Off-campus access
Using PhilPapers from home?
Click here to configure this browser for off-campus access.
- Chris Heunen, Klaas Landsman & Bas Spitters, The Principle of General Tovariance.We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr's interpretation of quantum mechanics, i.e. his doctrine of classical concepts and his principle of complementarity. An appropriate mathematical language for combining these ideas is topos theory, a framework earlier proposed for physics by Isham and collaborators. Our "Principle of general tovariance" states that any mathematical structure appearing in the laws of physics must be definable in an arbitrary topos (with natural numbers object) and must be preserved under so-called geometric morphisms. This principle identifies geometric logic as the mathematical language of physics and restricts the constructions and theorems to those valid in intuitionism: neither Aristotle's principle of the excluded third nor Zermelo's Axiom of Choice may be invoked. Subsequently, our "Equivalence principle" states that any algebra of observables (initially defined in the topos Sets) is empirically equivalent to a commutative one in some other topos.
Similar books and articles
It is often claimed that the geodesic principle can be recovered as a theorem in general relativity. Indeed, it is claimed that it is a consequence of Einstein's equation (or of the conservation principle that is, itself, a consequence of that equation). These claims are certainly correct, but it may be worth drawing attention to one small qualification. Though the geodesic principle can be recovered as theorem in general relativity, it is not a consequence of Einstein's equation (or the conservation principle) alone. Other assumptions are needed to drive the theorems in question. One needs to put more in if one is to get the geodesic principle out. My goal in this short note is to make this claim precise (i.e., that other assumptions are needed).
Reading list
| Discuss | Edit | Categorize | My bibliography
| Export citation | Other links: lps.uci.edu | Scholar | More options ...
| | Other links: lps.uci.edu | Scholar | More options ... Summary Boltzmann's principle is part of classical physics, and one of the corner-stones of Planck's quantum theory. It is shown, why Planck's theory of radiation can be derived from this principle without abandoning classical physics, if due regard is taken of atomism. Finally, there is given an outline of a quantum theory completely based on statistical axioms without any appeal to nonclassical physical principles.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: springerlink.com dx.doi.org | Scholar | At my library | More options ...
| | Other links: springerlink.com dx.doi.org | Scholar | At my library | More options ... Niels Bohr’s “correspondence principle” is typically believed to be the requirement that in the limit of large quantum numbers (n→∞) there is a statistical agreement between the quantum and classical frequencies. A closer reading of Bohr’s writings on the correspondence principle, however, reveals that this interpretation is mistaken. Specifically, Bohr makes the following three puzzling claims: First, he claims that the correspondence principle applies to small quantum numbers as well as large (while the statistical agreement of frequencies is only for large n); second, he claims that the correspondence principle is a law of quantum theory; and third, Bohr argues that formal apparatus of matrix mechanics (the new quantum theory) can be thought of as a precise formulation of the correspondence principle. With further textual evidence, I offer an alternative interpretation of the correspondence principle in terms of what I call Bohr’s selection rule. I conclude by showing how this new interpretation of the correspondence principle readily makes sense of Bohr’s three puzzling claims.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | More options ...
| | Scholar | More options ... Harvey Brown believes it is crucially important that the "geodesic principle" in general relativity is an immediate consequence of Einstein's equation and, for this reason, has a different status within the theory than other basic principles regarding, for example, the behavior of light rays and clocks, and the speed with which energy can propagate. He takes the geodesic principle to be an essential element of general relativity itself, while the latter are better seen as contingent facts about the particular matter fields we happen to encounter. The situation seems much less clear and clean to me. There certainly is a sense in which the geodesic principle can be recovered as a theorem in general relativity. But one needs more than Einstein's equation to drive the theorems in question. Other assumptions are needed. One needs to put more in if one is to get the geodesic principle out. My goal in this note is to make this claim precise, i.e., that other assumptions are needed.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | More options ...
| | Scholar | More options ... We discuss some logico-mathematical systems which deviate from classical logic and mathematics with respect to the concept of identity. In the first part of the paper we present very general formulations of the principle of identity and show how they can be ‘relativized’ to objects and to properties. Then, as an application, we study the particular cases of physics (the transgression of the principle of identity by quantum objects) and logic (some logics in which the principle of replacement is not valid are presented). In the last part of the paper, we discuss the alphabar logics, that is, those logical systems which violate a formulation of one of the most fundamental versions of the principle of identity; in these logics, there are formulas which are not deducible from themselves.
