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NASA ADS
F.W.O-Vlaanderen
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At present I am a
postdoc research physicist at CLEA (Center Leo
Apostel) and FUND (Foundations of Exact Sciences) of the Vrije
Universiteit Brussel, with activities both in physics and
interdisciplinary problems. While at TENA (Theoretical Physics
department), I finished my Ph.D. dissertation concerning the quantum
description of few body systems in relativistic interaction (in '94,
with Prof. J. Reignier and Prof. J. Bijtebier). My physics licentiate
dissertation ('87) concerned the quantum decay law and the quantum Zeno
effect (with Prof. J. Reignier). Over the years my affiliation to TENA,
FUND and CLEA have lead me to a variety of research topics.
(Present
work)
-
The development of a scalar-vector gravitation model with Lorentz-
Poincaré type interpretation in concordance with General
Relativity
Theory. This model requires gravitationally modified Lorentz
transformations ("GMLT") and enables to give -at present- a Hamiltonian
description of particles and photons till 1-PN of GRT. Like standard
Lorentz transformations in Special Relativity, the GMLT endorse an
underlying non-observable presentist space and time ontology (due to
the Poincaré Principle of relativity of movement any
preferredframe
remains unobservable). While this physical analysis of Relativity
Theory conceptually contrasts its usual geometrical analysis,
Poincaréan geometric conventionalism should be able to bridge
these
with one common observable empiry, i.e. the experimentally confirmed
one from SRT and GRT.
(more below... ) (publications)
(Previous
topics)
-
The application of the operational quantum formalism to aspects of
formal cognition. The quantum aspect of contextuality was adapted to
the description of the liar paradox, and tentatively applied as
self-reference in consciousness and some connectionist models (with
Prof. D. Aerts et al.). (publications)
-
Integrating scientific worldviews (the layered structure model of
reality based on the operational quantum formalism, emergence and
downward causation, the problem of the emergence of properties, but
also the scientific process in its relation to worldviews (with Prof.
D. Aerts et al.). (publications)
-
The description of few body systems in relativistic interaction using
Bethe-Salpeter equations and constraints theory. The approach uses
coupled Dirac and Klein-Gordon equations, which requires a reduction of
the multitemporal description (Ph.D. Thesis subject). (publications)
Publications (Thematic)
- A Lorentz- Poincaré type
interpretation of General Relativity Theory
- Broekaert, J., (2006), "A
Lorentz-Poincaré-Type Interpretation
of the Weak Equivalence Principle", Arxiv ref.: gr-qc/0604107
(submitted)
- Broekaert, J., (2005), "A
`Lorentz-Poincaré'-Type Interpretation
of Relativistic Gravitation", Proc. ESA SP-605 November 2005, (ed.) M.
Cruise, Arxiv ref.: gr-qc/0510017 (to appear)
- Broekaert, J., (2005),"On a
modified-Lorentz-transformation based
gravity model confirming basic GRT experiments", Foundations of
Physics, 35, 5, 839-864, Arxiv ref.:gr-qc/0309023.
- Broekaert, J., (2004),"A spatially-VSL gravity
model: Gyroscopic
dynamics", in PIRT IX proceedings, (ed.) Duffy M.C., (to be submitted)
- Broekaert, J., (2004),"A spatially-VSL gravity
model with 1-PN
limit of GRT", conference talk, 17th International Conference on
General Relativity and Gravitation, Dublin, 18-23 July 2004, Arxiv ref:
gr-qc/0405015, (submitted)
- Broekaert, J., (2002), "Verification of the
`essential' GRT
experiments in a scalar Lorentz-covariant gravitation", in PIRT VIII
proceedings, (ed.) Duffy M.C., PD Publications, Liverpool, Vol. 1, pp
37 - 54.
- Operational quantum formalism in formal
cognition
- Aerts, D., Broekaert, J., D'Hooghe, B., (2003).
"The Generalised
Liar Paradox: A Quantum Model and Interpretation", Foundations of
Science, (to appear) Arxiv ref.: quant-ph/0404066.
