Fundamental Physics 3 (Modern Physics) Physics Education Department Sebelas Maret University Surakarta Physics Education Department - UNS1

Content 1. Special Relativity 2. Introduction to quantum physics 3. Atoms 4. The Nucleus and Nuclear Energy Physics Education Department - UNS2

What Is Physics ? Physics is the activity of trying to find the rules by which nature plays. We Believe that “ There are rules, that nature is in some sense orderly ” Physics Education Department - UNS3 Rules : Our Brain Can Imagine Order : In Lit., Soc., Math, Eco., Bio., etc. forms

The Goal of Physicists Matter Hierarchy: matter atoms nuclei protons 2U quarks 1 D quark neutrons 1 U quark 2 D quarks electrons Physics Education Department - UNS4

Modern Physics After 1905, the lately developed physics are called modern physics Special Relativity ‚Quantum Mechanics ƒGeneral Relativity Physics Education Department - UNS5

The Goal of Physicists To Explain physical phenomena in simplest and most economical terms, i.e., elegant form Physics Education Department - UNS6

Classifications of physics Concept: a physical quantity can be used to analyze natural phenomena Laws & Principles: math ’ s relationships － laws ； general statements － principles Models: a convenient representation of a physical system Theories: a theory uses a combination of priciples, a model, and initial assumptions to deduce specific consequences or laws Physics Education Department - UNS7

Category of Physics Physics Education Department - UNS8

Relativity and Modern Physics Physics changed drastically in the early 1900’s New discoveries — Relativity and Quantum Mechanics Relativity – Changed the way we think about space and time Quantum mechanics – Changed our conceptions of matter. Physics Education Department - UNS9

10 Special Relativity

Basic Problems The speed of every particle in the universe always remains less than the speed of light The speed of every particle in the universe always remains less than the speed of light Newtonian Mechanics is a limited theory – It places no upper limit on speed It is contrary to modern experimental results – Newtonian Mechanics becomes a specialized case of Einstein’s Theory of Special Relativity When speeds are much less than the speed of light Physics Education Department - UNS11

Special Relativity From 1905 to 1908, Einstein developed the special theory of relativity. Came up completely different idea of time and space. Everything is relative. No absolute lengths, times, energies. Physics Education Department - UNS12 Showed that our usual conceptions of space and time are misguided.

Frames of reference Frame of reference: – The coordinate system in which you observe events. – e.g. The room around you. – You judge how fast a thrown ball goes by its velocity relative to some stationary object in the room. – You judge how high a thrown ball goes by distance from the floor, ceiling, etc. Physics Education Department - UNS13 inertial frame of reference: is one in which an object is observed to have no acceleration when no forces act on it.

Galilean Relativity Choose a frame of reference – Necessary to describe a physical event, the laws of mechanics are the same in all inertial frames of reference 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 Physics Education Department - UNS14

Galilean relativity Physics Education Department - UNS15 Coordinate Transformation □ An observer O in an inertial frame S describes the event with space–time coordinates (x, y, z, t), An observer O’ in an inertial frame S’ uses the coordinates (x’, y’, z’, t’) to describe the same event

Galilean relativity Physics Education Department - UNS16 Non Relativistic Addition of Velocities There is no limit Velocities!

Which reference frame? Suppose you are on the bus to tawangmangu driving at 80 km/hour, and throw a ball forwards at 40 km/hour. From your seat on the bus, the speed of ball is the same as in this classroom. To someone on the side of the road, your 40 km/hour throw has become a 120 km/hour fastball. Physics Education Department - UNS17 Who is correct ? But what exactly is the absolute velocity of the ball?

