LORENTZ TRANSFORMATION
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The document discusses Lorentz transformations, which relate the space and time coordinates between frames of reference moving at constant velocities. It states that Lorentz transformations supersede Galilean transformations by accounting for velocities close to the speed of light. The key equations for Lorentz transformations and their inverse are presented, along with an example showing how the transformations ensure light speed remains constant between frames.
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LORENTZ TRANSFORMATION Pooja chouhan
The document discusses the Lorentz transformations, which replace the Galilean transformations of position and time. It derives the Lorentz transformations for position and time, which relate the coordinates of an event in one inertial reference frame to those in another frame moving at constant velocity. The inverse transformations are also derived. An example application of the transformations is provided.
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This document summarizes a physics assignment on key concepts including space, time, motion, frames of reference, and the Michelson-Morley experiment. It defines these concepts and describes the experimental setup and calculations used in the Michelson-Morley experiment. The experiment found no fringe shift, inconsistent with the expected results if the Earth moved through the hypothesized luminiferous ether. This led to the conclusion that the speed of light is constant regardless of motion through the ether, questioning the concept of the stationary ether.
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its about relativity</BR.about sir albert Einstein. quotes about relativity...michelsone and morleys law about relativity....general theory of relativity ..Einstein laws about relativity...Einstein description of laws about theory of special relativity ....first postulates of special law,,sceond postulates of special laws of relativity.........Galilian transformation of relativity....................Lorentz transformation.......... Lorentz transformation about the laws of relativity........Length contractiion .....Time dilation........Mass expansion........E= MC^2 ( theory & provens ))......The life cycle of stars.......Black holes ( slides).............Formation And Properties of blackholes ................Concluation .........Thankyou slide ...............ANY QUESATION ?????????................thank YOU SO MUCH :P :P :P
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Introduction to Special theory of relativity
This document provides an introduction to Einstein's special theory of relativity. It discusses key concepts like Galilean transformations, Michelson-Morley experiment, postulates of relativity, and consequences like time dilation and length contraction. The document explains that special relativity applies to observers in uniform motion and the speed of light in a vacuum is the same for all observers, regardless of their motion. It also presents the Lorentz transformations and equations for time dilation and length contraction.
Michelson - Morley Experiment - B.Sc Physics - I Year- Mechanics
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The Michelson-Morley experiment aimed to detect the motion of the Earth through the hypothesized luminiferous ether by measuring fringe shifts in an interferometer when the apparatus was rotated. However, the experiment yielded a null result, finding no difference in the speed of light in different directions. This contradicted the ether theory and provided early experimental evidence for Einstein's theory of relativity by showing there was no ether drag. The null result meant the Earth's speed could not be measured relative to the ether, disproving its existence and revolutionizing our understanding of space and time.Relativity
The document discusses key concepts from Einstein's special theory of relativity, including:
1) Frames of reference and the distinction between inertial and non-inertial frames. The laws of motion only hold in inertial frames.
2) The postulates of special relativity - that the laws of physics are the same in all inertial frames, and that the speed of light is constant.
3) Consequences of these postulates, including Lorentz transformations, length contraction, time dilation, and the relativity of simultaneity.
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1. The document summarizes Albert Einstein's special theory of relativity, beginning with a discussion of the Michelson-Morley experiment and its implications for the ether hypothesis and Galilean transformations.
2. It then outlines Einstein's two postulates: the principle of relativity, which states that the laws of physics are the same in all inertial frames; and the constancy of the speed of light in all reference frames.
3. The Lorentz transformations are presented as Einstein's solution to reconcile the constancy of the speed of light with Maxwell's equations, incorporating time dilation and length contraction effects between reference frames.
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The document discusses the Lorentz transformations, which replace the Galilean transformations of position and time. It derives the Lorentz transformations for position and time, which relate the coordinates of an event in one inertial reference frame to those in another frame moving at constant velocity. The inverse transformations are also derived. An example application of the transformations is provided.
