Physics. Special Relativity
|
|
- Lambert Roberts
- 5 years ago
- Views:
Transcription
1 Physics Special Relativity 1
2 Albert Einstein, the high school dropout and patent office clerk published his ideas on Special Relativity in
3 Special vs. General Relativity Special Relativity deals with non-accelerated motion or uniform motion. General Relativity deals with motion in an accelerated frame of reference. 3
4 Motion is Relative A frame of reference is a place from which motion is observed and measured. An object may have different velocities relative to different frames of reference. 4
5 Old Ideas Originally, it was though that space was filled with a mysterious substance called ether. 5
6 First Postulate All laws of nature are the same in all uniformly moving frames of reference. 6
7 Second Postulate The speed of light in free space has the same measured value for all observers regardless of the motion of the source or the motion of the observer; that is, the speed of light is a constant. 7
8 Second Postulate 8
9 Simultaneity 9
10 Simultaneity 10
11 How many dimensions are there? It takes 3 dimensions to locate a point. There is a 4th Dimension: TIME 11
12 Space and Time are Integrally Linked SPACETIME! 12
13 Time Dilation 13
14 Time Dilation 14
15 Time Dilation 15
16 Time Dilation 16
17 Time Dilation 17
18 Time Dilation 18
19 Lorentz Factor as a Function of Speed 19
20 Twin Paradox 20
21 Length Contraction As objects move through spacetime, space as well as time changes. In a nutshell, space is contracted, making the objects look shorter when they move by us at relativistic speeds. 21
22 Length Contraction Lorentz Contraction George F. FitzGerald Hendrik A. Lorentz 22
23 Length Contraction 23
24 Length Contraction 24
25 Length Contraction 25
26 Length Contraction 26
27 Length Contraction 27
28 Length Contraction 28
29 Twin Paradox 29
30 Let s Do a Thought Experiment We have two ships, identical except for their color. (Same Size, Length) Ships are traveling in opposite directions, at constant and equal speeds. First, let s define 4 different events that we can observe from different frames of reference. 30
31 A C B D 31
32 From the Yellow Ship s Perspective A The blue ship appears contracted. What are the implications? B Events B and C no longer occur simultaneously! Event B happens first. 32
33 From the Yellow Ship s Perspective C Then comes Event C after Event B D 33
34 From the Blue Ship s Perspective The yellow ship appears contracted. What are the implications? A Event C occurs before Event B! C 34
35 From the Blue Ship s Perspective Event B occurs after Event C B D 35
36 Relativity Breaks Simultaneity Event order for the yellow ship - A B C D Event order for the blue ship - A C B D The amount of time elapsed from A to D is the same for each ship. BUT The amount of time from A to B is very different! 36
37 So how does this apply to the twin paradox? From the perspective of the rocket, passing Earth at 0.9c on its way to a distant planet. A 37
38 So how does this apply to the twin paradox? Rocket went from A to B. Event C has not yet occurred. B DONE! 38
39 So how does this apply to the twin paradox? A But now let s examine the situation from Earth s perspective. 39
40 So how does this apply to the twin paradox? C From Earth s perspective, Event C will occur a long time before Event B ever does! 40
41 So how does this apply to the twin paradox? Waiting 41
42 So how does this apply to the twin paradox? Event B! Finally! B 42
43 So how does this apply to the twin paradox? In Earth s reference frame, more time has elapsed from A to B. We can see that because event C happened in the interim. But in the Rocket s reference frame, event C has not occurred at all! The time from A to B was shorter. So the twin on Earth has aged much more than the twin in the Rocket. When they meet up again in the same reference frame, more time has elapsed for one than the other! 43
44 Relativistic Velocities
45 Relativistic Velocities 45
46 Relativistic Velocities 46
47 Relativistic Velocities 47
48 Relativistic Velocities 48
49 Relativistic Momentum The Stanford Linear Accelerator 49
50 Relativistic Momentum 50
51 Mass Effects Mass, like time and length, is also affected by the motion of objects. As the speed of an object approaches c, the mass of the object, m, increases. 51
52 Relativistic Momentum 52
53 Mass and Energy E = mc 2 53
54 The Correspondence Principle 54
55 Check Questions 1. What is the perceived length of a meterstick if it is moving with a velocity of 0.5c (50% of the speed of light) relative to Earth? 2. A spaceship traveling at 0.8c passes parallel to Earth. A rod of length L is inside the spaceship. According to an astronaut inside the spaceship, what is the length of the rod? 55
56 Check Questions 3. A spacecraft with a speed of 0.99c in the +x direction passes by a stationary observer. The dimensions of the spacecraft will appear altered along which axis or axes (x, y, or z)? 4. Two spaceships approach each other. Spaceship A has a speed of 80% the speed of light. Spaceship B has a speed of 60% the speed of light. A passenger on spaceship A aims a laser at spaceship B. How fast does the laser light appear to be moving as observed by a passenger on spaceship B? 56
57 57 General Relativity
58 Special vs. General Relativity Special Relativity deals with non-accelerated motion or uniform motion. General Relativity deals with motion in an accelerated frame of reference. 58
59 Principle of Equivalence In a spaceship far from gravitational influences, at rest or in uniform motion, a person would float freely; there would be no up and no down. But when the rocket motors were turned on and the ship accelerated, things would be different; phenomena similar to gravity would be observed. 59
60 Principle of Equivalence Is she in an accelerated reference frame or under the influence of gravity? Both interpretations are equally valid! 60
61 61 Principle of Equivalence Observations made in an accelerated reference frame are indistinguishable from observations made in a Newtonian gravitational field. So what? Why do we care? Because Einstein went further. He said the principle holds for all natural phenomena; optical as well as electromagnetic!
