7 research outputs found
Statistical mechanics of covariant systems with multi-fingered time
Recently, in [Class. Quantum Grav. 33 (2016) 045005], the authors proposed a
new approach extending the framework of statistical mechanics to
reparametrization-invariant systems with no additional gauges. In this work,
the approach is generalized to systems defined by more than one Hamiltonian
constraints (multi-fingered time). We show how well known features as the
Ehrenfest- Tolman effect and the J\"uttner distribution for the relativistic
gas can be consistently recovered from a covariant approach in the
multi-fingered framework. Eventually, the crucial role played by the
interaction in the definition of a global notion of equilibrium is discussed.Comment: 5 pages, 2 figure
On entropic gravity: the entropy postulate, entropy content of screens and relation to quantum mechanics
We consider the controversial hypothesis that gravity is an entropic force
that has its origin in the thermodynamics of holographic screens. Several key
aspects of entropic gravity are discussed. In particular, we revisit and
elaborate on our criticism of the recent claim that entropic gravity fails to
explain observations involving gravitationally-bound quantum states of neutrons
in the GRANIT experiment and gravitationally induced quantum interference. We
argue that the analysis leading to this claim is troubled by a
misinterpretation concerning the relation between the microstates of a
holographic screen and the state of a particle in the emergent space,
engendering inconsistencies. A point of view that could resolve the
inconsistencies is presented. We expound the general idea of the aforementioned
critical analysis of entropic gravity in such a consistent setting. This
enables us to clarify the problem and to identify a premise whose validity will
decide the faith of the criticism against entropic gravity. It is argued that
in order to reach a sensible conclusion we need more detailed knowledge on
entropic gravity. These arguments are relevant to any theory of emergent space,
where the entropy of the microscopic system depends on the distribution of
matter in the emergent space.Comment: 15 pages; v2: presentation and arguments improved, particularly in
section 5; accepted to Phys. Lett.
Three possible implications of spacetime discreteness
We analyze the possible implications of the discreteness of spacetime, which is defined here as the existence of a minimum observable interval of spacetime. First, it is argued that the discreteness of spacetime may result in the existence of a finite invariant speed when combining with the principle of relativity. Next, it is argued that when combining with the uncertainty principle, the discreteness of space seems to require that spacetime is curved by matter, and the dynamical relationship between matter and spacetime holds true not only for macroscopic objects but also for microscopic particles. Moreover, the Einstein gravitational constant can also be determined in terms of the minimum size of discrete spacetime. Thirdly, it is argued that the discreteness of time may result in the dynamical collapse of the wave function, and the minimum size of discrete spacetime also yields a plausible collapse criterion consistent with experiments. These heuristic arguments might provide a deeper understanding of the special and general relativity and quantum theory, and also have implications for the solutions to the measurement problem and the problem of quantum gravity
Conservative entropic forces
Entropic forces have recently attracted considerable attention as ways to
reformulate, retrodict, and perhaps even "explain'" classical Newtonian gravity
from a rather specific thermodynamic perspective. In this article I point out
that if one wishes to reformulate classical Newtonian gravity in terms of an
entropic force, then the fact that Newtonian gravity is described by a
conservative force places significant constraints on the form of the entropy
and temperature functions. (These constraints also apply to entropic
reinterpretations of electromagnetism, and indeed to any conservative force
derivable from a potential.)
The constraints I will establish are sufficient to present real and
significant problems for any reasonable variant of Verlinde's entropic gravity
proposal, though for technical reasons the constraints established herein do
not directly impact on either Jacobson's or Padmanabhan's versions of entropic
gravity. In an attempt to resolve these issues, I will extend the usual notion
of entropic force to multiple heat baths with multiple "temperatures'" and
multiple "entropies".Comment: V1: 21 pages; no figures. V2: now 24 pages. Two new sections (reduced
mass formulation, decoherence). Many small clarifying comments added
throughout the text. Several references added. V3: Three more references
added. V4: now 25 pages. Some extra discussion on the relation between
Verlinde's scenario and the Jacobson and Padmanabhan scenarios. This version
accepted for publication in JHE
Interpreting Quantum Mechanics in Terms of Random Discontinuous Motion of Particles
This thesis is an attempt to reconstruct the conceptual foundations of quantum mechanics. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown to be consistent with existing experiments and our macroscopic experience. In addition, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and dynamical collapse theories, and briefly analyze the problem of the incompatibility between quantum mechanics and special relativity
On the possibility of stable regularities without fundamental laws
This doctoral dissertation investigates the notion of physical necessity. Specifically, it studies whether it is possible to account for non-accidental regularities without the standard assumption of a pre-existent set of governing laws. Thus, it takes side with the so called
deflationist accounts of laws of nature, like the humean or the antirealist. The specific aim is to complement such accounts by providing a
missing explanation of the appearance of physical necessity.
In order to provide an explanation, I recur to fields that have not
been appealed to so far in discussions about the metaphysics of laws.
Namely, I recur to complex systems’ theory, and to the foundations
of statistical mechanics. The explanation proposed is inspired by how
complex systems’ theory has elucidated the way patterns emerge, and
by the probabilistic explanations of the 2nd law of thermodynamics.
More specifically, this thesis studies how some constraints that make
no direct reference to the dynamics can be a sufficient condition for
obtaining in the long run, with high probability, stable regular behavior. I hope to show how certain metaphysical accounts of laws might benefit from the insights achieved in these other fields.
According to the proposal studied in this thesis, some regularities are
not accidental not in virtue of an underlying physical necessity. The
non-accidental character of certain regular behavior is only due to
its overwhelming stability. Thus, from this point of view the goal becomes to explain the stability of temporal patterns without assuming a set of pre-existent guiding laws. It is argued that the stability can be the result of a process of convergence to simpler and stable regularities from a more complex lower level. According to this project, if successful, there would be no need to postulate a (mysterious) intermediate category between logical necessity and pure contingency.
Similarly, there would be no need to postulate a (mysterious) set of
pre-existent governing laws.
Part I of the thesis motivates part II, mostly by arguing why further
explanation of the notions of physical necessity and governing laws
should be welcomed (chapter 1), and by studying the plausibility of a
lawless fundamental level (chapters 2 and 3). Given so, part II develops the explanation of formation of simpler and stable behavior from
a more complex underlying level
Is Gravity an Entropic Force?
The remarkable connections between gravity and thermodynamics seem to imply that gravity is not fundamental but emergent, and in particular, as Verlinde suggested, gravity is probably an entropic force. In this paper, we will argue that the idea of gravity as an entropic force is debatable. It is shown that there is no convincing analogy between gravity and entropic force in Verlinde’s example. Neither holographic screen nor test particle satisfies all requirements for the existence of entropic force in a thermodynamics system. Furthermore, we show that the entropy increase of the screen is not caused by its statistical tendency to increase entropy as required by the existence of entropic force, but in fact caused by gravity. Therefore, Verlinde’s argument for the entropic origin of gravity is problematic. In addition, we argue that the existence of a minimum size of spacetime, together with the Heisenberg uncertainty principle in quantum theory, may imply the fundamental existence of gravity as a geometric property of spacetime. This may provide a further support for the conclusion that gravity is not an entropic force