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
It should be helpful, special thanks to our teacher (whose name is in the power point and the one who made it) from whom I asked his permission to post it here.
1. Isaac Newton considered what would happen if a cannon ball was shot from a mountain at increasing speeds. He realized that at a certain speed, the projectile would enter into orbit around the Earth due to gravity.
2. Astronauts are not truly weightless in space, but are in a state of constant free fall around the Earth at the same rate as its curvature.
3. To enter into orbit, a satellite must be launched at a velocity less than the escape velocity from Earth, which is around 8km/s. Significant thrust is required to accelerate a satellite to this velocity.
1) General Relativity abolished the concept of absolute space and time, showing that inertial and gravitational mass are equivalent and that acceleration and gravity are indistinguishable (Equivalence Principle).
2) The Cosmological Principle states that the universe looks the same from any location (isotropic and homogeneous), supporting the Big Bang theory of an expanding universe.
3) Black holes are predicted by General Relativity as regions where spacetime curvature becomes infinite, and their existence is supported by observations like gravitational lensing.
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.
This document summarizes key concepts from a presentation on special and general relativity:
1) Special relativity is based on two postulates - the laws of physics are the same in all inertial frames, and the speed of light is constant. This leads to time dilation and length contraction.
2) The twin paradox is resolved by recognizing that only inertial frames can apply Lorentz transformations - the traveling twin accelerates so experiences more time.
3) General relativity extends these ideas to frames with gravity by proposing spacetime is curved by mass-energy. This predicts bending of light and gravitational lensing.
General relativity presentation.ragesh,asmitha,m.d.trageshthedon
1. The document discusses Albert Einstein's theory of general relativity and how it improved upon Isaac Newton's theory of gravity.
2. General relativity explains gravity as a distortion of spacetime caused by massive objects, rather than an attractive force.
3. Some key predictions of general relativity include gravitational time dilation, gravitational lensing of light, and gravitational waves. The theory has been confirmed by various observational tests.
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.
It should be helpful, special thanks to our teacher (whose name is in the power point and the one who made it) from whom I asked his permission to post it here.
1. Isaac Newton considered what would happen if a cannon ball was shot from a mountain at increasing speeds. He realized that at a certain speed, the projectile would enter into orbit around the Earth due to gravity.
2. Astronauts are not truly weightless in space, but are in a state of constant free fall around the Earth at the same rate as its curvature.
3. To enter into orbit, a satellite must be launched at a velocity less than the escape velocity from Earth, which is around 8km/s. Significant thrust is required to accelerate a satellite to this velocity.
1) General Relativity abolished the concept of absolute space and time, showing that inertial and gravitational mass are equivalent and that acceleration and gravity are indistinguishable (Equivalence Principle).
2) The Cosmological Principle states that the universe looks the same from any location (isotropic and homogeneous), supporting the Big Bang theory of an expanding universe.
3) Black holes are predicted by General Relativity as regions where spacetime curvature becomes infinite, and their existence is supported by observations like gravitational lensing.
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.
This document summarizes key concepts from a presentation on special and general relativity:
1) Special relativity is based on two postulates - the laws of physics are the same in all inertial frames, and the speed of light is constant. This leads to time dilation and length contraction.
2) The twin paradox is resolved by recognizing that only inertial frames can apply Lorentz transformations - the traveling twin accelerates so experiences more time.
3) General relativity extends these ideas to frames with gravity by proposing spacetime is curved by mass-energy. This predicts bending of light and gravitational lensing.
General relativity presentation.ragesh,asmitha,m.d.trageshthedon
1. The document discusses Albert Einstein's theory of general relativity and how it improved upon Isaac Newton's theory of gravity.
2. General relativity explains gravity as a distortion of spacetime caused by massive objects, rather than an attractive force.
3. Some key predictions of general relativity include gravitational time dilation, gravitational lensing of light, and gravitational waves. The theory has been confirmed by various observational tests.
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.
1) Time dilation describes how time passes more slowly for objects in motion compared to an observer. The time interval between two events is longer for an observer in a stationary frame compared to an observer in the moving frame.
2) According to the theory of relativity, the mass of an object increases as its velocity increases, approaching infinity at the speed of light. Mass is related to rest mass, velocity, and the speed of light by the equation m = m0/(1 - v^2/c^2).
3) Einstein's mass-energy equivalence states that mass and energy are the same physical entity and can be changed into each other. The famous equation E=mc^2 describes this relationship, where
This unit carry information of Acceleration Due to the Gravity (g), Satellite and Planetary Motion and Gravitational Field, Potential Energy, Kinetic Energy and Total energy of the satellite. in each section, there is an example so as you could be able to manipulate those equations that are associated with this unit. Also, there is problem practice so as to straighten the understanding of this module.
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.
The document discusses how space and time can be warped based on one's frame of reference and motion. It introduces concepts from special and general relativity such as length contraction, time dilation, gravitational time dilation, and how matter warps space-time. It explains how the expansion of space causes galaxies to appear to move away from each other, providing evidence for the Big Bang theory that the universe has expanded over billions of years from a hot, dense state.
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.