Earth spins (rotates) on its axis – One rotation in (24 hrs)(60 min/hr)(60 sec/min)=86400 sec – Point on surface moves 2πR E in one rotation. – Surface velocity = 2πR E /T=2π(6.4x10 6 m)/86400 sec = 465 m/s Earth revolves around sun – One revolution in (365 days)(86400 sec/day)=3.15x10 7 sec – Earth velocity = 2π(1.5x10 11 m)/ 3.15x10 7 sec=3x10 4 m/s Physics Education Department - UNS18

Galilean Relativity – Example A passenger in an airplane throws a ball straight up – It appears to move in a vertical path – The law of gravity and equations of motion under uniform acceleration are obeyed 19Physics Education Department - UNS

Galilean Relativity – Example, cont 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 20Physics Education Department - UNS

Galilean Relativity – Example, conclusion 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 Physics Education Department - UNS21

What about electromagnetism? Maxwell equations say that – Light moves at constant speed c=3x10 8 m/sec in vacuum Seems at odds with Galilean relativity: Physics Education Department - UNS22 –Tentrem would expect to see light pulse propagate at c+v –But Maxwell says it should propagate at c, if physics is same in all inertial reference frames. –If it is different for Ayem and Tentrem, then in which frame is it c? Tentrem Ayem

The Ether To resolve this, 19 th century researchers postulated existence of medium in which light propagates, rather than vacuum. – i.e. similar to gas in which sound waves propagate or water in which water waves propagate. Then Maxwell’s equations hold in the ether Physics Education Department - UNS23 PlusesMinuses Allows speed of light to be different in different frames (Maxwell’s eqns hold in frame at rest with respect to ether). Ether must be rigid, massless medium, with no effect on planetary motion Light then becomes like other classical waves, No experimental measurement has ever detected presence of ether Ether is absolute reference frame.

The Michelson-Morley experiment If the earth moves through a medium in which light moves at speed c, along the direction of the earth’s motion, light should appear from earth to move more slowly. Physics Education Department - UNS24

Physics Education Department - UNS25 Ether wind would change average speed of light on the different paths. Waves will interfere when they recombine. Both can not be observed! M1M1 M2M2 M0M0 teleskop Lengan 2 Lengan 1 Angin eter v Sumber cahaya Animasi MM

Einstein’s principle of relativity Physics Education Department - UNS26 In 1905, at the age of 26, he published four scientific papers that revolutionized physics. Two of these papers were concerned with what is now considered his most important contribution: the special theory of relativity. Albert Einstein German-American Physicist (1879–1955) Was born in Ulm, Germany

Einstein’s principle of relativity Principle of relativity: – All the laws of physics are identical in all inertial reference frames. Constancy of speed of light: – Speed of light is same in all inertial frames (e.g. independent of velocity of observer, velocity of source emitting light) Physics Education Department - UNS27 (These two postulates are the basis of the special theory of relativity)

Simultaneity with sound Suppose you hear two loud shots about 1/2 second apart. Did they occur at the same time? Physics Education Department - UNS28 Let’s think about it Suppose you find out one of the shots was fired closer to you than the other. Sound travels at 340 m/s. If one gun were fired 170m closer to you then they were fired at the same time.

Simultaneity If you know your distance from the shots, you can easily determine if they were simultaneous. And everyone will agree with you, after doing the same correction for distance. You might even come up with a definition – Event (x 1, t 1 ) is simultaneous with event (x 2, t 2 ) if sound pulses emitted at t 1 from x 1 and at t 2 from x 2 arrive simultaneously at the midpoint between x 1 and x 2. Einstein came up with a similar definition for relativistic simultaneity. – Due to the requirement of the consistency of speed of light not everyone agrees events are simultaneous Physics Education Department - UNS29

Consequences of Einstein’s relativity Many ‘common sense’ results break down: – Events simultaneous for observer in one reference frame not necessarily simultaneous in different reference frames. – The distance between two objects is not absolute. Different for observers in different reference frames – The time interval between events is not absolute. Different for observers in different inertial frames Physics Education Department - UNS30

Simultaneity thought experiment Boxcar moving with constant velocity v with respect to Tentrem standing on the ground. Ayem rides in exact center of the boxcar. Two lightning bolts strike the ends of the boxcar, leaving marks on the boxcar and the ground underneath. On the ground, Tentrem finds that she is halfway between the scorch marks. Physics Education Department - UNS31

Simultaneity, continued Tentrem (on the ground) observes that light waves from each lightning strike at the boxcar ends reach her at exactly the same time. Since each light wave traveled at c, and each traveled the same distance (since O is in the middle), the lightning strikes are simultaneous in the frame of ground observer. Physics Education Department - UNS32

