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Physics: Science which observes (measures) fundamental physical phenomena and attempts to explain and predict them in the simplest and most self-consistent way: experiment + theory, both essential
Classical physics: A wonderful set of very few equations & principles with which a great many phenomena can be explained quantitatively:
Conservation of energy, linear & angular momentum,charge
Newton’s Laws of Motion: 3Maxwell’s Equations for electricity and magnetism:
4 plus Lorentz Force LawThermodynamics: 2, maybe 3The Kinetic Theory of Gases—beginning to look at
atomic levelBasic forces: gravity and coulombic repulsion/attraction
But limited to large objects (atom or larger), velocities much less than the speed of light, other difficulties or inconsistencies
Modern physics: Developed since ca. 1900, applies to subatomic objects, speeds approaching that of light, new forces, new particles,…
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SOME PROBLEMS WITH CLASSICAL PHYSICS CA. 1900
•How does light propagate? A matter wave? Constant speed in vacuum?
•How do electric and magnetic fields change from one observer (e.g. fixed) to another (e.g. moving)?
•What electromagnetic spectrum is emitted by a hot object?
•How do we reconcile particle motion vs. wave motion?
•Why do some spectra show lines rather than continua?
•How are x-rays produced by atoms?
•What is radioactivity?
•How does the electron fit in: much smaller and lighter than atom
•And others…
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NO EVIDENCEFOR “ETHER”AS MEDIUM IN WHICH LIGHT PROPAGATES
Sun
vorbit 30 km/s→-vether
Ether (fixed)
Earth
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SOME PROBLEMS WITH CLASSICAL PHYSICS CA. 1900
•How does light propagate? A matter wave? Constant speed in vacuum?
•How do electric and magnetic fields change from one observer (e.g. fixed) to another (e.g. moving)?
•What electromagnetic spectrum is emitted by a hot object?
•How do we reconcile particle motion vs. wave motion?
•Why do some spectra show lines rather than continua?
•How are x-rays produced by atoms?
•What is radioactivity?
•How does the electron fit in: much smaller and lighter than atom
•And others…
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E B oF F F q E v B
( )
v
What happens if test charge and negative charge are at rest?
Watchv (vee)-velocityvs (nu)-frequency!
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SOME PROBLEMS WITH CLASSICAL PHYSICS CA. 1900
•How does light propagate? A matter wave? Constant speed in vacuum?
•How do electric and magnetic fields change from one observer (e.g. fixed) to another (e.g. moving)?
•What electromagnetic spectrum is emitted by a hot object?
•How to reconcile particle motion vs. wave motion?
•Why do some spectra show lines rather than continua?
•How are x-rays produced by atoms?
•What is radioactivity?
•How does the electron fit in: much smaller and lighter than atom
•And others…
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SPECTRA EMITTEDBY HOT OBJECTS =“BLACKBODIES”
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NO CLASSICALTHEORYWHICH EXPLAINSEXPERIMENTAL DATA, ESP.FOR SHORT WAVELENGTHS
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SOME PROBLEMS WITH CLASSICAL PHYSICS CA. 1900
•How does light propagate? A matter wave? Constant speed in vacuum?
•How do electric and magnetic fields change from one observer (e.g. fixed) to another (e.g. moving)?
•What electromagnetic spectrum is emitted by a hot object?
•How to reconcile particle motion vs. wave motion?
•Why do some spectra show lines rather than continua?
•How are x-rays produced by atoms?
•What is radioactivity?
•How does the electron fit in: much smaller and lighter than atom
•And others…
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SOME PROBLEMS WITH CLASSICAL PHYSICS CA. 1900
•How does light propagate? A matter wave? Constant speed in vacuum?
•How do electric and magnetic fields change from one observer (e.g. fixed) to another (e.g. moving)?
•What electromagnetic spectrum is emitted by a hot object?
•How to reconcile particle motion vs. wave motion?
