Wednesday, September 26, 2012

What does the universe look like?

Our universe is a wrinkled 3D surface on a 4D sphere. To image what this looks like, start by thinking about the wrinkled 2D surface of the 3D spherical earth, but realize that this is only an analogy of what a 3D surface looks like on a 4D sphere. Just as the Earth is not a perfect 3D sphere, the universe is not a perfect 4 dimensional sphere. On Earth, there are valleys and mountains. Likewise, the surface of the 4D sphere is wrinkled due to the inhomogenity of mass/energy. As Einstein showed, the 3D surface of the 4D sphere is curved at different points on the surface depending on the amount of mass/energy. The 3D surface curves into the 4th dimension (time). The time dimension is the radius of the 4D sphere. For example, the Sun's mass/energy causes the change in the curvature of the 3D surface, and it creates a small valley about which the planets can orbit around in ellipses.

On average, the mass/energy causes the universe to take the shape of a 4D sphere but near locations of large amounts of energy/mass, the 3D surface curves more than the average curvature...this is like a valley caused by an impact crater which has more curvature than the average curvature of the Earth's surface. The location of the center of the large clump of energy/mass is lower than the surrounding environment. What I mean by lower is nearly the same as what we mean by lower on Earth. Here, lower means closer to the center of the Earth. In the 4D sphere, lower means closer to the center of the 4D sphere. And since the radius from the center of the sphere to location of the energy/mass is what we mean by 'time', the center of energetic/massive clumps of particles is actually further back in time. Around us, the clumps of mass/energy are like tiny valleys, but there are locations like blackholes in which the well is so deep that particles that fall into the well are so far back in time that they can't travel fast enough to catch back up to our present time near the surface of the 4D sphere. Since we live on a 3D surface, there is no edge to the universe. In any direction you look, all you see more galaxies. And if you look really far away in any direction, all you see is photons from the aftermath of the Big Bang.

Stated again, the universe as a wrinkled 3D surface on a 4D sphere, and the size of the wrinkles is proportional to the amount of mass/energy (and momentum/shear to be precise) at any location. But that's not it. The universe is actually getting larger. The Earth is not getting larger, but one can think about the increasing 2D surface of an inflating balloon to get a feel for this inflation. Points on the surface of the balloon are getting further apart. The evidence we have for this is the red-shift in photons from distant galaxies. The further away the galaxy is, the more the photons increase in wavelength. It's like the fabric of space itself has increased during the time that it took to travel from the galaxy in the past to our galaxy in the present. Space itself has increased over time...but this is redundant statement because the total  surface area of sphere obviously increases as the radius from the center of the sphere to its surface increases. Time is the radius of the 4D sphere (the radius is not the same at all locations.) On average, the radius is increasing, but locally, the radius can decrease (such as for a blackhole.)

The question is: why is the radius of the universe expanding on average? Einstein's theory of general relativity can tell you about how space-time is curved by mass/energy, but it doesn't specify the actual shape of the universe, and it doesn't specify whether the surface area will increase, remain the same or decrease. It's just an equation, not a solution. So, in other words, the answer to the question of why the universe is expanding is still not completely known, but here is my best guess based off of the evidence available presently about the universe:

The total 3D surface area of the universe can only increase (or remain the same if it reaches a final equilibrium.) The surface area of the universe is proportional to the discrete, finite entropy of the universe (See http://arxiv.org/pdf/1003.1528v3.pdf). The entropy is extremely large, which is why the universe is extremely large right now. The 3D surface area encodes the entropy of the universe...in other words the 3D surface encodes the exchange symmetry group of the universe. As the exchange symmetries between similar particles of the universe increases, the surface area increases. The surface area increases due to irreversible processes that increase the symmetry group of the universe. Irreversible processes require the weak nuclear force and either (a) gradients in temperature/composition or (b) an increase in the number of exchangeable particles. The weak nuclear force is the only of the four known forces that breaks space-time reflection symmetry, and because that force is not time reversible, the weak nuclear force can actually increase the exchange symmetries between particles. Basically, my argument here is that these irreversible processes can increase the exchange symmetries and that this information is encoded as an increase in the surface area of the 4D sphere. While the surface area might decrease in some locations, it can do so only by increasing the surface area in other locations (i.e. the total entropy only increases.) The effect of an irreversible process is to encode information (symmetry information) into the surface of the universe, which has the effect of locally increasing the surface area. When there are lots of irreversible processes, the total surface area increases. The amount of increase in the surface area depends on the amount of gradients in temperature/composition, and it depends on collisions between particles that can interact via the weak nuclear force. This is why photons, which are bosons and don't interact via the weak nuclear force, can travel such long distances without converting into lower energy photons. This is also why superfluid helium (a boson) can move without friction or why superconductors can conduct bosonic electrons without electrical resistance. Elemental bosons don't interact via the weak nuclear force. If there were no weak nuclear force, the surface area of the universe would have to remain the same, and hence average radius to the center of the universe would likewise remain the same. If the exchange symmetries of the universe were to reach a maximum (such as if all of the universe were super-cold neutrinos in a perfectly distributed across the surface of the 4D sphere), then the surface area would stop expanding and time would stop (i.e. the radius would have stopped increasing.) [When and if this will happen is still an open debate]

The total mass of the universe stays the same, so on average the universe stays in a 4D spheric shape even as it expands. Mass/energy is what is causing the universe to make a spherical shape. If there were no mass/energy, space time would be like a flat surface that extends in all directions, and it would be perfectly flat if there were no mass/energy. The presence of mass/energy causes space-time to turn into a 4D spherical shape. Irreversible processes cause the surface area to increase because the information associated with the symmetry group of the universe is encoded on the surface. The surface has no choice but to increase in size because more information is being encoded into the surface. Therefore, the objects in the universe are forced apart and this is why we see a red-shift when we look as distant galaxies.

