Bell’s Theorem and Einstein’s Worry about Quantum Mechanics

With the use of a local dependency on instrument setting parameters of the probability density of local hidden variables, it is demonstrated that a Kolmogorov formulation reproduces the quantum correlation. This is the novelty of the work. In a Bell experiment, one cannot distinguish between Bell’s formula and the here presented local Kolmogorov formula. With the presented formula, no CHSH can be obtained. Therefore, the famous CHSH inequality has no excluding power concerning local extra Einstein parameter models. This result concurs with other previous research concerning difficulties with Bell’s formula.

Testing Bell’s Theorem with Circular Polarization

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.

Collapse of Bell’s Theorem

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.

Interval Based Analysis of Bell’s Theorem

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.

Categories of Nonlocality in EPR Theories and the Validity of Einstein’s Separation Principle as Well as Bell’s Theorem

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.

Bell’s Theorem and Instantaneous Influences at a Distance

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.

Whole Perfect Vectors and Fermat’s Last Theorem

A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm definition, and some vector-specific structures.

Biased Random Number Generator Based on Bell's Theorem

We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser Home inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotational asymmetry of the quantum state, the ratio of Os to ls varies with the measurement bases. The experimental partners can then use their measurement outcomes to generate the biased random bit string. The bias of their bit string can be adjusted by altering their choices of measurement bases. When this protocol is implemented in a device-independent way, we show that the bias of the bit string can still be ensured under the collective attack.

The Bell Inequality, Inviolable by Data Used Consistently with Its Derivation, Is Satisfied by Quantum Correlations Whose Probabilities Satisfy the Wigner Inequality

It is not generally known that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of ±1’s that are writable on paper. This surprising fact is not immediately obvious from Bell’s inequality derivation based on causal random variables, but follows immediately if the same mathematical operations are applied to finite data sets. For laboratory data, the inequality is identically satisfied as a fact of pure algebra, and its satisfaction is independent of whether the processes generating the data are local, non-local, deterministic, random, or nonsensical. It follows that if predicted correlations violate the inequality, they represent no three cross-correlated data sets that can exist, or can be generated from valid probability models. Reported data that violate the inequality consist of probabilistically independent data-pairs and are thus inconsistent with inequality derivation. In the case of random variables as Bell assumed, the correlations in the inequality may be expressed in terms of the probabilities that give rise to them. A new inequality is then produced: The Wigner inequality, that must be satisfied by quantum mechanical probabilities in the case of Bell experiments. If that were not the case, predicted quantum probabilities and correlations would be inconsistent with basic algebra.

Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane

Noether theorem is applied to a variable order fractional multiscale mechano-electrophysiological model of neuron membrane dynamics.The variable orders fractional Lagrange equation of a multiscale mechano-electrophysiological model of neuron membrane dynamics is given.The variable orders fractional Noether symmetry criterion and Noether conserved quantities are given.The forms of variable orders fractional Noether conserved quantities corresponding to Noether symmetry generators solutions of the model under different conditions are discussed in detail,and it is found that the expressions of variable orders fractional Noether conserved quantities are closely dependent on the external nonconservative forces and material parameters of the neuron.

Recovery from Bell’s palsy after treatment using uncultured umbilical cord-derived mesenchymal stem cells:A case report

BACKGROUND Bell’s palsy is an idiopathic facial palsy with an unknown cause,and 75%of patients heal spontaneously.However,the other 25%of patients continue experiencing mild or severe disabilities,resulting in a reduced quality of life.Currently,various treatment methods have been developed to treat this disease.However,there is controversy regarding their effectiveness,and new alternative treatments are needed.CASE SUMMARY The patient suffered from left-sided facial paralysis due to Bell’s palsy for 7 years.The patient received an uncultured umbilical cord-derived mesenchymal stem cell transplant eight times for treatment.After follow-up for 32 mo,the paralysis was cured,and there was no recurrence.CONCLUSION Uncultured umbilical cord-derived mesenchymal stem cell transplantation may be a potential treatment for patients with Bell’s palsy who do not spontaneously recover.

Bell’s Palsy Post COVID-19 Vaccination: A Retrospective Cross-Sectional Study in a Single Tertiary Center

