Rafael Sorkin

Research Interests

[Most references still to be added]

OVERVIEW OF MY WORK

More than anything else, my work in physics has been guided by a desire
to overcome the disunity which characterizes our present conception of
nature, and which shows itself most obviously in our failure to have
reconciled our best theory of spacetime structure (general relativity)
with the best dynamical framework we know of for describing the behavior
of matter on small scales (quantum field theory). Ever since I
encountered it in graduate school, the greater part of my efforts has
been devoted directly or indirectly to this problem, which can also be
viewed as the task of completing the twin revolutions initiated early in
the last century in connection with the study of the very small (atoms),
the very fast (light), and the very big (astronomy).

In addressing this "quantum gravity" problem, I first explored the idea
("Regge Calculus") that spacetime can be represented as a simplicial
complex, an essentially topological notion which today provides the
basis for the causal dynamical triangulation and spin-foam approaches to
quantum gravity. Regarded not just as an artificial finite-differencing
of the Einstein equations, but as a hypothesis about the inner basis of
spacetime, Regge Calculus fit in well with the expectation that the
continuum is only an effective description of some more fundamental --
discrete -- structure. However, after some work, I came to feel that if
topology was to be the ultimate source of spatio-temporal geometry, then
a more flexible and natural structure than the simplicial complex was
the finite topological space. By a kind of duality, such a space can
also be regarded as a partially ordered set or "poset", and this links
topology to the arguably more basic concept of order. But in the end
the poset-type of topology seemed no more satisfactory as a substitute
for spacetime than the simplicial complex had been. At best it could
produce a metric-space with all distances positive, but not the kind of
Lorentzian geometry which characterizes the spacetime of special and
general relativity. Understood, however, not topologically but
temporally or causally, an order-relation does contain the seeds of
Lorentzian geometry, and this led me, finally, to the idea of the causal
set as the deep structure of spacetime. At present, this is the road I
am taking, and a separate web page describes causal set theory in more
depth, including its recent great progress and current prospects.

Although I no longer believe that topology enjoys a fundamental status,
that does not mean that topological questions are unimportant for
quantum gravity, and exploring the novel topological possibilities
inherent in curved spacetime has always been an important strand in my
work. Emerging from an underlying discreteness, potential topological
effects will first arise on those length-scales -- possibly still close
to Planckian -- where the spacetime manifold itself begins to make
sense. In this regime spacetime topology possesses kinematic resources
sufficient to reproduce all the degrees of freedom of the standard
model. For example, extra spatial dimensions could give rise to gauge
fields in the "Kaluza-Klein" manner, while topological geons
(quasi-local excitations of the spatial topology) could serve as quarks,
at least as far as kinematics is concerned. In particular, geons can
exhibit fermionic statistics for purely topological reasons, without the
need to introduce any fundamental fermions into the story. In this way,
the causal set in its role as the source of an emergent spacetime
topology could in principle be all there is.

Beyond the potential to reproduce well established types of fields and
particles, spacetime topology might also give rise to novel behaviours
not so far observed or even theorized in other contexts, for example
certain types of exotic statistics. But the study of spacetime
topology, and especially of its temporal variation, also seems to me to
have furnished important clues to the nature of quantum gravity in
general. For example, my work with geons led me to believe that the
spin-statistics correlation will break down unless quantum gravity
provides for transitions from one topology to another. In the contrary
case of frozen spatial topology, geons (including Kaluza-Klein
monopoles) could not be pair-produced, and with the loss of that process
one would lose the source from which, plausibly, the correlation between
spin and statistics springs in general. Recovery of spin-statistics for
geons thus points at the necessity for topology change, and in the
context of the gravitational path integral, it turns out to place
definite constraints on the amplitudes associated with the cobordisms
involved in pair-creation. No less importantly, the need for
topology-change reinforces the belief that a path-integral formulation
of quantum mechanics is the only one that can meet the needs of quantum
gravity, an encouraging conclusion from the point of view of causal
sets, which seem to admit no other form of quantal dynamics.

In this connection, I should also mention Skyrmions and anyons, two
other instances of topological phenomena I have worked on. In the case
of Skyrmions, the topology in question is that of the group SU2 or SU3,
regarded as the "target manifold" of a meson field. The Skyrmion itself
is a topological excitation of the vacuum to be identified with the
nucleon or one of the other baryons, and fermionic statistics arises in
close analogy to how it does for topological geons in quantum gravity.
Even dynamically, the analogy with geons remains close, with the
exception that (thanks to the absence of gauge-issues) one can actually
compute the energy-spectrum and understand how the uncertainty principle
can stabilize the Skyrmion against collapse. The resulting
zero-parameter fit to the low lying baryon masses turned out to be
surprisingly accurate.

Thinking about geon statistics also led me to try to analyze the meaning
of particle-statistics in general, as a kind of nonlocal interaction
among particles which is expressed topologically. As a byproduct I
noticed the possibility of so-called anyons, which actually had been
pointed out a few years earlier by Leinaas and Myrheim.

Along with topology and topology-change, black hole entropy has long
interested me as another clue to the nature of quantum gravity. When I
first learned that a black hole carries entropy and that (up to a
coefficient of proportionality of order unity) this entropy equals the
surface-area of the black hole in Planck units, the thought that
suggested itself almost immediately was that this was telling us
something important about the micro-structure of spacetime because the
most natural reading of such an area law is that the horizon is somehow
carrying about one bit of information per unit (Planck) area, and this
in turn is most easily explained if the deep structure of spacetime is
discrete so that the horizon is actually composed of large but still
finite number of "molecules" of Planckian magnitude. In relation to
causal sets, the lesson is that the fundamental discreteness scale must
be near to 1e-32 cm, consistent with many other indications that sizes
shorter than this lack physical meaning. (The subsequently popular idea
of "holography" must have sprung from a train of thought similar to
mine, but it has led in different directions and does not seem to have
shed much light on the structure of the horizon, or on how the entropy
can be "located there".) A correct counting of horizon "degrees of
freedom" must of course be conducted quantum mechanically. To that end,
I computed what is now called the entanglement entropy across the
horizon, regarded as a surface separating the outside of the black hole
from the inside. The calculation did indeed yield an entropy
proportional to the area, or rather an entropy given by the horizon area
in units of the cutoff that one needed to render finite an otherwise
divergent answer. This result, together with others of a similar
nature, furnishes to my way of thinking the single best argument in
favor of spatio-temporal discreteness, and the most direct indication so
far of where the discreteness-scale lies. If, for example, the
kinematic counting of "horizon molecules" in causal set theory were to
find a dynamical justification, one would be able to derive the
coefficient of proportionality relating the true discreteness scale to
the nominal Planck length of 0.81019e-32 cm.

[mention fractal horizon, entropy as shapes]

[mention Lambda prediction, or refer to accompanying web page on causets]
[unimodular gravity?]

The last strand of my work that I will sketch here concerns the
path-integral and its interpretation. Or maybe it would be better to
say that it concerns the possibility of re-formulating quantum mechanics
entirely as a theory of quantal histories, without ever needing to call
on state-vectors, measurements, or external agents as fundamental
notions.

But what purpose would such a re-formulation serve, and would it aid in
the quest for quantum gravity? Part of the answer which I've already
alluded to above is that quantum gravity seems to resist the Hamiltonian
framework of "canonical quantization". This statement reflects first of
all the so-called problem of time and the need to deal with
diffeomorphism-invariant quantities, but when, as with causets, we add
to the mix a discreteness which is not only spatial but temporal, the
contradiction with the Hamiltonian as a generator of continuous
time-evolution becomes severe. And when we allow for topology change
(or do away with the continuum altogether) any thought of quantum
gravity as a theory of operator-valued fields on a fixed manifold also
fades out.

A second part of the answer harks back directly to the question of the
unity of physics. The lack of a theory of quantum gravity is an obvious
symptom of the disunity in our present understanding, but it is not the
only symptom one can point to. Another notorious instance is the "cut"
which quantum mechanics supposedly forces on us, that severs the
macroscopic world of classical physics from the microscopic world of
quantal objects and processes. (Some authors have taken this cut so
seriously as to deny reality to the micro-world altogether.) This issue
of the quantal cut might appear to be remote from quantum gravity, but
insofar as "quantum vs. gravity" reduces to "micro vs. macro", we are
dealing with something rather similar in both situations; hence one
might suspect that the two problems are in fact closely related. Even
if such suspicions are mistaken, though, the practical need for a
histories formulation remains, and further reasons to desire a more
realistic re-formulation of quantum mechanics crop up when one tries to
generalize to the quantal case the condition of "Bell Causality" that
figures so heavily in connection with classical models of "sequential
growth" for causal sets.

How then does the path-integral offer an alternative to the textbook
formalism of state-vectors, Hamiltonians, and external observers? A
first answer is that from the path integral one can derive a functional
mu_quantum -- the quantal measure -- which directly furnishes the
probability of any desired "instrument-event" E. (This measure is
closely related to the so called decoherence functional.) In saying
this, I am presupposing that the Born rule (or rule of thumb!) is
correct, and then just taking note of the fact that the Bornian
probabilities for any specified set of "pointer readings" are furnished
directly by mu_quantum, without any appeal to Schroedinger evolution of
the wave-function or its "collapse" during the measurement. In this way
mu_quantum is analogous to the classical measure mu_classical that
furnishes the probability of a set of histories -- an "event" -- in the
case of a purely classical stochastic process like diffusion or Brownian
motion. If one construes the path-integral in this way, namely as a
generalized measure on a space of "histories", then one sees not only
how quantal processes differ from classical stochastic processes, but
also how closely the two resemble each other, the primary difference
being simply that mu_classical and mu_quantum satisfy different
sum-rules. The former obeys a "2-slit" sum-rule that expresses the
absence of interference between alternative histories, the latter obeys
a weaker, "3-slit" sum-rule that expresses the absence of "higher order"
interference beyond pairwise. (This 3-slit sum-rule, which reflects the
quadratic nature of Bornian probabilities, has now been tested directly
in a literal 3-slit experiment with individual photons.)

The formal framework I have just sketched rests mathematically on a
space of histories and a notion of integration thereon that allows one
to compute the quantal measure mu(A) for any (sufficiently regular)
subset of the history-space. Satisfactory as this framework is in some
ways, the interpretation of mu(A) as a probability still does not take
us beyond the realm of "pointer events" that occur in laboratory
instruments or other macroscopic objects. But the laboratory, or even
the observatory, is not the place where we expect to encounter quantum
gravity. There are no laboratories deep inside black holes or in the
very early universe. Not instrument-events, but events like the "big
bang" are the natural domain of quantum gravity, and one would like to
be able to reason about these events in direct physical terms. When one
ventures into such realms, however, the physical significance of the
quantal measure becomes uncertain: the Born rule loses its force and,
because of interference, one can no longer interpret mu(A) as a
probability in any ordinary sense. The question then is whether mu
admits of a broader interpretation that remains serviceable outside the
city limits of Copenhagen. (If it does not, then perhaps an entirely
different type of dynamical framework will be called for.)

