Pythagoras’ Theorem: a2+b2=c2
Historical Reference: Attributed to Pythagoras, an ancient Greek mathematician.
Meaning: Describes the relationship between the lengths of the sides of a right triangle, where aa and bb are the lengths of the two shorter sides, and cc is the length of the hypotenuse.
Implication: Fundamental in geometry and trigonometry, providing a method to calculate unknown side lengths in right triangles.
Newton’s Law of Universal Gravitation: F = G(m1m2)/R2
Historical Reference: Proposed by Sir Isaac Newton in his work “Philosophiæ Naturalis Principia Mathematica” in 1687.
Meaning: States that every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Implication: Fundamental in classical mechanics, providing a quantitative description of the gravitational force between two objects.
Variation of Gravity with Height: gh = g (r/r+h)2
Historical Reference: Derived from Newton’s law of universal gravitation.
Meaning: The acceleration due to gravity at a height of h above the earth’s surface is gh, and the radius of the earth is R. This equation is used where h is a considerable distance compared to r.
Implication: Provides insight into the decrease in gravitational acceleration as altitude increases, influencing phenomena such as weightlessness in space travel and atmospheric dynamics.
Coulomb’s Law: F= ke*(q1* q2) / r2
Historical Reference: Developed by Charles-Augustin de Coulomb in the 18th century, Coulomb’s law describes the electrostatic force between two charged particles.
Meaning: Organizes energy into inverse square concentrations, illustrating how the strength of the electrostatic force decreases with distance according to the square of the separation distance.
Implication: Fundamental in understanding the behavior of electric charges and the interactions between them, forming the basis for electrostatics and contributing to the development of electromagnetic theory.
Gauss’s Law for Electric Fields: ∇·E= ρ/ε0εr
Historical Reference: Formulated by Carl Friedrich Gauss in the early 19th century, Gauss’s law for electric fields relates the electric flux through a closed surface to the charge enclosed within the surface.
Meaning: In vector calculus, this law describes the flow of electric field lines through a closed surface, providing insights into the distribution of electric charge.
Implication: Essential in analyzing the behavior of electric fields and charges, Gauss’s law helps in solving electrostatic problems and understanding the principles of electric field behavior in various contexts.
Gauss’s Law for Gravitation: ΦD= Qfree
Historical Reference: Inspired by Gauss’s work on electric fields, the gravitational form of Gauss’s law relates the gravitational flux through a closed surface to the mass enclosed within the surface
Meaning: States that the gravitational flux through any closed surface is proportional to the enclosed mass, providing a mathematical representation of gravitational interactions.
Implication: Fundamental in gravitational theory, Gauss’s law for gravitation helps in understanding the distribution of gravitational fields and predicting gravitational effects based on mass distribution.
Faraday’s Law of Electromagnetic Induction: E=dΦB/dt
Historical Reference: Discovered by Michael Faraday in the 19th century, Faraday’s law of electromagnetic induction describes how a changing magnetic field induces an electromotive force (EMF) or electric field.
Meaning: States that a changing magnetic field induces an electric field, demonstrating the connection between magnetic and electric phenomena.
Implication: Crucial in the development of electromagnetism and electrical engineering, Faraday’s law explains the principles behind generators, transformers, and various electrical devices.
Ohm’s Law: E=IR
Historical Reference: Named after Georg Simon Ohm, Ohm’s law defines the relationship between electric potential (voltage), current, and resistance in an electrical circuit.
Meaning: States that the electric potential (voltage) across a resistor is directly proportional to the current flowing through it and the resistance of the resistor.
Implication: Fundamental in circuit analysis and electrical engineering, Ohm’s law governs the behavior of electrical circuits and is used extensively in the design and analysis of electrical systems.
Stefan-Boltzmann Law: E=σT4
Historical Reference: Developed by Josef Stefan and Ludwig Boltzmann in the late 19th century, the Stefan-Boltzmann law relates the radiant power emitted by a surface to its temperature.
Meaning: States that the total radiant power emitted by a black body per unit surface area is directly proportional to the fourth power of its absolute temperature.
Implication: Essential in thermodynamics and astrophysics, the Stefan-Boltzmann law helps in understanding the energy radiation from various objects, including stars and planets
Maxwell’s Equations: c=1/√(ε0μ0) and Z0=√(μ0/ε0)
Historical Reference: Formulated by James Clerk Maxwell in the 19th century, Maxwell’s equations describe the behavior of electric and magnetic fields in classical electromagnetism.
Meaning: The first equation, c=1/√(ε0μ0), defines the speed of light (c) as the reciprocal of the square root of the product of the vacuum permittivity (ε0) and the vacuum permeability (μ0). The second equation defines the characteristic impedance of free space (Z0) as the square root of the ratio of vacuum permeability to vacuum permittivity.
Implication: Fundamental in electromagnetism and wave propagation, Maxwell’s equations unify electricity and magnetism and provide a theoretical foundation for the study of electromagnetic waves.
Maxwell’s Z0=√(μ0/ε0) shows energy concentrations are reflected as Z0 contours which are constantly adjusted, at the speed of c, to reflect energy field density movement.
