EINSTEIN’S PHYSICS A modern understanding
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EINSTEIN’S PHYSICS A modern understanding

Ta-Pei Cheng. talk based on …. . Oxford Univ Press . (2/ . 2013). Einstein’s Physics. Atoms, Quanta, and Relativity --- Derived,. Explained, and Appraised. ATOMIC NATURE OF MATTER. 1. Molecular size from classical fluids.

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Presentation on theme: "EINSTEIN’S PHYSICS A modern understanding"— Presentation transcript:

Slide1

EINSTEIN’S PHYSICS

A modern understanding

Ta-Pei Cheng

talk based on …

Oxford Univ Press

(2/

2013)

Einstein’s Physics

Atoms, Quanta, and Relativity --- Derived,

Explained, and Appraised

Slide2

ATOMIC NATURE OF MATTER

1. Molecular size from classical fluids

2. The Brownian motion

WALKING IN EINSTEIN’S STEPS16. Internal symmetry and gauge interactions

17.

The Kaluza–Klein theory and extra dimensionsSPECIAL RELATIVITY9. Prelude to special

relativity

10. The new kinematics and

E

=

mc

2

11. Geometric formulation of relativity

GENERAL RELATIVITY

12.

Towards a general theory of

relativity

13. Curved spacetime as a gravitational field

14. The Einstein field equation

15. Cosmology

3. Blackbody radiation: From Kirchhoff to

Planck

4. Einstein’s proposal of light quanta

5. Quantum theory of specific heat6. Waves, particles, and quantum jumps7. Bose–Einstein statistics and condensation8. Local reality and the Einstein–Bohr debate

QUANTUM THEORY

2TOC

Today’s talk

provideswithout math detailssome highlights in historical context

The book explains his Physicsin equations

Albert Einstein

1879 – 1955

Slide3

Molecular size & Avogadro’s number

classical liquids with suspended particles

3Atoms

(4/1905) U Zurich doctoral thesis: “On the determination of molecular dimensions”

→ 2 equations relating

P & NA to viscosity and diffusion coefficientsHydrodynamics Navier-Stokes equation, balance of osmotic and viscous forcesE’s most cited publication!

A careful measurement of this zigzag motion through

a simple microscope would allow us to deduce the

Avogadro number!

(11 days later)

the Brownian motion paper:

While

thermal forces change the direction and

magnitude of the

velocity of a suspended particle on such a small

time-scale

that

it cannot

be measured,

the

overall

drift

of

such

a particle is observable quantity.

Fluctuation of a particle system

random walk

as the prototype of discrete system

Jean Perrin

It finally convinced everyone, even the skeptics, of the reality of molecules & atoms.

Slide4

Blackbody Radiation

(

rad in thermal equilibrium) = cavity radiation4Quanta 1

Einstein, like Planck, arrived at the quantum hypothesis thru BBR

Kirchhoff (1860)

densities = universal functions 2

nd

law

Maxwell EM radiation = a collection of oscillators

u = E

2

, B

2

~

oscillator

energy

kx

2

The ratio of

oscillating energy

to

frequency

is an adiabatic

invariant

; p = u/3

Stefan (1878) Boltzmann (1884):

Wien’s

displacement law

(1893):

Wien’s distribution

(1896)

:

fits

data

well….

until IR

Planck’s distribution

(1900)

:

key: Wien 2 ->1

var

Excellent fit of all the data

Wien = high

ν

of Planck

What is the physics?

Planck found a relation

What microstate counting

W

that

can lead to this

S

via

Boltzmann’s principle

S=k

ln

W

?

