Special Relativity

1. VCE Physics Unit 3 Topic 3 Special Relativity The World at the Speed of Light. Einstein’s Contribution.

2. Unit Outline • To achieve the outcome the student should demonstrate the knowledge and skills to: • describe Maxwell’s prediction that the speed of light depends only on the electrical and magnetic properties of the medium it is passing through and not on the speed of the source or the speed of the medium; • contrast Maxwell’s prediction with the principles of Galilean relativity (no absolute frame of reference, all velocity measurements are relative to the frame of reference); • interpret the results of the Michelson Morley experiment in terms of the postulates of Einstein’s special theory of relativity; • the laws of physics are the same in all inertial frames of reference • the speed of light has a constant value for all observers; • compare Einstein’s postulates and the postulates of the Newtonian model; • use simple thought experiments to show that • the elapse of time occurs at different rates depending on the motion of the observer relative to the event; • spatial measurements are different when measured in different frames of reference; • explain the concepts of proper time and proper length as quantities that are measured in the frame of reference in which the objects are at rest; • explain movement at speeds approaching the speed of light in terms of the postulates of Einstein’s special theory of relativity; • model mathematically time dilation, length contraction and mass increase with respectively the equations t = toγ, L = Lo/γ, m = moγ where γ = 1/(1-v2/c2)1/2 • explain the relation between the relativistic mass of a body and the energy equivalent according to Einstein’s equation E = mc2 • explain the equivalence of work done to increased mass energy according to Einstein’s equation E = mc2 • compare special relativistic and non relativistic values for time, length and mass for a range of situations.

3. Galileo Galilei 1564 - 1642 Galilean Relativity One of the earliest of the great minds to ponder motion, both on Earth and in the heavens, was Galileo Galilei. He developed the principle of Galilean Relativity. This is best shown with a simple example: Imagine an observer in a house by the sea shore and another in the windowless hull of a ship. Neither will be able to determine that the ship is moving at constant velocity by comparing the results of experiments done inside the house or on the ship. In order to determine motion these observers must look at each other. • FRAMES OF REFERENCE • Frames of reference can be of 2 types: • Inertial Frames. These are systems (or groups of objects) which are either at rest or moving with constant velocity. • Non Inertial Frames. These are systems which are accelerating. Generalizing these observations Galileo postulated his relativity hypothesis: any two observers in inertial frames of reference with respect to one another will obtain the same results for all mechanical experiments. There is no absolute inertial frame of reference: all velocity measurements are relative to the frame of reference.

4. VTRAIN = 25.0 ms-1 VBALL = 5.0 ms-1 Stationary observer Galilean Motion In Galileo’s world, the idea of relative motion is clearly understood. This can be shown with a simple example. A train carriage is travelling to the right at a constant velocity of 25.0 ms-1. A boy standing in the carriage throws a ball to the right at a constant velocity of 5.0 ms-1. The boy in the carriage sees the ball travel away from him at 5.0 ms-1 But, an observer standing beside the track, sees the ball moving to the right at 30.0 ms-1. So what is the ball’s “correct” speed ? 5.0 ms-1 or 30.0 ms-1? Remember, according to Galileo, there is no absolute inertial frame of reference: all velocity measurements are relative to the frame of reference. BOTH answers are CORRECT. There is no single “correct” answer. The speed of an object depends on where the observer is when the speed was measured.

5. Isaac Newton, aged 26 Isaac Newton The next great mind to influence mankind’s understanding of the operation of the universe was Isaac Newton (1642 – 1727), when he developed his 3 laws, first mentioned in his 1687 book Philosophiaenaturalis principia mathematica (or just Principia). Law 1 (The Law of Inertia) A body will remain at rest, or in a state of uniform motion, unless acted upon by a net external force. Law 2 The acceleration of a body is directly proportional to net force applied and inversely proportional to its mass. Mathematically, a = F/m more commonly written as F = ma These Laws explained Galilean relativity and using Newton's laws, physicists in the 18th and 19th century were able to predict the motions of the planets, moons, comets, cannon balls, etc. Law 3 (Action Reaction Law) For every action there is an equal and opposite reaction. In classical Newtonian mechanics, time was universal and absolute.

6. The Clouds Gather Newton aged 38 For more than two centuries after its inception (in about the 1680’s), the Newtonian view of the world ruled supreme, to the point that scientists developed an almost blind faith in this theory. And for good reason: there were very few problems which could not be accounted for using this approach. Nonetheless, by the end of the 19th century, new experimental evidence, difficult to explain using the Newtonian theory, began to accumulate, and the novel theories required to explain this data would soon replace Newtonian physics.

