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Before we can establish what a multiverse is, we must consider what a universe is and what physical reality is. Physical reality is everything that exists, while our universe, is the part of physical reality that we can observe, at least, in principle. Thus, our universe would be the spherical region of space that light has had time to reach us since the 13.8 billion years since the Big Bang. We can also refer to this region as the observable universe, horizon volume or the region within our particle horizon.
As far as we know, our universe may contain:
10^11 galaxies
10^23 stars
10^80 protons
10^89 photons
Inflation predicts that there is even more.
The idea behind the multiverse is, indeed, hypothetical: that there could be other universes, living alongside ours.
Perhaps, the first one to propose the idea of a multiverse was Erwin Schrodinger, in 1952. His famous "Schrodinger equation" that won him the Nobel Prize, appeared to, describe different possible histories. Schrodinger proposed that, these were not "alternative" histories, however, that they all actually happened, simultaneously.
I would like to discuss the two biggest ways physicists have been able to produce a taxonomy, or classification, of the various hypothetical scenarios, for the multiverse.
Erwin Schrodinger
Max Tegmark
Brian Greene
Hugh Everett III
Max Tegmark's 4 levels:
1) A Hubble volume is a spherical area, that would surround an observer from a single point. Beyond the horizon of the Hubble volume, objects are receding from the observer, faster than the speed of light. A Hubble volume's size is defined as as the region within which galaxies are receding slower than light. This is due to the Universe's expansion. That being said, a Level I multiverse, would be a kind of, extension of our universe. Let me explain. This kind of multiverse, would be infinite in size. That being said, if it is infinite in size, it would have to contain all possible configurations of Hubble volumes. There are infinitely many. That being said, there must be one, that looks just like ours. Max Tegmark postulates that one identical to ours, should be at about: 10^10^115 meters away from ours. If there is infinite space, than there is an infinite number of Hubble volumes, some even identical ours. The Level I multiverse will include your doppelgangers.
Indeed, this is a speculation, not based on modern physics, however, one two premises: that the universe is infinite and that it is rather uniformly filled with matter.
Different Hubble volumes in a Level I multiverse.
Level I parallel universes are simply universe-sized parts of our space that are so far away that light from them has not had time to reach us yet. There are no physical boundaries between the neighboring universe, nor would we be holding a special place in the multiverse.
2) The Level II multiverse, is characterized by universes with different physical constants. The idea has to do with inflation and the expansion of the Universe. The Level II multiverse will be expanding, eternally, that is, forever. However, there will be some regions of space that stop stretching. These areas that have stopped stretching will form a kind of bubble, with different laws of physics. These are the different universes, each with different physical constants that govern them.
An example of bubble universes. Each with different laws of physics.
3) The Level III multiverse brings in quantum mechanics. This is the MWI or Many-Worlds interpretation of quantum mechanics. This was a proposal made by Hugh Everett III. It must first be understood, that, in quantum mechanics, certain observations, exist in a range of different potential or possible observations. This is known as the wave function of a quantum system. Each of these observations in quantum mechanics has a corresponding probability (of it being observed to have actually occurred). We say that the wave function is in a superposition (undetermined state) of several different potential outcomes (known as eigenstates in quantum mechanics). When the wave function, upon observation, is reduced to a single eigenstate, we call this the wave function collapse. Thus, the MWI, denies the actuality that the wave function collapse even happens. In the Many-Worlds interpretation, each of these possible observations, corresponds to a different universe! In the Level III multiverse, all possible histories, futures and realities are real. Anything that could have happened, and did not, did happen, in another universe. A good way to visualize the many-worlds interpretation is by throwing a die. There are 6 possible outcomes, you role a 1, 2, 3, 4, 5 or a 6. One of these will be observed in our physical universe. However, if the many-world's interpretation is correct, than, each of these possible outcomes, corresponds to a different universe, that exists on a quantum branch, in infinite dimensional space.
A way to visualize the Many-Worlds interpretation. Each possible outcome, has a corresponding universe, each equally real.
The MWI is an interpretation of quantum mechanics where, each potential outcome to an observable in a quantum system will actually reside in different universes, that somehow coexist.
