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
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
1 Categorisation of positions on the metaphysics of space
2 Emergent Spacetime vs. Substantivalism
3 Emergent Spacetime Research Programme
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
CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
T1: ‘Spacetime is primitive‘
T1
Substantivalism
¬T1
‘Spacetime is derivative....‘
‘...from matter‘
Relationalism
‘...from other fundamental d.o.f.‘
Emergent Spacetime
Niels Martens The Metaphysics of Emergent Spacetime Theories 5/28
CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
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
Niels Martens The Metaphysics of Emergent Spacetime Theories 6/28
CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
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
emergent ST & M super-emergent ST
Niels Martens The Metaphysics of Emergent Spacetime Theories 7/28
CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
T3 ¬T3
M is primitive M is derivative
T1: ST is primitive dualistic substantivalism supersubstantivalism
¬T1: ST is derivative dualistic emergent ST emergent ST & M
relationalism super-emergent ST
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CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
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
Niels Martens The Metaphysics of Emergent Spacetime Theories 9/28
Outline
1 Categorisation of positions on the metaphysics of space
2 Emergent Spacetime vs. Substantivalism
3 Emergent Spacetime Research Programme
4 Case Study
CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase 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
Niels Martens The Metaphysics of Emergent Spacetime Theories 11/28
CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
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
Niels Martens The Metaphysics of Emergent Spacetime Theories 12/28
Outline
1 Categorisation of positions on the metaphysics of space
2 Emergent Spacetime vs. Substantivalism
3 Emergent Spacetime Research Programme
4 Case Study
CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
Emergent Spacetime Research Programme I
Question 1
Is the theory a theory of emergent ST, super-emergent ST, oremergent ST&M?
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CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
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
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CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
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?
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CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
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?
Niels Martens The Metaphysics of Emergent Spacetime Theories 17/28
CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
Emergent Spacetime Research Programme V
Question 6
Why does spacetime emerge with 3+1 dimensions?
Niels Martens The Metaphysics of Emergent Spacetime Theories 18/28
Outline
1 Categorisation of positions on the metaphysics of space
2 Emergent Spacetime vs. Substantivalism
3 Emergent Spacetime Research Programme
4 Case Study
CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase 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)
Niels Martens The Metaphysics of Emergent Spacetime Theories 20/28
CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
Quantum GraphityQuantum superfluids
Quantum Graphity II
EST&M category
Non-technical sense of emergence
Fine-tuning
also the case for the Standard Modeldimensionality = f (v0)
Niels Martens The Metaphysics of Emergent Spacetime Theories 21/28
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
CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
Quantum GraphityQuantum superfluids
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,
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CategorisationEmergent Spacetime vs. Substantivalism
Emergent Spacetime Research ProgrammeCase Study
Quantum GraphityQuantum superfluids
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
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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)