### Four Lectures Leading to the Standard Model of Particle

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Head for
Understandable
Description of
Matter and
Forces at the
Most
Fundamental
Level
June 2001
Frank Sciulli - Lecture I
Page 1
Particles and Forces tell us about
the beginning of the Universe
June 2001
Frank Sciulli - Lecture I
Page 2
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Is this a
Belief
System?
NO!
Science does
use the beauty
of ideas, but
ultimately
relies on
EXPERIMENT!!
June 2001
Frank Sciulli - Lecture I
Page 3
Four Lectures Leading to the
Standard Model of Particle
Physics - A Paradigm
• Particles, Light, and Special Relativity
• Quantum Mechanics, Atoms and Particles
• Particles, Forces, and the Electroweak Interaction
• Hadrons, Strong Force and the Standard Model
Illustrate, hopefully, that Physics (Science) has as
ultimate
arbitrator
NATURE ! ! ! !
June 2001
Frank Sciulli - Lecture I
Page 4
Approach to the Subjects
Eclectic: factual, historical,
experimental, …
Lets start with pre-20th Century
Particles and
Forces:
June 2001
• Newton’s Laws (Galileo,…)
• Energy and Work
• Thermodynamics
• Chemistry … atoms?
• Optics, fluids, waves, ...
Frank Sciulli - Lecture I
Page 5
Classical particles and waves
Classical particle
scattering (balls)
June 2001
Water waves hit slits
Frank Sciulli - Lecture I
Page 6
Newton’s Laws for Particles
Forces from elsewhere
Gravity, electricity, magnetism, ….
Get acceleration from
F  ma
For no acceleration, its simple
x  x 0  vt
(Even Galileo knew the last one!)
June 2001
Frank Sciulli - Lecture I
Page 7
Consolidation of
Established clear
rules for fields as the
Electricity and
origin of EM force.
Magnetism by Maxwell Made rules consistent!
They read
(1864)
Q
Source of E is charge (Gauss Law)
 E 
1
0
2
 B  0
No magnetic charge
Faraday’s Law of Induction
Source of B is charge
motion + Maxwell’s new
Displacement Current
June 2001
c
B
 E  
t
E
  B  0J   0 0
t
Frank Sciulli - Lecture I
Page 8
Implications:
Electromagnetic Waves
c
June 2001
1
 0 0
Frank Sciulli - Lecture I
 3  10 m/s
8
Page 9
Michaelson Interferometer
Observer sees fringes
(light and dark pattern),
corresponding to constructive
and destructive interference:
For example, if 2d2 -2d1
changes by /2, fringe
pattern shifts
Became important element in
central problem of 100 yrs ago:
why is
c  1/  0 0  const??
June 2001
Frank Sciulli - Lecture I
Page 10
But the velocity of the
PROBLEM
mechanical wave relative to
Velocity of a mechanical the observer obeys the same rules
wave depends only on the
as a travelling particle:
medium, not the velocity
relative velocities
of the source (even though
frequency and wavelength
change - Doppler shift)
c 
2
B

Light also
has velocity
independent
of source
speed
June 2001
Example, it is possible for a
“listener” to travel faster than a
sound wave. In this case, the
sound will never catch up to the
listener. Sound wave in “A”
never catches “B” if v>c
But MEs state EM waves have v=c
Frank Sciulli - Lecture I
Page 11
Most obvious resolution:
Luminiferous Ether
• Provides transmission medium, in analogy
with that required by mechanical waves
• Provides a “special” frame of
motion … where the laws of E&M
(Maxwell’s Equations) are valid
- All other frames of reference
(in motion relative to the special
one), Maxwell’s Equations are only
approximately true!
• Essential element of scientific hypothesis:
provides a possibility for testing!
June 2001
Frank Sciulli - Lecture I
V=30km/s
Earth motion
around sun
Page 12
1887: Michaelson-Morley idea
June 2001
Frank Sciulli - Lecture I
Page 13
Michaelson - Morley Expt
Use velocity of Earth around the sun v =30km/s
Rotate apparatus by 90 deg… change in relative
phase of the two light rays by  is expected
 2
L


2dv
c
2
2
Apparatus on bed
of liquid mercury,
rotate by 90
degrees
June 2001
Frank Sciulli - Lecture I
Page 14
Michaelson Morley Experiment “Big” Physics of 1887
V=30km/s
Earth motion
around sun
  5 10-7 m
Make d as
large as
possible
June 2001
 2
L