When do the flashes reach Ayem? Tentrem can see when the two flashes reach Ayem on the boxcar. When light from front flash reaches Ayem, he has moved away from rear flash. —Front and rear flashes reach Ayem at different times Since speed of light always constant Ayem is equidistant from lightning strikes —Ayem is equidistant from the lightning strikes —Light flashes arrive at different times —Both flashes travel at c Therefore for Ayem, lightning strikes are not simultaneous. Physics Education Department - UNS33

Simultaneity and relativity, cont Means there is no universal or absolute time. – The time interval between events in one reference frame is generally different than the interval measured in a different frame. – Events measured to be simultaneous in one frame are in general not simultaneous in a second frame moving relative to the first. – Has other consequences for time? Physics Education Department - UNS34

Time dilation Observer O on ground Observer O’ on train moving at v relative to O Pulse of light emitted from laser, reflected from mirror, arrives back at laser after some time interval. Lets figure out what this time interval is for the two observers Physics Education Department - UNS35 Reference frame of observer O’ on train Reference frame of observer O on ground

Time dilation, continued Observer O’ on train: light pulse travels distance 2d. Observer O on ground: light pulse travels farther Relativity: light travels at velocity c in both frames – Therefore time interval between the two events (pulse emission from laser & pulse return) is longer for stationary observer This is time dilation This is time dilation Physics Education Department - UNS36

How large an effect is time dilation?  t = time interval between events in frame O (observer on ground)  t satisfies Physics Education Department - UNS37

Time dilation Time interval in boxcar frame O’ Time interval in ground frame O Physics Education Department - UNS38

Example Suppose observer on train (at rest with respect to laser and mirror) measures round trip time to be one second. Observer O on ground is moving at 0.5c with respect to laser/mirror. ∆t p = 1s maka ∆t = γ ∆t p =1.15s Observer O measures 1.15 seconds Physics Education Department - UNS39

Which way does time dilation go? Physics Education Department - UNS40 Example: Suppose the time interval of two events observed by someone in the rest frame of the clock (these occur at the same spatial location) is 5 minutes., so In frame moving with respect to clock, time interval is  (5 min) To this observer, clock is moving, and is measured to run slow by factor  -1 The shortest time measured between events is in the frame in which the events occur at the same spatial location. This is called the ‘proper time’ between events,  t p

Physics Education Department - UNS41 The period of a pendulum is measured to be 3.00 s in the reference frame of the pendulum. What is the period when measured by an observer moving at a speed of 0.950c relative to the pendulum? Example the proper time interval, measured in the rest frame of the pendulum, is ∆t p =3 s

Physics Education Department - UNS42 Example Because a clock moving with respect to an observer is measured to run more slowly than a stationary clock by a factor γ, we have

Physics Education Department - UNS43 At what speed does a clock move if it is measured to run at a rate that is half the rate of a clock at rest with respect to an observer?

Physics Education Department - UNS44 Does time dilation occur in the real world? “Yes!” One example is particles created by cosmic rays in the upper atmosphere which can penetrate a thousand meters or more below the surface of the Earth. E.g. the muon which decays at rest in about 2.2 microseconds. At c, it could travel about 660m. Because of time dilation, to us, it travels 10 km, or more!

Physics Education Department - UNS45 Muon decays into electron, a neutrino, and an antineutrino Muon – an electrically charged unstable elementary particle with a rest energy ~ 207 times greater than the rest energy of an electron. The muon has an average half-life of 2.2  s. Muons are created at high altitudes due to collisions of fast cosmic-ray particles (mostly protons) with atoms in the Earth atmosphere. (Most cosmic rays are generated in our galaxy, primarily in supernova explosions)

Physics Education Department - UNS46

Physics Education Department - UNS47 (a) Without relativistic considerations, muons created in the atmosphere and traveling downward with a speed of 0.99c travel only about 660 m before decaying with an average lifetime of 2.2 +s. Thus, very few muons reach the surface of the Earth. (b) With relativistic considerations, the muon’s lifetime is dilated according to an observer on Earth. As a result, according to this observer, the muon can travel about 4800m before decaying. This results in many of them arriving at the surface.