Bell’s theorem founded on Bell’s inequalities asserts that no local realistic theories can reproduce all quantum mechanical predictions for spin correlation of particle pairs. It is pointed out that the assumption o...Bell’s theorem founded on Bell’s inequalities asserts that no local realistic theories can reproduce all quantum mechanical predictions for spin correlation of particle pairs. It is pointed out that the assumption of setting-independent probability makes Bell’s inequalities not impose constraint on all local realistic models and thus constitutes a theoretical loophole of Bell’s theorem. A counterexample is presented by showing that a local realistic model with appropriate probability density reproduces all quantum mechanical predictions. It becomes clear that experiments violate Bell’s inequalities because the real correlation functions are not constrained by these inequalities. It is also exposed that, rigorous logical reasoning of counter factual deduction does not permit to exclude any premises of Bell’s inequalities by a certain amount of experimental violations of these inequalities.展开更多
An explicit model-example is presented to simulate Einstein-Podolsky-Rosen (EPR) experiments without invoking instantaneous influences at a distance. The model-example, together with the interpretation of past experim...An explicit model-example is presented to simulate Einstein-Podolsky-Rosen (EPR) experiments without invoking instantaneous influences at a distance. The model-example, together with the interpretation of past experiments by Kwiat and coworkers, uncovers logical inconsistencies in the application of Bell’s theorem to actual EPR experiments. The inconsistencies originate from topological-combinatorial assumptions that are both necessary and sufficient to derive all Bell-type inequalities including those of Wigner-d’Espagnat and Clauser-Horne-Shimony-Holt. The model-example circumvents these inconsistencies.展开更多
It briefly recalls the theory of Bell’s inequality and some experimental measures. Then measurements are processed on one hand according to a property of the wave function, on the other hand according to the sum defi...It briefly recalls the theory of Bell’s inequality and some experimental measures. Then measurements are processed on one hand according to a property of the wave function, on the other hand according to the sum definition. The results of such processed measures are apparently not the same, so Bell’s inequality would not be violated. It is a use of the wave function which implies the violation of the inequality, as it can be seen on the last flowcharts.展开更多
This paper introduces the concept and motivates the use of finite-interval based measures for physically realizable and measurable quantities, which we call -measures. We demonstrate the utility and power of -measures...This paper introduces the concept and motivates the use of finite-interval based measures for physically realizable and measurable quantities, which we call -measures. We demonstrate the utility and power of -measures by illustrating their use in an interval-based analysis of a prototypical Bell’s inequality in the measurement of the polarization states of an entangled pair of photons. We show that the use of finite intervals in place of real-numbered values in the Bell inequality leads to reduced violations. We demonstrate that, under some conditions, an interval-based but otherwise classically calculated probability measure can be made to arbitrarily closely approximate its quantal counterpart. More generally, we claim by heuristic arguments and by formal analogy with finite-state machines that -measures can provide a more accurate model of both classical and quantal physical property values than point-like, real numbers—as originally proposed by Tuero Sunaga in 1958.展开更多
In constructing his theorem, Bell assumed that correlation functions among non-commuting variables are the same as those among commuting variables. However, in quantum mechanics, multiple data values exist simultaneou...In constructing his theorem, Bell assumed that correlation functions among non-commuting variables are the same as those among commuting variables. However, in quantum mechanics, multiple data values exist simultaneously for commuting operations while for non-commuting operations data are conditional on prior outcomes, or may be predicted as alternative outcomes of the non-commuting operations. Given these qualitative differences, there is no reason why correlation functions among non-commuting variables should be the same as those among commuting variables, as assumed by Bell. When data for commuting and noncommuting operations are predicted from quantum mechanics, their correlations are different, and they now satisfy the Bell inequality.展开更多
