The Leo Apostel Center
		**********************
in collaboration with the Doctoral Programme of the VUB invites everyone to
the 31st of its interdisciplinary seminars in the Foundations series. In
this series CLEA invites scholars that are actively engaged in the research
on the foundations of a particular discipline. Their lectures will always
be directed to an interdisciplinary audience, and the discussions aim at
confronting the foundations of the different disciplines.


THE NEED TO VARY THE REAL NUMBER CONTINUUM
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		by Prof. Dr. John Corbett

	(Macquarie University, Sydney - Australia)

Tuesday, 15 September 1998 at 5 p.m. in room 3/C 207
(building C, 3rd floor)

	Vrije Universiteit Brussel, Campus Oefenplein


About the lecture
*****************

The formation of scientific theories of the physical world can be seen as a
particular development of the apparent need of humans to have a model of
the multitude of sense experiences and the correlations between them in
order that they can act and understand. When a theory leads to ambiguity
and a lack of cohesion, we look to vary some of components of the theory
even though a large part of it may correlate well with experience. This is
the situation with theories of atomic and sub-atomic phenomena and the
stories of the development of these theories should be of interest to all
who are interested in foundations. The story that I want to tell you is
about quantum mechanics. This means that we are assuming that there are
existing real objects, that we can control sufficiently to perform
experiments on, that are the objects of our theories. In classical theories
these objects would be assigned kinematical variables, such as position and
velocity, whose numerical values can be measured. The standard theories of
quantum mechanics do not permit us to assign exact numerical values to all
such variables at all times. Einstein was one of the leading opponents of
the acceptance of the standard theories as being more than rules for
calculation. The new ingredient in the story is a principle of invariance
of physical laws that states that the laws must be formulated so that they
are invariant under changes in the real number continuum used to evaluate
the laws. If the equations are simpler in a particular real number
continuum there is no loss of generality in using this continuum to
describe the physical laws. When this principle is applied to quantum
mechanics and the quantum real number continuum is used, Heisenberg's
equations of motion are obtained as local approximations to Newton's
equations expressed in terms of the quantum real numbers, kinematical
variables have numerical values, as quantum real numbers, at all times  and
the hypothesis of the collapse of the wave-packet is a local approximation
to the description, using quantum real numbers, of the passage of a
particle through a slit. The logic of the quantum real numbers is
intuitionistic and so the numbers are "variable". Therefore even though
this formulation of quantum phenomena gives us a more coherent picture, the
calculational algorithms of standard quantum theory will continue to be
used to give good approximations to measured quantities.

About the speaker
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John Corbett is an Australian, he is an Associate Professor in Mathematics
at Macquarie University in Sydney, Australia. He received his Ph.D. in
Mathematical Physics, in 1966, from the University of Adelaide. At Adelaide
he was fortunate to have Professors C A Hurst, H S Green and G Szekeres
amongst his teachers. Although his first serious research interest was
gravitational waves in general relativity, his Ph D thesis was on
mathematical models of nuclear physics. He subsequently held post-doctoral
and visiting positions at the University of California at Davis, CPT, CNRS
(Luminy) in Marseille, Toronto University, Indiana University Bloomington
and Adelaide University. He has been at Macquarie University since 1975.
His most important research has been on the  Pauli problem of wave
mechanics (his 1978 paper with C A Hurst is still cited), on algebraic
formulations of quantum scattering theories, and his recent work with M
Adelman on the foundations of quantum mechanics.


The presentations with questions will last about an hour. Afterwards, an
hour or more is reserved for an in-depth, group discussion of the topic.
More info at the CLEA office: phone 02-644 26 77 or via the Web-page:
http://pespmc1.vub.ac.be/CLEA/