An Outline of Tegmark’s Four Levels of the Multiverse

by Max Andrews

Contemporary physics seem to indicate that there are good reasons, theoretically and physically, for an idea that there is a plurality of worlds.  This concept has come to be understood as the multiverse.  The multiverse is not monolithic but it is modeled after the contemporary understanding of an inflationary model of the beginning of this universe.  Max Tegmark has championed the most prominent versions of the multiverse.[1]  Tegmark has made a four-way distinction.

Tegmark’s first version of the multiverse is called the level one multiverse.  The level one is, for the most part, more space beyond the observable universe.  So, theoretically, if we were to go to the “edge” of the universe there would be more space.  Having this model as a version of the multiverse may be misleading because there is still only one volume, landscape, or system involved.  A generic prediction of cosmological inflation is an infinite space, which contains Hubble volumes (what we see in our universe) realizing in all conditions—including an identical copy of each of us about 10^10^29 meters away.[2]

The level two multiverse is typically associated with other bubble universes spawning from a cosmic landscape and slow-roll inflation.  This version predicts that different regions of space can exhibit different laws of physics (physical constants, dimensionality, particle content, etc.) corresponding to different localities and a landscape of possibilities.[3]  Imagine the multiverse has a bathtub filled with tiny bubbles.  Each bubble in this larger system (the bathtub) is a single universe.  Or, imagine a pot of boiling water.  The bubbles arise from the bottom of the pot analogous to the way inflationary cosmology works.  These other domains (or bubble universes) are nearly infinitely far away in the sense that we could never get there even if we traveled faster than the speed of light (due to the constant stretching of space and creation of more volume).[4]  It may, however, not be the case that there is an infinite set of universes.  Andrei Linde and Vitaly Vanchurin have argued that the way slow-roll inflation works it could only produce a finite number of universes.  Hence, they propose that there are approximately 10^10^10^7 universes.[5]

The level three multiverse is particular to certain interpretations of quantum mechanics such as Hugh Everett’s Many Worlds Interpretation.  It is a mathematically simple model in support of unitary physics.  Everything that can happen in the particle realm actually does happen.  Observers would only view their level one multiverse, but the process of decoherence—which mimics wave function collapse while preserving unitary physics—prevents them from seeing the level three parallel copies of themselves.[6]

The fourth level is the all-encompassing version where mathematical existence is equivalent to physical existence.  Mathematical structures are physically real and the entire human language we use to describe it is merely a useful approximation for describing our subjective perceptions.  Other mathematical structures give different fundamental equations of physics for every region of reality.[7]  This would be Plato’s ideal reality.

What is most important about having this scientific evidence is that it provides us with reasonable evidence to support the idea of modal realism.  Modal realism cannot simply be brushed off anymore as being incoherent and baseless whereas this evidence may be an example of when purely mathematical, scientific, and philosophical theories may have physical support.  Additionally, each version of the multiverse allows for modal realism to be true.  The level one multiverse allows for an infinite space for different states of affairs to happen.  Level two and up depict a greater amount of creativity for God and a certainly more amicable to the idea given the separate systems of universes. It’s my contention that any level is perfectly compatible with theism.  Even the infinite models are consistent; for instance, Thomas Aquinas is clearly content with an infinite universe [or multiverse].[8]  Whether Linde and Vanchurin are correct in their finite version of the multiverse or whether Tegmark is correct is irrelevant to modal realism.  All that is required is that there be a time at which all possible states of affairs do occur—all events must not be simultaneous for modal realism to work.

(For more on theism and the multiverse please see:  Divine Simplicity and the Multiverse–Thomas Aquinas Approved and The Theological Attraction of the Multiverse).


[1] Max Tegmark, “The Multiverse Hierarchy,” Cornell University Library arXiv, arXiv:0905.1283v1, (accessed March 15, 2011).

[2] When Tegmark refers to an “identical” copy he simply refers to a similar copy.  There is a genuine ontological distinction.  Tegmark, 2.

[3] Ibid.

[4] Ibid., 7.  Additionally, there have been good scientific evidence suggesting observational grounds for inflation.  Researchers have taken the 7-year WMAP data and applied certain algorithms to pick up traces of thermal fluctuations in the early universe.  What they found were traces of what could be bubble collisions of the edges of our universe with another universe.  Stephen Feeney, et al., “First Observational Tests of Eternal Inflation:  Analysis Methods and WMAP 7-year Results,” Cornell University Library arXiv, arXiv:1012.3667v2 (accessed March 16, 2011).

[5] Andrei Linde and Vitaly Vanchurin, “How Many Universes are in the Multiverse?” Cornell University Library arXiv, arXiv:0919.1589v2 (accessed March 15, 2011).

[6] Tegmark, 10.

[7] Tegmark, 2, 12-13.

[8] Thomas, Scriptum Super Libros Sententiarum Magistri Petri Lobardi, in 3, dist. 1, q. 1, a. 2; ST 1 q. 46, a. 1, 2.


5 Responses to “An Outline of Tegmark’s Four Levels of the Multiverse”

  1. Thank you for this easy explanation. I enjoyed reading it.

  2. Hey. great, I thought hard about Tegmark’s multiverses a couple of years back, from a Christian perspective, and I’m glad to find someone else who considers his work useful. If you want (for example) to postulate that Eden was not in our space-continuum (because the rivers flow in a different direction, because our world always had mosquitos, lightining strikes, and death throughout), then Tegmark’s Level III Multiverse seems to be the best theoretical backdrop for such postulation.
    But I know next to nothing about modal realism, which is the philosophical position you seem keenest to defend.
    It crossed my mind that a modal realism might be used by God to bring about his sovereign will, with only 2 or 3 of the possible worlds actually injected with ‘life’. Why do you like modal realism?


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