From what I understand, QM is all about uncertainty. The wavefunction (or rather $|\Psi|^2$) gives us a probability of finding a particle at a certain point. Then, we measure the particle, and find what point it is at.   Now, here's my trouble - QM states that before we measured this particle, it was in a superposition of many states and did not have a definite position. This also implies the wave function is "perfect" because it gives as accurate information as possible about the position particle before we measure it.  So, how do we know this? Why can't there be a function $\phi$ that doesn't give probability distributions, but instead gives definite locations of particles, and we just haven't found a way of expressing or computing it? Why do we know that the position of particles is physically uncertain, and not just unknown to the experimenter?  Sure, Quantum Mechanics works out beautifully and fits the results, but perhaps it is simply a very good theory of probability when we have a much more elegant and simple theory?
121972
It was mentioned to me that it can be shown that there is no classical explanation for the uncertainty in Quantum Mechanics -- i.e. that there are no hidden workings that we have just not yet seen, which could be explained classically and would explain the probabilistic nature of Quantum events in a 'deterministic' fashion.  Can someone explain how this is known please?
90699
Let's say we have a wavefunction $\psi$ and a measurement operator $\hat A$.  I understand how eigenvalues and eigenvectors of $\hat A$ describe the possible outcomes of the measurement.  I also understand that the average measurement can be computed as $\langle \psi|\hat A|\psi\rangle$.  It's still not clear to me what the direct meaning of $\hat A |\psi\rangle$ is. It is a wavefunction; how does its corresponding quantum state relate (in physical terms) to the original state $\psi$ and the measurement $\hat A$?
95255
The collapse of the wave function by measurements is one of the most mysterious properties of quantum mechanics.    At what scale does the wave function collapse? What are the conditions for a collapse?  Can it be made precise?  Does the collapse happen instantaneously, or is it spread out in time?  What is the precise equation for the collapse?  Why is the collapse time-asymmetric, and can this explain the arrow of time?
108621
I saw the question  but it's a bit advanced for me and probably for some people who will search for this question.  I learned QM but not QFT, but I still hear all the time that "particles are the quanta of fields" and I don't really understand what it means.  Is there a simple explanation for people who know QM but not QFT?
106838
The standard interpretation of $|\psi|^2$ is taken as the probability density of the wave-function collapsing in the given infinitesimal small region. The way this probability is interpreted (at least in the text-book by Griffiths) is that if I prepare a large number of identical states and then perform a measurement on each of them then the probability associated with $|\psi|^2$ actually represents the statistical results of the measurements made (individually) on all these wave-functions of the entire ensemble. This seems like a good enough argument to accept $|\psi|^2$ as the probability density of the wave-function collapsing in a given infinitesimal small region even if I have only one wave-function.  But the  suggests that it is fundamentally impossible to make two states that are completely identical and thus, to my understanding, it makes absolutely no sense to talk about those identical wave-functions that were used to project $|\psi|^2$ as the probability density.  Put in other words, if I can't replicate a wave-function at all then how do I confirm in my laboratory that the probabilities obtained by $|\psi|^2$ actually represents the likely-hood of the collapse happening in a given region?   Edit Is it the catch that the No-Clone Theorem suggests only that a given state can't be evolved to a state identical to another state and it allows the two states being identical if they are so from eternity?
43286
I Appreciate the statement of Heisenbergs uncertainty principle however am a bit confused as to how exactly it applies to the Quantum Mechanical situation of an infinite square well.  I understand how to apply schrodingers equation and appreciate that energy Eigenvalues can be deduced  as   $$E_n=\frac{n^2\hbar^2\pi^2}{2mL^2}$$  However I have read somewhere that the reason that the quantum particle can not have $n = 0$ in other words $E = 0$ is because by having zero energy we also have a definite momentum with no uncertainty and by the Heisenberg uncertainty principle this should lead to an infinite uncertainty in the position of the particle however this cannot be in an infinite well as we know it should be somewhere in the box by definition. Therefore $n$ may be another greater or equal to one.  Surely when $n = 1$ we have the Energy as $\hbar^2 \pi^2 / (2mL^2)$ which is also a known energy and so why does this (as well as the other integer values of $n$) not violate the uncertainty principle.
