On The Matter Of Space

Putting the Pieces Together

Symmetric and Anti-Symmetric

Everything will already fit together if we are willing to give up some accepted notions. It is true that the metric tensor gives complete knowledge of the geometry of spacetime. This does not mean it gives complete knowledge of the physics of spacetime. We already know this for example with Killing fields. These fields represent a hidden symmetry in the metric. Such symmetries surely are part of the physics of spacetime. They are admitted by specific metrics, but are not evident in the metrics themselves. Such symmetries can be viewed as something going on below the level of the metric. That is precisely what we have described above. Gauge transformations of the metric can be broken down several ways. One way is a metric gauge tensor that can be split into symmetric (gravity) and anti-symmetric (electromagnetic) components. Once again, refer to my paper to see exactly how this decomposition works with metric tensors.

Fictitious Forces and Absolute Forces

Symmetric tensors can be diagonalized and normalized by a change of coordinates. Gravity and the other “fictitious” forces: Coriolis, centrifugal, can be made to disappear locally also, by choosing a proper coordinate system. Anti-symmetric tensors cannot be diagonalized (with Real numbers) and normalized. Likewise electromagnetic fields cannot be made to disappear with any coordinate transformation. The mapping between gravity and symmetric gauge fields and electromagnetism and anti-symmetric fields is obvious. Actually, that’s what started me off on this back in graduate school, c.1978. Like a fine wine, some things take time.

Special Relativity for Gauge Fields

Tensor Waves and Vector Waves

The Klein-Gordon equation with is the wave equation. Consider a symmetric tensor gauge field. It is symmetric so it is a gravitational field. Each component must satisfy the K-G equation. For we then have both gravity and a wave, gravitational radiation. If we use such a gauge field in the Einstein equation we get a mass-energy tensor on the right hand side that is identical to the result from the (approximate) linearized theory. Only now it is exact and covariant, i.e., a real tensor. The tensor has zero trace which means this wave has no rest mass so it travels at the speed of light.

Now consider a vector gauge field. Its antisymmetrized derivative is the EM field. Once again each component must satisfy the K-G equation. Also again if we have , then we have an EM field that is also a wave, an electromagnetic wave, light. If we put this as a gauge field in the Einstein equation we find that the mass-energy is zero. So this wave is also massless and travels at the speed of light. But also, the entire tensor is zero, not just the trace. This means that although light follows gravitational fields generated by masses, it is not a source of gravity itself. This is new. It is at odds with current accepted theory that puts the EM field’s stress-energy tensor, by hand, into the right hand side of the equation. There is no experimental result to back that up. To see what the impact of this is on the Equivalence Principle (EP), and how this relates to antimatter – you guessed it – check out my paper.

Negative matter

Antimatter mass and gravity

So what about antimatter? Current theory says it should behave exactly the same as matter. We now know that is true for the inertial mass of antimatter – it has been precisely measured for antiprotons and is the same as for protons. But what about its gravitational mass? The EP says it should be the same also. The EP is only known, experimentally, to apply to matter. That is because neither the gravitational field of EM radiation, nor that of antimatter have ever been measured. You would have to have an such enormous amount of EM energy in the form of waves to test it for gravity that it is unfeasible (except perhaps for the radiation dominated epoch of the Big Bang. There should be set to affecting evolution of cosmic time scales). However, how antimatter falls on Earth has recently been measured at the ALPHA project working on the LEAR (Low Energy Antiproton Ring) at CERN. They found that antihydrogen falls down like hydrogen. What does this mean? It means that anti-H is a tiny “test particle” that will follow the geodesics dictated by the Earth regardless of whether it has a positive or negative gravitational charge according to GR. (The gravitational potential at the “surface” of an antiproton due to the Earth is about times that of its own potential). If you want to see the details of the difference between matter and antimatter gravity – check out my paper.

Baryon Asymmetry

This is the name given to the question – where is all the antimatter? If it’s the same as matter and was created in equal amounts during the Big Bang, where is it now? It can’t be in any of the visible galaxies. They and their clusters are bathed in hot gas and we would see the characteristic annihilation radiation. It’s out there, together, beyond the cosmic horizon, having segregated from matter in the early epochs due to their mutual repulsion. It’s all in my paper.

The Big Bang

Equal amounts of matter and antimatter equally interspersed has zero energy and zero metric. That is no space and no time – a true vacuum. That is an appropriate boundary condition for t=0. Although we cannot see past decoupling, this working hypothesis is more reasonable than inflation and the initial singularity. So the universe put on weight over a period of time rather than coming into being infinite, hot and fast. Starting truly empty and cold, it grew, condensed, heated, ignited and then decoupled. The main point being that decoupling was approached from zero temperature and density rather than from an infinite singularity. Here is an actual simulation (re-scaled as it expands) to illustrate the process shown on the right, with 2217 discrete points emulating the continuum.

Here is the same simulation data mapped onto the 3D surface of a 4D sphere (with one spatial dimension suppressed) to the right using a FLRW metric with a spherical spatial section. It is continuously rescaled to compensate for the expansion. This indicates an evolution to separate matter and antimatter regions. Today each region is beyond the horizon of the other. This explains the baryon asymmetry.

Below are graphs of kinetic and potential energies over time showing a zero energy beginning, the creation event occurring over time, then each specie virializing as they approach their steady state, but still decreasing in energy as they move away from each other.

The Matter Of Space

and finally … what is The Matter Of Space? It is matter. As mentioned above, these gauge fields are distortions of coordinates – displacements of events in spacetime – which appear as forces. Analytically different types of gauge tensors represent the different forces, but it’s all in one tensor – a true complete unification. These gauge tensors give rise to the mass-energy tensor by the Einstein equation. So what we see as matter is simply a distortion of spacetime. In fact, matter condenses from spacetime the same way water, or ice, condenses from vapor. Just as they coexist in equilibrium in a closed vessel, so do spacetime and matter coexist in the universe. To avoid singularity as matter condenses it pulls inertia from spacetime. They are made of the same substance: matter, space, (distortion) field, a Higgs-like field. Call it what you will, there is but one thing giving rise to all things. And of course, check out my paper.

Metaphysics

Ultimately these spacetime displacements distill down to information about each event, perhaps all the information there is about an event. If the universe is nothing but information – as many physicists suspect – what is its relationship to consciousness? Is consciousness at is essence dynamically changing information? If so, can we consider consciousness a prerequisite of the universe, the sine qua non of existence? Is the universe a conscious Universe? Is the Universe, along with its massive complexity – arising from a simple Already-Unified Field Theory – a very clever idea in the mind of God? For my next paper ….