Pub Date : 2009-05-29DOI: 10.1103/PhysRevD.81.123524
M. Srednicki, J. Hartle
As observers of the universe we are quantum physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in spacetime. The physical conditions at these locations that are not specified by the data may differ. Predictions of our future observations therefore require an assumed probability distribution (the xerographic distribution) for our location among the possible ones. It is the combination of basic theory plus the xerographic distribution that can be predictive and testable by further observations.
{"title":"Science in a Very Large Universe","authors":"M. Srednicki, J. Hartle","doi":"10.1103/PhysRevD.81.123524","DOIUrl":"https://doi.org/10.1103/PhysRevD.81.123524","url":null,"abstract":"As observers of the universe we are quantum physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in spacetime. The physical conditions at these locations that are not specified by the data may differ. Predictions of our future observations therefore require an assumed probability distribution (the xerographic distribution) for our location among the possible ones. It is the combination of basic theory plus the xerographic distribution that can be predictive and testable by further observations.","PeriodicalId":416124,"journal":{"name":"The Quantum Universe","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131849813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Prediction in quantum cosmology requires a specification of the universe’s quantum dynamics and its quantum state. We expect only a few general features of the universe to be predicted with probabilities near unity conditioned on the dynamics and quantum state alone. Most useful predictions are of conditional probabilities that assume additional information beyond the dynamics and quantum state. Anthropic reasoning utilizes probabilities conditioned on ‘us’. This paper discusses the utility, limitations, and theoretical uncertainty involved in using such probabilities. The predictions resulting from various levels of ignorance of the quantum state are discussed including those related to uncertainty in the vacuum of string theory. Some obstacles to using anthropic reasoning to determine this vacuum are described.
{"title":"Anthropic Reasoning and Quantum Cosmology","authors":"J. Hartle","doi":"10.1063/1.1848335","DOIUrl":"https://doi.org/10.1063/1.1848335","url":null,"abstract":"Prediction in quantum cosmology requires a specification of the universe’s quantum dynamics and its quantum state. We expect only a few general features of the universe to be predicted with probabilities near unity conditioned on the dynamics and quantum state alone. Most useful predictions are of conditional probabilities that assume additional information beyond the dynamics and quantum state. Anthropic reasoning utilizes probabilities conditioned on ‘us’. This paper discusses the utility, limitations, and theoretical uncertainty involved in using such probabilities. The predictions resulting from various levels of ignorance of the quantum state are discussed including those related to uncertainty in the vacuum of string theory. Some obstacles to using anthropic reasoning to determine this vacuum are described.","PeriodicalId":416124,"journal":{"name":"The Quantum Universe","volume":"131 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2004-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127373780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-09-15DOI: 10.1142/9789811216404_0004
J. Hartle
If a cat, a cannonball, and an economics textbook are all dropped from the same height, they fall to the ground with exactly the same acceleration under the influence of gravity. This equality of gravitational accelerations of different things is one of the most accurately tested laws of physics. That law, however, tells us little about cats, cannonballs, or economics. This lecture expands on this theme to address the question of what features of our world are predicted by a fundamental ``theory of everything'' governing the regularities exhibited universally by all physical systems. This may consist of two parts: a dynamical law governing regularities in time (e.g superstring theory) and a law of cosmological initial condition governing mostly regularities in space (e.g. Hawking's no-boundary initial condition). The lecture concludes that: (1) ``A theory of everything'' is not a theory of everything in a quantum mechanical universe. (2) If the laws are short enough to be discoverable then they are probably too short to predict everything. (3) The regularities of human history, economics, biology, geology, etc are consistent with the fundamental laws of physics but do not follow from them. (Public lecture given at The Future of Theoretical Physics and Cosmology: Stephen Hawking 60th Birthday Symposium.)