52156
When an observer causes the wave function of a particle to collapse, how can we know that the wave function was not collapsed already before the measurement?  Suppose we measure the z-component of the spin of an electron. After the measurement, it is entirely aligned along the measured direction, e.g. the +z-direction. Before the measurement we need to assume that a probability distribution proportional to $|\Psi|^2$ of the two allowed directions is present.  If we repeat the measurement with many identically prepared electrons, we should see such a distribution finally. For example, we could measure 40% spin-down and 60% spin-up.  However, it seems we could also assume that all of these particles have a defined spin-direction before we measure them.  What is an intuitive (being aware that quantum phenomena as such are rarely intuitive) explanation for why we cannot simply assume that the spin was already aligned completely in that measured direction?    With regards to the suggestion that this two-year old question is a duplicate , I would like to point out that my question isn't limited to entanglement, but asks about a very fundamental principle in quantum mechanics, and as such is not a duplicate.
74910
I was looking at a website that claims to generate random numbers from observation of quantum effects. This lead me to question how we know that the numbers are truly random.  When we observe a probability wave and it collapses in one place into a particle, how do we know that the location of the particle is really random?  Do we have any evidence of the randomness, or is it just that no one can predict the location right now?
82890
The quantum-mechanical model of atoms was derived from Heisenberg's uncertainty principle, which states that the position and momentum of a particle cannot both be determined to an arbitrary degree of accuracy. In order to understand the distribution of electrons in an atom, the momentum of an electron in the uncertainty principle is converted into its energy. The principle becomes &quot;we cannot determine both the position of an electron and its energy to an arbitrary degree of accuracy&quot;. The idea that electrons exist in orbitals comes from the solving of the Schrödinger equation, which yields the principle quantum number, the angular momentum quantum number, the magnetic quantum number, and the spin quantum number. For each atom, a combination of the first three Schrödinger parameters specifies a unique electron orbital. It is noticeable that the Schrödinger equation simplifies the uncertainty principle to the extent that we are only uncertain about the position of an electron, but not its energy anymore. Each electron orbital represents a probability distribution map of electrons that fall under it. Theoretically, we can find an electron that falls under a given orbital at any position within the probability distribution map that it specifies. But the problem is, each orbital has a fixed energy value. No matter where in the orbital we find the electron, its energy does not vary. In other words, when we look at an atom and want to determine the position and energy of one of its electrons, we assign it to an orbital. The contradiction is that as soon as the electron is assigned an orbital, we fix its energy, and the only indeterminate variable is its position. So, does electron orbital theory contradict the uncertainty principle, where there are two indeterminate variables? A very concise version of my question: the Heisenberg uncertainty principle implies that we cannot simultaneously determine the position and energy of an electron. But if we divide the outer space of an atom into electron orbitals, like the electron orbital theory does, and assign each electron to an orbital, we wind up being able to determine the energy of each electron!
85016
I have read the quantum mechanical model of an atom which says that path of an electron around the nucleus is uncertain due to uncertainity principle which says that it is impossible to measure both momentum and position of an electron at the same time so it is impossible for an electron to move in a well defined circular orbit.But  what if we simply do not measure the elcetron then it should move in a well defined path.So what really restrict it from moving like that?
56827
I followed a basic course on QFT and know some basic concepts but I focussed mainly on calculations and understanding the Feynman rules e.g.. However, sometimes I have the idea that there a quite some fundamental concepts I might be missing, especially regarding the interpretation of QFT and &quot;what's happening&quot;. One of the things I wonder is how does wave collapsing of QM fit into QFT? In QM there was a lot of focus on measurements, probabilities, and (the collapsing) of the wave function. Of course, particles in QM and QFT are fundamentally different. In QM they are probability waves and in QFT they are (excitations of) fields. And if I'm not mistaken I would say that for the field of a particle, the excitations of the field are governed by the rules of Quantum Mechanics. However, is the wave function really completely gone, or is there some way to link fields to wave functions again and effects of measurements etc.
