A New Kind of Science

Guest Instructor: H. Kemal İlter e-mail: [email protected] web site: www.baskent.edu.tr
A New Kind of Science [Lecture name choosen from the name of Stephen Wolfram’s last book]

http://www.baskent.edu.tr/~kilter 2 Classical Physics Timeline

http://www.baskent.edu.tr/~kilter 3 Modern Physics Timeline

http://www.baskent.edu.tr/~kilter 4 At the age of 16, Einstein puzzled over
what it would be like to travel at the speed of light. In particular, what would one see in a mirror that is also moving at the speed of light? Einstein’s Mirror

http://www.baskent.edu.tr/~kilter 5 In 1905, at the age of 26, Einstein
published his theory of Special Relativity...

http://www.baskent.edu.tr/~kilter 6 “I was sitting in a chair in the
patent office at Bern when all of a sudden a thought occurred to me: If a person falls freely he will not feel his own weight... I was startled. This simple thought made a deep impression on me. It impelled me towards a theory of gravitation.” The “Happiest Thought” of Einstein’s Life (1907)

http://www.baskent.edu.tr/~kilter 7 Almost a decade later, in 1916, Einstein completed
his theory of General Relativity...

http://www.baskent.edu.tr/~kilter 8 And both theories completely revolutionized our concept of
time...

http://www.baskent.edu.tr/~kilter 9 “What, then, is time? I know well enough
what it is, provided that nobody asks me; but if I am asked what it is and try to explain, I am baffled.” St. Augustine (5th Century A.D.) Easier question: How do we measure time?

http://www.baskent.edu.tr/~kilter 10 The ‘second’ is the duration of 9,192,631,770 periods
of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. Definition of a Second

http://www.baskent.edu.tr/~kilter 11 Fact 1

http://www.baskent.edu.tr/~kilter 14 Conclusion: Time is not absolute, as common sense
and everyday experience might suggest It depends on the observer In other words, it is relative “When the Special Theory of Relativity began to germinate in me, I was visited by all sorts of nervous conflicts... I used to go away for weeks in a state of confusion.”

http://www.baskent.edu.tr/~kilter 15 Evidence for ‘Time Dilation’ Atomic clock travelling around
the world in a plane Muons reaching Earth from a cosmic ray shower Muons travelling round in a storage ring Global Positioning System (GPS)

http://www.baskent.edu.tr/~kilter 16 Hafele and Keating’s Classic Experiment Hafele and Keating
taking the atomic clocks around the world to test Einstein’s relativity theory

http://www.baskent.edu.tr/~kilter 17 A magnet has a ‘magnetic field’ distributed throughout
the surrounding space Faraday realised that ... Michael Faraday (1791-1867)

http://www.baskent.edu.tr/~kilter 18 Photo of magnet with iron filings

http://www.baskent.edu.tr/~kilter 19 Although two magnets may not be touching, they
still interact through their magnetic fields. This explains the ‘action at a distance’, say of a compass.

http://www.baskent.edu.tr/~kilter 20 Similarly, Faraday realized that the electric force is
transmitted by a electric field.

http://www.baskent.edu.tr/~kilter 21 Now, what is the medium through which the
electric and magnetic fields are transmitted? Question: Answer: vacuum?

http://www.baskent.edu.tr/~kilter 22 … are transmitted through air via ‘pressure vibrations’.
Recall that sound waves ...

http://www.baskent.edu.tr/~kilter 23 These vibrations eventually reach our ears and cause
them to vibrate. This is how we hear sounds.

http://www.baskent.edu.tr/~kilter 24 A wave is a vibration of some medium
through which it propagates. In general ...

http://www.baskent.edu.tr/~kilter 25 All of space was filled with a substance
called luminiferous aether. Electric and magnetic fields are ‘distortions’ or ‘twists’ of the aether. Maxwell hypothesised that ... James Clerk Maxwell (1831-1879)

http://www.baskent.edu.tr/~kilter 26 Two implications of Maxwell’s equations Light consists of
an oscillating electric and magnetic field Light travels at constant speed 0 0 1 µ ε = c

http://www.baskent.edu.tr/~kilter 27 The Electromagnetic Spectrum: Evidence for the wave nature
of light

http://www.baskent.edu.tr/~kilter 28 With respect to the aether, naturally!? What is
this speed c measured with respect to?

