Transcript Four Lectures Leading to the Standard Model of Particle
Head for Understandable Description of Matter and Forces at the Most Fundamental Level June 2001 Frank Sciulli - Lecture I Page 1
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Particles and Forces tell us about the beginning of the Universe
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June 2001 Frank Sciulli - Lecture I Page 2
Is this a Belief System?
June 2001 Frank Sciulli - Lecture I NO!
Science does use the beauty of ideas, but ultimately relies on EXPERIMENT!!
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 : • Newton’s Laws (Galileo,…) • Energy and Work • Thermodynamics • Chemistry … atoms?
• Optics, fluids, waves, ...
June 2001 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 Get acceleration from
F
ma
For no acceleration, its simple 0
vt
(Even Galileo knew the last one!) June 2001 Frank Sciulli - Lecture I Page 7
Consolidation of Electricity and Magnetism by Maxwell (1864) Source of E is charge (Gauss Law) Established clear rules for They read fields as the origin of EM force.
Made rules consistent!
E
Q
0 No magnetic charge 0
c
1 2 Faraday’s Law of Induction Source of B is charge motion + Maxwell’s new Displacement Current June 2001 Frank Sciulli - Lecture I
E
0
J
B
t
Page 8
E
t
Implications: Electromagnetic Waves
June 2001
c
1 Frank Sciulli - Lecture I 8 Page 9
Michaelson Interferometer
June 2001 Observer sees fringes (light and dark pattern), corresponding to constructive and destructive interference: For example, if 2d 2 -2d 1 changes by /2, fringe pattern shifts Became important element in central problem of 100 yrs ago: why is
c
1 / 0 0 const??
Frank Sciulli - Lecture I Page 10
PROBLEM Velocity of a mechanical wave depends only on the medium, not the velocity of the source (even though frequency and wavelength change - Doppler shift)
But
the velocity of the mechanical wave relative to the observer obeys the same rules as a travelling particle: relative velocities June 2001
c
2
B
Light also has velocity independent of source speed 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 Frank Sciulli - Lecture I Page 11
v=c
Most obvious resolution: Luminiferous Ether
• Provides transmission medium, in analogy with that required by mechanical waves V =30km/s • 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!
Earth motion around sun June 2001 Frank Sciulli - Lecture I 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 June 2001 2
dv c
2 2 Apparatus on bed of liquid mercury, rotate by 90 degrees Frank Sciulli - Lecture I Page 14
Michaelson Morley Experiment “Big” Physics of 1887
V =30km/s 5 10 -7 Make d as large as possible m Earth motion around sun 2
v c d
2 2 2 10
L
7 0.1 rad 8 2
dv c
2 2 CONCLUDE: No phase shift was observed NO ETHER … ?!%* June 2001 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… June 2001 Plane shoots rocket 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 source inertial frames (b) speed of light (in vacuum) independent of the motion of CARRY MANY IMPLICATIONS + Lorentz Contraction + Time Dilation June 2001 Frank Sciulli - Lecture I Page 18
Transformations of Position and Time Galilean (Newton)
x x y
y
'
t z
z
'
t
'
vt
' June 2001
c
8 1 0 0 1 1 Frank Sciulli - Lecture I 2 Lorentz (Einstein )
x
vt
')
z y
y z
' '
t
2 ) Page 19
Reversible
Check if these equations give correct answer: For x’=ct’ ….. x=ct ?
June 2001 Frank Sciulli - Lecture I 1
x
y
( '
vt
')
y
'
z
z
'
t
2 ) 2
x
' (
x
vt
)
y
'
z
'
z y t
' (
t
Page 20 2 )
1
v << c
2
Limiting cases
1 2
v
2 ...
