The Metaphysics of Emergent Spacetime Theories · Arguments from Philosophy Arguments from Physics Arguments from Physics \The end of space and time" (Rovelli, 2014) \QM + Gravity

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The Metaphysics of Emergent Spacetime Theories

Niels C.M. MartensDPhil candidate Philosophy of Physics

Oxford University

OZSW Graduate Conference for Theoretical Philosophy 2014VU Amsterdam

Slides available at http://users.ox.ac.uk/~corp2044

27 May 2014

http://users.ox.ac.uk/~corp2044

Outline

1 Categorisation of positions on the metaphysics of space

2 Emergent Spacetime vs. SubstantivalismArguments from PhilosophyArguments from Physics

3 Emergent Spacetime Research Programme

4 Case StudyQuantum Graphity

Outline


2 Emergent Spacetime vs. Substantivalism


4 Case Study

CategorisationEmergent Spacetime vs. Substantivalism

Emergent Spacetime Research ProgrammeCase Study

The Classical Debatesubstantivalism vs. relationalism

the classical debate = a dilemmaT1 vs. ¬T1

Substantivalism/Absolutism vs. Relationalism

What is T1?

Niels Martens The Metaphysics of Emergent Spacetime Theories 4/28



T1: ‘Spacetime is primitive‘

T1

Substantivalism

¬T1

‘Spacetime is derivative....‘

‘...from matter‘

Relationalism

‘...from other fundamental d.o.f.‘

Emergent Spacetime




T2 ¬T2

ST & M are distinct ST & M are ontologically linked

T1: ST is primitive dualistic substantivalism supersubstantivalism

¬T1: ST is derivative dualistic emergent ST relationalism




T2 ¬T2

ST & M are distinct ST & M are ontologically linked


¬T1: ST is derivative dualistic emergent ST relationalism

emergent ST & M super-emergent ST




T3 ¬T3

M is primitive M is derivative


¬T1: ST is derivative dualistic emergent ST emergent ST & M

relationalism super-emergent ST




T3 ¬T3

M is primitive M is derivative

T1: ST is primitive Dual Subst SupSubst

¬T1: ST is derivativeT2: ST & M are distinct Dual EST EST&M

¬T2: ST & M are linked Rel SupEST


Outline




4 Case Study



Arguments from PhilosophyArguments from Physics

Arguments from PhilosophyStatic Leibniz Shift (& Hole Argument)

Matter

Spacetime

Fundamental d.o.f.

Haecceitism - Sophisticatedsubstantivalism (Pooley,

forthcoming)

Parity violating laws ofnature (Earman, 1989)

Kinematic shifts




Arguments from PhilosophyArguments from Physics

Arguments from Physics

“The end of space and time”(Rovelli, 2014)

“QM + Gravity = spacetime is doomed” “Quantized gravity is non-renormalisable”(Arkani-Hamed, 2010) (All textbooks)

spacetime matter

Gµν= 8πGTµν

classical classical

Effective theory only: intrinsically classical gravity and spacetime as anemergent phenomenon


Outline




4 Case Study



Emergent Spacetime Research Programme I

Question 1

Is the theory a theory of emergent ST, super-emergent ST, oremergent ST&M?




Emergent Spacetime Research Programme II

Question 2

What notion of emergence is used, and how does this relate to the notion ofemergence within the relationalist approach?

Emergence = Supervenience + ‘irreducibility’/‘novelty’

Epistemological emergence

Psychological emergence

Inter-theoretic emergence

Ontological emergence

Permanentism vs. temporaryism

Non-technical sense of emergence (Dennett)

(Useful) properties or entities are formed/arise in a certain regime only




Emergent Spacetime Research Programme III

Question 3

What happens to the notion of matter in the regime wherespacetime does not emerge?

Question 4

What additional structure emerges compared to the standardconstrual of spacetime manifolds?

Primitive identities?

An orientational structure?




Emergent Spacetime Research Programme IV

Question 5

1 Conspiracy of Inertia (Brown,2005)

2 Pooley’s Mystery of Mysteries (Pooley,2012)

Conspiracy of non-inertial motion

3 Laughlin’s Mystery of Mysteries (Laughlin, 2005)

Why any symmetries at all?

4 Brown’s Mystery of Mysteries (Brown,2005)

Universal Lorentz covariance

5 Earman’s Mystery of Mysteries (Earman, 1989)

How can the Weak Force violate parity?

6 Pauli’s Mystery of Mysteries (Gardner, 1964)

Why does only the Weak Force violate parity?




Emergent Spacetime Research Programme V

Question 6

Why does spacetime emerge with 3+1 dimensions?


