The idea discussed in previous posts satisfies Smolin's requirements for explaining why our universe has the laws it does.
There is a mathematical structure T that is a formal system such that 1. T contains the necessity modal operator and 2. T can refer to itself, and it satisfies the condition
i.e., T implies necessarily necessarily ... necessarily T exists.
T in some sense it has the most right to exist.
One still has to interpret time and quantum probabilities in this mathematical object.
The physical universe is identified with T. One looks for the structure (1) in the laws of the universe. It becomes an physical assertion that the existence of the universe is (maximally) necessary.
In Smolin's language T is in a post-Newtonian paradigm.
See previous posts.
"1) The Newtonian paradigm takes the dynamical law as input. It cannot be the basis
of explaining why that law is the one that applies to our universe. Hence to adopt
this paradigm as the framework of a cosmological theory will leave a great deal of
mystery in our understanding of the world. We will fail to fulfill the demand to give
sufficient reason for every cosmological question.
2) Similarly, the Newtonian paradigm takes the specification of the initial state as input.
It cannot justify or explain the choice of initial state. The demand for sufficient
reason will again not be answered.
3) The Newtonian paradigm assumes that there is an absolute distinction between the
role of state and the role of the dynamical law. This distinction can be operationally
realized on small subsystems because we can prepare a system many times in different
initial states and observe what aspects of the resulting evolution are universal
and what are consequences of the choice of initial state. The dynamical law is inferred
from observations of universal features of the motion which are independent
of the choice of initial state. When we come to the universe there is only a single
history and so we have no way to operationally or experimentally distinguish the
role of the law from the choice of initial state.
This can be a practical as well as a theoretical issue because there can be degeneracies
in cosmological models arising from the fact that a single observation can be
explained equally well by modifying the law of motion or the choice of initial conditions.
One sees examples of this in attempts to fit inflationary models to data such
as the possible non-guassianities.
4) Any theory formulated in the Newtonian paradigm will have an infinite number of
solutions. But, the universe is unique-so only one cosmological history is physically
real. The Newtonian paradigmis then very extravagant when applied to cosmology
because it not only makes predictions about the future of the one real universe, it
offers predictions for an infinite number of universes which are never realized. The
Newtonian paradigm cannot explain why the one solution that is realized is picked
out from the infinite number of possibilities."
A perspective on the landscape problem
Perimeter Institute for Theoretical Physics,
31 Caroline Street North, Waterloo, Ontario N2J 2Y5, Canada
February 16, 2012
I discuss the historical roots of the landscape problem and propose criteria for its
successful resolution. This provides a perspective to evaluate the possibility to solve
it in several of the speculative cosmological scenarios under study including eternal
inflation, cosmological natural selection and cyclic cosmologies.
Invited contribution for a special issue of Foundations of Physics titled Forty Years
Of String Theory: Reflecting On the Foundations.