Strings, Quantum Gravity, and Reduction

Universidad de NavarraSebastian de HaroJune 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 bearersof the torch of discovery in our quest for knowledge. The purpose of this book is to give theanswers that are suggested by recent discoveries and theoretical advances. They lead us to a newpicture of the universe and our place in it that is very different from the traditional one, anddifferent even from the picture we might have painted just a decade or two ago. Still, the firstsketches of the new concept can be traced back almost a century.” (The Grand Design).

Greek science: The First Theory 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: waterAnaximander: apeironAnaximenes: airHeraclitus: fireEmpedocles:

four elementsDemocritus andLeucippus: 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 octave2:3 perfect fifth3:4 perfect fourth4:5 major third5:6 minor third

6 8 9 121 2D 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 octave2:3 perfect fifth3:4 perfect fourth4:5 major third5:6 minor third

6 8 9 121 2D E F# G A B C# D

4/3

3/2 arithmetic mean 𝛽 =1

2𝛼 + 𝛾

harmonic mean 𝛽 =2𝛼𝛾

𝛼+𝛾

Properties of elementary triangles linked withharmonies 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 airrarification, condensation

5/2 air ⇄ 1 waterevaporation

condensation

2 air + 1 fire ⇄ 1 water

2 × 24 = 485

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”.



?

Steven Weinberg:

Petty reductionism: whole to parts.

Grand reductionism: “To reduce the world of physical phenomena to a finite set of fundamentalequations (or principles)” (Freeman Dyson). “Search for the common source of allexplanations.”



Particle physics / gravity

String Theory, 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.”


Philip Anderson: “They [the results of particle physics] are in no sense more fundamental than what Alan Turing did in founding the computer science, or what Francis Crick and James Watson 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 Quantum Theory. 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 in Texas 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. Ihope 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 =2𝐺N𝑀

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 =2𝐺N𝑀

𝑐2~𝐸

𝑆BH =𝑘𝑐3𝐴

4𝐺ℏ

𝑆 <𝑘𝑐3𝐴

4𝐺ℏ

Gravity in the Bulk⇔

Theory on BoundaryStrings and Quantum Gravity. Pamplona, June 2011. SdH, AUC. 42

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 thermaltransport 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

String Theory

GeologyMedicine

Astronomy

BiologyChemistry

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

Science

Transcript of Strings, Quantum Gravity, and Reduction