**Cosmology and our View of the
World**

**Multiple Universes****
Lead: ****Adam Mirando & Erica
Westerman**

**3/20/2007**

**Summary by Melissa Russell**

**Multiple Universes**

The presentation lead by Adam Mirando and Erica Westerman was on multiple universes. The class began with the definition of a multiverse, which is a set of disconnected space times. A universe was described as a model of connected space time, and a universe domain is an observable universe or some similar part of space-time, such as our cosmic horizon. A model of single connected space time in the sense of chaotic inflation models was defined as a multi-domain universe.

Adam started the conversation off with the topic of wormholes. These were illustrated
as a topological feature of space-time that connects two locations of the same
(intra-universe) or different (inter-universe) universes. The linked
graphic (Fig. 1) shows what a wormhole could possibly look like.

Einstein and Nathan Rosen postulated that this could occur when a black hole
and a white hole connected. The problem with this was that John Wheeler and
Robert Fuller concluded that this would be extremely unstable and pinch off
immediately. Mike Dunn inquired about the definition of a white hole. Professor
Moebius explained this by saying white holes are continuously expanding. The
universe can be seen as a white hole and that matter may be disappearing beyond
the boundary of our observable universe. Matter leaves the universe, however
gravitational influence does not. A black hole is where everything disappears
and shrinks. A white hole is where everything merges and expands.

Mike Dunn brought the conversation to singularities. Black holes collapse into singularities and white holes start from them. It was questioned if singularities are infinitely small, then how can matter pass through the singularity of a black hole. Sam Meehan suggested that perhaps they are the same singularity and that it folds over and touches. Professor Moebius pointed out we can only observe the event horizon but never the singularity. At the event horizon the force is so strong that not even light escapes.

Adam brought the idea of exotic matter, which is matter with negative mass and energy, this would theoretically stabilize the wormhole from collapsing and pinching off. He then went on to the idea of traveling through a wormhole. When going through a wormhole, it seems that one is traveling faster than the speed of light, but this is not really true. If the wormhole is connecting two parts of space that is folded over, as seen in Figure 1, then the person is not traveling the full length from point A to point B, but is merely taking a short cut. Thus while it may seem like they are traveling faster than the speed of light, they are not. Erica Westerman questioned if this meant that people could travel through wormholes but light could not. Adam suggested that the theory said nothing about light not being able to travel through wormholes.

In response to Professor Davis’ question about there being empirical evidence, Adam mentioned that although there were no observable wormholes, they are compatible with the theory of general relativity. Theoretically it is not disallowed. Mike Dunn continued the conversation by asking if black holes could be observable. Professor Moebius brought up that although we cannot see into black holes doesn’t mean we cannot their effects, such as their gravitational influence. If a black hole was stumbled upon, you would only be able to see up to the event horizon and no farther. Beyond the event horizon there is no information available to us. The only things that can change the event horizon are rotation of the black hole and an electric charge.

Adam then moved the topic of conversation to Tegmark’s Taxonomy of Multiple Universes. Level one was comprised of an open multiverse where the universe is spatially unbounded with an infinite number of observable universes all connected by space-time. Due to the fact there are an infinite number of observable universes in this open multiverse, there are bound to be duplicates. The theoretical closest identical copy of an individual may be 10^(10^29) meters away. The most controversial issues with this theory are that there is an infinite number of universes and that it is unclear how the big bang plays a role. Mike Dunn proposed that if the universes are side by side and expanding they could potentially overlap. Sam Meehan brought up the point that if it is overlapping in our domain, because it is within our domain it is indistinguishable. Professor Davis remarked that if this were the case then we should notice things moving towards our universe which is not the case. Professor Moebius then explained that if the system on the whole is expanding, then every thing would be moving away from the other parts. This was equated to baking raisin bread, as the bread expands the distance between the raisins increases. This idea moved the conversation to infinite expansion, which is what has been perceived in our observable universe. Other galaxies appear to be moving away from us and each other. Professor deVries asked for clarification of whether this was unbounded or infinite. He found it was easy to visualize and unbounded expansion, but that the idea of an infinite expansion would be like adding to the set of natural numbers and that doesn’t make sense. This brought Professor Moebius to a sphere model.

