Transcript Document

Lecture I: Concepts in Classical Physics
Lecture II: Concepts in Special Relativity
and Quantum Mechanics
Lecture III: The World of the Small and
the Fast.
The Origin of Mass in
Particle Physics
60th Compton Lectures
Ambreesh Gupta
Nobel Prize 2004
"for the discovery of asymptotic freedom in the theory of the strong
interaction"
David J. Gross University of California, Santa Barbara
H. David Politzer California Institute of Technology, Pasadena
Frank Wilczek Massachusetts Institute of Technology, Cambridge
http://mitworld.mit.edu/video/204/
Frank Wilczek’s Lecture
Origin of Mass and Feebleness of Gravity
Getting Directions
y
0,0
10,0
z
10,1
0,1
x
Reference Frame
3 Space + 1 Time
are sufficient to describe nature!
But...Is it possible that there are extra space dimensions?
We will get back to this in the seventh lecture
Greek Science and Numerology
Thales: The father
of Greek mathematics.
Pythagoras: Entire
universe can be
described in numbers.
Aristotle: Systematized logic, which forms the basis of
western science.
Aristotelian Logic
It is impossible for the same thing at the same time to belong
and not belong to the same thing in the same respect . . .
Not ( A )  A
Earth at the Center: Geocentric Universe
Aristotle:
. Earth is at the center of the
Universe
. ‘Prime Movers’ responsible
for movement of
planets and stars.
Ptolemy:
. 100 A.D
. Refined Aristotle’s model
. Calculation devise for
astronomical
predictions.
Dominant view for over 2000 years.
Sun at the Center: Heliocentric Model
Nicolaus Copernicus (1514)
. Geocentric model too complicated . . . Ockham’s Razor?
. First attempts resulted in worse
predictions
. “On the Revolutions”,
published when he was on
his deathbed.
Galileo
. Modified the telescope created in 1608 to magnify objects
30 times
. He increasingly believed that the
geocentric picture was wrong
. Published “Dialogue Concerning the two
world system: Ptolemaic and Copernican”
Kepler
. Used Tycho Brahe’s astronomical data to
infer elliptical planetary orbits
- 8 minute discrepancy
. Gave three laws of planetary motion
- elliptical planetary orbits
- equal time sweeps equal area
- relation between time period and average distance
Why do planets follow these
rules?
Newton
The laws of physics until the time of Newton’s, involved only
space and time.
Newton for the first time introduced
the concept of mass in the laws of
physics.
Revolutionary implication: Same
underlying law for all massive objects!
The Mathematical Principles of Natural Philosophy: Principia
…considered the most influential publication in the history of
science.
Principia : Definitions
Principia defines three “Fundamental quantities”
Length,
Time,
Meter
Second
Mass
Kilogram
as measurable and objective.
Principia: Newton’s Law
Three laws of motion
1st Law of Inertia
2nd Law of Acceleration
3rd Law of Action and Reaction
The Universal Law of Gravity
F=ma
F = G (m1m2 / r2)
m1
Two laws of Conservation
1st Law of conservation of Mass
2nd Law of Conservation of Momentum
r
m2
Unification
With these laws, Newton could
account for all types of motion:
falling bodies on the surface of
earth and heavenly bodies in the
sky.
Which body reaches the lower edge first?
“I have seen farther, it is by standing on the shoulders
of giants”
- Newton in a letter to Robert Hooke
“. . .Our understanding does not advance just by slow
and steady building on previous work. Sometimes as
with Copernicus and Einstein, we have to make a leap
to new world picture. Maybe Newton should have
said “I used the shoulders of giants as a springboard.”
- Stephan Hawking in “On the Shoulder of Giants”
A little more on the “Why’s”
Q. Why do planets follow elliptical path? (Kepler)
A. Because of the Nature of gravitational force. (Newton)
Q. Why do massive bodies attract each other? (Newton)
A. Because massive bodies curve space-time fabric. (Einstein)
Q. Do the why’s ever end?
A. I don’t know.
Newton’s Second Law: F=ma
Defines Force or Mass?
Ernest Mach’s definition:
Use Newton’s second & third law
mA/mB = - (aB/A/aA/B)
Herman Weyl’s definition:
mA
r
uA
mA/mB = - (uB/uA)
mB
uB
mA mB
Inertial vs. Gravitational Mass
Newton’s Gravitation Law
Newton’s Second Law
mi a = G(mgMg /r2)
mi, mg
r
Are mi and mg the same?
Equivalence Principle
Mg
Testing Equivalence Principle
Newton
- fractional accuracy of 1 part in 100
Loránd Eötvös (1848-1919 )
- fractional accuracy of 1 part in 100000000
Eöt-Wash Group
- fractional accuracy of 1 part in 10000000000000
STEP: Satellite test of the equivalence principle
- fractional accuracy of 1 part in 1000000000000000000
Units:
How do we define units of length, time and mass?
Some early definitions,
. The Kings arm or span of his foot
. Weights convenient quantities carried in hand or back
. Time followed astronomical variation of the Earth and Moon
Average height of the
crowd?!
Natural Units
Max Planck based the natural units on the “Fundamental Constants of
Nature”
Gravitational Constant
G = 6.6742 x 10-11 m3 kg-1 s-2
Planck's Constant
h = 6.626 0693 x 10-34 kg-m2/s
Speed of Light
c =299 792 458 m s-1
Electron Charge
e = 1.602 176 53 x 10-19 C
Are the fundamental constants of nature truly constant?
