Looks like my query is your forte. I would like to know about wormholes. Besides the plethora of science fiction shows (Stargate, Star Trek, Event Horizon, etc) which revolve around the existence of wormholes, is there any viable theories regarding their existence or possible creation?. In the beginning of Event Horizon Sam Neill explains the concept using Vale tensors, singularities, interdimensional conduits, etc.
Can you explain some of the theories regarding this topic if there are any?. What is the Vale tensor. I am about to complete my B.S. in Math and I know some Physics so don't be afraid to show some of the math if you have to. I find this topic interesting albeit fantastic.
Thank you,
Cody
Answer Hello Cody.
The Vale tensor is something that I haven't researched yet but I will try to help you with these interesting ideas.
The universal constants are precisely balanced in the universe.
Now take those finely tuned constants out hundreds, thousands, millions, billions ...trillions of decimal places. Slight, almost infinitesimal differences between the constants of each universe which are actually resonances of a quantum "multiverse", mean that each resonance is unique.
From the graph of the normal curve, we can see that there are at least two universes exactly alike.
Also, there are many[millions? billions? ] of universes that are "almost" exactly alike.
The universes[timelines] begin to diverge more, as the curve diverges.
The worm-holes or Riemann cuts, connecting the different realities are where realities "overlap" for brief instants.
It seems to be related to consciousness.
I have wondered why the phase shift is a form of "changing places" with another version of oneself. What happens if someone fell through a worm-hole into the vacuum of empty space, of another universe?
Scary thought!
The fall of a solitary object to the ground for one location on the Earth can be locally transformed away by a correct choosing of a system of accelerating coordinates, but the fall of objects all over the Earth cannot. Effectively, these objects can be visualized as a spherical cloud of tiny particles, each following its own geodesic path, and the multiplicity of paths are all converging, such, that the cloud's volume is shrinking at an accelerating rate, and, as the shell/cloud collapses toward the Earth, the rate of acceleration, which is the second time derivative, is proportional to the mass of the Earth, in accordance with the Einstein field equations.
Basic tensors:
Einstein says that for empty space, far from any gravitating object, the spacetime will be Minkowskian [flat], requiring that the Riemann curvature tensor R_abcd should vanish.
But in a spacetime near a gravitating object, there will be a non-zero intrinsic curvature, because the total gravitational field of an object, cannot be simply "transformed away" to the second order. This necessary condition is given by the non-vanishing Riemann curvature tensor. Although, at points where the full curvature tensor R_abcd is non-zero, the contracted curvature tensor of the second rank tensor, R_ab = g^ab R_abcd = R^c_acb also known as the "Ricci tensor" , may ...vanish.
Therefore the equations for the gravitational field in the vacuum of empty space are: Ricci tensor, R_ab = 0
The R_ab = 0 represents ten equations in the ten components of g_ab at each point in empty spacetime, devoid of matter or electomagnetic energy, while not eliminating the gravitational metric-field itself. The equations are generally covariant, thus, given any single solution, infinitely many others may also be constructed via applying arbitrary, albeit continuous coordinate transformations. The conditions to be satisfied by the field equations must be the vanishing of the covariant derivatives - guaranteeing the conservation of any energy-momentum source term, that may be placed on the right side of the equation. Although it seems to make one think about the energy of the energy of the....of the ... of the ...of the energy of a gravitational field!
The divergence generalizes to the covariant derivative in tensor calculus, such, that the covariant derivatives of the metrical field equations must identically vanish. The Ricci tensor R_ab in and of itself does not satisfy this necessary requirement, but a new tensor can be created which does satisfy the requirement via a slight modification of the Ricci tensor, and, without disturbing the relation R_ab = 0 for the vacuum of empty space.
Subtracting half the metric tensor times the invariant Ricci scalar R = g^ab R_ab gives the Einstein Tensor:
G_ab = R_ab - (1/2) g_ab R
Since R_ab = 0
G_ab = 0
The covariant energy-momentum tensor is T_ab , regarded as the cause, or the "source" of the metric curvature. "Mass tells space how to curve and space tells mass how to move." It gives the conservation of energy-momentum, and it implies gravitational energy "gravitates" just as all other forms of energy do.
G_ab = k T_ab
k = -8pi G where G is Newton's universal gravitational constant.
the question becomes "what is space?" "What is time?"
Space is relational. The thermodynamic arrow of time is the self referential, gravitational feedback looping-geometric stacking-that occurs directly from the present moment being created and recreated constantly - analogous to continually opposing/juxtaposing reflective mirror images… originating deep in quantum phase space. The Heisenberg uncertainty relation provides both a resolution boundary and the invariant relational fabric for a translation between quantum[Planck scale] space and
experiential reality. It is the quantum T-dual compactification that
provides the Heisenberg resolution boudaries for
experiential[perceptual] reality. Unstable or chaotic states at a given level are always "compactified" (stabilized and bounded by eigenstates) into 6 higher dimensions condensing to the next level of
"event density".