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This document summarizes a physics assignment on key concepts including space, time, motion, frames of reference, and the Michelson-Morley experiment. It defines these concepts and describes the experimental setup and calculations used in the Michelson-Morley experiment. The experiment found no fringe shift, inconsistent with the expected results if the Earth moved through the hypothesized luminiferous ether. This led to the conclusion that the speed of light is constant regardless of motion through the ether, questioning the concept of the stationary ether.
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The Michelson-Morley experiment aimed to detect the motion of the Earth through the hypothesized luminiferous ether by measuring fringe shifts in an interferometer when the apparatus was rotated. However, the experiment yielded a null result, finding no difference in the speed of light in different directions. This contradicted the ether theory and provided early experimental evidence for Einstein's theory of relativity by showing there was no ether drag. The null result meant the Earth's speed could not be measured relative to the ether, disproving its existence and revolutionizing our understanding of space and time.Relativity
The document discusses key concepts from Einstein's special theory of relativity, including:
1) Frames of reference and the distinction between inertial and non-inertial frames. The laws of motion only hold in inertial frames.
2) The postulates of special relativity - that the laws of physics are the same in all inertial frames, and that the speed of light is constant.
3) Consequences of these postulates, including Lorentz transformations, length contraction, time dilation, and the relativity of simultaneity.
4) Experiments that motivated relativity, like the Michelson-Morley experiment, and equations like Lorentz transformations that were developed to be consistent with the postulates
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1. The document summarizes Albert Einstein's special theory of relativity, beginning with a discussion of the Michelson-Morley experiment and its implications for the ether hypothesis and Galilean transformations.
2. It then outlines Einstein's two postulates: the principle of relativity, which states that the laws of physics are the same in all inertial frames; and the constancy of the speed of light in all reference frames.
3. The Lorentz transformations are presented as Einstein's solution to reconcile the constancy of the speed of light with Maxwell's equations, incorporating time dilation and length contraction effects between reference frames.
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Albert Einstein was born in Germany in 1879 and worked as a patent clerk. In 1905, at age 26, he published his first paper on the special theory of relativity. This theory 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. In 1915, Einstein published his general theory of relativity, which described gravity as a geometric property of space and time. Einstein received the Nobel Prize in Physics in 1921 for his services to theoretical physics and especially for his discovery of the law of the photoelectric effect. Some key ideas from Einstein's theories include that time slows down for moving objects, moving objects appear contracted, mass and energy are equivalent, and nothing
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This document provides an introduction to the special theory of relativity, including:
- It defines the special theory of relativity as dealing with objects moving at constant speeds, while the general theory deals with accelerating objects.
- Frames of reference and inertial frames are introduced, with inertial frames obeying Newton's laws of motion.
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The Michelson-Morley experiment was conducted between 1887 and 1926 using increasingly precise interferometers to attempt to detect the hypothesized luminiferous ether and measure the speed of Earth through it. Michelson and Morley's 1887 experiment at Case Western Reserve University used an 11 meter interferometer and found no detectable fringe shift, contrary to predictions. Subsequent repeated experiments by multiple observers using improved designs up to 32 meters also found no detectable fringe shift, establishing that the luminiferous ether hypothesis was invalid and that the speed of light appears constant regardless of the motion of the light source. This result was one of the important experimental evidences leading to the development of special relativity.
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Periodic motion repeats at regular time intervals. Examples include planetary orbits and clock hands. Oscillation involves to-and-fro motion about a mean position, like a pendulum swing. It is always periodic but periodic motion need not involve oscillation. The time for one full cycle is the period (T). Frequency (ν) is the number of cycles per second. Angular frequency (ω) relates frequency and period. Displacement variables describe the changing quantity in oscillations, like position or angle. Simple harmonic motion involves a restoring force proportional to displacement towards the equilibrium point, like a spring. It can be modeled by sine and cosine functions and includes oscillations of springs and pendulums.