2dv 2
v2
8

4

10
c2
d
2  107

  0.1 rad
c 2
CONCLUDE: No phase shift
was observed
NO ETHER … ?!%*
Frank Sciulli - Lecture I
Page 15
Einstein’s Reasoning
Maxwell’s Equations (eg Law of Induction at left)
do not depend on which is moving relative to what.
So it is reasonable that the value of c coming out of
the equations should not depend on state of motion
of anyone! Sound a bit crazy? Not to Albert
Einstein!
Newtonian mechanics with objects or
(mechanical) waves: velocity is relative
to motion of observer! OLDTHINK…
Plane shoots rocket
June 2001
Frank Sciulli - Lecture I
Plane shoots laser
Page 16
Conundrum
EITHER light is like mechanical waves:
E&M only valid in one frame!?
OR light is NOT like mechanical waves;
E&M valid in all frames, independent of
their motion
Einstein chose the latter
Einstein “Laws of Physics the same in all inertial frames”
MEANS
Maxwell’s equations valid in all non-accelerating coord. systs
BUT this implies that velocity of light = c in vacuum
no matter where
the light comes from and how fast you are moving
c  1/  0 0
June 2001
Frank Sciulli - Lecture I
Page 17
Einstein Postulates (1905) require
(a) speed of light (in vacuum) same in all inertial frames
(b) speed of light (in vacuum) independent of the motion of
source
CARRY MANY IMPLICATIONS
+
June 2001
Frank Sciulli - Lecture I
Lorentz
Contraction
+
Time Dilation
Page 18
Transformations
of Position and
Time
Galilean (Newton)
x  x ' vt '
y  y'
z  z'
t  t'
June 2001
c  3  10 m/s
8
 
1
Lorentz (Einstein)
x   ( x ' vt ')
v/c  0  1
y  y'
z  z'
v/c  0  1
t   (t ' vx '/ c 2 )
1  (v / c)2
Frank Sciulli - Lecture I
Page 19

Reversible
1
1  ( v / c)
2
x   ( x ' vt ')
y  y'
z  z'
t   (t ' vx '/ c 2 )
Check if these equations
give correct answer:
For x’=ct’ ….. x=ct ?
June 2001
Frank Sciulli - Lecture I
x '   ( x  vt )
y'  y
z'  z
t '   (t  vx / c )
2
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v << c
Limiting cases
2
1v
 
 1     ... So this  is
2
2c
1  (v / c)
essentially ONE
unless the
object is near
the velocity of
light… where it
rises very
rapidly.
1
June 2001
= v/c
Frank Sciulli - Lecture I
Page 21
Time Dilation and Lorentz
Contraction
t   (t ' v x '/ c )
2
Happening in S’ at x’=0
over t’
t   t '
x '   (x  vt )
Rod at rest in S’, with length L0
Length in S is L, measure ends
at same time: t=0
L
June 2001
Frank Sciulli - Lecture I
L0
Page 22

Relativistic
Invariants

1
1  ( v / c)
2
x   ( x ' vt ')
y  y'
z  z'
t   (t ' vx '/ c 2 )
x  y  z  c t  invariant
2
2
2
2 2
 (x ')  ( y ')  (z ')  c (t ')
2
June 2001
2
Frank Sciulli - Lecture I
2
2
Page 23
2
Implications of Relativity for
Particle Momentum and Energy
Nonrelativistic
p  mv
1 2
K  mv
2

Relativistic
1
1  ( v / c)
2
K  (  1)mc
Implication:
Matter is a
form of energy.
At v=0, E=mc2.
E  p c m c
2
June 2001
p   mv
2 2
2 4
Frank Sciulli - Lecture I
E  K  mc
E   mc
2
2
Prove it!
Page 24
2
Transformation of
Momenta/Energy