Planck was “compelled” to make the hypothesis of

energy quantization

Slide5

Einstein’s 1905 proposal of light quanta

was

not a direct follow-up of Planck’s

Rayleigh-Jeans = the low frequency limit of the successful Planck’s distribution

5Quanta 2

Einstein

used

Planck’s calculation

and

invoked the

equipartition theorem

of

stat

mech

to derive the

Rayleigh-Jeans law

noted its solid theoretical foundation

and the problem of ultraviolet catastrophe

showing

BBR = clear challenge to classical physics

The high frequency limit (

Wien’s distribution

)

=

new physics

Statistical study of (BBR)

wien

entropy change due to volume change: (BBR)

wien

~ ideal gas → (BBR)wien= a gas of light quanta with energy of Einstein arrived at energy quantization independently---- cited Planck only in 2 places

concentrate on

Slide6

The history of Rayleigh–Jeans law:

June 1900

, Rayleigh, applying the equipartition theorem to radiation, he obtained the result of C1ν

2T . Only a limit law? Intro cutoff ρ = C1ν2

T exp(-C

2ν/T)October–December 1900, The Planck spectrum distribution was discovered; energy quantization proposed two months laterMarch 1905, Einstein correctly derived the R-J law noted its solid theoretical foundation and the problem of ultraviolet catastrophe

May 1905

,

Rayleigh

returned

with

a

derivation of

C

1

. But

missed a factor of 8

June 1905, James Jeans

corrected Rayleigh’s error… But, explained away the incompatibility with experimental results by insisting that the observed radiation was somehow out of thermal equilibrium

.A.Pais: “It should really be called Rayleigh-Einstein-Jeans law”.6Quanta 2

An historical aside:

“Planck’s fortunate failure”?

Slide7

The quantum idea

Einstein

vs Planck 7Quanta 3

1906 Einstein came in agreement with Planck’s. Also

, gave a new derivation of Planck’s law

It clearly explained why energy quantizationcan cure ultraviolet catastropheThe new physics must be applicable beyond BBR: quantum theory of specific heat

Einstein

1905

:

as P’s

W

-

calculation unreliable…

E’s quantum “in

opposition” to

P’s quantum

Einstein

:

the

quantum idea must represent

new physics

;

proposed

photoelectric effect

as test.

Einstein’s photon idea was strongly resisted by the physics community for many years because it conflicted with the known evidence for the

wave nature

of light(Millikan 1916): “Einstein’s photoelectric equation . . . cannot in my judgment be looked upon at present as resting upon any sort of a satisfactory theoretical foundation”, even though“it actually represents very accurately the behavior” of the photoelectric effect”. Planck did not accept Einstein’s photon for at least 10 years

Planck 1900: is only a formal relation, not physical (radiation not inherently quantum: only during transmission, packets of energy, somehow)

Slide8

(1909) Light quanta = particles ?

8Quanta 4

1st time stated

: quanta carried

by point-like particles

point of view of

Newtonian emission theory

Photon carries energy + momentum

Wave-Particle Duality: a deep riddle

Slide9

9 Quanta 5

1916–17, Einstein used Bohr’s quantum jump idea to construct a microscopic theory of radiation–matter interaction:

absorption and emission of photons (A and B coefficients); he showed how Planck’s spectral distribution followed. The central novelty and lasting feature is the introduction of probability in quantum dynamics

Modern quantum mechanics : states

= vectors in Hilbert space (superposition)

observables = operators (commutation relations) Classical radiation field = collection of oscillatorsQuantum radiation field = collection of quantum oscillators

A

firm mathematical

foundation for Einstein’s photon idea

Quantum jumps

naturally accounted for by

ladder operators

Looking beyond Einstein:

His discoveries in quantum theory:

Wave/particle nature of light and quantum jumps

can all be accounted for in the framework of

quantum field theory

The picture of interactions broadened

QFT description:

Interaction

can change not only motion

,

but also allows for

emission and absorption of radiation

creation and annihilation of particles

Slide10

three-man paper

” of (Born, Heisenberg, and Jordan 1926): The same calculation of fluctuation of a system of waves, but replacing classical field by operators

The riddle of wave–particle duality in radiation fluctuationelegantly resolved in QFT

10Quanta

6

Was Einstein just too set-in-his-ways

to appreciate the new advances ?

