In is shown that when two observers carry out a simultaneous measurement on a pair of spin-? particles in a "singlet" state a possibility exists for an outcome that lacks physical meaning. More specifically, despite the fact that the two commuting operators formally possess simultaneous eigenvectors it is not possible for physical reasons these eigenvectors to exist simultaneously. It is pointed out that the possibility for such non-physical outcome is observed only in the case of "singlet" state which puts into question the physical meaning of such state, and following from it exotic notions such as "non-locality". This hints that probably QM in its present form should be reconsidered with regard to its limitations.
In is shown that when two observers carry out a simultaneous measurement on a pair of spin-? particles in a "singlet" state a possibility exists for an outcome that lacks physical meaning. More specifically, despite the fact that the two commuting operators formally possess simultaneous eigenvectors it is not possible for physical reasons these eigenvectors to exist simultaneously. It is pointed out that the possibility for such non-physical outcome is observed only in the case of "singlet" state which puts into question the physical meaning of such state, and following from it exotic notions such as "non-locality". This hints that probably QM in its present form should be reconsidered with regard to its limitations.
Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The question is answered as to when the consecutive applications of measuring apparatuses give a simultaneous measurement of their observables. For this purpose, all the possible state reductions caused by measurements of an observable is also characterized by their operations.
We discuss the fact that a single spin observable σx in a quantum state does not have a counterpart in physical reality. We consider whether a single spin-1/2 pure state has a counterpart in physical reality. It is an eigenvector of Pauli observable σz or an eigenvector of Pauli observable σx. We assume a state , which can be described as an eigenvector of Pauli observable σz. We assume also a state , which can be described as an eigenvector of Pauli observable σx. The value of transition probability is 1/2. We consider the following physical situation. If we detect , then we assign measurement outcome as +1. If we detect , then we assign measurement outcome as −1. The existence of a single classical probability space for the transition probability within the formalism of the measurement outcome does not coexist with the value of the transition probability = 1/2. We have to give up the existence of such a classical probability space for the state or for the state , as they define the transition probability. It turns out that the single spin-1/2 pure state or the single spin-1/2 pure state does not have counterparts in physical reality, in general. We investigate whether the Stern-Gerlach experiment accepts hidden-variables theories. We discuss that the existence of the two spin-1/2 pure states and rules out the existence of probability space of specific quantum measurement. If we detect , then we assign measurement outcome as +1. If we detect , then we assign measurement outcome as −1. This hidden-variables theory does not accept the transition probability . Therefore we have to give up the hidden-variables theory. This implies the Stern- Gerlach experiment cannot accept the hidden-variables theory. A single spin-1/2 pure state (e.g., is a single one-dimensional projector. In other word, a single one-dimensional projector does not have a counterpart in such physical reality, in general. The one-dimensional projectors are commuting with each other. Our discussion shows that we cannot assign the specific definite values (+1 and −1) to the two commuting operators, simultaneously. We study whether quantum phase factor accepts a hidden-variables theory. We discuss that the existence of two spin-1/2 pure states |0_ = ( + )/√2 and = ( + e iθ )/√2 rules out the existence of probability space of a hidden-variables theory. If we detect , then we assign measurement outcome as +1. If we detect , then we assign measurement outcome as −1. The hidden-variables theory does not accept the transition probability Therefore we have to give up the hidden-variables theory for quantum phase factor. We explore phase factor is indeed a quantum effect, not classical. Our research gives a new insight to the quantum information processing which relies on quantum phase factor, such as Deutsch’s algorithm.