Bell tests with entangled light have been performed many times in many ways using linear polarizers, but the same tests have never been done with a circular polarizer. Until recently there has never been a true circul...Bell tests with entangled light have been performed many times in many ways using linear polarizers, but the same tests have never been done with a circular polarizer. Until recently there has never been a true circular polarization beamsplitter—an optical component that separates light directly into left and right handed polarizations. Using a true circular polarization beamsplitter based on birefringent gratings, entangled light has been analyzed with unexpected results.展开更多
Work on quantum entanglement is currently emphasizing the nonlocal nature of theories that attempt to explain spatially separated Einstein-Podolsky-Rosen (EPR) correlation experiments. It is frequently claimed that no...Work on quantum entanglement is currently emphasizing the nonlocal nature of theories that attempt to explain spatially separated Einstein-Podolsky-Rosen (EPR) correlation experiments. It is frequently claimed that nonlocal instantaneous influences, or equivalently a breakdown of Einstein’s separation principle, are a signature property of (quantum) entanglement. This paper presents a categorization of the various forms of nonlocality in physical theories. It is shown that, even for Einstein’s theory of relativity, correlations of spatially separated measurements cannot be explained without the involvement of some nonlocal or global knowledge and facts. Instantaneous Influences at a distance are, however, in a special category of nonlocality and, as is well known, Einstein called them spooky. Following a separation of nonlocalities into four distinctly different categories 0, 1, 2, 3, with number 3 corresponding to theories containing instantaneous influences at a distance, I show that any theory of EPR experiments must be at least in category 1 or 2 and does not need to be in category 3. In particular, the Bell theorem, valid for category 0 theories, may be violated for categories 1 and 2 and does not require category 3 theories. Category 0 enforces Bell’s theorem. However, it does not apply to relativistic theories of space like separated measurements.展开更多
The Extended Wigner’s Friend thought experiment, comprising a quantum system containing an agent who draws conclusions upon observing the outcome of a measurement of a quantum state prepared in two nonorthogonal vers...The Extended Wigner’s Friend thought experiment, comprising a quantum system containing an agent who draws conclusions upon observing the outcome of a measurement of a quantum state prepared in two nonorthogonal versions by another agent, led its authors to conclude that quantum theory cannot consistently describe the use of itself. It has also been proposed that this thought experiment is equivalent to entangled state (Bell-type) experiments. It is argued in this paper that the assumption of the freedom of choice of the first Wigner’s friend regarding how to prepare a quantum state in one of the two available nonorthogonal versions invalidates such equivalence.展开更多
Quantum mechanics is a probabilistic theory of the universe suggestive of a mean value theory similar to thermodynamics prior to the introduction of the atomic theory. If QM will follow a similar path to thermodynamic...Quantum mechanics is a probabilistic theory of the universe suggestive of a mean value theory similar to thermodynamics prior to the introduction of the atomic theory. If QM will follow a similar path to thermodynamics, then a local deterministic theory must be developed which matches QM predictions. There have been four tough barriers to a local theory of light, of which Bell’s Theorem has been considered the ultimate barrier. The other three barriers are explaining spontaneous emission, the reflection of a small fraction of light at a dielectric interface and the splitting action of a polarizer on polarized light (Malus’ Law). The challenge is that in a local theory of light, everything must have a specific cause and effect. There can be nothing spontaneous or hidden. Local solutions to all four of these barriers are presented in this paper, integrating results from two previous papers and adding the solution paths to the third and fourth barriers as well, which are nearly identical. A previous paper [1] used results from Einstein’s famous 1917 paper on stimulated emission to provide a deterministic local model for spontaneous emission. A second paper [2] showed that QM predictions in tests of Bell’s theorem could be matched with a local model by modifying the definition of entanglement in a manner invisible to quantum mechanics. This paper summarizes and extends those two results and then presents a deterministic model of reflection from a dielectric interface and transmission of polarized light through a polarizer that both match quantum mechanics. As the framework of a local theory of light emerges, it is not surprising that we find corners of physics where small disagreements with quantum mechanics are predicted. A new Bell type test is described in this paper which can distinguish the local from the nonlocal theory, giving predictions that must disagree slightly but significantly with quantum mechanics. If such experiments are proven to disagree with quantum mechanics, then the door to a local theo展开更多