62 Bending of Light by Gravity To an inside observer, the path of the ball bends as if in a gravitational field. 62
63 Bending of Light by Gravity The same holds true for a beam of light. To observers in the spaceship, the light has followed a downward curving path just as the thrown ball was deflected. 63
64 Bending of Light by Gravity Light bends when it travels in a spacetime geometry that is bent. The presence of mass results in the bending or warping of spacetime. 64
65 Bending of Light by Gravity Einstein predicted that starlight passing close to the sun would be deflected by an angle of 1.75 seconds of arc large enough to be measured. And we have measured it Einstein was right! 65
66 Bending of Light by Gravity Light bends in the Earth's gravitational field also but not as much. We don't notice it because the effect is so tiny. 66
67 Gravity and Time One (experimentally proven) prediction of Einstein s General Relativity is that gravitation causes time to slow down. Really!
68 Gravity and Time 68
69 Gravity and Time This slowing down will apply to all clocks, whether physical, chemical, or biological. An executive working on the ground floor of a tall city skyscraper will age more slowly than her twin sister working on the top floor. The difference is very small, only a few millionths of a second per decade, because by cosmic standards, the distance is small and the gravitation weak. 69
70 Gravitational Red Shift All atoms emit light at specific frequencies characteristic of the vibrational rate of electrons within the atom. Every atom is therefore a clock, and a slowing down of atomic vibration indicates the slowing down of such clocks. An atom on the sun should emit light of a lower frequency (slower vibration) than light emitted by the same element on the Earth. 70
71 Gravity and Time So time depends not only on relative motion, but also upon gravity! Often these are competing effects. 71
72 Gravity and Time Imagine an indestructible volunteer who stands on the surface of a giant star that begins collapsing. We, as outside observers, will note a progressive slowing of time on the clock of our volunteer as the star surface recedes to regions of stronger gravity. He himself, however, does not notice any differences in his own time, nothing unusual. 72
73 Gravity and Time As the collapsing star proceeds toward becoming a black hole and time proceeds normally from the viewpoint of the volunteer, we on the outside perceive time for the volunteer as approaching a complete stop; we see him frozen in time with an infinite duration between the ticks of his clock or the beats of his heart. 73
74 Motion of Mercury Einstein directed his attention to the varying gravitational fields experienced by the planets orbiting the sun and found that the elliptical orbits of the planets should precess independently of the Newtonian influence of other planets. 74
75 Gravity, Space, and a New Geometry Recall the Lorentz contraction from special relativity: The measuring stick will appear contracted to any observer not moving along with the stick, while an identical measuring stick moving much more slowly near the center will be nearly unaffected. 75
76 Gravity, Space, and a New Geometry The familiar rules of Euclidean geometry pertain to various figures you can draw on a flat surface are are valid only in flat space, but if you draw these figures on a curved surface like a sphere or a saddle-shaped object, the Euclidean rules no longer hold. 76
77 Geodesics Lines of shortest distance in a given space are called geodesic lines or simply geodesics. The path of a light beam follows a geodesic. 77
78 Geodesics One familiar example of a positively curved space is the surface of the Earth. Our planet forms a closed curvature, so that if you travel along a geodesic, you come back to your starting point. 78
79 Mass warps spacetime We cannot visualize the four-dimensional bumps and depressions in spacetime because we are three-dimensional beings, but we can get a glimpse by considering a simplified analogy in two dimensions: a heavy ball resting on the middle of a waterbed. 79
80 Gravitational Waves Every object has mass and therefore warps the surrounding spacetime. When an object undergoes a change in motion, the surrounding warp moves in order to readjust to the new position. These readjustments produce ripples in the overall geometry of spacetime, called gravitational waves. 80
81 Newtonian and Einsteinian Gravitation 81
82 82
16 Relativity Momentum, Mass, Energy, and Gravity
According to special relativity, mass and energy are equivalent. According to general relativity, gravity causes space to become curved and time to undergo changes. One of the most celebrated outcomes
More informationChapter 26. Relativity
Chapter 26 Relativity Time Dilation The vehicle is moving to the right with speed v A mirror is fixed to the ceiling of the vehicle An observer, O, at rest in this system holds a laser a distance d below
More informationPhysics 120 Quantum Physics and Beyond Today!