1) An event is a physical happening that occurs at a specific place and time, as recorded by observers using reference frames consisting of coordinate systems and clocks at rest relative to the frames.
2) Special relativity has two postulates: 1) the laws of physics are the same in all inertial reference frames, and 2) the speed of light has the same value in all inertial frames regardless of the motion of the light source or observer.
3) Time dilation occurs such that clocks in motion run slower than clocks at rest, as observed from another frame, with the time interval between ticks increasing with the relative velocity between frames. Proper time is the time interval measured in the frame at rest with the clock
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.
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.
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.
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.
Introduction to the General Theory of RelativityArpan Saha
1) The document outlines Albert Einstein's theory of general relativity, beginning with an introduction to Isaac Newton's theory of universal gravitation.
2) It describes how Einstein realized that Newtonian gravity is incompatible with special relativity, and how this led Einstein to formulate his principle of equivalence and theory that gravity is the curvature of spacetime.
3) The document provides an overview of key mathematical concepts in general relativity such as manifolds, tensors, geodesics, and the Einstein field equations.
The document discusses key concepts from the theory of relativity, including:
1) The Michelson-Morley experiment failed to detect the "aether wind" and proved that the speed of light is constant regardless of the motion of the observer.
2) According to relativity, time dilation and length contraction occur so that the speed of light remains constant, and simultaneity is relative to the observer's frame of reference.
3) Key consequences of relativity include that moving clocks run more slowly and the length of objects decreases as their speed increases.
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.
General relativity is Einstein's theory of gravitation published in 1915. It explains gravitational phenomena by describing how spacetime is curved by mass and energy. Some key points:
- General relativity superseded Newton's theory of gravity and describes gravity not as a force but as a curvature of spacetime.
- Einstein made several predictions with general relativity including the bending of starlight and gravitational time dilation, which have all been confirmed by observations.
- Tests of general relativity include measuring the precession of Mercury's orbit, the deflection of starlight near the sun, and gravitational redshift of light escaping gravitational fields.
Einstein published two theories of relativity - Special Relativity, which described how space and time are relative based on the observer's frame of reference and that the speed of light is constant, and General Relativity, which explained that gravity results from the curvature of spacetime caused by massive objects. Some key effects are time dilation, length contraction, and the bending of light near massive bodies like the sun.
A Brief Tour of Relativity and CosmologyRobert McNees
This document provides an overview of relativity and cosmology, covering special relativity, general relativity, and cosmology in under an hour. Special relativity introduced spacetime and showed that measurements of space and time depend on observers' motion. General relativity describes gravity as the curvature of spacetime caused by mass and energy. Cosmological models apply general relativity to the universe as a whole, showing that observations of galaxies receding in all directions indicates an expanding universe beginning from a hot, dense initial state.
Introduction to Special theory of relativityROHIT PANJABI
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.
Special and General theory of Relativity Einsteinshubhy patel
This document summarizes key concepts from Einstein's special and general theories of relativity presented in a seminar. It discusses that all physical laws are independent of reference frame and the speed of light is constant. It also covers time dilation, length contraction, relativity of simultaneity, and the twin paradox from special relativity. For general relativity, it describes gravity as the warping of spacetime, the equivalence principle, gravitational time dilation, bending of light by gravity, gravitational redshift, black holes, and experimental tests supporting the theories.
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.
The document discusses Einstein's theory of relativity. It introduces classical relativity which states that two spaceships approaching each other at the same speed would see the other moving at twice the speed. It then explains special relativity, including that the speed of light is constant for all observers regardless of their motion. General relativity holds that gravity is caused by the warping of spacetime itself by massive objects, causing free-falling objects to follow curved paths through warped spacetime.
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.
This document summarizes key concepts from a physics lecture on special relativity. It discusses how measurements of time, length, and simultaneity depend on the observer's inertial reference frame. The three main points are: 1) time dilation causes moving clocks to run slow relative to proper time in the rest frame; 2) length contraction makes moving objects appear shorter than their proper length; 3) whether two events occur simultaneously is frame-dependent. Examples are provided to illustrate time dilation, length contraction, and their consequences.
1) Time dilation describes how time passes more slowly for objects in motion compared to an observer. The time interval between two events is longer for an observer in a stationary frame compared to an observer in the moving frame.
2) According to the theory of relativity, the mass of an object increases as its velocity increases, approaching infinity at the speed of light. Mass is related to rest mass, velocity, and the speed of light by the equation m = m0/(1 - v^2/c^2).
3) Einstein's mass-energy equivalence states that mass and energy are the same physical entity and can be changed into each other. The famous equation E=mc^2 describes this relationship, where
This unit carry information of Acceleration Due to the Gravity (g), Satellite and Planetary Motion and Gravitational Field, Potential Energy, Kinetic Energy and Total energy of the satellite. in each section, there is an example so as you could be able to manipulate those equations that are associated with this unit. Also, there is problem practice so as to straighten the understanding of this module.
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.
