PresocraticsParticles & FieldsPhysics Foundations
Special RelativityGeneral RelativityQuantum MechanicsQuantum Field Theory
Quantum GravityPlanck ScaleLoop Quantum GravityString/M!Theory
Outline
Presocratic Timeline-600 -500 -400 -300 -200
Thales Leucippus
Anaximander Socrates
Anaximenes Democritus
Pythagoras Plato
Parmenides Aristotle
Zeno of Elea Zeno the Stoic
Heraclitus Epicurus
Anaxagoras Cleanthes
Empedocles Chrysippus
Two World ViewsHeraclitus
All is flux
Everything changes
Parmenides
Change is an illusion
Nothing changes
Zeno Defends Parmenides
Zeno paradoxes transcend the historical Zeno
Relevant to modern views of space & time
Zeno’s ParadoxesMotion Unexists
The Dichotomy
The Achilles
The Arrow
The Stadium
Plurality Unexists
†
1+ 12 + 1
4 + 18 +L?( )
†
12 T = 2T ?( )
†
• ¥ 0 = ?( )
Finite path:
But no logical exit direction, as no last mirror
Zeno’s Zigzag
†
S = 1+12
+14
+18
+L fi
2S = 2 +1+12
+14
+L = 2 + S fi S = 2
PresocraticsParticles & FieldsPhysics Foundations
Special RelativityGeneral RelativityQuantum MechanicsQuantum Field Theory
Quantum GravityPlanck ScaleLoop Quantum GravityString/M!Theory
Outline
Chasing Democritus
Molecules
Atoms
Nuclei & Electrons
Nucleons
Quarks
atom
nucleus
neutron & proton
quarks & electron
sizein atoms
sizein meters
< 10-18
10-15
10-14
10-101
110,000
1100,000
1100,000,000
Particle/Forces
fermions
bosons(forces)
(matter)
quarks
leptons
u (up)
d (down)
e (electron)
n (neutrino)
g (photon)
g (gluon)
W (weakon)
PresocraticsParticles & FieldsPhysics Foundations
Special RelativityGeneral RelativityQuantum MechanicsQuantum Field Theory
Quantum GravityPlanck ScaleLoop Quantum GravityString/M!Theory
Outline
Special Relativity "SR#
†
ds2 = dx( )2+ dy( )2
+ dz( )2- cdt( )2
†
- mc 2( )2
= pxc( )2+ pyc( )
2+ pzc( )2
- E 2
Fundamental scale, invariant speed of light
Relative lengths & durations, invariant spacetime
Energy, momentum, mass
†
c ~ 108 m s
Special Relativity "SR#Worldlines in spacetimeBeing, not becomingNo “moving now”
t
s
14 March 1879Ulm, Württemberg,
Germany
18 April 1955Princeton, New Jersey,
USA
The distinction between past, present, and future is only an
illusion, even if a stubborn one.
Albert Einstein
PresocraticsParticles & FieldsPhysics Foundations
Special RelativityGeneral RelativityQuantum MechanicsQuantum Field Theory
Quantum GravityPlanck ScaleLoop Quantum GravityString/M!Theory
Outline
General Relativity "GR#Fundamental scale
Newton’s gravity constant
Gravity is spacetime curvature
Spacetime is a dynamical variable†
F = G Mmd2†
G ~ 10-10 N ⋅ m2 kg2
†
Rmn -12
gmn R =8pGc 4 Tmn
PresocraticsParticles & FieldsPhysics Foundations
Special RelativityGeneral RelativityQuantum MechanicsQuantum Field Theory
Quantum GravityPlanck ScaleLoop Quantum GravityString/M!Theory
Outline
Quantum Mechanics "QM#
Fundamental scale
Non!commuting operators
Uncertainty "Indeterminacy# Relation
†
qp - pq = ih
†
DqDp ≥ h
†
h ~ 10-34 J ⋅ s
Atoms don’t behave classically
Described by a wave function "or vector# rotating deterministically in an infinite dim Hilbert space
Wave functions can describe counterintuitive nonclassical states like “superpositions” of live and dead cats
In 1920s, physicists explained away this weirdness by postulating that “observations” randomly collapse wave functions into classical states
Quantum Many Worlds
Einstein objected, “God does not play dice”
In 1957, Everett showed that quantum mechanics is consistent without the random collapse postulate
Rather, classical reality continually splits into superpositions of many different realities
Observers experience splitting as randomness
Quantum Many Worlds
Either way, all possible states exist at any moment
Now you are in Universe A looking at this slide...
