The study of motion of the object is an important section of the physics. The motion of a body is can be measured as absolute motion and relative motion. Practically any motion is measured is relative only, because one or the other way all the bodies are in motion. In this case we as observer can not measure the exact speed of the an object, because measured quantity of motion of other object is vary with the magnitude and direction of our motion. This can be studied with mathematical proof in this chapter. The Inertial frame and non inertial frame of reference, Special theory of relativity is covered here.
The document summarizes the Michelson-Morley experiment, which attempted to detect the motion of Earth through the hypothesized luminiferous ether but found no evidence of such motion. It describes the experimental setup, calculations of expected results assuming an ether, and the actual null results. It then explains how Einstein's theory of special relativity, including postulates that the speed of light is constant and physics is the same in all inertial frames, provides the proper explanation for why no ether drag was detected.
This document discusses reference frames and summarizes key findings from the Michelson-Morley experiment. It provides definitions for inertial and non-inertial reference frames. The Michelson-Morley experiment aimed to detect the motion of Earth through the luminiferous ether but found no evidence of ether drift. This led to developments in relativity. Lorentz transformations were derived based on relativity postulates and reduce to Galilean transformations for low speeds. Galilean transformations violate relativity while Lorentz transformations form its foundation.
The classical mechanics of the special theory of [autosaved]AmeenSoomro1
1) The document discusses the basic postulates of Einstein's special theory of relativity, which were formulated to resolve inconsistencies between Newtonian mechanics and Maxwell's electromagnetic theory regarding the speed of light being constant.
2) It introduces the Lorentz transformations, which relate the spacetime coordinates between two inertial frames in relative motion.
3) The transformations show that time is relative between frames and leads to effects like time dilation, where moving clocks are measured to tick slower than stationary ones.
Special theory of -Relativity presentation.pptdeoeo112
Special Relativity addresses limitations of classical Newtonian mechanics at high speeds approaching the speed of light. Key points:
- Michelson-Morley experiment found the speed of light is constant in all inertial reference frames, contradicting Galilean transformations.
- Einstein postulated (1) laws of physics are the same in all inertial frames and (2) the speed of light is constant.
- Simultaneity and time intervals are relative concepts depending on the observer's frame of reference, challenging notions of absolute time.
- Time dilation occurs such that moving clocks measure time intervals as longer than stationary observers, demonstrated by the train experiment.
B.Tech sem I Engineering Physics U-III Chapter 1-THE SPECIAL THEORY OF RELATI...Abhi Hirpara
The document discusses Einstein's theory of special relativity. It provides background on Einstein's two postulates: 1) the laws of physics are the same in all inertial frames of reference, and 2) the speed of light in a vacuum is the same for all observers regardless of their motion. It describes how these postulates led Einstein to develop the Lorentz transformations, which show that time and space are relative between different frames of reference moving at a constant velocity with respect to each other.
B.tech sem i engineering physics u iii chapter 1-the special theory of relati...Rai University
This document provides an overview of Einstein's Special Theory of Relativity. It begins by defining frames of reference and discussing the Michelson-Morley experiment, which found that the speed of light is constant regardless of the observer's motion. It then outlines Einstein's two postulates of special relativity: 1) the laws of physics are the same in all inertial frames; and 2) the speed of light in a vacuum is the same for all observers, regardless of their motion. The document concludes by deriving the Lorentz transformations, which describe how space and time are related for observers in different inertial frames of reference according to special relativity.
General and Special Theory Of Reletivity.pptxcafpres2344
The theory of relativity consists of two related theories developed by Albert Einstein:
1) Special Theory of Relativity explains the relationship between space, time, mass and energy in the absence of gravity.
2) General Theory of Relativity explains the law of gravitation and its relation to other forces, applying to astrophysical and cosmological realms including astronomy. It describes gravity as the curvature of spacetime caused by the uneven distribution of mass.
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.
The document summarizes the Michelson-Morley experiment, which attempted to detect the motion of Earth through the hypothesized luminiferous ether but found no evidence of such motion. It describes the experimental setup, calculations of expected results assuming an ether, and the actual null results. It then explains how Einstein's theory of special relativity, including postulates that the speed of light is constant and physics is the same in all inertial frames, provides the proper explanation for why no ether drag was detected.
This document discusses reference frames and summarizes key findings from the Michelson-Morley experiment. It provides definitions for inertial and non-inertial reference frames. The Michelson-Morley experiment aimed to detect the motion of Earth through the luminiferous ether but found no evidence of ether drift. This led to developments in relativity. Lorentz transformations were derived based on relativity postulates and reduce to Galilean transformations for low speeds. Galilean transformations violate relativity while Lorentz transformations form its foundation.
The classical mechanics of the special theory of [autosaved]AmeenSoomro1
1) The document discusses the basic postulates of Einstein's special theory of relativity, which were formulated to resolve inconsistencies between Newtonian mechanics and Maxwell's electromagnetic theory regarding the speed of light being constant.
2) It introduces the Lorentz transformations, which relate the spacetime coordinates between two inertial frames in relative motion.
3) The transformations show that time is relative between frames and leads to effects like time dilation, where moving clocks are measured to tick slower than stationary ones.
Special theory of -Relativity presentation.pptdeoeo112
Special Relativity addresses limitations of classical Newtonian mechanics at high speeds approaching the speed of light. Key points:
- Michelson-Morley experiment found the speed of light is constant in all inertial reference frames, contradicting Galilean transformations.
- Einstein postulated (1) laws of physics are the same in all inertial frames and (2) the speed of light is constant.
- Simultaneity and time intervals are relative concepts depending on the observer's frame of reference, challenging notions of absolute time.
- Time dilation occurs such that moving clocks measure time intervals as longer than stationary observers, demonstrated by the train experiment.
B.Tech sem I Engineering Physics U-III Chapter 1-THE SPECIAL THEORY OF RELATI...Abhi Hirpara
The document discusses Einstein's theory of special relativity. It provides background on Einstein's two postulates: 1) the laws of physics are the same in all inertial frames of reference, and 2) the speed of light in a vacuum is the same for all observers regardless of their motion. It describes how these postulates led Einstein to develop the Lorentz transformations, which show that time and space are relative between different frames of reference moving at a constant velocity with respect to each other.
B.tech sem i engineering physics u iii chapter 1-the special theory of relati...Rai University
This document provides an overview of Einstein's Special Theory of Relativity. It begins by defining frames of reference and discussing the Michelson-Morley experiment, which found that the speed of light is constant regardless of the observer's motion. It then outlines Einstein's two postulates of special relativity: 1) the laws of physics are the same in all inertial frames; and 2) the speed of light in a vacuum is the same for all observers, regardless of their motion. The document concludes by deriving the Lorentz transformations, which describe how space and time are related for observers in different inertial frames of reference according to special relativity.
General and Special Theory Of Reletivity.pptxcafpres2344
The theory of relativity consists of two related theories developed by Albert Einstein:
1) Special Theory of Relativity explains the relationship between space, time, mass and energy in the absence of gravity.
2) General Theory of Relativity explains the law of gravitation and its relation to other forces, applying to astrophysical and cosmological realms including astronomy. It describes gravity as the curvature of spacetime caused by the uneven distribution of mass.