Fine Structure Constant: 
Coulombs Law
+q1
F  (q1q2)/r2
r
-q2
= e2/ħc = 1./137.03559 Dimensionless Constant of Nature
“…one of the greatest damn mysteries of physics: a magic numbe
that comes to use with no understanding by man. You might say t
‘hand of God’ wrote that number, and ‘we don’t know how He
pushed His pencil.’” – Richard P. Feynman, QED
Realms of Physical Laws
Small
Classical
Mechanics
Quantum
Mechanics
Relativistic
Mechanics
Quantum
Field Theory
Fast
How do we define length and time?
Natural Units
Max Planck based the natural units on the “Fundamental Constants of
Nature”
Gravitational Constant
G = 6.6742 x 10-11 m3 kg-1 s-2
Planck's Constant
h = 6.626 0693 x 10-34 kg-m2/s
Speed of Light
c =299 792 458 m s-1
Electron Charge
e = 1.602 176 53 x 10-19 C
Are the fundamental constants of nature truly constant?
Fields
The concept was introduced by
Michael Faraday in 1844-46
Electric Field
E = k Q /r2
Gravitational Field g= GM /r2
Scalar Field
Electromagnetic Waves
Until now we have dealt primarily
with particles…
- have mass, momentum, energy etc.
Waves are disturbance that carry energy
- without transporting matter
- can refracts, reflect, interfere
EM waves are disturbances in electric
and magnetic field
Ether & Michelson-Morley Experiment
Successive experimentation
Gave null result...no ether.
Difficulties between Newtonian relativity and EM
There is no reference frame in which an EM wave can be
at rest…in conflict with Newtonian(Galilean) relativity
Special Relativity
In 1905, Albert Einstein postulated
1. Physical law’s invariant between
reference frames.
2. Speed of light is same in all
inertial frames.
Solved Newtonian relativity conflict.
…changed notion of space and time.
Energy, momentum and mass
E2 = p2 + m2c4
Deriving magnetic field from EM and SR
. We do not know about the
existence of magnetic field
+ + + + + + + + + + + + + +
v - - - - -- - - - - - -r
. No electric force on ‘q’ in lab
frame
v
u
q
. Net force on ‘q’ in its rest frame
. Transform force from ‘q’ rest
frame to lab frame
The form of this transformed
force is like magnetic force!
++++++++++++++++ ++++
 v- -
-
-
r
q
-
-
v+ 
More on Units
1 eV ( electron Volt ) is the energy required to move an electron
through a potential difference of 1 volt.
1 eV = 1.6  10-19 J (kg-m2/s2)
In the rest frame of electron: E (=mc2) = 81.9  10-14 J
Mass of electron: me = 0.511 MeV/c2
h/2=1, c=1 (Energy Units)
1 kg ~ 1027 GeV ;
1 m = 1016 GeV-1;
1 TeV = 1000 GeV = 1000000 MeV = 1012 eV
Mass of a Proton: mp ~ 1 GeV
1 s = 1024 GeV-1
Black Body Radiation
Classical theory predicted that
E()  2
In 1900 Max Planck proposed
E() = h
This was the first step
toward Quantum Physics!
De’Broglie, Schroedinger and Heisenberg
De’Broglie relates particle and wave =h/p
- provides a description for Bohr’s atomic model
Schroedinger’s equation of matter wave
- wave functions encapsulate probability…success
with hydrogen atom.
Heisenberg’s Uncertainty Principle
- presence of probability implies uncertainty
- x p  h/2
- t E  h/2
The Archetypical Double Slit Experiment
1
2
3
Electron
source
Which of the three distributions should one expect in an
experiment ?
Feynman’s Path Formalism
Consider all paths between two points
Assign amplitude to each path
Probability of event =
|Sum of amplitude of all path|2
Classical Path
For 1g particle: non classical path
Probability zero.
For electron 10-27 g: similar probability
for either path.
Non
Classical
Identical Particle Collision
A
The probability of observing
particles at detectors 1 and 2
depends if the particles are
Identical or not.
1
If ‘p’ is the probability to observe
A or B particle at 1 or 2….

B
Probability( particle at 1 or 2 ) = 2p
(not identical)
Probability( particle at 1 or 2 ) = 4p
(identical in QM)
2
Mass…A clarification
Weight = mass  gravitational acceleration
Energy and Mass
The most famous equation of Physics
E=mc2
Mass of 2 proton and 2 neutron separately
is larger than the mass of helium nucleus
Mass difference
28 MeV
Mass of a Proton
Proton is made of u u d quarks
Mass of proton
= Mass of u and d quarks
+ Kinetic Energy of quarks
+ Potential Energy between quarks
Most of Proton mass comes from energy components!
As far as we know,
Quark, Lepton and Force carrying Bosons are fundamental
Where does their mass comes from?
Bubble of Ignorance
A simplified view of particle physics
experiment
A
D
?
B
C
Dirac’s Equation
Dirac combined Quantum Mechanics and
Special Relativity in one equation
Successes
- spin of electron occurred naturally
- prediction of anti-matter
Failures
- magnetic moment of electron
- creation and annihilation of particles
Quantum Mechanics of Fields
A theory that can handle particle creation and annihilation.
Quantum field theory describes the quantum mechanics of fields,
such as the electromagnetic field and the electron field. In this
setup, particles and waves, both are different faces of the same type
of object: the quantum field.
Feynman’s pictorial representation of possibilities in the bubble
of ignorance
Quantum Electrodynamics
The quantum field theory of electric charge and
photons was formulated by R.P Feynman,
J. Schwinger and S. Tomonaga (1965 Nobel Prize)
Crown jewel of its prediction, magnetic moment electron
Dirac Theory
QED
Experiments
1.0
1.00115965221(4)
1.00115965246(20)
Deviation of these numbers, especially magnetic moment of muon
could hint the presence of new physics beyond Standard Model.