# Tag Info

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Will wave function collapse without measurement? Yes and no. Collapse is a sometimes useful fiction. Sometimes you can pretend a subsystem has evolved into a particular state, a collapsed state. Since all matters are described by wave functions, then in principle, I should be able to describe wave function collapse by Schrodinger's equation. (I ...

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According to the standard presentation of QM, yes, there is a collapse. The wave function evolves in space not in a local manner, in the way, say a particle travels along line, but in the way a balloon evolves when air is blown in. A measurement, or interaction is local; the wave-function - the balloon collapses, say where I pricked it with a needle. But ...

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Following von Neumann, the measurement process is just a special type of interaction between two systems, that follows special rules when it comes to averaging a specific observable $X$. Let $H$ be a Hilbert space, $(\Omega,\mathscr{B})$ a Borel space, with $\Omega\subseteq \mathbb{R}$ and $\mathscr{B}$ a Borel $\sigma$-algebra on $\Omega$. By means of the ...

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Entanglement is not necessarily equivalent to measurement, if the entanglement is reversible. Measurement has to do with an irreversible event, like photon absorption or emission. Until an irreversible event occurs with X or Y, the entanglement of X with Y just results in the creation of an entangled, composite, XY wave function (and composite XY density ...

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The situation here is a bit complicated. The problem is that with a measurement process, you are not allowed to consider only the evolution of the measured system, but you have to take into account the evolution of the global system formed by the measured system and measurement apparatus. For that system, the (global) wavefunction always evolves by means of ...

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The wave function is "reduced", meaning that there is a reduction in size of the continuous range of states (positions) that have non-zero probability. However, it never goes to being a single eigenstate, due to the quantum uncertainty of the probe used in the measurement or of the measurement apparatus, itself. That uncertainty can never go to exactly zero. ...

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The state is "measured" in the sense you are imagining - that is, it becomes definite - at whatever time it becomes possible in principle to infer its having a particular measurement outcome. In your case, if the probe provides unambiguous information about the measurement result, the time of measurement will be found to have been delta-t back in time. This ...

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Better calibrated response: I'm a little confused about your first argument, that decoherence should somehow reduce entropy. Decoherence is the coupling of a system to a much larger system and of course adds entropy. Another way of putting it: if one ignores the environmental degrees of freedom, decoherence essentially maps pure states (zero entropy) to ...

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The quantum state is a vector in a Hilbert space. Each basis vector in the Hilbert space is a possible observation one can make. For example, when modelling the position of a free particle, we assign one basis vector to each point in space. The length of the shadow that the state casts upon each vector is the (square root of) the probability that a ...

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So, the wave function is collapsed even though the particle seems to have never interacted with the detector. Is this accurate? Totally. There is even a whole class of measurements called quantum nondemolition measurements, where you can detect whether or not a single photon could set off a trigger without actually setting off the trigger. Would the ...

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One has to decide what the observable to measure is, and expand the state onto its eigenstates accordingly. In your example one wants to measure the position of the particle, hence it is convenient to expand the state $|\psi\rangle$ as $$|\psi\rangle = \int \textrm{d}x'\,|x'\rangle\langle x'|\psi\rangle.$$ In order to measure the possible position of the ...

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I think the fundamental misunderstanding of superposition has a lot to do with the popular interpretation of quantum mechanics. That is, how Schrödinger's cat is portrayed in popular science. When a quantum system is in a state of superposition, it means that the outcome of a measurement of some property of that system is uncertain. The wacky thing about ...

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The process of "collapse" can almost entirely be handled just by including your measurement apparatus in a quantum description. It's the quantum interaction between observer and observed that causes collapse. For the mathematics of this process, you might want to look at my answer to Particle interactions which are NOT considered observations? for more on ...

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Just regarding question number 3: 1) If your friend knows anything at all about quantum mechanics, he will not say "Both", because quantum mechanics does not allow anything to be in two states at once, ever. 2) If your friend knows a small amount about quantum mechanics, he might make the mistake of saying "Neither", because, after all, most coins ...

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I would say that you are suffering from a little bit of pop-science fatigue. You don't need to be convinced of these things because the great majority of working physicists don't think about quantum mechanics in this way. What if a brain dead person looks and doesn't comprehend? This is called "begging the question", I think. Except for a handful ...

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At the moment, one observe a state, not the state does collapse, but it's our knowledge about this state, that collapses. This is right for cats in boxes with poison watches. An other thing is, if you have to do with superposition of quantum states. In a Bose-Einstein condensate all involved atoms are in a superosition and a powerful enouth observation of ...

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According to this paper, an experiment was performed that measured the single electron's physical wave function by causing it to interfere with itself. The interference pattern matched the predictions of the Schrodinger equation. So, apparently this was a direct measurement of an electron's wave. Hydrogen Atoms under Magnification: Direct Observation of ...

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In addition to these two excellent answers I'd like to point out that the deceptively smooth surfaces of orbital graphical representations found in text books and web pages, like this excellent rendition of a 2p orbital, below are surfaces where the electron probability density is the same. In no way do they represent paths or 'orbits'.

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As usual, you can re-express the wave-function in momentum space (it's just a Fourier transform away from the spacial wave-function for bound state which is really nice). But that does not tell you how the electron moves anymore than the spacial wave function tells you where it is. Instead, it tells you the probability distribution function for results of ...

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The lobes are regions where you have a non-zero probability of finding an electron. These regions have varying shapes for different types of orbitals. It wouldn't make sense to think that orbitals are actually paths of some sort, where electrons whizz around. You'll know this is wrong if you try to understand the uncertainty principle. The uncertainty ...

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When performing a measurement based on a predicate $P$, such as the first qubit $P(\left|xy\right\rangle) = x$ or the second qubit $P(\left|xy\right\rangle) = x$ or some combination like $P(\left|xy\right\rangle) = x \text{ and } y$, you generally do the same thing: Let $S$ be the set of states that match P. Let $Z$ be the set of states that don't match P. ...

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