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.
1) Einstein's theory of special relativity resolved contradictions between Galilean relativity and the constant speed of light by postulating that the laws of physics are the same in all inertial frames and that the speed of light has the same value in all frames.
2) Time dilation occurs such that moving clocks are observed to tick slower than stationary clocks. This effect increases as the relative velocity approaches the speed of light.
3) The twin paradox is resolved by recognizing that only one twin experiences accelerations during a round trip, so their frame of reference is not inertial for the entire journey.
Special theory of relativity:Michelson-Morley experiment,Galilean and Lorentz Tranformation,Length contraction,Time Dilation,Relativity of mass,mass-energy equivalence
Here are the key points about rate of change of velocity:
- Rate of change of velocity is also known as acceleration.
- Acceleration is a vector quantity which indicates the rate at which the velocity of an object is changing.
- The SI unit of acceleration is meter per second squared (m/s2).
- If an object's velocity is increasing with time, it has a positive acceleration. If velocity is decreasing with time, acceleration is negative.
- Acceleration can be caused by a change in the object's speed, direction of motion, or both.
- Constant acceleration means the rate of change of velocity remains the same over time. This results in a linear relationship between velocity and time
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.
1) Einstein introduces his theory of special relativity, which holds 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.
2) He describes an experiment showing that the definition of simultaneity is relative between different frames of reference moving at a constant velocity relative to each other.
3) He develops the equations relating space and time coordinates between two frames in uniform motion, showing that lengths contract and times dilate for objects in motion.
This document provides solutions to 24 problems in special relativity from an undergraduate physics textbook. It was created by Charles Asman, Adam Monahan and Malcolm McMillan at the University of British Columbia for their physics students. The problems cover various topics in special relativity including time dilation, length contraction, relativistic Doppler shift, and Lorentz transformations. Standard frames of reference and equations are defined. Detailed step-by-step solutions are provided for each problem.
This document discusses Einstein's theory of special relativity and its implications. It begins by describing Galilean relativity and frames of reference. It then discusses Michelson-Morley's famous experiment which found that the speed of light is constant regardless of the motion of the observer, contradicting the theory of the luminiferous aether. This led Einstein to postulate that the laws of physics are the same in all inertial frames and that the speed of light in a vacuum is constant. The document explores the implications of these postulates through various thought experiments, showing that simultaneity is relative, time dilates and lengths contract for moving observers. It concludes by discussing some implications of special relativity like mass-energy equivalence and the twins paradox
This document discusses photoelasticity, which is a stress analysis technique that uses the relative retardation between two components of light passing through a photoelastic model. Key points:
1) Photoelasticity measures the difference in refractive indices along principal stress directions in a stressed transparent model, allowing calculation of principal stresses and strains.
2) When unstressed, photoelastic models are isotropic, but stress causes temporary birefringence by changing refractive indices along stress directions.
3) Relative retardation between light components is measured using polariscopes and relates to stress difference through the stress optic law and material properties.
4) Isoclinics and isochromatics appear as loci of points with specific principal stress orientations
Schrodinger wave equation and its application
a very good animated presentation.
Bs level.
semester 6th.
how to make a very good appreciable presentation.
The special theory of relativity proposed in 1905 by Einstein describes how measurements of time, space, and phenomena appear different in reference frames moving at constant velocity relative to each other. Unlike Newtonian mechanics, special relativity is not restricted to a particular type of phenomenon and instead affects all fundamental physical theories. The theory of relativity led to profound changes in how we perceive space and time, showing that measurements are not the same in different reference frames moving relative to one another.
The special theory of relativity proposed in 1905 by Einstein describes how measurements of time, space, and phenomena appear different in reference frames moving at constant velocity relative to each other. Unlike Newtonian mechanics, special relativity is not restricted to a particular type of phenomenon and instead affects all fundamental physical theories. The theory of relativity led to profound changes in how we perceive space and time, showing that measurements are not the same in different reference frames moving relative to one another.
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.
The document discusses various types of motion that rigid bodies can undergo, including pure translation, translation plus rotation, and rotation. It defines a rigid body as one with a fixed, unchanging shape and derives equations to calculate the center of mass for systems of particles and continuous rigid bodies. The center of mass depends on the mass and position coordinates of the composing particles or elements and can be used to describe the motion of the entire rigid body. Symmetry arguments show that for certain regularly shaped rigid bodies like rods, rings, discs, spheres, and cylinders, the center of mass will coincide with the geometric center.
This document provides an overview of Albert Einstein and his theories of special and general relativity. It discusses key ideas such as:
- Einstein was born in Germany in 1879 and developed the theories of special and general relativity.
- Special relativity is based on two postulates about the laws of physics being the same in all inertial frames and the constant speed of light. This theory explains phenomena like time dilation and length contraction.
- General relativity holds that gravity is a result of the curvature of spacetime caused by massive objects. It predicts effects like light deflection and Mercury's orbit that have been observed.
This document discusses various topics related to motion including:
1) Motion can be classified as one-dimensional, two-dimensional, or three-dimensional depending on the number of axes the object moves along.
2) Key concepts in three-dimensional motion include location vectors, displacement, velocity, acceleration, and equations of motion.
3) Forces obey Newton's Laws - the acceleration of an object is directly proportional to net force and inversely proportional to mass, and every action has an equal and opposite reaction.
4) Circular motion involves centripetal force which acts towards the center of the circle, and centripetal acceleration which is required to move in a circular path.
1. The document discusses the key concepts of Einstein's special theory of relativity, including the postulates that the laws of physics are the same in all inertial frames and that the speed of light is constant.
2. It describes time dilation and length contraction derived from these postulates and the Lorentz transformations. Moving clocks are found to run slow and moving objects are length contracted.
3. The relativity of simultaneity is discussed, whereby the order of events can depend on the observer's frame of reference. This relates to the failure of Galilean transformations to describe electromagnetism.
this project is basically based "motion", the way it's directly or indirectly linked to us. Viewing this power point presentation will enable you to study as a whole in descriptive way.In physics, motion is a change in position of an object with respect to time. Motion is typically described in terms of displacement, distance (scalar), velocity, acceleration, time and speed.Motion of a body is observed by attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame n If the position of a body is not changing with the time with respect to a given frame of reference the body is said to be at rest, motionless, immobile, stationary, or to have constant (time-invariant) position. An object's motion cannot change unless it is acted upon by a force, as described by Newton's first law. Momentum is a quantity which is used for measuring motion of an object. An object's momentum is directly related to the object's mass and velocity, and the total momentum of all objects in an isolated system (one not affected by external forces) does not change with time, as described by the law of conservation of momentum.
Hope you will like it and feedbacks are welcomed.
1) The document provides an overview of classical mechanics, including definitions of key concepts like space, time, mass, and force. It summarizes Newton's three laws of motion and how they relate to concepts like momentum and inertia.
2) Key principles of classical mechanics are explained, such as reference frames, Newton's laws, and conservation of momentum. Vector operations and products are also defined.
3) Examples are given to illustrate fundamental principles, like Newton's third law and how it relates to conservation of momentum in systems with multiple objects. Coordinate systems are briefly introduced.
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.