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The document summarizes key principles of Einstein's Special Theory of Relativity, including:
1) The principle of relativity states that the laws of physics are the same in all inertial reference frames.
2) The principle of the constant speed of light asserts that the speed of light in vacuum is the same for all observers, regardless of their motion.
3) These principles lead to two consequences - time dilation, where time passes more slowly for moving observers, and length contraction, where objects contract along the direction of motion as they approach the speed of light.
Oscillation 2017
this is class 12 Maharashtra board physics subject content. this is complete content with notes with easily explaination.
for buying or neet attractive ppt in any subject contact me 8879919898. go to my site akchem.tk
blog akchem.blogspot.com
Einstein's theory of relativity - Explained!
Einstein’s Theories of Relativity revolutionized how Today’s Scientific world thinks about Space, Time, Mass, Energy and Gravity. This is purely an imaginative Science that worked in the Laboratory of Einstein's Brain..
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1. The document discusses Albert Einstein's special theory of relativity, which proposes that the concepts of space and time need to be revised based on two postulates: the principle of relativity and the principle of the independence of the velocity of light.
2. It describes key effects of special relativity including time dilation, length contraction, and the twin paradox. Time dilation refers to clocks slowing down relative to observers in motion, while length contraction is the decrease in measured length of an object based on the observer's motion.
3. The twin paradox hypothetically examines the scenario of twin sisters aging at different rates if one takes a space voyage, demonstrating time dilation. The document provides formulas and explanations for these effects of special relativity.
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* L0 = 45 m (length as measured by crew in rest frame)
* v = 0.50c
* c = 3×10^8 m/s
* Using the Lorentz contraction formula:
L = L0√(1-(v^2/c^2))
= 45√(1-(0.50c)2/c2)
= 45√(1-0.25)
= 45√0.75
= 33.75 m
Therefore, the length of the spaceship as measured by mission control in Texas is 33.75 m.
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The document discusses the principles of superposition and interference of waves. Constructive interference occurs when wave crests and troughs overlap, increasing amplitude, while destructive interference occurs when crests and troughs cancel out. Interference is responsible for the colors seen in soap bubbles and is exploited in holography and interferometry. Examples of interference include light waves, water waves, radio waves, and sound waves.
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The document discusses Albert Einstein's theories of special and general relativity. Special relativity introduced concepts like the constancy of the speed of light and reference frames. General relativity holds that gravity is not a force but a consequence of objects warping the geometry of spacetime. It predicts phenomena like light deflection near massive objects and gravitational time dilation, which were later confirmed. The document also provides background on the Michelson-Morley experiment and quotes from Einstein and Hawking about the implications of relativity theory.
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2) It discusses experimental evidence for concepts like time dilation from observations of muon decay lifetimes and provides equations for length contraction, time dilation, velocity addition and relativistic mass.
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1) It showed that Newton's ideas of absolute space and time were incorrect and implied that matter and energy are interconvertible.
2) It established two postulates - the laws of physics apply in all inertial frames, and the speed of light is constant in all frames.
3) This leads to effects like time dilation and length contraction, as measurements of space and time differ for observers in different inertial frames moving relative to one another.
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2. Photoelectric effect shows that light behaves as particles called photons. Einstein's equation explained it using the photon energy.
3. Compton scattering showed that photons can collide with and transfer energy to electrons. The Compton wavelength was derived from this.
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General Theory of Relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
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1. Einstein used thought experiments and his principle that indistinguishable phenomena are the same to formulate the theory of special relativity.
2. The two postulates of special relativity are that all physical laws are the same in any inertial reference frame and that the speed of light is constant.
3. Key consequences of special relativity include time dilation, where moving clocks run slow, and length contraction, where lengths appear shorter to observers in motion.
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1. Special relativity describes the laws of physics in different inertial reference frames where the speed of light in a vacuum is constant. It includes time dilation and length contraction effects at relativistic speeds.