http://www.baskent.edu.tr/~kilter 29 Roemer’s First Measurement of c (1676) Used the
shadows cast on Jupiter by its moons Measurements were made at position A, and then at B six months later The time lapse recorded implies that light has a finite speed

http://www.baskent.edu.tr/~kilter 30 Photo of Io’s shadow I

http://www.baskent.edu.tr/~kilter 31 Photo of Io’s shadow II

http://www.baskent.edu.tr/~kilter 32 Date Author Method Result (km/s) Error 1676 Olaus
Roemer Jupiter's satellites 214,000 1726 James Bradley Stellar aberration 301,000 1849 Armand Fizeau Toothed wheel 315,000 1862 Leon Foucault Rotating mirror 298,000 +-500 1879 Albert Michelson Rotating mirror 299,910 +-50 1907 Rosa, Dorsay Electromagnetic constants 299,788 +-30 1926 Albert Michelson Rotating mirror 299,796 +-4 1947 Essen, Gorden-Smith Cavity resonator 299,792 +-3 1958 K. D. Froome Radio interferometer 299,792.5 +-0.1 1973 Evanson et al Lasers 299,792.4574 +-0.001 1983 Adopted value 299,792.458 Measurements of the speed of light Today c is defined to be exactly 299,792,458 m/s, and this is used to define the meter

http://www.baskent.edu.tr/~kilter 33 Search is on for the aether ... The
Michelson-Morley Experiment (1887) Albert Michelson (1852-1931) Edward Morley (1838-1923)

http://www.baskent.edu.tr/~kilter 34 Einstein’s Dramatic Explanation There is no such thing
as luminiferous aether The speed of light is the same (constant) in any direction, which explains the null results of M&M Although we have come one big circle, this realization of Einstein paved the way for his theory of relativity …

http://www.baskent.edu.tr/~kilter 35 Galileo’s Principle of Relativity Imagine yourself in a
train moving on a straight track at a constant speed If you closed the windows, you would not be able to tell whether the train is moving or at rest! In other words … The laws of physics are the same for all observers moving at steady speeds with respect to each other Galileo Galilei (1564-1642)

http://www.baskent.edu.tr/~kilter 36 Motion is Relative: it is impossible to say
who is actually at rest According to the driver of red car, blue car is overtaking But according to the driver of blue car, red car is reversing backwards

http://www.baskent.edu.tr/~kilter 37 How did Einstein arrive at the special theory
of relativity?

http://www.baskent.edu.tr/~kilter 38 And everything else follows ... Two starting assumptions
or Postulates: The speed of light is constant regardless of the motion of the observer or of the sender Galileo’s relativity principle: The laws of physics are the same for all observers moving at steady speeds with respect to each other

http://www.baskent.edu.tr/~kilter 39 Predictions of Special Relativity (SR) Simultaneous events to
one observer need not be simultaneous to another Time dilation Length contraction

http://www.baskent.edu.tr/~kilter 40 Consider the experiment for a train at rest
Flash arrives at both ends simultaneously

http://www.baskent.edu.tr/~kilter 41 The same experiment for a moving train Flash
arrives at rear end of the train first

http://www.baskent.edu.tr/~kilter 42 Suppose a murder has occurred in which someone
is shot This could make life rather confusing ... Would another observer moving past see the victim die before the gun is fired??

http://www.baskent.edu.tr/~kilter 43 The order of cause and effect, called causality,
is always preserved Fortunately, this can never happen in SR

http://www.baskent.edu.tr/~kilter 44 Consider the experiment with a ball: (a) Straight
trajectory of ball as seen by person on moving lorry (b) Parabolic trajectory of ball as seen by stationary person on the ground

http://www.baskent.edu.tr/~kilter 45 Consider similar experiment with light: (a) Luke’s perception
of the path of light from the moving train (b) Your perception of the path of light from the ground

http://www.baskent.edu.tr/~kilter 46 Experiment with light (cont’d): Luke, who is on
the train, wants to measure the speed of light He sends a light pulse straight up and down, and measures the time taken by his clock Meanwhile, you are outside the train watching the same experiment being performed You also try to measure the speed of light, by your own clock

http://www.baskent.edu.tr/~kilter 47 Experiment with light (cont’d): Since the train is
moving, you see the light pulse to travel a longer distance But by Einstein’s first postulate, both Luke and you would measure the same speed Since, speed equals distance/time, you would think that the time taken for the experiment to complete is longer

http://www.baskent.edu.tr/~kilter 48 In other words ... You think that Luke’s
time has slowed down! Time dilation formula

http://www.baskent.edu.tr/~kilter 49 Gamma Factor: Convenient to introduce the notation: So
time dilation formula can be written as

http://www.baskent.edu.tr/~kilter 50 Properties When speed is low (<0.1c), γ is
almost one. So the time dilation effect is very small When speed approaches that of light, γ becomes larger and larger. Time slows down more and more Graph of gamma

http://www.baskent.edu.tr/~kilter 51 Note: Time dilation is a relative effect Luke
would not notice himself ‘slow down’ Instead, he would everything outside the train slow down in time Time dilation affects all types of time: physical, mechanical, psychological, biological …

