The Einstein field equation (EFE) can be directly linked to the Schrödinger equation (SE) by meditation of the quantity of quantum information and its units: qubits
•
One qubit is an “atom” both of Hilbert space and Minkovski space underlying correspondingly quantum mechanics and special relativity
•
Pseudo-Riemannian space of general relativity being “deformed” Minkowski space therefore consists of “deformed” qubits directly referring to the eventual “deformation” of Hilbert space
The document provides an overview of quantum mechanics concepts including:
- Erwin Schrodinger developed the Schrodinger wave equation which describes the energy and position of electrons.
- The time-dependent and time-independent Schrodinger equations are presented for 1D systems. Solutions include plane waves and wave packets.
- The postulates of quantum mechanics are outlined including the use of wavefunctions and Hermitian operators to represent physical quantities.
- Differences between the interpretations of quantum mechanics by Heisenberg and Schrodinger are briefly discussed.
1. Quantum mechanics describes the behavior of matter and light at the atomic scale, which is very different from classical mechanics. Particles have both wave-like and particle-like properties.
2. The de Broglie hypothesis proposed that all particles have an associated wavelength that depends on their momentum. This was confirmed experimentally by observing electron diffraction patterns.
3. Heisenberg's uncertainty principle states that it is impossible to precisely measure both a particle's position and momentum simultaneously. This limits our ability to predict the future behavior of particles.
This document describes a particle confined in a one-dimensional box of length L. The particle is free to move within the box from 0 to L, but faces infinite potential at the boundaries. The Schrodinger equation for this system is solved. The boundary conditions require that the wavefunction vanishes at 0 and L. This leads to discrete energy levels given by En = (nπħ/2mL)2, with corresponding wavefunctions Ψn = (2/L)sin(nπx/L). Normalization of the wavefunctions determines the normalization constant. As an example, the normalization of a plane wave Ψ(x) = Neicx over the region -a to a is calculated
This document provides an overview of quantum mechanics concepts related to light and atomic structure. It discusses how light behaves as both a wave and particle, and introduces the electromagnetic spectrum. It then covers atomic structure concepts like electron configurations, energy levels, quantum numbers, and orbital shapes and filling diagrams. The document aims to explain how electrons are arranged in atoms and the underlying quantum mechanical principles.
Schrodinger equation and its applications: Chapter 2Dr.Pankaj Khirade
Wave function and its physical significance, Schrodinger time dependent equation, Separation in time dependent and time independent parts, Operators in quantum Mechanics, Eigen functions and Eigen values, Particle in one dimensional and three dimensional box (Energy eigen values). Qualitative analysis of potential barrier Tunneling effect). Simple Harmonic Oscillator (Qualitative analysis of Zero point energy)
This document presents on the topics of quantum mechanics, including the Schrodinger equation, potential barriers and tunneling, and the infinite potential well. It discusses how classically a particle cannot pass through a potential barrier with energy lower than the barrier potential, but quantum mechanically there is a probability of tunneling. It derives the wave functions and transmission coefficients for particles incident on potential barriers and wells. The transmission probability for tunneling decreases exponentially with increasing barrier thickness and potential. The infinite potential well confines particles within fixed boundaries, with allowed quantum states and energies determined by the boundary conditions.
The WKB approximation is a method to find approximate solutions to the Schrodinger equation. It was developed in 1926 by Wentzel, Kramer, and Brillouin. The approximation assumes the wavefunction is an exponentially varying function with amplitude and phase that change slowly compared to the de Broglie wavelength. It can be used to obtain approximate solutions and energy eigenvalues for systems where the classical limit is valid. The approximation breaks down near classical turning points where the particle's energy is equal to the potential energy. The document provides examples of using the WKB approximation to solve the time-independent Schrodinger equation in one dimension for cases where the particle's energy is both greater than and less than the potential energy.
The document provides an overview of quantum mechanics concepts including:
- Erwin Schrodinger developed the Schrodinger wave equation which describes the energy and position of electrons.
- The time-dependent and time-independent Schrodinger equations are presented for 1D systems. Solutions include plane waves and wave packets.
- The postulates of quantum mechanics are outlined including the use of wavefunctions and Hermitian operators to represent physical quantities.
- Differences between the interpretations of quantum mechanics by Heisenberg and Schrodinger are briefly discussed.
1. Quantum mechanics describes the behavior of matter and light at the atomic scale, which is very different from classical mechanics. Particles have both wave-like and particle-like properties.
2. The de Broglie hypothesis proposed that all particles have an associated wavelength that depends on their momentum. This was confirmed experimentally by observing electron diffraction patterns.
3. Heisenberg's uncertainty principle states that it is impossible to precisely measure both a particle's position and momentum simultaneously. This limits our ability to predict the future behavior of particles.
This document describes a particle confined in a one-dimensional box of length L. The particle is free to move within the box from 0 to L, but faces infinite potential at the boundaries. The Schrodinger equation for this system is solved. The boundary conditions require that the wavefunction vanishes at 0 and L. This leads to discrete energy levels given by En = (nπħ/2mL)2, with corresponding wavefunctions Ψn = (2/L)sin(nπx/L). Normalization of the wavefunctions determines the normalization constant. As an example, the normalization of a plane wave Ψ(x) = Neicx over the region -a to a is calculated
This document provides an overview of quantum mechanics concepts related to light and atomic structure. It discusses how light behaves as both a wave and particle, and introduces the electromagnetic spectrum. It then covers atomic structure concepts like electron configurations, energy levels, quantum numbers, and orbital shapes and filling diagrams. The document aims to explain how electrons are arranged in atoms and the underlying quantum mechanical principles.
Schrodinger equation and its applications: Chapter 2Dr.Pankaj Khirade
Wave function and its physical significance, Schrodinger time dependent equation, Separation in time dependent and time independent parts, Operators in quantum Mechanics, Eigen functions and Eigen values, Particle in one dimensional and three dimensional box (Energy eigen values). Qualitative analysis of potential barrier Tunneling effect). Simple Harmonic Oscillator (Qualitative analysis of Zero point energy)
This document presents on the topics of quantum mechanics, including the Schrodinger equation, potential barriers and tunneling, and the infinite potential well. It discusses how classically a particle cannot pass through a potential barrier with energy lower than the barrier potential, but quantum mechanically there is a probability of tunneling. It derives the wave functions and transmission coefficients for particles incident on potential barriers and wells. The transmission probability for tunneling decreases exponentially with increasing barrier thickness and potential. The infinite potential well confines particles within fixed boundaries, with allowed quantum states and energies determined by the boundary conditions.
The WKB approximation is a method to find approximate solutions to the Schrodinger equation. It was developed in 1926 by Wentzel, Kramer, and Brillouin. The approximation assumes the wavefunction is an exponentially varying function with amplitude and phase that change slowly compared to the de Broglie wavelength. It can be used to obtain approximate solutions and energy eigenvalues for systems where the classical limit is valid. The approximation breaks down near classical turning points where the particle's energy is equal to the potential energy. The document provides examples of using the WKB approximation to solve the time-independent Schrodinger equation in one dimension for cases where the particle's energy is both greater than and less than the potential energy.
This document discusses the Schrodinger wave equation and its application to modeling a particle in a one-dimensional box. It introduces the history and derivation of the Schrodinger equation, then applies it to solve for the energy and wave functions of a particle confined to a box. The energy is found to be quantized and depend on an integer quantum number. Graphs of the wave functions and probability densities are presented.
The slides are designed for my guided study in MSc CUHK.
It is about the brief description on classical mechanics and quantum mechanics .
Some Slides I got from the slideshare clipboards for better illustration of the ideas in Physics. Thanks to slideshare, I make a milestone on presenting one of the prominent fields in modern physics.
Derivation of Schrodinger and Einstein Energy Equations from Maxwell's Electr...iosrjce
1) The document derives both the Schrodinger quantum equation and Einstein's relativistic energy-momentum relation from Maxwell's electric wave equation.
2) It does so by considering particles as oscillators and using Planck's quantum hypothesis. The electric field intensity vector is replaced by the wave function.
3) Several steps and equations are shown to first derive the Schrodinger equation, and then the electric polarization and special relativity concepts are used to derive Einstein's energy-momentum relation.
The document provides an outline for a course on quantum mechanics. It discusses key topics like the time-dependent Schrodinger equation, eigenvalues and eigenfunctions, boundary conditions for wave functions, and applications like the particle in a box model. Specific solutions to the Schrodinger equation are explored for stationary states with definite energy, including the wave function for a free particle and the quantization of energy for a particle confined to a one-dimensional box.
CHAPTER 6 Quantum Mechanics II
6.0 Partial differentials
6.1 The Schrödinger Wave Equation
6.2 Expectation Values
6.3 Infinite Square-Well Potential
6.4 Finite Square-Well Potential
6.5 Three-Dimensional Infinite-Potential Well
6.6 Simple Harmonic Oscillator
6.7 Barriers and Tunneling in some books an extra chapter due to its technical importance
This document provides an introduction to quantum mechanics concepts including:
1. It describes Schrodinger's wave equation and its applications, including quantized energy levels and tunneling effects.