2. General relativity describes gravity as a consequence of the curvature of spacetime caused by the uneven distribution of mass/energy. It predicts phenomena like gravitational time dilation, gravitational lensing, and the bending of light by massive objects.
3. Both theories have been validated experimentally through observations of subatomic particles, GPS satellites, and images of distant galaxies. They form the basis of modern physics.
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The document discusses key concepts in Newtonian mechanics and Galilean transformations and how they break down at high speeds. It introduces Einstein's special theory of relativity, which corrected Newtonian mechanics by proposing new transformation equations that keep the speed of light constant for all observers, making Maxwell's equations of electromagnetism invariant. This resolved the incompatibility between mechanics and electromagnetism at high velocities predicted by Galilean transformations.
trasformations
The document introduces the Lorentz transformations, which relate spatial and temporal coordinates between different inertial reference frames according to Einstein's theory of special relativity. The Lorentz transformations were originally derived by Lorentz and others to make Maxwell's laws of electromagnetism invariant. They describe how an event that is specified by its coordinates (x, y, z, t) in one reference frame would be specified by transformed coordinates (x', y', z', t') in another reference frame. At low velocities, the Lorentz transformations reduce to the classical Galilean transformations.
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Albert Einstein was born in Germany in 1879 and worked as a patent clerk. In 1905, at age 26, he published his first paper on the special theory of relativity. This theory 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. In 1915, Einstein published his general theory of relativity, which described gravity as a geometric property of space and time. Einstein received the Nobel Prize in Physics in 1921 for his services to theoretical physics and especially for his discovery of the law of the photoelectric effect. Some key ideas from Einstein's theories include that time slows down for moving objects, moving objects appear contracted, mass and energy are equivalent, and nothing
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The document discusses Albert Einstein's Special Theory of Relativity, which established that the laws of physics are the same in all inertial reference frames and that the speed of light in a vacuum is constant. It explains key concepts such as length contraction, time dilation, and mass-energy equivalence that arise from these postulates. Examples are provided to illustrate how observations of phenomena can change depending on the reference frame of the observer.
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This document provides an introduction to the special theory of relativity, including:
- It defines the special theory of relativity as dealing with objects moving at constant speeds, while the general theory deals with accelerating objects.
- Frames of reference and inertial frames are introduced, with inertial frames obeying Newton's laws of motion.
- Galilean transformations are described as relating the coordinates of particles between inertial frames, including equations for position, velocity, acceleration, and forces.
- The drawbacks of Galilean transformations are that they are invalid for objects moving at the speed of light or for electromagnetism.
Michelson Morley experiment
The Michelson-Morley experiment was conducted between 1887 and 1926 using increasingly precise interferometers to attempt to detect the hypothesized luminiferous ether and measure the speed of Earth through it. Michelson and Morley's 1887 experiment at Case Western Reserve University used an 11 meter interferometer and found no detectable fringe shift, contrary to predictions. Subsequent repeated experiments by multiple observers using improved designs up to 32 meters also found no detectable fringe shift, establishing that the luminiferous ether hypothesis was invalid and that the speed of light appears constant regardless of the motion of the light source. This result was one of the important experimental evidences leading to the development of special relativity.
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Periodic motion repeats at regular time intervals. Examples include planetary orbits and clock hands. Oscillation involves to-and-fro motion about a mean position, like a pendulum swing. It is always periodic but periodic motion need not involve oscillation. The time for one full cycle is the period (T). Frequency (ν) is the number of cycles per second. Angular frequency (ω) relates frequency and period. Displacement variables describe the changing quantity in oscillations, like position or angle. Simple harmonic motion involves a restoring force proportional to displacement towards the equilibrium point, like a spring. It can be modeled by sine and cosine functions and includes oscillations of springs and pendulums.
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The document summarizes key principles of Einstein's Special Theory of Relativity, including:
1) The principle of relativity states that the laws of physics are the same in all inertial reference frames.
