Chapter 18

Electromagnetic Waveforms The and fields are perpendicular to each other Both fields are perpendicular to the direction of motion Therefore, electromagnetic waves are transverse waves With all periodic waves Since v = c in a vacuum [11.1]

Electromagnetic Waves, Summary A static electric charge produces an electric field. A uniformly changing (moving) electric field produces an magnetic field A uniformly changing (moving) magnetic field produces a electric field **But NONE of these produces an EM WAVE. For this you need an accelerating charge.**

Velocity of Light c = 3 x 10 8 m/s (In a vacuum) Slower values in other mediums, even air slows down light, but frequency will stay the same

Frequency, Wavelength and Velocity Wavelength alters along with velocity in order to keep frequency constant Objects’ COLOR is determined by frequency, NOT wavelength Wavelengths normally listed in the EM spectrum for the visual range are VACUUM wavelengths (in space) As light passes from that vacuum of space into a medium with a higher index of refraction, its velocity is reduced, and thus wavelength must also reduce in order to preserve frequency and color

The Spectrum of EM Waves Forms of electromagnetic waves exist that are distinguished by their frequencies and wavelengths c = ƒλ Wavelengths for visible light range from 400 nm to 700 nm There is no sharp division between one kind of em wave and the next

The EM Spectrum Note the overlap between types of waves Visible light is a small portion of the spectrum Types are distinguished by frequency or wavelength

Radiowaves Radio Waves Used in radio and television communication systems Wavelengths range from 100s of meters to less than a cm

Radio Telescopes Large dish focuses the energy of radio waves onto a small receiver (antenna) Amplified signals are stored in computers and converted into images, spectra, etc.

Radio Interferometry Just as for optical telescopes, the resolving power of a radio telescope is  min = 1.22 /D. For radio telescopes, this is a big problem: Radio waves are much longer than visible light  Use interferometry to improve resolution!

Microwaves Wavelengths from about 1 mm to 30 cm Well suited for radar systems Microwave ovens are an application

Infrared Infrared waves Incorrectly called “heat waves” 1mm down to 700nm Produced by hot objects and molecules Readily absorbed by most materials

Visible Light Visible light Part of the spectrum detected by the human eye Most sensitive at about 560 nm (yellow-green)

Ultraviolet Ultraviolet light Covers about 400 nm to 0.6 nm Sun is an important source of UV light Most UV light from the sun is absorbed in the stratosphere by ozone

X-rays Most common source is acceleration of high-energy electrons striking a metal target Used as a diagnostic tool in medicine

Gamma Rays Gamma rays Emitted by radioactive nuclei Highly penetrating and cause serious damage when absorbed by living tissue

18.2

Proving Light Is A Wave Thomas Young, in 1807, used Diffraction to prove that light experiences both Constructive and Destructive Interference.

Diffraction The shape of a wave front is altered (bent) as it passes through a hole or slit in another medium. A Diffraction Grating is a screen with a series of slits which create constructive/destructive interference patterns A Spectrometer uses a diffraction grating to create a spectrum measuring the wavelengths on incoming light. This can be used to identify materials emitting that light

Diffraction

Polarization Light travels as a transverse wave, and it can thus displace within a plane with a specific orientation. White Light consists of all wavelengths essentially travelling in all polarizations – it is UNpolarized. Polarization of a light wave is defined by the orientation of the Electric Wave

Polarizers Filter out all light wave polarizations EXCEPT one The light transmitted through a polarizer is now “polarized”—it has a single polarization Can be used to block out some portion of sunlight (sunglasses), create images on an LCD screen by filtering certain values of RGB light and even to identify mineral composition of rocks viewed in thin section

18.3

Foundation of Special Relativity Reconciling of the measurements of two observers moving relative to each other Normally observers measure different speeds for an object Special relativity relates two such measurements **Rests on the foundation that the speed of light (c) is the same for ALL observers, regardless of either THEIR motion or any motion of the light SOURCE.**

Consequences of SR Time Dilation Length Contraction Increased Mass of particles Loss of Simultaneity **But FIRST---a little historical perspective….**

Galilean Relativity Choose a frame of reference Necessary to describe a physical event According to Galilean Relativity, the laws of mechanics are the same in all inertial frames of reference An inertial frame of reference is one in which Newton’s Laws are valid Objects subjected to no forces will move in straight lines

Galilean Relativity – Example A passenger in an airplane throws a ball straight up It appears to move in a vertical path This is the same motion as when the ball is thrown while at rest on the Earth The law of gravity and equations of motion under uniform acceleration are obeyed

Galilean Relativity – Example There is a stationary observer on the ground Views the path of the ball thrown to be a parabola The ball has a velocity to the right equal to the velocity of the plane