7. Lord Kelvin 19th Century Clouds • In 1884 Lord Kelvin (of temperature scale fame) in a lecture delivered in Baltimore, Maryland, mentioned the presence of “Nineteenth Century Clouds'' over the physics of the time, referring to certain problems that had resisted explanation using the Newtonian approach. • Among the problems of the time were: • Light had been recognized as a wave, but the properties (and the very existence!) of the medium that conveys light appeared inconsistent. • The equations describing electricity and magnetism were inconsistent with Newton's description of space and time. • The orbit of Mercury, which could be predicted very accurately using Newton's equations, presented a small but disturbingly unexplained discrepancy between the observations and the calculations. • Materials at very low temperatures do not behave according to the predictions of Newtonian physics. • Newtonian physics predicted that an oven at a stable constant temperature has infinite energy.

8. Albert Einstein Mercury The Revolution The first quarter of the 20th century witnessed the creation of the revolutionary theories which explained these phenomena. They also completely changed the way we understand Nature. The first two problems concerning the nature of light and electricity and magnetism required the introduction of the Special Theory of Relativity. The third item concerning Mercury’s orbit required the introduction of the General Theory of Relativity. The last two items low temperature materials and infinite energy ovens can be understood only through the introduction of a completely new mechanics: quantum mechanics. The new theories that superseded Newton's had the virtue of explaining everything Newtonian mechanics did (with even greater accuracy) while extending our understanding to an even wider range of phenomena.

9. Charles Coulomb James Maxwell Maxwell’s Contribution One interesting consequence of Maxwell’s unification is that you can calculate the velocity of electromagnetic waves based on properties of capacitors and inductors. • Throughout 1700’s and 1800’s, many individual laws about electricity and magnetism had been discovered, such as Coulomb’s law of electrostatic force. c = Speed of EM Waves μ0 = Permeability of free space ε0 = Susceptibility of free space In Maxwell’s own words: This velocity is so nearly that of light, that it seems we have strong reasons to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws. James Clerk Maxwell (1831-1879) had, by 1855, unified some laws and finally by 1873 had found that all of these laws could be summarised by four partial differential equations. A triumph of unification! (Which of course is the holy grail of Physics)

10. 19th Century Physics • Around this time, Physicists were trying to find a way to measure the ABSOLUTE VELOCITY of an object relative to some fixed point which was COMPLETELY AT REST. • But what, in our universe, is completely at rest ? Certainly not the Earth, which as well as spinning on its axis at 500 ms-1 (1800 kmh-1), travels around the sun at 30 kms-1 (108,000 kmh-1). The sun, of course, is in orbit around the centre of our galaxy at 250 kms-1 (900,000 kmh-1). And our galaxy is in some kind of orbit amongst the other galaxies (velocity unknown). SO MUCH FOR USING THE EARTH AS A STATIONARY LABORATORY.

11. The Ether By the 1880’s scientists knew that waves transferred energy from one place to another and their movement depended upon them travelling through a MEDIUM (water waves in water, sound waves in air and other materials). This led them to believe that ALL waves required a medium for travel, and so to development of the concept of the luminiferous ether, (or aether) which was the name given to the medium through which light supposedly travelled from the sun to earth. The ether was a hypothetical medium in which it was believed that electromagnetic waves (visible light, infrared radiation, ultraviolet radiation, radio waves, X-rays), would propagate.

12. Speed = c Speed = c Ether Speed = v Ether Speed = v Speed = c + v Speed = c Actual result The Speed of Light In 1887, Albert A. Michelson and Edward W. Morley working at the Case School in Cleveland, Ohio, tried to measure the speed of the ether, (or more precisely the speed of the Earth through the ether). They expected to find the speed of light (symbol, c) differed depending on its direction with respect to the “ether wind”. This result would accord with Galilean relativity. Michelson explained his experiment to his children this way: two swimmers race; one struggles upstream and back while the other swims the same distance across and back. The second swimmer will always win, if there is any current in the river. The result of the Michelson-Morley experiment was that the speed of the Earth through the ether (or the speed of the ether wind) was zero. Therefore, they also showed that there is no need for any ether at all, and it appeared that the speed of light (in a vacuum) was independent of the velocity of the observer! Expected result

13. ether Michelson Morley in Detail The experiment was set up using a “monochromatic” (single colour) light source split into two beams. Using an interferometer floating on a pool of mercury, they tried to determine the existence of an ether wind by observing interference patterns between the two light beams. One beam travelling with the "ether wind" as the earth orbited the sun, and the other at 90º to the ether wind. The interference fringes produced by the two reflected beams were observed in the telescope. It was found that these fringes did not shift when the table was rotated. That is, the time required to travel one leg of the interferometer never varied with the time required to travel its normal counterpart. They NEVER got a changing interference pattern.