The document discusses how space and time can be warped based on one's frame of reference and motion. It introduces concepts from special and general relativity such as length contraction, time dilation, gravitational time dilation, and how matter warps space-time. It explains how the expansion of space causes galaxies to appear to move away from each other, providing evidence for the Big Bang theory that the universe has expanded over billions of years from a hot, dense state.
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.
1) An event is a physical happening that occurs at a specific place and time, as recorded by observers using reference frames consisting of coordinate systems and clocks at rest relative to the frames.
2) Special relativity has two postulates: 1) the laws of physics are the same in all inertial reference frames, and 2) the speed of light has the same value in all inertial frames regardless of the motion of the light source or observer.
3) Time dilation occurs such that clocks in motion run slower than clocks at rest, as observed from another frame, with the time interval between ticks increasing with the relative velocity between frames. Proper time is the time interval measured in the frame at rest with the clock
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.
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.
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.
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.
Introduction to the General Theory of RelativityArpan Saha
1) The document outlines Albert Einstein's theory of general relativity, beginning with an introduction to Isaac Newton's theory of universal gravitation.
2) It describes how Einstein realized that Newtonian gravity is incompatible with special relativity, and how this led Einstein to formulate his principle of equivalence and theory that gravity is the curvature of spacetime.
3) The document provides an overview of key mathematical concepts in general relativity such as manifolds, tensors, geodesics, and the Einstein field equations.
The document discusses key concepts from the theory of relativity, including:
1) The Michelson-Morley experiment failed to detect the "aether wind" and proved that the speed of light is constant regardless of the motion of the observer.
2) According to relativity, time dilation and length contraction occur so that the speed of light remains constant, and simultaneity is relative to the observer's frame of reference.
3) Key consequences of relativity include that moving clocks run more slowly and the length of objects decreases as their speed increases.
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.
General relativity is Einstein's theory of gravitation published in 1915. It explains gravitational phenomena by describing how spacetime is curved by mass and energy. Some key points:
- General relativity superseded Newton's theory of gravity and describes gravity not as a force but as a curvature of spacetime.
- Einstein made several predictions with general relativity including the bending of starlight and gravitational time dilation, which have all been confirmed by observations.
- Tests of general relativity include measuring the precession of Mercury's orbit, the deflection of starlight near the sun, and gravitational redshift of light escaping gravitational fields.
Einstein published two theories of relativity - Special Relativity, which described how space and time are relative based on the observer's frame of reference and that the speed of light is constant, and General Relativity, which explained that gravity results from the curvature of spacetime caused by massive objects. Some key effects are time dilation, length contraction, and the bending of light near massive bodies like the sun.
A Brief Tour of Relativity and CosmologyRobert McNees
This document provides an overview of relativity and cosmology, covering special relativity, general relativity, and cosmology in under an hour. Special relativity introduced spacetime and showed that measurements of space and time depend on observers' motion. General relativity describes gravity as the curvature of spacetime caused by mass and energy. Cosmological models apply general relativity to the universe as a whole, showing that observations of galaxies receding in all directions indicates an expanding universe beginning from a hot, dense initial state.
Introduction to Special theory of relativityROHIT PANJABI
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.
Special and General theory of Relativity Einsteinshubhy patel
This document summarizes key concepts from Einstein's special and general theories of relativity presented in a seminar. It discusses that all physical laws are independent of reference frame and the speed of light is constant. It also covers time dilation, length contraction, relativity of simultaneity, and the twin paradox from special relativity. For general relativity, it describes gravity as the warping of spacetime, the equivalence principle, gravitational time dilation, bending of light by gravity, gravitational redshift, black holes, and experimental tests supporting the theories.
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.
The document discusses Einstein's theory of relativity. It introduces classical relativity which states that two spaceships approaching each other at the same speed would see the other moving at twice the speed. It then explains special relativity, including that the speed of light is constant for all observers regardless of their motion. General relativity holds that gravity is caused by the warping of spacetime itself by massive objects, causing free-falling objects to follow curved paths through warped spacetime.
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.
This document summarizes key concepts from a physics lecture on special relativity. It discusses how measurements of time, length, and simultaneity depend on the observer's inertial reference frame. The three main points are: 1) time dilation causes moving clocks to run slow relative to proper time in the rest frame; 2) length contraction makes moving objects appear shorter than their proper length; 3) whether two events occur simultaneously is frame-dependent. Examples are provided to illustrate time dilation, length contraction, and their consequences.
Albert Einstein published his special theory of relativity in 1905, which established two postulates - the laws of physics are the same in all inertial reference frames, and the speed of light has the same value in all reference frames. This challenged the prevailing notion of Galilean relativity and the existence of the luminiferous ether, and led to predictions such as time dilation and length contraction that have since been widely verified.
Albert Einstein published his special theory of relativity in 1905, which established two postulates - the laws of physics are the same in all inertial reference frames, and the speed of light has the same value in all reference frames. This challenged the prevailing Newtonian mechanics and the concept of the luminiferous ether. Experiments like the Michelson-Morley experiment found no evidence of the ether or different light speeds. Relativity led to phenomena like time dilation, where clocks in motion run slower, and length contraction, where objects appear shorter along the direction of motion.