4) A level IV universe is known as the "ultimate ensemble". This was Max Tegmark's own idea. It is based on the assumption that our physical reality is a kind of mathematical structure. That being said, under this assertion: all universes are equally real, under different mathematical structures. The hope is that this would encompasses any even conceivable kind of physical universe, removing the potential for a level V multiverse.
Brian Greene, gives us 9 potential kinds of multiverses.
1. The quilted multiverse: "Conditions in an infinite universe necessarily repeat across space, yielding parallel worlds."
This universe works only for a universe that is infinite in size.
The idea is: an infinite amount of space = every possible event will occur an infinite number of times.
The only reason that we cannot see these other universes, is because the speed of light is not fast enough for their information to have reached us yet.
2. The inflationary multiverse: "Eternal cosmological inflation yields an enormous network of bubble universes, of which our universe would be one."
This kind of multiverse is based on the idea that inflation could be eternal.
This multiverse will be broken up into little bubbles or pockets, where inflation has stopped.
These bubbles could have properties that differ from one another, such as, their physical constants.
3. The brane multiverse: "In string/M-theory's brane world scenario, our universe exists on one 3-dimensional brane, which floats in a higher dimensional expanse potentially populated by other branes - other parallel universes."
In this picture, our universe is restricted to a higher dimensional (although in our case, 4-dimensional) object, called a brane, embedded, in some sort of higher dimensional arena.
This higher dimensional arena is technically called the bulk, or, more commonly referred to as: hyperspace.
The brane that we are confined to would be 4-dimensional, however, there can be branes of many sizes. In this bulk, there can be other branes. Each with the potential to harbor their own universe.
Also, the collision of branes, is more than enough energy to give rise to a Big Bang. This could be a potential explanation for how string theory (as this proposal requires extra dimensions) could take us before the Big Bang.
4. The cyclic multiverse: "Collisions between brane worlds can manifest as Big Bang-like beginnings, yielding universes that are parallel in time."
This multiverse contains multiple branes, that each carry a universe.
When the branes collide, they can cause another Big Bang, creating another universe.
This process could be happening over and over again: destroying the old universes, and creating new ones in the process.
5. The landscape universe: "By combining inflationary cosmology and string theory, the many different shapes for string theory's extra dimensions give rise to many different bubble universes.
In string theory, there is a vast landscape of possible physical configurations that a universe could comprise.
Each of these possible universe configurations is known as a false vacua.
All of the possible configurations together is known as the string theory landscape.
The total number of potential false vacua in string theory is thought to be somewhere between 10^10 to 10^500.
These are all different ways, in which, Calabi-yau manifolds can be compactified.
In superstring theory, the respective 6 extra dimensions are conjectured to take on the form of the Calabi-yau manifold. This is a special shape that satisfies the stringent requirements for extra dimensions in string theory. The extra dimensions would be compactified (curled up) on these tiny geometries, at the scale of string theory and quantum gravity, the Planck scale (10^-35 meters).
6. The quantum multiverse: "Quantum mechanics suggests that every possibility embodied in its probability waves is realized in a vast number of parallel universes."
This is similair to the Many-world's interpretation of quantum mechanics, which I have described above.
Every time a diversion in events occurs, there is a new universe created.
7. The holographic multiverse: "The holographic principle asserts that our universes is exactly mirrored by phenomenon taking place on a distant boundary surface, a physically equivalent parallel universe."
The holographic principle is the proposal that: the volume of a space, can be simulated by the boundary.
Although the descriptions exist in 1 different dimension, they have contained equivalent information.
8. The simulated multiverse: "Technological leaps suggest that one day, simulated universes may be possible."
This proposal is that our universe, exists as a computer simulation.
Also, this computer, can simulate other universes, each with their own independent properties.
9. The ultimate multiverse: "The principle of fecundity asserts that every possible universe is a real universe, thereby obviating the question of why one possibility - ours - is special. These universes instantiate all possible mathematical equations."
This is every mathematically possible universe, under every possible configuration of the laws of physics.
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