This means that the universe had a much smaller radius when it had a much smaller surface area. [As stated earlier, time is the radius from the center to the surface of the 4D sphere.] Most likely, the surface area was initially really small. How small? It's not clear, but this is what we mean by the Big Bang (the surface area and the radius were extremely small at some point in time.)

Most likely, the energy/mass was initial in the form of a few really heavy particles. The entropy associated with this state is extremely small because there's just not that many exchange symmetries available when there are only a few particles. Over time, the weak nuclear force caused these massive particles to split apart, and the number of particles increases. As the number of particles increases, the exchange symmetries increase, and the surface area increased as these symmetries were encoded into the surface of the sphere. But since there is always conservation of energy, the average temperature of the universe decreased. (The temperature is the ratio of the energy compared with the entropy...i.e. a ratio of the total mass/energy divided by the total entropy or a ratio of the total mass to the total 3D surface area. Since total energy/mass is a constant, the average temperature is inversely proportional to the total surface area.)

Over time, the weak nuclear force continued to break particles apart. For example, top/bottom quarks turned into strange/charm quarks and up/down quarks, while releasing leptons (electrons/neutrinos.) The exchange symmetries of the universe started increasing rapidly as the neutrinos were created from heavier particles because now there are a lot more exchange symmetries (entropy) for the same amount of energy. As the exchange symmetries increased, the surface area increased and matter started spreading out. There was an abundance of neutrinos throughout the universe because they came from the breaking apart of the massive quarks at the early stages of the universe. Collisions of quarks and anti-quarks created massive amounts of neutrinos (and likely not equal amounts of neutrinos and anti-neutrinos since the weak nuclear force violates CP symmetry.) Neutrinos are essentially the lowest energy state for matter. The remnants of the neutrinos from the Big Bang are the likely the dark matter in galactic halos. We are bathed in a sea of weakly interacting neutrinos. As gradients in the neutrino density disappear, the entropy increases as the exchange symmetries between neutrinos increases. When neutrinos collide with electrons and quarks, these collisions are not time reversible because the weak nuclear force is not time reversible, just as the process of breaking apart quarks is not time reversible. Collisions of the weak nuclear force encode the symmetry group of the universe into the surface of the universe, and what's interesting is that the symmetry group of the future contains the symmetry group of the past.  (For example, the symmetry group between three particles, S(3), contains S(2) as a sub-group. The number of symmetries increases from 2 in S(2) to 6 in S(3), and then to 24 in S(4). This is what I mean by space-time is expanding. The surface area is likely proportional to the logarithm of the number of symmetry operations. Encoded into the surface is the symmetry group of the past at every point in time in the past. There is a permanent record of the past...but we can't read this record. All we can do is estimate the size of the record.)

So, now I'll step back and summarize and then conclude with a list of open questions and speculations.

(1) We live on a wrinkled 3D surface on a 4-D sphere.
(2) Time is the radius of the 4D sphere. The radius to the surface is not constant, but there is a clear relationship between the average radius and the total surface area.
(3) The center of a blackhole is further back in time than the space outside of the event horizon because the radius from the beginning of time to center of the black hole is less than the radius to the 3D space outside of the blackhole. (Think of the black hole as a really deep trench in the ocean...and a star is like a small impact crater on the surface.)
(4) The 3-D surface of the 4D sphere is proportional to the amount of entropy in the universe. (See http://arxiv.org/pdf/1003.1528v3.pdf)
(5) Entropy increases due to irreversible processes associated with the weak nuclear force. And we are bathed in a sea of neutrinos created in the Big Bang, which are likely the cause of the dark matter in galactic halos.
(6) Entropy is proportional to the logarithm of the number of exchange symmetries, and the symmetry group of the future contains the symmetry group of the past as a sub-group.

Further questions/suggestions:
(1) Why are there only 4 dimensions to space-time? Is this related to the fact that there are only 4 forces of nature, which is most likely due to the fact that there are only 4 normed division algebras (over the real numbers...gravity, over the imaginary numbers...E&M, over the quaternions...weak nuclear, and over the octonions...strong nuclear.)
(2) Are more than 4-dimensions of space-time not possible because there are only 4 normed division algebras?
(3) Is the reason that there are 3 surface dimensions and 1 radial dimension (to our 4D sphere) due to the face that 3 of the forces of nature of space-time reversible (gravity, E&M, and strong nuclear) and one of the forces is space-time irreversible (weak nuclear)?
My guess is that answering these questions will help us reach the answers to the following questions.

Open questions:
(1) Why are there 4 basic fermions (up quark, down quark, electron and neutrinos)? Why are there three families of these basic fermions (and their anti-particles)?
(2) Why do the particles have the color, charge and mass that they do?

In future posts, I'll go into the reasons why I think that we need to adjust our way of thinking about these questions now that some of the theories proposed to help answer these questions are failing to do so. (In particularly, I'm talking about the failures of string theory, supersymmetry, Grand Unified Theories, and even the failures of inflation theory to get to the heart of question of the why particles have the color, charge and mass that they do. These were all good first steps...but we need to start developing new theories that don't make predicts of particles that we aren't finding or that create more problems that they help solve.) Let me know if you are working solutions to the questions above that avoid the problems associated with the theories of string theory, supersymmetry, GUT, and inflation.