http://www.baskent.edu.tr/~kilter 52 The length of a moving object appears to
be contracted in its direction of motion Length contraction formula: Length (Lorentz-Fitzgerald) Contraction

http://www.baskent.edu.tr/~kilter 53 Properties When speed is low, γ is almost
one. So the length contraction effect is very small When speed approaches that of light, γ becomes larger and larger. Length becomes zero Length contraction graph

http://www.baskent.edu.tr/~kilter 54 Space-time Hermann Minkowski (1864-1909) was unimpressed by Einstein
as his student, and once called him ‘a lazy dog’. In 1908, Minkowski realized that time can be unified with three-dimensional space to give a four-dimensional ‘space-time’ Consider a horse in motion:

http://www.baskent.edu.tr/~kilter 55 In terms of a space-time diagram: Horse in
motion Horse at rest

http://www.baskent.edu.tr/~kilter 56 All objects trace out worldlines in space-time

http://www.baskent.edu.tr/~kilter 57 The axes are usually chosen so that light
travels at 45° Many problems in special relativity can be analysed in terms of space-time diagrams

http://www.baskent.edu.tr/~kilter 58 Suppose Leia and Luke are twins After celebrating
their 21st birthday together, Luke flies off in his X- wing at 24/25 c to a distant star system He travels for 7 years, then turns round and returns home at the same speed What are the ages of the twins when Luke returns? The Twin Paradox

http://www.baskent.edu.tr/~kilter 59 According to Leia, Luke’s clock will slow down
… … so he will be younger than Leia when he returns According to Luke, Leia (and the Earth) will be moving and so it is her clock that will slow down … … so she will be younger than Luke when he returns! The Twin Paradox (cont’d)

http://www.baskent.edu.tr/~kilter 60 One of the twins must be wrong Luke
is wrong, because he will experience acceleration in his X- wing and so he knows he is the one actually moving Detailed calculations show that Luke will indeed be younger than Leia when he returns Who is the younger twin?

http://www.baskent.edu.tr/~kilter 61 Luke 21+7+7 = 35 years old Leia 21+25+25
= 71 years old Ages of the twins can be deduced using a space-time diagram:

http://www.baskent.edu.tr/~kilter 62 What happens if we are travelling at the
speed of light? When v = c, γ = ∞ which means: time stands still? length becomes zero? This is an indication that something is wrong

http://www.baskent.edu.tr/~kilter 63 Nothing can travel faster than c Reasons: Addition
law for velocities Mass increase for moving particles All science fiction fans know this! “Chewy, let’s make the jump to light-speed.”

http://www.baskent.edu.tr/~kilter 64 Addition law for velocities Usual velocity addition formula:
Correct velocity addition formula: With this formula, it is impossible to exceed c!

http://www.baskent.edu.tr/~kilter 65 Example 1 When Luke looks back, at what
speed will he see Vader receding? Normal way to add velocities: Correct way to add velocities:

http://www.baskent.edu.tr/~kilter 66 Example 2 When Luke looks back, at what
speed will he see the laser approaching? Normal way to subtract velocities: Correct way to subtract velocities:

http://www.baskent.edu.tr/~kilter 67 Doppler Effect Christian Doppler (1803-53) Sound of a
train moving towards us is higher pitched Sound of a train moving away from us is lower pitched

http://www.baskent.edu.tr/~kilter 68 Doppler effect for passing aircraft Aircraft moving at
less than speed of sound Aircraft moving at the speed of sound

http://www.baskent.edu.tr/~kilter 69 What if aircraft is moving faster than the
speed of sound? You would hear a sonic boom

http://www.baskent.edu.tr/~kilter 70 Objects moving towards us appears blue-shifted Objects moving
away from us appears red-shifted Doppler Effect for Light

http://www.baskent.edu.tr/~kilter 71 M87 Black Hole

http://www.baskent.edu.tr/~kilter 72 M87 Black Hole Doppler Shift

http://www.baskent.edu.tr/~kilter 73 In special relativity, there is a new type
of Doppler effect An object moving sideways at high speeds can appear red-shifted because of time dilation Observed in the jets of SS433 Transverse Doppler Effect SS433 is a binary star system. A black hole or neutron star is blasting out two jets of gas in opposite directions, at 0.25c

http://www.baskent.edu.tr/~kilter 74

http://www.baskent.edu.tr/~kilter 75 Principle of Energy Conservation The different forms of
energy - chemical, - electrical, - magnetic, - mechanical, - heat, etc., can be transformed into each other, but the total amount of energy always remains the same Julius Robert von Mayer (1814- 1878) was the first to realise a relation between mechanical work and heat energy