No categories
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | More options ...
| | Scholar | More options ... We analyze the possible implications of spacetime discreteness for the special and general relativity and quantum theory. It is argued that the existence of a minimum size of spacetime may explain the invariance of the speed of light in special relativity and Einstein’s equivalence principle in general relativity. Moreover, the discreteness of spacetime may also result in the collapse of the wave function in quantum mechanics, which may provide a possible solution to the quantum measurement problem. These interesting results might have some important implications for a complete theory of quantum gravity.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | More options ...
| | Scholar | More options ... In classical mechanics, the Galilean covariance and the principle of relativity are completely equivalent and hold for all possible dynamical processes. In relativistic physics, on the contrary, the situation is much more complex: It will be shown that Lorentz covariance and the principle of relativity are not equivalent. The reason is that the principle of relativity actually holds only for the equilibrium quantities characterizing the equilibrium state of dissipative systems. In the light of this fact it will be argued that Lorentz covariance should not be regarded as a fundamental symmetry of the laws of physics.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | At my library | More options ...
| | Scholar | At my library | More options ... We start from John Norton's analysis (1985) of the reach of Einstein's version of the principle of equivalence which is not a local principle but an extension of the relativity principle to reference frames in constant acceleration on the background of Minkowski spacetime. We examine how such a point of view implies a profound, and not generally recognised, reconsideration of the concepts of inertial system and field in physics. We then reevaluate the role that the infinitesimal principle, if adequately formulated, can legitimately be claimed to play in general relativity. We show that what we call the 'punctual equivalence principle' has significant physical content and that it permits the derivation of the geodesic law.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Other links: linkinghub.elsevier.com dx.doi.org | Scholar | At my library | More options ...
| | Other links: linkinghub.elsevier.com dx.doi.org | Scholar | At my library | More options ... Symmetry, intended as invariance with respect to a transformation (more precisely, with respect to a transformation group), has acquired more and more importance in modern physics. This Chapter explores in 8 Sections the meaning, application and interpretation of symmetry in classical physics. This is done both in general, and with attention to specific topics. The general topics include illustration of the distinctions between symmetries of objects and of laws, and between symmetry principles and symmetry arguments (such as Curie's principle), and reviewing the meaning and various types of symmetry that may be found in classical physics, along with different interpretative strategies that may be adopted. Specific topics discussed include the historical path by which group theory entered classical physics, transformation theory in classical mechanics, the relativity principle in Einstein's Special Theory of Relativity, general covariance in his General Theory of Relativity, and Noether's theorems. In bringing these diverse materials together in a single Chapter, we display the pervasive and powerful influence of symmetry in classical physics, and offer a possible framework for the further philosophical investigation of this topic.
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | More options ...
| | Scholar | More options ... Among the principles that are generally taken to underlie the general theory of relativity is a general principle of relativity. Such a principle is supposed to extend the special principle of relativity, which holds observers in uniform motion to be indistinguishable by appeal to the laws of physics, to a requirement on observers in arbitrary states of motion. Starting with physical intuitions described graphically by Galileo, proceeding through a series of formal requirements on reference frames defined on models of space-time theories, and considering other "observations" commonly associated with relativity principles, this paper argues that the general principle of relativity is neither justified by "fact", nor exemplified by the general theory of relativity.
No categories
Reading list
| Discuss | Edit | Categorize | My bibliography | Export citation | Scholar | At my library | More options ...
| | Scholar | At my library | More options ... Discussion of Chris Heunen , Klaas Landsman & Bas Spitters, The principle of general tovariance
 Back
All discussions
Start a new thread
|
There are no threads in this forum |
Nothing in this forum yet.
