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Head for Understandable Description of Matter and Forces at the Most Fundamental Level

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## Head for Understandable Description of Matter and Forces at the Most Fundamental Level

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Head for Understandable Description of Matter and Forces at the Most Fundamental Level

Frank Sciulli - Lecture I

Is this a Belief System?

NO!

Science does use the beauty of ideas, but ultimately relies on EXPERIMENT!!

Frank Sciulli - Lecture I

Illustrate, hopefully, that Physics (Science) has as ultimate

arbitrator

NATURE ! ! ! !

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

Frank Sciulli - Lecture I

Approach to the Subjects

Eclectic: factual, historical,

experimental, …

Lets start with pre-20th Century

- Newton’s Laws (Galileo,…)
- Energy and Work
- Thermodynamics
- Chemistry … atoms?
- Optics, fluids, waves, ...

Particles and Forces:

Frank Sciulli - Lecture I

Double slit

Classical particles and wavesWater waves hit slits

Classical particle scattering (balls)

Frank Sciulli - Lecture I

Consolidation of Electricity and Magnetism by Maxwell (1864)

Established clear rules for fields as the origin of EM force.

Made rules consistent!

They read

Source of E is charge (Gauss Law)

No magnetic charge

Faraday’s Law of Induction

Source of B is charge motion + Maxwell’s new Displacement Current

Frank Sciulli - Lecture I

Implications: Electromagnetic Waves

Frank Sciulli - Lecture I

(light and dark pattern),

corresponding to constructive

and destructive interference:

For example, if 2d2 -2d1

changes by /2, fringe

pattern shifts

Michaelson InterferometerBecame important element in central problem of 100 yrs ago: why is

Frank Sciulli - Lecture I

mechanical wave relative to

the observer obeys the same rules

as a travelling particle:

relative velocities

Light also

has velocity

independent

of source

speed

PROBLEMVelocity of a mechanical wave depends only on the medium, not the velocity of the source (even though frequency and wavelength change - Doppler shift)

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

Earth motion

around sun

- Essential element of scientific hypothesis: provides a possibility for testing!

- 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!

Frank Sciulli - Lecture I

1887: Michaelson-Morley idea

Frank Sciulli - Lecture I

Apparatus on bed of liquid mercury, rotate by 90 degrees

Michaelson - Morley ExptUse 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

Frank Sciulli - Lecture I

around sun

V=30km/s

5 10-7 m

Make d as

large as

possible

Michaelson Morley Experiment - “Big” Physics of 1887CONCLUDE: No phase shift was observed

NO ETHER … ?!%*

Frank Sciulli - Lecture I

Plane shoots laser

Einstein’s ReasoningMaxwell’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…

Frank Sciulli - Lecture I

ConundrumEITHER 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 motionEinstein 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

Frank Sciulli - Lecture I

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 sourceCARRY MANY IMPLICATIONS

Lorentz Contraction

+

Time Dilation

+

Frank Sciulli - Lecture I

Transformations of Position and Time

Frank Sciulli - Lecture I

Reversible

Check if these equations

give correct answer:

For x’=ct’ ….. x=ct ?

Frank Sciulli - Lecture I

= v/c

Limiting casesSo this is essentially ONE unless the object is near the velocity of light… where it rises very rapidly.

Frank Sciulli - Lecture I

Time Dilation and Lorentz Contraction

Happening in S’ at x’=0

over t’

Rod at rest in S’, with length L0

Length in S is L, measure ends

at same time: t=0

Frank Sciulli - Lecture I

Relativistic Invariants

Frank Sciulli - Lecture I

Implications of Relativity for Particle Momentum and Energy

Relativistic

Nonrelativistic

Implication: Matter is a form of energy. At v=0, E=mc2.

Frank Sciulli - Lecture I

Transformation of Momenta/Energy

Frank Sciulli - Lecture I

X

eV eV/c eV/c2

MeV MeV/c MeV/c2

GeV GeV/c GeV/c2

Energy/Momentum/Mass and UnitsUniversal energy

units are joules (traditionally);

but a much simpler one for dealing with particles:

(with electric charges that are multiples of the electron)

Frank Sciulli - Lecture I

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~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?

Frank Sciulli - Lecture I

Mass Disappears-Energy AppearsFUSION

Mass difference of .0304u = 28.3 MeV/c2 becomes energy

Frank Sciulli - Lecture I

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

Frank Sciulli - Lecture I

or half-life (T1/2 = ln2 = 0.7 )

1000

100

10

1

Metastable Matter(Radioactive Decay makes a clock)Example 128I nuclide

with T1/2 = 25 minutes.

Compare:

14C has T1/2 = 5730 yrs.

has T1/2= 3.75 10-8 sec

Frank Sciulli - Lecture I

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

Frank Sciulli - Lecture I

Four mile circumference Tevatron Ring

Real World Test of Relativity: Fermilab ComplexFrank Sciulli - Lecture I

velocity

= v/c

Accelerators Raise Kinetic Energy using Electric FieldsEach loop, the energy of protons are raised by increment determined by electric potential: E =eV

= E/m

Proton total Energy

versus velocity

Frank Sciulli - Lecture I

target (Et=m) with

very large kinetic energy

= Eb/m

Extracted protons have

energy E 800 GeV

Accelerated protons have very large energyWhat happens????

Frank Sciulli - Lecture I

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.

Frank Sciulli - Lecture I

Beams of pions made from collisions of high energy protons

WRONG!!

Beam line, 0.78 km long,

transports 140 GeV ’s made at tgt

Frank Sciulli - Lecture I

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!

Frank Sciulli - Lecture I

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