2. Wave-particle duality is discussed through experiments demonstrating the wave-like and particle-like properties of electrons.
3. The uncertainty principle and solutions to Schrodinger's wave equation for simple potential wells are presented, showing energy levels are quantized.
Quantum mechanics describes the behavior of matter and light on the atomic and subatomic scale. Some key points of the quantum mechanics view are that particles can exhibit both wave-like and particle-like properties, their behavior is probabilistic rather than definite, and some properties like position and momentum cannot be known simultaneously with complete precision due to the Heisenberg uncertainty principle. Quantum mechanics has successfully explained various phenomena that classical physics could not and led to important technologies like lasers, MRI machines, and semiconductor devices.
Introduction to Classical Mechanics:
UNIT-I : Elementary survey of Classical Mechanics: Newtonian mechanics for single particle and system of particles, Types of the forces and the single particle system examples, Limitation of Newton’s program, conservation laws viz Linear momentum, Angular Momentum & Total Energy, work-energy theorem; open systems (with variable mass). Principle of Virtual work, D’Alembert’s principle’ applications.
UNIT-II : Constraints; Definition, Types, cause & effects, Need, Justification for realizing constraints on the system
This document summarizes classical dynamics and small amplitude oscillations. It discusses oscillatory motion near equilibrium positions and developing the theory using Lagrange's equations. Normal modes of coupled oscillating systems are explored, where the normal coordinates represent eigenvectors that oscillate at characteristic frequencies. The principles of superposition and matrix representations are used to analyze examples like two coupled pendulums and a system of two masses connected by three springs.
1) A quantum particle is described by a wave function ψ(x) which is a function of position. This provides a complete description of the particle's state.
2) The wave function does not indicate a precise position for the particle. Instead, the particle is considered delocalized, meaning it does not have a well-defined position more precise than the spread of the wave function.
3) Certain properties of the wave function, like whether it is nonzero in a particular region of space, provide some information about where the particle might be found if its position were measured. But the particle does not have a well-defined position until a measurement is made.
1. The document discusses key concepts in quantum physics including Planck's quantum theory, de Broglie's hypothesis of matter waves, Heisenberg's uncertainty principle, and Schrodinger's time-independent wave equation.
2. It provides details on experiments that verified the wave-like properties of matter including electron diffraction experiments by Davisson and Germer.
3. The document derives expressions for the energy levels of particles confined in one-dimensional potential wells and boxes in terms of Planck's constant and other variables.
1) Bohr's atomic model proposed that electrons revolve around the nucleus in well-defined orbits. However, the uncertainty principle showed that the exact path of an electron cannot be known.
2) To address this, scientists developed quantum mechanics using the de Broglie wave equation. This incorporated the dual particle-wave nature of electrons.
3) The time-independent Schrodinger wave equation was formulated and solved for a particle in a 1D, 2D, or 3D "box" to calculate the particle's energy levels.
1) The time-independent Schrodinger wave equation describes a standing wave with wavelength λ that has an amplitude at any point along the x direction.
2) In three dimensions, the Schrodinger wave equation incorporates second derivatives with respect to x, y, and z coordinates.
3) The Hamiltonian operator Ĥ in the time-independent Schrodinger wave equation is the Laplacian operator ∇2 plus 8π2m/h2 times the potential energy V.
This document provides a summary of quantum mechanical concepts and solid state physics. It begins with a review of quantum mechanics and the Schrodinger equation. It then discusses the wave nature of electrons and how the Schrodinger equation describes the wavefunction and probability of finding an electron. It also covers energy band diagrams and how the periodic potential in solids leads to the formation of allowed energy bands. It discusses these concepts for isolated atoms, silicon crystals, and the one-dimensional Kronig-Penny model.
This document discusses the quantization of electromagnetic radiation fields within the framework of quantum electrodynamics (QED). It begins by introducing the classical description of radiation fields in terms of vector potentials that satisfy the transversality condition. Next, it describes quantizing the classical radiation field by treating it as a collection of independent harmonic oscillators, with each oscillator characterized by a wave vector and polarization. Finally, it discusses how the quantization of these radiation oscillators leads to treating their canonical variables as non-commuting operators, in analogy to the quantization of position and momentum in non-relativistic quantum mechanics. This lays the foundation for a quantum description of radiation phenomena using the formalism of QED.
SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH INVERSELY QUADRATIC HELLMANN PLUS ...ijrap
The solutions of the Schrödinger equation with inversely quadratic Hellmann plus Mie-type potential for
any angular momentum quantum number have been presented using the Nikiforov-Uvarov method. The
bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms
of the Laguerre polynomials. Several cases of the potential are also considered and their eigen values obtained.
The document discusses the development of quantum electrodynamics (QED) from its origins in Dirac's 1927 paper on the quantum theory of radiation. It provides an overview of the key topics covered in the subsequent chapters, including particles and fields, quantization of the electromagnetic field, Feynman diagrams, and renormalization in QED. The goal is to show how electrons and photons interact using quantum field theory by representing particles as excitations of underlying fields and developing perturbative techniques to calculate processes like scattering and radiation.
This document provides a summary of key developments in the foundations of quantum mechanics. It discusses Planck's discovery that led to defining Planck's constant h, which established that energy is quantized. Einstein's work on the photoelectric effect supported this and introduced the photon concept. Bohr used classical mechanics and energy quantization to develop his model of the hydrogen atom. The document outlines the revolutionary changes brought by quantum theory and its greater scope and applicability compared to classical physics. It provides context for understanding quantum mechanics from first principles.
The harmonic oscillator played a key role in early quantum theory. Planck, Einstein, and others assumed that atoms, radiation, and solids behaved like quantum harmonic oscillators to explain phenomena like blackbody radiation and heat capacities. This led to the development of quantum theory for electromagnetic and mechanical oscillators. Solving the Schrödinger equation for the harmonic oscillator yields discrete energy levels and eigenfunctions that describe its quantized energy spectrum.
MORE THAN IMPOSSIBLE: NEGATIVE AND COMPLEX PROBABILITIES AND THEIR INTERPRETA...Vasil Penchev
What might mean “more than impossible”?
For example, that could be what happens without any cause or that physical change which occurs without any physical force (interaction) to act ⦁
Then, the quantity of the equivalent physical force, which would cause the same effect, can serve as a measure of the complex probability
Furthermore, the same effect is interpretable as re-ordering and thus as a certain quantity of information ⦁
One can write a very intriguing equation:
Physical force = The same effect = Information
This document discusses the Schrodinger wave equation and its application to modeling a particle in a one-dimensional box. It introduces the history and derivation of the Schrodinger equation, then applies it to solve for the energy and wave functions of a particle confined to a box. The energy is found to be quantized and depend on an integer quantum number. Graphs of the wave functions and probability densities are presented.
The slides are designed for my guided study in MSc CUHK.
It is about the brief description on classical mechanics and quantum mechanics .
Some Slides I got from the slideshare clipboards for better illustration of the ideas in Physics. Thanks to slideshare, I make a milestone on presenting one of the prominent fields in modern physics.
Derivation of Schrodinger and Einstein Energy Equations from Maxwell's Electr...iosrjce
1) The document derives both the Schrodinger quantum equation and Einstein's relativistic energy-momentum relation from Maxwell's electric wave equation.
2) It does so by considering particles as oscillators and using Planck's quantum hypothesis. The electric field intensity vector is replaced by the wave function.
3) Several steps and equations are shown to first derive the Schrodinger equation, and then the electric polarization and special relativity concepts are used to derive Einstein's energy-momentum relation.
The document provides an outline for a course on quantum mechanics. It discusses key topics like the time-dependent Schrodinger equation, eigenvalues and eigenfunctions, boundary conditions for wave functions, and applications like the particle in a box model. Specific solutions to the Schrodinger equation are explored for stationary states with definite energy, including the wave function for a free particle and the quantization of energy for a particle confined to a one-dimensional box.
CHAPTER 6 Quantum Mechanics II
6.0 Partial differentials
6.1 The Schrödinger Wave Equation
6.2 Expectation Values
6.3 Infinite Square-Well Potential
6.4 Finite Square-Well Potential
6.5 Three-Dimensional Infinite-Potential Well
6.6 Simple Harmonic Oscillator
6.7 Barriers and Tunneling in some books an extra chapter due to its technical importance
This document provides an introduction to quantum mechanics concepts including:
1. It describes Schrodinger's wave equation and its applications, including quantized energy levels and tunneling effects.
2. Wave-particle duality is discussed through experiments demonstrating the wave-like and particle-like properties of electrons.
3. The uncertainty principle and solutions to Schrodinger's wave equation for simple potential wells are presented, showing energy levels are quantized.
Quantum mechanics describes the behavior of matter and light on the atomic and subatomic scale. Some key points of the quantum mechanics view are that particles can exhibit both wave-like and particle-like properties, their behavior is probabilistic rather than definite, and some properties like position and momentum cannot be known simultaneously with complete precision due to the Heisenberg uncertainty principle. Quantum mechanics has successfully explained various phenomena that classical physics could not and led to important technologies like lasers, MRI machines, and semiconductor devices.