1
1  ( v / c) 2
x   ( x ' vt ')
y  y'
z  z'
t   (t ' vx '/ c )
2
p x   ( px  vE  / c 2 )
p y  py
pz  pz
E   ( E   vpx )
June 2001
Frank Sciulli - Lecture I
Page 25
Energy/Momentum/Mass and Units
Universal energy
units are joules
(traditionally);
but a much
simpler one for
dealing with
particles:
E pX
c m X
c
2
eV
MeV
GeV
2
eV/c
MeV/c
GeV/c
2
2
4
eV/c2
MeV/c2
GeV/c2
Sensible units for discussion
(with electric
of atoms and subatomic particles
charges that
is the electron volt = eV
are multiples of
1 eV = energy gained by electron
the electron)
(or proton) by acceleration through
q  1.6  1019 Coulomb
precisely V = one volt.
1 ev = q V  1.6  1019 joules
June 2001
Frank Sciulli - Lecture I
Page 26
Mass is Energy and vice versa
N
• Macroscopic systems, mass stays essentially the same and
kinetic energies small compared to rest mass energy: separate!
• Microscopic systems (atoms), energies of electrons are small
compared to mass of system:
in hydrogen atom, U=13.6 eV but M~109 eV/c2
Note that mass of proton is ~ 1 GeV/c2
• Ultra - microscopic systems (nuclei and smaller), energies of
constituents get comparable or larger than their rest mass
What about
EM fields?
June 2001
Photons have no rest mass
E  p c
Frank Sciulli - Lecture I
Page 27
Mass Disappears-Energy Appears
FUSION
Mass difference of .0304u = 28.3 MeV/c2 becomes energy
June 2001
Frank Sciulli - Lecture I
Page 28
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Relativity is the way the world
works
Example: NAVSTAR Satellite system to track
velocity of airplanes uses Doppler shifts.
If non-relativistic Doppler formula were used,
precision on velocity would be about 21 cm/s.
If relativistic Doppler formula used,
precision  1.4 cm/s
Examples: Real-life everyday
observations in particle and nuclear
physics, where new matter is made
and it spontaneously decays
June 2001
Frank Sciulli - Lecture I
Page 29
Metastable Matter
(Radioactive Decay makes a clock)
Characterized by lifetime ()
or half-life (T1/2 =  ln2 = 0.7 )
1000
100
10
1
June 2001
Example 128I nuclide
with T1/2 = 25 minutes.
Compare:
14C has T
1/2 = 5730 yrs.
 has T1/2= 3.75  10-8 sec
N  N0e
R  R0e
Frank Sciulli - Lecture I
t


t


Page 30
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Working with
Unstable
Matter Can
Make for
Problems!
Just kidding …
It’s actually
not that hard!
Here we use pions, unstable particles with
mass of 140 Mev and lifetimes of ~ 3 10-8 sec
June 2001
Frank Sciulli - Lecture I
Page 31
Real World Test of Relativity:
Fermilab Complex
Four mile circumference Tevatron Ring
June 2001
Frank Sciulli - Lecture I
15 story high rise
Page 32
Accelerators Raise Kinetic
Energy using Electric Fields
Each loop, the energy of protons are
raised by increment determined by
electric potential: E =eV
 = E/m
Proton total Energy
versus velocity
measure
velocity
= v/c
June 2001
Frank Sciulli - Lecture I
Page 33
Accelerated protons have
very large energy
Beam protons hit stationary
target (Et=m) with
very large kinetic energy
 = Eb/m
What happens????
June 2001
Extracted protons have
energy E  800 GeV
Frank Sciulli - Lecture I
Page 34
Collision of 300 GeV
proton with
stationary nucleon
New kinds of particles made out
of kinetic energy: mesons (pions)
with mass of 140 MeV each.
p  p  p  p  28

Total Energy available for mass
M 2  (E  mp )2  p 2
with E  mp
M  2mpE  2(1 GeV )(300 GeV )
2
M  24.5 GeV  28 m  3.9 GeV
June 2001
Frank Sciulli - Lecture I
Page 35
Beams of pions made from
collisions of high energy protons
L0  780 m
  2.6  10 8 sec
v  3  108 m / sec & t  L0 /v
t  2.6  10 6 sec
t
Nonrelativistic,  100

so fraction left  e 100  3.7  10 44
WRONG!!
June 2001

Beam line, 0.78 km long,
transports 140 GeV ’s
made at tgt
Frank Sciulli - Lecture I
Page 36
Right answer: Lab perspective
E 140 GeV
 

 1000
m 140 MeV
v

Observer: Time dilation
 lab    1000  2.6  10 8
 lab  2.6  10 5 sec
t  2.6  10 6 sec
t
 0.1 so
 lab
Right!!!
fraction left  e 0.1  0.90
June 2001
Frank Sciulli - Lecture I
Page 37
Right answer: pion perspective
E 140 GeV
 

 1000
m 140 MeV

Pion sees: Lorentz Contraction
v
L 780 m
L  
 0.78 m

1000
t 
June 2001
L
c
 2.6  10 7 sec
  2.6  10 8
t
Right!!!
 0.1 so

fraction left  e 0.1  0.90
Frank Sciulli - Lecture I
Page 38
Conclusions - Special Relativity
• Relativity was required by experimental
information at the time it was invented
(1905)
• It is essential now to describe the world,
especially since we can directly observe
objects travelling near the speed of light
• The rules are, in fact, simple - see handout
or website!
• Do the problems and prove the simplicity!
June 2001
Frank Sciulli - Lecture I
Page 39
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