Alas, Einstein never accepted this beautiful resolution

as he never accepted the new framework of quantum mechanics

forgotten history

Slide11

Local reality & the Einstein-Bohr debate

Bell’s theorem

(1964) : these seemingly philosophical questions could lead to observable results. The experimental vindication of the orthodox interpretation has sharpened our appreciation of the nonlocal features of quantum mechanics. Einstein’s criticism allowed a better understanding of the meaning of QM.Nevertheless, the counter-intuitive picture of objective reality as offered by QM still troubles many, leaving one to wonder whether quantum mechanics is ultimately a complete theory

11Quanta 7The orthodox view (measurement actually produces an object’s property) the measurement of one part of an entangled quantum state would instantaneously produce the value of another part, no matter how far the two parts have been separated.

Einstein, Podolsky

& Rosen (1935) : a thought experiment highlighting this “spooky action-at-a-distance” feature ; the discussion and debate of “EPR paradox” have illuminated some of the fundamental issues related to the meaning of QMOrthodox interpretation of QM

(

Niels Bohr

& co): the attributes of a physical object (position, momentum, spin, etc.) can be assigned only when they have been measured.

Local realist viewpoint of reality

(

Einstein

,…): a physical object has definite attributes whether they have been measured or not. …. QM is an incomplete theory

Slide12

Special Relativity

Maxwell’s equations: EM

wave – c Contradict relativity? 2 inertial frames

x’ = x - vt get velocity add’n rule u’ = u - v

The then-accepted interpretation:

Max eqns valid only in the rest-frame of ether12SR 1

Q:

How should EM

be described for sources and observers

moving with respect to the ether-frame?

“The

electrodynamics of a moving

body”

Einstein’s very different approach ..

1895 Lorentz’s theory (a particular

dynamics

theory

of ether/matter

)

could account all

observation

stellar aberration, Fizeau’s

expt

… to O(v/c) [

+ a math construct ‘local time’] Michelson-Morley null result @ O(

v2/c

2)  length contraction Lorentz transformation Maxwell ‘covariant’ to all orders (1904)

Slide13

Special Relativity

13SR 2

Case I

: moving charge in

B

(ether frame) Lorentz force (per unit charge)Case II: changing B induces an E

via

Faraday’s law, resulting exactly the

same force.

yet such diff descriptions

▪ Invoke

the

principle of relativity

This equality can be understood naturally as two cases have the same relative motion

Dispense with

ether

The magnet-conductor thought

expt

c

onstructive theory

vs

theory of principle

Einstein’s very different approach ..

Relativity = a symmetry in physics

Physics unchanged under some transformation

How to reconcile (Galilean) relativity

u’ = u - v

with the constancy of

c

?

Resolution:

simultaneity is relative

Time is not absolute, but frame dependent

Relation among

inertial frames

Correctly given by Lorentz transformation,

with

Galilean transformation

as low

v/c

approx

Slide14

The

new kinematics

allows for an simple derivation of the Lorentz transformation.All unfamiliar features follow from .

time dilation, length contraction, etc.

14SR 3

Special Relativity 1905From “no absolute time” to the complete theory in five weeks 10yr

Transformation rule for EM fields, radiation energy,..

Lorentz force law from Max field equations

Work-energy theorem

to

mass-energy equivalence

E = mc

2

Slide15

Even simpler perspective

Hermann Minkowski

(1907) Essence of SR: time

is on an equal footing as space. To bring out this, unite them in a single math structure, spacetimeGeometric formulation

Emphasizes the

invariance of the theory: c → s

s

= a spacetime length

(c as the conversion factor)

Lorentz-transformation = rotation → SR features

4-tensor equations are automatically relativistic

Special Relativity

Einstein was initially not impressed

,

calling it

superfluous

learnedness

15SR 4

SR:

The arena of physics is the 4D

spacetime

.. until he tried to formulate

General relativity

(non-inertial frames)

= Field theory of gravitation

Gravity = structure of

spacetime

SR = flat spacetime

GR = curved spacetime

Slide16

The Equivalence Principle (1907)

played a key role in the formulation of

general theory of relativity

16GR 1

Why does GR principle automatically bring gravity into consideration?

