New answers tagged quantum-mechanics
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How can non-realism alone explain quantum entanglement?
Bell’s Inequality shows us that a local realism model cannot work.
Bell's inequality itself does not show that. Bell-inspired experiments showing violation of such inequality show that.
How can non-...
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-1
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Doesn't nonlocality follow from nonrealism in the EPR thought experiment and Bell tests? (Or: How is nonlocal realism viable?)
If you deny realism and say a signal travels faster than light between photons in Bell's Theorem then cause and effect are restored. This shows that denying reality (denying speed of light barrier) ...
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Doesn't nonlocality follow from nonrealism in the EPR thought experiment and Bell tests? (Or: How is nonlocal realism viable?)
Apologies for this 2nd answer, but it is a response to the updated question and my original answer is already far too long. In the updated version the OP introduces a thought experiment that involves ...
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How to identify $\hat{d}_x$ with $\hat{p}_x/\hbar$?
In that chapter (excelent book, by the way), the author shows how unitary transformations are used to implement or represent symmetry transformations. For instance, spatial homogeneity implies that ...
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Time-dependent perturbation theory for hydrogen atom transition
Well... this is first order perturbation theory so you know by assumption that the probability has to be small else you'd need to go to higher order.
This being said, your not going to get help by ...
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How to Construct Arbitrary Rotations from Discrete Rational Rotations?
I found this post on the QCSE which proves that you can make an irrational angle about some axis from just the discrete gates, because the rotations form the sides of a triangle on a sphere, and the ...
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Do quantum entangled particle pairs actually interact?
You haven't accurately described the problem with entanglement. Suppose you have two particles $S_1$ and $S_2$. For each particle you can measure two quantities $X$ and $Z$. The quantity $X$ has two ...
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Do quantum entangled particle pairs actually interact?
When photons are entangled, their properties (like spin) are correlated, not necessarily "opposite," but linked in a specific way. For example, if you measure one photon to have a certain ...
2
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Do quantum entangled particle pairs actually interact?
Well, the problem is when you design an experiment in which two far away observers measure the two different spins, but where each of the two far away observers decide randomly in which of two ...
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How can non-realism alone explain quantum entanglement?
After two recent questions on this (here's the other one), I felt it was time to write up a long account on why there are no “local non-realist” theories which can explain Bell Correlations. (A few ...
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Separability of Hamiltonian and Factorization of Wavefunction
Proposition: If the Hamiltonian of the system is the sum of two or more parts, $\widehat{H}=\widehat{H}_1+\widehat{H}_2$, one of which contains only the coordinates $q_1$ and the other $q_2$, then (1)...
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2
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Accepted
Verification of electron variable mass and charge from universe observations
There are many observational limits on variations in the electron-to-proton mass ratio ($\mu=m_e/m_p$) and the fine structure constant ($\alpha\propto e^2)$ over cosmological times and distances. (In ...
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Translation Operator for Quantum Walk
If |$\uparrow$> means coin toss represents by vector (1 0), what does <$\uparrow$ | mean and why we need it?
If $|\uparrow\rangle$ is the "ket" represented by the column vector
$$
|\...
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Is there any reference where Roger Penrose addresses the "effective size" of the mass density in a neutron star which must be at least 100 fermis?
I can't find any direct comment on the paper about heating of neutron stars, or any of the other calculations which constrain the rate of spontaneous collapse. But here are some recent quotes:
"....
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Why the probability density for a finite potential well is more inside the well compared to outside where potential is zero for higher value of $n$?
You seem to have chosen a resonant energy where there is perfect transmission through the barrier. The particle travels slower where the potential is higher, so the particle lingers there longer. ...
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Is it possible to detect entanglement by observing only one of the entangled particles?
Let V and W be the state spaces of the individual particles. An observable G acting on V acts on $V\otimes W$ by acting on the first factor, and it's easy to check that the eigenspaces are all of the ...
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Why are electron wavefunctions standing waves?
In quantum theory the outcome of experiments in general depends on what happens to all of the possible states of that system because of quantum interference, see Section 2 of this paper for an example:...
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Are orbitals observable physical quantities in a many-electron setting?
As the abstract of the paper you linked says, the answer depends on your assumptions.
Let's assume my unstated and unconscious assumptions. One line of evidence suggesting that orbitals could exist is ...
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How can non-realism alone explain quantum entanglement?