Fundamentals of Superconductivity and its applicationsPraveen Vaidya
"Superconductivity" is a topic related to Physics, Chemistry and Engineering and Technology, anybody who would like to know about superconductor can read this article. This article explains about the fundamental's of superconductors, its various effects like Meissner effect, its theory and applications in MRI, Magneto encephalography, flying vehicle or levitating vehicles etc.
Modulus of rigidity is an elastic constant. that measures the elastic behavior of a material when it is twisted or sheared.
torsion pendulum consists of a weight of given shape hanged to the ceiling through a metallic wire, on twisting this load through an angle and left, it starts to oscillate, back and forth, The number of oscillations per unit time is measured.
In this article the theory and experimental procedure of the measurement of modulus rigidity of the given metallic wire is presented by using the principle of torsional pendulum
1) Einstein's theory of special relativity resolved contradictions between Galilean relativity and the constant speed of light by postulating that the laws of physics are the same in all inertial frames and that the speed of light has the same value in all frames.
2) Time dilation occurs such that moving clocks are observed to tick slower than stationary clocks. This effect increases as the relative velocity approaches the speed of light.
3) The twin paradox is resolved by recognizing that only one twin experiences accelerations during a round trip, so their frame of reference is not inertial for the entire journey.
Special theory of relativity:Michelson-Morley experiment,Galilean and Lorentz Tranformation,Length contraction,Time Dilation,Relativity of mass,mass-energy equivalence
Here are the key points about rate of change of velocity:
- Rate of change of velocity is also known as acceleration.
- Acceleration is a vector quantity which indicates the rate at which the velocity of an object is changing.
- The SI unit of acceleration is meter per second squared (m/s2).
- If an object's velocity is increasing with time, it has a positive acceleration. If velocity is decreasing with time, acceleration is negative.
- Acceleration can be caused by a change in the object's speed, direction of motion, or both.
- Constant acceleration means the rate of change of velocity remains the same over time. This results in a linear relationship between velocity and time
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.
1) Einstein introduces his theory of special relativity, which holds 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.
2) He describes an experiment showing that the definition of simultaneity is relative between different frames of reference moving at a constant velocity relative to each other.
3) He develops the equations relating space and time coordinates between two frames in uniform motion, showing that lengths contract and times dilate for objects in motion.
This document provides solutions to 24 problems in special relativity from an undergraduate physics textbook. It was created by Charles Asman, Adam Monahan and Malcolm McMillan at the University of British Columbia for their physics students. The problems cover various topics in special relativity including time dilation, length contraction, relativistic Doppler shift, and Lorentz transformations. Standard frames of reference and equations are defined. Detailed step-by-step solutions are provided for each problem.
This document discusses Einstein's theory of special relativity and its implications. It begins by describing Galilean relativity and frames of reference. It then discusses Michelson-Morley's famous experiment which found that the speed of light is constant regardless of the motion of the observer, contradicting the theory of the luminiferous aether. This led Einstein to postulate that the laws of physics are the same in all inertial frames and that the speed of light in a vacuum is constant. The document explores the implications of these postulates through various thought experiments, showing that simultaneity is relative, time dilates and lengths contract for moving observers. It concludes by discussing some implications of special relativity like mass-energy equivalence and the twins paradox
This document discusses photoelasticity, which is a stress analysis technique that uses the relative retardation between two components of light passing through a photoelastic model. Key points:
1) Photoelasticity measures the difference in refractive indices along principal stress directions in a stressed transparent model, allowing calculation of principal stresses and strains.
2) When unstressed, photoelastic models are isotropic, but stress causes temporary birefringence by changing refractive indices along stress directions.
3) Relative retardation between light components is measured using polariscopes and relates to stress difference through the stress optic law and material properties.
4) Isoclinics and isochromatics appear as loci of points with specific principal stress orientations
Schrodinger wave equation and its application
a very good animated presentation.
Bs level.
semester 6th.
how to make a very good appreciable presentation.
The special theory of relativity proposed in 1905 by Einstein describes how measurements of time, space, and phenomena appear different in reference frames moving at constant velocity relative to each other. Unlike Newtonian mechanics, special relativity is not restricted to a particular type of phenomenon and instead affects all fundamental physical theories. The theory of relativity led to profound changes in how we perceive space and time, showing that measurements are not the same in different reference frames moving relative to one another.
The special theory of relativity proposed in 1905 by Einstein describes how measurements of time, space, and phenomena appear different in reference frames moving at constant velocity relative to each other. Unlike Newtonian mechanics, special relativity is not restricted to a particular type of phenomenon and instead affects all fundamental physical theories. The theory of relativity led to profound changes in how we perceive space and time, showing that measurements are not the same in different reference frames moving relative to one another.
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.
The document discusses various types of motion that rigid bodies can undergo, including pure translation, translation plus rotation, and rotation. It defines a rigid body as one with a fixed, unchanging shape and derives equations to calculate the center of mass for systems of particles and continuous rigid bodies. The center of mass depends on the mass and position coordinates of the composing particles or elements and can be used to describe the motion of the entire rigid body. Symmetry arguments show that for certain regularly shaped rigid bodies like rods, rings, discs, spheres, and cylinders, the center of mass will coincide with the geometric center.
This document provides an overview of Albert Einstein and his theories of special and general relativity. It discusses key ideas such as:
- Einstein was born in Germany in 1879 and developed the theories of special and general relativity.
- Special relativity is based on two postulates about the laws of physics being the same in all inertial frames and the constant speed of light. This theory explains phenomena like time dilation and length contraction.
- General relativity holds that gravity is a result of the curvature of spacetime caused by massive objects. It predicts effects like light deflection and Mercury's orbit that have been observed.
This document discusses various topics related to motion including:
1) Motion can be classified as one-dimensional, two-dimensional, or three-dimensional depending on the number of axes the object moves along.
2) Key concepts in three-dimensional motion include location vectors, displacement, velocity, acceleration, and equations of motion.
3) Forces obey Newton's Laws - the acceleration of an object is directly proportional to net force and inversely proportional to mass, and every action has an equal and opposite reaction.
4) Circular motion involves centripetal force which acts towards the center of the circle, and centripetal acceleration which is required to move in a circular path.
1. The document discusses the key concepts of Einstein's special theory of relativity, including the postulates that the laws of physics are the same in all inertial frames and that the speed of light is constant.
2. It describes time dilation and length contraction derived from these postulates and the Lorentz transformations. Moving clocks are found to run slow and moving objects are length contracted.
3. The relativity of simultaneity is discussed, whereby the order of events can depend on the observer's frame of reference. This relates to the failure of Galilean transformations to describe electromagnetism.
this project is basically based "motion", the way it's directly or indirectly linked to us. Viewing this power point presentation will enable you to study as a whole in descriptive way.In physics, motion is a change in position of an object with respect to time. Motion is typically described in terms of displacement, distance (scalar), velocity, acceleration, time and speed.Motion of a body is observed by attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame n If the position of a body is not changing with the time with respect to a given frame of reference the body is said to be at rest, motionless, immobile, stationary, or to have constant (time-invariant) position. An object's motion cannot change unless it is acted upon by a force, as described by Newton's first law. Momentum is a quantity which is used for measuring motion of an object. An object's momentum is directly related to the object's mass and velocity, and the total momentum of all objects in an isolated system (one not affected by external forces) does not change with time, as described by the law of conservation of momentum.
