I argue that, contrary to the standard view, one cannot understand the structure and nature of ou... more I argue that, contrary to the standard view, one cannot understand the structure and nature of our knowledge in physics without an analysis of the way that observers (and, more generally, measuring instruments and experimental arrangements) are modeled in theory. One upshot is that standard pictures of what a scientific theory can be are grossly inadequate. In particular, standard formulations assume, with no argument ever given, that it is possible to make a clean separation between, on the one hand, one part of the scientific knowledge a physical theory embodies, viz., that encoded in the pure mathematical formalism and, on the other, the remainder of that knowledge. The remainder includes at a minimum what is encoded in the practice of modeling particular systems, of performing experiments, of bringing the results of theory and experiment into mutually fruitful contact---in sum, real application of the theory in actual scientific practice. This assumption comes out most clearly i...
al-Antitrypsin (alAT) deficiency is a hereditary disorder associated with reduced serum alAT leve... more al-Antitrypsin (alAT) deficiency is a hereditary disorder associated with reduced serum alAT levels and the development of pulmonary emphysema. An alAT gene is defined as "Null" when no alAT in serum is attributed to that alAT gene. Although all alAT Null genes have identical phenotypic consequences (i.e. no detectable alAT in the serum), different genotypic mechanisms can cause the Null state. This study defines the molecular basis for the alAT gene Nullf,,,,, identified and cloned from genomic DNA of an individual with the NullNull phenotype and emphysema resulting from the heterozygous inheritance of the Nullm.,w, and Nullb.Iuigm genes. Sequencing of exons Ic-V and all exon-intron junctions of the Null",,Vt. gene demonstrated it was identical to the common normal Ml(Va1213) alAT gene except for the insertion of a single nucleotide within the coding region of exon V, causing a 3' frameshift with generation ofa premature stop signal. Family analysis using oligonu...
I sketch here the construction of Geroch (1969) (whose exposition I closely follow), which ground... more I sketch here the construction of Geroch (1969) (whose exposition I closely follow), which grounds the arguments of section 3 in Curiel (2016). (I simplify his construction in non-essential ways for our purposes, and gloss over unnecessary technicalities.) Consider a 1-parameter family of relativistic spacetimes, by which I mean a family {(Mλ, g(λ))}λ∈(0,1], where each (Mλ, g(λ)) is a relativistic spacetime with signature (+, −, −, −) for g(λ). (It will be clear in a moment why I work with the contravariant form of the metric tensor.) In particular, I do not assume that Mλ is diffeomorphic to Mλ′ for λ 6= λ′. The problem is to find a limit of this family, in some suitable sense, as λ → 0. To solve the problem in full generality, we will use a geometrical construction, gluing the manifolds Mλ of the family together to form a 5-dimensional manifold M, so that each Mλ is itself a 4-dimensional submanifold of M in such a way that the collection of all of them foliate M. λ becomes a scal...
arXiv: General Relativity and Quantum Cosmology, 2016
The standard argument for the uniqueness of the Einstein field equation is based on Lovelock'... more The standard argument for the uniqueness of the Einstein field equation is based on Lovelock's Theorem, the relevant statement of which is restricted to four dimensions. I prove a theorem similar to Lovelock's, with a physically modified assumption: that the geometric object representing curvature in the Einstein field equation ought to have the physical dimension of stress-energy. The theorem is stronger than Lovelock's in two ways: it holds in all dimensions, and so supports a generalized argument for uniqueness; it does not assume that the desired tensor depends on the metric only up second-order partial-derivatives, that condition being a consequence of the proof. This has consequences for understanding the nature of the cosmological constant and theories of higher-dimensional gravity. Another consequence of the theorem is that it makes precise the sense in which there can be no gravitational stress-energy tensor in general relativity. Along the way, I prove a result...
Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a fre... more Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a free scalar particle in R D are shown to be the result of summing over all dimensions D ′ ≥ D of R D ′ , each summand taken in the absence of quantum gravity.
The notions of two-dimensional area, Killing fields and matter flux are introduced in the setting... more The notions of two-dimensional area, Killing fields and matter flux are introduced in the setting of causal fermion systems. It is shown that for critical points of the causal action, the area change of two-dimensional surfaces under a Killing flow in null directions is proportional to the matter flux through these surfaces. This relation generalizes an equation in classical general relativity due to Ted Jacobson setting of causal fermion systems.
An energy condition, in the context of a wide class of spacetime theories (including general rela... more An energy condition, in the context of a wide class of spacetime theories (including general relativity), is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that we have no clear understanding of the nature of these conditions, what theoretical status they have with respect to fundamental physics, what epistemic status they may have, when we should and should not expect them to be satisfied, and even in many cases how they and their consequences should be interpreted physically. Or so I shall argue, by a detailed analysis of the technical and conceptual character of all the standard conditions used in physics today, including examination of their consequences and the circumstances in which they are believed to be violated.
