Sometimes an answer appears to a question that wasn't even considered at the time. Looking at a progressive 3D slice of a hypertorus makes one think about what the spacetime manifold looks like over time. Not just for the first instant but how it is shaped over all of time. The first instant of time may actually be symmetrical to the shape of the present space manifold. But maybe only looking at it from a side view instead of a front view, in a manner of speaking. This has the beauty of simplicity. It implies that the manifold is fixed and unchanging. It is only the matter of understanding the nature of momentum traveling along the manifold.
The figure of a hypertorus being progressively sliced leads to an observation similar to the description for the breaking of symmetry. What it implies is that symmetry was never broken. It is only the type of observation that makes it seem so. The slicing of a hypertorus and presenting the individual cross sections in a progressive scan leads to an impression of progressive transformation. In reality, all the cross sections are connected.
Consider that what looks like an ellipsoid in the first image is just an orthogonal view of the double pairs of torus in the center view. The first ellipsoid image may look like the first instant in time, immediately after the 'big bang'. But a point in the present time has exactly the same manifold structure as the first instant. Calling the first instant something unique and special is like calling the north and south pole the first instant of the planet. They are special only to our planet, but even then due to rotation. [While there may be rotation of the manifold, a non zero spin, which does make the points unique, a question of spin with respect to what (back to Mach's view).] The assumption here is that with respect to a manifold there is no spin or rotation. The first instant is not unique.
We may observe microwave background radiation, and deduce that all the energy and mass now present in the universe all existed at a single point for an instant. But this deduction may be one possible explanation for what is observed. Considering that mass-energy curves spacetime, one would have to conclude that the point at the first instant would make the manifold look different than it does now. That is an assumption that there was the starting point. It is only when scanning through the manifold cross sections that breaking symmetry is seen. It can be expected that the manifold seemingly changes as a result of the expansion. While the manifold may, in fact, not be in expansion. Only our observation makes it special. It would be similar to looking through a lens. When one is viewing through a lens, there is a special point on the other side of the lens, but only because there one point from which we are making the observation. Every point of observation has one point that is associated on the other side of the lens. But there is not a point truly unique. One may argue that the focal point is unique because the corresponding point is at infinity. Points at infinity are not unique in my understanding of projective geometry. What is the being observed when looking at microwave background radiation?
The possibility that the manifold is actually fixed in size allows for the possibility that what we observe is just a close up of the zero point energy of vacuum. Instead of gravitational lensing effect, it is a global spacetime lensing effect. Viewing from the far end of spacetime a particle on this side of the universe may may observe the particle pair production interior to an electron as microwave background. Zooming in closer and closer to the ideal center point of an electron, raises the mass of particles to ever higher and higher energies. The negative energy calculated in renormalization prevents us from seeing the infinite limit of particle energies. The negative energy from renormalization should be able to be applied during the first instant of time.
We may conclude that every particle can be viewed as a big bang event, when viewed from the opposite side of the universe.
This makes for a most unusual cosmology however. It would state that the spacetime manifold is fixed and unchanging. The momentum traveling throughout its dimensions may be in constant flux. This creates a universe that seemingly different than what we experience. We experience a flat progressive universe. Our observation is based on the constant speed of light. This creates cross section observations of the universe. Our observed first moment of the universe may be just a view of the the structure of an electron. What we see, as the big bang at that first instant, may be nothing more than a static particle.
Last updated: April 10, 2002
©2002 Robert D Rutkiewicz