Hope you will like it and feedbacks are welcomed.
1) The document provides an overview of classical mechanics, including definitions of key concepts like space, time, mass, and force. It summarizes Newton's three laws of motion and how they relate to concepts like momentum and inertia.
2) Key principles of classical mechanics are explained, such as reference frames, Newton's laws, and conservation of momentum. Vector operations and products are also defined.
3) Examples are given to illustrate fundamental principles, like Newton's third law and how it relates to conservation of momentum in systems with multiple objects. Coordinate systems are briefly introduced.
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.
Fundamentals of Superconductivity and its applicationsPraveen Vaidya
"Superconductivity" is a topic related to Physics, Chemistry and Engineering and Technology, anybody who would like to know about superconductor can read this article. This article explains about the fundamental's of superconductors, its various effects like Meissner effect, its theory and applications in MRI, Magneto encephalography, flying vehicle or levitating vehicles etc.
Modulus of rigidity is an elastic constant. that measures the elastic behavior of a material when it is twisted or sheared.
torsion pendulum consists of a weight of given shape hanged to the ceiling through a metallic wire, on twisting this load through an angle and left, it starts to oscillate, back and forth, The number of oscillations per unit time is measured.
In this article the theory and experimental procedure of the measurement of modulus rigidity of the given metallic wire is presented by using the principle of torsional pendulum
This experiment is for the Undergraduate students of Engineering and Science background. The optical fiber experiment explains the principle of working of optical fiber and theory to determine the angle of acceptance and numerical aperture.
This document describes an experiment to determine the spring constants of individual springs and springs connected in series and parallel. Springs were loaded with incremental weights and the displacements measured. Spring constants were calculated using Hooke's law. The spring constants of individual springs, springs in series, and springs in parallel were measured experimentally and calculated theoretically to compare results.
To detemine the wavelength of semiconductor laserPraveen Vaidya
The document describes an experiment to determine the wavelength of a semiconductor laser using diffraction. A laser beam is directed at a metal scale with graduations. The diffraction patterns are observed on a screen and the distances between the direct beam and diffraction spots are measured. These measurements are used to calculate the path difference and apply the diffraction equation to determine the laser's wavelength. The experiment is repeated to obtain an average wavelength value.
This document discusses semiconductor physics concepts including:
1. Semiconductors have long-range symmetry of atomic arrangement and are mostly crystalline materials. They have a moderate bandgap (1-2 eV) compared to insulators (6 eV).
2. Semiconductors have a valence band and conduction band separated by an energy gap. At higher temperatures, electrons can gain enough energy to cross this gap and contribute to conductivity.
3. Semiconductors are classified as intrinsic or extrinsic. Extrinsic semiconductors have impurities added which create majority carriers, making them either n-type or p-type.
4. The position of the Fermi energy level depends on whether
Fundamentals of modern physics, the de-Broglie hypothesisPraveen Vaidya
The presentation uploaded here educates about the failure of classical physics to explain Blackbody radiation and the success of quantum theory to explain the Blackbody radiation spectrum and other phenomena, the de-Broglie hypothesis and its significance, nature of de-broglie waves and the representation. Numerical problems are given at the end.
Young's modulus by single cantilever methodPraveen Vaidya
Young's modulus is a method to find the elasticity of a given solid material. The present article gives the explanation how to perform the experiment to determine the young's modulus by the use of material in the form of cantilever. The single cantilever method is used here.
The present article gives the fundamental properties magnetism, different materials, properties of different magnetic materials like, dia,para and ferro magnetic materials. The notes also explain how magnetism appear in materials, type of magnets and brief applications of magnetic materials. The materials is best for undergraduate science and engineering students and any other people of interest in magnetism
Engineering Physics study materials discusses nanoscience and nanotechnology. It defines nanotechnology as manipulating matter at the atomic or molecular scale to produce novel structures and devices. When matter is reduced to the nanoscale, quantum confinement occurs and energy levels become quantized. This can increase the band gap and surface area to volume ratio. Nanomaterials are classified based on dimensionality (0D, 1D, 2D) and properties (metallic, semiconducting, insulating). Synthesis methods include top-down (milling) and bottom-up (self-assembly) approaches. Carbon nanotubes are discussed in detail, including their unique electrical, mechanical, and thermal properties, and applications in fields like electronics, composites,
The Zener diode is fabricated in such a way that, its advantage is in its reverse bios. After a sufficient increase in reverse voltage across the junction, the minority carriers get sufficient kinetic energy due to the strong electric field. The high kinetic energy free electrons can collide strongly with the lattice ions so that they emit more free electrons, these liberated electrons also get high kinetic energy due to reverse applied electric field and they create more free electrons by collision cumulatively. This process may continue repeatedly and soon large free electron gas is created in the depletion layer, at which a small change in potential creates huge recombination and surge of carriers across the junction and hence large current through the circuit spontaneously and hence the entire diode will become conductive.
Zener diode is an important electronic device mainly used as voltage regulator. The experiment explains the determination of zener voltage and resistance of diode.
Maxwell's equations and their derivations.Praveen Vaidya
Being the partial differential equations along with the Lorentz law the Maxwell's equation laid the foundation for classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. Maxwell's equations describe how electric and magnetic fields are generated by charges, currents, and changes of the fields.[note 1] One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at a constant speed (c) in the vacuum, the "speed of light". Known as electromagnetic radiation, these waves may occur at various wavelengths to produce a spectrum from radio waves to γ-rays. The equations are named after the physicist and mathematician James Clerk Maxwell, who between 1861 and 1862 published an early form of the equations that included the Lorentz force law. He also first used the equations to propose that light is an electromagnetic phenomenon.
This is the experiment for undergraduate science and engineering students in the subjects of Physics, Applied Physics, Basic electronics etc. The experiment is explained in detail so that the students and faculty member can get the better knowledge of the experiment.
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.
Optical fibers are thin strands of glass or plastic that guide light along their length via total internal reflection. They have three main parts - a core with a higher refractive index surrounded by a cladding and outer protective sheath. Light is confined to the core due to the difference in refractive indices, allowing transmission with very low loss. Optical fibers come in single mode and multimode varieties depending on the number of light modes they can carry simultaneously. Single mode fibers have a small core and support only one mode, enabling high bandwidth transmission over long distances. Multimode fibers have larger cores and support multiple modes, making them suitable for short-distance applications.
The chapter contains fundamentals of Modern physics, the Quantumtheory explanation of Black body radiation photoelectric effect and Compton effect, and the beginning of the de-Broglie hypothesis, wave-like properties of matter, and its proof explained in detail. It is highly useful for first-year B.Tech and BE students.
The optical fibers are the hair thin fibers made of ultra transparent glass or plastic material. The optical fiber flexible and it is used to transmit the light.
The presentation here mainly focused on the brief explanation of principle, theory, characteristics, losses in fibers and applications.
degradation of pollution and photocatalysisPraveen Vaidya
The presentation deals with the use of conduction of photocatalytic reaction using the transition metal doped transparent semiconducting thinfilms. The precursor to film is prepared by the SILAR method, which is a chemical method.