So this is essentially ONE unless the object is near the velocity of light… where it rises very rapidly. June 2001
= v/c
Frank Sciulli - Lecture I Page 21
June 2001 Time Dilation and Lorentz Contraction
t
t
' Happening in S’ at x’=0 over
t’
2 )
t
'
x
(
x v t
) Rod at rest in S’, with length L
0
Length in S is L, measure ends at same time:
t=0 L
L
0 Frank Sciulli - Lecture I Page 22
Relativistic Invariants
1 2
x
y
( '
vt
')
y
'
z
z
'
t
2 )
x
2
y
2
z
2
x
2 June 2001 2 Frank Sciulli - Lecture I invariant
z
2 ( ') 2 Page 23
Nonrelativistic
p K
Implications of Relativity for Particle Momentum and Energy
mv
1 2
mv
2 1 2 Implication: Matter is a form of energy. At v=0, E=mc
2
.
p K E E
Relativistic
mv
(
K
1)
mc
2
mc
2
m c
2
E
2 2
p c
2 2
m c
4 June 2001 Frank Sciulli - Lecture I
Prove it!
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Transformation of Momenta/Energy
x
( '
vt
') 1
y
z
y z
' '
t
2 ) June 2001
p x p y
(
p y
p x
p z E
p z
(
E
vp x
) Frank Sciulli - Lecture I 2 ) Page 25 2
Energy/Momentum/Mass and Units Universal energy units are joules (traditionally); but a much simpler one for dealing with particles:
q
(with electric charges that are multiples of the electron) June 2001
E
2
X
X
eV eV/c eV/c 2 MeV MeV/c MeV/c 2 GeV GeV/c GeV/c 2 Sensible units for discussion of atoms and subatomic particles is the electron volt = eV 1 eV = energy gained by electron (or proton) by acceleration through precisely V = one volt.
1 ev =
q V
19 joules Frank Sciulli - Lecture I Page 26
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Mass is Energy and vice versa
• 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~10 9 eV/c 2 Note that mass of proton is ~ 1 GeV/c 2 • Ultra - microscopic systems (nuclei and smaller), energies of constituents get comparable or larger than their rest mass What about EM fields?
Photons have no rest mass
E
p c
June 2001 Frank Sciulli - Lecture I Page 27
Mass Disappears-Energy Appears
FUSION
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Mass difference of .0304u = 28.3 MeV/c 2 becomes energy June 2001 Frank Sciulli - Lecture I Page 28
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 June 2001 Examples: Real-life everyday observations in particle and nuclear physics, where new matter is made and it spontaneously decays Frank Sciulli - Lecture I Page 29
Metastable Matter (Radioactive Decay makes a clock)
Example 128 I nuclide Characterized by lifetime ( ) or half-life (T 1/2 = ln2 = 0.7 ) with T 1/2 = 25 minutes.
1000 100
Compare: 14 C has T 1/2 = 5730 yrs.
has T 1/2 = 3.75 10 -8 sec
t
10
0
1
t
0 June 2001 Frank Sciulli - Lecture I Page 30
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
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Real World Test of Relativity: Fermilab Complex
Four mile circumference Tevatron Ring 15 story high rise June 2001 Frank Sciulli - Lecture I 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 June 2001 Frank Sciulli - Lecture I
= v/c
Page 33
Accelerated protons have very large energy
Beam protons hit stationary target (E = E t =m) with very large kinetic energy b /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.
28 Total Energy available for mass
M
2 (
p
) 2
p
2 with
E
m p M
2
M
2
m E
24.5
GeV
June 2001 2(1
GeV
28 )(300
m
GeV
3.9
)
GeV
Frank Sciulli - Lecture I Page 35
L
0
v
Beams of pions made from collisions of high energy protons
780
m
8 8
m
/ sec & 0 /
t
6 Nonrelativistic,
t
so fraction left 100
e
100 44
WRONG!!
Beam line, 0.78 km long, transports 140 GeV made at tgt
’s
June 2001 Frank Sciulli - Lecture I Page 36
Right answer: Lab perspective
E m
140
GeV
140
MeV v
1000 Observer: Time dilation
lab
lab t t
lab
fraction left
e
0.1
0.1 so 5 6 0.90
c
Right!!!
8 June 2001 Frank Sciulli - Lecture I Page 37
Right answer: pion perspective
E m
June 2001 140
GeV
140
MeV
1000 Pion se es: Lorentz Contraction
v
L
L
780
m
1000
t
L
c
t
0.1 so fraction left Frank Sciulli - Lecture I
e
0.1
0 8 7 0.78
m Right!!!
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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