The document provides background information on Einstein's special theory of relativity. It discusses the two postulates of special relativity: 1) the principle of relativity, and 2) the constancy of the speed of light. It then summarizes some key consequences of special relativity, including time dilation, length contraction, relativistic Doppler effect, relativistic mass, mass-energy equivalence, and Lorentz transformations. Examples are provided to demonstrate calculations for these various consequences.
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.
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.
This document discusses Einstein's theory of general relativity and the recent direct detection of gravitational waves. It describes how Einstein predicted that masses curve spacetime and that freely falling objects move along geodesics in curved spacetime. The recent detection by an international collaboration provides direct evidence of Einstein's prediction that changing gravity generates ripples in spacetime called gravitational waves. This confirmation of gravitational waves validates general relativity and opens new opportunities for astronomy.
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.
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.
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) The document is an open letter from Le Van Cuong to scientists and professors suggesting they correct Einstein's theory of special relativity before teaching it to students.
2) Cuong argues that Einstein's postulate that the speed of light is constant is incorrect and has confused science for over a century. He believes light speed depends on the motion of the light source.
3) Cuong provides a proof using equations and diagrams showing that when an object emitting light is in motion, the observed speed of the light (c') is not actually equal to the constant speed of light (c) and is given by c' = (c^2 + v^2)^1/2, where v is the velocity
Nature is quirky. Whenever things don't quite match up, She changes them so they will. The results often seem to be bizarre and nonsensical, but the more you study it you realize how profoundly wise Nature is. It all started with a thought experiment that Einstein said he came up with at around the age of 16. The young Einstein wondered what would happen if he chased a light beam and caught up with it. This essay describes two of the most important discoveries in science: The Special Theory of Relativity and the General Theory of Relativity. Both of these discoveries were made by a single man, Albert Einstein, over a period of one decade (1905 – 1915). This essay is directed at an audience of amateur scientists like myself. I will approach these two theories on the basis of their underlying principles, deriving as much as possible using basic geometry and a bit of elementary calculus. I will not go into the depth needed to become a “relativist.” Mastery of general relativity would require a good working knowledge of tensors, which is beyond the scope of this essay. Nevertheless, I think amateur scientists like myself will get something useful out of it.
This document discusses key concepts from special relativity. It begins with an example of measuring the rate of dripping water from a pot on a moving train from the perspective of an observer on the train (Ali) and an observer on the ground (Baba). It notes that both measurements are equally valid and can be related using Lorentz transformations. It then discusses that events can be considered from any reference frame, with no frame being superior, and that the choice of reference frame is a matter of convenience. It also explains that accurately locating events requires accounting for the finite speed of light to avoid simultaneity issues. Overall, the document introduces the idea that the laws of physics must appear the same in all reference frames according to Einstein's principle
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.
Einstein's theories of relativity challenged classical mechanics in three key ways:
1. Special relativity 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 invariant.
2. It also found that measurements of time and length change for observers in different reference frames based on their motion and that mass increases with speed.
3. General relativity later described gravity as a consequence of spacetime being curved by mass and energy, rather than as a force, and that free-falling objects and light rays follow curved paths called geodesics.
This document provides an overview of differentiation strategies that can be used in the classroom. It defines differentiation as accommodating differences between students so that all have the best chance of learning. There are three main types: differentiation by outcome, support, and task. Differentiation requires clearly defined learning objectives and outcomes, and backwards planning from the outcomes. The document outlines various strategies for differentiating by outcome, support, and task, emphasizing the importance of planning to avoid stigmatizing students. Teachers are then tasked with developing a differentiated lesson plan and resource to implement in their own classroom.
This document discusses the motor effect and how it is used in electric motors and other devices. It explains that a torque is produced when a force acts on a current-carrying coil placed in a magnetic field, causing the coil to rotate. This effect is used in DC motors, which have a split-ring commutator that reverses the current to keep the motor spinning. The motor effect is also used in devices like galvanometers and loudspeakers.
The document discusses different types of AC motors, including their construction and operation. It explains that AC motors have a slip-ring commutator rather than split rings, allowing the current in coils to change direction with the alternating current. Induction motors are then described in more detail, having a stator that produces a rotating magnetic field which induces eddy currents in the rotor coils, causing the rotor to spin. The rotor coils in an induction motor form a "squirrel cage" structure. Finally, examples of energy transfers in homes and industries are given, such as electrical to kinetic in motors, electrical to thermal in heating elements, and electrical to sound in speakers.
This document discusses generators and power transmission. It explains that rotating a coil in a magnetic field induces an alternating current (AC) in the coil. AC generators use a slip ring commutator to produce an AC output as the coil cuts magnetic lines of flux. Power is transmitted at high voltages for efficiency and then stepped down before distribution. There were competing DC and AC systems, with AC winning out due to its ability to transmit power over long distances using transformers.
1. Michael Faraday discovered electromagnetic induction in the 1830s when he found that moving a wire through a magnetic field generated a small electric current in the wire.
2. He determined that the changing magnetic field exerted a force on the electrons in the wire, causing them to move and generating an electromotive force (emf).
