-
What
Can It Mean to Ask, Why Is There Something Rather Than
Nothing? (back to paper)
The bald question, Why is there something rather than
nothing?, is hopelessly ambiguous. One needs explicative
disambiguation to render it amenable to philosophical
attack. If one wants to do so in such a way that an
appropriate answer is grounded, at least in part, on
scientific knowledge, then one comes to realize that one
needs first to understand what one can mean by
“nothing” in the context of our best physical
theories. I argue that to do so requires deep and
comprehensive modifications to any traditional account of
the idea of “nothing”.
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The Many Definitions
of a Black Hole (back to
paper)
Although black holes are objects of central importance
across many fields of physics, there is no agreed upon
definition for them, a fact that does not seem to be
widely recognized. Physicists in different fields
conceive of and reason about them in radically different,
and often conflicting, ways. All those ways, however,
seem sound in the relevant contexts. After examining and
comparing many of the definitions used in practice, I
consider the problems that the lack of a universally
accepted definition leads to, and discuss whether one is
in fact needed for progress in the physics of black holes.
I conclude that, within reasonable bounds, the profusion
of different definitions is in fact a virtue, making the
investigation of black holes possible and fruitful in all
the many different kinds of problems about them that
physicists consider, although one must take care in trying
to translate results between fields.
-
Kinematics,
Dynamics, and the Structure of Physical Theory
(back to paper)
Every physical theory has (at least) two different forms
of mathematical equations to represent its target systems:
the dynamical (equations of motion) and the kinematical
(kinematical constraints). Kinematical constraints are
differentiated from equations of motion by the fact that
their particular form is fixed once and for all,
irrespective of the interactions the system enters into.
By contrast, the particular form of a system’s
equations of motion depends essentially on the particular
interaction the system enters into. All contemporary
accounts of the structure and semantics of physical theory
treat dynamics, i.e., the equations of motion, as the
most important feature of a theory for the purposes of its
philosophical analysis. I argue to the contrary that it
is the kinematical constraints that determine the
structure and empirical content of a physical theory in
the most important ways: they function as necessary
preconditions for the appropriate application of the
theory; they differentiate types of physical systems; they
are necessary for the equations of motion to be well posed
or even just cogent; and they guide the experimentalist in
the design of tools for measurement and observation. It
is thus satisfaction of the kinematical constraints that
renders meaning to those terms representing a
system’s physical quantities in the first place,
even before one can ask whether or not the system
satisfies the theory’s equations of motion.
-
Measure,
Topology and Probabilistic Reasoning in Cosmology
(back to paper)
I explain the difficulty of making various concepts of and
relating to probability precise, rigorous and physically
significant when attempting to apply them in reasoning
about objects (e.g., spacetimes) living in
infinite-dimensional spaces, working through many examples
from cosmology. I focus on the relation of topological to
measure-theoretic notions of and relating to probability,
how they diverge in unpleasant ways in the
infinite-dimensional case, and are even difficult to work
with on their own. Even in cases where an appropriate
family of spacetimes is finite-dimensional, and so admits
a measure of the relevant sort, however, it is always the
case that the family is not a compact topological space,
and so does not admit a physically significant, well
behaved probability measure. Problems of a different but
still deeply troubling sort plague arguments about
likelihood in that context, which I also discuss. I
conclude that most standard forms of argument used in
cosmology to estimate the likelihood of the occurrence of
various properties or behaviors of spacetimes have serious
mathematical, physical and conceptual problems.
-
Classical Black
Holes Are Hot (back to
paper)
In the early 1970s it is was realized that there is a
striking formal analogy between the Laws of black-hole
mechanics and the Laws of classical thermodynamics.