My current belief is that the quantal-measure (meaning in effect the
path-integral) does have a direct microscopic significance, not as a
probability per se, but as an arbiter of whether a given event can occur
at all. In other words, we concede that an event A of vanishing measure
mu(A) will never occur. Drawing out the implications of this
"preclusion principle", one soon finds that it conflicts with the
classical conception of reality as a single history (a single point in
the "history space" over which the path-integral integrates). Of
course, such a contradiction with classical conceptions of reality is
just what one would have expected, but an escape route also opens up.
It turns out that -- at least so far -- the preclusion principle does
not seem to conflict with a modified conception of reality that replaces
the single classical history with a set of one or more histories. Such
a set is a special case of what is called an "anhomomorphic coevent",
and the new point of view is that reality is best described by such a
coevent. (In the resulting re-formulation of quantum theory, it is most
natural to reason about events using rules of inference that differ from
those of classical logic. One could even regard these modified rules as
the essence of the new formulation, but one should not confuse them with
what has previously been called "quantum logic".) We thus acquire an
interpretation of the quantal measure in conjunction with a particular
answer to the question, What is quantum mechanics telling us about the
nature of reality? As a byproduct of this development, one solves the
"measurement problem", or more properly, one obtains a solution of that
problem if instrument-events can be proved to obey a certain
separability condition. It remains to be seen whether this condition
can be established in sufficient generality. It also remains to be seen
whether the new formulation will be be able to accomplish the task for
which it was ultimately intended, namely to provide a more precise
framework for thinking about quantum gravity, and thereby to help clear
away some of the obstacles standing between us and that theory.

[mention QBC (Quantal Bell Causality) here or above?]

Positions Held

• 2006 - present, Perimeter Institute for Theoretical Physics, Senior Researcher
• 2006 - present, University of Waterloo, Adjunct Professor
• 2006 - present, Guelph-Waterloo Physics Institute (GWPI), Member
• 2012-2015, Raman Research Institute, Bangalore, India, Adjunct Professor
• Dec 2011, Raman Research Institute, Bangalore, India, Visiting Professor of Physics
• Jun 2009, University of Tours, Tours, France, Visiting Professor of Physics
• Jan 2004 - Dec 2005, Perimeter Institute for Theoretical Physics, Visiting Professor of Physics
• Jun 2001 - Dec 2001, University of London, Visiting Professor of Physics
• 1995 - 1997, ICN-UNAM, Mexico City, Investigador Titular C
• Jan 1991 - Aug 1991, University of Chicago, Visiting Professor of Physics
• Jan 1987 - Aug 1987, Institute for Advanced Study, Princeton, Member
• 2006 - present, Syracuse University, Professor emeritus of Physics
• 1992 - 2006, Syracuse University, Professor of Physics
• 1987 - 1992, Syracuse University, Associate Professor of Physics
• 1983 - 1987, Syracuse University, Assistant Professor of Physics
• 1982 - 1983, Center for Theoretical Physics, University of Maryland at College Park, Fellow
• 1981, Institute for Advanced Study, Princeton, Member
• 1978 - 1980, Enrico Fermi Institute, University of Chicago, Research Associate
• 1977 - 1978, Cardiff University College, SERC Fellow
• 1974 - 1977, Cardiff University College, Research Associate
• Mar 1974 - Aug 1974, California Institute of Technology, Research Associate

Awards

• NSERC Discovery Grant, Award, NSERC (Canada), April 1 2012-March 31 2017
• Continuous National Science Foundation grant, Award, NSF (US), 1984-2006
• US-Mexico Cooperative Research, Award, NSF (US), 2002-2005
• EPSRC Senior Fellowship, Award, EPSRC (UK), 2001
• Chancellor's Citation for Exceptional Academic Achievement, Honour, Syracuse University, 2000-2001
• US-Mexico Cooperative Research, Award, NSF (US), 2000-2001
• Fellow of the American Physical Society, Honour, American Physical Society, since 1999
• Catedra Patrimonial de Exelencia, Award, CONACYT, (Mexico), 1995-1997
• US-Ireland Cooperative Research, Award, NSF (US), 1989-1992
• CTP Fellowship, Honour and Award, University of Maryland (College Park), 1982-83
• SERC Fellowship, Award, SERC (UK), 1977-78
• Predoctoral Fellowship, Award, National Science Foundation (US), 1966
• Phi-Beta-Kappa at Harvard University, Honour, Phi-Beta-Kappa, 1965
• Valedictorian, Honour, New Trier Township High School, Winnetka, Illinois, 1963
• National Merit Scholarship, Honour and Award, US National Merit Scholarship, 1963