2) The principle of the constant speed of light asserts that the speed of light in vacuum is the same for all observers, regardless of their motion.
3) These principles lead to two consequences - time dilation, where time passes more slowly for moving observers, and length contraction, where objects contract along the direction of motion as they approach the speed of light.
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this is class 12 Maharashtra board physics subject content. this is complete content with notes with easily explaination.
for buying or neet attractive ppt in any subject contact me 8879919898. go to my site akchem.tk
blog akchem.blogspot.com
Einstein's theory of relativity - Explained!
Einstein’s Theories of Relativity revolutionized how Today’s Scientific world thinks about Space, Time, Mass, Energy and Gravity. This is purely an imaginative Science that worked in the Laboratory of Einstein's Brain..
Time dilation & length contraction
1. The document discusses Albert Einstein's special theory of relativity, which proposes that the concepts of space and time need to be revised based on two postulates: the principle of relativity and the principle of the independence of the velocity of light.
2. It describes key effects of special relativity including time dilation, length contraction, and the twin paradox. Time dilation refers to clocks slowing down relative to observers in motion, while length contraction is the decrease in measured length of an object based on the observer's motion.
3. The twin paradox hypothetically examines the scenario of twin sisters aging at different rates if one takes a space voyage, demonstrating time dilation. The document provides formulas and explanations for these effects of special relativity.
Relativity (1)
* L0 = 45 m (length as measured by crew in rest frame)
* v = 0.50c
* c = 3×10^8 m/s
* Using the Lorentz contraction formula:
L = L0√(1-(v^2/c^2))
= 45√(1-(0.50c)2/c2)
= 45√(1-0.25)
= 45√0.75
= 33.75 m
Therefore, the length of the spaceship as measured by mission control in Texas is 33.75 m.
SUPERPOSITION PRINCIPLE
The document discusses the principles of superposition and interference of waves. Constructive interference occurs when wave crests and troughs overlap, increasing amplitude, while destructive interference occurs when crests and troughs cancel out. Interference is responsible for the colors seen in soap bubbles and is exploited in holography and interferometry. Examples of interference include light waves, water waves, radio waves, and sound waves.
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The document discusses Albert Einstein's theories of special and general relativity. Special relativity introduced concepts like the constancy of the speed of light and reference frames. General relativity holds that gravity is not a force but a consequence of objects warping the geometry of spacetime. It predicts phenomena like light deflection near massive objects and gravitational time dilation, which were later confirmed. The document also provides background on the Michelson-Morley experiment and quotes from Einstein and Hawking about the implications of relativity theory.
Ph 101-6
1) The document outlines key concepts from Einstein's theory of special relativity including reference frames, the Michelson-Morley experiment, postulates of relativity, Lorentz transformations, length contraction and time dilation.
2) It discusses experimental evidence for concepts like time dilation from observations of muon decay lifetimes and provides equations for length contraction, time dilation, velocity addition and relativistic mass.
3) The twin paradox is introduced as a thought experiment exploring time dilation between twins where one takes a high speed journey into space and back while the other remains on Earth. Accelerations are identified as the resolution for why the traveling twin ages less.
Special Theory Of Relativity
The document summarizes key aspects of Einstein's special theory of relativity, including:
1) It showed that Newton's ideas of absolute space and time were incorrect and implied that matter and energy are interconvertible.
2) It established two postulates - the laws of physics apply in all inertial frames, and the speed of light is constant in all frames.
3) This leads to effects like time dilation and length contraction, as measurements of space and time differ for observers in different inertial frames moving relative to one another.
Physics - Oscillations
The document discusses periodic motion and simple harmonic motion (SHM). It provides examples of objects that exhibit periodic motion which may or may not be SHM. SHM occurs when the net force on an object is directly proportional to the object's displacement from equilibrium and acts to restore the object to equilibrium. Examples of SHM include a pendulum with small angular displacement and a loaded spring oscillating about its equilibrium position. The document defines terms related to SHM like period, frequency, amplitude, displacement, angular frequency, phase and phase difference. It also provides examples of free oscillations that are SHM.