Y0=√(ε0/μ0) is the inverse of Maxwell’s “Z0 or Impedance and shows the rate energy admitted into the EM field.
Einstein’s Mass-Energy Equivalence: E=mc2
Historical Reference: Proposed by Albert Einstein in his theory of special relativity in 1905, the mass-energy equivalence principle states that mass and energy are equivalent and interchangeable.
Meaning: Expresses the relationship between mass (m) and energy (E), where the energy of an object is equal to its mass multiplied by the speed of light squared
Implication: Revolutionized physics by showing that mass can be converted into energy and vice versa, leading to the development of nuclear energy and contributing to the structure of the universe.
Planck’s Equation: E=hf
Historical Reference: Introduced by Max Planck in 1900.
Meaning: Relates the energy of a photon to its frequency, where h is Planck’s constant.
Implication: Foundational in quantum mechanics, providing a key relationship between the energy and frequency of electromagnetic radiation
Lorentz Factor γ=1/√(1- v2/c2)
Historical Reference: Introduced in the context of special relativity by Hendrik Lorentz and confirmed by Albert Einstein.
Meaning: The Lorentz factor (γ) quantifies the effect of time dilation and length contraction on moving objects relative to a stationary observer, increasing with velocity according to the formula , where v is the velocity and c is the speed of light.
Implication: The Lorentz factor plays a crucial role in relativistic mechanics, accounting for the observed phenomena of time dilation and length contraction at speeds approaching the speed of light. It’s essential for understanding the behavior of particles in particle accelerators, the stability of high-speed spacecraft, and the fundamentals of cosmology.
Lorentz Force Law: F=qE+qv*B
Historical Reference: Introduced by Max Planck in 1900.
Meaning: Describes the force experienced by a charged particle in an electromagnetic field.
Implication: Essential in understanding the behavior of charged particles in electromagnetic fields and the principles of electromagnetism. Historical Reference: Introduced by Max Planck in 1900.
Lorentz Magnetic Force (Torque) Equation τ=q (r×B)
Historical Reference: This concept is derived from the Lorentz force law and is fundamental in understanding the rotational motion of charged particles in magnetic fields.
Meaning: This equation describes the additional rotational force experienced by a charged particle moving through a magnetic field. It accounts for the interaction between the magnetic field and the motion of the particle, resulting in a twisting or rotational motion.
Implication: The magnetic Lorentz force (torque) is essential for understanding phenomena such as the behavior of charged particles in cyclotrons, where particles are accelerated in circular paths by magnetic fields, as well as the dynamics of magnetic materials and electromagnetic devices.
Lorentz Time Dilation Equation Δt′=Δt/√ (v2/c2)
Historical Reference: Developed by Hendrik Lorentz as part of his transformations to account for the effects of relative motion between inertial frames of reference, contributing to the foundation of special relativity.
Meaning: The Lorentz time dilation equation describes how time intervals appear to be dilated or stretched when observed from a frame of reference moving at a significant fraction of the speed of light relative to a stationary frame.
Implication: This equation has profound implications for the nature of time and motion, leading to phenomena such as time dilation in high-speed travel and relativistic effects in particle accelerators and astrophysical phenomena.
Schwarzschild metric r=2Gm/c2
Historical Reference: Developed by Karl Schwarzschild in 1916 as a solution to Einstein’s field equations of general relativity.
Meaning: Describes the force experieMeaning: Represents the Schwarzschild radius (rr), which defines the size of the event horizon of a non-rotating black hole. It relates the mass (mm) of an object to its Schwarzschild radius, gravitational constant (GG), and the speed of light (cc).
Implication: Fundamental in the study of black holes and gravitational phenomena, providing a theoretical framework for understanding the curvature of spacetime around massive objects.
Schrödinger Equation: HΨ=iℏ(∂t/∂)Ψ
Historical Reference: Proposed by Erwin Schrödinger in 1926 as part of the development of quantum mechanics.
Meaning: Represents the fundamental wave equation of quantum mechanics, where H is the Hamiltonian operator, Ψ is the wave function, i is the imaginary unit, ℏ is the reduced Planck constant, and ∂t/∂ represents the partial derivative with respect to time.
Implication: Describes the behavior of quantum systems, including the time evolution of wave functions, and serves as a cornerstone in quantum mechanics, facilitating the prediction of particle behavior and the interpretation of experimental results.
QA Gravitational Acceleration: Gv = dc/dx
Historical Reference: Formulated by Rod Mack in 2019
Meaning: Represents the gravitational coefficient (Gs), which quantifies the rate of gravitational acceleration within the framework of QA. It relates changes in the rate of energy propagation (dx) in both physical and temporal dimensions to variations in the square root of the product of the vacuum permittivity (ε0) and vacuum permeability (μ0).
Implication: Challenges the traditional concept of a universal gravitational constant by proposing that gravity arises from changes in the rate of energy travel, rather than solely from mass. This perspective suggests that gravity is intimately linked to energy density rather than mass alone, potentially eliminating singularities and altering our understanding of the fundamental nature of the universe. By decoupling gravity from mass, QA opens new avenues for exploring gravitational phenomena and redefines our conceptual framework for the cosmos.