Physics 120 Quantum Physics and Beyond Today! General Relativity Accelerated Frames General Relativity Light in General Relativity Motion and Time in General Relativity Back to Quantum Entanglement? More
More informationLecture 10: General Relativity I
Lecture 10: General Relativity I! Recap: Special Relativity and the need for a more general theory! The strong equivalence principle! Gravitational time dilation! Curved space-time & Einstein s theory
More informationChapter S3 Spacetime and Gravity. Agenda. Distinguishing Crackpots
Chapter S3 Spacetime and Gravity Agenda Announce: Online Quizzes Observations Extra Credit Lecture Distinguishing Crackpot/Genuine Science Review of Special Relativity General Relativity Distinguishing
More informationReview Special Relativity. February 3, Absolutes of Relativity. Key Ideas of Special Relativity. Path of Ball in a Moving Train
February 3, 2009 Review Special Relativity General Relativity Key Ideas of Special Relativity No material object can travel faster than light If you observe something moving near light speed: Its time
More informationE = mc 2. Inertial Reference Frames. Inertial Reference Frames. The Special Theory of Relativity. Slide 1 / 63. Slide 2 / 63.
Slide 1 / 63 The Special Theory of Relativity E = mc 2 Inertial Reference Frames Slide 2 / 63 Newton's laws are only valid in inertial reference frames: n inertial reference frame is one which is not accelerating
More informationClass 16. Prof J. Kenney October 31, Relativity
Class 16 Prof J. Kenney October 31, 2016 Relativity Length contraction (moving sticks are shorter) A measuring stick at rest has a length Lo. When it is propelled at velocity v, it has a shorter length
More informationLecture Outline Chapter 29. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.
Lecture Outline Chapter 29 Physics, 4 th Edition James S. Walker Chapter 29 Relativity Units of Chapter 29 The Postulates of Special Relativity The Relativity of Time and Time Dilation The Relativity of
More informationCollege Physics B - PHY2054C. Special & General Relativity 11/12/2014. My Office Hours: Tuesday 10:00 AM - Noon 206 Keen Building.
Special College - PHY2054C Special & 11/12/2014 My Office Hours: Tuesday 10:00 AM - Noon 206 Keen Building Outline Special 1 Special 2 3 4 Special Galilean and Light Galilean and electromagnetism do predict
More informationPHSC 1053: Astronomy Relativity
PHSC 1053: Astronomy Relativity Postulates of Special Relativity The speed of light is constant in a vacuum and will be the same for ALL observers, independent of their motion relative to the each other
More informationLimitations of Newtonian Physics
Limitations of Newtonian Physics 18 th and 19 th Centuries Newtonian Physics was accepted as an ultimate truth Science is never absolute Hundreds of experiments can t prove my theory right but only one
More informationRelativity. Class 16 Prof J. Kenney June 18, boss
Relativity Class 16 Prof J. Kenney June 18, 2018 boss Length contraction (moving sticks are shorter) A measuring stick at rest has a length Lo. When it is propelled at velocity v, it has a shorter length
More informationTest 3 results B A. Grades posted in Learn
Test 3 results Grades posted in Learn D C B A End of the Semester approaches - make sure that your test, clicker and homework grades are what you think they should be on Learn F Clicker Question: What
More informationWallace Hall Academy
Wallace Hall Academy CfE Higher Physics Unit 1 - Universe Notes Name 1 Newton and Gravity Newton s Thought Experiment Satellite s orbit as an Application of Projectiles Isaac Newton, as well as giving
More informationToday in Astronomy 102: Einstein studies gravity
Today in Astronomy 102: Einstein studies gravity The principle of equivalence Gravitational time dilation, specialrelativistic time dilation, and the Doppler effect Curved spacetime and the nature of tides
More informationChapter S3 Spacetime and Gravity Pearson Education, Inc.