Galilean Relativity – Example The two observers disagree on the shape of the ball’s path Both agree that the motion obeys the law of gravity and Newton’s laws of motion Both agree on how long the ball was in the air Conclusion: There is no preferred frame of reference for describing the laws of mechanics

Galilean Relativity – Limitations Galilean Relativity does not apply to experiments in electricity, magnetism, optics, and other areas Results do not agree with experiments The observer should measure the speed of the pulse as v+c Actually measures the speed as c

Luminiferous Ether 19 th Century physicists compared electromagnetic waves to mechanical waves Mechanical waves need a medium to support the disturbance The luminiferous ether was proposed as the medium required (and present) for light waves to propagate Present everywhere, even in empty space Massless, but rigid medium Could have no effect on the motion of planets or other objects

Verifying the Luminiferous Ether Associated with an ether was an absolute frame where the laws of e & m take on their simplest form Since the earth moves through the ether, there should be an “ether wind” blowing If v is the speed of the ether relative to the earth, the speed of light should have minimum (b) or maximum (a) value depending on its orientation to the “wind”

Michelson-Morley Experiment First performed in 1881 by Michelson Repeated under various conditions by Michelson and Morley Designed to detect small changes in the speed of light By determining the velocity of the earth relative to the ether

Michelson-Morley Equipment Used the Michelson Interferometer Arm 2 is aligned along the direction of the earth’s motion through space The interference pattern was observed while the interferometer was rotated through 90° The effect should have been to show small, but measurable, shifts in the fringe pattern

Michelson-Morley Results Measurements failed to show any change in the fringe pattern No fringe shift of the magnitude required was ever observed Light is now understood to be an electromagnetic wave, which requires no medium for its propagation The idea of an ether was discarded The laws of electricity and magnetism are the same in all inertial frames The addition laws for velocities were incorrect

Lorentz-FitzGerald Contraction Proposed in 1892 by G. Fitzgerald to retain the aether wind. Every object moving at speed v contracts along the direction of motion by a factor equal to Where  = v /c Re-emerged over a decade later as part of Einstein’s Special Theory of Relativity

Albert Einstein 1879 – published four papers 2 on special relativity 1916 published about General Relativity Searched for a unified theory Never found one

Einstein’s Principle of Relativity Resolves the contradiction between Galilean relativity and the fact that the speed of light is the same for all observers Postulates The Principle of Relativity: All the laws of physics are the same within all inertial frames The Constancy of the Speed of Light: the speed of light in a vacuum has the same value in all inertial reference frames, regardless of the velocity of the observer or the velocity of the source emitting the light

The Principle of Relativity This is a sweeping generalization of the principle of Galilean relativity, which refers only to the laws of mechanics The results of any kind of experiment performed in a laboratory at rest must be the same as when performed in a laboratory moving at a constant speed past the first one No preferred inertial reference frame exists!!! It is impossible to detect absolute motion!!!

Consequences of Special Relativity Restricting the discussion to concepts of length, time, and simultaneity In relativistic mechanics There is no such thing as absolute length There is no such thing as absolute time Events at different locations that are observed to occur simultaneously in one frame are not observed to be simultaneous in another frame moving uniformly past the first

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 the mirror The laser emits a pulse of light directed at the mirror (event 1) and the pulse arrives back after being reflected (event 2)

Time Dilation, Moving Observer Observer O’ carries a clock She uses it to measure the time between the events (Δt S ) t S is the proper time (see forward 5 slides for proper time) She observes the events to occur at the same place Δt S = distance/speed = (2d)/c

Time Dilation, Stationary Observer Observer O is a stationary observer on the earth He observes the mirror and O’ to move with speed v By the time the light from the laser reaches the mirror, the mirror has moved to the right The light must travel farther with respect to O than with respect to O’

Time Dilation, Observations Both observers must measure the speed of the light to be c The light travels farther for O The time interval, Δt M, for O is longer than the time interval for O ', Δt S

Time Dilation, Time Comparisons where Observer O measures a longer time interval than observer O ' d

Time Dilation, Summary The time interval Δt between two events measured by an observer moving with respect to a clock is longer than the time interval Δt S between the same two events measured by an observer at rest with respect to the clock A clock moving past an observer at speed v runs more slowly than an identical clock at rest with respect to the observer by a factor of  -1

Identifying Proper Time The time interval Δt S is called the proper time The proper time is the time interval between events as measured by an observer who sees the events occur at the same position You must be able to correctly identify the observer who measures the proper time interval

Alternate Views The view of O’ that O is really the one moving with speed v to the left and O’s clock is running more slowly is just as valid as O’s view that O’ was moving The principle of relativity requires that the views of the two observers in uniform relative motion must be equally valid and capable of being checked experimentally

Time Dilation – Generalization All physical processes slow down relative to a clock when those processes occur in a frame moving with respect to the clock These processes can be chemical and biological as well as physical Time dilation is a very real phenomena that has been verified by various experiments