Before the discovery of Hawking radiation, however, it was
generally thought that the analogy was only formal, and
did not reflect a deep connection between gravitational
and thermodynamical phenomena. It is still commonly held
that the surface gravity of a stationary black hole can be
construed as a true physical temperature and its area as a
true entropy only when quantum effects are taken into
account; in the context of classical general relativity
alone, one cannot cogently construe them so. Does the use
of quantum field theory in curved spacetime offer the only
hope for taking the analogy seriously? I think the answer
is ‘no’. To attempt to justify that answer, I
shall begin by arguing that the standard argument to the
contrary is not physically well founded, and in any event
begs the question. Looking at the various ways that the
ideas of “temperature” and
“entropy” enter classical thermodynamics then
will suggest arguments that, I claim, show the analogy
between classical black-hole mechanics and classical
thermodynamics should be taken more seriously, without the
need to rely on or invoke quantum mechanics. In
particular, I construct an analogue of a Carnot cycle in
which a black hole “couples” with an ordinary
thermodynamical system in such a way that its surface
gravity plays the role of temperature and its area that of
entropy. Thus, the connection between classical general
relativity and classical thermodynamics on their own is
already deep and physically significant, independent of
quantum mechanics.
This paper started life as several vestigial
manuscripts that I began in the early 2000s, which, in
an act of Schumpeterian creative destruction, I merged
around 2008. I began giving talks based on the
material at physics and philosophy departments and
conferences around 2011. A manuscript more or less in
this form, albeit with many and variegated
modifications, clarifications, emendations, deletions
and just plain old changes over the years, has been
floating around the community since 2014. Even the
title has oscillated over the years, between the
present bold declaration and the more diffident
“Are Classical Black Holes Hot or Cold?”,
reflecting my waxing and waning skepticism and
enthusiasm with regard to my own arguments and
conclusions at the time. Since 2018, both the
manuscript and my attitude (enthusiasm), and so the
title, have remained remarkably stable against
peturbations, with only minimal evolution of each.
-
Singularities
and Black Holes (back to
paper)
A review of the state of the art concerning philosophical
investigation of issues pertaining to singular structure
and black holes in relativistic spacetimes. Issues
treated include: the definition and existence of singular
structure; cosmic censorship and indeterminism;
foundational problems associated with classical black
holes; black hole thermodynamics; black holes and quantum
theory; cosmology and the arrow of time; analogue black
holes.
-
On
Geometric Objects, the Non-Existence of a Gravitational
Stress-Energy Tensor, and the Uniqueness of the Einstein
Field Equation (back to
paper)
The question of the existence of gravitational
stress-energy in general relativity has exercised
investigators in the field since the inception of the
theory. Folklore has it that no adequate definition of a
localized gravitational stress-energetic quantity can be
given. Most arguments to that effect invoke one version
or another of the Principle of Equivalence. I argue that
not only are such arguments of necessity vague and
hand-waving but, worse, are beside the point and do not
address the heart of the issue. Based on a novel analysis
of what it may mean for one tensor to depend in the proper
way on another, which, en
passant, provides a precise characterization of the
idea of a “geometric object”, I prove that,
under certain natural conditions, there can be no tensor
whose interpretation could be that it represents
gravitational stress-energy in general relativity. It
follows that gravitational energy, such as it is in
general relativity, is necessarily non-local. Along the
way, I prove a result of some interest in own right about
the structure of the associated jet bundles of the bundle
of Lorentz metrics over spacetime. I conclude by showing
that my results also imply that, under a few natural
conditions, the Einstein field equation is the unique
equation relating gravitational phenomena to
spatiotemporal structure, and discuss how this relates to
the non-localizability of gravitational stress-energy.
-
On the Existence of
Spacetime Structure (back to
paper)
there are
technical
appendices of the paper working out the
details of some of the constructions and arguments and
supplementing some of the philosophical discussion,
which limitations of space did not allow for inclusion
of in the published version
I examine the debate between substantivalists and
relationalists about the ontological character of
spacetime and conclude it is not well posed. I argue
that the so-called Hole Argument does not bear on the
debate, because it provides no clear criterion to
distinguish the positions. I propose two such precise
criteria and construct separate arguments based on each
to yield contrary conclusions, one supportive of
something like relationalism and the other of something
like substantivalism. The lesson is that one must fix
an investigative context in order to make such criteria
precise, but different investigative contexts yield
inconsistent results. I examine questions of existence
about spacetime structures other than the spacetime
manifold itself to argue that it is more fruitful to
focus on pragmatic issues of physicality, a notion that
lends itself to several different explications, all of
philosophical interest, none privileged a priori over any of the others. I
conclude by suggesting an extension of the lessons of my
arguments to the broader debate between realists and
instrumentalists.