3. Faraday's law of induction states that an emf is induced in a coil of wire when there is a change in the magnetic flux through the coil. The magnitude of the induced emf depends on the rate of change of magnetic flux.
1. The document discusses the motor effect, which is the force experienced by a current-carrying conductor in a magnetic field. It describes how the interaction between the magnetic field generated by the current and an external magnetic field produces a force.
2. Key factors that influence the magnitude of the motor effect force are outlined, including the strength of the magnetic field, current magnitude, length of the conductor in the field, and angle between the field and conductor.
3. Rules for determining the direction of the force are provided, such as the left hand motor rule. Parallel conductors experience attractive or repulsive forces depending on whether their currents are parallel or anti-parallel.
Transformers are electrical devices that convert alternating current from one voltage to another by using two coils of wire wrapped around an iron core. Transformers that step up voltage increase it, while transformers that step down voltage decrease it. They work by generating a changing magnetic field in the primary coil using AC power, which induces a voltage in the secondary coil. The ratio of turns between the two coils determines the ratio of voltages out and in. While efficient, transformers have some energy losses through eddy currents in the core and resistance in the windings. They are widely used to adjust voltages for transmission on power grids and in devices.
1. The document discusses gravitational fields and the simple pendulum experiment. It describes how the period of a pendulum is affected by the mass of the bob and the length of the string. The experiment can be used to calculate the acceleration due to gravity.
2. Gravitational potential energy is introduced. Lifting an object increases its gravitational potential energy, which is defined to be zero at an infinite distance. Calculations of gravitational potential energy are shown for objects near and far from Earth.
3. The formula for gravitational field strength is derived, showing that it decreases with the square of the distance from the object's center. Values of g are calculated for the major planets based on their masses and radii.
This document discusses projectile motion and related concepts. It defines a projectile as any object moving only under the influence of gravity. The horizontal and vertical motions of a projectile are independent, allowing the use of kinematic equations separately in each direction. Galileo first discovered that objects fall at the same rate regardless of mass by dropping objects from the Leaning Tower of Pisa. The document provides examples of solving projectile motion problems by separating the horizontal and vertical components.
The document discusses gravitational fields and the law of universal gravitation. It defines gravitational field lines and how they represent the gravitational field around an object. The closer the field lines, the stronger the gravitational field. The law of universal gravitation describes the gravitational force between two objects using mass, distance, and the gravitational constant. Gravitational potential energy is the energy an object has due to its position in a gravitational field and depends on mass and distance from attracting objects.
When a wave crosses a boundary between two media, it is partially transmitted and partially reflected. The amount depends on the boundary - a hard boundary reflects the wave out of phase, while a soft boundary reflects it in phase. Reflection follows the law that the angle of incidence equals the angle of reflection. Refraction occurs when a wave crosses into a medium with a different wave speed, causing it to change direction according to Snell's law. Diffraction spreads waves out when they pass through an opening or obstacle. Superposition combines overlapping waves constructively or destructively based on their phase difference.
The document discusses different types of waves including transverse waves, where the vibration is perpendicular to the direction of propagation, and longitudinal waves, where the vibration is parallel. It also covers characteristics of waves like frequency, wavelength, amplitude, intensity, and speed; how waves transfer energy without transferring matter; and the electromagnetic spectrum.
This document discusses damped and forced harmonic motion. It explains that in damped harmonic motion, a damping force acts opposite to the velocity to dissipate energy and stop vibrations. The damping causes the amplitude to decay exponentially over time. A system can be under-damped, over-damped, or critically damped depending on how quickly it stops oscillating. Forced harmonic motion occurs when an external periodic force drives the system, like pushing a swing. At resonance, the driving frequency matches the natural frequency, causing large amplitude oscillations. While resonance can be dangerous if it causes collapse, it can also be useful in applications like radios and musical instruments.
This document defines key terms and equations related to simple harmonic motion (SHM). It discusses oscillating systems that vibrate back and forth around an equilibrium point, like a mass on a spring or pendulum. The key parameters of SHM systems are defined, including amplitude, wavelength, period, frequency, displacement, velocity, acceleration. Equations are presented that relate the displacement, velocity, acceleration as sinusoidal functions of time. The concepts of kinetic, potential and total energy are also explained for oscillating systems undergoing SHM.
The document discusses the properties and behavior of ideal gases. It defines ideal gases as having point-like particles that exert no forces on each other except during elastic collisions. The document then derives the ideal gas law (PV=nRT) by considering the momentum transfer during particle collisions with the container walls and relating gas pressure to temperature via the kinetic energy and speeds of the particles. It concludes by noting that the ideal gas law can provide approximate descriptions of real gases.
The document discusses the particle model of matter and how it relates to the different phases of matter and phase changes. It explains that in solids, particles vibrate around fixed positions, in liquids they can move slowly, and in gases they can move quickly. A phase change occurs when the kinetic energy of particles changes enough for them to overcome attractive forces. Evaporation involves single particles escaping while boiling happens when vapor pressure exceeds atmospheric pressure. Thermal capacity and specific heat capacity are introduced to quantify how much energy is required to change an object's temperature. Latent heat also quantifies energy absorbed or released during phase changes.
