Fundamental Physics 3 (Modern Physics)

Physics Education Department - UNS

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Fundamental Physics 3(Modern Physics)

Physics Education Department Sebelas Maret University

Surakarta


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Content

1. Special Relativity2. Introduction to quantum physics

3. Atoms4. The Nucleus and Nuclear Energy


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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”

Rules : Our Brain Can ImagineOrder : In Lit., Soc., Math, Eco., Bio., etc. forms


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The Goal of Physicists

• Matter Hierarchy:


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Modern Physics

• After 1905, the lately developed physics are called modern physics

①Special Relativity②Quantum Mechanics③General Relativity


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The Goal of Physicists

• To Explain physical phenomena in simplest and most economical terms, i.e., elegant form


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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


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Category of Physics


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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.


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Special Relativity


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Basic Problems• 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


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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.

Showed that our usual conceptions of space and time are misguided.


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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.

• inertial frame of reference: is one in which an object is observed to have no acceleration when no forces act on it.


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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


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Galilean relativity

Coordinate Transformation □

tt

zz

yy

vtxx

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


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Galilean relativityNon Relativistic Addition of Velocities

vuu xx

There is no limit Velocities!


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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.

Who is correct?

km/hour 1208040 vuu xx

But what exactly is the absolute velocity of the ball?


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• Earth spins (rotates) on its axis – One rotation in (24 hrs)(60 min/hr)(60 sec/min)=86400

sec– Point on surface moves 2πRE in one rotation.– Surface velocity = 2πRE /T=2π(6.4x106 m)/86400 sec = 465 m/s

• Earth revolves around sun– One revolution in (365 days)(86400 sec/day)=3.15x107

sec– Earth velocity = 2π(1.5x1011 m)/ 3.15x107 sec=3x104 m/s

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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

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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


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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


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What about electromagnetism?• Maxwell equations say that

– Light moves at constant speed c=3x108 m/sec in vacuum• Seems at odds with Galilean relativity:

– 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


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The Ether• To resolve this, 19th 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

Pluses MinusesAllows 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.


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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.


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• Ether wind would change average speed of light on the different paths.

• Waves will interfere when they recombine.

Both can not be observed!

M1

M2

M0

teleskop

Lengan 2

Leng

an 1

Angin eter

v

Sumber cahaya

Animasi MM


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Einstein’s principle of relativity

In 1905, at the age of 26, he published four scientific papers that revolutionized physics. Two of these papers were concernedwith what is now considered hismost important contribution: thespecial theory of relativity.

Albert EinsteinGerman-American

Physicist(1879–1955)

Was born in Ulm, Germany


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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)

(These two postulates are the basis of the special theory of relativity)


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Simultaneity with sound• Suppose you hear two loud shots

about 1/2 second apart.• Did they occur at the same time?

• 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.


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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 (x1, t1) is simultaneous with event (x2, t2) if sound pulses emitted at t1 from x1 and at t2 from x2 arrive simultaneously at the midpoint between x1 and x2.

• 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


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Consequences of Einstein’s relativityMany ‘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


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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.


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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.


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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.


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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?


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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

Reference frame of observer O’ on train

Reference frame of observer O on ground


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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


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How large an effect is time dilation?

• t = time interval between events in frame O (observer on ground)

• t satisfies

ct /2 2 vt /2 2 d2,

t 2c 2 v 2 2

2d 2

t 2d / c 2 v 2 2d

c

1

1 (v /c)2


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Time dilation• Time interval in boxcar frame O’

• Time interval in ground frame O

tp round trip distance

velocity

2d

c

t 2d

c

1

1 (v /c)2

tp

1 (v /c)2tp

1

1 (v /c)2


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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.

∆tp = 1s maka ∆t = γ ∆tp =1.15s • Observer O measures 1.15 seconds

1

1 (v /c)2

1

1 (0.5c /c)2

1

1 0.251.15


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Which way does time dilation go?

• 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, tp


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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∆tp =3 s


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Example

Because a clock moving with respect to anobserver is measured to run more slowly than a stationary clock by a factor γ, we have

p

pp

t

t

c

ctt

902.01

1

)95,0(1

1

2

2

s 6.9)s 00.3)(20.3(


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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?

ptt 2


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Does time dilation occur in the real world? “Yes!”

• One example is particles created by cosmicrays in the upper atmosphere which canpenetrate a thousand meters or more belowthe 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!


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Muon decays into electron, a neutrino, and an antineutrino

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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 10-6 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)


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e


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(a) Without relativisticconsiderations, muons createdin the atmosphere and travelingdownward with a speed of 0.99ctravel only about 660 mbefore decaying with an averagelifetime of 2.2 +s. Thus, very fewmuons reach the surface of theEarth.

(b) With relativisticconsiderations, the muon’s

lifetimeis dilated according to an

observeron Earth. As a result,

according tothis observer, the muon can

travelabout 4800m before decaying.This results in many of them

arriving at the surface.

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Fundamental Physics 3 (Modern Physics)