Let’s just assume we accept that non-realism is true, QM is fundamentally probabilistic, and particles have no defined state until measured. This alone doesn’t explain how measuring one particle ...
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How can non-realism alone explain quantum entanglement?
Entanglement already exists in a state prior to measurement. It is not created by a measurement. Instead, it is always created locally by some nonlinear process or interaction. The entangled particles ...
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Why should we use time independent states to derive the ideal gas law?
The basis being chosen is the basis of eigenstates of the Hamiltonian operator. One reason this basis is useful in statistical mechanics because often a crucial question in statistical mechanics is to ...
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Semigroup property in Markov processes
Binary operation in semigroups
In a semigroup,the binary operation is about combining two operators to get new one. So, if you have operators $T_\tau$ and $T_{\tau'}$, which describe how evolution ...
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I have been trying to solve this Gaussian integral, which comes up during the perturbation theory
Following the suggestion in the comment, you can write the integral as
$$\int_{-\infty}^{+\infty} \int_{-\infty}^{+\infty} e^{-2 x^2 - 2 y^2 + 2 x y} dx dy = \int \int e^{-2 (x \ y) \begin{bmatrix} 1 &...
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Clarification on when to apply the Born Rule in quantum mechanical measurement problems
In general the right way to deal with cases in which you don't understand what is happening in a quantum measurement is to use quantum theory to work it out, not to use a collapse rule.
Suppose you ...
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Doesn't nonlocality follow from nonrealism in the EPR thought experiment and Bell tests? (Or: How is nonlocal realism viable?)
Sorry for adding yet another answer to the already long list of answers, most of which provide much valuable information. However, it seems to me that core misunderstanding in the OP question has not ...
- 15.6k
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Clarification on when to apply the Born Rule in quantum mechanical measurement problems
You can simplify notation by assuming that the states $|\psi\rangle$, $|a_i\rangle$, and $|b_j\rangle$ are all normalized. So, suppose without loss of generality that
$$
\langle \psi | \psi \rangle = \...
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Double slit experiment with electrons
The equations of motion of quantum theory don't include collapse and aren't compatible with it. To add collapse to quantum theory you have to modify the equations of motion, e.g. - spontaneous ...
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Doesn't nonlocality follow from nonrealism in the EPR thought experiment and Bell tests? (Or: How is nonlocal realism viable?)
In this context a theory being "realist" means that you can explain measurement outcomes in terms of a hidden variable theory.
A local realistic theory is then one which admits an ...
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Double slit experiment with electrons
When I first heard about wave function collapse, I didn't like it. It was Re: $\psi(x) \propto \delta(x-x_0)$ for a particle at $x_0$. So I retorted: but the wave function $\phi(p)$ just expanded to ...
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Why is the principal quantum number specifically defined as 𝑛 = 𝑁 + 𝑙 when solving the radial part of Schrödinger equation for the hydrogen atom?
It's the 'accidental' degeneration of the spectrum of the Coulomb-Schrödinger operator.
For a general form of the spherical potential $V(r)$ one solves $$-R''(r) - \frac{2}{r} R' + \frac{l(l+1)}{r^2} \...
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Algebraic formulation of statistical mechanics
It's a bit more complicated. Pure states are represented by vectors in a Hilbert space representing the algebra of observables by linear maps.
A pure state is a linear form, mapping each element of ...
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Doesn't nonlocality follow from nonrealism in the EPR thought experiment and Bell tests? (Or: How is nonlocal realism viable?)
It is often said that the Bell test disqualifies "local realistic"
theories from quantum physics.
This implies that there are 3 out of 4 classes of theories from the following list, that ...
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Doesn't nonlocality follow from nonrealism in the EPR thought experiment and Bell tests? (Or: How is nonlocal realism viable?)
I agree with most of WillO's answer and some of Ken's. (Ken, I disagree with Norsen on many points, so that is our point of departure.) But a little more on this might help address the OP's question....
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17
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Accepted
"There is a bra for every ket, but there is not a ket for every bra"
The kets and bras do not always live in a Hilbert space, but when you write something like the "position eigenbras" $\langle x\rvert$, this lives in a larger space that is part of the Gel'...
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Doesn't nonlocality follow from nonrealism in the EPR thought experiment and Bell tests? (Or: How is nonlocal realism viable?)
Quantum theory describes systems in terms of observables represented by Hermitean operators that describe the evolution of multiple possible values of the system in question. This contradicts the idea ...
