a wave function.
That's not quite accurate. It would be better to say that it interacts like a particle but propagates like a wave. In particular, ...
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Yes, if you measure the spin again and assuming the absence of a magnetic field, the measured value of $j_z$ of a particular electron will be the same as it was after the latest measurement of the same quantity – if nothing else was measured or happened in between.
This is true whether the observer is called Alice, Bob, or Barack. The reason why $j_z$ ...
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Quantum statistical irreversibility ("the second law") and quantum measurement irreversibility are almost the same thing. Indeed,the latter is the special case of the former where one assumes a more specific situation in which you consider the statistical mechanics of a small system coupled to a large one. Equilibrium and nonequilibrium statistical ...
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