- Gershenson, C., Broekaert, J., Aerts, D., (2003),
"Contextual
random boolean networks", Lecture Notes in Artificial Intelligence,
2801, pp. 615-624
- Aerts, D., Broekaert, J., Gabora, L., (2002a), "A
Case for
Applying an Abstracted Quantum Formalism to Cognition", in Mind in
Interaction, (Eds.), Bickhard M.H., Campbell R.L., O'Nuallain S., John
Benjamins. (to appear), Arxiv ref.: quant-ph/040406
- Aerts, D., Broekaert, J., Gabora, L., (2002b),
"Intrinsic
contextuality as the crux of consciousness.", in `No Matter, Never
Mind', Edited by, Kunio Yasue, Mari Jibu and Tarcisio Della Senta, John
Benjamins Publishing Company, Amsterdam/Philadelphia, (Published as
Vol. 33 of the series Advances in Consciousness Research, ISSN 1381
-589X)
- Aerts, D., Aerts, S., Broekaert, J., Gabora, L.,
(2000), "The
Violation of Bell Inequalities in the Macroworld", Foundations of
Physics, 30, 9, pp. 1387-1414.
- Aerts, D., Broekaert, J., Smets, S., (2000), "A
Quantum Structure
Description of the Liar-paradox", International Journal of Theoretical
Physics, 38, 12, pp. 3231-3239. Arxiv ref.: quant-ph/0106131
- Broekaert, J., D'Hooghe, B., (2000), "A Model with
Quantum Logic,
but Non-Quantum Probability: The Product Test Issue", Foundations of
Physics, 30, 9, pp. 1481-1502.
- Aerts, D., Broekaert, J., Gabora L., (1999),
"Nonclassical
contextuality in cognition. From quantum mechanical approaches to
indeterminism and observer dependence", in Proceedings of Mind IV,
(Ed.), Campbell, R. , Dublin, Dialogues in Psychology, 10.0
- Aerts, D., Broekaert, J., Smets, S., (1999), "The
Liar-Paradox in
a Quantum Mechanical Perspective", Foundations of Science, 4, 2, pp.
115-132.
- Aerts, D., Broekaert, J., Smets, S., (1998),
"Inconsistencies in
Constituent Theories of World Views: Quantum Mechanical Examples",
Special Issue section "Worldviews and Inconsistencies", Foundations of
Science, 3, No 2, pp. 313-340
- Integrating scientific worldviews
- Broekaert, J., (2005), "The intrinsic multiplicity
of science. Its
internal and external confrontations", in Worldviews, Science and Us.
Redemarcating Knowledge and Its Social and Ethical Implications, (eds),
Aerts, D., D'Hooghe, B., Note, N., World Scientific Publishing Company,
Singapore, pp. 59-72.
- Broekaert, J., (1998), "World Views. Elements of
the Apostelian
and General Approach", Foundations of Science, 3, No 2, pp. 235 - 258
- Few
body systems in relativistic interaction
- Bijtebier, J., Broekaert, J., (1997), "Using
Salpeter's propagator
for solving the Bethe-Salpeter equation", Nuclear Physics, A, 612, pp.
279-296
- Bijtebier, J., Broekaert, J., (1996), "On the
three-dimensional
reductions of the Bethe-Salpeter equation and their one-body limits,
(two bosons and boson-fermion cases)", J. Phys. G: Nucl. Part Phys.,
22, pp. 1727-1740
- Bijtebier, J., Broekaert, J., (1996), "On the
three-dimensional
reductions of the Bethe-Salpeter equation and their one-body limits,
(two-fermion case)", J. Phys. G: Nucl. Part Phys., 22, pp. 559-578
- Bijtebier, J., Broekaert, J., (1995), "The infinite
mass limit of
the improved Salpeter equation.", Proceedings of the Inter. Conference
on Quark Confinement and the Hadron Spectrum, N. Brambilla and G.M.
Prosperi, (eds.), World Scientific, pp. 291-293
- Bijtebier, J., Broekaert, J., (1994), "What happens
with the
relative time excitations after a three-dimensional reduction of the
Bethe-Salpeter equation?", Nuovo Cimento, A,107, pp. 1275-1291.
