2,269 research outputs found

### Arrow(s) of Time without a Past Hypothesis

The paper discusses recent proposals by Carroll and Chen, as well as Barbour,
Koslowski, and Mercati to explain the (thermodynamic) arrow of time without a
Past Hypothesis, i.e., the assumption of a special (low-entropy) initial state
of the universe. After discussing the role of the Past Hypothesis and the
controversy about its status, we explain why Carroll's model - which
establishes an arrow of time as typical - can ground sensible predictions and
retrodictions without assuming something akin to a Past Hypothesis. We then
propose a definition of a Boltzmann entropy for a classical $N$-particle system
with gravity, suggesting that a Newtonian gravitating universe might provide a
relevant example of Carroll's entropy model. This invites comparison with the
work of Barbour, Koslowski, and Mercati that identifies typical arrows of time
in a relational formulation of classical gravity on shape space. We clarify the
difference between this gravitational arrow in terms of shape complexity and
the entropic arrow in absolute spacetime and work out the key advantages of the
relationalist theory. We end by pointing out why the entropy concept relies on
absolute scales and is thus not relational.Comment: Contains small corrections with respect to the previous versio

### Essentially Ergodic Behaviour

I prove a theorem on the precise connection of the time and phase space average of the Boltzmann equilibrium showing that the behaviour of a dynamical system with a stationary measure and a dominant equilibrium state is qualitatively ergodic. Explicitly, I will show that, given a measure-preserving dynamical system and a region of overwhelming phase space measure, almost all trajectories spend almost all of their time in that region. The other way round, given that almost all trajectories spend almost all of their time in a certain region, that region is of overwhelming phase space measure. In total, the time and phase space average of the equilibrium state approximately coincide. Consequently, equilibrium can equivalently be defined in terms of the time or the phase space average. Even more, since the two averages are almost equal, the behaviour of the system is essentially ergodic. While this does not explain the approach to equilibrium, it provides a means to estimate the fluctuation rates

### Essentially Ergodic Behaviour

I prove a theorem on the precise connection of the time and phase space average of the Boltzmann equilibrium showing that the behaviour of a dynamical system with a stationary measure and a dominant equilibrium state is qualitatively ergodic. Explicitly, I will show that, given a measure-preserving dynamical system and a region of overwhelming phase space measure, almost all trajectories spend almost all of their time in that region. The other way round, given that almost all trajectories spend almost all of their time in a certain region, that region is of overwhelming phase space measure. In total, the time and phase space average of the equilibrium state approximately coincide. Consequently, equilibrium can equivalently be defined in terms of the time or the phase space average. Even more, since the two averages are almost equal, the behaviour of the system is essentially ergodic. While this does not explain the approach to equilibrium, it provides a means to estimate the fluctuation rates

### Arrow(s) of Time without a Past Hypothesis

he paper discusses recent proposals by Carroll and Chen, as well as Barbour, Koslowski, and Mercati to explain the (thermodynamic) arrow of time without a Past Hypothesis, i.e., the assumption of a special (low-entropy) initial state of the universe. After discussing the role of the Past Hypothesis and the controversy about its status, we explain why Carroll's model - which establishes an arrow of time as typical - can ground sensible predictions and retrodictions without assuming something akin to a Past Hypothesis. We then propose a definition of a Boltzmann entropy for a classical $N$-particle system with gravity, suggesting that a Newtonian gravitating universe might provide a relevant example of Carroll's entropy model. This invites comparison with the work of Barbour, Koslowski, and Mercati that identifies typical arrows of time in a relational formulation of classical gravity on shape space. We clarify the difference between this gravitational arrow in terms of shape complexity and the entropic arrow in absolute spacetime, and work out the key advantages of the relationalist theory. We end by pointing out why the entropy concept relies on absolute scales and is thus not relational

### Arrow(s) of Time without a Past Hypothesis

The paper discusses recent proposals by Carroll and Chen, as well as Barbour, Koslowski, and Mercati to explain the (thermodynamic) arrow of time without a Past Hypothesis, i.e. the assumption of a special (low-entropy) initial state of the universe. After discussing the role of the Past Hypothesis and the controversy about its status, we explain why Carroll's model - which establishes an arrow of time as typical - can ground sensible predictions and retrodictions without assuming something akin to a Past Hypothesis. We then propose a definition of a Boltzmann entropy for a classical N-particle system with gravity, suggesting that a Newtonian gravitating universe might provide a relevant example of Carroll's entropy model. This invites comparison with the work of Barbour, Koslowski, and Mercati that identifies typical arrows of time in a relational formulation of classical gravity on shape space. We clarify the difference between this gravitational arrow in terms of shape complexity and the entropic arrow in absolute spacetime, and work out the key advantages of the relationalist theory. We end by pointing out why the entropy concept relies on absolute scales and is thus not relational

### The Point of Primitive Ontology

Bohmian mechanics grounds the predictions of quantum mechanics in precise dynamical laws for a primitive ontology of point particles. In an appraisal of the de-Broglie-Bohm theory, the paper discusses the crucial epistemological and conceptual role that a primitive ontology plays within a physical theory. It argues that quantum theories without primitive ontology fail to make contact with observable reality in a clear and consistent manner. Finally, it discusses Einstein's epistemological model and why it supports the primitive ontology approach

### Arrow(s) of Time without a Past Hypothesis

The paper discusses recent proposals by Carroll and Chen, as well as Barbour, Koslowski, and Mercati to explain the (thermodynamic) arrow of time without a Past Hypothesis, i.e. the assumption of a special (low-entropy) initial state of the universe. After discussing the role of the Past Hypothesis and the controversy about its status, we explain why Carroll's model - which establishes an arrow of time as typical - can ground sensible predictions and retrodictions without assuming something akin to a Past Hypothesis. We then propose a definition of a Boltzmann entropy for a classical N-particle system with gravity, suggesting that a Newtonian gravitating universe might provide a relevant example of Carroll's entropy model. This invites comparison with the work of Barbour, Koslowski, and Mercati that identifies typical arrows of time in a relational formulation of classical gravity on shape space. We clarify the difference between this gravitational arrow in terms of shape complexity and the entropic arrow in absolute spacetime, and work out the key advantages of the relationalist theory. We end by pointing out why the entropy concept relies on absolute scales and is thus not relational

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