14. Double Slit Incident Light Interference Pattern Michelson Morley in Detail 2 The travel times for the two beams were compared in a very sensitive manner. If the travel times were different the two beams, when combined, would have produced an “interference pattern”. This is the same as the pattern produced when a monochromatic beam of light is allowed to pass through two narrow slits. NO CHANGE IN THE PATTERN COULD EVER BE DETECTED WHEN THE EQUIPMENT TURNED THROUGH 900 Michelson and Morley repeated their experiment many times up until 1929, but always with the same results and conclusions. Michelson won the Nobel Prize in Physics in 1907. Probably the only prize ever awarded for a failed experiment. The result proved to be an extremely perplexing and frustrating to the physicists of the day who firmly believed in the ether theory. The result proved, beyond doubt, that the speed of light is CONSTANT, no matter how fast an observer was travelling when measuring it. In other words, it led to the death of the ether concept and, more importantly, the death of Galilean Relativity It took nearly 20 years to develop the theory to match this experimental result.

15. 1000 ms-1 100 ms-1 10 ms-1 I agree it’s c 1000 ms-1 c = 3 x 108 ms-1 I agree it’s c 10 ms-1 Newton versus Maxwell Under Galileo and Newton, the speed of light would vary depending the inertial frame of reference. No, its c - 1000 The Speed of Light (c) is 3 x 108 ms-1 No, its c - 100 No, its c - 10 Whilst under Maxwell, the speed of light is constant no matter what the inertial frame of reference. I agree it’s c 100 ms-1

16. Fig 1 Fig 2 Einstein’s Insight It was Einstein who finally found an answer to the seemingly unbelievable result – that the speed of light in inertial frames of reference is always the same. The answer was to change the understanding of the term simultaneity. Two physical events that occur simultaneously in one inertial frame are only simultaneous in any other inertial frame if they occur at the same time and at the same place. This means: TIME IS RELATIVE! The figures to the left, seen from two different inertial frames, help clarify the concept of simultaneity: Fig 1:In the inertial frame of the wagon, the lamps are switched on simultaneously and the two light impulses reach the girl at the same time. Fig 2:In the inertial frame of the observer outside the wagon, it seems that the left lamp is switched on first, although for the girl in the wagon the lamps are switched on simultaneously.

17. Speeds of objects Inertial Frames Non inertial Frames Introducing Relativity Special Relativity deals with large velocity differences between frames of reference (Inertial Frames). General Relativity deals with large acceleration differences between frames of reference (Non inertial Frames) Einstein developed the theory of Special Relativity in 1905 and the more comprehensive and far more complex theory of General Relativity about 10 years later. At low speeds, Newton’s laws are adequate to explain motion. But the relativity theories need to be applied to objects travelling at or near c, the speed of light. Newton’s Laws Plus Fake Forces Very much less than c Newton’s Laws Close to c General Relativity Special Relativity

18. Einstein – The Patent Clerk SpecialRelativity • The theory of Special Relativity was developed by Einstein in 1905 when, as a 26 year old, he was working as a clerk in the Swiss Government Patents Office. • Basically the theory states: 1. The laws of physics are identical for all observers, provided they are moving at constant velocity with respect to one another, i.e., they are all in inertial frames of reference. 2. The SPEED OF LIGHT is CONSTANT. This is true no matter how fast the observer is travelling relative to the source of light. This theory was completely at odds with the classical physics of Aristotle, Galileo and Newton.