Bell’s theorem, first presented by John Bell in 1964, has been used for many years to prove that no classical theory can ever match verified quantum mechanical predictions for entangled particles. By relaxing the def...Bell’s theorem, first presented by John Bell in 1964, has been used for many years to prove that no classical theory can ever match verified quantum mechanical predictions for entangled particles. By relaxing the definition of entangled slightly, we have found a mathematical solution for two entangled photons that produces the familiar quantum mechanical counting statistics without requiring a non-local theory such as quantum mechanics. This solution neither is claimed to be unique nor represents an accurate model of photonic interactions. However, it is an existence proof that there are local models of photonic emission that can reproduce quantum statistics.展开更多
文摘Bell’s theorem founded on Bell’s inequalities asserts that no local realistic theories can reproduce all quantum mechanical predictions for spin correlation of particle pairs. It is pointed out that the assumption of setting-independent probability makes Bell’s inequalities not impose constraint on all local realistic models and thus constitutes a theoretical loophole of Bell’s theorem. A counterexample is presented by showing that a local realistic model with appropriate probability density reproduces all quantum mechanical predictions. It becomes clear that experiments violate Bell’s inequalities because the real correlation functions are not constrained by these inequalities. It is also exposed that, rigorous logical reasoning of counter factual deduction does not permit to exclude any premises of Bell’s inequalities by a certain amount of experimental violations of these inequalities.
文摘An explicit model-example is presented to simulate Einstein-Podolsky-Rosen (EPR) experiments without invoking instantaneous influences at a distance. The model-example, together with the interpretation of past experiments by Kwiat and coworkers, uncovers logical inconsistencies in the application of Bell’s theorem to actual EPR experiments. The inconsistencies originate from topological-combinatorial assumptions that are both necessary and sufficient to derive all Bell-type inequalities including those of Wigner-d’Espagnat and Clauser-Horne-Shimony-Holt. The model-example circumvents these inconsistencies.
文摘It briefly recalls the theory of Bell’s inequality and some experimental measures. Then measurements are processed on one hand according to a property of the wave function, on the other hand according to the sum definition. The results of such processed measures are apparently not the same, so Bell’s inequality would not be violated. It is a use of the wave function which implies the violation of the inequality, as it can be seen on the last flowcharts.
文摘This paper introduces the concept and motivates the use of finite-interval based measures for physically realizable and measurable quantities, which we call -measures. We demonstrate the utility and power of -measures by illustrating their use in an interval-based analysis of a prototypical Bell’s inequality in the measurement of the polarization states of an entangled pair of photons. We show that the use of finite intervals in place of real-numbered values in the Bell inequality leads to reduced violations. We demonstrate that, under some conditions, an interval-based but otherwise classically calculated probability measure can be made to arbitrarily closely approximate its quantal counterpart. More generally, we claim by heuristic arguments and by formal analogy with finite-state machines that -measures can provide a more accurate model of both classical and quantal physical property values than point-like, real numbers—as originally proposed by Tuero Sunaga in 1958.
文摘In constructing his theorem, Bell assumed that correlation functions among non-commuting variables are the same as those among commuting variables. However, in quantum mechanics, multiple data values exist simultaneously for commuting operations while for non-commuting operations data are conditional on prior outcomes, or may be predicted as alternative outcomes of the non-commuting operations. Given these qualitative differences, there is no reason why correlation functions among non-commuting variables should be the same as those among commuting variables, as assumed by Bell. When data for commuting and noncommuting operations are predicted from quantum mechanics, their correlations are different, and they now satisfy the Bell inequality.