-
A Primer on
Energy Conditions (back to
paper)
An energy condition, in the context of a wide class of
spacetime theories (including general relativity), is,
crudely speaking, a relation one demands the
stress-energy tensor of matter satisfy in order to try
to capture the idea that “energy should be
positive”. The remarkable fact I will discuss in
this paper is that such simple, general, almost trivial
seeming propositions have profound and far-reaching
import for our understanding of the structure of
relativistic spacetimes. It is therefore especially
surprising when one also learns that we have no clear
understanding of the nature of these conditions, what
theoretical status they have with respect to fundamental
physics, what epistemic status they may have, when we
should and should not expect them to be satisfied, and
even in many cases how they and their consequences
should be interpreted physically. Or so I shall argue,
by a detailed analysis of the technical and conceptual
character of all the standard conditions used in physics
today, including examination of their consequences and
the circumstances in which they are believed to be
violated.
-
Classical Mechanics Is
Lagrangian; It Is Not Hamiltonian (back to paper)
One can (for the most part) formulate a model of a
classical system in either the Lagrangian or the
Hamiltonian framework. Though it is often claimed that
those two formulations are equivalent in all important
ways, this is not true: the underlying geometrical
structures one uses to formulate each theory are not
isomorphic. This raises the question whether one of the
two is a more natural framework for the representation of
classical systems. In the event, the answer is yes: I
state and sketch proofs of two technical results, inspired
by simple physical arguments about the generic properties
of classical systems, to the effect that, in a precise
sense, classical systems evince exactly the geometric
structure Lagrangian mechanics provides for the
representation of systems, and none that Hamiltonian
mechanics does. The argument not only clarifies the
conceptual structure of the two systems of mechanics,
their relations to each other, and their respective
mechanisms for representing physical systems. It also
shows why naively structural approaches to the
representational content of physical theories cannot work.
-
Singularities
and Black Holes First Version (with P. Bokulich)
A review of the state of the art concerning philosophical
investigation of issues pertaining to singular structure
and black holes in relativistic spacetimes. Issues
treated include: the definition and existence of singular
structure; cosmic censorship and indeterminism;
foundational problems associated with classical black
holes; black hole thermodynamics; black holes and quantum
theory; cosmology and the arrow of time; analogue black
holes.
-
General
Relativity Needs No Interpretation (back to paper)
I argue that, contrary to the recent claims of physicists
and philosophers of physics, general relativity requires
no interpretation in any substantive sense of the term. I
canvass the common reasons given in favor of the alleged
need for an interpretation, including the difficulty in
coming to grips with the physical significance of
diffeomorphism invariance and of singular structure, and
the problems faced in the search for a theory of quantum
gravity. I find that none of them shows any defect in our
comprehension of general relativity as a physical theory.
I conclude by comparing general relativity with quantum
mechanics, a theory that manifestly does stand in need of
an interpretation in an important sense. Although many
aspects of the conceptual structure of general relativity
remain poorly understood, it suffers no incoherence in its
formulation as a physical theory that only an
“interpretation” could resolve.
-
Against the
Excesses of Quantum Gravity: A Plea for Modesty
(back to paper)
In 1672, Isaac Newton published in the “Transactions
of the Royal Society” his theory of the structure of
light rays. It was not understood by even his most
brilliant contemporaries, scientific luminaries such as
Robert Hooke and Christian Huygens. The primary obstacle
hindering their understanding was their conception of
proper scientific methodology, the hypethetico-deductive
method as applied solely in the theater of the mechanical
philosophy. Neither Newton’s account of the
derivation of his theory nor the theory itself conformed
to this conception of science, much to the discredit of
that conception.