Chapter S3 Spacetime and Gravity What are the major ideas of general relativity? Spacetime Special relativity showed that space and time are not absolute. Instead, they are inextricably linked in a four-dimensional
More informationEPGY Special and General Relativity. Lecture 4B
Lecture 4B In the previous lecture we found that the proper description of the universe is one consisting of a four-dimensional manifold (space) endowed with a Lorentzian metric, (of course we are restricting
More informationSpecial Relativity 05/09/2008. Lecture 14 1
How Fast Are You Moving Right Now? Special Relativity Einstein messes with space and time 0 m/s relative to your chair 400 m/s relative to earth center (rotation) 30,000 m/s relative to the sun (orbit)
More informationModern Physics. Light and Relativity
Modern Physics Light and Relativity Electromagnetism In the late 1800 s, Electricity and Magnetism were united as one force: Electromagnetism Electromagnetism In the late 1800 s, Electricity and Magnetism
More informationCURVED SPACE. 6 mon line of latitude. But you can get there in 3,605 miles if you fly
CURVED SPACE - J7 - ing your compass for 3,707 miles almost straight east, along their com 6 mon line of latitude. But you can get there in 3,605 miles if you fly CURVED SPACE along a great circle, heading
More informationChapter 37. Relativity. PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow
Chapter 37 Relativity PowerPoint Lectures for University Physics, 14th Edition Hugh D. Young and Roger A. Freedman Lectures by Jason Harlow Learning Goals for Chapter 37 Looking forward at why different
More informationMr Green sees the shorter, straight, green path and Mr. Red sees the longer, curved, red path.
Mr Green sees the shorter, straight, green path and Mr. Red sees the longer, curved, red path. In an accelerated frame, time runs slow compared to a non-accelerated frame. The Equivalence Principle tells
More informationRelativity. Physics April 2002 Lecture 8. Einstein at 112 Mercer St. 11 Apr 02 Physics 102 Lecture 8 1
Relativity Physics 102 11 April 2002 Lecture 8 Einstein at 112 Mercer St. 11 Apr 02 Physics 102 Lecture 8 1 Physics around 1900 Newtonian Mechanics Kinetic theory and thermodynamics Maxwell s equations
More informationExperimental Values of Lorentz Transformations of Mass and Time
Experimental Values of Lorentz Transformations of Mass and Time Lorentz Transformation Thought Experiment GPS Clock Calculations Pound-Rebka Experiment Triplet Paradox Experiment The Lorentz transformation
More informationLecture 10: General Relativity I
Lecture 10: General Relativity I! Einstein Tower Experiment! Gravitational redshifting! Strong Equivalence Principal! Read Chapter 8! Due to snow and confusion the mid-term is delayed to Thursday March
More informationAstronomy 122 Outline
Astronomy 122 Outline This Class (Lecture 19): Black Holes Next Class: The Milkyway Last Nightlab tonight! HW7 due on Friday. Mar Lecture report due in discussion class on April 5 th th. Nightlab report
More information7/5. Consequences of the principle of equivalence (#3) 1. Gravity is a manifestation of the curvature of space.
7/5 Consequences of the principle of equivalence (#3) 1. Gravity is a manifestation of the curvature of space. Follow the path of a light pulse in an elevator accelerating in gravityfree space. The dashed
More informationCHAPTER 2 Special Theory of Relativity-part 1
CHAPTER 2 Special Theory of Relativity-part 1 2.1 The Apparent Need for Ether 2.2 The Michelson-Morley Experiment 2.3 Einstein s Postulates 2.4 The Lorentz Transformation 2.5 Time Dilation and Length Contraction
More informationGravity and Spacetime: Why do things fall?
Gravity and Spacetime: Why do things fall? A painless introduction to Einstein s theory of space, time and gravity David Blair University of WA Abstract I present a simple description of Einstein s theory
More informationThe interpretation is that gravity bends spacetime and that light follows the curvature of space.
7/8 General Theory of Relativity GR Two Postulates of the General Theory of Relativity: 1. The laws of physics are the same in all frames of reference. 2. The principle of equivalence. Three statements
More informationThe result is; distances are contracted in the direction of motion.
The result is; distances are contracted in the direction of motion. t = t/(1 v 2 /c 2 ) 0.5 d = d(1- v 2 /c 2 ) 0.5 These are the Lorentz equations. The Twin-Paradox. A woman astronaut is going to fly
More informationSpace and Time Before Einstein. The Problem with Light. Admin. 11/2/17. Key Concepts: Lecture 28: Relativity
Admin. 11/2/17 1. Class website http://www.astro.ufl.edu/~jt/teaching/ast1002/ 2. Optional Discussion sections: Tue. ~11.30am (period 5), Bryant 3; Thur. ~12.30pm (end of period 5 and period 6), start
More informationRelativity and Black Holes
Relativity and Black Holes Post-MS Evolution of Very High Mass (>15 M Θ ) Stars similar to high mass except more rapid lives end in Type II supernova explosions main difference: mass of iron core at end
More informationExperimental Values of Lorentz Transformations of Mass and Time
Experimental Values of Lorentz Transformations of Mass and Time Measuring the Fitzgerald Contraction Lorentz Transformation Thought Experiment GPS Clock Calculations Pound-Rebka Experiment Triplet Paradox
More informationCAN A MOTHER BE YOUNGER THAN HER DAUGHTER? (and other curiosities of relativity) Everyday view (Newton and Galileo).