Energy bands and electrical properties of metals newPraveen Vaidya
The chapter gives brief knowledge about formation of bands in solids. What are free electrons how they contribute for conductivity in conductors, but can be extended to semiconductors also.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
1. “Theory of Relativity”. Engineering Physics Study Materials by Praveen N. Vaidya Page 1
Theory of Relativity:
Einstein overthrew many assumptions underlying earlier physical theories, redefining in the process the fundamental
concepts of space, time, matter, energy, and gravity on the basis of new theory called Relativity. Along with quantum
mechanics, theory of relativity is also take important stage in modern physics. In particular, relativity lays foundations
for understanding cosmic processes and the geometry of the universe itself many technologies like GPS and
positioning satellites.
According to the theory relativity, motion of a body never been an absolute quantity but it is relative to an observer.
The magnitude of motion of a body moving a particular frame is depending on the magnitude and direction of
observer w.r.t to that body.
For example, consider moving train A, another train B moving on left side in same direction of train A and a stationary
observer (C) is standing right side of train A. The velocity of train A, reference to the observer in train B is not same as
that of stationary observer C. Therefore, the motion of a body is not absolute but it is relative.
Some definitions relative to the theory of relativity:
Event: An event is something that happens at a particular point in space and at a particular instant of time,
independent of the reference frame. Which we may use to described it.
Observer: An observer is a person or equipment meant to observe and take measurement about the event. The
observer is supposed to have with him scale, clock and other needful things to observe that event.
Frame of reference: A point object either at rest or in motion or any event can be described using a coordinate system.
This coordinate system is called the Frame of Reference. For example, a Cartesian coordinate system represented X, Y
and Z axes in which position of point object is shown by coordinates x, y, z respectively.
This coordinate system with X, Y, Z axes, which gives the details of point object, is called a frame of reference. For Ex.
In below fig, S is a frame of reference, a is point with coordinates (x, y, z, t) is at location A at time t, if it did not change
its location w.r.t to time then it is said to be at rest. If point changed its location to B with coordinates (x’, y’, z’, t’) then
it is said to be in motion.
In fig. 2, the two frames define the motion of the point ‘p’, and then observations of both frames need not be same
even they are explaining same point.
2. “Theory of Relativity”. Engineering Physics Study Materials by Praveen N. Vaidya Page 2
There are two frames of references 1) Inertial frame of reference and 2) Non Inertial frame of reference.
Inertial Frame of Reference:
The frame of reference in motion relative to an observer is said to be Inertial frame of reference, only when the
law of inertia or Newton’s first law holds well in the system, i.e. there is no external force acting on the system.
This is also called as an un-accelerated frame of reference because, the frame remains at rest or is moving with an
uniform motion along straight line. It is free from linear acceleration or rotational acceleration.
If another frame that is moving uniformly relative to the observer’s frame is also inertial.
Consider a train running with a uniform velocity a boy bouncing a rubber ball to the floor, even a ball remains in air
some time; it directly goes into the hand of boy, this same for the observer in train and stationary observer outside
train it happens in Inertial frames only.
If two frames are moving relative to each other the relative velocity measured by them measured by persons both
the frames is same (velocity of one frame measured sitting in another frame)
Non-inertial Frame of reference:
The frame of reference in motion relative to an observer is said to be Inertial frame of reference, I the law of
inertia or Newton’s first law holds good in the system, i.e. there is no external force acting on the system.
For example, when a uniformly moving vehicle changed its speed, there would be change in the nature of
passenger, the passenger fall forward on reducing the speed or fall backward on increase in the speed.
The force act upon passenger is called as pseudo force because there is source of existence for this force; it is
acting opposite to the direction of acceleration of frame.
The relative motion due to non inertial frame cannot directly explained by the newton’s first law of motion.
GALILEAN TRANSFORMATION EQUATIONS:
When an event is observed two different inertial frames, then the relationship between the coordinates of two frames
are obtained in the form of equations called Galilean transformations.
Case I: For the observer O in frame ‘S’
Consider two inertial reference frames named as S and S’ are two frames with coordinate axes XYZ and X’Y’Z’
respectively, also O and O’ are the origins of both coordinate axes.
In inertial frame of reference, relative motion does not affect the length so we have, x’ = x – vt, along x-axis, there
is no motion along Y and Z axes, therefore y’ = y, z’ = z,
The time at which event observed by S and S’ is t and t’ time respectively and as time is absolute quantity t = t’
The above equations x’ = x – vt, y’ = y, z’ = z, t’ = t are called the Galilean transformation equations.
x’
x
Consider frame S is stationary and frame S’ is moving with a uniform
velocity ‘v’ along positive X-axis. Assume the time, t=t’=0 when two
frames are coincided with each other.
At time ‘t’ an event observed by observers in two frames, at point ‘P’, at a
distance x from frame S and at x’ from frame S’ respectively. By this time
the frame S’ may travelled through distance vt from S, as shown in figure.
3. “Theory of Relativity”. Engineering Physics Study Materials by Praveen N. Vaidya Page 3
CaseII: For observer O’ in S’
The above transformation equations are called as inverse Galilean transformation equations.
MICHELSON MORLEY EXPERIMENT:
Michelson strongly believed that the light waves also travel at different speeds in ether relative to that in a vacuum
and any medium having a density will change the direction of light passing through it due to the phenomenon of
refraction. He had also developed an interferometer to experiment on the arriving light beams and prove his theory.
The Michelson Morley experiment was conducted to determine the presence of ether as a medium to propagate light
and to find the speed of earth. The method of theory of relativity is used here, so it also became an experiment to
verify the invariance of light.
MICHELSON MORLEY EXPERIMENT:
Michelson strongly believed that the light waves also travel at different speeds in ether relative to that in a
vacuum and any medium having a density will change the direction of light passing through it due to the
phenomenon of refraction. He had also developed an interferometer to experiment on the arriving light
beams and prove his theory.
The Michelson Morley experiment was conducted to determine the presence of ether as a medium to
propagate light and to find the speed of earth. The method of theory of relativity is used here, so it also
became an experiment to verify the invariance of light.
The fig. 1 above gives the schematic diagram of Michelson Morley Experiment. It consists of a half silvered
mirror (S) in the middle a two reflecting mirrors M1 along horizontal direction and M2 along vertical
direction from the ‘S’ at a distance of ‘d’ as shown.
Fig. 1 fig. 2
x
SM2
S
M1
M2 M2’
d
d
M2
S
M1
–
x
x’
In this case one should think that the observer in S’ is stationary and
frame S moving backward. The dimensions of length and time are
same as Case I.
The velocity of frame S observed by ‘S’ is –v.
Now we can write the equation x = x’ – (–vt) , y=y’, z=z’ and t=t’. or
x = x’ + vt, y = y’, z = z’ and t = t’.
4. “Theory of Relativity”. Engineering Physics Study Materials by Praveen N. Vaidya Page 4
Consider a input beam of light from source focused on the half silvered mirror as shown in fig. 1, the single
beam splits into two beams of light one reflect in the direction of mirror M1 along horizontal direction and
other transmits through the ‘S’ and reaches mirror M2 along vertical direction. Both the beams reflect back
to ‘S’ and both travel towards the detector (R) as combined beam.