Introduction to Classical Mechanics:
UNIT-I : Elementary survey of Classical Mechanics: Newtonian mechanics for single particle and system of particles, Types of the forces and the single particle system examples, Limitation of Newton’s program, conservation laws viz Linear momentum, Angular Momentum & Total Energy, work-energy theorem; open systems (with variable mass). Principle of Virtual work, D’Alembert’s principle’ applications.
UNIT-II : Constraints; Definition, Types, cause & effects, Need, Justification for realizing constraints on the system
This document summarizes classical dynamics and small amplitude oscillations. It discusses oscillatory motion near equilibrium positions and developing the theory using Lagrange's equations. Normal modes of coupled oscillating systems are explored, where the normal coordinates represent eigenvectors that oscillate at characteristic frequencies. The principles of superposition and matrix representations are used to analyze examples like two coupled pendulums and a system of two masses connected by three springs.
1) A quantum particle is described by a wave function ψ(x) which is a function of position. This provides a complete description of the particle's state.
2) The wave function does not indicate a precise position for the particle. Instead, the particle is considered delocalized, meaning it does not have a well-defined position more precise than the spread of the wave function.
3) Certain properties of the wave function, like whether it is nonzero in a particular region of space, provide some information about where the particle might be found if its position were measured. But the particle does not have a well-defined position until a measurement is made.
1. The document discusses key concepts in quantum physics including Planck's quantum theory, de Broglie's hypothesis of matter waves, Heisenberg's uncertainty principle, and Schrodinger's time-independent wave equation.
2. It provides details on experiments that verified the wave-like properties of matter including electron diffraction experiments by Davisson and Germer.
3. The document derives expressions for the energy levels of particles confined in one-dimensional potential wells and boxes in terms of Planck's constant and other variables.
1) Bohr's atomic model proposed that electrons revolve around the nucleus in well-defined orbits. However, the uncertainty principle showed that the exact path of an electron cannot be known.
2) To address this, scientists developed quantum mechanics using the de Broglie wave equation. This incorporated the dual particle-wave nature of electrons.
3) The time-independent Schrodinger wave equation was formulated and solved for a particle in a 1D, 2D, or 3D "box" to calculate the particle's energy levels.
1) The time-independent Schrodinger wave equation describes a standing wave with wavelength λ that has an amplitude at any point along the x direction.
2) In three dimensions, the Schrodinger wave equation incorporates second derivatives with respect to x, y, and z coordinates.
3) The Hamiltonian operator Ĥ in the time-independent Schrodinger wave equation is the Laplacian operator ∇2 plus 8π2m/h2 times the potential energy V.
This document provides a summary of quantum mechanical concepts and solid state physics. It begins with a review of quantum mechanics and the Schrodinger equation. It then discusses the wave nature of electrons and how the Schrodinger equation describes the wavefunction and probability of finding an electron. It also covers energy band diagrams and how the periodic potential in solids leads to the formation of allowed energy bands. It discusses these concepts for isolated atoms, silicon crystals, and the one-dimensional Kronig-Penny model.
This document discusses the quantization of electromagnetic radiation fields within the framework of quantum electrodynamics (QED). It begins by introducing the classical description of radiation fields in terms of vector potentials that satisfy the transversality condition. Next, it describes quantizing the classical radiation field by treating it as a collection of independent harmonic oscillators, with each oscillator characterized by a wave vector and polarization. Finally, it discusses how the quantization of these radiation oscillators leads to treating their canonical variables as non-commuting operators, in analogy to the quantization of position and momentum in non-relativistic quantum mechanics. This lays the foundation for a quantum description of radiation phenomena using the formalism of QED.
SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH INVERSELY QUADRATIC HELLMANN PLUS ...ijrap
The solutions of the Schrödinger equation with inversely quadratic Hellmann plus Mie-type potential for
any angular momentum quantum number have been presented using the Nikiforov-Uvarov method. The
bound state energy eigenvalues and the corresponding un-normalized eigenfunctions are obtained in terms
of the Laguerre polynomials. Several cases of the potential are also considered and their eigen values obtained.
The document discusses the development of quantum electrodynamics (QED) from its origins in Dirac's 1927 paper on the quantum theory of radiation. It provides an overview of the key topics covered in the subsequent chapters, including particles and fields, quantization of the electromagnetic field, Feynman diagrams, and renormalization in QED. The goal is to show how electrons and photons interact using quantum field theory by representing particles as excitations of underlying fields and developing perturbative techniques to calculate processes like scattering and radiation.
This document provides a summary of key developments in the foundations of quantum mechanics. It discusses Planck's discovery that led to defining Planck's constant h, which established that energy is quantized. Einstein's work on the photoelectric effect supported this and introduced the photon concept. Bohr used classical mechanics and energy quantization to develop his model of the hydrogen atom. The document outlines the revolutionary changes brought by quantum theory and its greater scope and applicability compared to classical physics. It provides context for understanding quantum mechanics from first principles.
The harmonic oscillator played a key role in early quantum theory. Planck, Einstein, and others assumed that atoms, radiation, and solids behaved like quantum harmonic oscillators to explain phenomena like blackbody radiation and heat capacities. This led to the development of quantum theory for electromagnetic and mechanical oscillators. Solving the Schrödinger equation for the harmonic oscillator yields discrete energy levels and eigenfunctions that describe its quantized energy spectrum.
MORE THAN IMPOSSIBLE: NEGATIVE AND COMPLEX PROBABILITIES AND THEIR INTERPRETA...Vasil Penchev
What might mean “more than impossible”?
For example, that could be what happens without any cause or that physical change which occurs without any physical force (interaction) to act ⦁
Then, the quantity of the equivalent physical force, which would cause the same effect, can serve as a measure of the complex probability
Furthermore, the same effect is interpretable as re-ordering and thus as a certain quantity of information ⦁
One can write a very intriguing equation:
Physical force = The same effect = Information
The generalization of the Periodic table. The "Periodic table" of "dark matter"Vasil Penchev
The thesis is: the “periodic table” of “dark matter” is equivalent to the standard periodic table of the visible matter being entangled. Thus, it is to consist of all possible entangled states of the atoms of chemical elements as quantum systems. In other words, an atom of any chemical element and as a quantum system, i.e. as a wave function, should be represented as a non-orthogonal in general (i.e. entangled) subspace of the separable complex Hilbert space relevant to the system to which the atom at issue is related as a true part of it. The paper follows previous publications of mine stating that “dark matter” and “dark energy” are projections of arbitrarily entangled states on the cognitive “screen” of Einstein’s “Mach’s principle” in general relativity postulating that gravitational field can be generated only by mass or energy.
Albert Einstein (1879-1955) developed the theories of special and general relativity. Special relativity, published in 1905, established that the laws of physics are the same in all inertial frames of reference and that the speed of light in a vacuum is constant. General relativity, published in 1915, introduced gravitation as a result of the curvature of spacetime caused by the uneven distribution of mass and energy. One of Einstein's most famous equations is E=mc2, which shows that mass and energy are equivalent and interconvertible.
The Kochen - Specker theorem in quantum mechanics: A philosophical commentVasil Penchev
The document summarizes the key ideas and findings of the Kochen-Specker theorem in quantum mechanics. It discusses:
1) The theorem proves the nonexistence of local hidden variables by demonstrating the impossibility of embedding quantum-mechanical quantities into a commutative algebra, going beyond von Neumann's argument about non-commuting operators.
2) Implicitly, the theorem only concerns local hidden variables and does not address nonlocal ones or issues related to Bell's inequalities.
3) A necessary condition for hidden variables is embeddability into a commutative algebra, which the paper shows cannot be done for a finite partial algebra of observables.
4) This suggests the fundamental difference
MORE THAN IMPOSSIBLE: NEGATIVE AND COMPLEX PROBABILITIES AND THEIR INTERPRET...Vasil Penchev
What might mean “more than impossible”? For example, that could be what happens without any cause or that physical change which occurs without any physical force (interaction) to act. Then, the quantity of the equivalent physical force, which would cause the same effect, can serve as a measure of the complex probability.
Quantum mechanics introduces those fluctuations, the physical actions of which are commensurable with the Plank constant. They happen by themselves without any cause even in principle. Those causeless changes are both instable and extremely improbable in the world perceived by our senses immediately for the physical actions in it are much, much bigger than the Plank constant.
Vasil Penchev. Gravity as entanglement, and entanglement as gravityVasil Penchev
1. The document discusses interpreting gravity as entanglement by investigating the conditions under which general relativity and quantum mechanics can be mapped to each other mathematically.
2. It outlines a strategy to interpret entanglement as inertial mass and gravitational mass, and to view gravity as another interpretation of any quantum mechanical or mechanical movement.
3. This would allow gravity to be incorporated into the standard model by generalizing the concept of quantum field to include entanglement, represented by a cyclic Yin-Yang mathematical structure.
