Our observable universe can be defined as the spherical region of space from which light
has had time to reach us during the 14 billion years since the Big Bang. It is the part of
our physical reality that contains everything that exists which we can in principle observe.
But is there anything that lies beyond our observable region or our Hubble volume? Well,
given that our universe may be infinite in size with an intrinsic property known as inflation,
chances for the existence of the Multiverse are extremely high. So, for physicists like
Max Tegmark of MIT, the question is not whether the multiverse exists but rather how many
levels it has. He has classified as many as 4 distinct types of Multiverses in his book
“Our Mathematical Universe”. So, let’s take a brief look at what these different
levels of the Multiverse are like!
The first, and the least controversial level of our Multiverse is simply a region of space
that is too far away for us to have observed yet. The furthest we can observe in any direction
is currently about 46 billion light-years which is the distance that light has been
able to travel since the beginning of the Big Bang. But just because we can’t see
something, doesn’t necessarily mean that it doesn’t exist. In fact, the cosmic microwave
background radiation allows us to perform extremely sensitive tests for whether our
universe is finite, and so far, all the evidence seems to be against it. Now, since the flat
infinite models fit the observed data, it is reasonable to assume that our universe
is infinite, or at least sufficiently large, which makes the level 1 multiverse a trivial
consequence of these tests and the cosmological theory of inflation. Furthermore, observations
of our galaxy distribution and the microwave background radiation have shown that the arrangement
of matter on large scales collapses to dull uniformity with no coherent structures larger
than about a billion light-years. If this is true, then there is no reason to believe
that our part of the cosmic horizon is the only one with physical stuff or matter in
it. So, with an infinite amount of space and matter available, the level 1 multiverse contains
an infinite number of regions similar to our own observable universe. This means that there
may be an identical copy of you somewhere out there in the multiverse as we speak! But
not just 1 identical copy, but infinitely many identical copies of you may exist as
there may be an infinite number of Hubble volumes identical to our own in the level
1 Multiverse. In fact, Max Tegmark estimates that if you traveled in a straight line for
about 10^10^118 meters, you would come across an identical copy of our observable universe.
But if you wanted to meet an identical copy of you, then the distance to that would be
relatively less, about 10^10^29 meters away, which is still astronomically huge. So, we
can think of observers living in Level 1 parallel universes as experiencing the same effective
laws of physics but with different possible histories.
Now, if you think that the level 1 Multiverse may be all there is, you are in for a surprise!
Imagine an infinite set of these distinct level 1 multiverses, some perhaps with different
space-time dimensionality and different physical constants, only then you would have a structure
that would constitute a Level 2 Multiverse as predicted by the current popular theory
of chaotic eternal inflation. Andrei Linde, Alex Vilenkin, Alan Guth, and their colleagues
have shown that space as a whole is stretching and will continue doing so forever, but some
regions of space stop stretching and form distinct bubbles, like gas pockets in a loaf
of rising bread. These distinct bubbles are level 1 multiverses that are infinite in size
occurring infinitely many times filled with the same energy field that drove inflation.
But these bubbles are infinitely far from each other. Meaning, that if you live in one
of these Level I multiverses, it would be impossible for you to visit a neighboring
level 1 multiverse since inflation will keep creating space between your bubble and its
neighbors faster than you can travel through it. So, your descendants will never see their
identical copies elsewhere in the Level II Multiverse. In comparison, you can in principle
travel to any arbitrarily distant part of our Level I multiverse if you’re patient
enough and the cosmic expansion decelerates. Now, the Level II multiverse is far more diverse
than the Level I multiverse. The bubbles vary not only in their initial conditions but also
in seemingly unchanging aspects of nature. Meaning, they must obey the same fundamental
laws of physics governed by the same mathematical equations but may have different effective
laws of physics, or particular solutions to those mathematical equations in different
bubbles.
Now, so far, we have looked at structures that we can point to in space, at least in
theory. But the next level of the Multiverse, the Level 3 Multiverse, gets super weird.
It is believed that the level 3 Multiverse is right here all around us arising from the
famous, and controversial, many-worlds interpretation of quantum mechanics. It is the idea that
random quantum processes cause the universe to branch into multiple copies, one for each
possible outcome. In the early 20th century, the theory of quantum mechanics described
the state of our universe not in the classical terms such as the positions and velocities
of all particles, but in terms of a mathematical object called a wave function. According to
the Schrödinger equation, this state of the wave function evolves over time in a way that
mathematicians call it “unitary,” meaning that the wave function rotates in an abstract
infinite-dimensional space called Hilbert space before evolving in a deterministic way.
So, to explain away all the weirdness of the wave function with its many different possibilities,
physicists in the 1920s postulated that the wave function must ‘collapse’ into a definite
state once an observation is made. However, Hugh Everett showed that the collapse postulate
is unnecessary and that all the possible outcomes are equally as real as the one that the observer
is observing. In other words, superposition of all the classical worlds is the level 3
Multiverse. So, these universes are located not in ordinary space but in an abstract realm
of all possible states. Every conceivable way that the world could be, within the scope
of quantum mechanics, corresponds to a different universe. But, given infinite possibilities
even at the level 1 and level 2 multiverse, the Level III multiverse adds nothing new.
It just adds an infinite number of indistinguishable copies of the same universes to the already
infinite level 1 and level 2 multiverse.
Well, if a level 3 Multiverse adds nothing new to the previous levels, then surely there
can be nothing else beyond it, right? Not according to Max Tegmark! He argues that our
physical reality isn’t just described by mathematics, but it ultimately is mathematics!
So, just like the initial conditions and physical constants in the Level I, Level II, and Level
III multiverses can vary, the very fundamental laws that govern nature itself can vary in
the level 4 Multiverse! In other words, a universe at this level may exist that obeys
the laws of classical physics, but without any quantum effects, or a universe that is
just an empty dodecahedron, or better yet, a universe with discrete-time intervals instead
of continuous. An indication that such a multiverse might not be just mere speculation is the
tight correspondence between the worlds of abstract reasoning and observed reality. Equations
and, more generally, mathematical structures such as numbers, vectors, and geometric objects
describe the world with remarkable accuracy and precision. In his 1960 article, "The Unreasonable
Effectiveness of Mathematics in the Natural Sciences", physicist Eugene Wigner argues
that a physical theory's mathematical structure often points the way to further advances in
that theory and even to empirical predictions. Moreover, according to Tegmark, mathematical
structures have an eerily real feel to them. They satisfy a central criterion of objective
existence, meaning, they are the same no matter who studies them. For example, a theorem is
true regardless of whether it is proved by a human, a computer, or any other intelligent
lifeform for that matter. So, intelligent alien civilizations would find the exact same
mathematical structures as we have found here on Earth. Appropriately then, mathematicians
commonly say that they discover mathematical structures rather than invent them. So, for
Tegmark, all Mathematical structures are physically real immutable entities existing outside of
space and time. Every mathematical structure corresponds to a parallel universe constituting
a level 4 Multiverse. This ultimate level of the Multiverse opens up the full realm
of possibilities. Here, universes can differ not just in location, cosmological properties,
or quantum state but also in the laws of physics. Existing outside of space and time, they are
almost impossible to visualize; the best we can do is to think of them abstractly, as
static sculptures that represent the mathematical structure of the physical laws that govern
them.
And these are the four distinct levels of the Multiverse defined by Max Tegmark and
others. If you enjoyed it, give it a thumbs up, share with everyone you know, and subscribe
to our channel for more content like this! Also, if you want to see a more in-depth analysis
of these levels, let us know down below in the comment section! Until then, we’ll see
you in the next one!