Consider the motion of the experimental system is along horizontal direction with velocity ‘v’ and velocity of
light is ‘c’
Case I: Horizontal direction: distance between S and M1 i.e., SM1 = d, during forward journey ( S M1) the
relative velocity of light is, c – v and time taken to travel is, 𝑡𝑎 =
𝑑
𝑐−𝑣
After reflection at mirror M1, beam returns to ‘S’, with relative velocity is c+v, time taken for this is 𝑡𝑏 =
𝑑
𝑐+𝑣
Time taken for complete travel S to M1 to back S is,
𝑡1 = 𝑡𝑎 + 𝑡𝑏 =
𝑑
𝑐−𝑣
+
𝑑
𝑐+𝑣
=
2𝑑
𝑐
[1 +
𝑣2
𝑐2
]
Case II: Vertical direction: here when light leave mirror ‘S’, beam cannot reach M2 in its original place (M2),
because the mirror keep moving with system, hence the beam reaches it at a distance ‘x’ from original
direction (at point M2’) as shown in fig 2.
The original distance between S and M2 i.e. SM2 = d, distance between M2 and M2’ is ‘x’, then we get, new
distance traveled by light is
(SM2’)2
= (SM2)2
+ x2
= d2
+ x2
(cta’)2
= d2
+ (vta’)2
or (cta’)2
- (vta’)2
= d2
Or 𝒕𝒂
′𝟐
=
𝒅𝟐
𝒄𝟐−𝒗𝟐
Or 𝒕𝒂
′
=
𝒅
√𝒄𝟐−𝒗𝟐
𝒐𝒓 𝒕𝒂
′
=
𝟐𝒅
𝒄
[𝟏 +
𝒗𝟐
𝟐𝒄𝟐
]
In case of return journey after reflecting at M2 to reach ‘S’ it takes same time, i.e. 𝒕𝒃
′
=
𝒅
√𝒄𝟐−𝒗𝟐
Therefore taken to vertical journey is 𝑡2 = 𝑡𝑎
′
+ 𝑡𝑏
′
=
𝒅
√𝒄𝟐−𝒗𝟐
+
𝒅
√𝒄𝟐−𝒗𝟐
=
𝟐𝒅
√𝒄𝟐−𝒗𝟐
=
𝟐𝒅
𝒄
[𝟏 +
𝒗𝟐
𝟐𝒄𝟐
]
Hence difference in the velocity of light during horizontal and vertical journey is given by,
∆𝑡 = 𝑡1 − 𝑡2 =
2𝑑
𝑐
[1 +
𝑣2
𝑐2
] −
𝟐𝒅
𝒄
[𝟏 +
𝒗𝟐
𝟐𝒄𝟐
]
∆𝒕 =
𝟐𝒅
𝒄
[
𝒗𝟐
𝟐𝒄𝟐
] 𝒕𝒉𝒆𝒓𝒆𝒇𝒐𝒓𝒆, ∆𝒕 = 𝒅 [
𝒗𝟐
𝒄𝟑
]
This is the time difference should arise between the horizontally and vertically travelled light beams while
reaching the detector.
The Michelson Morley experiment performed to show the presence of ether and hence to find correct speed
of earth moving around son. It would have succeeded if there should be time difference between the light
beams reaching detector as shown in theory. But experimental results did not shown any sign of if
difference but, t =0.0, hence it failed prove the presence of ether.
5. “Theory of Relativity”. Engineering Physics Study Materials by Praveen N. Vaidya Page 5
Secondly it failed to prove the relative velocity of light. If velocity of light follow the relativity concept then
the beams may reach detector at different time, but difference in reach is negligible. Hence Michelson
Morley experiment is considered as a failed experiment. It proved that light speed is absolute on all frames
and not involved in the relativity concept.
EINSTEIN’S SPECIAL THEORY OF RELATIVITY
Einstein proposed the special theory of relativity in 1905. This theory deals with the problems of mechanics
in which one frame moves with constant velocity relative to the other frame.
The two postulates of the Special Theory of Relativity are:
1. The laws of physics are the same in all inertial systems. No preferred inertial system exists.
2. The speed of light(c) in free space has the same value in all the inertial systems.
LORENTZ TRANSFORMATION EQUATION
Results of Galilean Transformation equations cannot be applied for the objects moving with a speed
comparative to the speed of the light.
Therefore, new transformations equations are derived by Lorentz for these objects and these are known as
Lorentz transformation equations for space and time.
Assume short comes of the Galilean transforms can be corrected by multiplying them with an independent
constant ‘K’,
Therefore, x = K (x’ + vt’) and x’ = K (x – vt) --------------------- 1
From fig. we have t2
=
x2
c2 or x2
− c2
t2
= 0, similarly, x′2
− c2
t′2
=0
From the above two equations we get, x2
− c2
t2
= x′2
− c2
t′2
----------------------- 2
Using transformation equations (1) in Equations (2) we get, the new transformation equations of S’
measured by S frame
𝑥′
=
𝑥−𝑣𝑡
√1−
𝑣2
𝑐2
, y’ = y, z’ = z and 𝑡′
=
[𝑡−
𝑣𝑥
𝑐2]
√1−
𝑣2
𝑐2
are called Lorentz transformation equations,
Similarly the Transformation equations measured by frame S’ for frane S are,
𝑥 =
𝑥′ +𝑣𝑡′
√1−
𝑣2
𝑐2
, y’ = y, z’ = z and 𝑡 =
[𝑡′+
𝑣𝑥′
𝑐2 ]
√1−
𝑣2
𝑐2
These are called inverse Lorenz transformation equations.
Merits of Lorentz transformation:
1. The Lorentz transformation equations can be in compatible with the relativistic velocity of light
v
S S’
x’
x
P
X
Y
Let there are two inertial frames of references S and S’. S is at rest
and S’ is moving w.r.t S with velocity ‘v’ along positive X-axis.
At time t=t’=0, origins O and O’ of both frames are coincided. After
time‘t’ an event happens at position P in the frame space. The
coordinates of the P will be x’ according to the observer O’ in S’ and
it will be x according to observer O in S.
6. “Theory of Relativity”. Engineering Physics Study Materials by Praveen N. Vaidya Page 6
2. The Maxwell’s electromagnetic equations are remain invariant under the Lorentz transformation
equations.
3. The invariance of velocity of light can be proved with Lorentz transformation equations.
Applications of Lorentz transformation equations:
1. Length Contraction:
Lo
The stationary observer in the frame of reference S measure this length as L, then L < Lo
Now, The length of the rod according to stationary observer in frame S, L = x2 –x1 ……………………… 1
The length of the rod according to the observer in moving frame S’, Lo = x2‘–x1’ ……………………… 2
According to Lorentz transformation,
𝑥2
′
=
𝑥2−𝑣𝑡
√1−
𝑣2
𝑐2
and 𝑥1
′
=
𝑥1−𝑣𝑡
√1−
𝑣2
𝑐2
------------------------------------------------3
From equation 1. Lo =x2’– x1’ Substitute eqn 3 in eqn 1
𝐿𝑜 =
𝑥2−𝑣𝑡
√1−𝑣2
𝑐2
−
𝑥1−𝑣𝑡
√1−
𝑣2
𝑐2
=
𝑥2−𝑥1
√1−
𝑣2
𝑐2
but L = x2 –x1
Therefore 𝐿𝑜 =
𝐿
√1−
𝑣2
𝑐2
or 𝐿𝑜 × √1 −
𝑣2
𝑐2 = 𝐿--------------------------------4
From equation 4 it is found that, v<<c, therefore,
𝑣2
𝑐2 < 1, therefore, √𝟏 −
𝒗𝟐
𝒄𝟐 < 1,
Intern this implies L’< L, this proved length appeared contracted when length measured from the moving
frame of reference.