{"title":"Theories of Everything and Hawking’s Wave Function of the Universe","authors":"J. Hartle","doi":"10.1142/9789811216404_0004","DOIUrl":"https://doi.org/10.1142/9789811216404_0004","url":null,"abstract":"If a cat, a cannonball, and an economics textbook are all dropped from the same height, they fall to the ground with exactly the same acceleration under the influence of gravity. This equality of gravitational accelerations of different things is one of the most accurately tested laws of physics. That law, however, tells us little about cats, cannonballs, or economics. This lecture expands on this theme to address the question of what features of our world are predicted by a fundamental ``theory of everything'' governing the regularities exhibited universally by all physical systems. This may consist of two parts: a dynamical law governing regularities in time (e.g superstring theory) and a law of cosmological initial condition governing mostly regularities in space (e.g. Hawking's no-boundary initial condition). The lecture concludes that: (1) ``A theory of everything'' is not a theory of everything in a quantum mechanical universe. (2) If the laws are short enough to be discoverable then they are probably too short to predict everything. (3) The regularities of human history, economics, biology, geology, etc are consistent with the fundamental laws of physics but do not follow from them. (Public lecture given at The Future of Theoretical Physics and Cosmology: Stephen Hawking 60th Birthday Symposium.)","PeriodicalId":416124,"journal":{"name":"The Quantum Universe","volume":"22-23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114764172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-09-13DOI: 10.1142/9789811216404_0022
J. Hartle
What is the quantum state of the universe? That is the central question of quantum cosmology. This essay describes the place of that quantum state in a final theory governing the regularities exhibited universally by all physical systems in the universe. It is possible that this final theory consists of two parts: (1) a dynamical theory such as superstring theory, and (2) a state of the universe such as Hawking's no-boundary wave function. Both are necessary because prediction in quantum mechanics requires both a Hamiltonian and a state. Complete ignorance of the state leads to predictions inconsistent with observation. The simplicity observed in the early universe gives hope that there is a simple, discoverable quantum state of the universe. It may be that, like the dynamical theory, the predictions of the quantum state for late time, low energy observations can be summarized by an effective cosmological theory. That should not obscure the need to provide a fundamental basis for such an effective theory which gives a a unified explanation of its features and is applicable without restrictive assumptions. It could be that there is one principle that determines both the dynamical theory and the quantum state. That would be a truly unified final theory. (talk given The Future of Theoretical Physics and Cosmology: Stephen Hawking 60th Birthday Symposium)
{"title":"The State of the Universe","authors":"J. Hartle","doi":"10.1142/9789811216404_0022","DOIUrl":"https://doi.org/10.1142/9789811216404_0022","url":null,"abstract":"What is the quantum state of the universe? That is the central question of quantum cosmology. This essay describes the place of that quantum state in a final theory governing the regularities exhibited universally by all physical systems in the universe. It is possible that this final theory consists of two parts: (1) a dynamical theory such as superstring theory, and (2) a state of the universe such as Hawking's no-boundary wave function. Both are necessary because prediction in quantum mechanics requires both a Hamiltonian and a state. Complete ignorance of the state leads to predictions inconsistent with observation. The simplicity observed in the early universe gives hope that there is a simple, discoverable quantum state of the universe. It may be that, like the dynamical theory, the predictions of the quantum state for late time, low energy observations can be summarized by an effective cosmological theory. That should not obscure the need to provide a fundamental basis for such an effective theory which gives a a unified explanation of its features and is applicable without restrictive assumptions. It could be that there is one principle that determines both the dynamical theory and the quantum state. That would be a truly unified final theory. (talk given The Future of Theoretical Physics and Cosmology: Stephen Hawking 60th Birthday Symposium)","PeriodicalId":416124,"journal":{"name":"The Quantum Universe","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130481861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1997-01-11DOI: 10.1142/9789814350860_0010
J. Hartle
Two fundamental laws are needed for prediction in the universe: (1) a basic dynamical law and (2) a law for the cosmological initial condition. Quantum cosmology is the area of basic research concerned with the search for a theory of the initial cosmological state. The issues involved in this search are presented in the form of eight problems. (To appear in Physics 2001, ed. by M. Kumar and in the Proceedings of the 10th Yukawa-Nishinomiya Symposium}, November 7-8, 1996, Nishinomiya, Japan.)
{"title":"Quantum Cosmology: Problems for the 21st Century","authors":"J. Hartle","doi":"10.1142/9789814350860_0010","DOIUrl":"https://doi.org/10.1142/9789814350860_0010","url":null,"abstract":"Two fundamental laws are needed for prediction in the universe: (1) a basic dynamical law and (2) a law for the cosmological initial condition. Quantum cosmology is the area of basic research concerned with the search for a theory of the initial cosmological state. The issues involved in this search are presented in the form of eight problems. (To appear in Physics 2001, ed. by M. Kumar and in the Proceedings of the 10th Yukawa-Nishinomiya Symposium}, November 7-8, 1996, Nishinomiya, Japan.)","PeriodicalId":416124,"journal":{"name":"The Quantum Universe","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122604729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1996-01-29DOI: 10.1142/9789811216404_0005
J. Hartle
Existing physical theories do not predict every feature of our experience but only certain regularities of that experience. That difference between what could be observed and what can be predicted is one kind of limit on scientific knowledge. Such limits are inevitable if the world is complex and the laws governing the regularities of that world are simple. Another kind of limit on scientific knowledge arises because even simple theories may require intractable or impossible computations to yield specific predictions. A third kind of limit concerns our ability to know theories through the process of induction and test. Quantum cosmology -- that part of science concerned with the quantum origin of the universe and its subsequent evolution -- displays all three kinds of limits. This paper briefly describes quantum cosmology and discusses these limits. The place of the other sciences in this most comprehensive of physical frameworks is described.