•Why do some spectra show lines rather than continua?
•How are x-rays produced by atoms?
•What is radioactivity?
•How does the electron fit in: much smaller and lighter than atom
•And others…
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dsin = n
d
| |● Measuring emission spectra:
In phase
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LINE SPECTRA OF DIFFERENT SOURCES:
Atomic hydrogen
Sodium
Helium
Neon
Mercury
Molecular hydrogen = H2
WHY LINES?
Sodium- D-line emiss.
Sodium- D-line absorp.
The Sun: blackbody emission plus absorption
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SOME PROBLEMS WITH CLASSICAL PHYSICS CA. 1900
•How does light propagate? A matter wave? Constant speed in vacuum?
•How do electric and magnetic fields change from one observer (e.g. fixed) to another (e.g. moving)?
•What electromagnetic spectrum is emitted by a hot object?
•How to reconcile particle motion vs. wave motion?
•Why do some spectra show lines rather than continua?
•How are x-rays produced by atoms?
•What is radioactivity?
•How does the electron fit in: much smaller and lighter than atom
•And others…
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SOME PROBLEMS WITH CLASSICAL PHYSICS CA. 1900
•How does light propagate? A matter wave? Constant speed in vacuum?
•How do electric and magnetic fields change from one observer (e.g. fixed) to another (e.g. moving)?
•What electromagnetic spectrum is emitted by a hot object?
•How to reconcile particle motion vs. wave motion?
•Why do some spectra show lines rather than continua?
•How are x-rays produced by atoms?
•What is radioactivity?
•How does the electron fit in: much smaller and lighter than atom
•And others…
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How does light propagate?How do different observers see things?
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NON-SIMULTANEITY OF EVENTS AS VIEWED IN DIFFERENT INERTIAL SYSTEMS
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FUNDAMENTAL DIFFERENCES IN WHAT IS OBSERVED--BOATS ON WATER
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TIME DILATIONPassage of time as seen by Mary vs. Frank & Fred
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WHAT IS ROUNDTRIP TIME FOR LIGHT IN THE TWO FRAMES?
Mary in K’: :Frank and Fred in K
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RADIOACTIVE DECAY—SOME BASICS(Thornton and Rex, Section 12.6)
At t = 0, N0 radioactive nuclei
Rate of decay = -dN(t)/dt = N(t)
dN(t)/N(t) = - dt
0
t t
o ot t0 0
t /t0 0 0
1 / 2 0 1 / 2 0
IntegratingdN dtN
n N t
N(t ) N (0 )e N (0 )e , with 1 /Or ,when half of number gone,
1 n(1 / 2 ) n(2 )N(t ) N (0 ) t 0.6932
N0(t=0)
N(t)
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MUON DECAY AND TIME DILATIONThe view from the ground
Non-relativistically:T = 2000 m/(0.98x3.0x108ms-1) =
6.8 x 10-6 s 3.1 0down by e-3.1 1/22So expect 1000/22 =45, not 542 !
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MUON DECAY AND TIME DILATIONComparing views from ground and muon
Top of mountain
1000e-6.8/11.0 = 538 muons
1000e-6.8(.2)/2.2 = 539 muons
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LENGTH CONTRACTION
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)
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, mass increase as observedfrom “rest” frame, mass-energy equivalence
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β = v/cAir molecules @
room temp.: 1.3 x 10-6
Passenger jet: 1 x 10-6
Fighter plane: 2-3 x 10-6
Moon rocket: 3 x 10-5
Furthest objectsseen in universe: 0.2-0.3
Particles inside atomor in accelerator: 0.999999..
