Special relativity

l The laws of physics arethe same in allcoordinate systemseither at rest or movingat constant speed withrespect to one another

l The speed of light in avacuum has the samevalue regardless of thevelocity of the observeror the velocity of thesource emitting the light

Cosmic rays

l Some come from the sun(relatively low energy)and some fromcatastrophic eventselsewhere in thegalaxy/universe

Collision of a high energy cosmic ray particle with a photographic emulsion

Cosmic rays interact with the Earth’s upper atmosphere andproduce a shower of particles; eventually only subatomic particlescalled muons are left.Crab nebula

Cloud chamber

l A way of observingcosmic ray tracks insupersaturatedalcholol vapor thatcondenses on ionsleft in the wake of thecosmic rays

l A little like the bubblechamber that wetalked about earlier

Massl Remember Newtons second law F=mal If I keep a constant force on an object, then I have a constant

acceleration, i.e. the velocity keeps increasing at a constant ratel We’ve seen this doesn’t work at extreme speeds; as the velocity

gets closer to the speed of light, the acceleration decreasesl The object behaves as if its inertia is increasingl But inertia is mass, so the object behaves as if its mass is

increasing; the mass increase becomes very noticeable as theobject approaches the speed of light

l Newtons second law still ok if I reframe it; force is proportional totime rate of change of momentum (mv)

l Changes in momentum and kinetic energy come not only fromchanges in v but also changes in m

l So, mass is a form of energy, just as heat is a form of energy

u E=mc2

Energy and momentum

l Total energy of aparticle

u = kinetic energy + mc2

u = gmc2

u as v->0, g->1; energy=mc2 (just the restmass energy)

l Relativisticexpressions

u energy: E=gmc2

u momentum: p=gmv

u E2=p2c2+(mc2)2

u …for a masslessparticle (like aphoton)…E=pc

Convenient to quote particle energies in eV1 eV = 1.6 X 10-19 Jme=9.11X10-31 kgmec2=(9.11X10-31 kg)(3.0X108 m/s)2 = 8.2X10-19 J =(8.2X10-14 J)/(1.6X10-19 J/eV)=0.511 MeV

Particle Accelerators

Fermilab LHC

1 TeV (trillion electron-volts)7 TeV

Speed and Energy

0.9999999917 TeV

0.999999561 TeV (1012 eV)

0.8751 GeV (109 eV)

0.0461 MeV (106 eV)

0.000051 eV

Fraction ofspeed oflight

Energy ofproton

l Usually we don’tthink in terms of thespeed of protonssince we’reasymptoticallyapproaching thespeed of light

Pair production and annihilation

Energy can be converted into mass, or vice versa. More on thislater.

General Relativity

We said that special relativity applies for inertial frames of reference. What about for non-inertial (accelerating) frames?

That’s the realm of general relativity (also by A. Einstein). His equivalence principle stated that one can not tell the differencebetween gravity and an accelerating frame of reference.

General relativity

l Consider two equationsyou learned in PHY231

u Fg = G mgm’g/r2

u Fi=mia

l What do I mean by the gand the i?

u g refers to gravitationalmass and I to inertial mass

u Why should the inertialmass be equal to thegravitational mass?

u That’s what Einstein laidout in his theory of generalrelativity

l Postulates of generalrelativity

u All the laws of nature havethe same form forobservers in any frame ofreference, whetheraccelerated or not.

u In the vicinity of any givenpoint, a gravitational fieldis equivalent to anaccelerated frame ofreference without agravitational field.

Deflection of starlight

Energy and mass are equivalent. Starlight has energy; starlightshould be affected by gravitational fields.Einstein’s big prediction. Verified by an astronomer (Sir ArthurEddington) in a total eclipse in 1918.

Einstein became a celebrity.

Celebrity

l This was not whatthe world thought ascientist looked like

Curvature of space

l Newton’s idea of gravityu action at a distance

l Einstein’s ideau gravity is the result of the

curvature of spaceoccuring around any mass

u the larger the mass thegreater the curvature ofspace

u what happens when spacegets really curved?

Now it starts to get weirdl We’re going to start looking at

phenomena that occur onvery small distance scalesand quantum effects are goingto become important

l …so we’ll start off with MaxPlanck

u 1858-1947u at age of 16, entered

University of Munichu was advised that physics is a

complete science with littleprospect for furtherdevelopments

u majored in physics anywayu Nobel prize in physics in 1918u basic ideas of quantum

theory introduced by MaxPlanck

…more in keeping with publicidea of what a physicist shouldlook like

What’s the problem?l Blackbody radiationl An object at any temperature

radiates thermal radiationl Careful study of thermal radiation

shows that it consists of acontinuous distribution ofwavelengths from infrared,visible and ultraviolet portions ofspectrum

l From classical viewpoint, thermalradiation originates fromaccelerated charged particlesnear surface of object

u those charges emit radiationlike small antennas

u charges can havedistributions of accelerations,so continuous distribution ofradiation

lSo what’s the problem?

lProblem was in understanding the

observed distribution of wavelengths

in radiation emitted by a black body

Blackbody radiation

l Radiated energy varieswith wavelength andtemperature

l As temperature ofblackbody increases,total amount of energyincreases

l With increasingtemperature, peak alsoshifts to shorterwavelengths

l Shift follows Wien’sdisplacement law

u lmaxT=0.2898X10-2 m.K

Ultraviolet catastrophel Attempts to describe results

based on classical theorydidn’t work

l Rayleigh-Jeans lawu I(l,T)=2pckT/l4

u k is Boltzmann’s constant,l is the wavelength, T isthe temperature

l Agreement looks ok at higherwavelengths

l As l approaches 0, theintensity goes to infinity

l Oopsl The ultraviolet catastrophe

Max Planck comes to the rescue

l In 1900, Max Planckdiscovered a formula forblackbody radiation incomplete agreement withexperiment at all wavelengths

u I(l,T)=2phc2/[l5(ehc/lkT - 1)]u where h is a constant that

can be adjusted to fit thedata

u h (Planck’s constant)=6.626X 10-34 J.s

s …remember, we cameacross this h before,when we talked about theenergy in light (E=hf)

u agrees with Rayleigh-Jeanlaw at higher wavelength

…so how did he do it?l Consider molecules in interior of

black body as oscillatorl Planck made 2 bold assumptions

regarding these oscillatorsu oscillating molecules that emit

the radiation could only havediscrete units of energy Engiven by

s En=nhfs n is integer and f is

frequencyu molecules can emit or absorb

energy in discrete units calledquanta or photons

s they do so by jumpingfrom one quantum stateto another

l Key point is the assumption ofquantized energy states; thismarked the birth of quantumtheory

Quiz1. According to the special

theory of relativity, which ofthe following happens to thelength of an object,measured in the dimensionparallel to the motion of itsinertial frame of reference, asthe velocity of this frameincreases with respect to astationary observer?a) its length increasesb) its length decreasesc) its length stays the samed) its length, width and height

all increasee) its length, width and height

all decrease

2. According to the specialtheory of relativity, if a 30-year old astronaut is sent ona space mission and isaccelerated to speeds closeto that of light, and thenreturns to earth after aperiod of 20 years (asmeasured on earth), whatwould his biological age beon returning?

a) 50 yearsb) less than 50 yearsc) greater than 50 yearsd) exactly 100 yearse) 20 years