19. Earliest known picture of Einstein - as a 3 year old Einstein- aged 14 Einstein’s Early History An only child, Albert Einstein was born in Ulm, Germany, on the 14th of March 1879. His parents - Herman, an electrical engineer, and Pauline, were worried their son may be retarded, as he did not speak his first words until after his 3rd birthday. In 1894, as a 15 year old, he was expelled from Catholic College for disruptive behaviour. In 1896, he managed to talk himself into a place at the Swiss Federal Polytechnic Academy in Zurich, graduating in 1900 (at age 21), as a secondary school teacher of Maths and Physics. At age 23 he married his university sweetheart MilevaMaric

20. Einstein and 1st wife Mileva From Student to Professor Einstein did not take up a teaching position immediately, but in 1902 obtained a position as a Patent’s Clerk at the Swiss Patents Office in Bern where he worked until 1909. During his time there he completed an astonishing number of papers on theoretical physics, mostly completed in his spare time. He submitted one of his papers to the University of Zurich for which he obtained his PhD degree in 1905. In 1908, he submitted a further paper to the University of Bern leading to an offer of employment as a lecturer. In 1909 he received an offer of an associate professorship in physics at the University of Zurich. He jumped into various university professorships throughout German speaking Europe, finally landing Europe’s most prestigious post as physics professor at Kaiser-Wilhelm Gesellschaft in Berlin.

21. Special Relativity • After studying the results of the Michelson - Morley experiments, Einstein proposed the following: • THE SPEED OF LIGHT IS ALWAYS THE SAME, REGARDLESS OF WHO MEASURES IT AND HOW FAST THEY ARE GOING RELATIVE TO THE LIGHT SOURCE. • From this simple statement a number of startling consequences arise:

22. Time Dilation The first of these consequences is known as “Time Dilation” • It requires that, depending on the motion of an observer, time must pass at different rates. • Two observers, one stationary, the other moving near the speed of light, observe the same event. • In order for each to get the same speed for the event, each must see it occur during different time intervals. • The faster the observer travels the slower the rate at which his time appears to pass to stationary observer.

23. Photon Earth Earth Earth Time Dilation Mirror In order to demonstrate this change in the rate at which time passes, let us produce a simple clock. A photon of light (travelling at c) is bouncing backwards and forwards between two parallel mirrors. One back and forth motion of the photon represents one tick of the clock. Mirror An observer, stationary in space with respect to the Sun, sees the Earth (with its attached “clock”), go zooming past on its orbit around the sun. “1 Tick” In the time, we (standing on Earth), see the photon bounce back and forth once, the space observer sees the Earth move a little way along its orbit path. Hence, if the photon is to strike the mirrors, the space observer requires it to travel on a diagonal path, as shown.

24. Time Dilation Speed = c Short Distance Long Distance Speed = c Earth Earth Earth and this gets bigger this must also get bigger If this has to stay the same Clock as seen by Earth bound observer Clock as seen by Space observer Since the photon MUST travel at the Speed of Light, c, the only logical outcome for the space observer is to conclude that the photon on Earth takes a LONGER TIME to cover the APPARENTLY LONGER DISTANCE it needs to travel. The space observer thus concludes the Earth clock runs slow compared to his clock. This same argument holds true for the earth bound observer, who would see the space observer’s clock running slow. Remember, Speed = distance time Thus, MOVING CLOCKS RUN SLOW.

25. to 1 t = γ = where v2 v2 1 - 1 - So c2 c2 Time Dilation The mathematical representation of Time Dilation is shown in the formula: t = γto where: t = moving observer’s time as measured by the stationary observer. to = time measured by stationary observer’s clock. (“proper time”) v = speed of moving observer. c = Speed of Light. • The formula has a number of consequences: • If v << c, the term v2/c2 approaches zero and the square root term approaches 1. • Thus t = to and no change in time (the rate at which time passes) is observed. • As v approaches c (say v = 0.9c), the stationary observer sees the moving observer’s clock tick over only 0.4 sec for every 1 second on his own clock. • If v = c, the term v2/c2 = 1 and the square root term becomes zero. Dividing a number by zero equals infinity. • Thus, when v = c the time interval becomes infinite. In other words, time stops passing. γ is called the “Lorentz Factor” My Clock My observation of the moving clock

26. The Twins Paradox Twins, Adam and Eve, are thinking how they will age if one of them goes on a space journey, travelling at say 0.866c. Will Eve be younger, older, or remain the same age as her brother if she does a round trip of some years duration ? Assume that Adam and Eve’s clocks are synchronized before Eve leaves. At 0.866c, Adam will “see” Eve’s time pass at exactly half the rate his time passes. So when Eve returns, she will have aged by 1 year for every 2 years Adam has aged. Thus, Eve is younger than Adam. However, can you turn the discussion around and say that Eve has been at rest in her space-ship while Adam has been on a "space journey" with planet Earth? In that case, Adam must be younger than Eve at the reunion! Adam is at rest all the time on Earth, i.e., he is in the same inertial frame all the time, but Eve is not - she will have felt forces when her space-ship accelerates and retards, and Adam will not feel such forces. So the argument is not an interchangeable one. The travelling twin is the younger upon their reunion. P.S. Eve's space-ship has to consume fuel, which means that it costs to keep yourself young!