Lorentz Contraction of Lengths
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Cool movies for sound at:http://www.gmi.edu/~drussell/Demos/doppler/doppler.html
THE DOPPLER EFFECT—Sound and Light
● Sound:
●● 0
v(+)
0 =cs /0 = no. wavelengths/scs= 00=speed of sound
If source at rest:
= cs / = no. wavelengths/s= cs /0(cs/(cs+v) = 0 (cs/(cs+v) = 0/(1+v/cs) = 0/(1+βs) 0(1- βs) for <<1
Light: Same, but also time dilated for observer at rest. /0 willbe smaller by or2 1/ 21/ (1 )
2 1/ 1/ 22 1/ 2 1/ 20 0(1 ) /(1 ) (1 ) (1 ) /(1 )
Top signs: ● ●Bottom (or blue) signs: ● ●
for1/2
0 0 0 0 0
2
1/2 2 2(1 ) 1 / 2 (1 / 2)(1 / 2) 1 / 4 [1 ] 1
1 / 2(1 ) (1 / 2) 1 / 4
v(+)v(-)
What does observerat rest see? v(-)
- - - - +
Note:Greek nu = = frequency (2nd Ed.)
= f in text (3rd Ed.)
Same
Rev.
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TIME DILATION
NEARLY IDENTICAL
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)
22.2
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DOPPLER RADARX-band (3 cm wavelength) and S-band (10 cm wavelength)
Reflectivity Rainlocation
Doppler-shiftbeatsignalChangein freq. Windvelocity
More discussion at:http://www.usatoday.com/weather/wearadar.htmhttp://radar.wrh.noaa.gov/radar/radinfo/radinfo.html,http://cimms.ou.edu/~schuur/radar.html#Q5
Doppler 1 andDoppler 2--Two polarizationsof radiation:
E2
E1
Raindrop,Snowflake,
Insect
Scatteredwave
And reflectedradiation seestwice as muchdoppler shift!
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S
S’ First point:Not inertial
here
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Second point:Do they both see the same
events somehow?
Yes, they both see the same events!!
L= 20 Light-yearsv = 0.8 c = 0.8; = 1/[1-.64]1/2 = 1.666… = 5/3
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)
And agedifferencesare possible,just like clocksIn airplanes:
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How to go beyond Galileo?
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Event:
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More generally, if t not equal to t’ at start:
s2 x2 + y2 + z2 – (ct)2 =(s’)2 (x’)2 + (y’)2 + (z’)2 – (ct’)2
s2 = “Spacetime invariant” connecting any two inertial frames
Or with two events 1 and 2 in 1 space dim.:
s2 = (s12 – s2
2) = (x12 – x2
2) –c(t12 – t2
2) =(s’)2 = (s’12 – s’22) = (x’12 – x’22) –c(t’12 – t’22)
Another invariant
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Event:
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THE LORENTZ TRANFORM:(From S to S’)
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THE LORENTZ TRANFORM:(From S’ to S)
++
+
+ ′′ ′
′
′′
′′
′
′′
′′
′′′
′ ′
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NON-SIMULTANEITY OF EVENTS AS VIEWED IN DIFFERENT INERTIAL SYSTEMS
= S’
= S
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THE LORENTZ TRANFORM: Distortion of moving objects
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( )E B oF F F q E v B
v
What happens if test charge and negative charge are at rest?
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v
v
(a)
(b)
(c)
(d)
L’
L
Lorentz contractionBoth Frank and Mary see the same force,but Frank from magnetic field, Mary from electric field
Net positive charge density along wire
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FORCE BETWEEN TWOPARALLEL CURRENT-CARRYING WIRES?
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K’
Collision seenfrom center of mass of two balls:
Frank concludesMary’s ball has a greatermomentum,or greatereffective (relativistic) mass,and viceversa
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= meff2 2
; ( )1 /
rel reld d up mu F mu mdt dt u c
v/c
=
(Effe
ctiv
e R
elat
ivis
tic M
ass)
/(Res
t Mas
s) =
mef
f/m
Therefore, no object can be accelerated to the speed of light!
Relativistic momentum and force:
; m = “rest mass” = constant2 2
11 /u c
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)
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, mass increase as observedfrom “rest” frame, mass-energy equivalence