In the 1990s, quantum gravity came into its own as an
accepted, even a sexy field of research in theoretical
physics. Except for adherence to the mechanical
philosophy, all the major research programs in quantum
gravity today do conform to the conception of science
championed by Newton’s contemporaries, much to the
discredit of quantum gravity.
In this paper I make the case for this claim, and discuss
a few of its unfortunate corollaries. I also examine the
scientific standing of various programs in quantum gravity
as reported by proponents of those programs in order to
criticize what I see as their immodestyunwarranted
in light of my arguments in the first part of the
paperwhich at times seems to cross the border into
disingenuity. It is no mere Pauline gripe I have against
this immodesty; I think it does real damage to science on
many levels. I conclude with a few reflections on this
matter and on the role, if any, that philosophers of
science ought to play in the maintenance of working
science’s integrity.
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The
Constraints General Relativity Places on Physicalist
Accounts of Causality (back to
paper)
All accounts of causality that presuppose the propagation
or transfer of some physical stuff to be an essential part
of the causal relation rely for the force of their causal
claims on a principle of conservation for that stuff.
General Relativity does not permit the rigorous
formulation of appropriate conservation principles.
Consequently, in so far as General Relativity is
considered a fundamental physical theory, such accounts of
causality cannot themselves be considered fundamental.
The continued use of such accounts of causality perhaps
ought not be proscribed, but justification is due from
those who would use them.
-
The Analysis of
Singular Spacetimes (back to
paper)
Much controversy surrounds the question of what ought to
be the proper definition of “singularity” in
general relativity, and the question of whether the
prediction of such entities leads to a crisis for the
theory. I argue that there is no single canonical
definition of such a thing, and that none is
requiredvarious definitions present themselves,
respectively suitable for different sorts of
investigations. In particular, I argue that a definition
in terms of curve incompleteness is adequate for most
purposes, though the idea that singularities correspond to
“missing points” has insurmountable problems.
I conclude that singularities per
se pose no serious problem for the theory, but
their analysis does bring into focus several problems of
interpretation at the foundation of the theory often
ignored in the philosophical literature.
-
The Delicacy of
Causal Ascription and Bell’s Theorem (back to paper)
I neither attack nor defend
Jarrett’s (1984) conclusions
concerning adequacy constraints appropriate to (models of)
physical theories mooted in discussions of Bell’s
Theorem. Rather I attempt to clarify what sorts of
arguments can and cannot coherently be made when
Jarrett-type premises are accepted (or are accepted at
least for the sake of argument). In particular I show
that certain recent construals of
Jarrett’s 1984 argument that
focus on the notion of causality not only are beside the
point of Jarrett’s argument but, more importantly,
obfuscate what is salutary that can be gleaned from his
argument.
Martin
Jones and Rob Clifton among recent commentators on
Jarrett not only are notable for their clarity, precision
and thoroughness of argument, but they also are typical in
what, I suspect, is the main culprit behind confused
arguments that are concerned with issues of causality,
viz., a careless deployment of
the notion of “causality” itself. For this
reason I have chosen them as a foil, precisely because
theirs seems to me the clearest, best case for what I take
to be at bottom a confused way both of thinking of
Jarrett’s argument in particular, and of deploying
causal arguments in general.
-
Scientific
Models Are Not Fictions (back to paper)
Scientific models are not best understood as fictions.
If one wants to use such an idiom, it is perhaps better
to think of them as metaphors.