Quantum mechanics
1. Quantum mechanics began with Max Planck's paper in 1900 explaining black body radiation. It extends physics to small dimensions and includes classical laws as special cases.
2. Photoelectric effect shows that light behaves as particles called photons. Einstein's equation explained it using the photon energy.
3. Compton scattering showed that photons can collide with and transfer energy to electrons. The Compton wavelength was derived from this.
Einstein's theory of general relativity
General Theory of Relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
Relativity
1. Einstein used thought experiments and his principle that indistinguishable phenomena are the same to formulate the theory of special relativity.
2. The two postulates of special relativity are that all physical laws are the same in any inertial reference frame and that the speed of light is constant.
3. Key consequences of special relativity include time dilation, where moving clocks run slow, and length contraction, where lengths appear shorter to observers in motion.
special relativity
1. Special relativity describes the laws of physics in different inertial reference frames where the speed of light in a vacuum is constant. It includes time dilation and length contraction effects at relativistic speeds.
2. General relativity describes gravity as a consequence of the curvature of spacetime caused by the uneven distribution of mass/energy. It predicts phenomena like gravitational time dilation, gravitational lensing, and the bending of light by massive objects.
3. Both theories have been validated experimentally through observations of subatomic particles, GPS satellites, and images of distant galaxies. They form the basis of modern physics.
Classical Mechanics-MSc
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
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The document discusses the Laplace transform, which takes a function of time and transforms it into a function of complex frequency. This transformation converts differential equations into algebraic equations, simplifying solving problems involving systems. The Laplace transform has many applications in fields like engineering, physics, and astronomy by allowing analysis of linear time-invariant systems through properties like derivatives becoming multiplications in the frequency domain.
Laplace transform
The document discusses the Laplace transform and its applications. Specifically:
- The Laplace transform was developed by mathematicians including Euler, Lagrange, and Laplace to solve differential equations.
- It transforms a function of time to a function of complex frequencies, allowing differential equations to be written as algebraic equations.
- For a function to have a Laplace transform, it must be at least piecewise continuous and bounded above by an exponential function.
- The Laplace transform can reduce the dimension of partial differential equations and is used in applications including semiconductor mobility, wireless networks, vehicle vibrations, and electromagnetic fields.
Laplace transform
The document discusses the Laplace transform and its applications. Specifically:
- The Laplace transform was developed by mathematicians including Euler, Lagrange, and Laplace to solve differential equations.
- It transforms a function of time to a function of complex frequencies, allowing differential equations to be written as algebraic equations.
- For a function to have a Laplace transform, it must be at least piecewise continuous and bounded above by an exponential function.
- The Laplace transform can reduce the dimension of partial differential equations and is used in applications including semiconductor mobility, wireless networks, vehicle vibrations, and electromagnetic fields.
Barnett's Presentation
Lorentz transformations are used in particle physics because they describe how measurements of space and time are related between observers moving at constant velocities, which is important when particles move near the speed of light. Galilean transformations do not account for the speed of light and are therefore not accurate enough for particle physics where velocities approach light speed. Applying Lorentz transformations to experimental data sets of particles brings their measurements into a common rest frame and allows for symmetrical analysis that reveals insights about particle behavior.
Relativistic formulation of Maxwell equations.
This document discusses the relativistic formulation of Maxwell's equations. It begins by introducing the key concepts of special relativity that are needed, including Lorentz transformations and four-vectors. It then shows how the electric and magnetic fields transform under Lorentz transformations and how they can be combined into the electromagnetic field tensor. The document also discusses how charge and current densities transform and satisfy the continuity equation as a four-vector. Finally, it presents Maxwell's equations in their compact relativistic form in terms of the field tensor and its derivatives.