http://www.baskent.edu.tr/~kilter 76 Conservation of mass (matter) Atoms can neither be
created nor destroyed John Dalton (1766-1844) performed experiments that verified the postulate for the conservation of mass

http://www.baskent.edu.tr/~kilter 77 Einstein’s equation E = mc2 combines the principles
of energy and mass conservation

http://www.baskent.edu.tr/~kilter 78 Concept of Mass The mass of an object
measures its resistance to motion But if the object is already moving, then its mass measures how difficult it is to stop In this case, the ‘stopping power’ required is better described by …

http://www.baskent.edu.tr/~kilter 79 Momentum

http://www.baskent.edu.tr/~kilter 80 Conservation of momentum When two objects collide, the
total momentum remains unchanged pinitial = pfinal

http://www.baskent.edu.tr/~kilter 81 Mass increases for moving objects where m0 is
the mass of the object when it is at rest. m0 is known as the rest mass and m is the relativistic mass. m = γm0 Note: When an object approaches the speed of light, its mass becomes larger and larger.

http://www.baskent.edu.tr/~kilter 82 Imagine watching Luke zooming past at 0.99c …
He wants to go faster, so he adds more power to the engines of his X-wing … His speed will go up slightly, but his mass will go up drastically With more mass, more power is needed to increase his speed further, … and so on

http://www.baskent.edu.tr/~kilter 83 Conclusion Luke would need an infinite amount of
power to reach the speed of light In other words, it is impossible to accelerate a massive object up to the speed of light

http://www.baskent.edu.tr/~kilter 84 So how can a photon travel at the
speed of light? A photon has no rest mass: m0 = 0 Because it is impossible to find a photon ‘at rest’ So the above arguments are not valid: m = 0/0 = can be anything

http://www.baskent.edu.tr/~kilter 85 In the formula E=mc2 It is the relativistic
mass which appears: E = mc2 = γm0 c2

http://www.baskent.edu.tr/~kilter 86 Implications An object at rest has energy E=m0
c2, the so-called rest mass energy The faster it moves, the more mass, and therefore energy, it has

http://www.baskent.edu.tr/~kilter 87 Kinetic Energy The difference between the total energy
of an object and its rest mass energy is the kinetic energy: By the binomial theorem, this formula reduces to the usual Newtonian one for small speeds

http://www.baskent.edu.tr/~kilter 88 Further implications of mass-energy equivalence A ball in
motion has more mass than one at rest A hot gold sphere has more mass than a cold one So conservation is mass is not true, although this change of mass is very minute (since c is so large)

http://www.baskent.edu.tr/~kilter 89 Imagine you convert one gram of matter into
pure energy ... How much energy would be released?

http://www.baskent.edu.tr/~kilter 90 Amount of energy released: E = mc2 =
8.987 x 1013 Joules = 2.497 x 107 kW hr

http://www.baskent.edu.tr/~kilter 91 What does this translate into? The energy produced
by burning 15 453 barrels of crude oil The total consumption of energy in Singapore in 1999! This shows that there is an enormous amount of energy locked inside matter

http://www.baskent.edu.tr/~kilter 92 Structure of an Atom

http://www.baskent.edu.tr/~kilter 93 An atom is composed of: Electrons: light, -ve
charged particles A heavy nucleus made up of protons and neutrons (which have roughly the same mass) Protons: +ve charged particles Neutrons: neutral particles

http://www.baskent.edu.tr/~kilter 94 Aristotle’s Law of Free Fall Heavier objects fall
faster than lighter ones

http://www.baskent.edu.tr/~kilter 95 Galileo’s Law of Free Fall All objects fall
at the same speed

http://www.baskent.edu.tr/~kilter 96 Newton’s Law of Universal Gravity The force which
makes an apple fall to the ground is the same force which makes the moon go round the Earth

http://www.baskent.edu.tr/~kilter 97 Gravitational Force The force on an object is
proportional to its mass. This is called the gravitational mass of the object F ∝ mG

http://www.baskent.edu.tr/~kilter 98 Inertial Mass Mass measures an object’s resistance to
motion. This is called the inertial mass of the object F = mI a

http://www.baskent.edu.tr/~kilter 99 Newton’s ‘Equivalence Principle’ Gravitational mass is equivalent to
inertial mass: mG = mI This is remarkable because there is absolutely no reason why this should be so

http://www.baskent.edu.tr/~kilter 100 This Explains Galileo’s Law Consider two objects A
and B, with masses m and 2m, respectively The gravitational force on B is twice that on A But twice as much force is needed to get B moving the same rate as A So A and B fall at the same rate!