Everyday view (Newton and Galileo). Einstein s view (constancy of the speed of light). Two postulates of Special Relativity and their effect on space and time. Einstein s famous equation. CAN A MOTHER
More informationAstronomy 1 Fall 2016
Astronomy 1 Fall 2016 Lecture 14; November 10, 2016 Previously on Astro 1 Late evolution and death of intermediate-mass stars (about 0.4 M to about 4 M ): red giant when shell hydrogen fusion begins, a
More information0 : Einstein s postulates of Special Relativity
Class 2 : The Special Theory of Relativity Recap of Einstein s postulates Time dilation Length contraction Energy and momentum Causality 0 : Einstein s postulates of Special Relativity Consider a group
More informationTheory of General Relativity
Theory of General Relativity Expansion on the concept of Special relativity Special: Inertial perspectives are Equivalent (unaccelerated) General: All perspectives are equivalent Let s go back to Newton
More informationPHYSICS - CLUTCH CH 34: SPECIAL RELATIVITY.
!! www.clutchprep.com CONCEPT: INERTIAL REFERENCE FRAMES A reference frame is a coordinate system that you make measurements in, and there are two types: - Inertial reference frames, which move at velocity
More informationBlack Holes -Chapter 21
Black Holes -Chapter 21 The most massive stellar cores If the core is massive enough (~3 M ; total initial mass of star > 25 M or so), even neutron degeneracy pressure can be overwhelmed by gravity. A
More informationNo material object, particle or future
RELATIVITY MOMENTUM, MASS, ENERGY, AND GRAVITY Objectives Describe how an object s momentum changes as it approaches the speed of light. (16.1) Describe how mass and energy are related. (16.2) Describe
More informationChapter 36 The Special Theory of Relativity. Copyright 2009 Pearson Education, Inc.
Chapter 36 The Special Theory of Relativity Units of Chapter 36 Galilean Newtonian Relativity The Michelson Morley Experiment Postulates of the Special Theory of Relativity Simultaneity Time Dilation and
More informationModern Physics. Third Edition RAYMOND A. SERWAY CLEMENT J. MOSES CURT A. MOYER
Modern Physics Third Edition RAYMOND A. SERWAY CLEMENT J. MOSES CURT A. MOYER 1 RELATIVITY 1.1 Special Relativity 1.2 The Principle of Relativity, The Speed of Light 1.3 The Michelson Morley Experiment,
More informationRelativity. Astronomy 101
Lecture 29: Special & General Relativity Astronomy 101 Common Sense & Relativity Common Sense is the collection of prejudices acquired by the age of 18. Albert Einstein It will seem difficult at first,
More informationToday in Astronomy 102: Einstein studies gravity
Today in Astronomy 102: Einstein studies gravity q The principle of equivalence q Gravitational time dilation, specialrelativistic time dilation, and the Doppler effect q Curved spacetime and the nature
More informationUnit- 1 Theory of Relativity
Unit- 1 Theory of Relativity Frame of Reference The Michelson-Morley Experiment Einstein s Postulates The Lorentz Transformation Time Dilation and Length Contraction Addition of Velocities Experimental
More informationRelativity. An explanation of Brownian motion in terms of atoms. An explanation of the photoelectric effect ==> Quantum Theory
Relativity Relativity In 1905 Albert Einstein published five articles in Annalen Der Physik that had a major effect upon our understanding of physics. They included:- An explanation of Brownian motion
More informationGeneral Relativity and Black Holes
General Relativity and Black Holes Lecture 19 1 Lecture Topics General Relativity The Principal of Equivalence Consequences of General Relativity slowing of clocks curvature of space-time Tests of GR Escape
More informationLecture 18 Spacetime and Gravity A2020 Prof. Tom Megeath. Midterm 2 Grade Distribution. Review: Inertial Reference Frames
Lecture 18 Spacetime and Gravity A2020 Prof. Tom Megeath Midterm 2 Grade Distribution Review: Inertial Reference Frames Speed limit sign posted on spacestation. How fast is that man moving? The Solar System
More informationAstronomy 421. Lecture 24: Black Holes
Astronomy 421 Lecture 24: Black Holes 1 Outline General Relativity Equivalence Principle and its Consequences The Schwarzschild Metric The Kerr Metric for rotating black holes Black holes Black hole candidates
More informationAgenda. S3. Spacetime and Gravity. George Bush SOTU 2/1/06
S3. Spacetime and Gravity Agenda Nature conceals her secrets because she is sublime, not because she is a trickster. SOTU Flag Waving Speed of light Chapter S3 Spacetime and Gravity Lab 2 Measurement Lab
More informationEinstein s Special Theory of Relativity. Dr. Zdzislaw Musielak UTA Department of Physics
Einstein s Special Theory of Relativity Dr. Zdzislaw Musielak UTA Department of Physics OUTLINE Einstein s Miraculous Year 1905 Time and Space before 1905 Einstein s Paper # 3 Time and Space after 1905
More informationClass 5: Equivalence Principle
Class 5: Equivalence Principle In this class we will discuss the conceptual foundations of General Relativity, in which gravity may be associated with the reference frames in which perceive events Class
More informationEinstein in a Nutshell
Einstein in a Nutshell Richard Wolfson Benjamin F. Wissler Professor of Physics Middlebury College Insight Cruises/Scientific American January 15, 2011 Relativity in Recent News http://newscenter.berkeley.edu/2011/12/05/record-black-holes-bigger-than-our-solar-system/,
More information! Exam 2 in this classroom on Friday! 35 Multiple choice questions! Will cover material from Lecture 12 to 22.!
