Cosmic rays. l Some come from the sun (relatively low energy) and some from catastrophic events elsewhere in the galaxy/universe

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1 Special relativity The laws of physics are the same in all coordinate systems either at rest or moving at constant speed with respect to one another The speed of light in a vacm has the same vale regardless of the velocity of the observer or the velocity of the sorce emitting the light

2 Cosmic rays l Some come from the sn (relatively low energy) and some from catastrophic events elsewhere in the galaxy/niverse Crab nebla Collision of a high energy cosmic ray particle with a photographic emlsion Cosmic rays interact with the Earth s pper atmosphere and prodce a shower of particles; eventally only sbatomic particles called mons are left.

3 Clod chamber A way of observing cosmic ray tracks in spersatrated alcholol vapor that condenses on ions left in the wake of the cosmic rays A little like the bbble chamber that we talked abot earlier

4 Mass Remember Newtons second law F=ma If I keep a constant force on an object, then I have a constant acceleration, i.e. the velocity keeps increasing at a constant rate We ve seen this doesn t work at extreme speeds; as the velocity gets closer to the speed of light, the acceleration decreases The object behaves as if its inertia is increasing Bt inertia is mass, so the object behaves as if its mass is increasing; the mass increase becomes very noticeable as the object approaches the speed of light Newtons second law still ok if I reframe it; force is proportional to time rate of change of momentm (mv) Changes in momentm and kinetic energy come not only from changes in v bt also changes in m So, mass is a form of energy, jst as heat is a form of energy E=mc 2

5 Energy and momentm Total energy of a particle = kinetic energy + mc 2 = gmc 2 as v->0, g->1; energy =mc 2 (jst the rest mass energy) Relativistic expressions energy: E=gmc 2 momentm: p=gmv E 2 =p 2 c 2 +(mc 2 ) 2 for a massless particle (like a photon) E=pc Convenient to qote particle energies in ev 1 ev = 1.6 X J m e =9.11X10-31 kg m e c 2 =(9.11X10-31 kg)(3.0x10 8 m/s) 2 = 8.2X10-19 J =(8.2X10-14 J)/(1.6X10-19 J/eV)=0.511 MeV

6 Particle Accelerators Fermilab LHC 1 TeV (trillion electron-volts) 7 TeV

7 Speed and Energy Usally we don t think in terms of the speed of protons since we re asymptotically approaching the speed of light Energy of proton 1 ev 1 MeV (10 6 ev) 1 GeV (10 9 ev) Fraction of speed of light TeV (10 12 ev) TeV

8 Pair prodction and annihilation Energy can be converted into mass, or vice versa. More on this later.

9 General Relativity We said that special relativity applies for inertial frames of reference. What abot for non-inertial (accelerating) frames? That s the realm of general relativity (also by A. Einstein). His eqivalence principle stated that one can not tell the difference between gravity and an accelerating frame of reference.

10 General relativity Consider two eqations yo learned in PHY231 F g = G m g m g /r2 F i =m i a What do I mean by the g and the i? g refers to gravitational mass and I to inertial mass Why shold the inertial mass be eqal to the gravitational mass? That s what Einstein laid ot in his theory of general relativity Postlates of general relativity All the laws of natre have the same form for observers in any frame of reference, whether accelerated or not. In the vicinity of any given point, a gravitational field is eqivalent to an accelerated frame of reference withot a gravitational field.

11 Deflection of starlight Energy and mass are eqivalent. Starlight has energy; starlight shold be affected by gravitational fields. Einstein s big prediction. Verified by an astronomer (Sir Arthr Eddington) in a total eclipse in Einstein became a celebrity.

12 Celebrity This was not what the world thoght a scientist looked like

13 Crvatre of space Newton s idea of gravity action at a distance Einstein s idea gravity is the reslt of the crvatre of space occring arond any mass the larger the mass the greater the crvatre of space what happens when space gets really crved?

14 Now it starts to get weird We re going to start looking at phenomena that occr on very small distance scales and qantm effects are going to become important so we ll start off with Max Planck at age of 16, entered University of Mnich was advised that physics is a complete science with little prospect for frther developments majored in physics anyway Nobel prize in physics in 1918 basic ideas of qantm theory introdced by Max Planck more in keeping with pblic idea of what a physicist shold look like

15 What s the problem? Blackbody radiation An object at any temperatre radiates thermal radiation Carefl stdy of thermal radiation shows that it consists of a continos distribtion of wavelengths from infrared, visible and ltraviolet portions of spectrm From classical viewpoint, thermal radiation originates from accelerated charged particles near srface of object those charges emit radiation like small antennas charges can have distribtions of accelerations, so continos distribtion of radiation So what s the problem? Problem was in nderstanding the observed distribtion of wavelengths in radiation emitted by a black body

16 Blackbody radiation Radiated energy varies with wavelength and temperatre As temperatre of blackbody increases, total amont of energy increases With increasing temperatre, peak also shifts to shorter wavelengths Shift follows Wien s displacement law l max T=0.2898X10-2 m. K

17 Ultraviolet catastrophe Attempts to describe reslts based on classical theory didn t work Rayleigh-Jeans law I(l,T)=2pckT/l 4 k is Boltzmann s constant, l is the wavelength, T is the temperatre Agreement looks ok at higher wavelengths As l approaches 0, the intensity goes to infinity Oops The ltraviolet catastrophe

18 Max Planck comes to the resce In 1900, Max Planck discovered a formla for blackbody radiation in complete agreement with experiment at all wavelengths I(l,T)=2phc 2 /[l 5 (e hc/lkt - 1)] where h is a constant that can be adjsted to fit the data h (Planck s constant) =6.626X J.s s remember, we came across this h before, when we talked abot the energy in light (E=hf) agrees with Rayleigh-Jean law at higher wavelength

19 so how did he do it? Consider molecles in interior of black body as oscillator Planck made 2 bold assmptions regarding these oscillators oscillating molecles that emit the radiation cold only have discrete nits of energy E n given by s E n =nhf s n is integer and f is freqency molecles can emit or absorb energy in discrete nits called qanta or photons s they do so by jmping from one qantm state to another Key point is the assmption of qantized energy states; this marked the birth of qantm theory

20 Qiz 1. According to the special theory of relativity, which of the following happens to the length of an object, measred in the dimension parallel to the motion of its inertial frame of reference, as the velocity of this frame increases with respect to a stationary observer? a) its length increases b) its length decreases c) its length stays the same d) its length, width and height all increase e) its length, width and height all decrease 2. According to the special theory of relativity, if a 30- year old astronat is sent on a space mission and is accelerated to speeds close to that of light, and then retrns to earth after a period of 20 years (as measred on earth), what wold his biological age be on retrning? a) 50 years b) less than 50 years c) greater than 50 years d) exactly 100 years e) 20 years