Recent Publications

• For up-to-date copies of some of my publications please follow this link: http://www.perimeterinstitute.ca/personal/rsorkin/some.papers/
• R.D. Sorkin, Expressing entropy globally in terms of (4D) field-correlations, J. Phys. Conf. Ser. 484, 012004 (2014), arXiv: 1205.2953
• Maqbool Ahmed, Rafael D. Sorkin, Everpresent Lambda - II: Structural Stability, Phys. Rev. D 87 (6), 063515 (2013), arXiv: 1210.2589
• Rafael Sorkin, Does a quantum particle know its own energy?, J. Phys. Conf. Ser. 442, 012014 (2013), arXiv: 1304.7550
• N. Afshordi, M. Buck, H.F. Dowker, D. Rideout, R.D. Sorkin, Y.K. Yazdi, A Ground State for the Causal Diamond in 2 Dimensions, JHEP, 2012, Number 10, 088 (2012), arXiv: 1207.7101
• David Rideout, Thomas Jennewein, Giovanni Amelino-Camelia, Tommaso F. Demarie, Brendon L. Higgins, Achim Kempf, Adrian Kent, Raymond Laflamme, Xian Ma, Robert B. Mann, Eduardo Martin-Martinez, Nicolas C. Menicucci, John Moffat, Christoph Simon, Rafael Sorkin, Lee Smolin, Daniel R. Terno, Fundamental quantum optics experiments conceivable with satellites -- reaching relativistic distances and velocities, Class. Quantum Grav. 29 224011 (2012), arXiv: 1206.4949
• N. Afshordi, S. Aslanbeigi, R.D. Sorkin, A Distinguished Ground-State for a Quantum Field in a Curved Spacetime: Formalism, Features, and Cosmology, JHEP, 2012, Number 8, 137 (2012), arXiv: 1205.1296
• Rafael D. Sorkin, Toward a fundamental theorem of quantal measure theory, Mathematical Structures in Computer Science 22, issue 05, 816-852 (2012), arXiv: 1104.0997
• Rafael D. Sorkin, Scalar Field Theory on a Causal Set in Histories Form, J. Phys. Conf. Ser. 306, 012017 (2011), arXiv: 1107.0698
• Stan Gudder and Rafael D. Sorkin, Two-Site Quantum Random Walk, General Relativity and Gravitation 43, 3451-3475 (2011), arXiv: 1105.0705
• Fay Dowker, Joe Henson, Rafael D. Sorkin, Discreteness and the Direct Transmission of Light from Distant Sources, Phys. Rev. D82, 104048 (2010), arXiv: 1009.3058
• Fay Dowker, Steven Johnston and Rafael D. Sorkin, Hilbert Spaces from Path Integrals, Journal of Physics A: Math. Theor. 43, 275302 (2010), arXiv: 1002.0589
• Lydia Philpott, Fay Dowker and Rafael D. Sorkin, Massless particle diffusion in causal set theory, J. Phys. Conf. Ser. 174, 012048 (2009)
• Urbasi Sinha, Christophe Couteau, Zachari Medendorp, Immo Sollner, Raymond Laflamme, Rafael D. Sorkin and Gregor Weihs, Testing Born's Rule in Quantum Mechanics with a Triple Slit Experiment, in Foundations of Probability and Physics-5, L. Accardi, G. Adenier, C. Fuchs,G. Jaeger, A. Yu. Khrennikov, J.-. Larsson, S. Stenholm (Eds.), AIP Conf Proc, Vol. 1101, pp. 200-207, New-York (2009), arXiv: 0811.2068 [quant-ph]
• Lydia Philpott, Fay Dowker, Rafael Sorkin, Energy-momentum diffusion from spacetime discreteness, Phys.Rev.D79:124047,2009, arXiv: 0810.5591
• Rafael D. Sorkin, Light, Links and Causal Sets, Journal of Physics, Conf. Ser. 174, 012018, 2009, arXiv: 0910.0673
• Rafael D. Sorkin, Quantum Dynamics without the Wave Function, J.Phys. A40 (2007) 3207-3222, arXiv: quant-ph/0610204
• Rafael D. Sorkin (Perimeter Institute and Syracuse University), Is the cosmological "constant" a nonlocal quantum residue of discreteness of the causal set type?, AIPConf.Proc.957:142-153,2007, arXiv: 0710.1675
• David Craig, Fay Dowker, Joe Henson, Seth Major, David Rideout, Rafael D. Sorkin, A Bell Inequality Analog in Quantum Measure Theory, J.Phys.A40:501-523,2007, arXiv: quant-ph/0605008
• Joao Magueijo and Rafael D. Sorkin, Occam's razor meets WMAP, Mon.Not.Roy.Astron.Soc.Lett. 377, L39-L43 (2007), arXiv: astro-ph/0604410
• A.M. Ghezelbash, R.B. Mann, Rafael D. Sorkin, The Disjointed Thermodynamics of Rotating Black Holes With a NUT Twist, Nucl.Phys. B775 (2007) 95-119, arXiv: hep-th/0703030
• Rafael D. Sorkin, An exercise in `anhomomorphic logic', Journal of Physics Conf. Ser. 67, 012018 (2007), arXiv: quant-ph/0703276
• David Craig, Fay Dowker, Joe Henson, Seth Major, David Rideout and Rafael D. Sorkin, Noncontexuality in Quantum Measure Theory, AIP Conf. Proc. 844, 77 (2006)
• Luca Bombelli, Joe Henson, Rafael D. Sorkin, Discreteness without symmetry breaking: a theorem, Mod.Phys.Lett.A24:2579-2587,2009, arXiv: gr-qc/0605006
• Rafael D. Sorkin, Ten Theses on Black Hole Entropy, Stud.Hist.Philos.Mod.Phys. 36 (2005) 291-301, arxiv:hep-th/504037
• Rafael D. Sorkin, Big extra dimensions make Lambda too small, Braz.J.Phys. 35 (2005) 280-283, arxiv:gr-qc/503057
• Xavier Martin, Denjoe O'Connor, R.D. Sorkin, The Random Walk in Generalized Quantum Theory, Phys.Rev. D71 (2005) 024029, arXiv: gr-qc/0403085
• Rafael D. Sorkin, An energy bound deduced from the vanishing of the radiation reaction force during uniform acceleration, Modern Physics Letters A19, 543-545 (2004), arXiv: gr-qc/9811030
• Maqbool Ahmed, Scott Dodelson, Patrick B. Greene, Rafael Sorkin, Everpresent Lambda, Phys.Rev.D69:103523,2004, arXiv: astro-ph/0209274
• Fay Dowker, Joe Henson, Rafael D. Sorkin, Quantum Gravity Phenomenology, Lorentz Invariance and Discreteness, Mod.Phys.Lett. A19 (2004) 1829-1840, arxiv:gr-qc/311055
• Donald Marolf and Rafael D. Sorkin, On the Status of Highly Entropic Objects, Phys. Rev. D69, 024014 (2004), arXiv: hep-th/0309218
• Graham Brightwell, Fay Dowker, Raquel S. Garcia, Joe Henson and Rafael D. Sorkin, "Observables" in Causal Set Cosmology, Phys. Rev. D67, 084031 (2003), arXiv: gr-qc/0210061
• Rafael D. Sorkin, Indecomposable Ideals in Incidence Algebras, Modern Physics Letters A18, 2491-2500 (2003), arXiv: math.CO/0309126
• Djamel Dou and Rafael D. Sorkin, Black Hole Entropy as Causal Links, Foundations of Physics 33, 279-296 (2003), arXiv: gr-qc/0302009
• Rafael D. Sorkin, An example relevant to the Kretschmann-Einstein debate, Modern Physics Letters A17, 695-700 (2002) Pittsburgh Philosophy Archive: http://philsci-archive.pitt.edu, arxiv:PITT-PHIL-SCI 00000371
• Donald Marolf and Rafael D. Sorkin, Perfect Mirrors and the Self-Accelerating Box Paradox, Phys. Rev. D66, 104004 (2002), arXiv: hep-th/0201255
• Xavier Martin, Denjoe O'Connor, David Rideout and Rafael D. Sorkin, On the "renormalization" transformations induced by cycles of expansion and contraction in causal set cosmology, Phys. Rev. D63, 084026 (2001), arXiv: gr-qc/0009063
• David P. Rideout and Rafael D. Sorkin, Evidence for a Continuum Limit in Causal Set Dynamics, Phys. Rev. D63, 104011 (2001), arXiv: gr-qc/0003117
• Rafael D. Sorkin, Indications of Causal Set Cosmology, Int. J. Th. Physics 39, 1531-1536 (2000), arXiv: gr-qc/0003043
• David P. Rideout and Rafael D. Sorkin, A Classical Sequential Growth Dynamics for Causal Sets, Phys. Rev. D61, 024002 (2000), arXiv: gr-qc/9904062
• Rafael D. Sorkin and Daniel Sudarsky, Large Fluctuations in the Horizon and what they teach us about Quantum Gravity and Entropy, Classical & Quantum Gravity 16, 3835-3857 (1999), arXiv: gr-qc/9902051
• A. Borde, H.F. Dowker, R.S. Garcia, R.D. Sorkin and S. Surya, Causal Continuity in Singular Spacetimes, Classical & Quantum Gravity 16, 3457-3481 (1999), arXiv: gr-qc/9901063
• H.F. Dowker and R.D. Sorkin, A Spin-Statistics Theorem for Certain Topological Geons, Classical & Quantum Gravity 15, 1153-1167 (1998), arXiv: gr-qc/9609064
• Alan Daughton, Jorma Louko and Rafael D. Sorkin, Instantons and Unitarity in Quantum Cosmology with fixed 4-Volume, Phys. Rev. D58, 084008 (1998), arXiv: gr-qc/9805101
• R.D. Sorkin and Sumati Surya, An Analysis of the Representations of the Mapping Class Group of a Multi-geon Three-manifold, Int. J. Mod. Phys. A13, 3749-3790 (1998), arXiv: gr-qc/9605050
• Rafael D. Sorkin, Forks in the Road on the Way to Quantum Gravity, talk given at the conference entitled "Directions in General Relativity", held at College Park, Maryland, May, 1993, Int. J. Th. Phys. 36, no. 12, 2759-2780 (1997), arXiv: gr-qc/9706002
• J.W. Barrett, M.P. Galassi, W.A. Miller, R.D. Sorkin, P.A. Tuckey and R.M. Williams, A Parallelizable Implicit Evolution Scheme for Regge Calculus, Int. J. Th. Phys. 36, no. 4, 815-839 (1997), arXiv: gr-qc/9411008
• J. Louko and R.D. Sorkin, Complex Actions in Two Dimensional Topology Change, Classical & Quantum Gravity 14, 179-203 (1997), arXiv: gr-qc/9511023
• R.D. Sorkin and E. Woolgar, A Causal Order for Spacetimes with $C^0$ Lorentzian Metrics: Proof of Compactness of the Space of Causal Curves, Classical & Quantum Gravity 13, 1971-1994 (1996), arXiv: gr-qc/9508018
• Rafael D. Sorkin,R.D. Sorkin and E. Woolgar, A Causal Order for Spacetimes with $C^0$ Lorentzian Metrics: Proof of Compactness of the Space of Causal Curves, Classical & Quantum Gravity 13, 1971-1994 (1996), arXiv: gr-qc/9508018
• Rafael D. Sorkin and Madhavan Varadarajan, Energy Extremality in the Presence of a Black Hole, Classical & Quantum Gravity 13, 1949-1970 (1996), arXiv: gr-qc/9510031
• W. McGlinn, L. O'Raifeartaigh, S. Sen and R.D. Sorkin, Morse Theory and the Topology of Configuration Space, Int. J. Mod. Phys. 11, number 5, 823-843 (1996), arXiv: hep-th/9511078
• Rafael D. Sorkin, Quantum Mechanics as Quantum Measure Theory, Modern Physics Letters A9, 3119 (1994), arXiv: gr-qc/9401003
• Rafael D. Sorkin, On the Role of Time in the Sum-over-histories Framework for Gravity, paper given at the conference entitled "History of Modern Gauge Theories", held at Logan, Utah, July, 1987, Int. J. Th. Phys 33, 523-534 (1994)
