A fully covariant information-theoretic ultraviolet cutoff for scalar fields in expanding Friedmann Robertson Walker spacetimes

Kempf, Achim; Chatwin-Davies, Aidan; W., Martin, Robert T.

doi:10.1063/1.4790482

Cited by 22 publications

(47 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The general idea is to match exactly the dynamics of the continuum for a set of Fourier modes up to a cut-off K; see also the related arguments in [55,56].…”

Section: Refinement As Adding Degrees Of Freedom In the Vacuum Statementioning

confidence: 99%

Time evolution as refining, coarse graining and entangling

2014

View full text Add to dashboard Cite

We argue that refining, coarse graining and entangling operators can be obtained from time evolution operators. This applies in particular to geometric theories, such as spin foams. We point out that this provides a construction principle for the physical vacuum in quantum gravity theories and more generally allows construction of a (cylindrically) consistent continuum limit of the theory.In this paper we point out that time evolution maps, which appear in simplicial discretizations [13,14], can also be interpreted as refining and coarse graining maps. As we will argue here, this applies in particular to gravitational dynamics, e.g. spin foams [15][16][17][18].One reason why the appearance of time evolution as coarse graining or refining maps applies in particular to gravitational or other diffeomorphism invariant systems is the following: As argued in [19][20][21][22][23], diffeomorphism symmetry in discrete systems translates to a symmetry, which can be interpreted as moving vertices in the discrete space time described by the dynamical variables of the theory. These vertex translations can also be understood as time evolution. Now, vertices can be even moved on top of each other, which gives a coarse graining of the underlying state. Alternatively, vertices can split into two and in this way give a refinement. Indeed, this argument was used in [23] to show that diffeomorphism symmetry implies discretization independence.More generally, diffeomorphism invariant systems are totally constrained, i.e. the Hamiltonian is given by a combination of constraints. In the case of a totally constrained system, the time evolution operator should be a projection operator [24,25], projecting onto socalled physical states. Thus physical states should not evolve 1 .For discrete time evolutions that change the number of degrees of freedom, this leads to the puzzle of how to identify states from Hilbert spaces of 'different size' 2 . We will argue that such states describe indeed the same physical state, expressed, however on two different discretizations. The equivalence relation is provided by the refining time evolution operator. We will explain how this notion can be formalized into the construction of an inductive limit Hilbert space. Such an inductive limit construction is also used for the (kinematical) Hilbert space of loop quantum gravity [27,28].The inductive limit Hilbert spaces, however, which are defined via an equivalence relation between states from Hilbert spaces based on different discretizations, require (so-called cylindrical) consistency conditions: Physical observables should not depend on which representative they have been determined on. Indeed, we will connect these consistency conditions with a notion of path independence for (refining) time evolution. This relates, then, to the requirement of diffeomorphism invariance.Discrete (non-topological) theories typically break the diffeomorphism symmetry [22]. The hope, however, is that diffeomorphism symmetry can be recovered in the continuum limit. We will ex...

show abstract

“…The general idea is to match exactly the dynamics of the continuum for a set of Fourier modes up to a cut-off K; see also the related arguments in [55,56].…”

Section: Refinement As Adding Degrees Of Freedom In the Vacuum Statementioning

confidence: 99%

Time evolution as refining, coarse graining and entangling

2014

View full text Add to dashboard Cite

show abstract

“…Vice versa, this means that as, during expansion, comoving modes keep crossing the Hubble length, they become unfrozen in the sense that, literally, their bandwidth becomes finite. In the next section we will discuss the application of generalized Shannon sampling to cosmic inflation 39,40 . The generalization of Shannon sampling to black holes is in progress.…”

Section: Introductionmentioning

confidence: 99%

Quantum Gravity, Information Theory and the CMB

Kempf¹

2018

Found Phys

View full text Add to dashboard Cite

We review connections between the metric of spacetime and the quantum fluctuations of fields. In particular, we discuss the finding that the spacetime metric can be expressed entirely in terms of the 2-point correlators of the fluctuations of quantum fields. We also discuss the open question whether the knowledge of only the spectra of the quantum fluctuations of fields suffices to determine the spacetime metric. This question is of interest because spectra are geometric invariants and their quantization would, therefore, have the benefit of not requiring the modding out of the diffeomorphism group. Further, we discuss the fact that spacetime at the Planck scale need not necessarily be either discrete or continuous. Instead, results from information theory show that spacetime may be simultaneously discrete and continuous in the same way that information can. Finally, we review the finding that a covariant natural ultraviolet cutoff at the Planck scale implies a signature in the cosmic microwave background (CMB) that may become observable.

show abstract

“…In the former case, we will need to develop the presently only spatially covariant approach into a fully spacetime covariant approach, e.g., by the cutting of the spectrum of the d'Alembertian rather than that of the Laplacian. For work in this direction, see [15]. In this context, see also [16,8].…”

Section: Discussionmentioning

confidence: 99%