19

It is true that the reactions $$e + \gamma \to e, \quad e \to e + \gamma$$ cannot occur without violating energy or momentum conservation. But that doesn't mean that electrons can't interact with anything! For example, scattering $$e + \gamma \to e + \gamma$$ is perfectly allowed. And a classical electromagnetic field is built out of many photons, so the ...


18

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 mechanics,...


18

Well, I think you said the answer yourself when you used the words "projection operator." In the Heisenberg picture the operators get projected down to a subspace at the time of the collapse. In other words, the operator 'collapses' by picking up a projection piece that kills the unphysical part of the state. Forget about pictures for a second, the physical ...


17

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 ...


17

Assuming wave-function collapse is correct (which can be a relatively hefty philosophical claim in some circles), then think of measurement this way: When you measure an observable on a system, you collapse the wave-function of the system into a Dirac delta function in the eigenbasis for that observable. If you measure position, you get a delta function in ...


17

I think most arguments in the literature can be boiled down to the point that decoherence does in no way touch the linearity of the Schrödinger equation, and thus cannot make an "or" from an "and". This is complicated in the literature by very technical discussions, which I would like to avoid. Let me explain the basic point in more details. A widely ...


17

What you describe is the process known as decoherence: any interaction of a quantum system with its environment (e.g. with photons or other particles passing by, and, yes, most likely interacting through gravity, although we don't have a theory to fully describe this yet) has the potential to destroy its genuinely quantum nature, turning quantum ...


15

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 ...


15

There are many interpretations, and while there are good arguments in favor of one or another, they are currently not distinguished experimentally. Therefore it is often considered prudent to leave the question of which interpretation is best to the field of philosophy, and focus in a physics course on the falsifiable aspects of the theory. The field of ...


15

The system doesn't "know" anything. The only uncontroversial statement one can make about the (strong) measurement of a quantum system is that you will make the correct predictions if you assume that the state after the measurement was the eigenstate corresponding to the measured value of the observable (so, for position, indeed a $\delta$-function, if we ...


13

It's tempting to think of the light as a little ball (the photon), and since little balls have a definite position the little ball has to be in a superposition of a state where it goes through one slit and a state where it goes through the other. However this is not a good description of what actually happens. The light is not a photon, and it's not a wave -...


13

Unless the wavefunction collapses to an eigenstate of the Hamiltonian, the subsequent time-evolution will produce a superposition. The postulates clearly state that, if you measure the observable $\Lambda$ and obtain the outcome $\lambda$ (assumed non-degenerate for simplicity), then the state collapses to the eigenstate $\vert\psi_{\lambda}\rangle$ of $\...


13

The way I like to understand this is the following: suppose you have one observable $A$ with spectrum $\sigma(A) = \{ a_n : n \in \mathbb{N}\}$ which we will assume discrete and non-degenerate for simplicity. In constructing the theory you would like to have states where the value of $A$ is indeed certain. Those states, the postulates of QM tell you to be ...


12

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 ...


12

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 ...


11

Aren't the particles this quantum state consists of interacting with each other? Why doesn't that cause the state to collapse? We have a mathematical model for the observations we can make of any system in the micro world. This model is quantum mechanics and its predictions have been verified experimentally over and over again. Observables are quantities ...


11

The answer by Craig Gidney is quite adequate for the question, but I want to address the word "collapse" in the title, since search engines will be homing in on it. From webster.com 1: to fall or shrink together abruptly and completely : fall into a jumbled or flattened mass through the force of external pressure <a blood vessel that collapsed> 2:...


11

So we are taught collapse at school, although there is no experimental evidence of collapse. You don't think this is good. You suggest that we are taught many-worlds instead, although there is no experimental evidence of many worlds. Why is it better? I would say there is no generally accepted interpretation of quantum theory (the mere existence of ...


11

A theorem of von Neumann says that it doesn't make a bit of difference whether you model the cat (or anything else along the causal chain between closing the box and opening it to observe the cat) as capable of collapsing the wave function. You'll make exactly the same testable predictions no matter where along the way you place the collapse. (The argument ...


9

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.


9

When position is measured, the uncertainty of the resulting delta spike's position is 0 This notion is the root of the problem. Quantum states which are actually eigenstates of the position operator are mathematically pathological and also completely unphysical. Some math tools Consider a one dimensional system. Suppose $\{|x\rangle \}$ is an orthonormal ...


9

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 beam-...


9

Quantum mechanics was developed in order to match experimental data. The seemingly very weird idea that some observables do not have a definite value before their measurement is not something physicists have been actively promoting, it is something that theoretical considerations followed by many actual experiments have forced them to admit. I don't think ...


9

When something is taught a certain way in textbooks, then two things need to happen for that to change: Leading professionals in the field have to agree that the new approach is better, and start using it nearly universally in their research papers. The new approach gradually filters down into graduate textbooks, then upper-division undergrad textbooks, ...


9

Welcome to SE -- good question! Decoherence does not mean that there won't be a wavefunction anymore, it just means that if the electron becomes coupled to the surrounding environment, its state will be described by a probabilistic mixture of orbital wavefunctions rather than a (coherent) superposition thereof. The electron in an atom doesn't have some "non-...


8

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 ...


8

If you place a camera you will not see any interference pattern. So, the answer is yes. The camera will cause the wavefunction to "collapse". But I don't like the term "wavefunction collapse", because wavefunction is not really any physical object. What the camera will basically do is cause an abrupt change in the state of the particle. Here is the ...


8

Leaving aside the quantum measurement problem (i.e. whether or not there is a "collapse" of quantum state to an eigenstate of an observable on measurement) and talking wholly about quantum state between "measurements" and its unitary evolution, I'd say that the transition is definitely a smooth shifting from one "eigenstate" to another, so that the electron'...


8

I've never seen a single prediction based upon MWI. I've also never heard of the Cophenhagen interpretation called an approximation. If that were the case, then the Copenhagen interpretation must fail in at least one limit. Does Max provide such limits? Both of these statements seem to lean towards sensationalism than towards mathematical rigor.


8

The effect you are describing in your question is known as wave-particle duality and is a form of complementarity, it has been observed in various experiments. Realisations of Wheelers delayed choice thought experiment are what I find most interesting. In a delayed choice experiment the particles are not measured before they go through the slits but ...


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