文摘Bell tests with entangled light have been performed many times in many ways using linear polarizers, but the same tests have never been done with a circular polarizer. Until recently there has never been a true circular polarization beamsplitter—an optical component that separates light directly into left and right handed polarizations. Using a true circular polarization beamsplitter based on birefringent gratings, entangled light has been analyzed with unexpected results.
文摘Work on quantum entanglement is currently emphasizing the nonlocal nature of theories that attempt to explain spatially separated Einstein-Podolsky-Rosen (EPR) correlation experiments. It is frequently claimed that nonlocal instantaneous influences, or equivalently a breakdown of Einstein’s separation principle, are a signature property of (quantum) entanglement. This paper presents a categorization of the various forms of nonlocality in physical theories. It is shown that, even for Einstein’s theory of relativity, correlations of spatially separated measurements cannot be explained without the involvement of some nonlocal or global knowledge and facts. Instantaneous Influences at a distance are, however, in a special category of nonlocality and, as is well known, Einstein called them spooky. Following a separation of nonlocalities into four distinctly different categories 0, 1, 2, 3, with number 3 corresponding to theories containing instantaneous influences at a distance, I show that any theory of EPR experiments must be at least in category 1 or 2 and does not need to be in category 3. In particular, the Bell theorem, valid for category 0 theories, may be violated for categories 1 and 2 and does not require category 3 theories. Category 0 enforces Bell’s theorem. However, it does not apply to relativistic theories of space like separated measurements.
文摘The Extended Wigner’s Friend thought experiment, comprising a quantum system containing an agent who draws conclusions upon observing the outcome of a measurement of a quantum state prepared in two nonorthogonal versions by another agent, led its authors to conclude that quantum theory cannot consistently describe the use of itself. It has also been proposed that this thought experiment is equivalent to entangled state (Bell-type) experiments. It is argued in this paper that the assumption of the freedom of choice of the first Wigner’s friend regarding how to prepare a quantum state in one of the two available nonorthogonal versions invalidates such equivalence.
文摘Quantum mechanics is a probabilistic theory of the universe suggestive of a mean value theory similar to thermodynamics prior to the introduction of the atomic theory. If QM will follow a similar path to thermodynamics, then a local deterministic theory must be developed which matches QM predictions. There have been four tough barriers to a local theory of light, of which Bell’s Theorem has been considered the ultimate barrier. The other three barriers are explaining spontaneous emission, the reflection of a small fraction of light at a dielectric interface and the splitting action of a polarizer on polarized light (Malus’ Law). The challenge is that in a local theory of light, everything must have a specific cause and effect. There can be nothing spontaneous or hidden. Local solutions to all four of these barriers are presented in this paper, integrating results from two previous papers and adding the solution paths to the third and fourth barriers as well, which are nearly identical. A previous paper [1] used results from Einstein’s famous 1917 paper on stimulated emission to provide a deterministic local model for spontaneous emission. A second paper [2] showed that QM predictions in tests of Bell’s theorem could be matched with a local model by modifying the definition of entanglement in a manner invisible to quantum mechanics. This paper summarizes and extends those two results and then presents a deterministic model of reflection from a dielectric interface and transmission of polarized light through a polarizer that both match quantum mechanics. As the framework of a local theory of light emerges, it is not surprising that we find corners of physics where small disagreements with quantum mechanics are predicted. A new Bell type test is described in this paper which can distinguish the local from the nonlocal theory, giving predictions that must disagree slightly but significantly with quantum mechanics. If such experiments are proven to disagree with quantum mechanics, then the door to a local theo
文摘Bell’s theorem, first presented by John Bell in 1964, has been used for many years to prove that no classical theory can ever match verified quantum mechanical predictions for entangled particles. By relaxing the definition of entangled slightly, we have found a mathematical solution for two entangled photons that produces the familiar quantum mechanical counting statistics without requiring a non-local theory such as quantum mechanics. This solution neither is claimed to be unique nor represents an accurate model of photonic interactions. However, it is an existence proof that there are local models of photonic emission that can reproduce quantum statistics.
