[FOM] On Physical Church-Turing Thesis

[José Félix Costa]

Dear FOMers:

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Harvey Friedman asks

1. Given an integer N, will there be a collision within N units of time?
2. Given an integer N, will there be a collision at exactly N units of time,
and no earlier or later?
3. Will there ever be a collision?
4. Does the diameter of the system become arbitrarily large?
We want to know the recursion theoretic status of these algorithmic
questions.
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Relevant information to FOM:

We know many ''astonishing'' facts from not so recent work of Jeff Xia
(inter alia): he considered a 5-particle newtonian (inverse square law
gravity field) system to proof Poincare conjecture of singularity without
collisions, proving also that an infinite number of physical discrete events
(like going back and forth in a gravitational field) can happen in finite
time.

We know for a class of systems (e. g., a 5-body system in Xia's, collinear
4-body in Mather&McGehee's, planar 4-body in Saari's, planar 5-body in
Gerver's) that the answer to

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4. Does the diameter of the system become arbitrarily large?
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is yes «in very special cases»... more than yes, it becomes infinite in
finite time.

I think that the problems 1-4 were not solved for general case for the
gravitational field (we want to get really into it). Collisions on a
''equipotencial surface'' were studied in deep and decidability of events
proved / disproved.

CT on «off infinite in finite time» was discussed by Frank Tipler, many
years ago.

NOTE: I have list of papers on the subject.

Best regards,

Felix

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J. Felix Costa
Departamento de Matematica
Instituto Superior Tecnico
Av. Rovisco Pais, 1049-001 Lisboa, PORTUGAL
tel:      351 - 21 - 841 71 45
fax:     351 - 21 - 841 75 98
e-mail:   fgc at math.ist.utl.pt
www:    http://fgc.math.ist.utl.pt/jfc.htm
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