-
Schematizing
the Observer and the Epistemic Content of
Theories (back to paper)
what appears in this version as §5 “What
Measurements and the Observer Are” and §11
“Appendix: Précis” will not appear in
the published version due to length constraints;
otherwise the two versions are identical, except for
trivialities noted in the text
Following some observations of Howard Stein (1994), I
argue that, contrary to the standard view, one cannot
understand the structure and nature of our knowledge in
physics without an analysis of the way that observers
(and, more generally, measuring instruments and
experimental arrangements) are modeled in theory. One
upshot is that standard pictures of what a scientific
theory can be are grossly inadequate. In particular,
standard formulations assume, with no argument ever
given, that it is possible to make a clean separation
between, on the one hand, one part of the scientific
knowledge a physical theory embodies, viz., that encoded in the pure
mathematical formalism and, on the other, the remainder
of that knowledge. The remainder includes at a minimum
what is encoded in the practice of modeling particular
systems, of performing experiments, of bringing the
results of theory and experiment into mutually fruitful
contactin sum, real application of the theory in
actual scientific practice. This assumption comes out
most clearly in the picture of semantics that naturally
accompanies the standard view of theories: semantics is
fixed by ontology’s shining City on the Hill, and
all epistemology and methodology and other practical
issues and considerations are segregated to the ghetto
of the theory’s pragmatics. We should not assume
such a clean separation is possible without an argument,
and, indeed, I offer many arguments that such a
separation is not feasible. An adequate semantics for
theories cannot be founded on ontology, but rather on
epistemology and methodology.
-
Framework
Confirmation by Newtonian Abduction (back to paper)
The analysis of theory-confirmation generally takes the
form: show that a theory in conjunction with physical data
and auxiliary hypotheses yield a prediction about
phenomena; verify the prediction; provide a quantitative
measure of the degree of theory-confirmation this yields.
The issue of confirmation for an entire framework (e.g.,
Newtonian mechanics en bloc, as
opposed, say, to Newton’s theory of gravitation)
either does not arise, or is dismissed in so far as
frameworks are thought not to be the kind of thing that
admits scientific confirmation. I argue that there is
another form of scientific reasoning that has not received
philosophical attention, what I call Newtonian abduction,
that does provide confirmation for frameworks as a whole,
and does so in two novel ways. (In particular, Newtonian
abduction is not IBE, but rather
is much closer to Peirce’s original explication of
the idea of abduction.) I further argue that Newtonian
abduction is at least as important a form of reasoning in
science as the deductive form sketched above. The form is
beautifully summed up by Maxwell (1876): “The true
method of physical reasoning is to begin with the
phenomena and to deduce the forces from them by a direct
application of the equations of motion.”
-
If Metrical
Structure Were Not Dynamical, Counterfactuals in General
Relativity Would Be Easy (back to paper)
General relativity poses serious problems for
counterfactual propositions peculiar to it as a physical
theory, problems that have gone unremarked on in the
physics and in the philosophy literature. Because these
problems arise from the dynamical nature of spacetime
geometry, they are shared by all schools of thought on
how counterfactuals should be interpreted and
understood. Given the role of counterfactuals in the
characterization of, inter
alia, many accounts of scientific laws,
theory-confirmation and causation, general relativity
once again presents us with idiosyncratic puzzles any
attempt to analyze and understand the nature of
scientific knowledge and of science itself must face.
-
On
the Propriety of Physical Theories as a Basis for Their
Semantics (back to
paper)
I argue that an adequate semantics for physical theories
must be grounded on an account of the way that a theory
provides formal and conceptual resources appropriate
for—that have propriety in—the construction of
representations of the physical systems the theory
purports to treat. I sketch a precise, rigorous
definition of the required forms of propriety, and argue
that semantic content accrues to scientific
representations of physical systems primarily in virtue of
the propriety of its resources. That propriety largely
consists in the satisfaction of a subset of the relations
a theory posits among the quantities it treats, viz., the theory’s kinematical
constraints, rather than in the predictive accuracy of its
equations of motion. In particular, the adequacy
(soundness, accuracy, truth, …) of a theory’s
representations plays no fundamental role in the
determination of a representation’s semantic
content. One consequence is that anything like
traditional Tarskian semantics is inadequate for the task.
-
On the Formal
Consistency of Theory and Experiment, with Applications to
Problems in the Initial-Value Formulation of the
Partial-Differential Equations of Mathematical
Physics (back to paper)
The dispute over the viability of various theories of
relativistic, dissipative fluids is analyzed. The focus
of the dispute is identified as the question of
determining what it means for a theory to be applicable to
a given type of physical system under given conditions.
