Strings, Quantum Gravity, and Reduction

Universidad de Navarra
Sebastian de Haro
June 21, 2011

2Strings and Quantum Gravity. Pamplona, June 2011. SdH,AUC.
“Traditionally these are questions for philosophy, but
philosophy is dead. Philosophy has not kept up
with modern developments in science, particularly
physics. Scientists have become the bearers
of the torch of discovery in our quest for
knowledge. The purpose of this book is to give the
answers that are suggested by recent discoveries
and theoretical advances.They lead us to a new
picture of the universe and our place in it that is very
different from the traditional one, and
different even from the picture we might have
painted just a decade or two ago. Still, the first
sketches of the new concept can be traced back
almost a century.” (The Grand Design).

 Greek science:The FirstTheory of Everything
 Presocratic science
 Atomism and Plato’s Timaeus
 Unification and reductionism in modern
physics
 Strings and black holes
 The holographic principle
 Discussion
Strings and Quantum Gravity. Pamplona, June 2011. SdH,AUC. 3

Thales: water
Anaximander: apeiron
Anaximenes: air
Heraclitus: fire
Empedocles:
four elements
Democritus and
Leucippus: atoms

 “In the philosophy of Democritus the atoms are eternal and indestructible units
of matter, they can never be transformed into each other. With regard to this
question modern physics takes a definite stand against the materialism of
Democritus and for Plato and the Pythagoreans.The elementary particles are
certainly not eternal and indestructible units of matter, they can actually be
transformed into each other. As a matter of fact, if two such particles, moving
through space with a very high kinetic energy, collide, then many new
elementary particles may be created from the available energy and the old
particles may have disappeared in the collision. Such events have been frequently
observed and offer the best proof that all particles are made of the same
substance: energy. But the resemblance of the modern views to those of Plato
and the Pythagoreans can be carried somewhat further.The elementary particles
in Plato's Timaeus are finally not substance but mathematical forms. "All things
are numbers" is a sentence attributed to Pythagoras.The only mathematical
forms available at that time were such geometric forms as the regular solids or
the triangles which form their surface. In modern quantum theory there can be
no doubt that the elementary particles will finally also be mathematical forms
but of a much more complicated nature.” (Heisenberg, Physics and Philosophy:
The Revolution in Modern Science ).

 Theaetetus via Plato and Euclides.

Cube (rectangle)
Tetrahedron, octahedron, icosahedron
(equilateral triangles)
No 5!

 The numbers (1,2,3) are given by musical
octave and fifth. Generate the Dorian musical
scale:
1:2 octave
2:3 perfect fifth
3:4 perfect fourth
4:5 major third
5:6 minor third
6 8 9 12
1 2
D E F# G A B C# D
4/3
3/2

 The numbers (1,2,3) are given by musical
octave and fifth. Generate the Dorian musical
scale:
1:2 octave
2:3 perfect fifth
3:4 perfect fourth
4:5 major third
5:6 minor third
6 8 9 12
1 2
D E F# G A B C# D
4/3
3/2 arithmetic mean 𝛽 =
1
2
𝛼 + 𝛾
harmonic mean 𝛽 =
2𝛼𝛾
𝛼+𝛾

 Properties of elementary triangles linked with
harmonies of music.
 Platonic solids built up of such triangles.
Properties of triangles give properties of
solids and will ‘explain’ properties of matter.

6 × 4 = 24 6 × 8 = 48 6 × 20 = 120
Earth Fire Air Water

6 × 4 = 24 6 × 8 = 48 6 × 20 = 120
Earth Fire Air Water
2 fire ⇄ 1 air
rarification, condensation
5/2 air ⇄ 1 water
evaporation
condensation
2 air + 1 fire ⇄ 1 water
2 × 24 = 48
5
2
× 48 = 12024 + 2 × 48 = 120

 Largest volume when inscribed in sphere.
 Contains other Platonic solids.

 Numbers as universal language, at the root of
all natural processes.
 Symmetry leads to ‘conserved quantities’:
 Stable earth: isosceles triangle symmetric.
 Interchangeability fire, air, water.
 Link between numbers, physiology, and arts:
quantity and quality.
 Adds concept of ‘measure’, ‘form’ to
Ionian/atomistic ideas.

