physics9d.10.fadley.slides1.earlymeasurementsthroughe=mc2...

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,…

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…

NO EVIDENCEFOR “ETHER”AS MEDIUM IN WHICH LIGHT PROPAGATES

Sun

vorbit 30 km/s→-vether

Ether (fixed)

Earth





•How do we reconcile particle motion vs. wave motion?





•And others…

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!





•How to reconcile particle motion vs. wave motion?





•And others…

SPECTRA EMITTEDBY HOT OBJECTS =“BLACKBODIES”

NO CLASSICALTHEORYWHICH EXPLAINSEXPERIMENTAL DATA, ESP.FOR SHORT WAVELENGTHS










•And others…

dsin = n

d

| |● Measuring emission spectra:

In phase

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










•And others…

How does light propagate?How do different observers see things?

NON-SIMULTANEITY OF EVENTS AS VIEWED IN DIFFERENT INERTIAL SYSTEMS

FUNDAMENTAL DIFFERENCES IN WHAT IS OBSERVED--BOATS ON WATER

TIME DILATIONPassage of time as seen by Mary vs. Frank & Fred

WHAT IS ROUNDTRIP TIME FOR LIGHT IN THE TWO FRAMES?

Mary in K’: :Frank and Fred in K

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)

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 !

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

LENGTH CONTRACTION

, mass increase as observedfrom “rest” frame, mass-energy equivalence

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

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.

TIME DILATION

NEARLY IDENTICAL

)

22.2

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!

S

S’ First point:Not inertial

here

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

)

And agedifferencesare possible,just like clocksIn airplanes:

How to go beyond Galileo?

Event:

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

Event:

THE LORENTZ TRANFORM:(From S to S’)

THE LORENTZ TRANFORM:(From S’ to S)

++

+

+ ′′ ′

′

′′

′′

′

′′

′′

′′′

′ ′

NON-SIMULTANEITY OF EVENTS AS VIEWED IN DIFFERENT INERTIAL SYSTEMS

= S’

= S

THE LORENTZ TRANFORM: Distortion of moving objects

( )E B oF F F q E v B

v

What happens if test charge and negative charge are at rest?

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

FORCE BETWEEN TWOPARALLEL CURRENT-CARRYING WIRES?

K’

Collision seenfrom center of mass of two balls:

Frank concludesMary’s ball has a greatermomentum,or greatereffective (relativistic) mass,and viceversa

= 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

, mass increase as observedfrom “rest” frame, mass-energy equivalence

physics9d.10.fadley.slides1.earlymeasurementsthroughe=mc2...

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