the temporal and atemporal emergence of (space-)time · the temporal and atemporal emergence of...

The disappearance of spacetime in quantum gravityA temporal emergence of temporality?

Summary and conclusion

The temporal and atemporal emergence of(space-)time

Christian Wüthrich(Based on joint work with Nick Huggett)

British Society for the Philosophy of Science Annual ConferenceEdinburgh, 14 July 2017

This work was supported by a grant from the John Templeton Foundation.

Christian Wüthrich The temporal and atemporal emergence of (space-)time



An all too common sentiment...

Sklar, Lawrence. Prospects for a causal theory of space-time. In Richard Swinburne (ed.), Space, Time, andCausality, Synthese Library 157 (1983): 45-62.

What could possibly constitute a more essential, a moreineliminable, component of our conceptual framework than thatordering of phenomena which places them in space and time?The spatiality and temporality of things is, we feel, the verycondition of their existing at all and having other, less primordial,features. A world devoid of color, smell or taste we could, perhaps,imagine. Similarly a world stripped of what we take to be essentialtheoretical properties also seems conceivable to us. We couldimagine a world without electric charge, without the atomicconstitution of matter, perhaps without matter at all. But a worldnot in time? A world not spatial? Except to some Platonists, Isuppose, such a world seems devoid of real being altogether. (45)




The non-fundamentality of spacetimeSpace in string theorySpace and time in LQG

Why we need a quantum theory of gravity

Source: http://blog.michaelkcooke.com/

General relativity (GR) can’t be thelast word: it assumes classicalmatter

⇒ need a quantum theory of gravity,theory that combines quantumeffects and (strong) gravitationalfields

various approaches, string theoryand loop quantum gravity (LQG),non-commutative geometry, causalset theory


http://blog.michaelkcooke.com/




A generic prediction of fundamental quantum theories of gravity

Huggett, Nick and Wüthrich, Christian. Emergent spacetime and empirical (in)coherence. Studies in theHistory and Philosophy of Modern Physics 44 (2013): 276-285.

Huggett, Nick and Wüthrich, Christian. Out of Nowhere. Oxford University Press (forthcoming).

A quantum theory of gravity will be fundamental, at least relativeto currently held theories of physics.

Now, many approaches to formulating such a theory eitherpresuppose or entail that fundamentally, there is neither spacenor time (even though that denial comes in degrees).





Beyond Spacetime, beyondspacetime.net

General project by Nick Huggett and CW on the ‘emergence’ ofspacetime from less-than-fully spatiotemporal degrees of freedom.


beyondspacetime.net




ThesisSpacetime according to quantum theories of gravity in general, andaccording to loop quantum gravity/cosmology in particular, is notfundamental.





The non-fundamentality of spacetime

emergent

fundamental





Spacetime in string theory is not fundamental

Dualities such as AdS/CFT relate as physically equivalentspacetimes of different geometry—and dimensionality.

T-duality: relates as physically equivalent a string theory of‘large’ scale (R) with a string theory of ‘small’ inverse scale (1/R)

⇒ These dualities suggest that what we experience phenomenallyas spacetime must be emergent.





Loop quantum gravity (LQG)

Source: http://www.cpt.univ-mrs.fr/∼rovelli/

starts out from GR,incorporates its core lessons(dynamical spacetime)

applies canonical quantizationprocedure to GR

outstanding problems: (1)problem of time/ill-understooddynamics, (2) classicallimit/emergence of spacetimefrom basic quantum structure


http://www.cpt.univ-mrs.fr/~rovelli/




The ‘problem of time’ in canonical quantum gravity(or at least an indication of the problem)

Schrödinger equation for non-relativistic quantum mechanics:

H|ψ(t)〉 = i~∂

∂t|ψ(t)〉.

Wheeler-DeWitt equation for canonical quantum gravity:

H|ψ〉 = 0.

“ ⇒ ”∂

∂t|ψ〉 = 0.





Quantized space in LQG

‘kinematical states’ interpreted to correspond tothree-dimensional spatial structure, basis of so-called ‘spinnetworks’

⇒ physical space is generically a superposition of spin networkstates

spin networks: networks of interwoven loops with ‘spin’representations on nodes and edges

‘spin’-representations on vertices (represented by nodes ingraph) correspond to ‘size’ of the ‘space atoms’, those on edgescorrespond to ‘size’ of the surface connecting adjacent ‘chunks’of space





Quantum space in LQG: a spin network

2i

1i

1j

2j

3j





Quantum space in LQG: a spin network

spin networks are discrete structures (no affine or differentiablestructure)

no natural dimensionality

no metric structure, although spin networks are eigenstates ofoperators that afford geometric interpretation

space: superposition of these eigenstates, i.e. no well-definedgeometric properties

states in superpositions in general have different ‘connectivity’(and perhaps different cardinality)

⇒ different structures, and what is local in one term of thesuperposition will in general not be local in others

How local, i.e. topological, structures like relativistic spacetimesemerge from spin networks is at present little understood.