81219
Consider a particle in a potential well. Let’s assume it’s a simple harmonic oscillator potential and the particle is in its ground state with energy E0 = (1/2) &#8463;&omega;0. We measure its position (measurement-1) with a high degree of accuracy which localises the particle, corresponding to a superposition of momentum (and therefore energy) states.  Now we measure the particle’s energy (measurement-2) and happen to find that it’s E10 = (21/2) &#8463;&omega;0. Where did the extra energy come from?  In the textbooks it’s claimed that the extra energy comes from the act of observation but I wonder how that could work. Measurement-1 which probed the position of the particle can’t have delivered to it a precise amount of energy, while measurement-2 might just have been passive. No doubt there is entanglement here between the particle state and the measuring device but where, and which measurement?
75656
I got to read Volume I of Feynmann's lectures. It said that at absolute zero, molecular motion doesn't cease at all, because if that happens, we will be able to make precise determination of position and momentum of the atom. We do know that Heisenberg uncertainty principle holds for microscopic particles in motion. But what then is wrong to consider that all molecular motion ceases at absolute zero? In other words, does the uncertainty principle not hold when there is no motion?  Need some help!
73681
new finding by Minev et al. seems to suggest that transitions between atomic states are not instantaneous, but continuous processes wherein a superposition smoothly adjusts from favoring one state to another (if I understand it correctly). The authors also claim to be able to catch a system "mid-jump" and reverse it. Popular articles are  and .  I am curious if this finding rules out any interpretations of QM. It seems to generally go against the Copenhagen attitude, which describes measurements as collapsing physical systems into a definite classical state. The popular articles indeed claim that the founders of QM would have been surprised by the new finding.  The link with the asterisk mentions that something called "quantum trajectories theory" predicts what was observed. Is this an interpretation, or a theory? And are they implying that other interpretations/theories don't work?
119915
I have almost no background in physics and I had a question related to Schrodinger's Equation. I think, it is not really research level so feel free to close it, but I would request you to kindly suggest some existing literature which can help me develop a better understanding for the same.   While reading up about it from an introductory text on Quantum Physics, I wondered for a little while how does one derive this equation. Very soon, the author () added the detail that he just took it on faith when he was himself a student. He goes on to say Schrodinger equation rightly predicts the behavior of atomic transitions etc and people believe that it is a fundamental law of nature for quantum systems.  Then he raises the question himself which I wanted to know the answer to. Namely     What made Schrodinger write such an equation which became a fundamental equation, not to be derived from more fundamental equations?   He then adds that it will be an interesting topic for students of history of science which does not answer my question. Could you please try answering this question (or is this question really useless) ?  Thanks for your time
9178
I have heard several pseudoscientific explanations about the  and find them hard to believe.  As a mathematician mainly focusing on functional analysis, I have a considerable interest in this matter. Although I still have no idea about it, I aim to truly understand it one day. For now, the question is:  Can the Heisenberg Uncertainty Principle be explained so that a non-scientist can at least get a correct idea of what it says and what not?  One of the most heard explanations is the one that says naïvely that while trying to determine the position of a particle you send energy (light) so you modify its speed, therefore making it impossible to determine the speed. If I understand well this should only be a some sort of metaphor to explain it, right?
99022
Griffiths says that you can have only 1 well defined component of the angular momentum because of the uncertainty principle. From the uncertainty principle, we get that  $$ \sigma_{L_x}\sigma_{L_y} \geq \frac{\hbar}{2}|\langle L_z\rangle | $$  If we know $L_z$, can't we make $\sigma_{L_x}$ as small as possible while letting the deviation in the $y$ component get bigger, essentially making it so that we know 2 components?  Also from the uncertainty principle,  $$ \sigma_{L_y}\sigma_{L_z} \geq \frac{\hbar}{2}|\langle L_x\rangle | $$  So if we know the $z$ component, that means its deviation is zero, making the right hand side $\langle L_x \rangle$ zero as well?