http://www.baskent.edu.tr/~kilter 101 Einstein’s ‘Happiest Thought’ “I was sitting in a
chair in the patent office at Bern when all of a sudden a thought occurred to me: If a person falls freely he will not feel his own weight... I was startled. This simple thought made a deep impression on me. It impelled me towards a theory of gravitation.” This means that gravity can be cancelled out by acceleration

http://www.baskent.edu.tr/~kilter 102 Einstein’s ‘Equivalence Principle’ In any given location, it
is impossible to distinguish between the effects of accelerated motion and those of a gravitational field In short, gravity is equivalent to acceleration Explains Newton’s equivalence principle

http://www.baskent.edu.tr/~kilter 103 Consequence of Equivalence Principle Artificial gravity can be
created by acceleration If there were no windows in the elevator, Einstein would not be able to tell whether he is at rest on Earth or accelerating at a constant rate in space

http://www.baskent.edu.tr/~kilter 104 Bending of light by gravity The previous two
experiments both show that light would be bent by gravity Predicted by Einstein in 1911 (and corrected in 1915) Experimentally verified during a solar eclipse in 1919 by Eddington

http://www.baskent.edu.tr/~kilter 105 Effect Observed During a Solar Eclipse

http://www.baskent.edu.tr/~kilter 106 Bending of light by gravity (cont’d) Expected... because
light is energy, and by E = mc2, energy is equivalent to mass

http://www.baskent.edu.tr/~kilter 107 Light from a distant object (star or galaxy)
is bent by the gravity of another object in between it and Earth Gravitational Lenses

http://www.baskent.edu.tr/~kilter 108 Einstein Crosses

http://www.baskent.edu.tr/~kilter 109 Cosmic Magnifying Glass

http://www.baskent.edu.tr/~kilter 110 Gravitational Red-shift Light is red-shifted in a gravitational
field This is related to the slowing down of time in a gravitational field … … since atoms vibrate slower and emit light with longer wavelength (smaller frequency)

http://www.baskent.edu.tr/~kilter 111 Euclidean Geometry

http://www.baskent.edu.tr/~kilter 112 Actually describes geometry on a surface such as
a saddle Sum of angles of a triangle is less than 180°

http://www.baskent.edu.tr/~kilter 113 Example of Riemannian Geometry Sum of angles of
a triangle is more than 180°

http://www.baskent.edu.tr/~kilter 114 The surface of the Earth is curved A
small region on the surface of the Earth is almost flat A flat map is adequate to represent this region But a flat map cannot accurately represent the entire surface of the Earth. Distortions are inevitable, since the surface is actually curved.

http://www.baskent.edu.tr/~kilter 115 Mercator Projection There are large distor -tions of
area towards the polar regions The shortest path between two points is a great circle Actually appears as a longer curved path in this projection

http://www.baskent.edu.tr/~kilter 116 A geodesic is the shortest path between two
given points In flat space, geodesics are straight lines On the surface of the Earth, geodesics are great circles Geodesics

http://www.baskent.edu.tr/~kilter 117 The effects of gravity can be described in
terms of curved space-time Free particles follow geodesics in this space-time Einstein’s Theory of General Relativity (GR)

http://www.baskent.edu.tr/~kilter 118 Curvature Mimics a Force (acting between the ants)

http://www.baskent.edu.tr/~kilter 119 Geometry of space-time is curved by matter in
the space- time On the other hand, the curvature of space-time determines how the matter will move General Relativity (cont’d)

http://www.baskent.edu.tr/~kilter 120 Imagine Earth as a ball on a rubber
sheet

http://www.baskent.edu.tr/~kilter 121 Hertzsprung-Russel diagram

http://www.baskent.edu.tr/~kilter 122 Life history of the Sun

http://www.baskent.edu.tr/~kilter 123 The Sun as a red giant

http://www.baskent.edu.tr/~kilter 124 Red-giant Sun seen from Earth

http://www.baskent.edu.tr/~kilter 125 Model of an atom … an atom consists
of mainly empty space ...

http://www.baskent.edu.tr/~kilter 126 Schwarzschild radii for different objects

http://www.baskent.edu.tr/~kilter 127 A black hole is an infinite abyss in
space-time

http://www.baskent.edu.tr/~kilter 128 Photon orbits around a black hole

http://www.baskent.edu.tr/~kilter 129 Wormhole

http://www.baskent.edu.tr/~kilter 130 Heisenberg’s uncertainty principle Uncertainty in position and momentum
∆x ∆p ~ h Uncertainty in energy and time ∆E ∆t ~ h

http://www.baskent.edu.tr/~kilter 131 Hawking radiation Stephen W. Hawking (b1942)

http://www.baskent.edu.tr/~kilter 133 Travelling to the Future Imagine Pooh is going
off on a long space journey ... His spaceship accelerates at 1 g to the halfway point, and then decelerates at 1 g so that it comes to a rest at the destination How does Pooh’s time compare to Earth time?