Introduction: Bell’s palsy is an uncommon adverse effect of the COVID-19 vaccine that has been reported in clinical trials. Even though a few studies have linked the vaccination to Bell’s palsy, the actual mechanism is uncertain. Objectives: To describe the demographic data and COVID-19 vaccines-related data with Bell’s palsy in a tertiary centre of Malaysia, Hospital Kuala Lumpur. Methods: A retrospective cross-sectional study was observed among vaccinated recipients who developed Bell’s palsy within 60 days and sought treatment in the Otorhinolaryngology Department Hospital Kuala Lumpur, Malaysia between 1st May 2021 and 30th November 2021. The demographic data, clinical history, and vaccination history were collected from clinical records. The facial paralysis was graded according to the House-Brackmann grading system. Results: A total of 26 patients with a mean age was 38.5 years;higher incidence in younger age, below 60 years old (n = 24), specifically 18 - 30 years old (n = 11). We observed an equal number in relation to gender and onset (after the first or second dose) of facial palsy. Predominantly were Malay (n = 21) and only 6 patients had comorbidities. We found there was no difference in regard to the type of vaccine among Bell’s palsy patients;Pfizer (n = 9), followed by Sinovac (n = 9) and AstraZeneca (n = 8). Conclusion: Bell’s palsy was found to be a possible adverse event of the COVID-19 vaccine. Younger groups were noted as susceptible to this rare adverse effect. However, the benefits of vaccination outweigh the risk of Bell’s palsy, which has a good prognosis. More research with larger samples is needed to determine the true relationship between vaccination and Bell’s palsy.

Einstein-Local Counter-Arguments and Counter-Examples to Bell-Type Proofs

J. S. Bell’s well-known proofs of inequalities (and related work) are shown to be invalidated by two counter-arguments (-examples) that are based on Einstein-local propositions: Bell-type inequalities of Einstein-Podolsky-Rosen experiments must include, as virtually all physical theories do, elements of physical reality and their mathematical representations that relate to continua as opposed to exclusively finite numbers. Furthermore, Bell-type inequalities must be valid for all possible experimental geometries that lead to the quantum result. Based on these propositions, violations of Bell-type inequalities are demonstrated without violating Einstein locality, without conspiracy type theories and even for the case that all known “loopholes” are closed.

Misdiagnosis of Facial Nerve Palsy: A Case Report of Sporadic Vestibular Schwannomas (Non-NFM2) Causing Facial Nerve Palsy Be Misled by Bell’s Palsy in a Child

We report a case of a rare sporadic Vestibular Schwannoma of a 9-month-old girl who had a right-sided lower motor type facial nerve palsy. The patient was initially diagnosed with Bell’s palsy and received steroid treatment accordingly, two months later the patient’s condition deteriorated, and further evaluation of CT and MRI brain was conducted that showed a mass lesion in the posterior fossa causing compression on the facial nerve. Misdiagnosis of facial nerve paralysis is common among children due to multiple related etiologies and varying rates of incidence in comparison to adults. The authors hope to address this issue in this report. Background: Facial nerve paralysis has been a matter of concern for many researchers to understand its nature, causes and presentation according to different age groups. In adults, Bell’s palsy (BP), the idiopathic form of facial nerve paralysis, is more common compared to children where most cases are due to secondary etiologies. Therefore, pediatricians are in an important position to identify these patients early in order to launch the most effective diagnostic and treatment approaches.

Products of Odd Numbers or Prime Number Can Generate the Three Members’ Families of Fermat Last Theorem and the Theorem Is Valid for Summation of Squares of More Than Two Natural Numbers

Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that An + Bn = Cn, in which n is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple (A, B, C) following n = 2 and also it is applicable A2 + B2 + C2 + D2 + so on =An2 where all are natural numbers.

Logical Conflict between Bell’s Locality and Probability Theory

Based on “locality” considerations, John Stuart Bell and his followers have derived inequalities and theorems that, when taken together with actual experiments that have been performed by Aspect and others, appear to contradict physical reality as defined by Einstein. However, their specifically applied concept of locality is in conflict with the Fundamental Model of probability theory and the set theoretic definition of conditional probabilities. Bell-type inequalities are, therefore, not adequate to decide ponderous questions regarding physical reality.

On Fermat Last Theorem: The New Efficient Expression of a Hypothetical Solution as a Function of Its Fermat Divisors

Denote by a non-trivial primitive solution of Fermat’s equation (p prime).We introduce, for the first time, what we call Fermat principal divisors of the triple defined as follows. , and . We show that it is possible to express a,b and c as function of the Fermat principal divisors. Denote by the set of possible non-trivial solutions of the Diophantine equation . And, let (p prime). We prove that, in the first case of Fermat’s theorem, one has . In the second case of Fermat’s theorem, we show that , ,. Furthermore, we have implemented a python program to calculate the Fermat divisors of Pythagoreans triples. The results of this program, confirm the model used. We now have an effective tool to directly process Diophantine equations and that of Fermat. .

A Proof of Brouwer’s Fixed Point Theorem Using Sperner’s Lemma

This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.

Why Bell’s EPRBA Experiment Is Meaningless

We demonstrate that a Bell type of experiment asks the impossible of a Kolmogorovian correlation. An Einstein locality explanation in Bell’s format is therefore excluded beforehand by way of the experimental and statistical method followed.

Bell＇s Theorem Without Inequalities for Arbitrarily High-Dimensional Fermionic System

A generalized proof of Bell's theorem without inequalities via the singlet state of two spin-(2n + 1)/2 fermionic particles for two observers is proposed. It is a direct and meaningful extension of that presented by A. Cabello [Phys. Rev. A67 (2003) 032107] and the proof from A. Cabello is included in our proof as a special example.