• A.P. Balachandran, A. Daughton, Gu Zhichong, G. Marmo, R.D. Sorkin and A.M. Srivastava, A Spin-Statistics Theorem without Relativity or Field, Int. J. Mod. Phys. A8, 2993-3044 (1993)
• Supurna Sinha, Rafael D. Sorkin, Brownian motion at absolute zero, Physical Review B 45, 8123 (1992), arxiv:cond-mat/506196
• A.P. Balachandran, W.D. McGlinn, L. O'Raifeartaigh, S. Sen, R.D. Sorkin and A.M. Srivastava, Topological Spin-Statistics Theorems for Strings, Modern Physics Letters A7, 1427 (1992)
• A.P. Balachandran, W.D. McGlinn, L. O'Raifeartaigh, S. Sen, and R.D. Sorkin, The Spin-Statistics Connection from Homology Groups of Configuration Space, and an Anyon Wess-Zumino Term, Int. J. of Mod. Phys. A7, 6887-6906 (1992); and A9, 1395 (1994)
• Michele Bourdeau and R.D. Sorkin, When Can Identical Particles Collide?, Phys. Rev. D45, 687-696 (1992)
• Rafael D. Sorkin, The Gravitational-Electromagnetic Noether-Operator and the Second-Order Energy Flux, Proceedings of the Royal Society, London A435, 635-644 (1991)
• Sukanya Sinha and Rafael D. Sorkin, A Sum Over Histories Account of an EPR(B) Experiment, Found. of Phys. Lett. 4, 303-335 (1991)
• Rafael D. Sorkin, A Finitary Substitute for Continuous Topology?, Int. J. Th. Phys. 30, 923-947 (1991)
• A.P. Balachandran, A. Daughton, Gu Zhichong, G. Marmo, R.D. Sorkin and A.M. Srivastava, A Topological Spin-Statistics Theorem or A Use of the Antiparticle, Modern Physics Letters A5, 1575-1586 (1990) Also published in: Physica Scripta T36, 253-257 (1991)
• P. Jain, J. Schechter and R.D. Sorkin, Interpretation of the "quantum-stabilized skyrmion", Phys. Rev. D41, 3855-3856 (1990)
• Ch. Aneziris, A.P. Balachandran, M. Bourdeau, S. Jo, T.R. Ramadas and R.D. Sorkin, Aspects of Spin and Statistics in Generally Covariant Theories, Int. J. Mod. Phys. A4, 5459-5510 (1989)
• P. Jain, J. Schechter and R.D. Sorkin, Quantum Stabilization of the Skyrme Soliton, Phys. Rev. D39, 998-1001 (1989)
• Ch. Aneziris, A.P. Balachandran, M. Bourdeau, S. Jo, T.R. Ramadas and R.D. Sorkin, Statistics and General Relativity, Modern Physics Letters A4, 331-338 (1989)
• Joohan Lee and Rafael D. Sorkin, A Derivation of a Bogomol'ny Inequality in Five-dimensional Kaluza-Klein Theory, Comm. Math. Phys. 116, 353-364 (1988)
• J.L. Friedman, J.R. Ipser and R.D. Sorkin, Turning Point Method for Axisymmetric Stability of Rotating Relativistic Stars, Ap. J. 325, 722 (1988)
• L. Bombelli, J. Lee, D. Meyer and R.D. Sorkin, Bombelli et al. Reply, Phys. Rev. Lett. 60, 656 (1988)
• Rafael D. Sorkin, A General Relation between Kink Exchange and Kink Rotation, Comm. Math. Phys. 115, 421-434 (1988)
• Luca Bombelli, Joohan Lee, David Meyer and Rafael D. Sorkin, Spacetime as a Causal Set, Phys. Rev. Lett. 59, 521-524 (1987)
• A.P. Balachandran, F. Lizzi, J. Sparano and R.D. Sorkin, Topological Aspects of String Theories, Nuc. Phys. B287, 508-550 (1987)
• Luca Bombelli, Rabinder K. Koul, Gabor Kunstatter, Joohan Lee and Rafael D. Sorkin, On Energy in Five Dimensional Gravity and the Mass of the Kaluza Klein Monopole, Nuc. Phys. B289, 735-756 (1987)
• A.P. Balachandran, H. Gomm and R.D. Sorkin, Quantum Symmetries from Quantum Phases, Fermions from Bosons, a Z_2 Anomaly, and Galilean Invariance, Nuc. Phys. B281, 573-612 (1987)
• Rafael D. Sorkin, A Simplified Derivation of Stimulated Emission by Black Holes, Classical and Quantum Gravity 4, L149-L155 (1987)
• Luca Bombelli, Rabinder K. Koul, Joohan Lee and Rafael D. Sorkin, A Quantum Source of Entropy for Black Holes, Phys. Rev. D34, 373-383 (1986) Reprinted in: B.-K. Hu and L. Parker (eds.) Quantum Theory in Curved Spacetime (World Scientific, 1992)
• Rafael D. Sorkin, Toward a Proof of Entropy Increase in the Presence of Quantum Black Holes, Phys. Rev. Lett. 56, 1885-1888 (1986)
• Rafael D. Sorkin, Non-Time-Orientable Lorentzian Cobordism Allows for Pair Creation, Int. J. Theor. Phys. 25, 877-881 (1986)
• Rafael D. Sorkin, On Topology Change and Monopole Creation, Phys. Rev. D33, 978-982 (1986)
• Rafael D. Sorkin, Stochastic Evolution on a Manifold of States, Ann. Phys. (New York) 168, 119-147 (1986)
• Rafael D. Sorkin, Quantum Gravity, - Review of Quantum Theory of Gravity: Essays in Honor of the 60th Birthday of Bryce S. Dewitt; Steven M. Christensen (Editor) (Hilgar, Bristol, 1984) - Science 228, 572 (1985)
• Rafael D. Sorkin, A Quantitative Occam's Razor, Int.J.Theor.Phys. 22 (1983) 1091-1104, arxiv:astro-ph/511780
• Rafael D. Sorkin, A Kaluza-Klein Monopole, Phys. Rev. Lett. 51, 87-90 (1983); and 54, 86 (1985). Reprinted in: T. Appelquist, A. Chodos, and P.G.O. Freund (eds.), Modern Kaluza-Klein Theories (Benjamin, 1986)
• Rafael D. Sorkin, Particle Statistics in Three Dimensions, Phys. Rev. D27, 1787-1797 (1983)
• John L. Friedman and Rafael D. Sorkin, Statistics of Yang-Mills Solitons, Comm. Math. Phys. 89, 501-521 (1983)
• John L. Friedman and Rafael D. Sorkin, Kinematics of Yang-Mills Solitons, Comm. Math. Phys. 89, 483-499 (1983)
• John L. Friedman and Rafael D. Sorkin, Half-Integral Spin from Quantum Gravity, Gen. Rel. Grav. 14, 615-620 (1982)
• Rafael D. Sorkin, A Stability-Criterion for Many-Parameter Equilibrium Families, Ap. J. 257, 847-854 (1982)
• Rafael D. Sorkin, A Criterion for the Onset of Instability at a Turning Point, Ap. J. 249, 254-257 (1981)
• Rafael D. Sorkin, Robert M. Wald and Zhang Zhen-Jiu, Entropy of Self-Gravitating Radiation, Gen. Rel. Grav. 13, 1127-1146 (1981)
• J.B. Hartle and R.D. Sorkin, A Boundary Term in the Action for Regge Calculus, Gen. Rel. Grav. 13, 541-549 (1981)
• John L. Friedman and Rafael D. Sorkin, Spin-1/2 from Gravity, Phys. Rev. Lett. 44, 1100-1103 (1980); and 45, 148 (1980)
• John L. Friedman and Rafael D. Sorkin, A Spin-Statistics Theorem for Composites Containing both Electric and Magnetic Charges, Comm. Math. Phys. 73, 161-196 (1980)
• John L. Friedman and Rafael D. Sorkin, The Unitary Multiplicity-free Representations of $\overlineSL(4,R)$, J. Math. Phys. 21, 1269-1276 (1980)
• John L. Friedman and Rafael D. Sorkin, Dyon Spin and Statistics: A Fiber-Bundle Theory of Interacting Magnetic and Electric Charges, Phys. Rev. D20, 2511-2525 (1979)
• Rafael D. Sorkin, On the Meaning of the Canonical Ensemble, Int. J. Theor. Phys. 18, 309-321 (1979)
• Rafael D. Sorkin, The Quantum Electromagnetic Field in Multiply-Connected Space, J. Phys. A12, 403-421 (1979)
• Rafael D. Sorkin, On the Failure of the Time-Energy Uncertainty Principle, Found. Phys. 9, 123-128 (1979)
• Rafael D. Sorkin, The Triviality of Continuous Multipliers for the Real Line, Int. J. Theor. Phys. 17, 369-376 (1978); and 18, 777 (1979)
• Rafael D. Sorkin, On the Relation Between Charge and Topology, J. Phys. A10, 717-725 (1977); and A11, 795 (1978)
• J.M. Bardeen, J.L. Friedman, B.F. Schutz and R.D. Sorkin, A New Criterion for Secular Instability of Rapidly Rotating Stars, Ap. J. 217, L49-L53 (1977)
• Rafael D. Sorkin, On Stress-Energy Tensors, Gen. Rel. Grav. 8, 437-449 (1977)
• Bernard F. Schutz and Rafael Sorkin, Variational Aspects of Relativistic Field Theories, with Application to Perfect Fluids, Annals of Phys. (New York) 107, 1-43 (1977)
• Rafael D. Sorkin, The Electromagnetic Field on a Simplicial Net, J. Math. Phys. 16, 2432-2440 (1975); and 19, 1800 (1978)
• Rafael D. Sorkin, The Time-evolution Problem in Regge Calculus, Phys. Rev. D12, 385-396 (1974); and D23, 565 (1981)
• Siavash Aslanbeigi, Mehdi Saravani, Rafael D. Sorkin, Generalized Causal Set d'Alembertians, arXiv: 1403.1622
• Mehdi Saravani, Rafael D. Sorkin, Yasaman K. Yazdi, Spacetime Entanglement Entropy in 1+1 Dimensions, arXiv: 1311.7146
• Rafael D. Sorkin, To What Type of Logic Does the "Tetralemma" Belong?, arXiv: 1003.5735
• Rafael D. Sorkin, A Historical Perspective on Cancer, arXiv: physics/0011002
• R. Penrose, R.D. Sorkin and E. Woolgar, A Positive Mass Theorem based on the Focussing and Retardation of Null Geodesics, arXiv: gr-qc/9301015
• Graham Brightwell, H. Fay Dowker, Raquel S. Garcia, Joe Henson and Rafael D. Sorkin, General Covariance and the "Problem of Time" in a Discrete Cosmology, in Keith G. Bowden (ed) "Correlations" Proceedings of ANPA23, ANPA, 1-17 (2002), arXiv: gr-qc/0202097
• Fay Dowker and Rafael D. Sorkin, Spin and Statistics in Quantum Gravity, R.C. Hilborn and G.M. Tino (eds.) Proceedings of the international meeting on "Spin-statistics connections and commutation relations, experimental tests and theoretical implications", Capri, Italy, May 31-June 4, 2000, AIP, 205-218 (2001), arXiv: gr-qc/0101042
• Rafael D. Sorkin and Sumati Surya, Geon Statistics and UIR's of the Mapping Class Group, Juan Carlos D`Olivo, Martin Klein-Kreisler and Hector Mendez (eds.) Proceedings of the First Latin American Symposium on High Energy Physics and VII Mexican School of Particles and Fields, held Merida, Mexico, October, 1996, American Institute of Physics, Woodbury, NY, 505-514 (1997), arXiv: hep-th/9704081
• Rafael D. Sorkin, Quantum Measure Theory and its Interpretation, D. H. Feng and B. L. Hu (eds.), Quantum Classical Correspondence: the Fourth Drexel Symposium on Quantum Nonintegrability, held Philadelphia, September, 1994, 229-251 (International Press, 1997) arXiv: gr-qc/9507057
