Last time at the end of part 2 I mentioned that I would be going over how beings in the dimensions higher than 11 fit into the simulated universe hypothesis and also how the notion of nested simulations fit in.
To start of in string theory the number of spatial dimensions believed to exist is 11 which puts a lower bound on how many dimensions a multiverse will have in total.
Four of these dimensions are known to us while the other seven are curled up into a very small space at the quantum or Planck scale (named after German physicist Max Planck who originated quantum theory).
Before we can progress onto understanding how dimensions higher than 11 work we need to have an overview of string theory.
String theory is a theoretical framework in modern physics (everything from Einstein to now) in which point like particles are replaced by one dimensional objects called strings. String theory describes how these strings interact, move and propagate with each through space-time. According to String theory at distant scales string look just like ordinary point particles with its mass, charge and other fundamental properties determined by the string in question. Different vibrations produce different particles and thus reality can be thought of as a sea of strings vibrating at different frequencies to create what we call physical reality.
One of the major theories of string theory is just how bloody abstract it is with references to the multiverse (string landscape), quantum gravity and sometimes even metaphysics making it mostly incomprehensible to most people.
There are two types of string; a closed string and an open string.
The length of a string is typically that of a Planck particle i.e. 10^-35 metres.
Now we come to the notion of higher spatial dimensions.
In general relativity (the geometry of space-time or at least what we think is the geometry of space-time given our current primitive understanding of the universe) space and time are thought to be unified in a 4 dimensional space-time. Furthermore in general relativity the phenomenon known as gravity is thought to arise as a consequence of the Minkowski 4 dimensional space of the universe.
When string theory first came about in the 1960's in the form of Bosonic string theory space-time was thought to contain 26 dimensions which as you can see is a bit crazy even for the accepted 11 dimensions of modern string theory.
Beyond strings we have objects called branes; these are physical objects that generalize particles to higher dimensions of up to 11.
Beyond 11 dimensions we run into a little problem since we'll require the help of mathematics and something called M-theory.
M-theory stands for many things including but of course not limited to Master-theory (or maybe it's Missy-theory), Mother-theory and Matrix-theory.
M-theory was created by the brilliant physicist Edward Witten in an attempt to unify all the coherent models of superstring theory into a grand unified theory.
In M-theory didn't branes are meant to represent point particles in different dimensions.
A 0-brane represents a point particle.
A 1-brane represents a string.
A 2-brane represents a 2 dimensional particle.
A 3-brane represents a 3 dimensional particle.
A 4-brane represents a 4 dimensional particle.
And so on and so forth all the way up to 11 dimensional branes.
Now we come to the more abstract side of things with higher dimensional mathematics.
In mathematics one of the most infamous examplesof a higher dimensional space is a Hilbert space (can be anything from 0- infinite dimensional).
A hilbert space generalises Euclidean topological spaces to any finite or infinite number of dimensions.
A hilbert space is an abstract vector space possessing the inherent property of an inner product which allows length and angle to be measured. Furthermore Hilbert spaces are complete metric spaces which means that there are enough mathematical limits for operations such as calculus to be performed.
An infinite dimensional Hilbert space if one exists in the physical world (world in the sense of reality rather in the sense of planet) would be totally incomprehensible to us 3 dimensional beings. In fact depending on what kind of infinity you are using (ordinals most likely) the same infinite dimensional space might be incomprehensible to beings from a lower level of infinity.
Now that we have reached the limit of higher dimensional spaces we need to discuss how infinite dimensional beings might use finite dimensional beings as chess pieces.
It might be possible that an infinite dimensional being created our 11 dimensional universe as an experiment to see if they could test their new found discovery of finite spatial dimensions; since before this alarming discovery they only knew what it was like to live in an infinite dimensional space. This entity of immense power would be beyond the concepts of time, space and physics; existing in a realm which is so far from us as we are from the 5 dimensional space of the Imps.
Perhaps this infinite dimensional being is simulating all of the other lower infinite and higher and lower finite dimensions in an experiment which has been lasting an eternity from our point of view. Perhaps this infinite dimensional being is also being simulated by beings on an order of infinity even greater than his own and perhaps they too are being simulated by beings on an even greater order of infinity.
Theoretically there might exist a being which primitive humans and some educated humans call God that exists at the metaphysical apex of infinity known as Absolute infinity.
Now that concludes my 3 part series on the simulated universe hypothesis.