http://www.baskent.edu.tr/~kilter 142 A CTC is a worldline that loops back
onto itself. At some stage, the particle has to travel faster than light. A Closed Timelike Curve (CTC)

http://www.baskent.edu.tr/~kilter 143 In special relativity, if one could travel faster
than light, one could also go back in time.

http://www.baskent.edu.tr/~kilter 144 Paradoxes in Backward Time Travel Grandfather paradox Information
creation in a causal loop Hawking’s paradox: Where are all the time travellers from the future?

http://www.baskent.edu.tr/~kilter 145 Obtaining the Age of the Universe Extrapolate the
current expansion rate (Hubble constant) back to the Big Bang 10 to 20 billion years old Look for the oldest stars (in globular clusters) 11 to 18 billion years old Best current estimate is 13.4 ± 1.6 billion years M10 Globular Cluster

http://www.baskent.edu.tr/~kilter 146 Summary: Timeline of the Universe

http://www.baskent.edu.tr/~kilter 147 Timeline of the Universe 2

http://www.baskent.edu.tr/~kilter 148 Possible Fates of the Universe

http://www.baskent.edu.tr/~kilter 149 Will the Universe Recollapse? Gravitational pull of the
galaxies on each other is slowing down the rate of expansion Required density for the universe to recollapse is 4.5 x 10-30 g/cm3 Observed density of luminous material (stars, galaxies) is about 3 x 10-31 g/cm3

http://www.baskent.edu.tr/~kilter 150 If the universe recollapses ...

http://www.baskent.edu.tr/~kilter 151 If the universe expands forever ... “Some say
the world will end in fire, others say in ice.” – Robert Frost

http://www.baskent.edu.tr/~kilter 152 Newton’s Corpuscular Theory of Light Light consists of
small particles, because it travels in straight lines at great speeds is reflected from mirrors in a predictable way

http://www.baskent.edu.tr/~kilter 153 Particles Position x Momentum p = mv

http://www.baskent.edu.tr/~kilter 154 Waves

http://www.baskent.edu.tr/~kilter 155 Waves versus Particles A particle is localized in
space, and has discrete physical properties such as mass A wave is inherently spread out over many wave-lengths in space, and could have amplitudes in a continuous range Waves superpose and pass through each other, while particles collide and bounce off each other

http://www.baskent.edu.tr/~kilter 156 Diffraction

http://www.baskent.edu.tr/~kilter 157 Interference applet

http://www.baskent.edu.tr/~kilter 158 Blackbody Radiation A blackbody is an object which
totally absorbs all radiation that falls on it Any hot body (blackbodies included) radiates light over the whole spectrum of frequencies The spectrum depends on both frequency and temperature

http://www.baskent.edu.tr/~kilter 159 Planck’s Quantum Postulate (1900) Energy of radiation can
only be emitted in discrete packets or quanta, i.e., in multiples of the minimum energy E = hf where h is ...

http://www.baskent.edu.tr/~kilter 160 Planck’s Constant A new fundamental constant of nature:
h = 6.63 x 10-34 Joule sec (Joule = kg m2 / sec2)

http://www.baskent.edu.tr/~kilter 161 Discrete Packets of Energy

http://www.baskent.edu.tr/~kilter 162 Einstein’s Explanation (1905) Light consists of particles, called
photons Each photon has energy: E = hf

http://www.baskent.edu.tr/~kilter 163 Common Evidence for Photons Red light is used
in photographic darkrooms because it is not energetic enough to break the halogen-silver bond in black and white films Ultraviolet light causes sunburn but visible light does not because UV photons are more energetic Our eyes detect colour because photons of different energies trigger different chemical reactions in retina cells

http://www.baskent.edu.tr/~kilter 164 Double-Slit Experiment to illustrate wave nature of light

http://www.baskent.edu.tr/~kilter 165 Double-Slit Experiment with a machine gun!

http://www.baskent.edu.tr/~kilter 166 Double-Slit Experiment with electron gun

http://www.baskent.edu.tr/~kilter 167 Interference Pattern of Electrons applet Determines the probability
of an electron arriving at a certain spot on the screen

http://www.baskent.edu.tr/~kilter 168 Double-Slit Experiment with electron gun and detector The
act of measurement causes an electron to behave like a particle rather than a wave

http://www.baskent.edu.tr/~kilter 169 Determinism of Classical Mechanics Suppose the positions and
speeds of all particles in the universe are measured to sufficient accuracy at a particular instant in time It is possible to predict the motions of every particle at any time in the future (or in the past for that matter) “An intelligent being knowing, at a given instant of time, all forces acting in nature, as well as the momentary positions of all things of which the universe consists, would be able to comprehend the motions of the largest bodies of the world and those of the smallest atoms in one single formula, provided it were sufficiently powerful to subject all the data to analysis; to it, nothing would be uncertain, both future and past would be present before its eyes.” Pierre Simon Laplace

