In a recent article, M. Tegmark poses the hypothesis that our known universe is a ``baggage free'' mathematical structure among many other possible ones, which also correspond to other physical universes --Mathematical Universe Hypothesis, MUH. Naturally, questions arise, such as how to obtain the physical properties of our world from the mathematical structure, or how many possibilities exist for a Universe minimally similar to ours.
In this letter we present some results which can be regarded as a strengthening of MUH, as they give some hints on the derivation of spacetime in current physics from a baggage free mathematical structure.
Concretely, we argue that the set of mathematical structures which can be interpreted as a description of a spacetime is drastically reduced, if one admits some natural postulates on minimal symmetry. Furthermore, the apparently very particular form of classical Galilei-Newton and relativistic spacetimes, is not arbitrary and cannot be regarded as ``two possibilities among arbitrarily many others''. In fact, such theories are determined by a single mathematical structure which only permits four possible types of spacetimes. Finally, we show how the minimal postulates on symmetry can be endowed with a simple physical interpretation, i.e., they acquire ``baggage'' in a natural way.
[1]
Fundamental Units of Length and Time
,
2000,
gr-qc/0009041.
[2]
R. Penrose,et al.
A theory of everything?
,
2005,
Nature.
[3]
Max Tegmark.
Is “the Theory of Everything” Merely the Ultimate Ensemble Theory?☆
,
1997,
gr-qc/9704009.
[4]
Max Tegmark.
The Mathematical Universe
,
2007,
Foundations of Physics.
[5]
Leibnizian, Galilean and Newtonian structures of space–time
,
2002,
gr-qc/0211030.