The Internal Description of a Causal Set:¶What the Universe Looks Like from the Inside

Markopoulou, Fotini

doi:10.1007/s002200050826

Cited by 45 publications

(83 citation statements)

References 14 publications

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“…(1) + χ 0σ (0), where contributions of different order in momenta are given by (48), (49) and (43)), as well as the PBs between the primary and secondary constraints (63), and the exact form of the closure (66) are sufficient to find the generators of the gauge transformations. This possibility is Dirac's old conjecture [11] which became a well developed algorithm and exists in a few variations [25][26][27] 11 .…”

Section: The Gauge Generator and Transformation Of The Metric Tensormentioning

confidence: 99%

The Hamiltonian formulation of general relativity: myths and reality

Kiriushcheva¹,

Kuzmin²

2011

Open Physics

197

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Abstract:A conventional wisdom often perpetuated in the literature states that: (i) a 3 + 1 decomposition of spacetime into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation of General Relativity (GR); (ii) the canonical treatment unavoidably breaks the symmetry between space and time in GR and the resulting algebra of constraints is not the algebra of four-dimensional diffeomorphism; (iii) according to some authors this algebra allows one to derive only spatial diffeomorphism or, according to others, a specific field-dependent and non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac [21] and of ADM [22] of the canonical structure of GR are equivalent. We provide some general reasons why these statements should be questioned. Points (i-iii) have been shown to be incorrect in [45] and now we thoroughly re-examine all steps of the Dirac Hamiltonian formulation of GR. By direct calculation we show that Dirac's references to space-like surfaces are inessential and that such surfaces do not enter his calculations. In addition, we show that his assumption 0 = 0, used to simplify his calculation of different contributions to the secondary constraints, is unwarranted; yet, remarkably his total Hamiltonian is equivalent to the one computed without the assumption 0 = 0. The secondary constraints resulting from the conservation of the primary constraints of Dirac are in fact different from the original constraints that Dirac called secondary (also known as the "Hamiltonian" and "diffeomorphism" constraints). The Dirac constraints are instead particular combinations of the constraints which follow directly from the primary constraints. Taking this difference into account we found, using two standard methods, that the generator of the gauge transformation gives diffeomorphism invariance in fourdimensional space-time; and this shows that points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation of GR. We also demonstrate that ADM and Dirac formulations are related by a transformation of phase-space variables from the metric µν to lapse and shift functions and the three-metric , which is not canonical. This proves that point (iv) is incorrect. Points (i-iii) are mere consequences of using a non-canonical change of variables and are not an intrinsic property of either the Hamilton-Dirac approach to constrained systems or Einstein's theory itself. PACS

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Section: The Gauge Generator and Transformation Of The Metric Tensormentioning

confidence: 99%

The Hamiltonian formulation of general relativity: myths and reality

Kiriushcheva¹,

Kuzmin²

2011

Open Physics

197

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“…Consequently, given any two screens S(s) and S(t) it will almost never happen that the corresponding light sheets L(s) and L(t) form a complete pair. By a complete pair [42,43,44] is meant a pair of non-timelike surfaces such that L(s) is within the causal future of L(t) and is complete in that no event can be added to L(s) which is also in the causal future of L(t), which is acausal to L(s), and the same is true reversing s and t and past and future.…”

Section: The Null Holographic Principlementioning

confidence: 99%

“…Rather than being a boolean algebra, the algebra of propositions relevant for a classical cosmological theory is a multivalued Heyting algebra [42]. When quantized, the resulting algebra of projection-like operators cannot be represented on a single Hilbert space, instead, it requires a collection of Hilbert spaces, one for every possible event at which observations are made [43].…”

Section: Relational Approaches To Quantum Cosmologymentioning

confidence: 99%

The strong and weak holographic principles

Smolin

2001

Nuclear Physics B

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We review the different proposals which have so far been made for the holographic principle and the related entropy bounds and classify them into the strong, null and weak forms. These are analyzed, with the aim of discovering which may hold at the level of the full quantum theory of gravity. We find that only the weak forms, which constrain the information available to observers on boundaries, are implied by arguments using the generalized second law. The strong forms, which go further and posit a bound on the entropy in spacelike regions bounded by surfaces, are found to suffer from serious problems, which give rise to counterexamples already at the semiclassical level. The null form, proposed by Fischler, Susskind, Bousso and others, in which the bound is on the entropy of certain null surfaces, appears adequate at the level of a bound on the entropy of matter in a single background spacetime, but attempts to include the gravitational degrees of freedom encounter serious difficulties. Only the weak form seems capable of holding in the full quantum theory.The conclusion is that the holographic principle is not a relationship between two independent sets of concepts: bulk theories and measures of geometry vrs boundary theories and measures of information. Instead, it is the assertion that in a fundamental theory the first set of concepts must be completely reduced to the second. * smolin@phys.psu.edu 1

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“…They defined such living systems as self-producing mechanisms that maintain their particular form, despite material inflow and outflow, through self-regulation and self-reference [25]. Importantly for Maturana and Varela, the observer was "a living system and any understanding of cognition as a biological phenomenon must account for the observer and his role in it" [25, p. 48].…”

Section: The Observer and The Observational Cutmentioning

confidence: 99%

“…ALifers have been forced to "confront the difficulties posed by having multiple observers embedded within this world whose measurements are necessarily local and relative to each other and whose interactions can potentially alter its dynamic course" ( [10,25,33], as cited in [6, p. 16]). In ABSs it has been ascertained that it is not simply that the observer will cause what is observed, measured, and described to emerge differently, but that these observations, measurements, and descriptions are also defined by the order of the events that define the reality of what is measured: "the history (or order of events) measured by each observer creates the reality that this observer perceives as the evolution of the system" [6, p. 17].…”

Section: The Observer and The Observational Cutmentioning

confidence: 99%

Performative Apparatus and Diffractive Practices: An Account of Artificial Life Art

Prophet

Pritchard

2015

Artificial Life

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Drawing on our own art/science practices and a series of interviews with artificial life practitioners, we explore the entanglement of developments at the artistic edges of artificial life. We start by defining key terms from Karen Baradʼs agential realism. We then diffractively read artificial life together with agential realism to discuss the potential for interventions in the field. Through a discussion of artificial life computer simulations, ideas of agency are problematized, and artificial lifeʼs single purposeful actor, the agent, is replaced by agential, an adjective denoting a relationship rather than a subject-object duality. We then seek to reinterpret the difficult-to-define term "emergence." Agency in artificial life emerges through what Barad calls entanglement, in this case between observers and their apparatus, a perpetual engagement between observations of a system and their interpretations. The article explores the differences that this diffractive perspective makes to artificial life and accounts of its materialization.

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The Internal Description of a Causal Set:¶What the Universe Looks Like from the Inside

Cited by 45 publications

References 14 publications

The Hamiltonian formulation of general relativity: myths and reality

The Hamiltonian formulation of general relativity: myths and reality

The strong and weak holographic principles

Performative Apparatus and Diffractive Practices: An Account of Artificial Life Art

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