The Origin of Mass in Particle Physics

Lecture III: The World of the Small and the Fast.

60th Compton LecturesAmbreesh Gupta

Lecture I: Concepts in Classical Physics

Lecture II: Concepts in Special Relativity and Quantum Mechanics

Nobel Prize 2004"for the discovery of asymptotic freedom in the theory of the strong interaction"

David J. Gross University of California, Santa BarbaraH. David Politzer California Institute of Technology, PasadenaFrank Wilczek Massachusetts Institute of Technology, Cambridge

http://mitworld.mit.edu/video/204/Frank Wilczek’s LectureOrigin of Mass and Feebleness of Gravity

Getting Directions

y

x

z

0,0 0,1

10,110,0

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

Pythagoras: Entire universe can be described in numbers.

Greek Science and NumerologyThales: The father of Greek mathematics.

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 UniverseAristotle:. 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

Why do planets follow these rules?

. 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

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 defines three “Fundamental quantities”

Length, Time, Mass

Meter Second Kilogram

as measurable and objective.

Principia : Definitions

Principia: Newton’s Law

Three laws of motion 1st Law of Inertia 2nd Law of Acceleration F=ma 3rd Law of Action and Reaction

The Universal Law of Gravity F = G (m1m2 / r2)

Two laws of Conservation 1st Law of conservation of Mass 2nd Law of Conservation of Momentum

m1m2r

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?

“. . .Our understanding does not advance just by slowand 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”

“I have seen farther, it is by standing on the shouldersof giants”

- Newton in a letter to Robert Hooke

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/mB = - (uB/uA)

mAmBr

mAmB

uA uB

Inertial vs. Gravitational Mass

rmi, mgMg

mi a = G(mgMg /r2)

Newton’s Second Law Newton’s Gravitation Law

Are mi and mg the same?

Equivalence Principle

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 ConstantG = 6.6742 x 10-11 m3 kg-1 s-2

Planck's Constanth = 6.626 0693 x 10-34 kg-m2/s

Speed of Lightc =299 792 458 m s-1

Electron Chargee = 1.602 176 53 x 10-19 C

Are the fundamental constants of nature truly constant?

Fine Structure Constant:

Coulombs Law F (q1q2)/r2

+q1-q2r

= e2/ħc = 1./137.03559 Dimensionless Constant of Nature

“…one of the greatest damn mysteries of physics: a magic number that comes to use with no understanding by man. You might say the ‘hand of God’ wrote that number, and ‘we don’t know how He pushed His pencil.’” – Richard P. Feynman, QED

Realms of Physical Laws

ClassicalMechanics

QuantumMechanics

RelativisticMechanics

QuantumField Theory

Fast

Small

How do we define length and time?

Natural Units

Max Planck based the natural units on the “Fundamental Constants of Nature”

Gravitational ConstantG = 6.6742 x 10-11 m3 kg-1 s-2

Planck's Constanth = 6.626 0693 x 10-34 kg-m2/s

Speed of Lightc =299 792 458 m s-1

Electron Chargee = 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 electricand magnetic field

Ether & Michelson-Morley Experiment

Successive experimentationGave 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

. No electric force on ‘q’ in lab frame

. 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!

+ + + + + + + + + + + + + +

- - - - - - - - - - - - -

q

q

v

v+

v

v-

r

r

u

+ + + + + + + + + + + + + + + + + + + +

- - - - - -

More on Units1 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 s = 1024 GeV-1

1 TeV = 1000 GeV = 1000000 MeV = 1012 eV

Mass of a Proton: mp ~ 1 GeV

Black Body Radiation

Classical theory predicted that E() 2

In 1900 Max Planck proposed E() = h

This was the first step This was the first step toward Quantum Physics!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

1 2 3

Electronsource

The Archetypical Double Slit Experiment

Which of the three distributions should one expect in anexperiment ?

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

For 1g particle: non classical path Probability zero.

For electron 10-27 g: similar probability for either path.

Classical Path

Non Classical

Identical Particle Collision

A

1 2

B

The probability of observing particles at detectors 1 and 2 depends if the particles are Identical or not.

If ‘p’ is the probability to observe A or B particle at 1 or 2….

Probability( particle at 1 or 2 ) = 2p (not identical)

Probability( particle at 1 or 2 ) = 4p (identical in QM)

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

?

B C

A D

A simplified view of particle physics experiment

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 1.0QED 1.00115965221(4)Experiments 1.00115965246(20)

Deviation of these numbers, especially magnetic moment of muoncould hint the presence of new physics beyond Standard Model.