This Class (Lecture 24): Black Holes Are Fun Next Class: Death by Black Hole: Spaghettification Night Obs/Computer labs due in class on Nov 9 th. HW 2 due on the 7 th. Exam 2 on Friday!! Exam 2 in this
More informationOutline. General Relativity. Black Holes as a consequence of GR. Gravitational redshift/blueshift and time dilation Curvature Gravitational Lensing
Outline General Relativity Gravitational redshift/blueshift and time dilation Curvature Gravitational Lensing Black Holes as a consequence of GR Waste Disposal It is decided that Earth will get rid of
More informationLorentz Transformations and the Twin Paradox By James Carter
Lorentz Transformations and the Twin Paradox By James Carter The Lorentz transformation m = M/ 1-v 2 /c 2 is a principle of measurement that can be classed as one of the laws of physics. (A moving body
More informationGeneral Relativity and Cosmology. The End of Absolute Space Cosmological Principle Black Holes CBMR and Big Bang
General Relativity and Cosmology The End of Absolute Space Cosmological Principle Black Holes CBMR and Big Bang The End of Absolute Space (AS) Special Relativity (SR) abolished AS only for the special
More informationModern Physics Part 2: Special Relativity
Modern Physics Part 2: Special Relativity Last modified: 23/08/2018 Links Relative Velocity Fluffy and the Tennis Ball Fluffy and the Car Headlights Special Relativity Relative Velocity Example 1 Example
More informationSurvey of Astrophysics A110
Black Holes Goals: Understand Special Relativity General Relativity How do we observe black holes. Black Holes A consequence of gravity Massive neutron (>3M ) cannot be supported by degenerate neutron
More informationBasics of Special Relativity
Basics of Special Relativity You must understand special relativity in order to really understand general relativity. Here s a brief summary of the basic ideas and terminology of special relativity (there
More informationSpecial Theory of Relativity. The Newtonian Electron. Newton vs. Einstein. So if Newtonian Physics is wrong. It is all Relative.
Special Theory of Relativity Chapter 26 The Newtonian Electron Newtonian Theory (everything we have done so far in class) can be tested at high speeds by accelerating electrons or other charged particles
More informationCosmology - How the Universe Came to Be. PLATO: Cosmology
Cosmology - How the Universe Came to Be PLATO: Cosmology 1 Implications: PLATO: Cosmology 2 Implications: Today s best measurement of the Hubble constant: HHubble = 69.3 km/s per Mpc Universe is about
More informationIntroduction to General Relativity
Introduction to General Relativity 1 Recall Newtonian gravitation: Clearly not Lorentz invariant, since Laplacian appears rather than d'alembertian. No attempt to find Lorentz invariant equations that
More informationGravity: What s the big attraction? Dan Wilkins Institute of Astronomy
Gravity: What s the big attraction? Dan Wilkins Institute of Astronomy Overview What is gravity? Newton and Einstein What does gravity do? Extreme gravity The true power of gravity Getting things moving
More informationThe Problem of Slowing Clocks in Relativity Theory
The Problem of Slowing Clocks in Relativity Theory The basic premise of Relativity Theory is that the speed of light ( c ) is a universal constant. Einstein evolved the Special Theory on the assumption
More informationSpecial Relativity 1
Special Relativity 1 Special Relativity: A Summary Caitlyn Edwards Dr. Gan Modern Physics November 2017 Special Relativity 2 Abstract The physics of Einstein s theory of special relativity differs dramatically
More informationA100H Exploring the Universe: Black holes. Martin D. Weinberg UMass Astronomy
A100H Exploring the Universe: Black holes Martin D. Weinberg UMass Astronomy astron100h-mdw@courses.umass.edu March 22, 2016 Read: S2, S3, Chap 18 03/22/16 slide 1 Exam #2: March 29 One week from today!
