Our Mathematical Universe—My Quest for the Ultimate Nature of Reality

Author: Max Tegmark
Publisher: Vintage Books 2014

Tegmark divides this book into three parts: Zooming Out, Zooming In, and Stepping back.  The following is a brief summary of each part.  I enjoyed reading this book.  I would recommend this to a person who is interested in learning some interesting predictions of theoretical physics.

In part one he is zooming out from Earth all the way to the cosmic origin.  In the process he introduces two types of multiverses: level 1 multiverse and the level 2 multiverse.  He defines our universe as the spherical region from which light has had time to reach us during the 14 billion years since the Big Bang.  However, the inflationary matter that created more space and ordinary matter in 10^{-35} seconds at the beginning our universe stopped in our universe.  However, the inflationary theory predicts that for each volume of inflating substance that decays into a non-inflation Big Bang universe like ours, two other inflating volumes don’t decay, instead tripling their volume.  There result is a never ending process where the number of Big Bang universes increase as 1, 2, 2^2, etc, doubling at each step.  These universes are called Level I parallel universes and all Level I parallel universes together is called the Level I multiverse.  The same inflation theory predicts that inflation can create several adjacent volumes each of which is a Level I multiverse.  The region between each multiverse is in eternal inflation.  This tree like structure is called the Level II multiverse.

In the second part Tegmark zooms into the microscopic world.  The state of a particle is described by a wave function.  The change of this state over time is described by Schrodinger’s equation.  Bohr and Heisenberg came up with the Copenhagen interpretation in 1931 which says that the Schrodinger’s equation describes the change in the state of a particle if it is not observed.  If the particle is observed, then the wave function collapses.  In 1957 Hugh Everett proposed what is known as the Everrett Interpretation.  That is, the wave function never collapses.  This leads to the quantum parallel universes.  These type of universes are called Level III universes.  The collection of all such Level III universes is called the Level III multiverse.  (Hugh Everett’s son is a rock star.  His name is Mark Everett.)  

In the last part by stepping back he looks at everything from what he called a “bird perspective”.  There is an external mathematical reality.  Scientists are discovering the mathematical structure of this external reality.  Then for each mathematical structure there is an associated reality.  In other wards, each mathematical structure defines a Level IV universe.  The collection of all such Level IV universes is called the level IV multiverse.