How is gravity related to spacetime?starting from Galileo Remarkable empirical observationAll objects fall with the same acceleration“Gravity disappears in a free fall frame”

a ↑ = ↓ g

From mechanics

to electromagnetism… →

light deflection by gravity, time dilation

with such considerations...

Einstein proposed

a geometric theory of gravitation

in 1912

gravitational field = warped spacetime

Note: A curved space being locally flat, EP incorporated in GR gravity theory in a

fundamental way.

accelerated frame = inertial frame w/ gravity

EP as the handle of going from SR to GR

Einstein: “My happiest thought”

Slide17

Source particle Field Test particle

Field

eqn

Eqn

of motion

Source particle Curved spacetime Test particle

Einstein field

eqn

Geodesic

Eqn

gravitational field = warped spacetime

metric tensor

[

g

μν

]

=

rela

. grav

. potential

energy momentum tensor

Newton’s constant

1915

curvature tensor = nonlinear 2

nd

derivatives of

[

g

μν

]

Metric =

gravi

pot

Curvature = tidal forcesThe Einstein equation10 coupled PDEssolution = [gμν]

17GR 2

In the limit of test particles moving

with

non-relativistic velocity

in a static and

weak grav field Einstein → Newton (1/r 2 law explained!) ie new realms of gravity

Slide18

In relativity, space-dep → time-

dep, GR → gravitational wave

Indirect, but convincing, evidence thru decade-long observation of Hulse-Taylor binary pulse system3 classical testsGrav redshiftBending of lightPrecession of planet orbit

Black Holes = full power and glory of GRGravity so strong that even light cannot escapeRole of space and time is reversed: lightcones tip over across the horizon

Alas, Einstein

never believed the reality of BHGR = field theory of gravitation18GR 3

Slide19

19 cosmo

(Einstein 1917)

The 1st paper on modern cosmologyThe universe = a phys system the constituent elements being galaxiesGravity the only relevant interaction

GR = natural framework for cosmologySpatial homogeneity & isotropy (the cosmological principle) →Robertson-Walker metric : k, a(t)

In order to produce a

static universe he found a way to introduce a grav repulsion in the form of the cosmology constant ΛEasier to interpret it as a vacuum energy: constant density and negative pressure → repulsion that increases w/ distance. – significant only on cosmological scale

Λ

= a great discovery

key ingredient of modern cosmology

Inflation

theory of the big bang: a large

Λ→

the universe underwent an explosive superluminal expansion in the earliest mo

Λ

=

dark energy

→ the U’s expansion to

accelerate

in the present epoch

The concordant

Λ

CDM cosmology

Cosmology

Einstein equationderivatives Expanding Universe

GR

provide the

framework !

Still, Einstein missed the chance of its prediction before the discovery in late 1920’s

Slide20

20 sym

Einstein and the symmetry principle

Before Einstein, symmetries were generally regarded as mathematical curiosities of great value to crystallographers, but hardly worthy to be included among the fundamental laws of physics. We now understand that a symmetry principle is not only an organizational device, but also

a method to discover new dynamics.

Rotation symmetry

Tensors have def transf propertyTensor equations are automatically rotational symmetric.

Spacetime-independent

Global symmetry

Special relativity

=

Lorentz transformation

4

-

tensor

eqns

are auto relativistic

General relativity

curved spacetime with moving basis vectors

spacetime –dependent

metric [

g

] = [

g(x)

]

general coord transf = spacetime dependent Local symmetry

Differentiation results in a non-tensor

Must replace by

covariant differentiation

.