The Nature of Time
Either way, all possible states exist at any moment
Now you are in Universe A looking at this slide...
And now you are in Universe B looking at this slide "& with memories of looking at the last slide#
All universes are static & change is illusory
Time is simply a way to sequence the universes in the multiverse
The Nature of Time
Suppose you have perfect knowledge of the multiverse, including the life histories of all copies of you
There is no way for you tell which copy is you % they all feel like you
There is no way for you to predict your future % without living it
Implications for Determinism
PresocraticsParticles & FieldsPhysics Foundations
Special RelativityGeneral RelativityQuantum MechanicsQuantum Field Theory
Quantum GravityPlanck ScaleLoop Quantum GravityString/M!Theory
Outline
Quantum Field Theory "QFT#
QFT = SR + QM
Antimatter“Mirror image” particlesAnnihilate to pure energy:
Quantum VacuumSeething with virtual activityNothing’s something†
e+ + e- Æ g + g
Quantum Vacuum
Anything allowed by UP,Vacuum polarization & charge renormalizationClear tension "a.k.a dark energy#Casimir forces
t
s
†
DtDE ≥ h
PresocraticsParticles & FieldsPhysics Foundations
Special RelativityGeneral RelativityQuantum MechanicsQuantum Field Theory
Quantum GravityPlanck ScaleLoop Quantum GravityString/M!Theory
Outline
Compton Length
†
lC ~ h
mc
requires enough energy to create another particle m.
QM => determining position of mass m to within its Compton wavelength
Schwarzschild Length
†
l S ~ Gmc 2
creates a black hole.
GR => compressing mass m to within its Schwarzschild radius
versus
Both GR and QM needed when
†
tP ~ l P
c~ hG
c 5
†
lC ~ l S Æ m = mP ~ hcG
Æ
†
lC << l S Æ GRlC >> l S Æ QFT
and
†
l S ~ Gmc 2
†
lC ~ h
mc
†
l P ~ lC ~ l S ~ hGc 3
PresocraticsParticles & FieldsPhysics Foundations
Special RelativityGeneral RelativityQuantum MechanicsQuantum Field Theory
Quantum GravityPlanck ScaleLoop Quantum GravityString/M!Theory
Outline
2 Fundamental TheoriesGR
Includes gravity but excludes QM
Spacetime curved but no UP
QFT = SR + QM
Includes QM but excludes gravity
Includes UP but pretends spacetime flat
2 Roles for TimeGR
"space#time is dynamical
Depends on mass and motion
No preferred foliation
QM
Time is a global parameter
67
89 t
67
89t
Synthesis?Profound Difficulties
Technical / Mathematical
Conceptual / Philosophical
3 Approaches
Canonical quantization
Loop quantum gravity
Theory formerly know as superstrings
Loop Quantum Gravity
Gravity is curved spacetime "as in GR#
Not a GUT
Spacetime3+1 dimensionsDiscrete & quantizedFoamy network of interacting loopsSpin networks represent quantum states of spacetime geometry
†
~ l P
PresocraticsParticles & FieldsPhysics Foundations
Special RelativityGeneral RelativityQuantum MechanicsQuantum Field Theory
Quantum GravityPlanck ScaleLoop Quantum GravityString/M!Theory
Outline
"Super# String Theory
Replace 0!dim particles by 1!dim strings "of energy#Gravity mediated by gravitons "as in QFT#GUT unifies 4 forcesFundamental particles are different string vibration modes
1+1 Dim Spacetime StringsIn particle physics, interactions occur at points of zero volume leading to infinities
String theory spreads out interactions over nonzero volumes yielding finite predictions
t
"Super# String Theory
Spacetime9+1 dimensions
6 compacted or …we are fixed to a 3!brane
ContinuousT!Duality => there is a smallest size Requires supersymmetry
†
~ l P