It has been almost eighty years since Paul Dirac delivered a lecture on the relationship between mathematics and physics and since 1960 that Eugene Wigner wrote about the unreasonable effectiveness of mathematics in the natural sciences. The field of cosmology and efforts to define a more comprehensive theory have changed significantly since the 1960s; thus, it is time to refocus on the issue. This paper expands on ideas addressed by these two great physicists, specifically, the ultimate effectiveness of mathematics to (...) describe nature. After illustrating how theoretical physic predicted discoveries, the concepts of established theories are summarized. Then, the “world equation” which combines all key physics theories is conceptually described. As the possible last piece of the puzzle, String Theory is briefly defined. And last, a cursory overview of an extreme proposal is presented — the world as a mathematical object. However, there is no fundamental reason to believe that math will allow mankind to completely comprehend nature. If math does not provide a comprehensive theory, nature will retain her secrets. (shrink)

Since Einstein’s failure to define a Grand Unified Theory, physicists have pursued a comprehensive theory explaining nature, a Theory of Everything. But because General Relativity, Quantum Field Theory, and Cosmology have little in common, defining one theory is an imposing task, having eluded the best scientists for ninety years. So are we close to defining a Theory of Everything? This analysis, after defining requirements, identifies four possible options for a Theory of Everything. Quotes from prominent physicists express divergent views on (...) each alternative.The leading proposal for a Theory of Everything is String Theory, which has possible issues. It requires supersymmetry, has extra compacted dimensions, and is background-dependent. A second less comprehensive theory is Loop Quantum Gravity, which emphases background-independence based on discrete quantum space. Explaining how theories define relationships between spacetime, quantum space, quantum time, and quantum gravity, positions the role of background-independence in proposed theories. If supersymmetry and extra dimensions are discovered, String Theory or a modified String Theory integrated with Loop Quantum Gravity, may be the option. Or, possibly a radically new theory might be developed. Or, as the last option considers, the answer to the question — Does a Theory of Everything exist? — may be no; if so, nature will always be a mystery. (shrink)

Space is something. Space inherently contains laws of nature: universal rules, laws and symmetries. We have significant knowledge about these laws of nature because all our scientific theories assume their presence. Their existence is critical for developing either a unique theory of our universe or more speculative multiverse theories. Scientists generally ignore the laws of nature because they “are what they are” and because visualizing different laws of nature challenges the imagination. This article defines a conceptual model separating space from (...) the universe’s energy source and expansion. By considering the ramifications of changing the laws of nature, initial condition parameters, and two variables in the big bang theory, the model demonstrates that traditional fine tuning is not the whole story when creating a universe. Supporting the model, space and “nothing” are related to the laws of nature, mathematics and multiverse possibilities. Speculation on the beginning of time completes the model. (shrink)

Multiverses are predictions based on theories. Focusing on each theory’s assumptions is key to evaluating a proposed multiverse. Although accepted theories of particle physics and cosmology contain non-intuitive features, multiverse theories entertain a host of “strange” assumptions classified as metaphysical topics such as: infinity, duplicate yous, hypothetical fields, more than three space dimensions, Hilbert space, advanced civilizations, and reality established by mathematical relationships. It is easy to confuse multiverse proposals because many divergent models exist. This overview defines the characteristics of (...) eleven popular multiverse proposals. The characteristics compared are: initial conditions, values of constants, laws of nature, number of space dimensions, number of universes, and fine tuning explanations. Future scientific experiments may validate selected assumptions; but until they do, proposals by philosophers may be as valid as theoretical scientific theories. (shrink)