Outline




4 Case Study



Quantum GraphityQuantum superfluids

Quantum Graphity I

Complete graph of N nodes

H = Hlinks + Hvertices + Hloops + Hhop + HLQG

Links can be turned ‘on’ and ’off’

Hlinks = V∑a

(v0 −

∑b

Jab

)2

Ground state: graphs with valence v0

→ Geometrogenesis & Locality

(Markopoulou et al., 2006, 2008, 2010, 2011)





Quantum Graphity II

EST&M category

Non-technical sense of emergence

Fine-tuning

also the case for the Standard Modeldimensionality = f (v0)


Outlook

New dilemma: emergent spacetime vs. relationalism

Exciting research programme!

More mature theories of emergent spacetime: string theory,loop quantum gravity, causal sets (?),... (Hedrich, 2009; Carlip,

2012)

References I

N. Arkani-Hamed (2010), Messenger lecture 3: Space-time isdoomed, what replaces it?

J. Bain (2008), Condensed matter physics and the nature ofspacetime. In Dennis Dieks (ed.), The Ontology of SpacetimeII

J. Bain (2013), The emergence of spacetime in condensedmatter approaches to quantum gravity, Studies in History andPhilosophy of Modern Physics, 44:338-345

H.R. Brown (2005), Physical Relativity, Oxford UniversityPress

F. Caravelli & F. Markopoulou (2011), Properties of QuantumGraphity at Low Temperature, arXiv:1008.1340v3

S. Carlip (2012), Challenges for emergent gravity,arXiv:1207.2504v2

References II

J. Earman (1989), World Enough and Space-Time, MIT Press

M. Gardner (1964 [1990]), The New Ambidextruous Universe,New York: Dover Publications Inc.

R. Hedrich (2009) , Quantum Gravity: Has SpacetimeQuantum Properties?, arXiv:0902.0190

T. Konopka, F. Markopoulou & L. Smolin (2006), Quantumgraphity, arXiv:0611197v1

T. Konopka, F. Markopoulou, & S. Severini (2008), Quantumgraphity: a model of emergent locality, arXiv:0801.0861v2

R.B. Laughlin (2005), A Different Universe, New York: BasicBooks

D. Lehmkuhl (2009), Spacetime Matters, DPhil Thesis, OxfordUniversity

References III

D. Lehmkuhl (forthcoming), The Metaphysics ofSuper-Substantivalism

F. Markopoulou et al., Quantum Bose-Hubbard model with anevolving graph as a toy model for emergent spacetime,Physical Review D 81, 104032

O. Pooley (forthcoming), The Reality of Spacetime

O. Pooley (2012), Substantivalist and Relationalist approachesto spacetime, in R. Batterman (ed.), The Oxford Handbook ofPhilosophy of Physics.

C. Rovelli & F. Vidotto (2014), Covariant Loop QuantumGravity

J.A. Wheeler, C.W. Misner & K.S. Thorne (1973),Gravitation, New York: W.H. Freemand and Company




Appendix: Quantum superfluids Isuperfluid Helium 4

superfluid Helium 4 Bose-Einstein condensate (Bain, 2008, 2013)

Non-relativistic lagrangian on Neo-Newtonian spacetime:

L4He = iφ†∂tφ−1

2m∂iφ

†∂iφ+ µφ†φ− κ(φ†φ)2, i = 1, 2, 3,

Integrate out high energy fluctuations to obtain effective fieldtheory:

Leff =1

4κ(∂tθ + vi∂iθ)2 − ρ0

2m(∂iθ)2,

Formally identical to massless scalar field in a(3+1)-dimensional curved relativistic spacetime

Leff =1

2

√−ggµν∂µθ∂νθ, µ, ν = 0, 1, 2, 3,





Appendix: Quantum superfluids IIsuperfluid Helium 4

Bain: ignore flat spacetime, take condensate as fundamental.

Relationalism?Quantum Field theory requires background

Bain: Inter-theoretic emergence

Mere idealisation or approximation?

Dimensionality explained by dimensionality of flat spacetime

Miraculous appearance of Lorentz symmetry, but hardly aproper explanation


Appendix: Categorisation

T1,T2,T3: about entities T4: about properties

T3 ¬T3

M is primitive M is not a fundamental entity

¬T4 T4

M is a new property M is geometrical

T1: ST is primitive Dual Subst Modest SupSubst Radical SupSubst

¬T1: ST is derivativeT2: ST & M are distinct Dual EST EST&M -

¬T2: ST & M are linked Rel Modest SupEST Radical SupSubst

(Wheeler, 1973; Lehmkuhl, 2009, forthcoming)

The Metaphysics of Emergent Spacetime Theories · Arguments from Philosophy Arguments from Physics Arguments from Physics \The end of space and time" (Rovelli, 2014) \QM + Gravity

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