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How to use quantum mechanics to get Bohr velocity $ v_n=\frac{Ze^2}{4\pi\epsilon_0\boldsymbol{\hbar}}\frac1n $?
I try to calculate $ \langle \boldsymbol{p} \rangle $ in the ground state $ \psi_{100} = \sqrt{\frac{Z^3}{\pi a^3}}\exp[-\frac{Z}{a}r] $
\begin{align}
\langle \boldsymbol{p} \rangle = -i\hbar \frac{...
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0
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Accepted
Can a Foldy–Wouthuysen transformation of Dirac equation in an EM field highlight Thomas interaction?
The Thomas precession term cannot really be identified in the original Foldy-Wouthuysen transformed Dirac Hamiltonian. However, it can be seen when doing the same transformation for not the original, ...
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How can we prove that for an arbitrary operator $\hat{f}$ we can find what is called the transposed operator $\tilde{\hat{f}}$?
My Answer
What follows is limited in scope in two ways. First, I will only considering here integral operators with kernels that are defined for applications in quantum mechanics (i.e., kernels ...
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Extension of uncertainty principle to mixed-states
Consider the variance of an observable $A$ with respect to a generic mixed state $\rho$:
$$\operatorname{Var}[A|\rho] \equiv \operatorname{tr}(\rho A^2)-\operatorname{tr}(\rho A)^2,$$
also written ...
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How can we prove that for an arbitrary operator $\hat{f}$ we can find what is called the transposed operator $\tilde{\hat{f}}$?
The notation is old and cumbersome, but here goes:
Let the un-normalised state, ket vector, $\chi=\hat g\,\Phi$ so that
$$
\begin{align}
\int\Psi\hat f\hat g\,\Phi\,\mathrm dq
\tag1&=\int\...
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8
votes
Accepted
Doesn't nonlocality follow from nonrealism in the EPR thought experiment and Bell tests? (Or: How is nonlocal realism viable?)
(ADDED 9/16: My much longer response, explaining why there are no "local nonrealistic" models of entanglement, can now be found in this related recent question.)
original response:
You are ...
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Why the tunneling amplitude between two quantum states is $\left<n\right|H\left|n'\right>$?
Let me try to answer the question post by myself.
I went back to check Coleman's papers on the tunneling of false vacuum [1,2] ([2] with CG Callan Jr). The probability of tunneling per unit time per ...
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Doesn't nonlocality follow from nonrealism in the EPR thought experiment and Bell tests? (Or: How is nonlocal realism viable?)
The thrust of Bell's Theorem is that any classical random variables (which, by definition, satisfy the Kolmogorov axioms) have to satisfy certain inequalities. Some quantum mechanical observables ...
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3
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Accepted
Parity of the wave function
Quick question: have you thought about also multiplying the left hand side by the same phase $e^{i\theta}$? What you have in your question is essentially transforming the negative-$x$ part of the wave ...
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If momentum is a function of position, then how does the uncertainty principle work?
There are no trajectories in quantum mechanics. In classical mechanics, you can talk about the position of a particle as a function of time, $x(t)$. Then, from there, you can derive the momentum as a ...
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If momentum is a function of position, then how does the uncertainty principle work?
In classical physics the position of a particle is described at a a given time by a set of numbers $(x(t),y(t),z(t))$. If you were to measure the $x$ position of a particle at time $t$ you would get ...
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Doubt about dirac notation
You should think of the symbols inside the ket as a label first and foremost. A bit like the index of a basis vector. For instance, $e_2=(0,1,0)$, here "2" is a label for the vector, and you ...
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Doubt about dirac notation
The ket $\lvert x \rangle$ means a particle whose position is $x$.
The ket $\lvert -x \rangle$ means a particle whose position is $-x$.
It is not the case the one is minus the other, i.e.
$$
\lvert -x ...
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-1
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Doubt about dirac notation
The wave function $\psi(x)$ is represented in Dirac notation by $\langle\psi|x\rangle$. It represents the probability amplitude of the particle to be located at position $x$. Using this notation we ...
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Accepted
Doubt about dirac notation
By definition
$$
X |x\rangle = x | x \rangle , \qquad X | -x\rangle = (-x)|-x\rangle
$$
Suppose that $|-x\rangle = - |x\rangle$. Acting on both sides with $X$, we then have
$$
X |-x\rangle = - X |x\...
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