{"title":"Scientific Knowledge from the Perspective of Quantum Cosmology","authors":"J. Hartle","doi":"10.1142/9789811216404_0005","DOIUrl":"https://doi.org/10.1142/9789811216404_0005","url":null,"abstract":"Existing physical theories do not predict every feature of our experience but only certain regularities of that experience. That difference between what could be observed and what can be predicted is one kind of limit on scientific knowledge. Such limits are inevitable if the world is complex and the laws governing the regularities of that world are simple. Another kind of limit on scientific knowledge arises because even simple theories may require intractable or impossible computations to yield specific predictions. A third kind of limit concerns our ability to know theories through the process of induction and test. Quantum cosmology -- that part of science concerned with the quantum origin of the universe and its subsequent evolution -- displays all three kinds of limits. This paper briefly describes quantum cosmology and discusses these limits. The place of the other sciences in this most comprehensive of physical frameworks is described.","PeriodicalId":416124,"journal":{"name":"The Quantum Universe","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129519320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1995-08-08DOI: 10.1142/9789811216404_0021
J. Hartle
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which spacetime geometry is a quantum variable. The elements of generalized quantum theory are briefly reviewed and illustrated by generalizations of usual quantum theory that incorporate spacetime alternatives, gauge degrees of freedom, and histories that move forward and backward in time. A generalized quantum framework for cosmological spacetime geometry is sketched. This theory is in fully four-dimensional form and free from the need for a fixed causal structure. Usual quantum mechanics is recovered as an approximation to this more general framework that is appropriate in those situations where spacetime geometry behaves classically.
{"title":"Quantum Mechanics at the Planck Scale","authors":"J. Hartle","doi":"10.1142/9789811216404_0021","DOIUrl":"https://doi.org/10.1142/9789811216404_0021","url":null,"abstract":"Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which spacetime geometry is a quantum variable. The elements of generalized quantum theory are briefly reviewed and illustrated by generalizations of usual quantum theory that incorporate spacetime alternatives, gauge degrees of freedom, and histories that move forward and backward in time. A generalized quantum framework for cosmological spacetime geometry is sketched. This theory is in fully four-dimensional form and free from the need for a fixed causal structure. Usual quantum mechanics is recovered as an approximation to this more general framework that is appropriate in those situations where spacetime geometry behaves classically.","PeriodicalId":416124,"journal":{"name":"The Quantum Universe","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122715889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1992-10-13DOI: 10.1017/cbo9780511628863.013
J. Hartle
A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system. Not every set of alternative coarse-grained histories that can be described may be consistently assigned probabilities because of quantum mechanical interference between individual histories of the set. In the quantum mechanics of closed systems, containing both observer and observed, probabilities are assigned to those sets of alternative histories for which there is negligible interference between individual histories as a consequence of the system's initial condition and dynamics. Such sets of histories are said to decohere. Typical mechanisms of decoherence that are widespread in our universe are illustrated. Copenhagen quantum mechanics is an approximation to the more general quantum framework of closed subsystems. It is appropriate when there is an approximately isolated subsystem that is a participant in a measurement situation in which (among other things) the decoherence of alternative registrations of the apparatus can be idealized as exact. Since the quantum mechanics of closed systems does not posit the existence of the quasiclassical domain of everyday experience, the domain of the approximate aplicability of classical physics must be explained. We describe how a quasiclassical domain described by averages of densities of approximately conserved quantities could be an emergent feature of an initial condition of the universe that implies the approximate classical behavior of spacetime on accessible scales.
{"title":"The Quantum Mechanics of Closed Systems","authors":"J. Hartle","doi":"10.1017/cbo9780511628863.013","DOIUrl":"https://doi.org/10.1017/cbo9780511628863.013","url":null,"abstract":"A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system. Not every set of alternative coarse-grained histories that can be described may be consistently assigned probabilities because of quantum mechanical interference between individual histories of the set. In the quantum mechanics of closed systems, containing both observer and observed, probabilities are assigned to those sets of alternative histories for which there is negligible interference between individual histories as a consequence of the system's initial condition and dynamics. Such sets of histories are said to decohere. Typical mechanisms of decoherence that are widespread in our universe are illustrated. Copenhagen quantum mechanics is an approximation to the more general quantum framework of closed subsystems. It is appropriate when there is an approximately isolated subsystem that is a participant in a measurement situation in which (among other things) the decoherence of alternative registrations of the apparatus can be idealized as exact. Since the quantum mechanics of closed systems does not posit the existence of the quasiclassical domain of everyday experience, the domain of the approximate aplicability of classical physics must be explained. We describe how a quasiclassical domain described by averages of densities of approximately conserved quantities could be an emergent feature of an initial condition of the universe that implies the approximate classical behavior of spacetime on accessible scales.","PeriodicalId":416124,"journal":{"name":"The Quantum Universe","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115478411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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