The relation becomes totally "chaotic" below the Planck length. So yes, space could be described as a system of self similar feedback loops... Is spacetime a Gaussian distribution?
The Riemann tensor explains how a tangent vector, parallel translated around a tiny parallellogram is changed. So, to say that spacetime is "curved" means how much a tangent vector changes during parallel transport around a loop.
Is the universe a closed system? The million dollar question...
The geometric view of physics means that the laws of physics are the
same in every Lorentz reference system. Local Lorentz invariance. But
since the universe has no exterior reference frame, and it must refer
to itself, its world line intersects with itself. This
quantized-evolution of spacetime dictated by GR and QM, means that the
world line of the past intersects with the world lines of the present,
for the universe. A geometric stacking of space like slices,
parameterized by t, The universe is a function of itself. Spacetime
becomes compressed. As the time evolution proceeds in the
thermodynamic direction of t, the space like sheets continually
increase in density.
Does a nonlinear universe, give the "strange loop" of Goedelian
self-reference? The sharp distinction between an active transformer
and the passively transformed is no more... The state vector is no
longer the passive victim. It "fights back". The fusing of the
operator and the state vector is what completes the self-referential
feedback control circuit, which becomes the mechanism of free will...
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.
Actually, the increased Shannon entropy of the universe provides the
logical accounting for an observed Hubble red-shift and Einstein's
cosmological constant.
In quantizing spacetime geometry, the wavefunctions won't be based on a background space. The space of wavefunctions
can be expressed as the space of square-integrable wavefunctions over
classical configuration space. In ordinary quantum mechanics,
configuration space is space itself (i.e.,to describe the
configuration of a particle, location in space is specified). In
general relativity, there is a more general kind of configuration
space: taken to be the space of 3-metrics ("superspace", not to be confused with supersymmetric space) in the geometrodynamics formulation,or the space of connections (of an appropriate gauge group)in the Ashtekar/loop formulation. So the wavefunctions will be functions over these abstract spaces, not space
itself-- the wavefunction _defines_ "space itself".
Space "density" continually increases as a function of time. Analogous
to being inside a black hole, yet we do not feel the crushing force,
because our atoms are shrinking in correspondence to the increasing
density of space-time. We are, after all, made OF space-time.
Yes, the laws of physics break down at the "Planck scale" which is the
basis of the conjecture. From chaos, comes complex self organization and self configuration.
order-->chaos-->order--> ... chaos-->order...
Lee Smolin might be onto something with his wild idea that black holes
give birth to new universes. I take the logic one step further and
postulate a theory of quantum gravity. Our universe could really be
the inside of a collapsed star from a parent universe. The physics for
a compactified dimension of radius R is the same for the physics of a
compactified dimension of radius 1/R. There is no need to hypothesize
an external hyperspace for the "baby universe" to expand into. As the
star collapses, approaching the Plank scale, it becomes a chaotic
"quantum foam". This chaos self organizes into a compressed quantum
universe.
So what we observe as an absolute spacetime expansion is not really
true. The expansion is relative. From a local perspective, the
universe appears to expand with radius R. From a global perspective
energy density is compressed with radius 1/R.
If the locality principle is not going to be thrown into the trash
heap, then a viable option is that space is something analogous to
homogeneously distributed probability density functions(a perfect
fluid?) i.e. increasing energy-density gradients, giving the observed
thermodynamic arrow of time. The observed cosmic expansion is, again,
a "relative" one. A perspective effect from our local vantage point. A
shrinking object gives the illusion of receding motion. Increasing
*refractive* density gradients give the appearence of a
doppler-red-shift. Space increases density as matter is gravitationally "re-configured".
That is to say, the affine connections can always be transformed away locally, by transforming to any local free fall frame, which means basically that space-time is locally flat. The affine connections can be transformed away and the metric tensor will be reduced to that of special relativity.
Whenever matter is present, the Riemann curvature tensor is not zero. Even though the affine connections can always be locally transformed away to a "free fall" frame, the Riemann tensor is a tensor. One property of tensors is that if the tensor in question is not zero according to one frame, it is not zero according to any frame. Spacetime curvature, or a nonzero Riemann curvature tensor, is always present when, and where, there is any kind of matter, whether or not the affine connection has been locally transformed away. Matter intrinsically produces a field of curvature, not a field of Newtonian acceleration.
In the sense of spacetime curvature, gravity can never be transformed away, while the Newtonian acceleration field can always be transformed away. So from a general relativistic perspective, objects appear to accelerate because they follow geodesics on a curved spacetime. In general relativity, the field is actually a curvature field, i.e. the Riemann curvature tensor.
So when there is matter present, Enstein's "field" equations imply that the Riemann tensor is not zero in the presence of it. The Riemann tensor is then the "field" of spacetime curvature.