I argue that, contrary to the standard view, one cannot understand the structure and nature of ou... more I argue that, contrary to the standard view, one cannot understand the structure and nature of our knowledge in physics without an analysis of the way that observers (and, more generally, measuring instruments and experimental arrangements) are modeled in theory. One upshot is that standard pictures of what a scientific theory can be are grossly inadequate. In particular, standard formulations assume, with no argument ever given, that it is possible to make a clean separation between, on the one hand, one part of the scientific knowledge a physical theory embodies, viz., that encoded in the pure mathematical formalism and, on the other, the remainder of that knowledge. The remainder includes at a minimum what is encoded in the practice of modeling particular systems, of performing experiments, of bringing the results of theory and experiment into mutually fruitful contact---in sum, real application of the theory in actual scientific practice. This assumption comes out most clearly i...
al-Antitrypsin (alAT) deficiency is a hereditary disorder associated with reduced serum alAT leve... more al-Antitrypsin (alAT) deficiency is a hereditary disorder associated with reduced serum alAT levels and the development of pulmonary emphysema. An alAT gene is defined as "Null" when no alAT in serum is attributed to that alAT gene. Although all alAT Null genes have identical phenotypic consequences (i.e. no detectable alAT in the serum), different genotypic mechanisms can cause the Null state. This study defines the molecular basis for the alAT gene Nullf,,,,, identified and cloned from genomic DNA of an individual with the NullNull phenotype and emphysema resulting from the heterozygous inheritance of the Nullm.,w, and Nullb.Iuigm genes. Sequencing of exons Ic-V and all exon-intron junctions of the Null",,Vt. gene demonstrated it was identical to the common normal Ml(Va1213) alAT gene except for the insertion of a single nucleotide within the coding region of exon V, causing a 3' frameshift with generation ofa premature stop signal. Family analysis using oligonu...
I sketch here the construction of Geroch (1969) (whose exposition I closely follow), which ground... more I sketch here the construction of Geroch (1969) (whose exposition I closely follow), which grounds the arguments of section 3 in Curiel (2016). (I simplify his construction in non-essential ways for our purposes, and gloss over unnecessary technicalities.) Consider a 1-parameter family of relativistic spacetimes, by which I mean a family {(Mλ, g(λ))}λ∈(0,1], where each (Mλ, g(λ)) is a relativistic spacetime with signature (+, −, −, −) for g(λ). (It will be clear in a moment why I work with the contravariant form of the metric tensor.) In particular, I do not assume that Mλ is diffeomorphic to Mλ′ for λ 6= λ′. The problem is to find a limit of this family, in some suitable sense, as λ → 0. To solve the problem in full generality, we will use a geometrical construction, gluing the manifolds Mλ of the family together to form a 5-dimensional manifold M, so that each Mλ is itself a 4-dimensional submanifold of M in such a way that the collection of all of them foliate M. λ becomes a scal...
arXiv: General Relativity and Quantum Cosmology, 2016
The standard argument for the uniqueness of the Einstein field equation is based on Lovelock'... more The standard argument for the uniqueness of the Einstein field equation is based on Lovelock's Theorem, the relevant statement of which is restricted to four dimensions. I prove a theorem similar to Lovelock's, with a physically modified assumption: that the geometric object representing curvature in the Einstein field equation ought to have the physical dimension of stress-energy. The theorem is stronger than Lovelock's in two ways: it holds in all dimensions, and so supports a generalized argument for uniqueness; it does not assume that the desired tensor depends on the metric only up second-order partial-derivatives, that condition being a consequence of the proof. This has consequences for understanding the nature of the cosmological constant and theories of higher-dimensional gravity. Another consequence of the theorem is that it makes precise the sense in which there can be no gravitational stress-energy tensor in general relativity. Along the way, I prove a result...
Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a fre... more Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a free scalar particle in R D are shown to be the result of summing over all dimensions D ′ ≥ D of R D ′ , each summand taken in the absence of quantum gravity.
The notions of two-dimensional area, Killing fields and matter flux are introduced in the setting... more The notions of two-dimensional area, Killing fields and matter flux are introduced in the setting of causal fermion systems. It is shown that for critical points of the causal action, the area change of two-dimensional surfaces under a Killing flow in null directions is proportional to the matter flux through these surfaces. This relation generalizes an equation in classical general relativity due to Ted Jacobson setting of causal fermion systems.
An energy condition, in the context of a wide class of spacetime theories (including general rela... more An energy condition, in the context of a wide class of spacetime theories (including general relativity), is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that we have no clear understanding of the nature of these conditions, what theoretical status they have with respect to fundamental physics, what epistemic status they may have, when we should and should not expect them to be satisfied, and even in many cases how they and their consequences should be interpreted physically. Or so I shall argue, by a detailed analysis of the technical and conceptual character of all the standard conditions used in physics today, including examination of their consequences and the circumstances in which they are believed to be violated.
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Papers by Erik Curiel