BLACK HOLE HORIZONS:

The Gravity of Paradigms

Sebastian de Haro

Amsterdam University College

CREA, March 9, 2011

EINSTEIN’S HOLY GRAIL

• Search for unified theory.

• Incorporate relativity.

• Reject QM.

PHYSICS’ HOLY GRAIL: UNIFICATION

• Relativity and quantum theory.

PHYSICS’ HOLY GRAIL: UNIFICATION

• Relativity and quantum theory

• Look for clues: black holes.

• Both relativity and quantum mechanics play a role.

PLAN

• Classical properties of black holes.

• Quantum black holes: they are not black.

• Information paradox.

• Complementarity of observers.

• Holographic principle.

WHAT ARE BLACK HOLES?

• Pierre-Simon Laplace (1749-1827).

• Escape velocity.

• Earth: 𝑣 = 11,2 km/s

• ‘Black star’: 𝑣 = 299 972 km/s

WHAT ARE BLACK HOLES?

• Einstein 1915: mass implies curvature of space-time.

• Curvature is perceived as gravitational attraction.

WHAT ARE BLACK HOLES?

OBSERVATIONAL EVIDENCE

• Black hole itself cannot be seen.

• Indirect evidence: matter swallowed up by supermassive black object.

• Predictions: time delay, gravitational lensing.

OBSERVATIONAL EVIDENCE

• Black hole itself cannot be seen.

• Indirect evidence: matter swallowed up by supermassive black object.

• Predictions: time delay, gravitational lensing.

HOW LARGE IS A BLACK HOLE?

• If as heavy as the sun: one meter.

• Supermassive (one million suns): size of the solar system.

• Milky Way: Sagittarius A*.

𝑅 =2𝐺𝑀

𝑐2

SONIC BLACK HOLES

SONIC BLACK HOLES

THE RELATIVITY OF GRAVITY

• Free fall.

SUMMARY – PROPERTIES OF BLACK HOLES

• Heaviest objects, not even light can escape.

• Fish in the water analogy.

• Free fall.

HAWKING: BLACK HOLES AIN’T SO BLACK

• 1973 Bekenstein develops black hole thermodynamics.

• 1974 Hawking: black holes emit radiation.

• The key: quantum fluctuations of vacuum.

𝑆 =𝑘𝑐3𝐴

4𝐺ℏ

𝑇 =ℏ𝑐3

8𝜋𝐺𝑀𝑘= 6,2 × 10−8 K

HAWKING RADIATION

• 1973 Bekenstein develops the thermodynamics of black holes

• 1974 Hawking: black holes can emit radiation!

𝑆 =𝑘𝑐3𝐴

4𝐺ℏ

𝑇 =ℏ𝑐3

8𝜋𝐺N𝑀𝑘= 6,2 × 10−8

𝑀ʘ

𝑀K

HAWKING’S PROVOCATIVE CONCLUSION

• If we wait long enough, black hole evaporates.

• The radiation does not contain information about what went in.

• Information forever lost.

• Black holes violate the laws of physics.

INFORMATION LOSS

INFORMATION LOSS

SUMMARY – HAWKING’S ARGUMENT

• Black holes emit radiation.

• The radiation is thermal, contains no information.

• Information is lost.

• New level of unpredictability in physics.

INTERMEZZO – AN EXPERIMENT

INTERMEZZO – AN EXPERIMENT

INTERMEZZO – AN EXPERIMENT

INTERMEZZO – AN EXPERIMENT

INTERMEZZO – AN EXPERIMENT

COMPLEMENTARITY

ALICE IN WONDERLAND

ALICE IN WONDERLAND

ALICE IN WONDERLAND

ALICE IN WONDERLAND

SONIC BLACK HOLES

ALICE IN WONDERLAND

ALICE’S VIEW

AN EXPERIMENT

SUMMARY – BLACK HOLE COMPLEMENTARITY

• Alice and the cat have different descriptions of reality.

• Their points of view are mutually exclusive.

• Describe black hole from point of view of an observer.

• Led to holographic principle.

HOLOGRAPHY

(BBC Horizon, 2011)

Gravity in bulk ⇔

boundary theory

𝑆 =𝑘𝑐3𝐴

4𝐺ℏ

• 1993 ’t Hooft

• Gedanken experiment: box volume 𝑅3

• Entropy: measure of # of physical states

RE

#~ ES

𝑅s =2𝐺N𝑀

𝑐2~𝐸

𝑆BH =𝑘𝑐3𝐴

4𝐺ℏ

𝑆 <𝑘𝑐3𝐴

4𝐺ℏ

THE DISCOVERY OF HOLOGRAPHY

Gravity in bulk ⇔

boundary theory

HOLOGRAPHY

• ’t Hooft 1993 “dimensional reduction”

• Susskind 1994 “holography”

• Maldacena 1997 holography in string theory

• 2004 Hawking admits he lost his bet

𝑆 =𝑘𝑐3𝐴

4𝐺ℏ

HAWKING’S 2005 PAPER

There is no baby universe branching off, as I once thought. The

information remains firmly in our universe. I’m sorry to disappoint science

fiction fans, but if information is preserved, there is no possibility of using

black holes to travel to other universes. If you jump into a black hole, your

energy will be returned to our universe but in a mangled form which

contains the information about what you were like but in a state where it

can not be easily recognized. It is like burning an encyclopedia.

Information is not lost, if one keeps the smoke and the ashes. But it is

difficult to read. In 1997, Kip Thorne and I, bet John Preskill that

information was lost in black holes. The loser(s) of the bet were to provide

the winner(s) with an encyclopedia of their own choice, from which

information can be recovered with ease. I gave John an encyclopedia of

baseball, but maybe I should just have given him the ashes.

SUMMARY

• Black holes can radiate, which gives rise to information paradox

• Paradigm to solve this problem: holography – confirmed by string

theory: the world is 3- not 4-dimensional

• Gravity is a “fake” force

• Implications for reductionism?

• Essays: Gerard ‘t Hooft, Vincent

Icke, Ed van den Heuvel, Michiel

van der Klis, John Wheeler,

Jeroen van Dongen, Sebastian

de Haro

• Poems: Leo Vrooman, Maria

Barnas, Rogi Wieg, Mustafa

Stitou, Jan Baeke

• Prof. dr. F.H. van Lunteren:

Influence of cultural and

philosophical climate of

quantum mechanics during

Weimar Republic, March 29.

• WWW.HETWERELDBEELD.NL

SCIENCE & CULTURE BLACK HOLES IN De Gids