I was wondering about the same question, about the field outside a solenoid with a varying current in its wires.
I'm a bit puzzled by the part that \nabla \times \vec E = 0 = \frac{\partial B}{\partial t} outside the solenoid.
I'm guessing this is an affect by the "long" solenoid? Since...
time dilation is the slowing of time. Ofcourse as seen by someone else, you can never notice that ur time is running slow !? however you can compare its pace with other observers by monitoring something that should run at the same pace. You can quite easily understand why gravity must slow time...
i think its something like this
you have Sy|S k> = -S+k for k=0,1,...,2S+1
exp(i*pi*Sy)|S k> = exp(i*pi*(-S+k))|S k>
now
exp(i*pi*(-S+k)) = exp(-i*pi*S)*exp(i*pi*k) if k = 0 then
exp(i*pi*Sy)|S 0> = exp(i*pi*(-S))|S 0> = cos(Pi*S)|S 0> and cos(Pi*S) = (-1)^S
I can perhaps clarify what I mean.
To make this simpler I change the scenario a little.
Alice has the particles A anc C in the state.
|A,C> = (1/sqrt(2))(|00>+|11>)
and she has the particle D which is entangled with Bobs particle E in the similar state
|D,E> =...
your friend the professor he isn't a professor in Quantum Mechnics right ? One thing that you can be absolutley sure about is that there are such things as entanglement which make it possible to teleport qm states. Now I don't think entanglement or teleportation is possible in the classical world ?
Soppuse Alice have two particles A and C that are in a partly entangled state
|Y(A,C)>. We also have another person Bob (ofcourse) with whom Alice share a pair of entangled particles D and E in the singlet state.
Now suppose Alice make a measurement on her two particles C and D, she...
I must say this is fun but I wonder if this isn't just one of the wonders of statistics. Picking out things that obey this 3:1 law and ignoring all the rest. What other things are there that you found to obey this law ?
Let P be a density matrix. Then the von neumann entropy is defined as
S(P) = -tr(P*log(P))
But how is log(P) defined ?
--edit--
found the answer. the trace is independent of representation so that if P is diagonalized with eigenvalues {k} then S(P) = H({k}) where H is the shannon entropy.
Could somebody please explain or give me a link to an explanation of the idea about measerument that von neumann put forward. That is that a system interacts with a pointer state associated with the measurering device with the hamiltonian
H:=c * d(t) * A (X) * P
where d(t) is diracs delta...
Another interresting thing is that there might always be a small probability that I will die the next moment, that is one of my clones die (!?) but I myself live on (atleast for the moment). This gives the buddist idea of dying and beeing reborn again every moment a whole new meaning. They say...