Quantum Mechanics as a Measure Theory: The Theory of Quantum MeasureVasil Penchev
This document discusses representing quantum mechanics as a measure theory, with the key points being:
1. Quantum measure can unify the measurement of discrete and continuous quantities by treating them as "much" and "many".
2. The unit of quantum measure is the qubit, allowing it to jointly measure probability, quantity, order, and disorder.
3. All physical processes can be interpreted as computations of a quantum computer, with the universal substance being quantum information.
4. Quantum measure can provide a nonlocal explanation for the Aharonov-Bohm effect by linking it to the electromagnetic nature of space-time itself.
Gravity as entanglement, and entanglement as gravityVasil Penchev
1) The document discusses the relationship between gravity and quantum entanglement, exploring the possibility that they are equivalent or closely connected concepts.
2) It outlines an approach to interpret gravity in terms of a generalized quantum field theory that includes entanglement, which could explain why gravity cannot be quantized.
3) The key idea is that entanglement expressed "outside" of space-time points looks like gravity "inside", and vice versa, with gravity representing a smooth constraint on the quantum behavior of entities imposed by all others.
Relativity theory project & albert einstenSeergio Garcia
Albert Einstein was a German-born theoretical physicist who developed the theory of relativity, one of the pillars of modern physics. He was born in 1879 in Germany and died in 1955 in the United States. He is best known for his mass-energy equivalence formula E=mc2, which has been called the world's most famous equation. He developed the special theory of relativity, which describes the laws of motion at high speeds and led to his famous equation, and the general theory of relativity, which describes gravity as a geometric property of space and time.
Relativity theory project & albert einstenSeergio Garcia
Albert Einstein was a German-born theoretical physicist who developed the theory of relativity, one of the pillars of modern physics. He was born in 1879 in Germany and died in 1955 in the United States. He is best known for his mass-energy equivalence formula E=mc2, which has been called the world's most famous equation. The document provides background on Einstein's life and work, and summarizes his theories of special relativity, which describes physics at high speeds, and general relativity, which proposes that gravity results from the curvature of spacetime.
The Ancient-Greek Special Problems, as the Quantization Moulds of SpacesScientific Review SR
The Special Problems of E-geometry consist the , Mould Quantization , of Euclidean
Geometry in it , to become → Monad , through mould of Space –Anti-space in itself , which is the
material dipole in inner monad Structure as the Electromagnetic cycloidal field → Linearly , through
mould of Parallel Theorem [44-45], which are the equal distances between points of parallel and line →
In Plane , through mould of Squaring the circle [46] , where the two equal and perpendicular monads
consist a Plane acquiring the common Plane-meter → and in Space (volume) , through mould of the
Duplication of the Cube [46] , where any two Unequal perpendicular monads acquire the common
Space-meter to be twice each other , as analytically all methods are proved and explained . [39-41]. The
Unification of Space and Energy becomes through [STPL] Geometrical Mould Mechanism of Elements ,
the minimum Energy-Quanta , In monads → Particles , Anti-particles , Bosons , Gravity –Force , Gravity -Field , Photons , Dark Matter , and Dark-Energy ,consisting Material Dipoles in inner monad Structures
i.e. the Electromagnetic Cycloidal Field of monads. Euclid’s elements consist of assuming a small set of
intuitively appealing axioms , proving many other propositions . Because nobody until [9] succeeded to
prove the parallel postulate by means of pure geometric logic , many self-consistent non - Euclidean
geometries have been discovered , based on Definitions , Axioms or Postulates , in order that none of them
contradicts any of the other postulates . In [39] the only Space-Energy geometry is Euclidean , agreeing
with the Physical reality , on unit AB = Segment which is The Electromagnetic field of the Quantized on
AB Energy Space Vector , on the contrary to the General relativity of Space-time which is based on the
rays of the non-Euclidean geometries to the limited velocity of light and Planck`s cavity . Euclidean
geometry elucidated the definitions of geometry-content ,{ for Point , Segment , Straight Line , Plane ,
Volume, Space [S] , Anti-space [AS] , Sub-space [SS] , Cave, Space-Anti-Space Mechanism of the Six-Triple-Points-Line , that produces and transfers Points of Spaces , Anti -Spaces and Sub-Spaces in a
Common Inertial Sub-Space and a cylinder ,Gravity field [MFMF] , Particles } and describes the Space-Energy beyond Plank´s length level [ Gravity Length 3,969.10 ̄ 62 m ] , reaching the Point = L
v
=
e
i.
Nπ
2
b=10 N= − ∞
m = 0 m , which is nothing and zero space .[43-46] -The Geometrical solution of the
Special Problems is now presented
The document discusses key concepts in quantum mechanics including wavefunctions, operators, and the uncertainty principle. Some key points:
- A wavefunction Ψ(x,t) describes the probability of finding a particle at position x and time t. Operators like -iħ∂/∂x correspond to physical quantities like momentum.
- Applying these operators to Ψ yields the particle's momentum if Ψ is an eigenfunction, but not if Ψ is a superposition of momentum states.
- Heisenberg's uncertainty principle states the more precisely position is known, the less precisely momentum can be known, and vice versa. It is quantified as ΔxΔp ≥ ħ/
“No hidden variables!”: From Neumann’s to Kochen and Specker’s theorem in qua...Vasil Penchev
The talk addresses a philosophical comparison and thus interpretation of both theorems having one and the same subject:
The absence of the “other half” of variables, called “hidden” for that, to the analogical set of variables in classical mechanics:
These theorems are:
John’s von Neumann’s (1932)
Simon Kochen and Ernst Specker’s (1968)
1) Quantum entanglement is a property where quantum states of objects cannot be described independently, even if separated spatially. A practical example involves two cups of hot chocolate where tasting one instantly reveals the other's state.
2) Bra-ket notation is used to describe quantum states as vectors or functionals in a Hilbert space. Operators act on these states to model physical quantities.
3) A qubit is the quantum analogue of a classical bit, existing in superposition of states |0> and |1>. Quantum computers use entanglement between qubits to perform computations in parallel.
Quantum mechanics for Engineering StudentsPraveen Vaidya
The Quantum mechanics study material gives insight into the fundamentals of the modern theory of physics related to Heisenberg uncertainty principle, wavefunction, concepts of potential well etc.
A relationship between mass as a geometric concept and motion associated with a closed curve in spacetime (a notion taken from differential geometry) is investigated. We show that the 4-dimensional exterior Schwarzschild solution of the General Theory of Relativity can be mapped to a 4-dimensional Euclidean spacetime manifold. As a consequence of this mapping, the quantity M in the exterior Schwarzschild solution which is usually attributed to a massive central object is shown to correspond to a geometric property of spacetime. An additional outcome of this analysis is the discovery that, because M is a property of spacetime geometry, an anisotropy with respect to its spacetime components measured in a Minkowski tangent space defined with respect to a spacetime event P by an observer O who is stationary with respect to the spacetime event P, may be a sensitive measure of an anisotropic cosmic accelerated expansion. The presence of anisotropy in the cosmic accelerated expansion may contribute to the reason that there are currently two prevailing measured estimates of this quantity
The singularities from the general relativity resulting by solving Einstein's equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case?
DOI: 10.13140/RG.2.2.22006.45124/1
Armenian Theory of Special Relativity IllustratedRobert Nazaryan
The aim of this current article is to illustrate in detail Armenian relativistic formulas and compare them with Lorentz relativistic formulas so that readers can easily differentiate these two theories and visualize how general and rich our Armenian Theory of Special Relativity really is with a spectacular build in asymmetry.
Then we are going behind this comparison and illustrating that build in asymmetry inside Armenian Theory of Special Relativity is reincarnating the aether as a universal reference medium, which is not contrary to relativity theory. We mathematically prove the existence of aether and we show how to extract infinite energy from the time-space or sub-atomic aether medium. Our theory explains all these facts and peacefully brings together followers of absolute aether theory, relativistic aether theory or followers of dark matter theory. We also mention that the absolute aether medium has a very complex geometric character, which has never been seen before.
We are explaining why NASA’s earlier "BPP" and DARPA’s "Casimir Effect Enhancement" programs failed.
We are also stating that the time is right to reopen NASA’s BPP program and fuel the spacecrafts using the everywhere existing aether asymmetric momentum force.
Similar to The Einstein field equation in terms of the Schrödinger equation (20)
Modal History versus Counterfactual History: History as IntentionVasil Penchev
The distinction of whether real or counterfactual history makes sense only post factum. However, modal history is to be defined only as ones’ intention and thus, ex-ante. Modal history is probable history, and its probability is subjective. One needs phenomenological “epoché” in relation to its reality (respectively, counterfactuality). Thus, modal history describes historical “phenomena” in Husserl’s sense and would need a specific application of phenomenological reduction, which can be called historical reduction. Modal history doubles history just as the recorded history of historiography does it. That doubling is a necessary condition of historical objectivity including one’s subjectivity: whether actors’, ex-anteor historians’ post factum. The objectivity doubled by ones’ subjectivity constitute “hermeneutical circle”.