http://www.baskent.edu.tr/~kilter 170 Role of an Observer The observer is objective
and passive Physical events happen independently of whether there is an observer or not This is known as objective reality

http://www.baskent.edu.tr/~kilter 171 Role of an Observer in Quantum Mechanics The
observer is not objective and passive The act of observation changes the physical system irrevocably This is known as subjective reality

http://www.baskent.edu.tr/~kilter 172 Werner Heisenberg realised that ... In the world
of very small particles, one cannot measure any property of a particle without interacting with it in some way This introduces an unavoidable uncertainty into the result One can never measure all the properties exactly

http://www.baskent.edu.tr/~kilter 173 Measuring the position and momentum of an electron
Shine light on electron and detect reflected light using a microscope Minimum uncertainty in position is given by the wavelength of the light So to determine the position accurately, it is necessary to use light with a short wavelength

http://www.baskent.edu.tr/~kilter 174 Before ...

http://www.baskent.edu.tr/~kilter 175 After ...

http://www.baskent.edu.tr/~kilter 176 Example of Baseball A pitcher throws a 0.1-kg
baseball at 40 m/s So momentum is 0.1 x 40 = 4 kg m/s Suppose the momentum is measured to an accuracy of 1 percent , i.e., ∆p = 0.01 p = 4 x 10-2 kg m/s

http://www.baskent.edu.tr/~kilter 177 Example of Baseball (cont’d) The uncertainty in position
is then No wonder one does not observe the effects of the uncertainty principle in everyday life!

http://www.baskent.edu.tr/~kilter 178 Summary: Lessons from Heisenberg The idea of a
perfectly predictable universe cannot be true There is no such thing as an ideal, objective observer

http://www.baskent.edu.tr/~kilter 179 Solve this equation to obtain ψ Tells us
how ψ evolves or behaves in a given potential Analogue of Newton’s equation in classical mechanics Schrödinger’s Equation Erwin Schrödinger (1887-1961)

http://www.baskent.edu.tr/~kilter 180 Wave-like Behaviour of Matter Evidence: electron diffraction electron
interference (double-slit experiment) Also possible with more massive particles, such as neutrons and α-particles Applications: Bragg scattering Electron microscopes Electron- and proton-beam lithography

http://www.baskent.edu.tr/~kilter 181 Electron Diffraction X-rays electrons The diffraction patterns are
similar because electrons have similar wavelengths to X-rays

http://www.baskent.edu.tr/~kilter 182 SEM Images

http://www.baskent.edu.tr/~kilter 183 Proton Beam Micromachining (NUS)

http://www.baskent.edu.tr/~kilter 184 Discourse on Quantum Weirdness Einstein’s moon Schrödinger’s cat
EPR paradox

http://www.baskent.edu.tr/~kilter 185 Niels Bohr: “Anyone who is not shocked by
quantum theory has not understood it.” Richard Feynman: “… I think I can safely say that nobody understands quantum mechanics.” Quotes to ponder …

http://www.baskent.edu.tr/~kilter 186 Quantum Mechanics Operating on a Large Scale Lasers
Superfluidity Superconductivity Bose-Einstein condensate Future technologies?

http://www.baskent.edu.tr/~kilter 187 Paul Dirac (1902-84) First to try to combine
quantum mechanics with special relativity Obtained the relativistic version of Schrödinger’s equation in 1928 Known as the Dirac equation:

http://www.baskent.edu.tr/~kilter 188 The Dirac Equation Appears to have solutions with
negative energies Dirac identified them as ‘antiparticles’, with opposite charge to normal particles He (wrongly) identified the antiparticle of the electron with the proton

http://www.baskent.edu.tr/~kilter 189 Positron: Antiparticle of the Electron Discovered in cosmic
rays by Carl Anderson in 1932 Anderson saw a track in a cloud chamber left by “something positively charged, and with the same mass as an electron” Has the same mass as the electron but positive charge

http://www.baskent.edu.tr/~kilter 190 Every particle has an antiparticle 1955: antiproton 1960:
antineutron 1965: anti-deuteron 1995: anti-hydrogen atom (only 9 produced!) The photon is its own antiparticle, since it has no charge and spin

http://www.baskent.edu.tr/~kilter 191 What if we bring a particle and antiparticle
together?