2. Time Dilation: Consider two frames of reference, a stationary frame and a moving frame then, an
observer in stationary frame finds that, the time taken for an event in moving frame appears longer than the
same event taking place in stationary frame; this phenomenon is called time dilation.
Consider an event takes place in moving frame of reference S' and time taken to complete that event t2' – t1'.
An observer from a stationary frame of reference S, measures time taken to complete same event t2 – t1
From the Lorentz transport equation for time,
𝑡1
′
=
[𝑡1−
𝑣𝑥
𝑐2]
√1−
𝑣2
𝑐2
and 𝑡2
′
=
[𝑡2−
𝑣𝑥
𝑐2]
√1−
𝑣2
𝑐2
Now, 𝑡2
′
− 𝑡1
′
=
[𝑡2−
𝑣𝑥
𝑐2]
√1−
𝑣2
𝑐2
−
[𝑡1−
𝑣𝑥
𝑐2]
√1−
𝑣2
𝑐2
=
[𝑡2−𝑡1]
√1−
𝑣2
𝑐2
v
S S’
x’1
x1
X
Y
x’2
x2
When an object is moving relative to an observer, then length of
that object is appeared to be contracted along axis of relative
motion and inversely proportional to magnitude of relative
motion, this phenomenon is called as Length contraction.
Consider a rod of length Lo is in moving frame S’, is called as proper
length or actual length.
7. “Theory of Relativity”. Engineering Physics Study Materials by Praveen N. Vaidya Page 7
Substituting, 𝑡2
′
− 𝑡1
′
= 𝑡 and 𝑡𝑜 = 𝑡2 − 𝑡1
Therefore, 𝑡 =
𝑡𝑜
√1−
𝑣2
𝑐2
, is called equation of time dilation. When v≠0 and v < c. then t > to, i.e. time is dilated.
Relativistic Mass
The well known special theory of relativity also hints a stationary observer finds that there is an increase in the
mass of a particle moving with a relativistic velocity. This concept is relativistic mass. Comparable to length
contraction and time dilation a thing called mass increase happens when the object is in motion.
The relativistic mass formula is articulated as,
m =
m0
√1 −
v2
c2
Where, the rest mass is mo, the velocity of the moving body is v, the velocity of light is c.
Numericals:
1. A length of spaceship is measured to be half of its proper length. Find the relative velocity of the
observer.
Proper length of space ship = Lo
Improper length (length measured by observer) of spaceship is L =Lo /2
𝑳𝒐 =
𝐿
√1−
𝑣2
𝑐2
→→ 𝐿𝑜 =
𝐿𝑜 /2
√1−
𝑣2
(3𝑥108)
2
1
2
= √1 −
𝑣2
(3𝑥108)2 1
4
= 1 −
𝑣2
(3𝑥108)2
or 1 −
1
4
=
𝑣2
(3𝑥108)2 or
3
4
× (3𝑥108)2
= 𝑣2
therefore 𝑣 = 2.64 × 108
𝑚/𝑠
2. A hypothetical train moving with a speed of 0.6c passes by the platform of a small station without
being slowed down the observer on the platform notes the length of the train is just equal to the length
of platform equals to 200m. Find the real length of platform.
i) Find the real length of the train.
ii) Find the length of the platform as measured by the observer in the train.
i) V = 0.6c, L = 200m
Real length of the train is given by, 𝑳𝒐 =
𝐿
√1 −
𝑣2
𝑐2
=
200
√1−
(0.6𝑐)2
𝑐2
=
200
√1−0.62
, therefore Lo = 250m
ii) The lengths of platform measured by observe in train.
𝐿𝑜√1 −
𝑣2
𝑐2 = 𝐿 or 200√1 − (0.6)2 = 𝐿
8. “Theory of Relativity”. Engineering Physics Study Materials by Praveen N. Vaidya Page 8
Therefore L = 160m.
3. A circle of radius 5cm, lies at the rest in X-Y plane, for an observer, who is moving with uniform
velocity along the y- direction appears to be an ellipse with equation
𝒙𝟐
𝟐𝟓
+
𝒚𝟐
𝟗
= 𝟏, Find the
velocity of observer.
For moving observer the circle of radius 5cm appears to be ellipse, of equation
𝑥2
25
+
𝑦2
9
= 1
Compare above equation with
𝑥2
𝑏2 +
𝑦2
𝑎2 = 1
b = Semi major axis - Here Proper length Lo = 5m
a = Semi minor axis (decreased length along X- axis) And Improper length = 3cm
From the equation
𝐿𝑜√1 −
𝑣2
𝑐2 = 𝐿 (
𝐿
𝐿𝑜
)
2
= 1 −
𝑣2
𝑐2
1 − (
3
5
)
2
=
𝑣2
𝑐2 v = 2.4x108
m/s
4. Determine the relativistic time if an astronauts
1) One move in a spaceship with velocity 0.55c and time measured in his frame is 7years.
2) The other astronaut travels with speed 0.75c; time measured in his frame is also 7 years.
Solution 1) velocity of spaceship v = 0.55c, to= 7year, then relativistic time t is,
t =
to
√1−
v2
c2
=
7
√1−
(0.55c)2
c2
= 8.38 year
2) velocity of spaceship v = 0.75c, to= 7year, then relativistic time t is,
t =
to
√1−
v2
c2
=
7
√1−
(0.75c)2
c2
= 10.57 year
5) A particle of mass 1.67 × 10−24
kg travels with velocity 0.65c. Compute its rest mass?
Answer:
Given: Mass m = 1.67 × 10−24
kg, v = 0.65c, c = 3 × 108
m/s2.
The relativistic mass formula is articulated as,
m=m0 /√1 − v2/c2
1.67×10−24
=m0 √1 − (0.65)2c2/c2
Rest mass, mo = 1.26 × 10−24
kg (approximately). Thus, the rest mass of the particle is 1.26 × 10−24
kg
9. “Theory of Relativity”. Engineering Physics Study Materials by Praveen N. Vaidya Page 9
COMPLETE
10. “Theory of Relativity”. Engineering Physics Study Materials by Praveen N. Vaidya Page 10
The basic problem, first observed by the Michelson-Morley experiment, is that no matter how an
observer measures the local speed of light in a vacuum, the result is always c. There are two
approaches to making this fact consistent with our body of knowledge of physics. I here use a
structured list to enable point-by-point comparison of the two approaches. The two approaches are
labeled “a“ and “b“.