- Bijtebier, J., Broekaert, J., (1992), "The few-body
problem
between quantum field theory and relativistic quantum mechanics",
Extended Objects and Bound Systems, O.Hara, S. Ishida and S. Naka,
(eds.), World Scientific Singapore, pp. 161-174
- Bijtebier, J., Broekaert, J., (1992), "The
elimination of the
relative time in the Bethe-Salpeter equation for the two-body plus
potential problem", Hadron 91, S. Oneda and D.C. Peaslee, (eds), World
Scientific Publishing, Singapore, pp. 309-312.
- Bijtebier, J., Broekaert, J., (1992), "The two-body
plus potential
problem between quantum field theory and relativistic quantum
mechanics, (two-fermion and fermion-boson cases)", Nuovo Cimento,
A,105, pp. 625-640.
- Bijtebier, J., Broekaert, J., (1992), "The two-body
plus potential
problem between quantum field theory and relativistic quantum
mechanics, (spinless case)", Nuovo Cimento, A, 105, pp. 351-369.
Project Overview
A Lorentz-Poincaré-type interpretation of
General Relativity
Classical
General Relativity theory has been successfully submitted to a range
of
experimental tests [Will 1993, Will 2001]. However, from the
perspective of its interpretation, a fundamental debate continues.
Starting with Minkowski
[1908]
the
"geometrized" view of relativity originated; an
overview of this interpretation can be found in Stein [1968], Sklar [1985] and is recently
developed in e.g. Dieks
and Redei [2005] and examined -with
ample
detail- in Brown [2005].
One of the interpretational issuess follows from the fundamental
concepts of space and time: these are conceived
either, according the Minkowski "block" universe or, along the
classical
3+1 time-tensed universe. These contrasting conceptions support
respectively the "perdurant" versus
"endurant" timely persistence of the entities, e.g. Butterfield
[2004].
The
respective conceptions follow from the two main interpretations
of SRT;
the Einstein-Minkowski "geometrical" interpretation of the Lorentz
transformations based on the Principle of
Relativity and the Invariance of the velocity of light [Einstein,
1905]
versus, Lorentz-Poincaré's "physical" interpretation of
the Lorentz transformations with underpinning by rod contractions,
clock slowing and light
synchronization Poincaré
[1905], Poincare
[1906]. (The contributions
of Michelson, Morley, FitzGerald and
Larmor are discussed in Brown [2005].) The
"physical" interpretation of the
Lorentz transformations is developed in recent literature as well, by e.g. Mansouri
and Sexl [1977], Bell [1987], Brown [2005] and also Selleri
[2005].
(Note that a physical interpretation does not necessarily require a
"prefered" frame, cfr Brown [2005].)
An essential argument in the physical interpretation is precisely the
recognition of the process of synchronization, which is
reflected by the spatial term v.x c-2 \gamma in the time
equation of the Lorentz Transformation. This term evidently discards
invariant simultaneity.
General
Relativity has been analyzed mainly according to two distinct
interpretations as well. Most predominantly, again, Einstein's
"geometrical" interpretation, which dissolves gravitation into the
spacetime metric in order to assure the Equivalence Principle [Einstein
1916], in
contrast to the "physical" field interpretation in terms of massless
spin-2 fields (starting with Fierz [1939], Gupta [1957], Weinberg
[1965],
Cavalleri and
Spinelli [1975] ). The theory of
General Relativity implies, through the metric tensor g\mu\nu, distinct local
gravitational effects on spatial and temporal measurement (developed by
e.g. Wilson
[1921],
Thirring
[1961],
Dicke [1957], Dicke [1965]), which are similar
to the kinematical effects, through the \gamma-factor,
in the "physically" interpreted SRT; time dilation and length
contraction. It can be questioned therefor whether both effects can be
consistently combined and could lead to a gravitational
"Lorentz-Poincaré" interpretation of General Relativity. We
claim that
this should be possible, either to a given order in predictive
precision or in principle, based on Geometrical Conventionalism. GC is
understood as a
compensation between the intrinsic space and time metric and the laws
of physical measurement for space and time intervals, with conservation
of empiry.
Our reading of GC follows from Poincaré's work regarding the
Lorentz-transformations and the Relativity Principle [Poincaré
1902, Poincaré
1904, Poincaré
1914].
