To appear in Science and Ultimate Reality: From Quantum to Cosmos, honoring John Wheeler's 90th birthday, J.D. Barrow, P.C.W. Davies, & C.L. Harper eds., Cambridge University Press (2003) Parallel Universes
Max Tegmark Dept. of Physics, Univ. of Pennsylvania, Philadelphia, PA 19104; email@example.com (January 23 2003.) Abstract: I survey physics theories involving parallel universes, which form a natural four-level hierarchy of multiverses allowing progressively greater diversity. Level I: A generic prediction of inflation is an infinite ergodic universe, which contains Hubble volumes realizing all initial conditions
29 - including an identical copy of you about 1010 m away. Level II: In chaotic inflation, other thermalized regions may have different physical constants, dimensionality and particle content. Level III: In unitary quantum mechanics, other branches of the wavefunction add nothing qualitatively new, which is ironic given that this level has historically been the most controversial. Level IV: Other mathematical structures give different fundamental equations of physics. The key question is not whether parallel universes exist (Level I is the uncontroversial cosmological concordance model), but how many levels there are. I discuss how multiverse models can be falsified and argue that there is a severe "measure problem" that must be solved to make testable predictions at levels II-IV.
Is there another copy of you reading this article, deciding to put it aside without finishing this sentence while you are reading on? A person living on a planet called Earth, with misty mountains, fertile fields and sprawling cities, in a solar system with eight other planets. The life of this person has been identical to yours in every respect - until now, that is, when your decision to read on signals that your two lives are diverging.
You probably find this idea strange and implausible, and I must confess that this is my gut reaction too. Yet it looks like we will just have to live with it, since the simplest and most popular cosmological model today predicts that this person actually exists in a Galaxy about 101029 meters from here. This does not even assume speculative modern physics, merely that space is infinite and rather uniformly filled with matter as indicated by recent astronomical observations. Your alter ego is simply a prediction of the so-called concordance model of cosmology, which agrees with all current observational evidence and is used as the basis for most calculations and simulations presented at cosmology conferences. In contrast, alternatives such as a fractal universe, a closed universe and a multiply connected universe have been seriously challenged by observations.
The farthest you can observe is the distance that light has been able to travel during the 14 billion years since the big-bang expansion began. The most distant visible objects are now about 4?1026 meters away?, and a sphere
After emitting the light that is now reaching us, the most distant things we can see have receded because of the cosmic expansion, and are now about about 40 billion light years away. of this radius defines our observable universe, also called our Hubble volume, our horizon volume or simply our universe. Likewise, the universe of your above-mentioned twin is a sphere of the same size centered over there, none of which we can see or have any causal contact with yet. This is the simplest (but far from the only) example of parallel universes.