• Rafael D. Sorkin, How Wrinkled is the Surface of a Black Hole?, David L. Wiltshire (ed.) Proceedings of the First Australasian Conference on General Relativity and Gravitation, held February, 1996, Adelaide, Australia, 163-174, (U. of Adelaide Press, 1996), arXiv: gr-qc/9701056
• Rafael D. Sorkin, Two Topics concerning Black Holes: Extremality of the Energy, Fractality of the Horizon, S. A. Fulling (ed.), Proceedings of the Conference on Heat Kernel Techniques and Quantum Gravity, held Winnipeg, Canada, August, 1994, 387-407 (Discourses in Mathematics and its Applications, #4) (U. of Texas Press, 1995), arXiv: gr-qc/9508002
• A. Daughton, J. Louko and R.D. Sorkin, Initial Conditions and Unitarity in Unimodular Quantum Cosmology, in R. B. Mann and R. G. McLenaghan (eds.), Proceedings of the Fifth Canadian Conference on General Relativity and Relativistic Astrophysics held Waterloo, Canada, May, 1993, 181-185 (World Scientific, 1994), arXiv: gr-qc/9305016
• Rafael D. Sorkin, Impossible Measurements on Quantum Fields, B. L. Hu and T. A. Jacobson (eds.) Directions in General Relativity: Proceedings of the 1993, International Symposium, Maryland, Vol. II, Papers in honor of Dieter Brill, 293-305 (Cambridge University Press, 1993), arXiv: gr-qc/9302018
• Rafael D. Sorkin, Summary of Workshop A3: Mathematical Studies of Einstein's and Other Relativistic Equations Alternative Gravity Theories, R.J. Gleiser, C.N. Kozameh, O. M. Moreschi (eds.) "General Relativity and Gravitation 1992": Proceedings of the Thirteenth Conference on General Relativity and Gravitation held in Huerta Grande, Cordoba, June-July, 1992, 353-358 (Institute of Physics, Bristol, 1993)
• R.D. Sorkin and E. Woolgar, Causal Structure and the Positivity of Mass, in Proceedings of the sixth Marcel Grossman Conference held Kyoto, Japan, June, 1991, 754-756 (World Scientific, Singapore, 1992)
• R.D. Sorkin and E. Woolgar, New Demonstration of the Positivity of Mass, G. Kunstatter, D. E. Vincent, J. G. Williams (eds.) Proceedings of the Fourth Canadian Conference on General Relativity and Relativistic Astrophysics held Winnipeg, Canada, May, 1991, 206-210 (World Scientific, Singapore, 1992)
• Rafael D. Sorkin, Spacetime and Causal Sets, J.C. D'Olivo, E. Nahmad-Achar, M. Rosenbaum, M.P. Ryan, L.F. Urrutia and F. Zertuche (eds.), SILARG VII: Proceedings of the Seventh Latin American Symposium on Relativity and Gravitation, Relativity and Gravitation: Classical and Quantum, held Cocoyoc, Mexico, December, 1990, 150-173 (World Scientific, Singapore, 1991)
• Rafael D. Sorkin, First Steps with Causal Sets, R. Cianci, R. de Ritis, M. Francaviglia, G. Marmo, C. Rubano, P. Scudellaro (eds.), Proceedings of the Ninth Italian Conference on General Relativity and Gravitational Physics, held Capri, Italy, September, 1990, 68-90 (World Scientific, Singapore, 1991)
• Rafael D. Sorkin, Problems with Causality in the Sum-over-histories Framework for Quantum Mechanics, in A. Ashtekar and J. Stachel (eds.), Conceptual Problems of Quantum Gravity (Proceedings of the i988 Osgood Hill Conference, North Andover, Mass., May 1988), 217-227 (Birkhauser, Boston, 1991) (QC178.C63 1991)
• Rafael D. Sorkin, Does a Discrete Order underly Spacetime and its Metric?, A. Coley, F. Cooperstock and B. Tupper (eds.), Proceedings of the Third Canadian Conference on General Relativity and Relativistic Astrophysics held Victoria, Canada, May 1989, 82-86 (World Scientific, Singapore, 1990)
• Rafael D. Sorkin, Consequences of Spacetime Topology, A. Coley, F. Cooperstock and B. Tupper (eds.), Proceedings of the Third Canadian Conference on General Relativity and Relativistic Astrophysics held Victoria, Canada, May 1989, 137-163 (World Scientific, Singapore, 1990)
• Rafael D. Sorkin, Classical Topology and Quantum Phases: Quantum Geons, S. De Filippo, M. Marinaro, G. Marmo and G. Vilasi (eds.), Geometrical and Algebraic Aspects of Nonlinear Field Theory (Proceedings of the International Meeting on Geometrical and Algebraic Aspects of Nonlinear Field Theory, held Amalfi, Italy, May, 1988), 201-218, (Elsevier, Amsterdam, 1989)
• Ch. Aneziris, A.P. Balachandran, M. Bourdeau, S. Jo, T.R. Ramadas and R.D. Sorkin, Topological Objects in Quantum Gravity, in Proceedings of the MRST Conference: Progress in Theoretical Physics, Toronto, 1988, 94-102 (World Scientific, 1988)
• Rafael D. Sorkin, Conserved Quantities as Action Variations, James A. Isenberg (ed.) Mathematics and General Relativity: Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held June 1986 in Santa Cruz, California (Contemporary Mathematics Volume 71), 23-37 (American Mathematical Society, Providence, 1988) (QC173.6.A47 1986)
• Rafael D. Sorkin, A 5-Dimensional Monopole, J.L. Stone (ed.), Monopole '83 (Plenum, 1984) (proceedings of the Ann Arbor conference of the same name)
• Rafael D. Sorkin, Remarks on Diffeomorphisms as Particle Symmetries, B. Bertotti, F. de Felice, A. Pascolini (eds.), Tenth International Conference on General Relativity and Gravitation (held Padova, 4-9 July, 1983), Contributed Papers, vol. II, 1167-1169 (Roma, Consiglio Nazionale Delle Ricerche, 1983)
• Rafael D. Sorkin, A New Use for the Taub-NUT Metric, B. Bertotti, F. de Felice, A. Pascolini (eds.), Tenth International Conference on General Relativity and Gravitation (held Padova, 4-9 July, 1983), Contributed Papers, vol. I, 357-359 (Roma, Consiglio Nazionale Delle Ricerche, 1983)
• Rafael D. Sorkin, Posets as Lattice Topologies, B. Bertotti, F. de Felice, A. Pascolini (eds.), Tenth International Conference on General Relativity and Gravitation (held Padova, 4-9 July, 1983), Contributed Papers, vol. I, 635-637 (Roma, Consiglio Nazionale Delle Ricerche, 1983)
• Rafael D. Sorkin, On the Entropy of the Vacuum Outside a Horizon, B. Bertotti, F. de Felice, A. Pascolini (eds.), Tenth International Conference on General Relativity and Gravitation (held Padova, 4-9 July, 1983), Contributed Papers, vol. II, 734-736 (Roma, Consiglio Nazionale Delle Ricerche, 1983)
• Rafael D. Sorkin, Diffusion, Differential Geometry, and Black Holes, B. Bertotti, F. de Felice, A. Pascolini (eds.), Tenth International Conference on General Relativity and Gravitation (held Padova, 4-9 July, 1983), Contributed Papers, vol. II, 737-739 (Roma, Consiglio Nazionale Delle Ricerche, 1983)
• Rafael D. Sorkin, Logic is to the quantum as geometry is to gravity, Jeff Murugan, Amanda Weltman, George F. R. Ellis (eds), Foundations of Space and Time: Reflections on Quantum Gravity, Cambridge University Press, 363-384, ISBN: 9780521114400 (2012), arXiv: 1004.1226
• Rafael D. Sorkin, Is the spacetime metric Euclidean rather than Lorentzian?, Arundhati Dasgupta (Ed.), Recent Research in Quantum Gravity, Nova Science Publishers, NY, 115-135, ISBN: 978-1-61942-392-3, (2013), arXiv: 0911.1479
• Rafael D. Sorkin, Does Locality Fail at Intermediate Length-Scales?, Daniele Oriti (ed.) Approaches to Quantum Gravity - Towards a new understanding of space and time, Cambridge University Press, 26-43 (2009), arXiv: gr-qc/0703099
• Rafael D. Sorkin, Relativity theory does not imply that the future already exists: a counterexample, Vesselin Petkov (ed.) Relativity and the Dimensionality of the World, Springer series in the Fundamental Theories of Physics, Vol 153, 153-162 (2007), arXiv: gr-qc/0703098
• Rafael D. Sorkin, Geometry from Order: Causal Sets, Einstein Online Vol. 2, 1007
• Rafael D. Sorkin, Causal Sets: Discrete Gravity, Andres Gomberoff and Don Marolf (eds.) Lectures on Quantum Gravity, CECS Series of the Centro de Estudios Cientificos, Springer, 305-328 (2005), arXiv: gr-qc/0309009
• Rafael D. Sorkin, A Library of Lisp Functions for Posets (and other purposes), http://www.perimeterinstitute.ca/personal/rsorkin/lisp.library/ (1998, 2002)
• Rafael D. Sorkin, The Statistical Mechanics of Black Hole Thermodynamics, R.M. Wald (ed.) Black Holes and Relativistic Stars, U. of Chicago Press, 181-198 (1998), arXiv: gr-qc/9705006
• Rafael D. Sorkin, Some Memories of Chandra, Kameshwar S. Wali (ed.) S. Chandrasekhar; the Man behind the Legend Chandra Remembered, Imperial College Press, 70-75 (1997)
• Rafael D. Sorkin, A Specimen of Theory Construction from Quantum Gravity, Jarrett Leplin (ed.), The Creation of Ideas in Physics: Studies for a Methodology of Theory Construction, The University of Western Ontario Series in Philosophy of Science 55, Kluwer Academic Publishers, Dordrecht, 167-179 (1995), arXiv: gr-qc/9511063
• P. Dowben, E. Schiff and R.D. Sorkin, Physics for Science and Engineering Students, Kendall Hunt (1988)
• Rafael D. Sorkin, Introduction to Topological Geons, P.G. Bergmann and V. de Sabbata (eds.), Topological Properties and Global Structure of Space-Time, Plenum, 249-270 (1986)
• Rafael D. Sorkin, Quantum States (Still) Cannot be Local, University of Maryland preprint (1983)
• Rafael D. Sorkin, An Information-Theoretic Approach to "Curve Fitting", Institute for Advanced Study preprint (1981)
• Rafael D. Sorkin, Development of Simplicial Methods for the Metrical and Electromagnetic Fields, Ph.D. Thesis, California Institute of Technology (1974) (http://etd.caltech.edu/etd/available/etd-07242007-143000/) (also available from University Microfilms, Ann Arbor, Michigan)

