TaPei 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. ID: 719127 Download Presentation
TaPei 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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EINSTEIN’S PHYSICS
A modern understanding
TaPei Cheng
talk based on …
Oxford Univ Press
(2/
2013)
Einstein’s Physics
Atoms, Quanta, and Relativity  Derived,
Explained, and Appraised
Slide2ATOMIC 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
Slide3Molecular 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 NavierStokes 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
timescale
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.
Slide4Blackbody 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
Slide5Einstein’s 1905 proposal of light quanta
was
not a direct followup of Planck’s
RayleighJeans = 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
RayleighJeans 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
Slide6The 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 RJ 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 RayleighEinsteinJeans law”.6Quanta 2
An historical aside:
“Planck’s fortunate failure”?
Slide7The 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 pointlike particles
“
point of view of
Newtonian emission theory
”
Photon carries energy + momentum
WaveParticle Duality: a deep riddle
Slide99 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“
threeman 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 setinhisways
to appreciate the new advances ?
Alas, Einstein never accepted this beautiful resolution
as he never accepted the new framework of quantum mechanics
forgotten history
Slide11Local reality & the EinsteinBohr 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 counterintuitive 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 actionatadistance” 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
Slide12Special Relativity
Maxwell’s equations: EM
wave – c Contradict relativity? 2 inertial frames
x’ = x  vt get velocity add’n rule u’ = u  v
The thenaccepted interpretation:
Max eqns valid only in the restframe of ether12SR 1
Q:
How should EM
be described for sources and observers
moving with respect to the etherframe?
“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’] MichelsonMorley null result @ O(
v2/c
2) length contraction Lorentz transformation Maxwell ‘covariant’ to all orders (1904)
Slide13Special 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 magnetconductor 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
Slide14The
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
Workenergy theorem
to
massenergy equivalence
E = mc
2
Slide15Even 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)
Lorentztransformation = rotation → SR features
4tensor 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
(noninertial frames)
= Field theory of gravitation
Gravity = structure of
spacetime
SR = flat spacetime
GR = curved spacetime
Slide16The 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”
Slide17Source 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
nonrelativistic velocity
in a static and
weak grav field Einstein → Newton (1/r 2 law explained!) ie new realms of gravity
Slide18In relativity, spacedep → time
dep, GR → gravitational wave
Indirect, but convincing, evidence thru decadelong observation of HulseTaylor 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
Slide1919 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) →RobertsonWalker 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
Slide2020 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.
Spacetimeindependent
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 nontensor
Must replace by
covariant differentiation
.
.
symmetry → dynamics
Slide2121gauge1
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
Slide22Particle physics
Special relativity, photons, & BoseEinstein 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 trialanderror theoretical prepositions and experimental checks ED is a gauge interaction based on abelian (commutative) transf.1954 CN Yang + R Mills extend it to nonabelian (noncommutative)
Much richer, nonlinear theory, can
describe
strong
&
weak interactions
22gauge2
Quantization
and
renormalization
of YangMills
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]
Slide2323KK
KaluzaKlein 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 KaluzaKlein 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 =
multidimensional
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?
Slide2424
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)
Slide25These
PowerPoint
slides are posted @www.umsl.edu/~chengt/einstein.html
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