The emergence of classical worlds from a quantum universe
- Authors: Hjul, Karl Iver Hansen
- Date: 2025-04-02
- Subjects: Quantum Darwinism , Quantum theory , Science Philosophy , Physics Philosophy , Hilbert space
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/479130 , vital:78263
- Description: How does a classical world emerge from a quantum world? Can this emergence occur without invoking non-unitary processes such as measurements? Recently, an approach that makes use of just a Hilbert space and the associated Hamiltonian to explain the emergence of a classical world has been proposed. To understand this approach, we will require a clear understanding of the nature of measurements in quantum theory and the different interpretations of it. We then progress onto discussions regarding quantum Darwinism and related _elds of knowledge and how they \bypass" the problem of measurement in quantum theory. Then, we discuss how, using the appropriate choice of factorization of a Hilbert space into a system and an environment and using an acceptable basis observable, we can obtain a quasi-classical state of a system. This approach has previously been applied to study one limit (when interactions dominate the Hamiltonian), but we generalize by applying it to the opposite limit (when interactions are minimal) and suggest a method for the general case (when interactions are neither minimal nor dominant). We then look at Hilbert space fundamentalism, which is the idea that a vector in Hilbert space is the fundamental nature of reality. Hilbert space fundamentalism is a generalized application that takes the idea of the emergence of a classical world from a quantum one and applies it to the Universe as a whole. This leads to the question: could Hilbert space fundamentalism be a candidate for the fundamental theory? Before we evaluate Hilbert space fundamentalism as a candidate fundamental theory, we analyze the theory and inquire as to what makes something a fundamental theory. To understand Hilbert space fundamentalism, we see what a model of the world it predicts looks like. This is done by proposing a mapping from a fundamental Hilbert space to emergent space times utilizing entanglement and the aforementioned recently proposed approach that makes use of Hilbert spaces and Hamiltonians to explain the emergence of classical worlds. To determine if Hilbert space fundamentalism could be a fundamental theory, a set of criteria (completeness in all domains, self-contained, and that speci_c theories emerge from it) is noted. We find that Hilbert space fundamentalism, when viewed through these criteria, cannot be the fundamental theory. , Thesis (MSc) -- Faculty of Science, Physics and Electronics, 2025
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- Authors: Hjul, Karl Iver Hansen
- Date: 2025-04-02
- Subjects: Quantum Darwinism , Quantum theory , Science Philosophy , Physics Philosophy , Hilbert space
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/479130 , vital:78263
- Description: How does a classical world emerge from a quantum world? Can this emergence occur without invoking non-unitary processes such as measurements? Recently, an approach that makes use of just a Hilbert space and the associated Hamiltonian to explain the emergence of a classical world has been proposed. To understand this approach, we will require a clear understanding of the nature of measurements in quantum theory and the different interpretations of it. We then progress onto discussions regarding quantum Darwinism and related _elds of knowledge and how they \bypass" the problem of measurement in quantum theory. Then, we discuss how, using the appropriate choice of factorization of a Hilbert space into a system and an environment and using an acceptable basis observable, we can obtain a quasi-classical state of a system. This approach has previously been applied to study one limit (when interactions dominate the Hamiltonian), but we generalize by applying it to the opposite limit (when interactions are minimal) and suggest a method for the general case (when interactions are neither minimal nor dominant). We then look at Hilbert space fundamentalism, which is the idea that a vector in Hilbert space is the fundamental nature of reality. Hilbert space fundamentalism is a generalized application that takes the idea of the emergence of a classical world from a quantum one and applies it to the Universe as a whole. This leads to the question: could Hilbert space fundamentalism be a candidate for the fundamental theory? Before we evaluate Hilbert space fundamentalism as a candidate fundamental theory, we analyze the theory and inquire as to what makes something a fundamental theory. To understand Hilbert space fundamentalism, we see what a model of the world it predicts looks like. This is done by proposing a mapping from a fundamental Hilbert space to emergent space times utilizing entanglement and the aforementioned recently proposed approach that makes use of Hilbert spaces and Hamiltonians to explain the emergence of classical worlds. To determine if Hilbert space fundamentalism could be a fundamental theory, a set of criteria (completeness in all domains, self-contained, and that speci_c theories emerge from it) is noted. We find that Hilbert space fundamentalism, when viewed through these criteria, cannot be the fundamental theory. , Thesis (MSc) -- Faculty of Science, Physics and Electronics, 2025
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Analysing emergent time within an isolated Universe through the application of interactions in the conditional probability approach
- Authors: Bryan, Kate Louise Halse
- Date: 2020
- Subjects: Space and time , Quantum gravity , Quantum theory , Relativity (Physics)
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/146676 , vital:38547
- Description: Time remains a frequently discussed issue in physics and philosophy. One interpretation of growing popularity is the ‘timeless’ view which states that our experience of time is only an illusion. The isolated Universe model, provided by the Wheeler-DeWitt equation, supports this interpretation by describing time using clocks in the conditional probability interpretation (CPI). However, the CPI customarily dismisses interaction effects as negligible creating a potential blind spot which overlooks the potential influence of interaction effects. Accounting for interactions opens up a new avenue of analysis and a potential challenge to the interpretation of time. In aid of our assessment of the impact interaction effects have on the CPI, we present rudimentary definitions of time and its associated concepts. Defined in a minimalist manner, time is argued to require a postulate of causality as a means of accounting for temporal ordering in physical theories. Several of these theories are discussed here in terms of their respective approaches to time and, despite their differences, there are indications that the accounts of time are unified in a more fundamental theory. An analytic analysis of the CPI, incorporating two different clock choices, and a qualitative analysis both confirm that interactions have a necessary role within the CPI. The consequence of removing interactions is a maximised uncertainty in any measurement of the clock and a restriction to a two-state system, as indicated by the results of the toy models and qualitative argument respectively. The philosophical implication is that we are not restricted to the timeless view since including interactions as agents of causal interventions between systems provides an account of time as a real phenomenon. This result highlights the reliance on a postulate of causality which forms a pressing problem in explaining our experience of time.