Seminars

• How should we ask the Lambda Question(s)? (Keynote Lecture), Workshop on Lambda and Quasi-Lambda, Amherst Center for Fundamental Interactions, University of Massachusetts Amherst, 10/4/2014
• Gravity from Order and Number: Causal Sets (Colloquium), Indian Institute of Science, Bangalore, India, 2014-01-03
• Prediction of the Cosmological Constant (Informal Seminar), Raman Research Institute, Bangalore, India, 2013-12-30
• An Introduction to Histories Based Quantum Mechanics (Invited Lecture), Raman Research Institute, Bangalore, India, 2013-12-17
• Entanglement Entropy and the Area Law (A Series of Lectures), Raman Research Institute, Bangalore, India, 2013-12-12-13; 19-20
• If Spacetime is a Causal Set then Lorentz Symmetry is Unbroken (Invited Lecture), Peyresq 18 - Micro and Macro Structure of Spacetime, Peyresq, France, 2013-06-20
• A formula for the entropy of a spacetime region (Seminar), University of Barcelona, Spain, 2013-06-13
• A Tutorial on Causal Sets (Key Lecture), Causal Structure in Quantum Theory, Centro de Ciencias de Benasque Pedro Pascual, Benasque, Spain, 2013-06-05
• A formula for the entropy of a spacetime region (Invited Lecture), Black Holes IX - Theory and Mathematical Aspects, University of Saskatchewan, Saskatoon, 2013-05-13
• Does a quantum particle know its own energy? (invited lecture), ZiF Workshop: Quantum Theory without Observers III, Center for Interdisciplinary Research, Bielefeld University, Bielefeld, 2013-04-23
• Solved and Unsolved Problems of Time in Quantum Gravity (Colloquium), Raman Research Institute, Bangalore, India, 2013-1-15
• Does a quantum particle know its own energy? (Invited Lecture), International Conference on Quantum Information and Quantum Computing (ICQIQC), Indian Institute of Science, Bangalore, India, 2013-1-11
• Solved and Unsolved Problems of Time in Quantum Gravity (Seminar), Indian Institute of Mathematical Sciences, Chennai, India, 2013-1-7
• Geometry from Order & Number: Causal Sets (Public Colloquium), Golden Jubilee Celebrations Conference, Indian Institute of Mathematical Sciences, Chennai, India, 2013-1-4
• If Spacetime is a Causal Set then Lorentz Symmetry is unbroken (Seminar), Raman Research Institute, Bangalore, India, 2012-12-20
• Solved and Unsolved Problems of Time in Quantum Gravity (Invited Lecture), Conference on Do we need a Physics of Passage?, Cape Town, South Africa, 2012-12-14
• Does a quantum particle know its own energy? (Keynote Lecture), Foundations of Quantum Mechanics and Relativistic Spacetime: Quantum Theory Meets Relativity, National and Kapodistrian University of Athens, Athens, Greece, 2012-09-25
• Expressing entropy globally in terms of (4D) field-correlations (Invited Lecture), Sixth International Workshop DICE2012: Spacetime - Matter - Quantum Mechanics from the Planck scale to emergent phenomena, Castello Pasquini, Castiglioncello, Italy, 2012-09-19
• Expressing entropy globally in terms of (4D) field-correlations (Seminar), Imperial College, London, 2012-06-26
• Expressing entropy globally in terms of field-correlations (Invited Lecture), Peyresq17, Peyresq, France, 2012-06-17
• Black Holes and Information Conference, Black Hole Information (Panelist), KITP, UC Santa Barbara, 2012-05-21
• New Entropy Formula -- Old Opinions -- Some Questions (Invited Lecture), Black Holes and Information Conference, KITP, UC Santa Barbara, 2012-05-21
• Solved and Unsolved Problems of Time in Quantum Gravity (Invited Lecture), Time, Physics and Philosophy Workshop, UC San Diego, 2012-05-18
• Geometry from Order and Number: Causal Sets (Seminar), UC San Diego, 2012-05-17
• Expressing entropy globally in terms of (4D) field-correlations (Seminar), Black Hole Entanglement Entropy and Renormalization Working Group, KITP, UC Santa Barbara, 2012-05-14
• Bits, Branes, Black Holes Workshop, (Invited Participant), KITP, UC Santa Barbara, 2012-4-30 to 2012-05-20
• Geometry from Order & Number: Causal Sets (Invited Lecture), Joshfest, Syracuse University, Syracuse, 2012-04-20
• Gravity from Order and Number: Causal Sets (Plenary Lecture), ICGC-2011, Goa, India, 2011-12-18
• Expressing entropy globally in terms of field-correlations (Invited Lecture), Gravity as an Emergent Phenomenon Session at the ICGC-2011, Goa, India, 2011-12-15
• Expressing entropy globally in terms of field-correlations (Seminar), Raman Research Institute, Bangalore, India, 2011-12-13
• A quantum field theory with a covariant cutoff in which black hole radiance could be studied (Invited Lecture), ESF Exploratory Workshop on Gravity as Thermodynamics: towards the microscopic origin of geometry, Trieste, Italy, 2011-09-08
• Geometry from order: causal sets (Invited Lecture), Quantum Information meets Statistical Mechanics, Universidad Complutense de Madrid, El Escorial Summer School, Spain, 2011-07-12
• Does a quantum particle know its own energy? (Invited Lecture), Peyresq Physics 16, Micro and macro structure of spacetime, Peyresq, France, 2011-06
• Does a quantum particle know its own energy? (Invited Lecture), Workshop on Folding and Unfolding Interactions from Geometry, Ischia, Italy, 2011-06
• Does a quantum particle know its own energy? (Seminar), McGill University, Montreal, Canada, 2011-04-13
• Does a quantum particle know its own energy? (Invited Lecture), New Frontiers in Quantum Foundations, CUPI 2011 Clemson University, Clemson, South Carolina, U.S.A., 2011-03
• Dynamics of, and dynamics on causal sets (Invited Lecture), DICE 2010 Space-Time-Matter - current issues in quantum mechanics and beyond, Castello Pasquini/Castiglioncello, Tuscany, Italy, 2010-09
• A re-formulation of quantum theory in which events really do (or do not) happen (Invited Lecture), 21st-century directions in de Broglie-Bohm theory and beyond, Vallico-Sotto, Tuscany, Italy, 2010-08
• A couple of steps forward for causal sets (Invited Lecture), Peyresq Physics 15, Peyresq, France, 2010-06
• Quantum Field Theory on Causal Sets I&II (Invited Lectures), Causets at DIAS II A workshop on recent progress in The Causal Set Approach to Quantum Gravity, DIAS, Dublin, 2009-12
• Progress and open problems in Causal Sets (Invited Lecture), Causets at DIAS II A workshop on recent progress in The Causal Set Approach to Quantum Gravity, DIAS, Dublin, 2009-12
• Logic : the quantum = geometry : gravity (Invited Lecture), Foundations of Space & Time: Reflections on quantum gravity, Stellenbosch, South Africa, 2009-08
• Logic : the quantum = geometry : gravity (Seminar), Universite Francois-Rabelais, Tours, France, 2009-07-02
• Logic : the quantum = geometry : gravity (Plenary Lecture), Computability in Europe CiE 2009: Mathematical Theory and Computational Practice, Heidelberg, 2009-07
• Logic : the quantum = geometry : gravity (Invited Lecture), Theory Canada V, Fredericton, Canada, 2009-06
• What is a quantal reality? (Invited Lecture), Peyresq Physics 14, Peyresq, France, 2009-06
• A modified logic for quantum gravity (Invited Lecture), New Directions in the Foundations of Physics, Washington DC, 2009-05
• Nonlocality from Planck-scale discreteness: problem and opportunity for quantum gravity (Seminar), University of Maryland, College Park, 2009-04-30
• Direct transmission of light along causal links (Seminar), Syracuse University, Syracuse, 2008-11-21
• Direct transmission of light along causal links (Seminar), University of Wisconsin, Milwaukee, 2008-11-14
• Direct transmission of light along causal links (Invited Lecture), DICE 2008 - From Quantum Mechanics through Complexity to Spacetime: the role of emergent dynamical structures , Castello Pasquini/Castiglioncello (Tuscany) Italy, 2008-09
• Direct Transmission of Light along Causal Links (Invited Lecture), Theory Canada IV, Montreal, Canada, 2008-06
• Does Quantum Gravity give rise to Observable Non-Locality (2 Invited Lectures), Peyresq Physics 13, Peyresq, France, 2008-06
• Quantum Reality and Anhomomorphic Logic (Invited Lecture), Logic, Physics and Quantum Information Theory, Bellairs Research Centre, Holetown, Barbados, 2008-03
• Testing quantum mechanics with a 3-slit experiment (Colloquium), Institute for Quantum Computing, Waterloo, 2007-09-20
• Everpresent Lambda (Plenary Lecture), PASCOS 07, Imperial College, London, 2007-07
• Quantum reality and anhomomorphic logic (Invited Lecture), Loops 07, Morelia, Mexico, 2007-06
• Topological quantization of NUTty angular velocity (Invited Lecture), Black Holes VI, Nova Scotia, Canada, 2007-05
• Is Spacetime a past-finite Poset? (Colloquium), Georgia Southern University, Statesboro, 2007-04-06
• Genealogy of space time (Public Lecture), Georgia Southern University, Statesboro, 2007-04-05
• A discrete, Lorentz-invariant wave equation and its continuum limit (Invited Lecture), Primer encuentro sobre la microestructura del espacio-tiempo a la luz de la naturaleza de la materia con que se lo prueba, Patzcuaro, Mexico, 2006-11
• Three Lectures on Causal Sets (Invited Lectures), Causal Sets Summer School, Imperial College, London, 2006-09
• What is a quantum reality? (Invited Lecture), DICE 2006, Piombino, Italy, 2006-09
• Geometry from Order: Causal Sets (Colloquium), Rensselaer Polytechnic Institute, Troy, NY, 2006-03-29
• Some insights for Quantum Gravity derived from work on Causal Sets (Invited Lecture), John Friedman Fest, Oakland, Michigan, 2005-10
• Some insights for Quantum Gravity derived from work on Causal Sets (Invited Lecture), Loop05, AEI, Potsdam, Germany, 2005-10
• Toward a histories-based definition of entropy (Seminar), ICN-UNAM, Mexico City, 2005-07-05
• A family of box operators for a scalar field on a background causet (Seminar), CINVESTAV, Mexico City, 2005-06-28
• Toward a histories-based definition of entropy (2 Seminars), CINVESTAV, Mexico City, 2005-06-20&21
• Is a past finite order the inner basis of spacetime? (Seminar), McGill University, Montreal, Canada, 2004-11-16
• Is a past finite order the inner basis of spacetime? (Plenary Lecture), Ishamfest, Imperial College, London, 2004-09
• Is a past finite order the inner basis of spacetime? (Plenary Lecture), DICE 2004, Piombino, Italy, 2004-09
• Is Spacetime a past-finite Poset (Plenary Lecture), Spatial Representation: Discrete vs.Continuous Computational Models, Dagstuhl, Germany, 2004-08
• Is a past finite order the inner basis of spacetime? (Plenary Lecture), Glafka 2004, Athens, Greece, 2004-06
• Cosmological Constant from Poisson Fluctuations (Seminar), CCNY Theoretical Physics (Seminar), New York, 2004-05-07
• Is Spacetime a past-finite Poset (Seminar), New York Topology Seminar, CCNY, New York, 2004-05-06
• Everpresent Lamda (Seminar), University of Waterloo, Waterloo, Canada, 2004-01-22
• Ten Theses on Black Hole Entropy (Seminar), Syracuse University, Syracuse, 2003-11-14
• Everpresent Lambda (Colloquium), Perimeter Institute, Waterloo, Canada, 2003-08-13
• Observables in Causal Set Cosmology (Seminar), Mathematics Department, University of Athens, Greece, 2003-06-16
• Everpresent Lambda (Seminar), Physics Department, University of Athens, Greece, 2003-06-15
• Observables in Causal Set Cosmology (Plenary Lecture), Workshop on Causality in Computer Science and Physics, Ottawa, Canada, 2003-06
• Indecompsable Ideals in Incidence Algebras (Plenary Lecture), Balfest, Vietri, Italy, 2003-05
• Black Hole Entropy as Causal Links (Seminar), Syracuse University, Syracuse, 2003-04-14
• Black Hole Entropy as Causal Links (Seminar), University of Wisconsin, Milwaukee, 2003-03-14
• Black Hole Entropy as Causal Links (Talk) 6th East Coast Gravity Meeting, University of Maryland, College Park, 2003-03
• A Fluctuating Cosmological Term with a Quantum Origin (Seminar), Syracuse University, 2002-11-04
• A Fluctuating Cosmological Term with a Quantum Origin (Plenary Lecture), O' Raifeartaigh Memorial Conference, Dublin Institute for Advanced Studies, 2002-09