This document discusses key concepts in thermodynamics including:
1) All objects have internal energy due to the vibration and interactions of their internal particles; internal energy can be transferred as thermal energy.
2) Thermal energy flows spontaneously from hot to cold objects and can be transferred by conduction, convection, or radiation.
3) Temperature is a measure of average kinetic energy and different temperature scales (Celsius, Fahrenheit, Kelvin) are defined based on fixed points.
This document discusses circular motion and centripetal acceleration. It defines centripetal acceleration as the acceleration an object experiences when moving in a circular path, which causes a change in the direction of motion towards the center of the circle. The document provides equations for centripetal acceleration, relating it to the object's velocity, radius of the circular path, and angular speed. Examples are given of forces that provide centripetal acceleration, such as gravity keeping the moon in orbit or friction keeping cars from slipping outward while turning.
Kinematics is the study of linear motion. Key terms include displacement, velocity, and acceleration. Displacement is the distance from a starting point, velocity is speed in a direction, and acceleration is the rate of change of velocity. Average values are calculated by total distance or displacement over total time. Instantaneous values give a clearer picture of motion at a moment in time and can be derived from graphs of displacement, velocity, and acceleration over time. When acceleration is constant, five equations can be used to describe motion with constant acceleration.
The document discusses various concepts in mechanics including work, energy, power, and collisions. It defines work as the product of the applied force and displacement in the direction of force. It provides examples of calculating work done by pushing/lifting objects and moving in a current. Kinetic energy is defined as 1/2mv^2 and gravitational potential energy as mgh. The principle of conservation of energy states that total energy in a closed system remains constant as it can only be transferred or transformed. Power is defined as the rate of doing work and is measured in Watts. Collisions conserve momentum and kinetic energy may or may not be conserved depending on whether the collision is elastic or inelastic.
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.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
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Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
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.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
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.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
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 ...
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.
2. Galilean Relativity
In the Galilean view point, the laws of
physics should hold true in all
inertial frames of reference.
That is, so long as there is no
acceleration, all experiments should
yield the same result.
An experiment to measure g by using
a pendulum should give the same
result when it is stationary, or when
it is moving at a steady speed on a
train.
3. Frames of Reference
A frame of reference is simply a
“background” against which
measurements can be
measured.
Imagine a fully tiled swimming
pool.
The tiles form a grid on the
walls and floor.
The absolute position of
anything can be measured
relative to this grid.
The absolute displacement of
anything can be defined using
the corner of the pool as the
origin.
4. Galliean Relativity
Differences in observation between different
frames of reference can be explained by
considering the relative motion of the two
frames.
Consider an observer in the red frame of
reference looking at the clock.
They would see the clock ticking but not
moving
Consider an observer in the black frame of
reference looking at the red clock
They would see the clock ticking and
moving with speed v. Its position would
xbe s(x,y,z)=(vt,y,z)
If the black frame were also moving (say at
speed uthen the absolute velocity of the
x red clock would be u- vx
x
5. Newtonian Frames of Reference
A frame of reference is said to be inertial if Newton’s first law is valid
for it.
That is if it is not accelerating in any dimension
A frame of reference is said to be non-inertial if Newton’s second
law is valid for it.
That is it is accelerating in at least one dimension.
Newton realised that no frame of reference would be
more correct than any other. Therefore the concept of
absolute position is meaningless.
This is especially true in space where you have no
background grid to work with.
Different observers can have different frames of
reference, but in Newton’s view, they should agree
about when an event happened even if they both say
it was in a different position.
6. A First Thought Experiment
You are sat on a (very good)
train in a tunnel.
You cannot hear anything.
You cannot feel any
movement.
You are looking out of the
window and see another
train move from left to
right past your window.
What is your train doing?
7. A First Thought Experiment
Are you sat stationary in the red train
and the blue train moves from left to
right at speed v?
0
v
8. A First Thought Experiment
Are you sat in the red train moving
from right to left at speed v and the
blue train is stationary?
v
0
9. A First Thought Experiment
Are you sat in the red train moving
from right to left at speed ½ v and
the blue train is moving at ½ v in the
other direction?
½ v
½ v
10. A First Thought Experiment
Or is there something else going on?
Does it matter to the Physics?
3/2 v
½ v
11. A First Thought Experiment
Imagine that your friend on the red
train now hold 2 charges in her
hands. What do you see if you are
on the red train? On the blue train?
0
v
+
+
12. A First Thought Experiment
On the red train you only see the force of electrostatic repulsion.
On the blue train you see this same electrostatic force but because
the charges are moving, there appears to be a current, therefore
there is a magnetic force in the opposite direction.
The blue train always measures more force than the red train
The laws of physics are different to different observers!!!
FQ
v
+
+
+
FB
+
FQ
FQ FQ
13. Waves and Media
• All waves, such as sound waves and
water waves, had been observed to
require a medium in order to propagate.
• Light waves should also require a
medium.
• This medium was called the Aether (also
ether)
• The Aether was thought to be a transparent,
massless, colourless medium that was
present everywhere including in the vacuum.