We discuss the fact that a single spin observable σx in a quantum state does not have a counterpart in physical reality. We consider whether a single spin-1/2 pure state has a counterpart in physical reality. It is an eigenvector of Pauli observable σz or an eigenvector of Pauli observable σx. We assume a state ∣+z⟩, which can be described as an eigenvector of Pauli observable σz. We assume also a state ∣+x⟩, which can be described as an eigenvector of Pauli observable σx. The value of transition probability ∣⟨+z∣+x⟩∣2 is 1/2. We consider the following physical situation. If we detect ∣+z⟩, then we assign measurement outcome as +1. If we detect ∣+x⟩, then we assign measurement outcome as −1. The existence of a single classical probability space for the transition probability within the formalism of the measurement outcome does not coexist with the value of the transition probability ∣⟨+z∣+x⟩∣2=1/2. We have to give up the existence of such a classical probability space for the state ∣+z⟩ or for the state ∣+x⟩, as they define the transition probability. It turns out that the single spin-1/2 pure state ∣+z⟩ or the single spin-1/2 pure state ∣+x⟩ does not have counterparts in physical reality, in general. We investigate whether the Stern-Gerlach experiment accepts hidden-variables theories. We discuss that the existence of the two spin-1/2 pure states ∣↑⟩ and ∣↓⟩ rules out the existence of probability space of specific quantum measurement. If we detect ∣↑⟩, then we assign measurement outcome as +1. If we detect ∣↓⟩, then we assign measurement outcome as −1. This hidden-variables theory does not accept the transition probability ∣⟨↑∣↓⟩∣2=0. Therefore we have to give up the hidden-variables theory. This implies the Stern-Gerlach experiment cannot accept the hidden-variables theory. A single spin-1/2 pure state (e.g., ∣↑⟩⟨↑∣) is a single one-dimensional projector. In other word, a single one-dimensional projector does not have a counterpart in such physical reality, in general. The one-dimensional projectors ∣↑⟩⟨↑∣ and ∣↓⟩⟨↓∣ are commuting with each other. Our discussion shows that we cannot assign the specific definite values (+1 and −1) to the two commuting operators, simultaneously. We study whether quantum phase factor accepts a hidden-variables theory. We discuss that the existence of two spin-1/2 pure states ∣0⟩=(∣↑⟩+∣↓⟩)/2 and ∣θ⟩=(∣↑⟩+eiθ∣↓⟩)/2 rules out the existence of probability space of a hidden-variables theory. If we detect ∣0⟩, then we assign measurement outcome as +1. If we detect ∣θ⟩, then we assign measurement outcome as −1. The hidden-variables theory does not accept the transition probability ∣⟨0∣θ⟩∣2=cos2(θ/2). Therefore we have to give up the hidden-variables theory for quantum phase factor. We explore phase factor is indeed a quantum effect, not classical. Our research gives a new insight to the quantum information processing which relies on quantum phase factor, such as Deutsch's algorithm.
The Einstein-Podolski-Rosen paradox highlights several strange properties of quantum mechanics including the super position of states, the non locality and its limitation to determine an experiment only statistically. Here, this well known paradox is revisited theoretically for a pair of spin systems in a singlet state under the assumption that in classical physics time evolves in discrete time steps t while in quantum mechanics the individual spin system(s) evolve(s) between the eigenstates harmonically with a period of 4 t . It is further assumed that time is a single variable, that the quantum mechanics time evolution and the classical physics discrete time evolution are coherent to each other, and that the precision of the start of the experiment and of the measurement time point are much less than t . Under these conditions, it is demonstrated for a spin system that the fast oscillation between the eigen states spin up | ↑> and spin down | ↓> reproduce the expected outcome of a single measurement as well as ensemble measurements without the need of postulating a simultaneous superposition of the spin system in its quantum state. When this concept is applied to a spin system pair in a singlet state it is shown that no entanglement between the two spins is necessary to describe the system resolving the Einstein-Podolski-Rosen paradox.
The Einstein-Podolski-Rosen paradox highlights several strange properties of quantum mechanics including the super position of states, the non locality and its limitation to determine an experiment only statistically. Here, this well known paradox is revisited theoretically for a pair of spin 1/2 systems in a singlet state under the assumption that in classical physics time evolves in discrete time steps t while in quantum mechanics the individual spin system(s) evolve(s) between the eigenstates harmonically with a period of 4 t. It is further assumed that time is a single variable, that the quantum mechanics time evolution and the classical physics discrete time evolution are coherent to each other, and that the precision of the start of the experiment and of the measurement time point are much less than t. Under these conditions, it is demonstrated for a spin 1/2 system that the fast oscillation between the eigen states spin up | ↑> and spin down | ↓> reproduce the expected outcome of a single measurement as well as ensemble measurements without the need of postulating a simultaneous superposition of the spin system in its quantum state. When this concept is applied to a spin 1/2 system pair in a singlet state it is shown that no entanglement between the two spins is necessary to describe the system resolving the Einstein-Podolski-Rosen paradox.
It is shown that there is one purely deterministic outcome when measurement is made on the state function chosen by EPR to describe the combined two-particle system – the distance between the two particles is preserved the same. Further, it is shown that, surprisingly, the Ψ-function designed according to QM leads to the following paradox – despite the fact that the two particles move in opposite directions, in time the distance between them becomes shorter and shorter. As is known, Einstein, Podolsky and Rosen (EPR) [1] observe two particles which have interacted in the past (for 0 Tt< <) but the interaction between them has ceased for times Tt>. Nevertheless, both particles, even at times Tt> EPR consider to be described by one common state-function, namely 1 2 ( ,)x xΨ. The authors have chosen to explore one particular form of that state-function, namely ( ) 1 2 01 2 (), i x x x pdpex x − −Ψ = ∫ =. (1) This function may be rewritten as ( ) 2 0 11 2 (), i ix x p x pdpe ex x − +Ψ = ∫ = = (2) and then 1 i x p e = can be considered as the orthonormal basis of an observable A pertaining to particle 1 (position of particle 1) while the exponents