The idea of a physical theory’s regime of propriety is introduced, in
an attempt to clarify the issue, along with the
construction of a formal model trying to make the idea
precise. This construction involves a novel
generalization of the idea of a field on spacetime, as
well as a novel method of approximating the solutions to
partial-differential equations on relativistic spacetimes
in a way that tries to account for the peculiar needs of
the interface between the exact structures of mathematical
physics and the inexact data of experimental physics in a
relativistically invariant way. It is argued, on the
basis of these constructions, that the idea of a regime of
propriety plays a central role in attempts to understand
the semantical relations between theoretical and
experimental knowledge of the physical world in general,
and in particular in attempts to explain what it may mean
to claim that a physical theory models or represents a
kind of physical system. This discussion necessitates an
examination of the initial-value formulation of the
partial-differential equations of mathematical physics,
which suggests a natural set of conditionsby no
means meant to be canonical or exhaustiveone may
require a mathematical structure, in conjunction with a
set of physical postulates, satisfy in order to count as a
physical theory. Based on the novel approximating methods
developed for solving partial-differential equations on a
relativistic spacetime by finite-difference methods, a
technical result concerning a peculiar form of theoretical
under-determination is proved, along with a technical
result purporting to demonstrate a necessary condition for
the self-consistency of a physical theory.
-
On the
Challenges the Sons of Ariston Pose to Socrates in the Republic, Socrates’s Confounding
Responses to Them, and the Character of Justice: Part I, The
Challenges (back to
paper)
I examine an extraordinary circumstance of the work as a
whole, a circumstance that has gone largely, and oddly,
unremarked in the secondary literature. At the conclusion
of both Socrates’s antepenultimate (IV.445ab) and
penultimate (IX.580bc) answers to the brothers’
challenges, he asks Glaukon to render judgement on the
worth and intrinsic goodness of justice and the just
man’s life. Glaukon without hesitation declares
justice to be good in and of itself, and the just life to
be the best and the happiest of lives. In both places, to
drive the point home, Socrates makes sure to mention one
of the primary terms of the challenges: that justice and
the just life have this character whether the just man is
known to be just or not (IV.445a), in either the eyes of
god or men (IX.580c), which Glaukon readily grants. And yet, for the entirety of his construction
of the just city, his account of justice itself, and most
of all his characterization of the just man, the just man
both has seemed and has been known by all to be
just. Socrates has flagrantly flouted the most
fundamental term of the challenge, and not only this term
but all the rest as well, for the just man, in
Socrates’s recounting of his life, has had accrue to
him all the appurtenances, pleasures, rewards and good
repute that Glaukon and Adeimantos demanded be stripped
from him, so they could with surety conclude that justice
is good in and of itself rather than on account only of
its repute and rewards. Are Glaukon and Adeimantos
simpletons, dupes, that they would readily accept as an
answer to their challenges one that is, prima facie, an answer to no question
they had asked?
I do not think Plato wanted us to draw this conclusion.
What else, then, can be the resolution of this puzzle? I
attempt in this series of three papers to sketch one:
Socrates has, in fact, answered each of their challenges
to the letter. In working out the answers, Socrates and
the sons of Ariston have discovered that the nature of
true justice demands that the just man live a life that
will accrue to itself many (though by no means all) of the
concomitants and the rewards and much of the repute given,
according to common belief, to the just man (or, at least,
the seemingly just man) on account of his (seeming)
justice, not, however, as consequences of justice, but
rather as necessary constituents, in some way or other, of
justice itself. It follows that justice is, by its
nature, a virtue that demands that its agent inhabit a
definite sort of place in a richly appointed and textured
society—it is essentially a social virtue, without real
substance or sense in isolation from the social roles the
just man plays and the acts he performs.
In this first paper of the three, I explicate the
brothers’ challenges to demonstrate how, on the face
of it, Socrates does not answer them.