• This was the theory in the 1600’s through
until the end of the 1800’s!
14. Michelson and Morley
• Michelson and Morley set out to detect
the Aether in 1887.
• They assumed that the Aether was
moving with constant velocity and that
the Earth moved relative to it.
• They likened their experiment to two
boats moving on a fast flowing river.
• The two boats are capable of exactly the same speed.
• One moves parallel to the bank,
• The other perpendicular to it.
• They both travel the same distance before turning
round and coming back to the start.
15. Michelson and Morley
The speed of the boat is u and
the speed of the water is v.
The boat moving parallel to the
stream has speed u+v and
then u-v which averages to u.
The boat moving across the
stream has speed
in both directions
√ u2−v2
As the speeds are different, but
the distance travelled the
same, the time taken to travel
will be different!
v
v v
√ u2−v2
u u
u+v
u-v
16. The Interferometer
Michelson devised a device known as an
interferometer to test this theory.
Because light is a wave, it can interfere
with other light waves and form an
interference pattern.
Differences in times of travel result in a
“phase difference” which causes a
change in the pattern.
As the Earth rotated around the Sun, it was
expected that changes in the
interference pattern would be observed.
18. The Results
Michelson and Morley detected no
systematic change in the
interference pattern.
Any changes that were observed
were random errors.
More sensitive equipment has since
been built and to this day no
detectable change has been reliably
observed.
19. A Failed Experiment?
The Michelson-Morley experiment is
possibly the most famous “failed
experiment”.
However, whilst the experiment failed to
detect an Aether, it did suggest that the
postulate that “the Aether exists” was
incorrect.
This caused other Hypotheses to be put
forward, including Einstein’s special
relativity.
So the experiment did not truly fail.
20. An Unexpected Result
As shown using vectors, the speed of light
should be different in the two directions.
However, the time of travel is observed to
be the same, as is the distance of travel.
Therefore “the speed of light is the same in
all directions, regardless of motion”.
This is compatible with Maxwell’s equations
which showed that the speed of light is
given by:
c 1
e m
0 0
=
21. The implications of Einstein’s Postulates
1) Two events that are simultaneous
to one observer may not
necessarily appear simultaneous to
another observer in a different
frame of reference.
22. Simultaneity of Events
Consider a train moving at high speed, v, through a station.
As the train passes through 2 small explosions are set off at
either end of the train.
The two explosions are equidistant from a stationary
observer on the platform.
By simple calculation, the time taken for light to travel from
the head of the train (t) is given by t=
d
and from the tail
of the train (t’) is
c
t '=
d '
c
To the observer on the platform the events were
simultaneous.
d' d
23. Simultaneity of Events
Consider an observer now on the train moving with high
speed v.
The two explosions are still set off as before.
However, in the time taken for the light to travel, the observer
has moved forward by vt metres.
By simple calculation, the time taken for light to travel from
the head of the train (t) is now given by t=
d−vt
and
from the tail of the train (t’) is
d ' +vt
c
t '= c
To the observer in the train the events were not
simultaneous.
vt
d' d
d' d
24. Time Dilation
Zoe is travelling in her car at speed v past Jasper on his
verandah.
She has a type of clock that measures the time by reflecting
a light ray between two mirrors.
Jasper can also see the light ray bouncing and use this to
measure his own time.
25. Time Dilation
Before the experiment begins, Zoe parks
her car next to Jasper’s verandah and
they both agree on the timing and both
get the same result.
Zoe then drives from left to right at 0.8c
according to Jasper’s frame of reference.
Of course in Zoe’s frame of reference it is
Jasper’s verandah that moves from right
to left at 0.8c!
26. Time Dilation
The red counters count each time Jasper or Zoe sees a
reflection.
27. Time Dilation
Say the car is “w” wide and the time
Zoe measures between reflections
is t’.
Then the distance is given by
w=ct '
However, if t is the time to tick on
Jasper’s clock, he records the
distance travelled (using
Pythagoras) as
d 2=( ct )2=w2+( vt)2
28. Time Dilation
Combining the previous equations gives:
c2 t2=c2 t '2+v2 t2
This rearranges to:
t '=
t
√(1−v2
This is also written as:
Where tv is the time on the
moving clock as measured
by a stationary observer.
t0 is the time on the moving clock as
measured by an observer in the
same moving frame of reference.
c2 )
tv=
t0
√(1−
v2
c2 )
29. Time Dilation
In summary, a moving clock appears
to run slower according to
tv=
t0
√(1−
v2
c2 )
30. Length Contraction
If the speed of light is constant, and time
gets shorter (dilates) for a moving object,
then the length of the object must get
smaller as measured in the direction on
motion.
lv=l0 √(1−
v2
c2 )
lv is the length of the object when it is moving
l0 is the rest length of the object.
31. Mass Dilation
Experiments in the early 1900s
carried out by Kaufmann showed
that the charge/mass ratio of high
speed electrons decreased with
increasing speed.
However, the charge carried by the
electrons was a constant.
Therefore the mass must have been
increasing.
