The Universe Out of Information?

16th International Interdisciplinary Seminar

Netherhall House, London, January 5, 2014

Sebastian de Haro (ITFA and AUC, University of Amsterdam)

A Universe from Nothing?

• Fashionable to say and write that the universe arises ‘out of nothing’ due to ‘quantum randomness’.

• Dawkins: “Even the last remaining trump card of the theologian, ‘Why is there something rather than nothing?,’ shrivels up before your eyes as you read these pages. If On the Origin of Species was biology’s deadliest blow to supernaturalism, we may come to see A Universe From Nothing as the equivalent from cosmology. The title means exactly what it says.And what it says is devastating.”

• Not a metaphor!

A Universe from Nothing. Really?

• The physical and metaphysical principles “out of nothing, nothing arises” stay in place even in the wake of quantum mechanics.

• Rather than deconstructing the various proposals for “the universe out of nothing” in detail (see my YouTube video on the topic), I will concentrate on recent results from quantum gravity/string theory that hopefully contribute some balanced insights than just having ‘nothing’ do the conceptual work.

The Universe Out of Information? SdH, UvA

(A Very Short Argument) Why Physics Doesn’t Deal with Nothing

• Newtonian physics is about energy and momentum.• No energy and momentum ⇒ no physics

• In QFT (quantum field theory), energies can be negative (at least for short periods of time) and the total energy can be zero.• However, QFT (QM) are not about energy and momentum

but (ultimately) about information

• Microscopic information is conserved at all times• No information no physics

• ‘A Universe Out of Information’ must replace ‘A Universe from Nothing’.

The Universe Out of Information? SdH, UvA

Plan

• Motivating thoughts: • Black holes and entropy

• Holography

• Can gravity emerge from information?• Verlinde’s proposal (with D. Dieks and J. van Dongen,

forthcoming)

• Holography in de Sitter space?

The Universe Out of Information? SdH, UvA

Motivating Thoughts

• Hints from string theory, the holographic principle: there are solid indications that gravitational theories within a volume correspond to a theory without gravity on the boundary of the volume

• For the purposes of this talk, ‘information’ means ‘data’ (zeroes and ones). Entropy measures encoded information (Shannon)

𝑆 =𝑘𝑐3𝐴

4𝐺ℏ

Picture: http://www.zeropoint.ca/holoapple%20(3).jpg

(‘bulk’)

Could it be that gravity is “just the bulk description” of a world without gravity?

Picture: http://scienceblogs.com/startswithabang/files/2010/03/star-wars-hologram.jpg

Further Motivating Thoughts

• Gravity is special: it is universal. It applies to all matter and energy, regardless of specific interactions; it seems to relate to space itself.

• This universality reminds one of the universal character of thermodynamical behavior, which is independent of microscopic details

• Gravity distinguishes itself from other forces because it is difficult to quantize; is it fundamentally different?

Program of Research

• Start with a theory without gravity on a two-dimensional screen, e.g. the surface of a sphere

• Holography: this theory codifies information about matter in an additional spatial dimension (‘bulk’)

• The microscopic details of this gravitation-less theory remain unspecified: it is a mere information processing device, a theory of holographic “bits”

• Make gravity appear as a macroscopic thermodynamic phenomenon

Guiding idea about force as a thermodynamic phenomenon

• Entropic processes: as a result of random motion of its microscopic constituents a physical system will end up in a state of greater entropy, i.e. higher probability: the system seems to be directed

• Although there are no forces on the microscopic level, on the thermodynamic level the system appears driven, and this can be described by a “macroscopic force”

• Like a stretched polymer

Picture: http://www.thenakedscientists.com/HTML/uploads/RTEmagicC_RubberStretch-stretched.png.png

Working this out

Imagine a sphere whose area is divided into small cells with each one “bit”.

This information suffices to describe the inside (holography).

Picture: http://www.nature.com/scientificamerican/journal/v17/n1/images/scientificamerican0407-66sp-I3.jpg

Working this out

• On the sphere an entropic process takes place: the distribution of 0-s and 1-s tends to an equilibrium

• This process will correspond to gravitational motion inside the sphere

The Appearance of Space

• In the surface theory, there are no spatial dimensions other than those within the surface

• Consider several spheres, namely different surface theories that relate to each other via ‘coarse-graining’ (less accurate description)

Coarse Graining

50 × 38

800 × 600 640 × 480

200 × 150

1024 × 768 pixels

http://www.theflowersavenue.com/gallery/tulip/tulip_4.jpg

The Appearance of Space

• Coarse graining:• Removing some bits reduces the area of the sphere

• ‘Coarse-grained’ theories encode less information, i.e. describe less space

• Thus, a spatial dimension 𝑥 appears as a bookkeeping device that records the level of coarse graining on the sphere

Picture: http://media02.hongkiat.com/black-white-photo-water/black-and-white-drops.jpg

Information and Black Hole Entropy

• Bekenstein-Hawking: the entropy of a black hole is proportional to its surface area:

𝑆 =𝑘𝑐3𝐴

4𝐺ℏ

• Throwing a single particle into a black hole we throw away (at least) one bit of information. Entropy increases by an amount proportional to the particle’s mass (and the distance from which the particle is dropped):

−Δ𝐼 = Δ𝑆 = 𝑚 Δ𝑥

The Appearance of Gravity

1) Holography: number of bits on sphere

𝑁 ~ 𝐴 = 4𝜋𝑅2

2) Equipartition: 𝐸 = 𝑀𝑐2 ~ 𝑁 𝑇

3) Bekenstein: Δ𝑆 ~ 𝑚 ∆𝑥

4) Second law of thermodynamics: 𝐹 = 𝑇∆𝑆

∆𝑥

From which we get Newton’s law: 𝐹 ~𝑀𝑚

𝑅2

Thermodynamic limit(coarse graining)

micro-macro

Macroscopic theoryon sphere: no gravity

Microscopic theoryon sphere

Microscopic theoryin bulk

Holography

Macroscopic theoryin bulk: gravity

Thermodynamic limit(coarse graining)

micro-macro

Holography

• Holographic relation may well be a bijective map. • No reason in this case to think that one side is more

fundamental than the other (left-right).• But thermodynamic limit introduces the emergence

of gravity in an uncontroversial sense (top-bottom).

Thermodynamic limit(coarse graining)

micro-macro

Holography

Thermodynamic limit(coarse graining)

micro-macro

Holography

Does Gravity Emerge?

Conclusions

• In the holographic scenario, the microscopic surface theory is not necessarily more fundamental than the microscopic bulk theory.

• However, the appearance of gravity in the thermodynamic limit makes it a clear case of emergence, connected with robustness and novelty of behavior. This robustness explains the universality of gravity.

• That gravity is emergent could give rise to new predictions: the law of gravity is not exact but subject to fluctuations.

Back to the Bottom Line

• Holographic models of gravity apply to an expanding universe as well (de Sitter space)

• The emergent direction is not space but time!

• Prospect of describing the Big Bang in terms of information processing• Singularity seems connected to the existence of a

holographic description

• The universe does not emerge as a random bubble ‘out of nothing’, but holographically ‘out of information’!