 Although speculative, basic principle is a
chemistry of four elements.
 Reactions explained from mathematical
combinations allowed by geometry.
 Problem of ‘asymmetry’ always present:
‘likely account’. Hypothesis open to critique.

 “Our illustrator of the atomic model [in a
school text-book of physics] would have done
well to make a careful study of Plato before
producing his particular illustration”
(Heisenberg, cited by Guthrie).
 “My mind was formed by studying
philosophy, Plato and that sort of thing”.

?

 StevenWeinberg:
 Petty reductionism: whole to parts.
 Grand reductionism: “To reduce the world of
physical phenomena to a finite set of fundamental
equations (or principles)” (Freeman Dyson).
“Search for the common source of all
explanations.”

Particle physics / gravity
StringTheory, M-theory
Quantum mechanics/relativity/class.mech
Statistical physics/condensed matter
Biology
Chemistry
The rest

 Weinberg: “One of the members of the [SSC]
board argued that we should not give the
impression that we think that elementary
particle physics is more fundamental than other
fields, because it just tended to enrage our
friends in other areas of physics.The reason we
give the impression that we think that
elementary particle physics is more fundamental
than other branches of physics is because it is. I
do not know how to defend the amounts being
spent on particle physics without being frank
about this.”

 PhilipAnderson: “They [the results of particle
physics] are in no sense more fundamental
than what AlanTuring did in founding the
computer science, or what Francis Crick and
JamesWatson did in discovering the secret of
life.”

 “By far the most important [prediction] is super symmetry
which is fundamental to most attempts to unify Einstein's
General Relativity with QuantumTheory.This would be
confirmed by the discovery of super partners to the
particles that we already know.The Superconducting
Super Collider (the SSC) was being built inTexas and
would have reached the energies at which super partners
were expected. However, the United States went
through a fit of feeling poor and canceled the project
half way. At the risk of causing embarrassment, I have
to say I think this was a very short sighted decision. I
hope that the US, and other governments will do better in
the next millennium. (Stephen Hawking, Millennium
lecture)”

Snaartheorie, M-theorie
De rest
Intermediate areas:
Biology
Chemistry
The rest

 Singularities
 Big Bang
 Black Holes
 The problem of infinities
(‘renormalizability’)
 Most serious: information loss

Hawking Radiation
𝑅s =
2𝐺N 𝑀
𝑐2 ~𝐸

 If we wait long enough, the black hole will
evaporate.
 Radiation contains no information about
what went in.
 Information disappears.
 Black holes violate quantum
mechanics.

 1993 Gerard ’t Hooft

 1993 Gerard ’t Hooft
 Thought experiment: box volume 𝑅3
 Entropy: measure # states
RE 
#
~ ES
𝑅s =
2𝐺N 𝑀
𝑐2
~𝐸
𝑆BH =
𝑘𝑐3
𝐴
4𝐺ℏ
𝑆 <
𝑘𝑐3 𝐴
4𝐺ℏ
Gravity in the Bulk
⇔
Theory on Boundary

 Gravity 5d ⇔ 4d particle physics (QCD)
 Gravity 4d ⇔ 3d particle physics

 Gravity 5d ⇔ 4d particle physics (QCD)
 Gravity 4d ⇔ 3d particle physics
⇔

⇔
Temperature Hawking radiation ⇔ Temperature material
Charged condensate⇔Charged particles (black hole ‘hair’)

⇔
Temperature Hawking radiation ⇔ Temperature material
Electrical and thermal
transport properties
(conductivity)
⇔Small perturbations of black hole

 Common element in all holographic dualities:
“long” distances in one theory correspond to
“short” distances in the other.

Long-distance cutoff
⇔
UV cutoff
⇔

 Gravity seems equivalent with physics of
conducting materials
 Also connections with hydrodynamics

Biology
Chemistry
The rest

Sheldon Glashow
(1975)

Sheldon Glashow
(1975)
Cosmology
Quantum Mechanics
Particle Physics
StringTheory
Geology
Medicine
Astronomy
Biology
Chemistry
Big Bang
Oceanography

 Contextual models with local overlaps and
interaction within general framework.
 Unity: connection of distant areas (IR/UV).
 Important question: Fundamental variables?
Answer may depend on physical context.
 Roger Penrose and Plato: Grand reductionism
does not exclude (rather necessitates)
metaphysics. Connection math, arts, ethics.

Strings, Quantum Gravity, and Reduction

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