One criticism, of the hypothesis that consciousness causes collapse, is that 'consciousness' has not been well defined. Perhaps, in order to test whether consciousness causes collapse, it is best to test it definition by definition. One such definition is that of integrated information theory, wh...

This is not a duplicate, the other answers do not specifically solve the contradiction, nor do they give an exact answer. I have read this question: Are we so sure about superposition? How do we know superposition exists? Will there be two cats in the box (superposition) if I use virtual part...

Surely I must have a misconception?

I have to show that for the kinetic energy operator in spherical coordinates holds $\hat{T} = \dfrac{\hbar^2}{2mr^2} \lbrace \dfrac{1}{\hbar^2} \hat{L}^2-\dfrac{\partial}{\partial r} \left( r^2 \dfrac{\partial}{\partial r} \right) \rbrace$. What I tried is to write $\hat{L}^2$ with $\hat{r}$ and...

there is a particle A in the state |J,M>=|1,1> where J is the total angular momentum and M the z component, and has parity=-1. It decays in 2 particles B and C. B has spin =1/2 and parity =+1 while C has spin=1/2 and parity=-1. Parity and total angular momentum J are conserved during the decay. I...

I'm reading Dirac's Principles of Quantum Mechanics. He defines $\hbar$ to be the real number satisfying the following relation $$ uv - vu = i\hbar[u,v]$$ where $u$ and $v$ are dynamical variables, and $[u,v]$ is the classical Poisson bracket. He later defines the left hand side of this equation ...

I have read this question: What is energy band gap? What is the reason for formation of energy bands? https://en.wikipedia.org/wiki/Nuclear_shell_model If I understand correctly, the band gap (between the conduction and valence band) is due to quantization of energy. Now, what I do not unde...

When we read about orbitals, I'm sure we are all used to seeing illustrations of them by drawing some contour "along" the probability density function so that the electron's position is equiprobable on the contour and so that, for example, within the shape shown, the electron has a 99% chance of ...

Let the system formed by particle(microscopic or macroscopic)- environment coupling be described by $|\phi><\phi| $ . In decoherence approach, to retrieve the classical properties, one focuses on $Tr_a (|\phi><\phi|)$. Where the subscript 'a' denotes a particular basis spanning the Hilbert space ...

Suppose we have a composite system $AB$ and we are considering two joint (pure) states $$ \psi,\psi^\prime \in \mathcal{H}_{AB} . $$ Let's define the reduced or marginal states of $A$ and $B$ in the usual way, so $\rho_A = \mathrm{Tr}_B (|\psi><\psi|)$, $\rho^\prime_A = \mathrm{Tr}_B (|\psi^\prime><

Why is Heisenberg's uncertainty principle for the position and momentum operators in the Cartesian coordinates system defined as $$\sigma_{x}^{2} \sigma_{p_{x}}^{2} \geqslant\left(\frac{1}{2 i}\left\langle\left[x, p_{x}\right]\right\rangle\right)^{2}~ ?$$ I can't seem to find any proof of it...