Both classical and quantum information [autosaved]Vasil Penchev
Information can be considered a the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information. particularly by their units, bit and qubit, correspond and unify the finite and infinite:
As classical information is relevant to finite series and sets, as quantum information, to infinite ones. The separable complex Hilbert space of quantum mechanics can be represented equivalently as “qubit space”) as quantum information and doubled dually or “complimentary” by Hilbert arithmetic (classical information).
A CLASS OF EXEMPLES DEMONSTRATING THAT “푃푃≠푁푁푁 ” IN THE “P VS NP” PROBLEMVasil Penchev
The CMI Millennium “P vs NP Problem” can be resolved e.g. if one shows at least one counterexample to the “P=NP” conjecture. A certain class of problems being such counterexamples will be formulated. This implies the rejection of the hypothesis “P=NP” for any conditions satisfying the formulation of the problem. Thus, the solution “P≠NP” of the problem in general is proved. The class of counterexamples can be interpreted as any quantum superposition of any finite set of quantum states. The Kochen-Specker theorem is involved. Any fundamentally random choice among a finite set of alternatives belong to “NP’ but not to “P”. The conjecture that the set complement of “P” to “NP” can be described by that kind of choice exhaustively is formulated.
FERMAT’S LAST THEOREM PROVED BY INDUCTION (accompanied by a philosophical com...Vasil Penchev
A proof of Fermat’s last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat’s last theorem in the case of n=3 as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat’s approach of infinite descent. The infinite descent is linked to induction starting from n=3 by modus tollens. An inductive series of modus tollens is constructed. The proof of the series by induction is equivalent to Fermat’s last theorem. As far as Fermat had been proved the theorem for n=4, one can suggest that the proof for n≥4 was accessible to him.
An idea for an elementary arithmetical proof of Fermat’s last theorem (FLT) by induction is suggested. It would be accessible to Fermat unlike Wiles’s proof (1995), and would justify Fermat’s claim (1637) for its proof. The inspiration for a simple proof would contradict to Descartes’s dualism for appealing to merge “mind” and “body”, “words” and “things”, “terms” and “propositions”, all orders of logic. A counterfactual course of history of mathematics and philosophy may be admitted. The bifurcation happened in Descartes and Fermat’s age. FLT is exceptionally difficult to be proved in our real branch rather than in the counterfactual one.
The space-time interpretation of Poincare’s conjecture proved by G. Perelman Vasil Penchev
This document discusses the generalization of Poincaré's conjecture to higher dimensions and its interpretation in terms of special relativity. It proposes that Poincaré's conjecture can be generalized to state that any 4-dimensional ball is topologically equivalent to 3D Euclidean space. This generalization has a physical interpretation in which our 3D space can be viewed as a "4-ball" closed in a fourth dimension. The document also outlines ideas for how one might prove this generalization by "unfolding" the problem into topological equivalences between Euclidean spaces.
FROM THE PRINCIPLE OF LEAST ACTION TO THE CONSERVATION OF QUANTUM INFORMATION...Vasil Penchev
In fact, the first law of conservation (that of mass) was found in chemistry and generalized to the conservation of energy in physics by means of Einstein’s famous “E=mc2”. Energy conservation is implied by the principle of least action from a variational viewpoint as in Emmy Noether’s theorems (1918): any chemical change in a conservative (i.e. “closed”) system can be accomplished only in the way conserving its total energy. Bohr’s innovation to found Mendeleev’s periodic table by quantum mechanics implies a certain generalization referring to
the quantum leaps as if accomplished in all possible trajectories (according to Feynman’s interpretation) and therefore generalizing the principle of least action and needing a certain generalization of energy conservation as to any quantum change.The transition from the first to the second theorem of Emmy Noether represents well the necessary generalization: its chemical meaning is the ge eralization of any chemical reaction to be accomplished as if any possible course of time rather than in the standard evenly running time (and equivalent to energy conservation according to the first theorem). The problem: If any quantum change is accomplished in al possible “variations (i.e. “violations) of energy conservation” (by different probabilities),
what (if any) is conserved? An answer: quantum information is what is conserved. Indeed, it can be particularly defined as the counterpart (e.g. in the sense of Emmy Noether’s theorems) to the physical quantity of action (e.g. as energy is the counterpart of time in them). It is valid in any course of time rather than in the evenly running one. That generalization implies a generalization of the periodic table including any continuous and smooth transformation between two chemical elements.
From the principle of least action to the conservation of quantum information...Vasil Penchev
In fact, the first law of conservation (that of mass) was found in chemistry and generalized to the conservation of energy in physics by means of Einstein’s famous “E=mc2”. Energy conservation is implied by the principle of least action from a variational viewpoint as in Emmy Noether’s theorems (1918):any chemical change in a conservative (i.e. “closed”) system can be accomplished only in the way conserving its total energy. Bohr’s innovation to found Mendeleev’s periodic table by quantum mechanics implies a certain generalization referring to the quantum leaps as if accomplished in all possible trajectories (e.g. according to Feynman’s viewpoint) and therefore generalizing the principle of least action and needing a certain generalization of energy conservation as to any quantum change.
The transition from the first to the second theorem of Emmy Noether represents well the necessary generalization: its chemical meaning is the generalization of any chemical reaction to be accomplished as if any possible course of time rather than in the standard evenly running time (and equivalent to energy conservation according to the first theorem).
The problem: If any quantum change is accomplished in all possible “variations (i.e. “violations) of energy conservation” (by different probabilities), what (if any) is conserved?
An answer: quantum information is what is conserved. Indeed it can be particularly defined as the counterpart (e.g. in the sense of Emmy Noether’s theorems) to the physical quantity of action (e.g. as energy is the counterpart of time in them). It is valid in any course of time rather than in the evenly running one. (An illustration: if observers in arbitrarily accelerated reference frames exchange light signals about the course of a single chemical reaction observed by all of them, the universal viewpoint shareаble by all is that of quantum information).
That generalization implies a generalization of the periodic table including any continuous and smooth transformation between two chemical elements necessary conserving quantum information rather than energy: thus it can be called “alchemical periodic table”.
Poincaré’s conjecture proved by G. Perelman by the isomorphism of Minkowski s...Vasil Penchev
- The document discusses the relationship between separable complex Hilbert spaces (H) and sets of ordinals (H) and how they should not be equated if natural numbers are identified as finite.
- It presents two interpretations of H: as vectors in n-dimensional complex space or as squarely integrable functions, and discusses how the latter adds unitarity from energy conservation.
- It argues that Η rather than H should be used when not involving energy conservation, and discusses how the relation between H and HH generates spheres representing areas and can be interpreted physically in terms of energy and force.
Why anything rather than nothing? The answer of quantum mechnaicsVasil Penchev
Many researchers determine the question “Why anything
rather than nothing?” to be the most ancient and fundamental philosophical problem. It is closely related to the idea of Creation shared by religion, science, and philosophy, for example in the shape of the “Big Bang”, the doctrine of first cause or causa sui, the Creation in six days in the Bible, etc. Thus, the solution of quantum mechanics, being scientific in essence, can also be interpreted philosophically, and even religiously. This paper will only discuss the philosophical interpretation. The essence of the answer of quantum mechanics is: 1.) Creation is necessary in a rigorously mathematical sense. Thus, it does not need any hoice, free will, subject, God, etc. to appear. The world exists by virtue of mathematical necessity, e.g. as any mathematical truth such as 2+2=4; and 2.) Being is less than nothing rather than ore than nothing. Thus creation is not an increase of nothing, but the decrease of nothing: it is a deficiency in relation to nothing. Time and its “arrow” form the road from that diminishment or incompleteness to nothing.
The Square of Opposition & The Concept of Infinity: The shared information s...Vasil Penchev
The power of the square of opposition has been proved during millennia, It supplies logic by the ontological language of infinity for describing anything...
6th WORLD CONGRESS ON THE SQUARE OF OPPOSITION
http://www.square-of-opposition.org/square2018.html
Mamardashvili, an Observer of the Totality. About “Symbol and Consciousness”,...Vasil Penchev
The paper discusses a few tensions “crucifying” the works and even personality of the great Georgian philosopher Merab Mamardashvili: East and West; human being and thought, symbol and consciousness, infinity and finiteness, similarity and differences. The observer can be involved as the correlative counterpart of the totality: An observer opposed to the totality externalizes an internal part outside. Thus the phenomena of an observer and the totality turn out to converge to each other or to be one and the same. In other words, the phenomenon of an observer includes the singularity of the solipsistic Self, which (or “who”) is the same as that of the totality. Furthermore, observation can be thought as that primary and initial action underlain by the phenomenon of an observer. That action of observation consists in the externalization of the solipsistic Self outside as some external reality. It is both a zero action and the singularity of the phenomenon of action. The main conclusions are: Mamardashvili’s philosophy can be thought both as the suffering effort to be a human being again and again as well as the philosophical reflection on the genesis of thought from itself by the same effort. Thus it can be recognized as a powerful tension between signs anа symbol, between conscious structures and consciousness, between the syncretism of the East and the discursiveness of the West crucifying spiritually Georgia
Completeness: From henkin's Proposition to Quantum ComputerVasil Penchev
This document discusses how Leon Henkin's proposition relates to concepts in logic, set theory, information theory, and quantum mechanics. It argues that Henkin's proposition, which states the provability of a statement within a formal system, is equivalent to an internal and consistent position regarding infinity. The document then explores how this connects to Martin Lob's theorem, the Einstein-Podolsky-Rosen paradox in quantum mechanics, theorems about the absence of hidden variables, entanglement, quantum information, and ultimately quantum computers.
