- #1
Russell E. Rierson
- 384
- 0
Antisymmetric tensors combine with symmetric tensors to give the thermodynamic arrow of time, which is really a continual densification of spacelike surfaces?
More random thoughts on the unified field theory:
symmetric tensor: A^uv = A^vu
antisymmetric tensor: A^uv = -A^vu
asymmetric tensor: A^uv does not equal A^vu
Asymmetric tensor(A^uv) = (1/2)[A^uv + A^vu] + (1/2)[A^uv - A^vu]
The gravity tensor should be able to rotate into the electromagnetic tensor and the electromagnetic tensor should be able to rotate into the gravity tensor.
Time
^
|
|
|
|-------------->space
G
^
|
|
|
|-------------->EM
Distance is a property between objects in space. Space is a structure,
which is constructed of discrete units. The structure of space is
possibly a distributive lattice? A lattice is a partially ordered
set, closed under least upper and greatest lower bounds. Any lattice
which is isomorphic to a collection of sets, closed under
complementation and intersection, is a Boolean algebra.
If the universe is closed, the "information" or entangled quantum
states cannot leak out of the closed system. So the density of
entangled quantum states, continually increases, as the entropy must
always increase. While to us, it is interpreted as entropy or lost
information, it is actually recombined information, to the universe.
Shannon entropy.
The continual intersection and collapse of probability
distributions, also known as quantum phase entanglement, is a
continual increasing of the "total" combined information of the
universal wavefunction itself. Information density. With more
information, more complex structures can be created.
The information density of the universal system must be increasing.
The increase of information density is analogous to a pressure
gradient.
[density 1]--->[density 2]--->[density 3]---> ... --->[density n]
[<-[->[<-[-><-]->]<-]->]
Intersecting wavefronts = increasing density of spacelike slices
As the wavefronts intersect, it becomes a mathematical computation:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...2^n
The area of a spacetime surface and the maximum amount of information contained in a finite region of space, cannot be greater than one quarter of the area in Planck units. Spin networks can describe the quantum geometry of space at the intersection of horizon boundaries, where the spin networks intersect with the boundary at a finite number of points.
There is a finite amount of energy contained by a given region of spacetime. A finite amount of information. A finite number of quantum phase entanglements and random fluctuations.
A superconductor is a system of discrete units operating in two dimensions along a standing wave. By definition, a superconductor is a material that is precisely in balance, such, that it will not allow any external magnetic fields inside the superconductive domain.
The inner[scalar] product of two vectors, a and b, is given by a*b .
The outer product of two vectors a and b, is given by a /\ b .
a*b = b*a
a /\ b = -b /\ a
the geometric product ab is given by ab = a*b + a /\ b
a*b = [ab + ba]/2
a /\ b = [ab - ba]/2
The electromagnetic field in terms of the four potential A:
F = grad /\ A = grad A - div A
The electromagnetic field bivector, F, in terms of the orthonormal basis vectors v:
Electric field E
Magnetic field B
F = E + iB
E = [F - vFv]/2
iB = [F + vFv]/2
grad F = 4 current = J
F = inverse grad J
More random thoughts on the unified field theory:
symmetric tensor: A^uv = A^vu
antisymmetric tensor: A^uv = -A^vu
asymmetric tensor: A^uv does not equal A^vu
Asymmetric tensor(A^uv) = (1/2)[A^uv + A^vu] + (1/2)[A^uv - A^vu]
The gravity tensor should be able to rotate into the electromagnetic tensor and the electromagnetic tensor should be able to rotate into the gravity tensor.
Time
^
|
|
|
|-------------->space
G
^
|
|
|
|-------------->EM
Distance is a property between objects in space. Space is a structure,
which is constructed of discrete units. The structure of space is
possibly a distributive lattice? A lattice is a partially ordered
set, closed under least upper and greatest lower bounds. Any lattice
which is isomorphic to a collection of sets, closed under
complementation and intersection, is a Boolean algebra.
If the universe is closed, the "information" or entangled quantum
states cannot leak out of the closed system. So the density of
entangled quantum states, continually increases, as the entropy must
always increase. While to us, it is interpreted as entropy or lost
information, it is actually recombined information, to the universe.
Shannon entropy.
The continual intersection and collapse of probability
distributions, also known as quantum phase entanglement, is a
continual increasing of the "total" combined information of the
universal wavefunction itself. Information density. With more
information, more complex structures can be created.
The information density of the universal system must be increasing.
The increase of information density is analogous to a pressure
gradient.
[density 1]--->[density 2]--->[density 3]---> ... --->[density n]
[<-[->[<-[-><-]->]<-]->]
Intersecting wavefronts = increasing density of spacelike slices
As the wavefronts intersect, it becomes a mathematical computation:
2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...2^n
The area of a spacetime surface and the maximum amount of information contained in a finite region of space, cannot be greater than one quarter of the area in Planck units. Spin networks can describe the quantum geometry of space at the intersection of horizon boundaries, where the spin networks intersect with the boundary at a finite number of points.
There is a finite amount of energy contained by a given region of spacetime. A finite amount of information. A finite number of quantum phase entanglements and random fluctuations.
A superconductor is a system of discrete units operating in two dimensions along a standing wave. By definition, a superconductor is a material that is precisely in balance, such, that it will not allow any external magnetic fields inside the superconductive domain.
The inner[scalar] product of two vectors, a and b, is given by a*b .
The outer product of two vectors a and b, is given by a /\ b .
a*b = b*a
a /\ b = -b /\ a
the geometric product ab is given by ab = a*b + a /\ b
a*b = [ab + ba]/2
a /\ b = [ab - ba]/2
The electromagnetic field in terms of the four potential A:
F = grad /\ A = grad A - div A
The electromagnetic field bivector, F, in terms of the orthonormal basis vectors v:
Electric field E
Magnetic field B
F = E + iB
E = [F - vFv]/2
iB = [F + vFv]/2
grad F = 4 current = J
F = inverse grad J