Example 1 A college physics laboratory is under observation by aliens traveling on an asteroid. An undergrad seen measuring the period of a mass oscillating on a spring gets a value of 2.00 s. Given that the aliens are cruising by at a constant speed of 0.50c, what period will they determine? Given: v = 0.50c and the proper time measured by the student, ∆t S = 2.00 s. Find: The period determined by the aliens ∆t M

Example 1 Solution: Time dilation problem Use Eq. (26.2)

Time Dilation Verification – Muon Decays Muons are unstable particles that have the same charge as an electron, but a mass 207 times more than an electron Muons have a half-life of Δt S = 2.2µs when measured in a reference frame at rest with respect to them (a) Relative to an observer on earth, muons should have a lifetime of  Δt S (b) A CERN experiment measured lifetimes in agreement with the predictions of relativity

The Twin Paradox – The Situation A thought experiment involving a set of twins, Speedo and Goslo Speedo travels to Planet X, 20 light years from earth His ship travels at 0.95c After reaching planet X, he immediately returns to earth at the same speed When Speedo returns, he has aged 13 years, but Goslo has aged 42 years

The Twins’ Perspectives Goslo’s perspective is that he was at rest while Speedo went on the journey Speedo thinks he was at rest and Goslo and the earth raced away from him on a 6.5 year journey and then headed back toward him for another 6.5 years The paradox – which twin is the traveler and which is really older?

The Twin Paradox – The Resolution Relativity applies to reference frames moving at uniform speeds The trip in this thought experiment is not symmetrical since Speedo must experience a series of accelerations during the journey Therefore, Goslo can apply the time dilation formula with a proper time of 42 years This gives a time for Speedo of 13 years and this agrees with the earlier result There is no true paradox since Speedo is not in an inertial frame

Example 2 The nearest galaxy to ours is the shapeless star-island known as the Magellanic Cloud (about 1.70 x 10 5 ly distance). Assuming you can get up to a speed of c in a negligible amount of time, how long would you say the trip to that galaxy will take? Given: v = c, L S = 1.70 x 10 5 ly (as measured by an imaginary, stationary ruler). Find: ∆t S (proper time – flight time of traveler’s clock)

Example 2 Solution: L M is the length as seen by someone moving with respect to the physical system in which the proper length is L S The proper time ∆t S is

Length Contraction The measured distance between two points depends on the frame of reference of the observer The proper length, L S, of an object is the length of the object measured by someone at rest relative to the object The length of an object measured in a reference frame that is moving with respect to the object is always less than the proper length This effect is known as length contraction

Length Contraction – Equation Length contraction takes place only along the direction of motion LSLS

Example 3 A flying saucer descending straight toward the Earth at c is first observed by an astronomer on the planet when it passes a satellite at an altitude of 3000 km. At that instant, what will be the ship’s altitude as determined by its navigator? Given: the proper length as measured by someone on Earth, L S = 3000 km and v = c Find: The measure altitude

Example 3 Solution: An observer in motion will see a measured distance as shorter (length contraction.) Using Eq. (26.5):

Example 4 A starship is headed for a galaxy that, according to astronomers, is 200 light-years away from Earth. Flying a direct course, the ship quickly reaches a cruising speed of 0.999c. What will be the Earth- galaxy distance as then determined by the navigator? Given: proper distance, L S = 200 ly and v = 0.999c. Find: The navigator’s distance

Example 4 Solution: Proper length or distance is measured by an observer at rest. The distance measure by an observer in a moving space ship will be shorter (length contraction.)

Simultaneity In Special Relativity, Einstein abandoned the assumption of simultaneity Thought experiment to show this A boxcar moves with uniform velocity Two lightning bolts strike the ends The lightning bolts leave marks (A’ and B’) on the car and (A and B) on the ground Two observers are present: O’ in the boxcar and O on the ground

Simultaneity – Thought Experiment Set-up Observer O is midway between the points of lightning strikes on the ground, A and B Observer O’ is midway between the points of lightning strikes on the boxcar, A’ and B’

Simultaneity – Thought Experiment Results The light signals reach observer O at the same time He concludes the light has traveled at the same speed over equal distances Observer O concludes the lightning bolts occurred simultaneously

Simultaneity – Thought Experiment By the time the light has reached observer O, observer O’ has moved The light from B’ has already moved by the observer, but the light from A’ has not yet reached him The two observers must find that light travels at the same speed Observer O’ concludes the lightning struck the front of the boxcar before it struck the back (they were not simultaneous events)

Simultaneity – Thought Experiment Two events that are simultaneous in one reference frame are in general not simultaneous in a second reference frame moving relative to the first That is, simultaneity is not an absolute concept, but rather one that depends on the state of motion of the observer In the thought experiment, both observers are correct, because there is no preferred inertial reference frame