Sunday, October 22, 2017

Geometry of Our Universe 2

http://scienceblogs.com/startswithabang/2017/10/22/comments-of-the-week-final-edition/

Ethan wrote:
"From Frank on the curvature of the Universe: “What if Universe is surface of a 4d sphere where 3d surface (space) curved in the 4th dimension (time)?”"
"Well, there is curvature in the fourth dimension, but the laws of relativity tell you how the relationship between space and time occur. There’s no wiggle-room or free parameters in there. If you want the Universe to be the surface of a 4D sphere, you need an extra spatial dimension. There are many physics theories that consider exactly that scenario, and they are constrained but not ruled out."

Then what if I propose, gravitational field across the Universe is the fifth dimension (for the Universe to be the surface of a 4D sphere)? (And also think about why it seems gravity is the only fundamental force that effects all dimensions. Couldn't it be because gravity itself is a dimension, so it must be included together with other dimensions (of spacetime) in physics calculations.)

And why it is really important to know general shape/geometry of the Universe?

I think then we can really answer whether observable universe and global universe are the same or not, and if they are the same then we would also know that the Universe is finite in size. (And we could also calculate general curvature of the Universe for anytime, which would help cosmology greatly, no doubt.)

I am guessing currently known variations in CMB map of the Universe, match to the distribution of matter/energy in the observable Universe, only in a general (non-precise) way. I think, if the Universe is really the 3d (space) surface of a 4D sphere, curved in the 4th dimension (time), (with gravity as the 5th dimension), then, we could use CMB map of the Universe as CT scan data, and could calculate 3d/4d matter/energy distribution of the whole Universe from it. And then, if it matches (as a whole) to the matter/energy distribution of our real observational Universe, (which coming from other (non-CMB) observations/calculations), then we could know for sure, whether our observational and global Universes are identical or not. (If not, then by looking at the partial match, maybe we could still deduce how large really is our global Universe.)

Further speculation:

Let's start with, spacetime is 4D (3 space dimensions and a time dimension).
Gravitational curvature at any spacetime point must be a 4D value => 4 more dimensions for the Universe.
If electric field at any spacetime point is a 4D value => 4 more dimensions for the Universe.
If magnetic field at any spacetime point is a 4D value => 4 more dimensions for the Universe.
Then the Universe would have 4+4+4+4=16 dimensions total!
(Then the dimensions of the Universe could be 4 quaternions = 2 octonions = 1 sedenion.)
(But if electric and magnetic fields require 3d + 3d, then the dimensions of the Universe would be 4+4+3+3=14 dimensions!)

20171028:
If our Universe has 16 dimensions and if our reality is created by a CA QC at Planck Scale, then its cell neighborhood maybe like a tesseract or a double-cube (16 vertices). Or if our Universe has 14 dimensions and if our reality is created by a CA QC at Planck Scale, then its cell neighborhood maybe like a Cube-Octahedron Compound or Cube 2-Compound (14 vertices).

(20171104) What if Kaluza–Klein Theory (which unites Relativity and Electromagnetism, using a fifth dimension), is actually correct by taking gravitational field across the universe as the fifth (macro/micro) dimension? (Maybe compatibility with Relativity requires taking it as a macro, and QM requires taking it as a micro dimension? (Which would be fine!?))

(20171115) According to Newton Physics, speed of any object in the Universe always is:
|V|=(Vx^2+Vy^2+Vz^2)^(1/2) or V^2=Vx^2+Vy^2+Vz^2
But according to Special Theory of Relativity, it really is:
C^2=Vx^2+Vy^2+Vz^2+Vt^2 which also means Vt^2=C^2-Vx^2-Vy^2-Vz^2 and so |Vt|=(C^2-Vx^2-Vy^2-Vz^2)^(1/2)
So, if gravitational field across the Universe is actually its 5th (macro) dimension then:
C^2=Vx^2+Vy^2+Vz^2+Vt^2+Vw^2 which also means Vw^2=C^2-Vx^2-Vy^2-Vz^2-Vt^2 and so |Vw|=(C^2-Vx^2-Vy^2-Vz^2-Vt^2)^(1/2)
(Is this the equation to calculate spacetime curvature from 4D velocity in General Relativity?)
(Equivalence Principle says gravity is equivalent to acceleration => Calculate its derivative?)

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