From a mathematical stand point a sphere will transition to a plane, as the radius goes to infinity. If there were a pattern on the sphere, there would be the same pattern on the plane. The plane then can be stretched to infinity. Professor Davis didn’t agree that one could expand the sphere to infinity to get a plane and then stretch that to infinity. He claimed it has gotten bigger after it has been taken to the limit. Here the conversation turned to creating curvature. Saddle shapes are always open and have negative curvature. Moebius proposed that a pattern on a saddle shape that expanded would lend it self to a larger version of the original pattern. This theory was said to apply to flat surfaces, negative curvature, and the third and fourth dimensions. Professor deVries pursued the idea that any curvature that went on long enough folded back into itself. Professor Moebius countered this by using the saddle example. If a cross-section of a saddle were taken it would become a parabola or a hyperbola, two shapes that would never fold into themselves upon expansion due to their straight asymptotes. It was agreed upon that the flaw in the sphere model arises when lines are drawn on it, because there is a finite number of lines that could be drawn. Sam Meehan suggested instead of inflating a sphere to infinity, taking a finite sphere and zooming in to the point where it appears flat. Professor deVries pointed out that you would just need more accurate tools to see that it was a sphere.

Professor Davis brought the attention of the conversation back to the space between identical people. He viewed it as there being an infinite gradient of slightly different people between the two identical people. Professor deVries suggested there were only a viable number of differences between people, and that only these mattered, so it was not infinite. Mike Dunn added that being slightly different from one person could mean they were identical to another person. Professor deVries decided to approach the problem from a sphere with at radius of 10^(10^29) meters, instead of just the two points that had been discussed.

Adam Mirando moved the conversation to level two, the bubble universe. Erica
Westerman explained that there is a foam from which other bubbles are formed.
These bubbles expand. When they slow down they create a universe, so each bubble
is its own “Big Bang.” Bubbles come from other bubbles, thus there
are an infinite number of multiverses. Each bubble is much larger than our observable
universe. “In essence, one inflationary universe sprouts other inflationary
bubbles, which in turn produce other inflationary bubble.” *ad infinitum*.
Sam Meehan and Professor Moebius conversed trying to explain how the bubbles
were expanding. It was decided upon that the bubbles are generating their own
space through expansion, not expanding into preexisting space. Thus there is
no overlapping of the bubbles. Professor deVries suggested to look at the situation
as everything is shrinking instead of expanding. From the perspective inside
the bubble it could look like everything is expanding, but this would be due
to the fact that everything is shrinking and the distance between them is increasing.
Sam Meehan questioned if this meant atoms are shrinking and Professor deVries
agreed. Eventually the conclusion was reached that if there is shrinking, it
would be done in a coherent way that didn’t lead to things breaking down.

Erica Westerman turned the attention to level three, quantum mechanics. This has two processes to explain things. Process one was the discontinuous change brought about by the observation of a quantity with eigenstates. Process two was the continuous, deterministic change of state of an isolated system with time according to the wave equation. From these two processes parallel universes arise from all the possible eigenstates being available in a quantum mechanical wave function. The parallel universe model addresses the issue of one being realized and the others disappearing by assuming they are all realized, but each one in a separate parallel universe.

Schrödinger’s cat was explained as a cat in a box with radioactive material that has a fifty percent chance of decaying within an hour. If it did decay a hammer would smash a vile of poison that would then kill the cat. When the box is closed the cat could be dead or alive, but you don’t know until the box is opened. One interpretation that Erica mentioned was that, because the lid has not yet been opened, there is a period of time when the cat is both dead and alive. Professor Davis pointed out that Schrödinger made this concept as a parody. Erica Westerman then applied the idea of Schrödinger’s cat to parallel universes, for every solution there is a different universe.

Adam Mirando turned the conversation to the fourth level which consists of other mathematical structures. It suggests that mathematical equations don’t just describe aspects of the physical world, but all aspects of it. This is based on two assumptions: that the physical world is a mathematical structure and that all mathematical structures exist in the multiverse in a physical sense. Mathematics fits almost perfectly with the observable natural science. In general most things can be defined in mathematical terms. These can be compiled into a set of theoretical models. Professor Moebius brought up that in the physical world many things that we can observe fit a mathematical structure, given enough time for analysis. This does not necessarily mean that any mathematical structure that we can produce has to exist in the physical world. Sam Meehan questioned whether we conceive a mathematical structure, something comes into the physical world or was it always there. Professor deVries responded that in order for us to discover a new mathematical structure we very often have to impose a new physical structure that is a new system of notation and rules to manipulate the system. The relationship between mathematics and the physical world is very complicated and Professor deVries felt the conversation was over simplifying the relation. Wigner (1967) claimed “The enormous usefulness of mathematics in the natural sciences is something bordering the mysterious… there is no rational explanation for it.”

Adam Mirando moved the conversation to the second assumption, about why these particular equations with their specific constants work for our universe and not for others. The only conclusion to the reason why the equations work in our universe is that we wouldn’t be here if they didn’t work. String theory was quickly mentioned, Professor Moebius explained that scientifically we are not there yet, no decisive observational tests have been suggested yet. Professor Moebius continued on the testing of mathematical models and how they are used until the model does not support the observations and then thrown away. The conversation was concluded with the a graphic that shows the connections that can be made between the different levels.