I am not familiar with Quantum Decoherence, but I find it difficult to treat macroscopic states like; alive and deal on the same footing as quantum states that describes position, time, momentum and energy.
Like in a recent paper published by Frauchiger and Renner, they described states like...
I made a graph representing local hidden variables (HV) and Bell`s inequality.
Each plan of HV is represented by a shade of gray color. This can be interpreted as the number of particles emitted from the source following the plan protocol or by the proportion of the particles following the...
The Compton equation determines the shift of the wave-length of the scattered photon as a function of the ##cos\theta## of the scattered photon. It does not depend on the energy of the incident photon. With some manipulation using the equations of conservation of the momentum and energy, one...
Although this is excursion from the main point of the thread, I still think the first probability must be ##P(a|\psi)=|\langle a|\psi \rangle|^2## not ##|\langle a|\psi \rangle|## . Example, spin-1/2 has the state ##|\psi \rangle=\frac{1}{\sqrt2} |up \rangle+\frac{1}{\sqrt2} |down\rangle## So...
No great problem, just I am not familiar with this expression of probability. The probability is, in general, written in term of a value over the sum of all values representing the system. So the sum should be in the denominator. And the value in our case is the square of the projection of the...
I understand that the gradient of the field inside SG-device applies a force on the particle and separate the beam with particular spin in one direction from all other beam with different spin in the other direction. But, does it mean the time evolution operator I write above, with the gardient...
In a previous thread about an entangled pair, I proposed a thought experiment where one particle goes into a uniform magnetic field and the other set free. I remember you told me that the one goes into the field emits photon if it is anti-parallel to the field and this can be considered a type...
But if the particle goes inside a SG-device, it is measured and we get a real value eigenvalue. There is a gradient of the magnetic field inside the device and the time evolution operator of SG-device is ##e^\frac{-i\gamma(B_0+\nabla B.z)St}{\hbar}##. So how does this complex value operator...
What is then the difference between the collapse of the state and acting on it by an operator? The operator is a matrix and the state is a vector, so acting on a vector by a matrix given a value times the vector.
My question is, why the general state is still general? The unitary operator is like any other operator, once acts on the system, the state should collapse into the one with a definite value not a state of superposition of base vectors!
Any pure state of spin-1/2 particle can be represented by a superposition of spin up and spin-down relative to an arbitrarily direction.
lw>=a l+> + b l-> where a^2+b^2=1
If there is no magnetic field, the measurement of the spin is random and we get 50-50 chance to be spin up and spin down...
Thank you, yes I misunderstood the act of measurement as you said. I thought the outcome of that interaction, which is always spin-up, is the result of the measurement.
Just another point related to the interpretation of the meaning of the entangled state. You have pointed that the emission of...
The relative time reflects the order of measurement in the frame of reference of Alice-Bob. Even in the classical entanglement experiment, when Alice measures her particle first, the wave-function collapses and the state of Bob particle is reduced to the one with opposite spin along the same...
No, the position of the uniform magnetic field is before the location of Alice which means Bob can not measure his particle before Alice particle already passes though B0. See the picture.
But what does "end of entanglement" mean? Can passing the particle through the Stern-Gerlach device be considered as another sort of interaction? Why does not the Stern-Gerlach device end the entanglement and passing through B0 does?
I am not sure that I fully understand even the basic aspects of the Quantum measurement and entanglement but I just came across this thought experiment and I wish to resolve it.
In a setting of two entangled spin-1/2 particles, suppose that Alice applies a uniform magnetic field ##B_0## along...
But where in Bell`s inequality, a simultaneous reality of non-commuting observables is measured? My understanding is; Bell`s-like experiments only test whether an objective reality with particles have a predefined physical values before the measurement determined by the hidden variables exists...
Now I come to understand this statement in the following way.
1) EPR showed that the rules of quantum mechanics and the criterion of reality can not be both true which implies that quantum mechanics is not complete theory.
2) Bell`s type experiments confirmed that the rules of quantum mechanics...
I understood that EPR ruled out the possibility of having the rules of quantum mechanics consistent with the Criterion of Reality (COR) as they defined, because if it is consistent, a contradictory will ensue, therefore they concluded that quantum mechanics can not be complete. So long as this...
You confused me so much. You said that (A and -B) imply C and (A and -B) imply -C right? First let us agree about C. according to your post #15, you said:
I know that EPR showd that (A and -B) imply C. now I need to know how did they show (A and -B) imply -C which translates to the statement I...
Why math forums :) if I am questioning logical validity of statements that have physical meaning. I rather prefer to start another thread here in this forum asking the following: did EPR show in their paper that: the rules of quantum mechanics and the definition of the physical reality that...
I do not understand why you mentioned that (A and -B) implies C?. I agree that only A implies C and (A and -B) imply -C.
I then applied truth table for rigorous analysis, (I used ">" to mean: implies and "^" to mean "and".
When A implies C and (A and -B) implies -C, then this does not mean that...