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- Authors: Bryan, Kate Louise Halse
- Date: 2020
- Subjects: Space and time , Quantum gravity , Quantum theory , Relativity (Physics)
- Language: English
- Type: Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/146676 , vital:38547
- Description: Time remains a frequently discussed issue in physics and philosophy. One interpretation of growing popularity is the ‘timeless’ view which states that our experience of time is only an illusion. The isolated Universe model, provided by the Wheeler-DeWitt equation, supports this interpretation by describing time using clocks in the conditional probability interpretation (CPI). However, the CPI customarily dismisses interaction effects as negligible creating a potential blind spot which overlooks the potential influence of interaction effects. Accounting for interactions opens up a new avenue of analysis and a potential challenge to the interpretation of time. In aid of our assessment of the impact interaction effects have on the CPI, we present rudimentary definitions of time and its associated concepts. Defined in a minimalist manner, time is argued to require a postulate of causality as a means of accounting for temporal ordering in physical theories. Several of these theories are discussed here in terms of their respective approaches to time and, despite their differences, there are indications that the accounts of time are unified in a more fundamental theory. An analytic analysis of the CPI, incorporating two different clock choices, and a qualitative analysis both confirm that interactions have a necessary role within the CPI. The consequence of removing interactions is a maximised uncertainty in any measurement of the clock and a restriction to a two-state system, as indicated by the results of the toy models and qualitative argument respectively. The philosophical implication is that we are not restricted to the timeless view since including interactions as agents of causal interventions between systems provides an account of time as a real phenomenon. This result highlights the reliance on a postulate of causality which forms a pressing problem in explaining our experience of time.
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Geometry of deformed special relativity
- Authors: Sixaba, Vuyile
- Date: 2018
- Subjects: Special relativity (Physics) , Quantum gravity , Quantum theory , Geometry , Heisenberg uncertainty principle
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/59478 , vital:27615
- Description: We undertake a study of the classical regime in which Planck's constant and Newton's gravitational constant are negligible, but not their ratio, the Planck mass, in hopes that this could possibly lead to testable quantum gravity (QG) effects in a classical regime. In this quest for QG phenomenology we consider modifications of the standard dispersion relation of a free particle known as deformed special relativity (DSR). We try to geometrize DSR to find the geometric origin of the spacetime and momentum space. In particular, we adopt the framework of Hamilton geometry which is set up on phase space, as the cotangent bundle of configuration space in order to derive a purely phase space formulation of DSR. This is necessary when one wants to understand potential links of DSR with modifications of quantum mechanics such as Generalised Uncertainty Principles. It is subsequently observed that space-time and momentum space emerge naturally as curved and intertwined spaces. In conclusion we mention examples and applications of this framework as well as potential future developments.
- Full Text:
- Authors: Sixaba, Vuyile
- Date: 2018
- Subjects: Special relativity (Physics) , Quantum gravity , Quantum theory , Geometry , Heisenberg uncertainty principle
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/59478 , vital:27615
- Description: We undertake a study of the classical regime in which Planck's constant and Newton's gravitational constant are negligible, but not their ratio, the Planck mass, in hopes that this could possibly lead to testable quantum gravity (QG) effects in a classical regime. In this quest for QG phenomenology we consider modifications of the standard dispersion relation of a free particle known as deformed special relativity (DSR). We try to geometrize DSR to find the geometric origin of the spacetime and momentum space. In particular, we adopt the framework of Hamilton geometry which is set up on phase space, as the cotangent bundle of configuration space in order to derive a purely phase space formulation of DSR. This is necessary when one wants to understand potential links of DSR with modifications of quantum mechanics such as Generalised Uncertainty Principles. It is subsequently observed that space-time and momentum space emerge naturally as curved and intertwined spaces. In conclusion we mention examples and applications of this framework as well as potential future developments.
- Full Text:
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