• Quantum Gravity and the Unity of Physics (Colloquium), Instituto de Ciencias Nucleares, UNAM, Mexico City, 2002-06-12
• A Cyclically Expanding Universe in a Toy Quantum Gravity Model (Seminar), Syracuse University, 2002-03-18
• A Cyclically Expanding Universe in a Toy Quantum Gravity Model (Seminar), Fermilab, Chicago, 2002-03-11
• Quantum Gravity and the Unity of Physics (Colloquium), SUNY, Albany, NY, 2002-02-15
• A Cyclically Expanding Universe in a Toy Quantum Gravity Model (Seminar), London Relativity Seminars, Queen Mary College, 2001-12-12
• A Cyclically Expanding Universe in a Toy Quantum Gravity Model (Seminar), Dublin Institute for Advanced Studies, 2001-12-10
• Derivation of causal set dynamics from discrete general covariance and Bell causality: the classical sequential growth model (Seminar), Queen Mary College, University of London, 2001-12-05
• Derivation of causal set dynamics from discrete general covariance and Bell causality: the classical sequential growth model (Seminar), Imperial College, University of London, 2001-12-04
• A Cyclically Expanding Universe in a Toy Quantum Gravity Model (Seminar), Cambridge University, 2001-11-28
• Quantum Gravity and the Unity of Physics (Colloquium), Queen Mary and Westfield College, University of London, 2001-11-26
• General Covariance and the problem of time in a Discrete Cosmology (Seminar), Oxford University, 2001-11-22
• A Cyclically Expanding Universe in a Toy Quantum Gravity Model (Seminar), Birkbeck College, University of London, 2001-11-14
• A Cyclicaly Expanding Universe in a Toy Quantum Gravity Model (Seminar), Imperial College, University of London, 2001-10-09
• Discrete Posets and Quantum Gravity (A Series of Weekly Friday Seminars, Queen Mary, University of London, 2001 (Oct-Dec)
• A Cyclically Expanding Universe in a Toy Quantum Gravity Model (Plenary Lecture), Symposium on Discrete Random Geometry and Quantum Gravity, Utrecht, 2001-10
• General Covariance and the Problem of Time in a Discrete Cosmology (Plenary Lecture), ANPA 2001, Cambridge, 2001-08
• The Quantum Nature of Gravitation, Space, and Time, (Invited Participant), Seven Pines Symposium V, Minnesota, 2001-05
• Quantum Mechanics as Quantum Measure Theory (Seminar), Instituto de Ciencias Nucleares, Unam, Mexico City, 2001-04-30
• Quantum Mechanics as Quantum Measure Theory (Seminar), Centro de Investigacion de Estudios Avanzados, Mexico City, Mexico, 2001-04-20
• Classical Sequential Growth Dynamics for Causal Sets (Seminar), McGill University, Montreal, 2001-04-03
• Some Mathematical Questions arising in Quantum Gravity II (Joint Math/Physics Seminar), Syracuse University, 2001-03-21
• Ten Theses on Black Hole Entropy (Plenary Lecture), Gordon Conference on Modern Developments in Thermodynamics, Ventura, California, 2001-03
• Some Mathematical Questions arising in Quantum Gravity I (Joint Math/Physics Seminar), Syracuse University, 2001-02-28
• Recent developments in causal set dynamics (Invited Lecture) Workshop on Discrete Random Geometries, Niels Bohr Institute, Copenhagen, Denmark, 2000-09
• Classical sequential growth dynamics for causal sets (Seminar), UMass, Amherst, 2000-03-30
• Indications of Causal Set Cosmology (Seminar), Instituto de ciencias nucleares, Unam, Mexico City, 2000-03-17
• Indications of Causal Set Cosmology (Seminar), Centro de Investigacion de Estudios Avanzados, Mexico City, Mexico, 2000-03-15
• Quantum Cosmology with Fixed Four-Volume (Seminar), Syracuse University, Syracuse, 1999-11-29
• Quantum Cosmology and Quantum Gravity (Invited Lecture), The Workshop on Quantum Theory and Gravitation, Vancouver, Canada, 1999-06
• Causal Sets and Stochastic Spacetimes (Plenary Lecture), Workshop on Quantum and Stochastic Gravity, String Cosmology and Inflation, Peyresq, France, 1999-06
• A Growth Dynamics for Causal Sets (Plenary Lecture), The Structure of Spacetime, Minnowbrook, New York, 1999-05
• Classical sequential growth dynamics for causal sets (Seminar), University of Wisconsin, Milwaukee, 1999-04-09
• Why the Cosmological Constant can't quite vanish? (Talk), The Third Eastern Gravity Meeting, Cornell University, Ithaca, 1999-03
• A Family of Growth Dynamics for Causal Sets (Seminar), Syracuse University, Syracuse, 1999-01-25
• Percolation, Causal Sets and Renormalizability (Plenary Lecture), RG2000: Conference on Renormalization Group Theory at the Turn of the Millenium, Taxco, Mexico, 1999-01
• What is a Causal Set? (Seminar), Imperial College, London, 1998-11-19
• A Growth Dynamics for Causal Sets (Plenary Lecture), The 4th UK Quantum Minimeeting, Imperial College, London, 1998-11
• Can a Quantum Event induce Large Fluctuations in the Horizon Area? (Plenary Lecture), 3rd Mexican School on Gravitation and Mathematical Physics: Black Holes, Classical and Quantum, Mazatlan, Mexico, 1998-11
• Can a Quantum Event induce Large Fluctuations in the Horizon Area? (Plenary Lecture), Spinosa Meeting on the Quantum Black Hole, Utrecht, Netherlands, 1998-07
• Some Hurdles before Causal Set Dynamics (Talk) 2nd East Coast Gravity Meeting, Syracuse, 1998-03
• Review of Causal Set Approach to Quantum Gravity II (Seminar), Syracuse University, Syracuse, 1997-11-24
• Review of Causal Set Approach to Quantum Gravity I (Seminar), Syracuse University, Syracuse, 1997-11-21
• Review of Causal Set Approach to Quantum Gravity (Seminar), Tufts University, Medford, MA, 1997-10-31
• Quantum Gravity and the Unity of Physics (Plenary Lecture) NYSAPS Symposium: A Century of Modern Physics , Skidmore College, Saratoga, 1997-10
• A Review of the Causal Set Approach to Quantum Gravity (Invited Lecture) New Directions in Simplicial Quantum Gravity, Santa Fe, 1997-08
• A Growth Dynamics for Causal Sets (Invited Lecture), New Directions in Simplicial Quantum Gravity, Santa Fe, 1997-08
• Toward a definition of relativistic causality for closed systems in spacetime (and other causal spaces) (Plenary Lecture), Causality and Locality in Modern Physics and Astronomy: Open Questions and Possible Solutions, York U, Toronto, 1997-08
• Quantum Gravity and the Unity of Physics (Seminar), Instituto de Fisica, Universidad Michoacana, Morelia, Mexico, 1997-06-16
• Percolation, Causal Sets and Renormalizability (Seminar), Centro de Investigacion de Estudios Avanzados, Mexico City, Mexico, 1997-06-03
• The Statistical Mechanics of Black Hole Thermodynamics (Seminar), Instituto de Fisica de la Universidad de Guanajuato, Leon, Mexicio, 1997-03-06
• The Statistical Mechanics of Black Hole Thermodynamics (Plenary Lecture), First Caribbean Workshop on Quantum Mechanics, Particles and Fields, La Habana, Cuba, 1997-03
• Quantum Gravity and the Unity of Physics (Colloquium), University of Wisconsin, Milwukee, 1996-12
• The Statistical Mechanics of Black Hole Thermodynamics (Seminar), University of Wisconsin, Milwaukee, 1996-12
• The Statistical Mechanics of Black Hole Thermodynamics (Invited Lecture), Second Workshop on Mathematical Physics and Gravitation, Tlaxcala, Mexico, 1996-12
• The Statistical Mechanics of Black Hole Thermodynamics (Plenary Lecture), Symposium on Black Holes and Relativistic Stars, Chicago, 1996-12
• Novel Statistics and Topological Geons (Plenary Lecture), First Latin American Symposium on High Energy Physics, Merida, Mexico. 1996-11
• Toward a definition of relativistic causality for closed systems in spacetime (and other causal spaces) (Seminar), University of Alberta, Edmonton, Canada, 1996-09-27
• An Introduction to Topological Geons (Seminar), UAM, Iztapalapa, Mexico, 1996-09-18
• Toward a definition of relativistic causality for closed systems in spacetime (and other causal spaces) (Seminar), Syracuse University, 1996-09-06
• How Wrinkled is the Horizon of a Black Hole (Seminar), Centro de Investigacion de Estudios Avanzados, Mexico City, Mexico, 1996-05-30
• The Geon-Particle Group and its Representations (Plenary Lecture), Fourth Annual Meeting of the Mexican Physical Society: Division of Gravity and Mathematical Physics, Iztapalapa, Mexico, 1996-05
• Order and Gravity (Seminar), Instituto de Ciencias Nucleares, UNAM, Mexico City, Mexico, 1996-04-25
• How Wrinkled is the Horizon of a Black Hole (Seminar), University of Chicago, 1996-02-23
• Quantum Mechanics as Quantum Measure Theory (Colloquium), University of Adelaide, Australia, 1996-02-09
• How Wrinkled is the Surface of a Black Hole? (Plenary Lecture), First Australian Conference on General Relativity and Gravitation, Adelaide, Australia, 1996-02
• How Wrinkled is the Horizon of a Black Hole (Seminar), Instituto de Ciencias Nucleares, UNAM, Mexico City, Mexico, 1996-02-01
• Discrete Gravity (Series of Invited Lectures), First Workshop on Mathematical Physics and Gravitation, Oaxtepec, Mexico, 1995-12-1
• Energy Extremality in the Presence of a Black Hole (Seminar), Syracuse University, Syracuse, N.Y., 1995-10-23
• Black Hole Thermodynamics II (Seminar), Instituto de Ciencias Nucleares, UNAM, Mexico City, Mexico, 1995-06-02
• Black Hole Thermodynamics I (Seminar), Instituto de Ciencias Nucleares, UNAM, Mexico City, Mexico, 1995-06-01
• Is Locality Compatible with Discreteness and Lorentz Invariance?: Computer Investigations of Locality on a Background Causal Set (Seminar), Instituto de Ciencias Nucleares, UNAM, Mexico City, Mexico, 1995-05-29
• Quantum Gravity and the Unity of Physics (Seminar), Instituto de Ciencias Nucleares, UNAM, Mexico City, Mexico, 1995-05-25
• Is Locality Compatible with Discreteness and Lorentz Invariance?: Computer Investigations of Locality on a Background Causal Set (Seminar), University of Wisconsin, Milwaukee, 1995-05-05
• Quantum Gravity and the Unity of Physics (Colloquium), University of Wisconsin, Milwaukee, 1995-05-05
• Quantum Gravity and the Unity of Physics (Colloquium), Syracuse University, Syracuse, NY, 1995-04-09
• Is Locality Compatible with Discreteness and Lorentz Invariance?: Computer Investigations of Locality on a Background Causal Set (Seminar), Syracuse University, Syracuse, NY, 1995-04-03
• Is Locality Compatible with Discreteness and Lorentz Invariance?: Computer Investigations of Locality on a Background Causal Set (Plenary Lecture), Conference on Discretization Methods in Theoretical Physics, Vietri sul Mare, Italy, 1995-04
• Is Locality compatible with Discreteness and Lorentz Invariance? (Seminar), Tufts University, Medford, MA, 1994-10-21
• Quantum Gravity and the Unity of Physics (Colloquium), U. of Massachussetts, Amherst, 1994-10-19
• Is Locality compatible with Discreteness and Lorentz Invariance? (Plenary Lecture), Conference on Secondary Quantized Calculus and Nonlinear Problems in Physics, Vietri sul Mare, Italy, 1994-10
• Quantum Measure Theory and its Interpretation (Plenary Lecture), Conference on Quantum Nonintegrability, Philadelphia, 1994-08
• Energy Extremality in the Presence of a Black Hole (Plenary Lecture), Conference on Heat Kernels and Quantum Gravity, Winnipeg, Canada, 1994-08
• Is Locality compatible with Discreteness and Lorentz Invariance? (Plenary Lecture), Durham Symposium--Quantum Concepts in Space and Time, Durham, England, 1994-07
• Ordered Sets and Discrete Manifolds (Seminar), Oxford University, 1994-05-31
• Investigations of Locality on a Causal Set (Plenary Lecture), First Irish Quantum Field Theory Meeting, Trinity College, Dublin, 1994-05
• On the way to Quantum Gravity (Keynote Lecture), Maritime Meeting of Mathematical Physics, Halifax, Canada, 1994-04-24
• Ordered Sets and Discrete Manifolds (Colloquium), Dalhousie University, 1994-04-22
• Investigations of Locality on a background Causal Set (Seminar), University of Maryland, 1994-04-16
• Quantum Mechanics as Quantum Measure Theory (Seminar), University of Maryland, 1994-04-15
• Spacetime and Causal Sets (Seminar), Adelaide University, 1994-03-11
• Some Forks in the Road, on the Way to Quantum gravity (Colloquium), Adelaide University, 1994-03-09
• Quantum Mechanics as Quantum Measure Theory (Seminar), Syracuse University, 1994-01-28