27. y v = 0 v = 0.8c x This must also be less to keep this the same with this having become less Length Contraction The 2nd consequence of light having a constant speed is Length Contraction. An observer sees two set squares, one stationary in his inertial frame, the other in an inertial frame moving near the speed of light. Remember: Speed = distance time How does the speed difference affect the apparent size of the set square ? Remember the stationary observer sees the moving “frames” clock running slow. To get the same value for c in each frame, he must measure the length of the set square (in the direction of travel) to be shorter than his own stationary ruler. IMPORTANT NOTE: The length contraction only occurs in the direction of travel (x direction) and measurements at right angles to that direction are unaffected ! (no contraction in the y direction)

28. v = 0.86c v = 0.1c v = 0.90c v = 0.98c Length Contraction Land available on Mars and its free ! The Martians send an advertising rocket to fly past Earth. What is the best speed for the rocket so stationary Earthlings can read the sign ?

29. Length Contraction The formula has a number of consequences: 1. If the v <<c, the square root term approaches 1 and the length is unaffected, ie. L = Lo 2. As v approaches c, v2/c2 approaches 1 and the square root term approaches 0. Thus, the length approaches 0 ie. L = 0. v2 1 - Lo( ) So, L = c2 The mathematical representation of Length Contraction is shown in the formula. L = Lo/γ Where: L = Length of moving object as measured by stationary observer. Lo = Length of stationary object measured by stationary observer. (“Proper Length”) v = speed of moving object. c = Speed of Light. So, a photon of light travelling at c from the Sun to the Earth makes the journey in no time and travels no distance !!!!!! The moving observer’s view of the length contracted world The stationary observer’s view of the length contracted Superman

30. Mass Dilation The third effect of the invariance of the speed of light is mass dilation. As the speed of an object increases so too does its mass !!!!!! Under Einstein mass is whatever we measure it to be. We must use an operational definition for mass. He showed that the mass of an object depends on how fast the object is moving relative to a stationary observer. Under Newton, mass is an absolute quantity for each object and it is conserved, never changing for each object. This invariance of mass is the basis of Newton’s 2nd Law (F = ma), and our own every day experience seems to verify that mass is absolute.

31. Mass – Newton v Einstein Einstein’s relativity deals with faster speeds. Newtonian physics gives good results at speeds less than 10% of the speed of light. The mass of an object does not change with speed, it changes only if we cut off or add a piece to the object . As an object moves faster its mass increases. (As measured by a stationary observer). F = ma means that to accelerate a mass requires a force, by supplying sufficient force you can make an object go as fast as you like. Mass approaches infinity as speed approaches c. To reach c would require infinite force. Since mass changes with speed, a change in K.E. must involve both a change in speed and a change in mass. At speeds close to c most of the change occurs to the mass. Kinetic Energy = ½mv2, since mass does not change an increase in KE means an increase in speed.

32. v2 1 - c2 m0 So, m = 6m0 4m0 Apparent Mass 2m0 m0 0 20 40 60 80 100 % of Speed of Light Speed of object as seen by a stationary observer Mass - How Fast, How Heavy ? The mass of an object at rest is called its rest mass (m0) At low velocities the increase in mass is small. An object travelling at 20% of the speed of light (60,000 kms-1) has an apparent mass only 2% greater than its rest mass (m0). As speed increases, apparent mass increases rapidly. Mathematically: m = γmo where: m = Apparent Mass of the object m0 = Rest Mass of the object v = speed of object. c = Speed of Light. 1. When v <<c, the square root term approaches 1, and m = m0 2. As v approaches c, the square root term approaches 0, and m approaches infinity. There is insufficient energy in the universe to accelerate even the smallest particle up to the speed of light !!!!!!!!!!

