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#221
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I am not responding to myself :-)
I simply use the opportunity to draw everybody's attention to a very interesting paper on the concept of time: Hinweis zum Urheberrecht Bitte beziehen Sie sich beim Zitieren dieses Dokumentes immer auf folgende URN: urn:nbn:de:bvb:355-opus-4820 URL: http://www.opus-bayern.de/uni-regens...exte/2005/482/ -------------------------------------------------------------------------------- Simon, Johannes Change without time. Relationalism and field quantization pdf-Format: Dokument 1.pdf (828 KB) -------------------------------------------------------------------------------- Kurzfassung in englisch The nature of time has long been debated in human history and nowadays is considered of central importance for understanding quantum gravity. We focus on and advocate the relational concept of time, which was put forward in the 17th century in opposition to Newton's absolute time, and only in 1990 explored in a quantum mechanical framework by Carlo Rovelli. After a historical introduction the mathematical models of time are carefully analyzed in chapter 1, followed by a discussion of the role of time played in fundamental theories. Using as an example nonrelativistic mechanics, the process of parametrization is explained, leading to a separation of a 'canonical time coordinate' from an arbitrary evolution parameter. The discussion of the role of time in special and general relativity as well as in quantum mechanics shows that more fundamental theories use less structure of time. This is followed by an exposition of the history of the relational concept of time, which negates the existence of an absolute duration and therefore often is called "timeless". Next it is shown how fundamental theories can be formulated and re-interpreted using this concept. We put emphasis on the hitherto neglected connection between relationalism and non-extensibility, while absolute time is shown to be unproblematic in classical mechanics just because of the possibility to extend the system without changing its nature. We conclude chapter 1 with a new axiomatic basis for the construction of time observables based on a simultaneity relation between 'observations', which are treated as a primitive concept and intuitively correspond to measurement events, but without knowing 'when' these events occur. There is no fundamental time observable; any observable qualifies as a time observable, if it allows to separate all instants. Chapter 2 gives a brief account of three main problems connected with time: a) The problem of the arrow of time. This has to be disentangled from the problem of irreversibility: a solution of the latter essentially excludes cyclic motions and is required for a solution of the former, which consists in showing that a fundamental direction between any two non-identical instants is physically meaningful. We give a formal definition of the arrow of time. This classical analysis is followed by a review of the problem of the arrow of time in quantum theory, where the situation becomes more complicated because of indeterminism. The discussion shows that there is no experimental evidence for a fundamental arrow of time, so that no contradiction with the relational concept of time arises. b) The problem of time measurement, which is of particular importance for the relational approach, in which time has no reality except if measured by a clock. In quantum theory useful time operators seem to be possible only within the more general formalism of positive operator valued measures (POVM). Clocks based on an oscillation mechanism do however require phase measurements; quantum phase operators can be defined as certain POVMs. Phase difference operators do also exist in the traditional Hilbert space formalism, if another quantization is used, as is done with relational quantization. c) The problem of quantum gravity is sketched only briefly. Chapter 3 introduces and discusses a model of Rovelli consisting of two oscillators with no external time. In this model one oscillator is considered as a clock and defines a relational time for the other one. In the first section we introduce this model and generalize it to a free massless scalar field in one dimension. We establish the relation between a single field mode and the infrared behaviour of the field through constants of motion. In the second section after a short review of canonical quantization we review Rovelli's quantization and generalize it to the free field. We could not prove the existence of the quantization map, but calculations using computer algebra indicate that the quantization does exist. For an enlarged algebra we are able to prove the nonexistence of a quantization map similar to a proof by Groenewold and van Hove. In chapter 4 we observe that a clock time always requires infinitely many degrees of freedom, and we make the hypothesis that a time observable is given by the infrared behaviour of quantum fields, leading to a classical notion of time when using algebraic quantum mechanics. This does however not solve the main problem of quantum relationalism: Which conditions determine a particular evolution? ----------------------------------------------------------------------- 1.2.7 Summary of Chapter 1.2 The role of time in physical theories (pp. 26,27) Let us briefly summarize in which respect the structure of time in Newtonian mechanics has been reduced in increasingly fundamental theories. In special relativity the temporal ordering of spacelike events, duration and simultaneity become dependent on the choice of inertial frame. Duration transforms linearly between these frames. The choice of synchronization procedure is to some extent arbitrary. In general relativity the notion of inertial frame is generalized to a reference frame with curl-free velocity field. If a cosmic time does exist, the events along different worldlines of freely falling observers can be synchronized. The arbitrariness of synchronization remains. In quantum theory classical notions of time are used, but duration is not observable for isolated systems. See also pp. 38,39 of time.pdf: In special relativity the description of observations as seen from different Lorentz frames is equivalent. Each Lorentz frame defines a simultaneity relation and we can apply the above reasoning. A change of Lorentz frame also affects the equilocality relation, which like simultaneity is an equivalence relation among observations. Lorentz invariance of a theory can then be seen as the unobservability of certain changes of the simultaneity relation which are accompanied by certain changes of the equilocality relation. My comment: The unobservability justified the linking of time and location in the basic relations x' = alpha x + beta t t' = epsilon x + gamma t However, such linking leads to a formula (the Lorentz time transformation), which is incoherent. Marcel Luttgens |
#222
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The URL has been corrupted by Google.
It should read http://www.opus-bayern.de/uni-regens...exte/2005/482/ |
#223
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wrote in message ups.com... I am not responding to myself :-) I simply use the opportunity to draw everybody's attention to a very interesting paper on the concept of time: [snip without looking] My comment: The unobservability justified the linking of time and location in the basic relations x' = alpha x + beta t t' = epsilon x + gamma t However, such linking leads to a formula (the Lorentz time transformation), which is incoherent. Someone who does not understand what the variables x, t, x' and t' stand for in these equations is not very well placed to have an opinion about the coherence of the equations. You are an imbecile, Marcel, learn to face it. http://users.pandora.be/vdmoortel/di...chSimpler.html Dirk Vdm |
#224
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You wrote:
[snip without looking] This proves that your IQ is very low, perhaps 60. All you can do is "parroting". I hope that you are not representative of SRists. Your only justification is that you are suffering from Alzheimer's disease. Marcel Luttgens |
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