.

symmetry → dynamics

Slide21

21gauge1

Einstein & unified field theory

the last 30 years of his life , strong conviction:GR + ED → solving the quantum mystery?

Was not directly fruitful, but his insight had fundamental influence on effort by others:Gauge theories and KK unification, etc. But both made sense only in modern QM

Gauge invariance

of electrodynamicsE, B → A, Φ invariant under in quantum mechanics must + wf transf U(1) local transformation

Transformation in the internal charge space

“changing particle label”

Such

local symmetry

in a

charge space

is now called

gauge symmetry

Gauge principle

:

Regard

ψ

transf as more basic,

as it can be gotten

by changing

U(1)

from

global to be local. brings in the compensating field A ,the gauge field

Given A , Maxwell derived by

SR+gauge

ie the simplestElectrodynamics as a gauge interactionGauge principle can be used to extend consideration to other interactions

History: Inspired by Einstein’s geometric GR1919 H Weyl attempt GR+ED unification via

Local scale symmetry

[g’ (x)]=

λ

(x)[g(x)]

Calling it

eichinvarianz

1926

V Fock, after the advent of QM, discovered phase transf of ψ(x)F London: drop “i” is just Weyl transfWeyl still kept the name: gauge transf

Slide22

Particle physics

Special relativity, photons, & Bose-Einstein statistics = key elements

But Einstein did not work directly on any particle phys theory.Yet, the influence of his ideas had been of paramount importance to the successful creation of the Standard Model of particle physics

Symmetry principle as the guiding light.The Standard Model is a good example of a theory of principle: the gauge symmetry principle → dynamics,

as well as a constructive theory

: discoveries of * quarks and leptons, * the sym groups of SU(2)xU(1) & SU(3)follow from trial-and-error theoretical prepositions and experimental checks ED is a gauge interaction based on abelian (commutative) transf.1954 CN Yang + R Mills extend it to non-abelian (non-commutative)

Much richer, nonlinear theory, can

describe

strong

&

weak interactions

22gauge2

Quantization

and

renormalization

of Yang-Mills

th

extremely difficult. Furthermore, the truly

relevant degrees of freedom for strongly interacting particle are hidden

(quark confinement). The applicability of gauge sym to weak int was doubted because the symmetry itself is hidden (spontaneous sym breaking due to Higgs

mech) 1970’s renaissance of QFT → SM’s triumph

Straightforward extension of QED ?

SM is formulated in the framework of QMHoly grail of modern unification = [GR + QM]

Slide23

23KK

Kaluza-Klein theory

u

nification

of

GR+Maxwell

1919

Th

Kaluza : 5D GR

extra dimension w/ a particular geometry

[g]

kk

GR

5

kk

= GR

4

+ ED

4

The Kaluza-Klein miracle!

In physics , even a miracle requires an explanation

1926

O Klein

explained in

modern QM

*Gauge transf = coord transf

in

extra D Internal charge space = extra D

Foreshadowed

modern unification theories.

GR + SM

t

he

compactified space =

multi-dimensional

Einstein’s influence lives on!

*Compactified extra D → a tower of KK states

the decoupling of heavy particles

simplifies the metric to

[g]

kkQ: What is the charge space?

What’s the origin of gauge symmetry?

Slide24

24

h -- c --

gNform an unit system of mass/length/time

Natural

units, not human construct

Dimensions of a fundamental theory i.e. quantum gravity (GR + QM)The fundamental nature of

Einstein’s contribution

illustrated by

Planck unit system

Summary

Summary

of a summary

Fundamental nature of these constants

shown as

conversion factors

connecting disparate phenomena

All due to

Einstein

’s

e

ssential contribution !

h

:

Wave & Particle

c

: Space & Time

g

N

: Mass/energy & Geometry

(QT)

(SR)

(GR)

Slide25

These

PowerPoint

slides are posted @www.umsl.edu/~chengt/einstein.html