QM and "Commonsense" 1.In Quantum Mechanics the value of an observable results from the interaction between the "system" with the "Measuring gadget". But when the experimenter[or the technologist concerned] is devising/constructing the gadget he has a view the "system" with its stand alone properties/attributes.It seems to be so. But QM theory itself cannot ascribe the value of some observable to the system alone. How does one explain this? 2. On Bell's Theorem:You may consider the typical case where a source emits a positron and an electron with opposite spin so that total angular momentum and spin is zero.The QM expectation is given by: \(<\sigma_1.\vec{a} \sigma_2.\vec{b}>=-a.b\) --------- (1) a and b are unit vectors. In the above relation we are considering the measured value of spin which is the outcome between the value of some property of the system itself and the measuring gadget The "classical" formula for evaluating the expectation with the hidden variable is as follows: \(P(\vec{a}. \vec{b})=\int d\lambda \rho (\lambda)A(\vec{a})B(\vec{b})\) ---------- (2) Lambda is the "hidden variable" A(a) and B(b) are the measured values of spin along the unit vectors a and b Now some property of the system may depend on the value of λ and the probability distribution ρ(λ). Is the effect of measurement being fully accounted for by the the hidden variable λ and the pdf ρ(λ), especially in view of the fact that the process of measurement modifies the wave function itself. We must remember that relation (2) depends on classical intuition.Lambda should have some relationship with the process of measurement. Such relationship should be clearly visible in the integral given by relation (2). But it(the said visibility) is simply not there Would it be possible remove the contradiction between QM and commonsense intuition, expressed through Bell's Inequality, by considering the above factors? 3. Non-locality and Entanglement:Let’s consider a pair of particles [with their signals] comprising an isolated system. Any change in some property of either particle is due to the signal/s received from the other. Each particle has the knowledge of the signals emitted by it and the consequences of such signals on the other. This is a “continuous process” which may go simultaneously with increasing separation between the particles. The entanglement of some property ,between the particles, even in the highest level of non-locality seems to be intuitively “natural” so long the system remains an isolated one, comprising the two particles and the signals exchanged between them. Would it be correct to say that the entanglement of properties in the non-local context should not be considered as an injury to commonsense perceptions?