Even geometric eigenstates are ‘non-local’In LQG: locality must be explicated in terms of ‘adjacency’ relationsencoded in the fundamental structure.In general, two fundamentally adjacent nodes will not map in the sameneighbourhood of the emerging spacetime:

large distance

spin network

emergence

spacetime

Figure: A spin network (shown as shaded) with two regions (shownenlarged) connected by an adjacency relation and how they areembedded in an emerging spacetime.





The problem of space in LQG

I am glossing over many details here, no doubt, but it should beclear that the ‘locality’ structure of spin networks captured by thecombinatorial connectivity of the spin network structure is verydifferent from the one of relativistic spacetimes...

... although ‘non-localities’ in fundamental structure aresuppressed in approximation of the large scales relevant to theemergence of spacetimes.

⇒ fundamental ‘spatial’ structure in LQG is rather different from theone we know from GR: discrete, non-metrical, combinatorialstructure with different topology and hence locality structure

Real question: analogously to time, the question arises how dowe recover what we know is a very highly empirically successfuldescription of space(time) from fundamental structure?





ConclusionWe have a problem of spacetime: space and perhaps time, as theyfigure in our conceptions of the world, are emergent phenomena.

⇒ So we have an atemporal emergence of (spatio-)temporality.




Cosmology and a second questionLoop quantum cosmologyWhat happened before the Big Bang?

Cosmology: a temporal emergence of temporality?

In cosmological models based on QG, there appears to be a‘process’ of emergence:

‘transition’ from a state that has no effective classical spacetimedescription, to one that does, approximately ‘at the big bang’

But how can there be such a change without time? A before andafter? A process?

An aside: What becomes of classical singularities in quantumgravity?

Examples:Oriti’s ‘Geometrogenesis’ (lecture on beyondspacetime.net)Thébault and Gryb’s relational quantization cosmologyString Quantum CosmologyLoop Quantum Cosmology


beyondspacetime.net




The (a)temporal emergence of temporality

Two questions:

1 How can classical relativistic spacetime (or the space and timeof our experience) ultimately be constituted by a fundamentalstructure that is non-spatiotemporal?

2 How can the universe (which is fundamentally non-spatio-temporal) evolve from a non-spatiotemporal phase to aspatiotemporal one?





The atemporal emergence of temporality

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Time? Dynamics?

It turns out to be supremely difficult to get a good handle on howto conceive of the dynamics of the theory, or to identify a suitablenotion of time.

⇒ study a simplified system: Loop Quantum Cosmology (LQC)

To this end, restrict yourself at the kinematical level to quantumstates which are spatially isotropic and homogeneous. Alldegrees of freedom are thus frozen, except one, captured by the‘scale factor’ operator p, corresponding to the classical scalefactor a, clocked by a scalar field φ.





Claim: ‘Big bang’ singularity vanishes

Although problematic, a reading of the simplified dynamicalequation is as an evolution equation, with the scale factor as‘time variable’.

The relevant dynamical equation is a difference equation, not adifferential equation.

It turns out that the evolution near and at the big bang is (almost)well defined!





So... what happened before the Big Bang?





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Time? A proposal

If time is not fundamentally there, it emerges via the collectivebehaviour of the fundamental degrees of freedom, as a result ofricher physics.

analogy: the statistical emergence of thermodynamic propertiesof a sufficiently complex system

The direction of time emerges jointly with other temporal aspectsof the emerging structure.

Plausibly, it will be directed ‘away’ from the quantum souparound the big bang:





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Summary

Moving to quantum theories more fundamental than GR seemsto lead us to atemporal (or aspatiotemporal) structures.

It is from these atemporal structures that temporality must arise,in two ways:

1 There must be an atemporal relationship (of dependence)between the fundamental, non-spatiotemporal and thenon-fundamental, spatiotemporal structures; spacetime isgrounded in something non-spatiotemporal.

2 There must be a transition from an earlier quantum state,which lacks any correspondence to a classical emergentstate, to a later ‘classical’ cosmology well described byrelativistic spacetime.




Conclusion

I propose that we should think of this second relationship asinduced by the emergent temporally directed physics of the‘later’ universe.

This implies that cosmological models like the one I presentedshould be thought of as modelling the twin birth of two universesrather then one collapsing and then re-expanding universe.


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