(GC
is however subject to a variety of interpretations; Reichenbach
[1957],
Quine [1951], Grünbaum
[1973], Dieks [1987]).
A Lorentz-Poincaré type interpretation of GRT enables a
presentist
ontology of endurant entities. It should be stressed however that even
in this interpretation the prior-geometric space and cosmological time
remain non-observable because the Poincaré Principle of
Relativity
-implemented in the formalism- prohibits the perception of any
preferred, or "absolute" frame Poincaré
[1902], Poincaré
[1904].
We
have currently developed this program by means of a scalar-vector
gravitation model - i.e. with four fields {\Phi, w} - in accordance
with GRT till first Post-Newtonian order [Broekaert
2004a].
The basic requirement for the Lorentz- Poincaré interpretation
is the
introduction of Gravitationally Modified Lorentz Transformations [Broekaert
2002, Broekaert 2005b]
(static source, space-time scaling):
|
|
|
| {( d xpar
- u dt) \gamma (u) + d xperp }\Phi-1
|
|
|
(1) |
|
|
|
| {
dt - u . d x c (r)-2} \gamma (u) \Phi |
|
|
(2) |
with
a scalar scaling field \Phi, an intrinsical spatially-variable speed of
light c(r) = c' \Phi2
and, where primed quantities are observable in local coordinates while
unprimed quantities are "unobservable" coordinate space quantities. The
invariance of the locally observed velocity of light still remains
preserved under these relations [Broekaert,
2002].
In
general the GMLT's have an isotropic scaling factor \Phin
depending on the transformed quantities, and for non-static source
include an induced velocity field w. The Hamiltonian
description of
particles and photons, using (at O (w2)):
|
|
|
| m c(r)2
+ p . w (particles)
( m = m'0 \gamma (p) \Phi-3 ) |
|
|
(3) |
|
|
|
|
|
(4) |
and
where m'0
is the particle rest mass, recovers the 1-PN approximation of GRT [Broekaert 2004a], similarly for the
precession dynamics of (isotropic)
gyroscopes [Broekaert 2004b]. The
scaling field F and induced
velocity field w are given by
the field equations (no-retardation
approx.)
|
|
|
| 4 \pi Gc'-2
\rho (r) \Phi+ (\nabla \Phi )2 \Phi -1 |
|
|
(5) |
|
|
|
| -
16 \pi Gc'-2 \rho (r) v\rho (x, t) |
|
|
(6) |
We
have
shown the model does obey the Weak Equivalence Principle from a fixed
observer perspective and local inertial frame perspective, and that the
implied acceleration transformations
are equivalent with those of GRT [Broekaert
2005a,
Broekaert
2006].
Present developments in the model
concern the lagrangian formulation of the field dynamics.
Jan
Broekaert (last updated : 03 - 2006)
A
Lorentz- Poincaré type interpretation of General Relativity
Theory
Vrije
Universiteit Brussel
CLEA -
Center Leo Apostel
FUND -
Foundations of Exact Sciences
References
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-
Broekaert, J., (2006), "A Lorentz-Poincaré-Type Interpretation
of the Weak Equivalence Principle", Arxiv ref.: gr-qc/0604107
(submitted)
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- Broekaert J., A "Lorentz-Poincaré"-Type
Interpretation of Relativistic
Gravitation, Proc. ESA SP-605 November 2005, (ed.) M. Cruise, 2005 a,
Arxiv ref.: gr-qc/0510017
(to appear)
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- Broekaert J., On a modified-Lorentz-transformation
based gravity model confirming basic GRT experiments, Foundations
of Physics, 35, 5, 839-864, 2005 b, Arxiv ref.: gr-qc/0309023.
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- Broekaert J., A spatially-VSL gravity model:
Gyroscopic dynamics, conference paper Physical Interpretations of
Relativity Theory IX, 3-6 September 2004, London (to be submitted)
2004 a
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- Broekaert J., A spatially-VSL scalar gravity model
with 1-PN limit of GRT, conference paper 17th International
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Dublin, Arxiv ref: gr-qc/0405015
(submitted) 2004 b
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