Why anything rather than nothing? The answer of quantum mechanicsVasil Penchev
This document discusses the philosophical question of why there is something rather than nothing from the perspective of quantum mechanics. It argues that quantum mechanics provides a solution where creation is permanent and due to the irreversibility of time. The creation in quantum mechanics represents a necessary loss of information as alternatives are rejected in the course of time, rather than being due to some external cause like God's will. This permanent creation process makes the universe mathematically necessary rather than requiring an initial singular event like the Big Bang.
The outlined approach allows a common philosophical viewpoint to the physical world, language and some mathematical structures therefore calling for the universe to be understood as a joint physical, linguistic and mathematical universum, in which physical motion and metaphor are one and the same rather than only similar in a sense.
Hilbert Space and pseudo-Riemannian Space: The Common Base of Quantum Informa...Vasil Penchev
Hilbert space underlying quantum mechanics and pseudo-Riemannian space underlying general relativity share a common base of quantum information. Hilbert space can be interpreted as the free variable of quantum information, and any point in it, being equivalent to a wave function (and thus, to a state of a quantum system), as a value of that variable of quantum information. In turn, pseudo-Riemannian space can be interpreted as the interaction of two or more quantities of quantum information and thus, as two or more entangled quantum systems. Consequently, one can distinguish local physical interactions describable by a single Hilbert space (or by any factorizable tensor product of such ones) and non-local physical interactions describable only by means by that Hilbert space, which cannot be factorized as any tensor product of the Hilbert spaces, by means of which one can describe the interacting quantum subsystems separately. Any interaction, which can be exhaustedly described in a single Hilbert space, such as the weak, strong, and electromagnetic one, is local in terms of quantum information. Any interaction, which cannot be described thus, is nonlocal in terms of quantum information. Any interaction, which is exhaustedly describable by pseudo-Riemannian space, such as gravity, is nonlocal in this sense. Consequently all known physical interaction can be described by a single geometrical base interpreting it in terms of quantum information.
This document discusses using Richard Feynman's interpretation of quantum mechanics as a way to formally summarize different explanations of quantum mechanics given to hypothetical children. It proposes that each child's understanding could be seen as one "pathway" or explanation, with the total set of explanations forming a distribution. The document then suggests that quantum mechanics itself could provide a meta-explanation that encompasses all the children's perspectives by describing phenomena probabilistically rather than deterministically. Finally, it gives some examples of how this approach could allow defining and experimentally studying the concept of God through quantum mechanics.
This document discusses whether artificial intelligence can have a soul from both scientific and religious perspectives. It begins by acknowledging that "soul" is a religious concept while AI is a scientific one. The document then examines how Christianity views creativity as a criterion for having a soul. It proposes formal scientific definitions of creativity involving learning rates and probabilities. An example is given comparing a master's creativity to an apprentice's. The document argues science can describe God's infinite creativity and human's finite creativity uniformly. It analyzes whether criteria for creativity can apply to AI like a Turing machine. Hypothetical examples involving infinite algorithms and self-learning machines are discussed.
Analogia entis as analogy universalized and formalized rigorously and mathema...Vasil Penchev
THE SECOND WORLD CONGRESS ON ANALOGY, POZNAŃ, MAY 24-26, 2017
(The Venue: Sala Lubrańskiego (Lubrański’s Hall at the Collegium Minus), Adam Mickiewicz University, Address: ul. Wieniawskiego 1) The presentation: 24 May, 15:30
Ontology as a formal one. The language of ontology as the ontology itself: th...Vasil Penchev
“Formal ontology” is introduced first to programing languages in different ways. The most relevant one as to philosophy is as a generalization of “nth-order logic” and “nth-level language” for n=0. Then, the “zero-level language” is a theoretical reflection on the naïve attitude to the world: the “things and words” coincide by themselves. That approach corresponds directly to the philosophical phenomenology of Husserl or fundamental ontology of Heidegger. Ontology as the 0-level language may be researched as a formal ontology
The cost of acquiring information by natural selectionCarl Bergstrom
This is a short talk that I gave at the Banff International Research Station workshop on Modeling and Theory in Population Biology. The idea is to try to understand how the burden of natural selection relates to the amount of information that selection puts into the genome.
It's based on the first part of this research paper:
The cost of information acquisition by natural selection
Ryan Seamus McGee, Olivia Kosterlitz, Artem Kaznatcheev, Benjamin Kerr, Carl T. Bergstrom
bioRxiv 2022.07.02.498577; doi: https://doi.org/10.1101/2022.07.02.498577
hematic appreciation test is a psychological assessment tool used to measure an individual's appreciation and understanding of specific themes or topics. This test helps to evaluate an individual's ability to connect different ideas and concepts within a given theme, as well as their overall comprehension and interpretation skills. The results of the test can provide valuable insights into an individual's cognitive abilities, creativity, and critical thinking skills
The binding of cosmological structures by massless topological defectsSérgio Sacani
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
Immersive Learning That Works: Research Grounding and Paths ForwardLeonel Morgado
We will metaverse into the essence of immersive learning, into its three dimensions and conceptual models. This approach encompasses elements from teaching methodologies to social involvement, through organizational concerns and technologies. Challenging the perception of learning as knowledge transfer, we introduce a 'Uses, Practices & Strategies' model operationalized by the 'Immersive Learning Brain' and ‘Immersion Cube’ frameworks. This approach offers a comprehensive guide through the intricacies of immersive educational experiences and spotlighting research frontiers, along the immersion dimensions of system, narrative, and agency. Our discourse extends to stakeholders beyond the academic sphere, addressing the interests of technologists, instructional designers, and policymakers. We span various contexts, from formal education to organizational transformation to the new horizon of an AI-pervasive society. This keynote aims to unite the iLRN community in a collaborative journey towards a future where immersive learning research and practice coalesce, paving the way for innovative educational research and practice landscapes.
(June 12, 2024) Webinar: Development of PET theranostics targeting the molecu...Scintica Instrumentation
Targeting Hsp90 and its pathogen Orthologs with Tethered Inhibitors as a Diagnostic and Therapeutic Strategy for cancer and infectious diseases with Dr. Timothy Haystead.
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...Sérgio Sacani
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
Or: Beyond linear.
Abstract: Equivariant neural networks are neural networks that incorporate symmetries. The nonlinear activation functions in these networks result in interesting nonlinear equivariant maps between simple representations, and motivate the key player of this talk: piecewise linear representation theory.
Disclaimer: No one is perfect, so please mind that there might be mistakes and typos.
dtubbenhauer@gmail.com
Corrected slides: dtubbenhauer.com/talks.html
ESA/ACT Science Coffee: Diego Blas - Gravitational wave detection with orbita...Advanced-Concepts-Team
Presentation in the Science Coffee of the Advanced Concepts Team of the European Space Agency on the 07.06.2024.
Speaker: Diego Blas (IFAE/ICREA)
Title: Gravitational wave detection with orbital motion of Moon and artificial
Abstract:
In this talk I will describe some recent ideas to find gravitational waves from supermassive black holes or of primordial origin by studying their secular effect on the orbital motion of the Moon or satellites that are laser ranged.
The technology uses reclaimed CO₂ as the dyeing medium in a closed loop process. When pressurized, CO₂ becomes supercritical (SC-CO₂). In this state CO₂ has a very high solvent power, allowing the dye to dissolve easily.
Authoring a personal GPT for your research and practice: How we created the Q...Leonel Morgado
Thematic analysis in qualitative research is a time-consuming and systematic task, typically done using teams. Team members must ground their activities on common understandings of the major concepts underlying the thematic analysis, and define criteria for its development. However, conceptual misunderstandings, equivocations, and lack of adherence to criteria are challenges to the quality and speed of this process. Given the distributed and uncertain nature of this process, we wondered if the tasks in thematic analysis could be supported by readily available artificial intelligence chatbots. Our early efforts point to potential benefits: not just saving time in the coding process but better adherence to criteria and grounding, by increasing triangulation between humans and artificial intelligence. This tutorial will provide a description and demonstration of the process we followed, as two academic researchers, to develop a custom ChatGPT to assist with qualitative coding in the thematic data analysis process of immersive learning accounts in a survey of the academic literature: QUAL-E Immersive Learning Thematic Analysis Helper. In the hands-on time, participants will try out QUAL-E and develop their ideas for their own qualitative coding ChatGPT. Participants that have the paid ChatGPT Plus subscription can create a draft of their assistants. The organizers will provide course materials and slide deck that participants will be able to utilize to continue development of their custom GPT. The paid subscription to ChatGPT Plus is not required to participate in this workshop, just for trying out personal GPTs during it.
