presocratic quantum gravity - wooster physics...

PresocraticQuantum Gravity

John LindnerDepartment of PhysicsThe Coege of Wooster

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

Finite total path

But no final direction

Ray can’t continue

Ray can’t escape

Zeno’s Maze




Outline

Nothing exists but atoms and empty space;

everything else is opinion.Democritus

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)

Fundamental Interactions

e- n

W-

e-

g

e-

gRB

dR dB

t

weak strong

electric gravity

But particles and void are not so simple!




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




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

Spacetime CurvatureSlows time

Warps space

r

j

z




Outline

Quantum Mechanics "QM#

Fundamental scale

Non!commuting operators

Uncertainty "Indeterminacy# Relation

†

qp - pq = ih

†

DqDp ≥ h

†

h ~ 10-34 J ⋅ s

Quantum Mechanics "QM#

Wave!particle duality

Fields & quanta

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




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




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

Planck Scale

†

l P ~ 10-35meters

†

tP ~ 10-43seconds




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




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

Particles are Pythagorean notes played on strings

with fixed tension!

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

M!Theory

Subsumes 5 different string theories + supergravity

GUT unifies 4 forces

Spacetime10+1 Dim?Coherent vibrations of superstrings in graviton mode creates spacetime out of timeless, spaceless realmSpace, time, matter all made of super strings!

presocratic quantum gravity - wooster physics...

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