1. We suppose that
a. Light propagates at speed c with respect to some fixed coordinate system, hereafter
called “aether”. When an observer is moving with respect to the aether, the observer’s
velocity is subtracted from the velocity of light in accordance with Galilean relativity.
b. There is no fixed coordinate system with respect to which light propagates, or anything
else moves. Instead, space-time inherently has a geometry such that, if anything moves
with speed c as observed by any observer, any other observer, no matter how moving
in relation to that first observer, will observe that same speed, c. This is special
relativity, as proposed by Einstein.
2. In a measurement of the speed of light,
a. Whenever an observer who is moving in relation to the aether tries to measure the
speed of light, the observer and his/her equipment are affected by their own
movement in relation to the aether, in just the right way that the equipment will yield
the result c. Such effects, known collectively as the Lorentz transformation, are
i. shrinking of the observer and equipment along the direction of motion,
called FitzGerald contraction, and
ii. slowing-down of time affecting the observer and equipment, called time dilation.
b. The Lorentz transformation is just an effect of an observation from a different point of
view, which is influenced not only by change of location and rotation, but also by
velocity of the observer relative to that which is observed. Minkowski combined space
and time into four-dimensional space-time. By the neat trick of an odd definition of
distance in that four-dimensional space, Minkowski applied non-Euclidean
geometry of Riemann, simplified by the tensor calculus of Ricci-Curbastro and others,
so that the Lorentz transformation is described by the same mathematics as the varied
observations of a three-dimensional object as observed by stationary observers in
different relative locations and orientations.
3. An object has different shape according to observers with different velocities.
a. The Lorentz transformation is not entirely far-fetched. FitzGerald, after whom the
length contraction, item 2 a i is named, pointed out that the matter of which humans
and their equipment are composed is held together by electrostatic attraction between
oppositely charged electrons and protons. According to Maxwell’s equations, as
electric charges move through the aether, they create magnetic fields. FitzGerald
calculated that the magnetic fields of moving matter will make it contract along the
direction of motion just the right amount, per item 2 a i.
For example, a particularly simple argument of symmetry shows that an undisturbed
11. “Theory of Relativity”. Engineering Physics Study Materials by Praveen N. Vaidya Page 11
soap bubble should be spherical, yet a relatively moving observer will observe it
somewhat flattened along the direction of relative motion. FitzGerald’s finding is that
neither observation contradicts basic laws of physics.
I suppose that those magnetic fields would also slow down a clockwork mechanism the
right amount to conform to time dilation, although I am not aware of a direct
calculation of such an effect.
This explanation is a bit odd, because there is no particular reason why Maxwell’s
equations should participate in a mysterious conspiracy to conceal the relative velocity
of light.
b. Because of the simplicity and generality of the tensor transformations derived by
Minkowski, he was able to apply them to other phenomena besides dimension and
time changes of objects. When applied to an electric field, Minkowski’s tensor
expression of the transformation shows that a magnetic field is simply the appearance
of an electric field as observed by an observer in motion relative to the charge that is
the source of the field.
The soap bubble that is observed to be spherical by a relatively stationary observer
and flattened with added magnetic fields by a relatively moving observer are fully
consistent with each other, because they are just different views of the same thing,
related through the tensor expression of the Lorentz transformation, applied to both
the geometry and the internal forces of the bubble.
4. The shape of a solid body is set not only by electromagnetic force. In a large body of
matter, over about 400 kilometres diameter, the force of gravity becomes dominant over
the strengths of solids; any such body has a spherical shape (aside from effects of rotation),
because gravity pulls anything toward the most compact shape. Hereafter, I refer to a
“planet” for brevity, but the following is true of any such large body. One could in principle
use a planet as the basis of an instrument to measure the speed of light. We already have
done so, in effect, by combining signals from radio telescopes all over our planet to form
an effective radio telescope the size of Earth.
This means that gravitation must also conform to the Lorentz transformation. Therefore,
gravitation must also have a velocity-dependent component, like electric charge has
magnetism.
a. We therefore must suppose both electromagnetism and gravitation conspire to hide
the relative velocity of light.
This conspiracy theory is getting increasingly far-fetched. There is no particular reason
why gravitation should join the already unexplained conspiracy of electromagnetism to
obstruct attempts to measure the relative speed of light. The only direct observational
evidence for a velocity-dependent component of gravitation is that light that passes
near a gravitating body is deflected twice as much as Newtonian gravity predicts, as
12. “Theory of Relativity”. Engineering Physics Study Materials by Praveen N. Vaidya Page 12
was famously observed during solar eclipse of 1919. That observation gives little
guidance for constructing a velocity-dependent component of gravitation.
b. The source term for Newtonian gravitation is mass. When Einstein’s equivalence of
mass and energy is combined with Minkowski’s tensor formulation of the Lorentz
transformation, mass becomes a tensor quantity that combines mass, energy,
momentum, and stress, which credibly introduces velocity dependence to gravitation.
The tensor expression of space-time also enables description of gravitational effects on
space time in terms of Ricci-Curbastro’s metric tensor and curvature tensor. These
concepts, along with much work, enabled Einstein to discover the theory of general
relativity, which indeed shows the appropriate changes in shape of a gravitationally
formed body, and which yields many other distinctive results that have been confirmed
experimentally.
5. One can in principle suppose experiments in which the nuclear force and the weak force are
used as standards for measurement of the speed of light. In particular, the shapes of atomic
nuclei are determined by a combination of electrostatic and “strong” force.
a. To sustain the conspiracy to hide the “true” relative speed of light, the strong force
must have a velocity-dependent component that matches that of electrostatic force. At
the time that the two approaches were under discussion, these forces were unknown,
so no particular reason has been adduced for them to join the conspiracy.
b. Quantum field theory is our best explanation of the strong and weak forces, and is
made relativistically correct simply by the fact that it is formulated using Minkowski’s
application of tensor analysis to the four-dimensional space time in which the field
theory is set. (Quantum field theory and general relativity are at present mutually
inconsistent in certain respects, but that does not affect the consistency of nuclear
forces with special relativity.)
Thus, approach a is seen to be a rather improbable concatenation of coincidences, while approach b
is a self-consistent body of rigorous knowledge by considering the invariance of c to be an inherent
property of space-time. The question of why c is invariant thus becomes part of the question of why
space-time has the properties it has, along with the question of e.g. why space-time has three
(observable) spatial dimensions and one time dimension.
The reasons for these and other fundamental properties of the Universe could in principle be
explained by derivation from some more fundamental principle. An example of that sort of
explanation is Noether’s Theorem, which derives conservation of energy and momentum by the
assertion that the laws of physics are the same everywhere and everywhen (and similarly for other
conservation laws).
Even if an equivalent theorem is waiting to be discovered, that would similarly derive the nature of
space-time, including the invariance of c, from another principle, ultimately there must exist one or
more principles that are unexplained. Thus, there is no possibility, even in principle, of a much more
satisfactory explanation of the invariance of c than the assertion that it is a fundamental law of
13. “Theory of Relativity”. Engineering Physics Study Materials by Praveen N. Vaidya Page 13
physics, especially when that one fundamental law sews up in a clear explanation so many otherwise
untidy characteristics of the Universe.