• Quantum Mechanics as Quantum Measure Theory (Seminar), Los Alamos National Lab., Los Alamos, New Mexico, 1993-12-03
• Issues in Quantum Gravity with special emphasis on the Causal Set approach (Series of Seminars), Syracuse University, 1993 (Sep-Dec)
• Forks in the Road on the Way to Quantum Gravity (Plenary Lecture), International Symposium on Directions in General Relativity, College Park, Maryland, 1993-05
• Positivity of Energy from the Propagation of Light (Seminar), Syracuse University, 1993-02-19
• New Proof of Positive Energy in General Relativity using Focusing of Null Rays (Seminar), Trinity College, Dublin, Eire, 1992-06-02
• Introduction to Causal Sets (Plenary Lecture), Nor Amberd Workshop, Yerevan, U.S.S.R., 1991-09
• A Sum-Over-Histories Account of an EPR(B) Experiment (Seminar), Joint Institute of Nuclear Research (JINR), Dubna, U.S.S.R., 1991-09
• Causal Sets and Spacetime Geometry (Seminar), Moscow State University, Moscow, U.S.S.R., 1991-09
• Statistical Dimension of Causal Sets (Seminar), Imperial College, University of London, 1991-05-28
• A Sum-Over-Histories Account of an EPR(B) Experiment (Colloquium), University of Notre Dame, 1991-04-24
• Deducing the Dimension of a Causal Set (Colloquium), University of Wisconsin, Milwaukee, 1991-04-05
• Positivity of Energy from Focusing of Light (Seminar), University of Chicago, 1991-02-15
• Spacetime and Causal Sets (Series of Plenary Lectures), The Seventh Latin-American Symposium on Relativity and Gravitation (SILARG VII), Mexico City (Cocoyoc), Mexico, 1990-12
• Some Computational Problems for Discrete Spacetimes (Plenary Lecture), Workshop on Numerical Applications of Regge Calculus and Related Topics (Including the Role of Mini-Supercomputers), Amalfi, Italy, 1990-09
• First Steps with Causal Sets (Invited Lecture), Peter G. Bergmann's Celebration, Capri, Italy, 1990-09
• A Spin Statistics Theorem from Antiparticles, (Colloquium), University of Wisconsin, Milwaukee, 1990-05-22
• Time as Four-Volume (Talk) Quantum Cosmology Workshop, Vancouver, Canada, 1990-05
• The Spin-Statistics Connection (Series of Seminars), Dublin Institute of Advanced Studies, Dublin, Ireland, 1990-05
• Quantum Brownian Motion from the Fluctuation Dissipation Theorem (Seminar), Dublin Institute of Advanced Studies, Dublin, Ireland, 1990-04-01
• A Spin Statistics Theorem from Antiparticles (Seminar), Syracuse University, 1990-01-31
• The Kaluza Klein Monopole and Positive Energy in Five Dimensions (Series of Lectures), Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Mexico City, 1989-11
• Causal Sets in Quantum Gravity (Series of Seminars), Istituto Nazionale di Fisica Nucleare, Napoli, Italy, 1989-07
• The Spin-Statistics Connection (Series of Seminars), Istituto Nazionale di Fisica Nucleare, Napoli, Italy, 1989-07
• Consequences of Spacetime Topology (Invited Review Lecture), Third Canadian Conference on General Relativity and Relativistic Astrophysics Victoria, Canada, 1989-05
• Does a Discrete Order underly Spacetime and its Metric? (Two Plenary Lectures), Workshop on Fundamental Physics, Dublin Institute for Advanced Studies Dublin, Eire, 1989-05
• Does a Discrete Order underly Spacetime and its Metric? (Invited Talk), Third Canadian Conference on General Relativity and Relativistic Astrophysics Victoria, Canada, 1989-05
• A Specimen of Theory Construction from Quantum Gravity (Plenary Lecture) Thirteenth Annual Symposium in Philosophy - How Theories are Constructed: The Methodology of Scientific Creativity - Greensboro, North Carolina, 1989-03
• Quantum Gravity - Causal Sets (Seminar), University of Chicago, 1989-01-13
• Quantum Stabilization of the Skyrme Soliton (Seminar), University of Wisconsin, Milwaukee, 1989-01-06
• Quantum Gravity - Causal Sets (Colloquium), University of Wisconsin, Milwaukee, 1989-01-05
• Quantum Gravity and Causal Sets (Colloquium), Swarthmore College, 1988-12-01
• Acausal Measurements in Sum-over-histories Quantum Mechanics? (Seminar), Syracuse University, 1988-11-09
• Analytic continuation and topology change in two-dimensions (invited lecture), Workshop on Spinors, Twistors and Complex Structures in General Relativity, Durham, England, 1988-07
• On two-dimensional topology change (Seminar), Syracuse University, 1988-05-04
• Classical Topology and Quantum Geons (two invited lectures), Conference on Geometrical and Algebraic Aspects of Nonlinear Field Theories, Amalfi, Italy, 1988-05
• Framework for Quantum Mechanics (invited talk), Workshop on Conceptual Problems of Quantum Gravity, Andover, MA, Problems with Causality in the Sum over Histories, 1988-05
• Topology Change in General Relativity (Seminar), University of Maryland at College Park, 1988-04-13
• Spacetime as a Causal Set (Seminar), Raman Research Institute, Bangalore, India, 1987-12-28
• A Modified Sum Over Histories for Gravity (invited talk), International Conference on Gravitation and Cosmology, Goa, India, 1987-12
• On the Role of Time in the Gravitational Sum-Over-Histories (Seminar), Syracuse University, 1987-10-14
• On the Role of Time in the Sum-over-histories Framework for Gravity (plenary lecture) History of Modern Gauge Theories Conference, Logan, Utah, 1987-07
• Spacetime as a Causal Set (Seminar), Yale University, 1987-04-15
• Spacetime as a Causal Set (Seminar), Columbia University, 1987-04-13
• A Vision of Quantum Gravity, II (Seminar), University of Maryland, College Park, 1987-01-29
• A Vision of Quantum Gravity, I (Seminar), University of Maryland, College Park, 1987-01-28
• Some Interconnected Speculations on Quantum Spacetime: II (Seminar), Syracuse University, 1986-12-10
• Some Interconnected Speculations on Quantum Spacetime: I (Seminar), Syracuse University, 1986-12-03
• Conditions for Lorentzian Topology Change (Seminar), Institute of Theoretical Physics, Wroclaw, Poland, 1986-07-14
• Spin and Statistics of Kinks (Seminar), Institute of Theoretical Physics, Wroclaw, Poland, 1986-07-14
• Possibilities for Lorentzian Topology Change (Seminar), Institute of Theoretical Physics, Goteborg, Sweden, 1986-07-09
• Introduction to Topological Geons (Seminar), University of Cambridge, England, 1986-07-03
• Topological Particles in Quantum Gravity (Seminar), Rutherford Appleton Laboratories, Chilton, Oxford, England, 1986-07-02
• Conditions for Topology Change via Lorentzian Cobordism (invited talk), 11th International Conference on General Relativity and Gravitation, Stockholm, 1986-07
• The Spin-Statistics Correlation for Skyrmeons (Seminar), University of Cambridge, 1986-06-30
• Conserved Quantities from Action Variations (plenary lecture), American Mathematical Society Research Conference, Santa Cruz, 1986-06
• The Kochen-Specker Experiment (Colloquium), University of Wisconsin, Milwaukee, 1986-05-12
• Possibilities for Lorentzian Topology Change (Seminar), University of Chicago, 1986-05-09
• Conditions for Lorentzian Topology Change II (Seminar), Syracuse University, 1986-04-16
• Conditions for Lorentzian Topology Change I (Seminar), Syracuse University, 1986-04-09
• What I Heard in the Hallway at the Santa Barbara Conference (Seminar), Syracuse University, 1986-02-26
• The Kaluza-Klein Monopole Solution (Seminar), University of California, San Diego, 1986-02-13
• Conditions for Lorentzian topology Change (invited talk), Second Annual West Coast `Stevens' Meeting on General Relativity, held at Santa Barbara, California, 1986-02
• Black Holes ARE Black Bodies (Luncheon Seminar with J. Hartle) Workshop on Approaches to Quantum Gravity, Institute for Theoretical Physics, Santa Barbara (invited participant), 1986 (Jan-Feb)
• Topology as Particles in Quantum Gravity: II Workshop on Approaches to Quantum Gravity, Institute for Theoretical Physics, Santa Barbara (invited participant), 1986 (Jan-Feb)
• Topology as Particles in Quantum Gravity: I Workshop on Approaches to Quantum Gravity, Institute for Theoretical Physics, Santa Barbara (invited participant), 1986 (Jan-Feb)
• Energy in Five-Dimensional Gravity (Seminar), University of Winnipeg, 1986-01-03
• A Four-dimensional Expression for Energy in General Relativity II (Seminar), Syracuse University, 1985-12-11
• A Four-dimensional Expression for Energy in General Relativity I (Seminar), Syracuse University, 1985-12-04
• A Proposal for testing four-dimensional Regge Calculus (seminar), Workshop on Discrete Methods in Gravity, Institute for Theoretical Physics, Santa Barbara, (invited participant), 1985-07
• Toward an Explanation of Entropy Increase in the Presence of Quantum Black Holes (Seminar), University of Wisconsin, Milwaukee, 1985-07
• Approximating Topology with Posets (seminar), Workshop on Discrete Methods in Gravity, Institute for Theoretical Physics, Santa Barbara, (invited participant), 1985-07
• A Five Dimensional Monopole in Kaluza Klein Theory (Seminar), King's College, University of London, 1985-05-29
• Introduction to Topological Geons (Course of lectures), Erice School on Cosmology and Gravitation, 1985-05
• Particle Aspects of Topology in Quantum Gravity (Series of lectures), Syracuse University, 1985-04
• Remarks on Lorentzian Topology Change (talk) Syracuse University Discussion Conference on Classical and Quantum Gravity, 1985-04
• Remarks on Topology Change II (Seminar), Syracuse University, 1985-02-20
• Remarks on Topology Change I (Seminar), Syracuse University, 1985-02-13
• Half Integer Spin from Pure Gravity (Colloquium), University of Rochester, 1984-12-14
• Stochastic Evolution on a Manifold II (Seminar), Syracuse University, 1984-10-31
• Stochastic Evolution on a Manifold I (Seminar), Syracuse University, 1984-10-24
• Finite Topological Spaces as Lattice Spacetimes (Seminar), University of Wisconsin at Milwaukee, 1984-07-16
• Monopole in the Kaluza-Klein Theory (Colloquium), University of Toronto, 1984-02-29
• A Five-dimensional Monopole (Seminar), New York Area Relativity Seminar, NYU, 1984-02-17
• An Interpretation of Energy in General Relativity (Seminar), University of Chicago, 1983-11-17
• A Kaluza-Klein Monopole (Seminar), University of Chicago, 1983-11-14
• A Kaluza-Klein Monopole (Seminar), Syracuse University, 1983-10-31
• A Kaluza-Klein Monopole (invited lecture), Monopole '83 Conference, Ann Arbor, 1983-10
• Spin-half from Gravity (Seminar), Syracuse University, 1983-09-21
• Discrete Spacetimes (invited talk), 10th International Conference on General Relativity and Gravitation, Padova, Italy, 1983-07
• On the Entropy of the Vacuum Outside a Horizon (invited talk), 10th International Conference on General Relativity and Gravitation, Padova, Italy, 1983-07
• Topological and Global Issues in Quantum Gravity (invited review talk), 10th International Conference on General Relativity and Gravitation, Padova, Italy, 1983-07
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• PIRSA:09060014, What is a quantal reality?, 2009-06-01, Categories, Quanta, Concepts (CQC)
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• PIRSA:06060016, Nonlocal remnants of microscopic discreteness?, 2006-06-08, Strings/Quantum Gravity 5/Theory Canada 2
• Does quantum mechanics really need state vectors, Hilbert spaces and algebras of observables? 2005-11-1, Quantum Foundations
• PIRSA:05090001, Is a past-finite causal order the inner basis of spacetime?, 2005-09-07, Colloquium
• PIRSA:05060057, Audience Night, 2005-06-01, Perimeter Institute Public Lecture Series
• PIRSA:04100022, Is a past finite order the inner basis of space-time?, 2004-10-29, Workshop on Quantum Gravity in the Americas: Status and future directions
• Black Hole Entropy as Causal Links, 2004-02-23, Workshop on Quantum Gravity-Quantum Information-Quantum Computing
• Lorentz invariance of Poisson sprinklings, 2004-02-16, Quantum Gravity
• PIRSA:03080005, Everpresent Lambda, 2003-08-13, Workshop on Quantum Gravity in the Americas: Status and future directions