More informationWhy do we need a new theory?
Lecture 7: General Relativity We now begin our foray into the beautiful, yet sophisticated theory of General Relativity. At first we will explain the need for a new theory and then outline the ideas. We
More informationCorrect Resolution of the Twin Paradox
Correct Resolution of the Twin Paradox Michael Huemer In the following, I explain the Twin Paradox, which is supposed to be a paradoxical consequence of the Special Theory of Relativity (STR). I give the
More informationClass 6 : General Relativity. ASTR398B Black Holes (Fall 2015) Prof. Chris Reynolds
Class 6 : General Relativity ASTR398B Black Holes (Fall 2015) Prof. Chris Reynolds RECAP! Einstein s postulates " Laws of physics look the same in any inertial frame of reference. " The speed of light
More informationA100 Exploring the Universe: Black holes. Martin D. Weinberg UMass Astronomy
A100 Exploring the Universe: Black holes Martin D. Weinberg UMass Astronomy weinberg@astro.umass.edu October 30, 2014 Read: S2, S3, Chap 18 10/30/14 slide 1 Sizes of s The solar neighborhood visualized!
More informationEinstein s Space and Time
Einstein s Space and Time Re-examining the Obvious Familiar things happen, and mankind does not bother about them. It requires a very unusual mind to make an analysis of the obvious." Alfred North Whitehead
More informationLecture 10: General Relativity I
Lecture 10: General Relativity I Einstein Tower Experiment Gravitational redshifting Strong Equivalence Principal Sidney Harris 10/2/13 1 O: RECAP OF SPECIAL RELATIVITY Einstein s postulates Laws of physics
More informationElements of Physics II
Physics 132: Lecture 23 Elements of Physics II Agenda for Today Special Theory of relativity Inertial vs. non-inertial reference frames Postulates of SR Consequences of SR Time dilation Length contraction
More informationBlack Holes in Terms of Escape Velocity. Agenda for Ast 309N, Nov. 27. How Big is the Event Horizon? The Anatomy of a (Simple) Black Hole
Agenda for Ast 309N, Nov. 27 Black Holes in Terms of Escape Velocity Optional HW 3 - due now; Quiz 8 Thursday Next week: repeat survey (Tues), Exam 3 (Thurs) Feedback on black hole index cards Black hole
More informationSpecial Relativity. Principles of Special Relativity: 1. The laws of physics are the same for all inertial observers.
Black Holes Special Relativity Principles of Special Relativity: 1. The laws of physics are the same for all inertial observers. 2. The speed of light is the same for all inertial observers regardless
More informationLecture 18 Vacuum, General Relativity
The Nature of the Physical World Lecture 18 Vacuum, General Relativity Arán García-Bellido 1 Standard Model recap Fundamental particles Fundamental Forces Quarks (u, d, c, s, t, b) fractional electric
More informationRelativity. April 16, 2014 Chapter 35 1
Relativity April 16, 2014 Chapter 35 1 Announcements! Next week: Review of entire course, no exam! Final exam Wednesday, April 30, 8-10 PM Location: BPS 1410 (this room) Comprehensive, covers material
More informationToday HW#4 pushed back to 8:00 am Thursday Exam #1 is on Thursday Feb. 11
Today HW#4 pushed back to 8:00 am Thursday Exam #1 is on Thursday Feb. 11 Bring a calculator and a #2 pencil Allowed 1 page notes (front and back) E=mc 2, General Relativity, and exam review ISP209s10
More informationBasic Physics. Remaining Topics. Gravitational Potential Energy. PHYS 1403 Introduction to Astronomy. Can We Create Artificial Gravity?
