132 research outputs found
Optimal time travel in the Godel universe
Using the theory of optimal rocket trajectories in general relativity,
recently developed in arXiv:1105.5235, we present a candidate for the minimum
total integrated acceleration closed timelike curve in the Godel universe, and
give evidence for its minimality. The total integrated acceleration of this
curve is lower than Malament's conjectured value (Malament, 1984), as was
already implicit in the work of Manchak (Manchak, 2011); however, Malament's
conjecture does seem to hold for periodic closed timelike curves.Comment: 16 pages, 2 figures; v2: lower bound in the velocity and reference
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The Motion of a Body in Newtonian Theories
A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General
Relativity." Journal of Mathematical Physics 16(1), (1975)] provides the sense
in which the geodesic principle has the status of a theorem in General
Relativity (GR). Here we show that a similar theorem holds in the context of
geometrized Newtonian gravitation (often called Newton-Cartan theory). It
follows that in Newtonian gravitation, as in GR, inertial motion can be derived
from other central principles of the theory.Comment: 12 pages, 1 figure. This is the version that appeared in JMP; it is
only slightly changed from the previous version, to reflect small issue
caught in proo
Conformal proper times according to the Woodhouse causal axiomatics of relativistic spacetimes
On the basis of the Woodhouse causal axiomatics, we show that conformal
proper times and an extra variable in addition to those of space and time,
precisely and physically identified from experimental examples, together give a
physical justification for the `chronometric hypothesis' of general relativity.
Indeed, we show that, with a lack of these latter two ingredients, no clock
paradox solution exists in which the clock and message functions are solely at
the origin of the asymmetry. These proper times originate from a given
conformal structure of the spacetime when ascribing different compatible
projective structures to each Woodhouse particle, and then, each defines a
specific Weylian sheaf structure. In addition, the proper time
parameterizations, as two point functions, cannot be defined irrespective of
the processes in the relative changes of physical characteristics. These
processes are included via path-dependent conformal scale factors, which act
like sockets for any kind of physical interaction and also represent the values
of the variable associated with the extra dimension. As such, the differential
aging differs far beyond the first and second clock effects in Weyl geometries,
with the latter finally appearing to not be suitable.Comment: 25 pages, 2 figure
Time-of-arrival formalism for the relativistic particle
A suitable operator for the time-of-arrival at a detector is defined for the
free relativistic particle in 3+1 dimensions. For each detector position, there
exists a subspace of detected states in the Hilbert space of solutions to the
Klein Gordon equation. Orthogonality and completeness of the eigenfunctions of
the time-of-arrival operator apply inside this subspace, opening up a standard
probabilistic interpretation.Comment: 16 pages, no figures, uses LaTeX. The section "Interpretation" has
been completely rewritten and some errors correcte
Simultaneity as an Invariant Equivalence Relation
This paper deals with the concept of simultaneity in classical and
relativistic physics as construed in terms of group-invariant equivalence
relations. A full examination of Newton, Galilei and Poincar\'e invariant
equivalence relations in is presented, which provides alternative
proofs, additions and occasionally corrections of results in the literature,
including Malament's theorem and some of its variants. It is argued that the
interpretation of simultaneity as an invariant equivalence relation, although
interesting for its own sake, does not cut in the debate concerning the
conventionality of simultaneity in special relativity.Comment: Some corrections, mostly of misprints. Keywords: special relativity,
simultaneity, invariant equivalence relations, Malament's theore
Proper time and Minkowski structure on causal graphs
For causal graphs we propose a definition of proper time which for small
scales is based on the concept of volume, while for large scales the usual
definition of length is applied. The scale where the change from "volume" to
"length" occurs is related to the size of a dynamical clock and defines a
natural cut-off for this type of clock. By changing the cut-off volume we may
probe the geometry of the causal graph on different scales and therey define a
continuum limit. This provides an alternative to the standard coarse graining
procedures. For regular causal lattice (like e.g. the 2-dim. light-cone
lattice) this concept can be proven to lead to a Minkowski structure. An
illustrative example of this approach is provided by the breather solutions of
the Sine-Gordon model on a 2-dimensional light-cone lattice.Comment: 15 pages, 4 figure
Reconstructing Bohr's Reply to EPR in Algebraic Quantum Theory
Halvorson and Clifton have given a mathematical reconstruction of Bohr's
reply to Einstein, Podolsky and Rosen (EPR), and argued that this reply is
dictated by the two requirements of classicality and objectivity for the
description of experimental data, by proving consistency between their
objectivity requirement and a contextualized version of the EPR reality
criterion which had been introduced by Howard in his earlier analysis of Bohr's
reply. In the present paper, we generalize the above consistency theorem, with
a rather elementary proof, to a general formulation of EPR states applicable to
both non-relativistic quantum mechanics and algebraic quantum field theory; and
we clarify the elements of reality in EPR states in terms of Bohr's
requirements of classicality and objectivity, in a general formulation of
algebraic quantum theory.Comment: 13 pages, Late
Pre- and post-selected ensembles and time-symmetry in quantum mechanics
An expression is proposed for the quantum mechanical state of a pre- and
post-selected ensemble, which is an ensemble determined by the final as well as
the initial state of the quantum systems involved. It is shown that the
probabilities calculated from the proposed state agree with previous
expressions, for cases where they both apply. The same probabilities are found
when they are calculated in the forward- or reverse-time directions. This work
was prompted by several problems raised by Shimony recently in relation to the
state, and time symmetry, of pre- and post-selected ensembles.Comment: RevTex4, 17 pages, no fig
Generation of Closed Timelike Curves with Rotating Superconductors
The spacetime metric around a rotating SuperConductive Ring (SCR) is deduced
from the gravitomagnetic London moment in rotating superconductors. It is shown
that theoretically it is possible to generate Closed Timelike Curves (CTC) with
rotating SCRs. The possibility to use these CTC's to travel in time as
initially idealized by G\"{o}del is investigated. It is shown however, that
from a technology and experimental point of view these ideas are impossible to
implement in the present context.Comment: 9 pages. Submitted to Classical and Quantum Gravit
The structure of causal sets
More often than not, recently popular structuralist interpretations of
physical theories leave the central concept of a structure insufficiently
precisified. The incipient causal sets approach to quantum gravity offers a
paradigmatic case of a physical theory predestined to be interpreted in
structuralist terms. It is shown how employing structuralism lends itself to a
natural interpretation of the physical meaning of causal sets theory.
Conversely, the conceptually exceptionally clear case of causal sets is used as
a foil to illustrate how a mathematically informed rigorous conceptualization
of structure serves to identify structures in physical theories. Furthermore, a
number of technical issues infesting structuralist interpretations of physical
theories such as difficulties with grounding the identity of the places of
highly symmetrical physical structures in their relational profile and what may
resolve these difficulties can be vividly illustrated with causal sets.Comment: 19 pages, 4 figure
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