The phase plane of moving discrete breathers
1. The document studies discrete breathers in a periodic chain of 5 atoms coupled by quadratic-quartic springs. It uses discrete symmetries to simplify the analysis and visualize the phase space.
2. It finds that unlike even atom chains, odd atom chains have no energy threshold for breathers due to degenerate band edge modes. It observes long-lived "hopping breathers" that move chaotically in the separatrix region dividing pinned and moving states.
3. It applies linear stability analysis to measure quasi-phonon frequencies around breathers and map the stable and unstable manifolds of unstable breathers. This allows systematically launching moving or pinned breathers by perturbing stable or unstable breathers.
Einstein's Theory of relativity. Special Relativity
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Galactic Rotation
The document discusses Fourier transforms and their application to galactic spectroscopy. It begins by explaining what a Fourier transform is and how it can transform raw continuous data into a frequency distribution. It then discusses how Fourier spectroscopy uses an interferometer to collect scattered light data from different wavelengths, which is converted via a Fourier transform into a readable spectrum. The document goes on to explain how galactic rotation curves are measured using the Doppler shift of hydrogen emission lines to determine angular velocities at different radial distances from the galaxy's center. It describes how Vera Rubin's experiments in the 1960s found discrepancies between measured rotation curves and those predicted by Newtonian mechanics based on observable mass alone, providing early evidence for dark matter.
Spaceengine
1. The document discusses equations relating thermal conductivity, surface area, temperature gradient, and heat transfer rate for water flowing through a pipe.
2. It then discusses how the movement of water particles through a tube is analogous to the movement of a train on rails, and how the laws of special relativity may need to be combined with temperature and quantum mechanics.
3. Finally, it presents equations for a von-Neumann type interaction describing an open boundary quantum system, where the wave function of a pointer after time t depends on the initial wave function and a parameter relating position and time.
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LORENTZ TRANSFORMATION
- 1. CONTENT: ➢ Lorentz Transformation ➢ Superseding of Lorentz Transformation to Galilean Transformation ➢ Inverse Lorentz Transformation ➢ Relativity Equations
- 2. LORENTZ TRANSFORMATION The set of equations which in Einstein's special theory of relativity relate the space and time coordinates of one frame of reference to those of other. Or, The Lorentz transformation are coordinate transformations between two coordinate frames that move at constant velocity relative to each other. Note: The 'Lorentz Transformations' only refers to transformations between inertial frames, usually in the context of special relativity. The transformations are named after the Dutch Physicist Hendrik Lorentz
- 3. Superseding of Lorentz Transformation to Galilean Transformation Lorentz transformation supersede(replace) the Galilean transformation of Newtonian physics, which assumes an absolute space and time. The Galilean transformation is a good approximation only at relative speeds much smaller than the speed of light. What Einstein's special theory of relativity says is that to understand why the speed of light is constant, we have modify the way in which we relate the observation in one inertial frame to that of another. The Galilean transformation is, x'=x-vt, t'=t which is wrong. The correct relation is,
- 4. These are called the Lorentz transformation of space and time respectively.
- 6. We can see that if the relative velocity v between the two frames are much smaller than the speed of light c, then the ratio v/c can be neglected in this relation and we recover the Galilei transformation. So the reason why we did not have any problems with the Galilei transformation up to now is that v was small enough for it to be good approximation of the Lorentz transformation. Let's check that this relation does indeed show that the speed of light is same in both frames (x,t) and (x',t'). Let's say that a beam of light started out from the origin x'=x=0 at time t'=t=0. Since the speed of light is c,at time t=T, the beam of light would have travelled to the point x=cT in the (x,t) frame. In the other frame, this point is observed as,
- 7. So the speed of light in the (x',t') frame would also be:
- 8. Inverse Lorentz Transformation If we want to transform the coordinates from system S to S', then the transformation equations are : (Replace v by -v) These equations are known as Inverse Lorentz Transformation