I've worked through a Stern Gerlach experiment for the Sx and Sz directions using the density matrix formalism to account for the environment. This shows a result which I think is correct but relies on decoherence to give the "actual" value. I'm not confident about the result though. Would...
I've seen in some lecture notes that the proper distance dp(t) can be written as
##\int_{t_e}^{t_0} c dt/a = \int_0^z c dz /H(z)##
I can perform this integral ok using
##H =\dot a/a## and the fact that ##1 + z = 1/a(t_e)## but it requires associating the limits of the integration as te...
Thank you PeterDonis. I think I get this now thanks to your kind help. I'll try and have another think through it this evening and then see if it still makes sense. I'm really grateful for your help. Many thanks.
Hi I'm trying to put some notes together but have run into an anomaly which I seem to have overlooked in the past but puzzles me now. I've included a jpg file of the page I've written up so far with the problem indicated right at the end. I'm using Barbara Ryden's book as my source, but it...
OK so I think you are saying that the atom is initially in a superposition but very quickly decoheres into a state which the the detector picks up, thereby then being in either the detected (or undetected) state. The worlds have effectively split and so now you have the mixed state you show...
Yes it makes sense to me - but measuring instruments have got be "good" in the sense that the Hamiltonian has got to be such that any unitaristic evolution means the pointer will end up pointing in the right place indicating a correct outcome by deviation from any designed ready state.
I'm not sure I understand why |detector> precludes a state like
|ψ>=∑a_i|system>|detector ready>|row>.
→ a_1|system up>|detector up>|row up> + a_2|system down>|detector down>|row down>,
which is Everett's "universal wave function" and with say "detected" as meaning "detector read up"...
Thanks bhoppa for that, I had Hensen's paper on my reading list.
However,
From your answer I see that you are considering |rest of the world> = |row> to be a (pure) quantum state. which is clearly a macroscopic one, which can be part of a superposition like |ψ>=|∑a_i|system>|detector...
Max Tegmark in his paper “Many worlds in context” http://arxiv.org/abs/0905.2182
Argues that …. .“Everett’s MWI is simply standard QM with the collapse postulate removed, so that the Schrödinger equation holds without exception”. He also argues that from this we can deduce that not only...
But interference effects do depend on relative phases. These phases can be introduced in experiments like in the standard measurement ansatz below
Exp(iHt) |ψ_1>|a0> = exp(iθ_1)|ψ_1>|a_1>
Exp(iHt) |ψ_2>|a0> = exp(iθ_2)|ψ_2>|a_2>
Where the phases exp(iθ_i) are introduced (randomly?)by...
From the postulates of QM we know that any state |ψ> is the same as exp(iθ)|ψ>.
Ok so take the spin state of an electron in the x direction and expand in the z basis to get
|+x> = 1/sqrt2(|+> + |->)
= 1/sqrt2(|+> + exp(iθ) |->) using the above,
choosing theta =∏...
In the double slit experiment there are interference terms which are responsible for the way in which particles appear on a screen (diffraction pattern). The density matrix for an electron with spin |+X> going into a stern Gerlach alligned in the z direction also has off diagonal terms which...