PHYS 1403 Introduction to Astronomy Basic Physics Chapter 5 Remaining Topics Gravitational Potential Energy Escape Velocity Artificial Gravity Gravity Assist An Alternate Theory of Gravity Gravitational
More informationSpecial Relativity. Frames of Reference. Introduction
Special Relativity Introduction In 1905 Albert Einstein introduced his theory of special relativity. With this theory Einstein sought to make the laws of motion consistent with James Clerk Maxwell's (1831-1879)
More informationSpecial Relativity: Derivations
Special Relativity: Derivations Exploring formulae in special relativity Introduction: Michelson-Morley experiment In the 19 th century, physicists thought that since sound waves travel through air, light
More informationModern Physics notes Spring 2005 Paul Fendley Lecture 35
Modern Physics notes Spring 2005 Paul Fendley fendley@virginia.edu Lecture 35 Gravity and clocks Curved spacetime Born, chapter III (most of which should be review for you), chapter VII Fowler, Remarks
More informationMotivation. The Speed of Light. The Speed of Light. In Water Things Look Like This. Introduction to Special and General Relativity
Introduction to Special and General Relativity Motivation: Michelson-Morley Experiment Induction versus Force Law The Basics Events Principles of Relativity Giving up on absolute space and time What Follows
More informationChapter 34: Spacetime and General Relativity
The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth, space by itself, and time by
More informationLecture 21: General Relativity Readings: Section 24-2
Lecture 21: General Relativity Readings: Section 24-2 Key Ideas: Postulates: Gravitational mass=inertial mass (aka Galileo was right) Laws of physics are the same for all observers Consequences: Matter
More informationSpecial theory of relativity
Announcements l CAPA #9 due Tuesday April 1 l Mastering Physics Chapter 35 due April 1 l Average on exam #2 is 26/40 l For the sum of the first two exams (80 points); l >=67 4.0 l 61-66 3.5 l 50-60 3.0
More informationSMMG: Relativity. Jack S. Calcut III
SMMG: Relativity Jack S. Calcut III October 8, 2005 1 Physics Observation # A Few Principles of Motion # Description of Motion of Objects Over Time 2 Newtonian Physics Laws: 1. (Inertia) Body in constant
More informationENTER RELATIVITY THE HELIOCENTRISM VS GEOCENTRISM DEBATE ARISES FROM MATTER OF CHOOSING THE BEST REFERENCE POINT. GALILEAN TRANSFORMATION 8/19/2016
ENTER RELATIVITY RVBAUTISTA THE HELIOCENTRISM VS GEOCENTRISM DEBATE ARISES FROM MATTER OF CHOOSING THE BEST REFERENCE POINT. GALILEAN TRANSFORMATION The laws of mechanics must be the same in all inertial
More informationRecall from last time
Welcome back to Physics 215 Today s agenda: Relative Motion Special relativity Forces Physics 215 Spring 2017 Lecture 05-1 1 Recall from last time If we want to use (inertial) moving frames of reference,
More informationToday in Astronomy 102: relativity, continued
Today in Astronomy 10: relativity, continued Einstein s procedures and results on the special theory of relativity. Formulas and numerical examples of the effects of length contraction, time dilation,
More informationEinstein s Relativity and Black Holes
Einstein s Relativity and Black Holes Guiding Questions 1. What are the two central ideas behind Einstein s special theory of relativity? 2. How do astronomers search for black holes? 3. In what sense
More informationLecture Outlines. Chapter 22. Astronomy Today 8th Edition Chaisson/McMillan Pearson Education, Inc.
Lecture Outlines Chapter 22 Astronomy Today 8th Edition Chaisson/McMillan Chapter 22 Neutron Stars and Black Holes Units of Chapter 22 22.1 Neutron Stars 22.2 Pulsars 22.3 Neutron-Star Binaries 22.4 Gamma-Ray
More informationRELATIVITY. The End of Physics? A. Special Relativity. 3. Einstein. 2. Michelson-Morley Experiment 5
1 The End of Physics? RELATIVITY Updated 01Aug30 Dr. Bill Pezzaglia The following statement made by a Nobel prize winning physicist: The most important fundamental laws and facts of physical science have
More informationModern Physics notes Spring 2006 Paul Fendley Lecture 35
Modern Physics notes Spring 2006 Paul Fendley fendley@virginia.edu Lecture 35 Gravity and clocks Curved spacetime Born, chapter III (most of which should be review for you), chapter VII Fowler, Remarks
More informationPhysics 107: Ideas of Modern Physics
Physics 107: Ideas of Modern Physics Exam 2 March 8, 2006 Name ID # Section # On the Scantron sheet, 1) Fill in your name 2) Fill in your student ID # (not your social security #) 3) Fill in your section
More informationPhysics 107: Ideas of Modern Physics
Physics 107: Ideas of Modern Physics Exam March 8, 006 Name ID # Section # On the Scantron sheet, 1) Fill in your name ) Fill in your student ID # (not your social security #) 3) Fill in your section #
More informationLecture 34. General relativity
Lecture 34 The Shape of Space General Relativity Curvature of Space Critical Density Dark Energy Apr 17, 2006 Astro 100 Lecture 34 1 General relativity So far, just needed simple Newton's Gravity. Because
More information