33. m0 v2 1 - m = c2 Energy & Mass Increasing the speed of a mass requires energy. The truth of this is best seen in interactions between elementary particles. For example, if a positron and an electron collide at low speed (so there is very little kinetic energy) they both disappear in a flash of electromagnetic radiation. The fact that feeding energy into a body increases its mass suggests that the rest mass m0 of a body, multiplied by c2, can be considered as a quantity of energy. Einstein recognised the fundamental importance of the interchangeability of mass and energy which is summarised in his famous equation: E = mc2 This EM radiation can be detected and its energy measured. It turns out to be 2m0c2 where m0 is the mass of the electron (and the positron). So each particle must have possessed so called “rest energy” of m0c2 where m is the Apparent Mass. Remember,

34. Rest Energy If an object is at rest it possesses “rest mass energy” or more simply “rest energy” A Hiroshima sized atomic bomb releases about 1014 Joules, (100,000 billion joules). How much mass has been converted ? Einstein’s equation is then written as: E = m0c2 E = m0c2 Thus m0 = (1014)/(3 x 108)2 = 1.1 x 10-3 kg = 1.1 g Where E = Energy (joules) m0 = Rest Mass (kg) c = 3 x 108 ms-1 As can be seen a tiny mass converts to a huge amount of energy How much energy does 1 kg of mass, at rest, represent ? E = m0c2 = (1)(3 x 108)2 = 9 x 1016 Joules This represents the average annual output of a medium sized Power Station

35. The relativistic energy of a particle can also be expressed in terms of its momentum (p) in the expression: E = mc2 = p2c2 + m02c4 Moving Mass As a mass begins to move it possesses BOTH rest mass energy AND energy of motion (Kinetic Energy). This is essentially defining the kinetic energy of an object as the excess of the object’s energy over its rest mass energy. For low velocities this expression approaches the non-relativistic kinetic energy expression. Expressing Einstein’s equation as: E = mc2 Includes both rest mass and kinetic energy The Kinetic Energy of a fast moving particle can be calculated from: K.E. = mc2 – m0c2 For v/c << 1, KE = mc2 – m0c2≈ ½ m0v2 As an object’s speed increases more and more of the energy goes into increasing mass and less and less into increasing velocity.

36. The Speed of Light. A Limit ? These equations together are called “The Lorentz Transforms”. Each Lorentz Transform has a limiting factor. If v > c, then: • t becomes negative, and time runs backward !!!!!! (the bullet hits you BEFORE it is fired from the gun). • L becomes negative, and an object has a length less than zero!!!!!, • m becomes negative and objects have a mass less than zero!!!!! • Thus, c (the speed of light) is the limiting factor. • Speeds greater than c are not possible.

37. v =0.75c v’=0.75c v” = 0.96c Relativistic Speed Addition Imagine that you are standing between two space-ships moving away from you. One space-ship moves to the left with a speed of 0.75 c (relative to you) and the other one moves to the right also with a speed of 0.75 c (again relative to you). At what speed will each space-ship see the other moving away? 0.75 c + 0.75 c = 1.5 c? No, their relative speed will be 0.96 c (according to the relativistic addition of velocities), and it cannot, of course, be faster than the speed of light c. However, in special relativity, the velocities are added together as In classical Newtonian mechanics, two different velocities and are added together by the formula v” = v’ + v where v” is the sum of the two velocities. v” = v’ + v 1 + v.v’ c2 This formula is called the relativistic addition of velocities. Note that if v’ = c and/or v = c, then v” = c, and for small velocities v, v’ << c, then the classical formula is regained.

38. Special RelativityExperimental Proofs Experimental proof of the for each of the areas of Time Dilation, Length Contraction and Mass Dilation are available on Earth. These are shown below.

39. f = f0c – v c + v Relativistic Doppler Effect Suppose a source emits light of frequency f (or wavelength λ, remember that c = fλ). Then, an observer moving with a speed v away from the source, will observe the frequency: The Doppler Effect: Motion towards or away from a source will cause a change in the observed frequency f (or wavelength λ) as compared to the emitted frequency. All wave phenomena (e.g., water, sound, and light) behave in this way. This formula is called the relativistic Doppler formula. Note that f < f0 for all 0 < v < c, i.e., the frequency which the observer sees, is smaller than the "original" frequency in the inertial frame of the source. If you are driving towards a red traffic light (λ0= 650 nm) at a speed of approximately v = 0.17 c, the traffic light will actually appear to be green (λ = 550 nm)! (0.17 c is approximately 5.0 x107 ms-1.) Observers moving away from the source will see a redshift in the frequency of the light, since light with lower frequencies are "more red" and light with higher frequencies are "more blue." While observers moving towards the source will see a corresponding blueshift.

40. Special RelativityConclusion • I leave the last word to Einstein himself who, when asked to describe Special Relativity in laymen's terms, said: • “Put your hand on a hot stove for a minute, and it seems like an hour. • Sit with a pretty girl for an hour and it seems like a minute. • That’s relativity”

41. Ollie Leitl 2005 C THE END