Physical supertasks are completed, infinite sequences of events or interactions that occur within a finite amount of time. Examples thereof have been constructed to show that infinite physical systems may violate conservation laws. It is shown in this paper that this conclusion may be critically sensitive to a selection of numeral system. Weaker numeral systems generate physical reports whose inaccuracy simulates the violation of a conservation law. Stronger numeral systems can confirm this effect by allowing a direct computation of the quantities conserved. The supertasks presented in [2], [4] are used to illustrate this phenomenon from the point of view of the new numeral system introduced in [6].
Topics
News and events
REFERENCES
1.
D.
Atkinson
and P.
Johnson
, Foundations of Physics
39
, 937
–957
(2009
)2.
J.P.
Laraudogoitia
, Mind
105
, 81
–83
(1996
)3.
J.P.
Laraudogoitia
, Erkenntnis
70
, 365
–377
(2009
)4.
5.
J. D.
Norton
, Foundations of Physics
29
, 1265
–1302
(1999
)6.
Ya. D.
Sergeyev
, The Arithmetic of Infinity
(Edizioni Orizzonti Meridionali: Rende
, 2003
)7.
8.
Ya. D.
Sergeyev
, Nonlinear Analysis Series A: Theory, Methods & Applications
, 71
, e1688
–e1707
(2009
).9.
Ya. D.
Sergeyev
, Nonlinear Analysis Series A: Theory, Methods & Applications
, 72
(3-4
), 1701
–1708
(2010
).10.
11.
Ya. D.
Sergeyev
, p-Adic Numbers
, Ultrametric Analysis and Applications
3
(2
), 129
–148
(2011
).12.
Ya. D.
Sergeyev
, A.
Garro
, Journal of Supercomputing
65
(2
), 645
–663
(2013
).13.
J.
Thomson
, Analysis
15
, 1
–13
(1954
)
This content is only available via PDF.
© 2016 Author(s).
2016
Author(s)
You do not currently have access to this content.