The Einstein field equation in terms of the Schrödinger equation
1. The Einstein field equation
in terms of
the Schrödinger equation
The meditation of quantum
information
2. Vasil Penchev
• Bulgarian Academy of Sciences: Institute for
the Study of Societies of Knowledge
• vasildinev@gmail.com
March 17th, 15:00-15:30, A 60 (Architekturgebäude)
Technische Universität Berlin
The President Str. des 17. Juni 135
15 - 20 March, 2015: “100 years of General Relativity:
On the foundations of spacetime theories,”
in: the Annual Meeting of the DPG
4. The thesis:
• The Einstein field equation (EFE) can be directly
linked to the Schrödinger equation (SE) by
meditation of the quantity of quantum
information and its units: qubits
• One qubit is an “atom” both of Hilbert space and
Minkovski space underlying correspondingly
quantum mechanics and special relativity
• Pseudo-Riemannian space of general relativity
being “deformed” Minkowski space therefore
consists of “deformed” qubits directly referring to
the eventual “deformation” of Hilbert space
5. • Thus both equations can be interpreted as a two
different particular cases of a more general
equation referring to the quantity of quantum
information (QI)
• They can be represented as the transition from
future to the past for a single qubit in two
isomorphic form:
SE: the normed superposition of two successive
“axes” of Hilbert space
EFE: a unit 3D ball
• A few hypotheses to be ever proved are only
formulated on the ground of the correspondence
between the two equations in terms of quantum
information or for a single qubit
6. The underlying understanding of time,
energy, and quantum information
The flat case (SE, infinity,
the axiom of choice):
The curved case (EFE,
finiteness):
Future
Potential energy
Present
Kinetic energy
Past
Energy newly
=(SE)
2) =1)= 0
⊗
7. The underlying understanding of time,
energy, and quantum information
The flat case (SE, infinity,
the axiom of choice):
The “curved” case
(entanglement, infinity):
Future
Potential energy
Present
Kinetic energy
Past
Energy newly
=(SE) = ?
9. A sketch to prove the main hypothesis (1)
• The relative “curving” (Δ) of a curved qubit to
another can be represented by two curved qubits,
the latter of which is described to the former
• Each of them is equivalent to a state of pseudo-
Riemannian space in a moment of time
• The main hypothesis expresses the relation of one
and the same kind of decomposition taken two
times
• Consequently, that kind of decomposition is
sufficient to be discussed
• It turns out to be equivalent to a principle of GR:
10. A sketch to prove the main hypothesis (2)
• In fact, the main hypothesis is equivalent to
the premise of general relativity about the equality
of inertial and gravitational mass. Indeed:
• The main hypothesis is a form of Fourier expansion
if one considers the deformation of a qubit as an
impulse in Minkowski space (or as a three-
dimensional impulse): Then the sum bellow is just
its Fourier expansion
• At last, that sum is isomorphic to an arbitrary
trajectory in some potential field in Minkowski
space since the entanglement should be a smooth
function as both wave functions constituting it are
smooth
11. A short comment of the above sketch
• However the member in EFE involving the
cosmological constant (“𝑔𝜇νΛ”)means just that
gravitational and inertial mass are not equal
• As that constant was justified by Einstein (1918)’s
“Mach’s principle”, this means that “Mach’s
principle” had removed or generalized
the equality of gravitational and inertial mass,
which in turn is a generalization of the classical
energy conservation to energy-momentum
• The member of the cosmological constant added
still one kind of energy without any clear origin
12. The link between the generalizations
of energy conservation in EFE and SE
• SE also generalizes the classical energy
conservation adding the wave function and the
member of its change in time (“𝑖ħ
𝜕
𝜕𝑡
Ψ 𝒓,𝑡 ”):
• Indeed if Ψ 𝒓,𝑡 is a constant both in space and
time SE is to reduce to energy conservation
• However SE is fundamentally “flat” as well as
Hilbert space and cannot involve any member
analogical to the EFE generalization about
energy-momentum
13. From SE to the case of entanglement
• Consequently the member “𝑖ħ
𝜕
𝜕𝑡
Ψ 𝒓,𝑡 ” in SE is
what should correspond to the cosmological
constant in EFE (though its member is multiplied by
the metric tensor “𝑔𝜇ν”: “𝑔𝜇νΛ”)
• One might suggest that entanglement will introduce
some additional energy if the wave function
“Ψ 𝒓,𝑡 ” is substituted by its “curved” version:
{ 𝐴 Ψ 𝒓,𝑡 }, where 𝐴 is not any self-adjoint operator
in Hilbert space
• However the case of entanglement can take place
only in relation to the “global” EFE rather than to
the “local” EFE at a point because the local EFE
corresponds to the usual SE
15. The emphasized terms (in red):
They are new and mean:
“Temporal EM”: EM of a leap unit (or a bit) along
the geodesic line of space-time
“Potential Q”: a qubit in the physical dimension of
action, which is equivalent to a qubit in the physical
dimension of space-time for a unit of energy-
momentum (a tentative reference body or “material
point”)
“Kinetic Q”: a qubit in the physical dimension of the
energy-momentum of mechanical motion
“Deformed Q”: the Ricci tensor of
a “kinetic Q”
17. The other notations (SE):
• 𝑖, imaginary unit
• ħ, the Planck constant divided by 2π
• Ψ 𝒓, 𝑡 , wave function
• 𝑉 𝒓,𝑡 , potential energy
• 𝜇, reduced mass
• 𝛻2
,Laplacian
• 𝒓, space vector
• 𝑡, time
18. The sense of the correspondence
• The Ricci curvature tensor, 𝑅𝜇ν, is a quantity
designating the deformation of a unit ball
•
1
2
𝑔𝜇ν 𝑅 is the “half” of the Ricci curvature
tensor
• The subtraction of these is the “other half” of
the Ricci curvature tensor
• EFE states that this “other half” is equal to
energy-momentum eventually corrected by
the cosmological constant member
• SE states the analogical about the “flat” case
19. • Schrödinger equation is interpreting as generalizing
energy conservation to the past, present, and future
moments of time rather than only to present and future
moments as this does the analogical law in classical
mechanics
• The equation suggests the proportionality (or even
equality if the units are relevantly chosen) of the
quantities of both quantum and classical information
and energy therefore being a (quantum) information
analog of Einstein’s famous equality of mass and
energy (“E=mc2”)
20. A few main arguments
1. The three of the EFE members (sells 2.3, 2.4, and
2.5 of the table) are representable as Ricci tensors
interpretable as the change of the volume of a ball in
pseudo-Riemannian space in comparison to a ball in
the three-dimensional Euclidean space (3D).
2. Any wave function in SE can be represented as a
series of qubits, which are equivalent to balls in 3D,
in which two points are chosen: the one within it, the
other on its surface.
21. 3. The member of EFE containing the
cosmological constant corresponds to the
partial time derivative of the wave function in
SE (column 2 of the table).
This involves the energetic equality of a bit
and a qubit according to the quantum-
information interpretation of SE.
The zero cosmological constant corresponds
to the time-independent SE.
