The theory of General Relativity breaks down below the Planck scales. As Stephen Hawking explains, this means the the universe has a quantum mechanical origin.
Perhaps there is no escaping the fact that language[mathematics] corresponds to the perceptual universe, in that language describes discrete "things", and things themselves are representable by identity operators. Even if the theory [universe] is not completely constructed due to Godellian incompleteness, it must have an identity, such, that it may be represented as ...a variable?
A = identity
Truth = A V ~A
Whatever the mathematical structure that corresponds to physical existence is, it must be governed by invariance principles. The general contains the specific. Bivalent logics. Sure, fuzzy logic concepts also correspond to what we percieve, but those fuzzy logics can be represented as symmetry invariances, just as Aristotle's law can be
An invariance explains a symmetry.
Periodicity is also a symmetry. Rotate into the complex plane and we have real numbers on the horizonal axis and imaginary numbers on the
vertical axis. So a periodic function could exist with periodicity
along both the imaginary AND the real axis. Such functions would have
amazing symmetries. Functions that remain unchanged, when the complex
variable "z" is changed.
Where the elements a,b,c,d, are arranged as a matrix, forming an
algebraic group. An infinite number of possible variations that
commute with each other as the function f, is invariant under group
transformations. These functions are known as "automorphic forms".
Topologically speaking, the wormhole transformations must be
invariant with regards to time travel. In other words, by traveling
backwards in time, we "complete" the future, and no paradoxes are
So when spacetime tears and the wormhole is created, it must obey
certain transformative rules, which probably appear to be
discontinuities from a "3-D" perspective, but really, these
transformations are continuous!
So the number of holes[genus] on the surface of space, determine
whether there exist an infinite, or finite, number of solutions to
the universal equations?
Multiverse, or one Universe?
Strong Anthropic Principle or Weak Anthropic Principle?
For the universe as a whole, the boundary conditions must be specified with regards to the field configurations via, summing over the path integral, utilizing a Euclidean action. But by summing over compact metrics, Hartle and Hawking give us the "No Boundary Proposal", such, that the boundary condition for the universe is, that it has no boundary.
To artificially slice up space and time [e.g. canonical quantization] seems un-natural.
Actually, spacetime does not really need to be "sliced up" in that it can proceed in discrete steps, yet, still be continuous. The slices must be in Planck units.
E = hf
[density 1]--->[density 2]--->[density 3]---> ... --->[density n]
Intersecting wavefronts = increasing density of spacelike slices, but the slices are a transformation that is continuous.
As the wavefronts intersect, it becomes a mathematical computation:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...2^n
The information density of space increases. This is a relation and its inverse.
For example, unity is a constant, representable by:
[1 = c ] = [1/2 + 1/2] = [1/4 + 3/4] = [1/5 + 4/5] = [1/6 + 5/6]
The left fraction represents [energy/momentum] and the right fraction represents compressed [space/time] density, where space means "distance interval" , a relative measurement.
The physics for a circle of radius R, is the same for a circle of radius 1/R
E/p = S/T = c
[Space/time] and [energy/momentum] are two different forms of the same invariant quantity [c].
[E/p]_n = [E/p]_n+1 = [S/T]_n = [S/T]_n+1
Russell E. Rierson