http://www.baskent.edu.tr/~kilter 192 Particle – Antiparticle Annihilation / Creation A particle
can annihilate with its antiparticle to form gamma rays An example whereby matter is converted into pure energy by Einstein’s formula E = mc2 Conversely, a gamma ray with sufficiently high energy can turn into a particle – antiparticle pair Particle – antiparticle tracks in a bubble chamber

http://www.baskent.edu.tr/~kilter 193 Why is there so little antimatter in the
universe? A possible cloud of antimatter? A very small asymmetry between particles and antiparticles is predicted by the weak force During the big bang, for every billion antimatter particles produced, there were a billion and one matter particles This one matter particle out of a billion is all that is left today!

http://www.baskent.edu.tr/~kilter 194 Uses of Antimatter Antimatter propulsion? problems with manufacture
and storage Positron Emission Tomography (PET)

http://www.baskent.edu.tr/~kilter 195 A short-lived radioactive substance such as 18F is
injected into the bloodstream It would decay by emitting a positron, which would annihilate with an electron in the blood to produce gamma rays How PET Works Gamma rays fly off in opposite directions into the detectors. This enables the location of the original electron to be pinpointed

http://www.baskent.edu.tr/~kilter 196 Subject At Rest

http://www.baskent.edu.tr/~kilter 197 Undergoing Auditory Stimulation

http://www.baskent.edu.tr/~kilter 198 Undergoing Visual Stimulation

http://www.baskent.edu.tr/~kilter 199 Performing a ‘Thinking’ Task

http://www.baskent.edu.tr/~kilter 200 Remembering an Image for Later Recall

http://www.baskent.edu.tr/~kilter 201 Hopping Up and Down on Right Foot

http://www.baskent.edu.tr/~kilter 202 Fundamental Particles (circa 1930s) Photon (particle of light)
Electron, proton, neutron (making up atoms) Positron (antiparticle of electron)

http://www.baskent.edu.tr/~kilter 203 Neutrino Predicted by Pauli in 1931 to explain
the decay of the neutron: neutron → proton + electron + antineutrino Almost massless and interacts very weakly with other particles (via the weak force) Discovered only in 1956

http://www.baskent.edu.tr/~kilter 204 Particle Explosion (1940s to 60s) Leptons (light): electron,
muon, neutrino Mesons (middle): pion, kaon, ... Baryons (heavy): proton, neutron, Λ, Ω, Ξ, ...

http://www.baskent.edu.tr/~kilter 205 Are They All Truly Fundamental?

http://www.baskent.edu.tr/~kilter 206 Quark Hypothesis Proposed independently by Murray Gell-Mann and
George Zweig in 1961 Even more fundamental particles called quarks carrying charge 2/3 or -1/3 Mesons are composed of two quarks and baryons are composed of three quarks

http://www.baskent.edu.tr/~kilter 207 Six Quarks of Nature

http://www.baskent.edu.tr/~kilter 208 From Atoms to Quarks ...

http://www.baskent.edu.tr/~kilter 209 Properties of Fermions

http://www.baskent.edu.tr/~kilter 210 Properties of the Forces Force Range Relative Strength
Strong 10-15 1 Electromagnetic ∞ ~ 10-3 Weak 10-17 ~ 10-5 Gravity ∞ ~ 10-38

http://www.baskent.edu.tr/~kilter 211 Particles Mediating the Forces are Bosons Quantum electrodynamics
(QED) describes electro-magnetism in terms of exchange of photons Weak force: W±, Z bosons Quantum chromodynamics (QCD) describes the strong force in terms of exchange of 8 gluons carrying ‘colour’ charge

http://www.baskent.edu.tr/~kilter 212 Properties of Bosons

http://www.baskent.edu.tr/~kilter 213 Elementary Particles

http://www.baskent.edu.tr/~kilter 214 CERN

http://www.baskent.edu.tr/~kilter 215 Unification of the Four Forces

http://www.baskent.edu.tr/~kilter 216 Unification of the Four Forces (cont’d) Electromagnetism +
Weak = Electroweak Electroweak + Strong = Grand Unified Theory GUT + Gravity = Theory of Everything (??)

http://www.baskent.edu.tr/~kilter 217 Gravity: due to geometry rather than exchange of
particles Remains impossible to ‘quantise’ like the other forces

http://www.baskent.edu.tr/~kilter 218 Space-time Foam at Small Scales? How to describe
this mathematically?

http://www.baskent.edu.tr/~kilter 219 Superstring Theory Best candidate for a TOE is
superstring theory Assumes all fundamental particles are actually string-like objects rather than point-like objects Different particles correspond to different vibrational modes of the same string

http://www.baskent.edu.tr/~kilter 220 Point particles and strings interact differently

http://www.baskent.edu.tr/~kilter 221 Extra Dimensions? Superstring theory predicts that space-time is
10-dimensional (9 space + 1 time) The extra 6 dimensions are thought to be rolled up to a very small size

A New Kind of Science

A New Kind of Science

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