22. 4. The member of EFE, which is the
gravitational energy-momentum tensor,
corresponds to zero in SE as it express
that energy-momentum, which is a result
of the space-time deformation (column 5)
5. SE represents the case of zero space-
time deformation, EFE adds
corresponding members being due to the
deformation itself (row 3)
23. А “footnote” about quantum correlations
The flat case
(the axiom of choice):
The case of correlations
(Kochen-Specker theorem):
The future and present
in terms of the past:
well-ordered
Future and present
in terms of future:
unorderable
24. The “footnote” continuous:
The case of correlations
(Kochen-Specker theorem):
Entanglement: (the corre-
lations in terms of the past
The correlations
are certain
26. About “relativity” in general relativity
• One possible philosophical sense of relativity is
that the physical quantities are relations between
reference frames rather than their properties
• Nevertheless, if one formulates relativity both
special and general in terms of Minkowski or
pseudo-Riemannian space, any relation of
reference frames turns out to be a property of the
corresponding space
• The “relation” and “property” themselves as well
as relativity turn out to be also relative in turn
27. About “relativity” in quantum mechanics
• Quantum mechanics is formulated initially in terms
of properties, which are “points” in Hilbert space
• However all experimentally corroborated
phenomena of entanglement mean that it can be
not less discussed in terms of relations
• Thus both quantum mechanics and relativity turn
out to share the generalized relativity of relation
and property
• Even more, their “spaces of properties” relate to
each other as the two “Fourier modifications” of
one and the same generalized space in order to
realize the invariance of time (continuity) and
frequency or energy (discreteness)
28. Quantum invariance and the relativity
of relation and property
• One can call that invariance of time (continuity) and
frequency or energy (discreteness) “quantum
invariance” shortly
• Quantum invariance and the relativity of relation
and property are equivalent to each other and even
to wave-particle duality as follows
Continuity–
discreteness
Relation– property Wave–particle
Time Relation(parts) Particle
Frequency (energy) Property(awhole) Wave
29. The Standard model and that relativity
• The Standard model itself can be discussed in terms
of that relativity first of all in order to be elucidated
its relation to gravity remained out of it
• If general relativity is the theory of gravity, one can
deduce that the Standard model and general
relativity share the same duality as any pair of the
previous table
• This means that gravity is not more than an force
(interaction) equivalent to the rest three:
• The former is the continuous (classical) hypostasis,
the latters are the discrete (quantum) one of one
and the same
30. The “fixed point” of electromagnetism
• Electromagnetism turns out to be shared by
both the Standard model as the symmetry
U(1) and general relativity as the particular,
borderline “flat” case of Minkowski space
• Even more, it is shared by quantum
information as “free qubit”, i.e. as the sell of
qubit, in which is not yet “recorded” any value
• Consequently, electromagnetism is to be
discussed as the fixed point of quantum
invariance after it is that for the two
hypostases of general relativity and the
Standard model
31. The ridiculous equivalence of general
relativity and the Standard model
• If one gaze carefully at that equivalence of general
relativity and the Standard model, it turns out to
abound in corollaries ridiculous to common sense:
• For example, the quantum viewpoint is valid to an
external observer, and the relativity point of view is
valid to an internal observer, but both are
equivalent to each other after entering / leaving the
system:
• As if one leaves our world, it would be transformed
into a quantum one, as if one enters the quantum
world, it would look our as ours
32. The Standard model as a certain and
thus privileged reference frame
The “Big Bang” refers always to the past: Thus it can
be seen whenever only “outside”
Its privileged counterpart in pseudo-Riemannian
space is the space-time position of the observer “here
and now” wherever it is:
All possible “here and now” share one and the same
tangent Minkowski space determined by the constant
of the light speed, and by one and the same position
of the Big Bang, which is forever in the past and thus
outside
33. The “Big Bang” privileges a reference frame, and it
is consistent to the Standard model
Nevertheless, the positions inside distinguish from
each other by different curvature and therefore by
their different wave function
Even more, one can suggest that the Standard
model is exactly equivalent to the description to a
single inertial reference frame, that of the “Big
Bang”:
Whether as a common tangent to all possible
positions in space-time
Or as a common limit of converging of all possible
wave functions
34. Indeed the Standard model uses the intersection
of the tensor product of the three fundamental
symmetries [U(1)]X[SU(2)]X[SU(3)]:
However this is necessary in order to construct
the dual counterpart of an inertial reference
frame equivalent to a single qubit, to which all
possible wave functions in our universe converge
necessary
All this seems to be the only, which is able to be
consistent with the discussed equivalence of
general relativity and the Standard model:
That equivalence means the rather trivial
coincidence of a manifold and its tangent space
at any point
36. That equation, of which both EFE and
SE are particular cases
• Both turn out to be the two rather equivalent
sides of a Fourier-like transformation
• Thus the cherished generalized equation
seems to coincide with both EFE and SE
• Nevertheless a certain fundamental difference
between them should be kept:
• SE refers to the “flat” case of the tangent
space in any point of a certain manifold
described by EFE
37. SE as the EFE at a point
Thus SE refers to the representation into an infinite
sum (series) at a point of a manifold described by EFE
Roughly speaking, SE and EFE coincide only locally but
everywhere, i.e. at any point
This results both in coinciding the way for the present
to be described and in distinguishing the ways for the
past and future to be represented:
“Flatly” by SE, so a qubit can describe and refers
equally well to each modus of time: This is its sense
“Curvedly” by EFE, so that the past and future are
described as present moments however “curved” to
the real present, which is always “flat”
They describe time differently, but equivalently
38. The global EFE as the SE after entanglement
• Though locally coinciding, EFE and SE differs from
each other globally:
• Then the following problem appears: How one or
both of them to be generalized in order to coincide
globally, too
• The concept of quantum gravity suggests that EFE is
what needs generalization by relevant quantization,
in which nobody has managed, though
• The present consideration should demonstrate that
the SE generalization is both much easier and
intuitively more convincing
39. “Relative quant” vs. “quantum gravity”
• Once SE has been generalized, perhaps EFE will be
generalized reciprocally and mathematically, too
• One can coin the term of relative quant as the
approach opposite to quantum gravity
• Its essence is the manifold described by EFE to be
represented by the set of tangent spaces
smoothly passing into each other
• One needs only describing SEs in two arbitrarily
rotated Hilbert spaces as tangent spaces at two
arbitrarily points of pseudo-Riemannian space, i.e.
SE generalized about entanglement
40. Quant of entanglement as relative quant
• Consequently the concept of relative quant is to be
interpreted as the concept of entanglement applied
to general relativity and thus to gravity
• However the qubit is also the quant of
entanglement as well as the common quant of
Hilbert, Minkowski and even pseudo-Riemannian
space
• Indeed a qubit can express the relative rotation of
two axes of the same “n” in two arbitrarily rotated
Hilbert space exactly as well as the relation of two
successive axes in a single Hilbert space
41. A deformed qubit as a deformed unit
vector of the basis on Hilbert space
• One can think of a qubit as follows: its unit vector is
an “empty” unit ball (“𝑒 𝑖𝜔
= 𝑒 𝑖𝑛𝜔
”), in which two
points are chosen (“recorded”), the one of which on
the surface, the other within the ball
• The same ball can be transformed arbitrarily but
only smoothly (conformally):
• It will be also a deformed “relative quant” at a point
in pseudo-Riemannian space, and after this
represented as a wave function in the tangent
Hilbert space of the common entangled system
42. Involving Fock space
• Fock space serves to describe a collection of an
arbitrary number of identical particles whether
fermions or bosons, each of which corresponding
to a single Hilbert space
• Informally, it is the infinite sum of the tensor
product of 𝑖 (𝑖 = 0,1, … , ∞) Hilbert spaces
• Formally:
• Then pseudo-Riemannian space can be described
by infinitely many entangled Hilbert spaces by
means of Fock space as an entangled state of
infinitely many identical (bosonic) particles
43. Notations:
𝐹 𝐻 , Fock space on Hilbert space, H
ν, a parameter of two values, the one for
bosonic, the other for fermionic ensemble
𝑆ν, an operator symmetrizing or anti-
symmetrizing the tensor involution, which
follows, correspondingly for bosons or fermions
𝐻⊗𝑛
, the nth tensor involution of H
44. Entanglement by Fock space and the global
EFE
• Indeed the pseudo-Riemannian manifold can be
represented by infinitely many points of it
• There are infinitely many different wave functions
corresponding one-to-one to each point and a
tangent Hilbert space, to which the corresponding
wave function belongs
• However these Hilbert spaces are rotated to each
other in general
• Nevertheless one can utilize Fock space where the
Hilbert spaces are not entangled to represent the
entangled case as above
45. The main conclusion
• The global EFE is equivalent to an infinite set
of SEs, each of which is equivalent to the local
EFE at as infinitely many points as points are
necessary to be exhaustedly described the
only manifold corresponding to the global EFE
• In other words, that SE, which corresponds to
the global EFE, can be written down as a
single equation in Fock space for infinitely
many “bosons” describing exhaustedly the
pseudo-Riemannian manifold
46. How can one prove that?
• Entanglement of two Hilbert spaces can be equiva-
lently represented by an infinite sum in Fock space
• Indeed one can think of Fock space as that
generalization of Hilbert space where the complex
coefficients 𝐶𝑖 , 𝑖 = 1, … , ∞, of any element
(vector), which are constants, are generalized to
arbitrary functions of Hilbert space {Ψ𝑖}
• This implies the necessity of an infinite set of points
(i.e. members of Fock space or “bosons”) to be
represented the pseudo-Riemannian manifold
exhaustedly
47. Furthermore ...
• The curved manifold of entanglement can be better
and better approximated adding new and new,
higher and higher nonzero members in Fock space
• Thus coincidence is possible only as a limit
converging for infinitely many members of Fock
space
• Thus Fock space in infinity can represent a
generalized leap in probability distribution:
However if the limit as above exists, that leap will
be equivalent to a single smooth probability
distribution corresponding to a single and
thereupon “flat” Hilbert space of the entangled
system as a whole
48. Consequently:
1. The global EFE represent a generalized “quantum”
leap, that in probability distribution, and equivalent
to some entanglement just as the local one
2. Nevertheless, this is observable only “inside”: If the
corresponding relation is reduced to the equivalent
property, which means that the entangled system is
observed as a whole, i.e. “outside”, there will not be
both entanglement and gravity
3. Thus the Standard model being referred to a single
quantum system observed “outside” can involve
neither gravity nor entanglement: they exist only in
the present, but not in the past and future
49. References:
Einstein, A. 1918. Einstein, A. (1918) “Prinzipielles zur
allgemeinen Relativitätstheorie,” Annalen der Physik
55(4): 241-244.
Kochen, S., Specker, E. (1968) “The problem of hidden
variables in quantum mechanics,” Journal of
Mathematics and Mechanics 17(1): 59-87.
Here Δ means the relative “curving” of a curved qubit to another, also curved qubit.
However the Standard model seems to contain more information than that in a single qubit, which is equal to the complete information about a given inertial reference frame