32. Mass Dilation
Einstein’s theory of special relativity
showed how this could happen.
mv=
m0
√(1−
v2
c2 )
33. Practice.
Consider a pen of mass 100g and
length 15cm. What would be its
length and mass, as measured by a
stationary observer, when it is
moving at 340 ms-1 and 3x107 ms-1
relative to the observer?
34. Practice
NASA have invented a rocket that
can travel at 95% of the speed of
light. How long will it take to get to
the nearest star, 4.5ly away as
measured by the scientists at
Houston and by the astronauts on
board?
35. Practice
A type of subatomic particle called a
muon has a half-life of 2μs. What
will be the half-life of these particles
if they are travelling at 0.99c in the
laboratory?
36. What is a Thought Experiment
• Einstein's understanding of relativity
came about due to his use of thought
experiments.
• These are experiments where the logic of
the situation, and hence the results, is
flawless BUT the situation is usually
impossible (or at least highly improbable)
to replicate in reality.
• However, just because the experiment
cannot really be done does not mean
that the result cannot be significant!
37. Common limitations of thought experiments.
• Trains and spacecraft cannot
travel at relativistic velocities (due
to the consequences of special
relativity!!)
• An observer outside of the train
(travelling at nearly c) would find it
impossible to physically make any
valid or accurate observations of
events inside the train.
38. Common limitations of thought experiments.
• It is impossible to “see” the light
beam travelling from the source to
the mirror and back.
– Either the whole train carriage
lights up (the light spreads out)
– Or you need a laser beam and to
have dust particles in the path to
scatter it.
• Either way the light becomes
spread out.
39. Common limitations of thought experiments.
• It is impossible engineer an
infinitely long train and perfectly
identical fireworks.
• The relative simultaneity
experiment (fireworks at either
end of a long train) requires both
of these in order to register any
noticeable effect.
40. The implications of Special Relativity.
• As an object increases its speed towards c,
its mass increases (or dilates)
• This means that it becomes even more
difficult to accelerate the object ( F=ma=
m( v−u)
)
t
• Even at the maximum theoretical speed
(~0.99c), with the biggest engines possible, it
would take over 4 years to reach just out to
our nearest star. The rest of the galaxy is
just too far away!
41. The implications of Special Relativity
• Consider two identical twins. One remains on Earth
whilst the other takes a long trip to a distant star on a
spacecraft that can travel at 0.99c.
• From the Earth twin's point of view, the space twin is
moving whilst they stand still. Therefore the Space
twin's clock is running more slowly. Therefore the
Space twin will be younger when they return.
• However, from the space twin's point of view, the Earth
twin may just as well be moving whilst they sit still.
Therefore the Earth twin's clock runs slower and
therefore the Earth twin will be younger.
• They can't both be younger can they?
This is the so called twins paradox.
42. The implications of Special Relativity
• The twins paradox is really not a major
problem once you consider the limitation of
Special Relativity.
• Special relativity is ONLY valid in an inertial
frame of reference!
• The space twin must have accelerated to
0.99c, turned around the distant star, and
decelerated again.
• Therefore the space twin has not always
been in an inertial frame of reference,
therefore their conclusion is invalid.
• The space twin would indeed be the younger
of the two.
43. The implications of Special Relativity
• When the spacecraft is moving forward
through space at relativistic speeds it
appears that the space is moving
towards the spacecraft.
• Therefore the distance will appear
shorter to the pilots than the distance
measured by an external observer.
• This is a consequence of a slower
ticking clock (time dilation) and a
constant speed of light.
44. Measuring Time
• The passage of time in an inertial
frame of reference can be very
accurately measured using a
pendulum of a specific length.
• However, this requires knowledge
of the gravitational field strength
to be useful.
• It is also mostly useless in non-inertial
frames of references (i.e.
the deck of a boat that is rocking
up and down)
45. Measuring Time
• Watchmakers developed more and more
precise devices to measure time but the
definition of the second was still as being
1/8600 of the time for the Earth to rotate on
its axis.
• In 1967, following observations that the
Earth's rotation was slowing (very) slightly a
new definition of the second was formulated.
• 1 second is the time taken for an atom of Cs-
133 to oscillate 9129631770 times. In theory
this definition will remain accurate
everywhere in the Universe.
46. Measuring Distance
• The metre was originally defined as being
one ten-millionth of the distance from the
North pole to the Equator passing through
Paris.
• This distance was then scored onto 3
platinum bars kept in Paris.
• This allowed a common scale of distance to
be used by everyone and eventually has
replaced a much more complex English
system of Feet, Yards, Fathoms, Chains,
Furlongs and Miles in most of the world.
47. Measuring Distance
• As the surveyors had actually
made a slight mistake in their
calculations for the metre, the
bars became the standard rather
than the original definition.
• These bars were later replaced
with a more stable platinum-iridium
bar.
48. Measuring Distance
• The need to have an even more
precise standard of length that did
not rely on referencing a metal
bar in a vault somewhere brought
scientists to basing their definition
in the atom.
• The metre is now defined as
being the distance travelled by
light in 1/299792458 of a second.
– Note how this requires that the
speed of light is precisely known!