Cosmology and our View of the World
Lead: George Clark & Morgan O’Neil
Summary by Ben McBride
George and Morgan began class by sending around a handout containing four theories on the subject, an explanation of the theories, definitions of keywords, as well as critiques and opposing theories. George and Morgan then began their PowerPoint presentation.
The first question asked was from where did the idea of multiverses come? The answer is that theory came from physicists and mathematicians as a result of such theories as string theory and M-theory. Clark and O’Neil then stated that there are two ways the possibility of multiverses may arise: through mathematics and by intuition. The way multiple universes may arise mathematically is that a mathematical formulation may come to the point where in order for it to be self-consistent the possibility for multiple universes must exist in the form of multiple solutions. The concept of multiverses may arise intuitively by asking ‘what if’ questions, and pushing the extent of our knowledge.
George and Morgan then introduced four levels of multiple universe theory:
• Level I: Open multiverse
• Level II: Andre Linde’s bubble theory
• Level III: Hugh Everett III’s many-worlds interpretation
• Level IV: The ultimate “Ensemble theory” of Tegmark
The open multiverse theory calls for an infinite universe, and since the universe is infinite, every possible combination of atoms must play out eventually so that a carbon copy of yourself may exist 10^(10^28) light years away.
Andre Linde’s bubble theory arrives at multiple universes through fluctuations in the quantum foam. There exist peaks and valleys in the level of quantum fluctuations and at each valley there is a stable universe. This theory says that the Big Bang occurs often and parallel universes exist in which the laws and properties can vary greatly from our own. Bubble theory fits in well with inflation theory, which says that the early universe went through a period of exponential expansion driven by a negative pressure energy density. Quantum fluctuations in the universe during this inflationary period gave rise to the structure of our universe in the form of galaxies and vast expanses of empty space. On cosmic scales, if the separation between two receding objects is large enough, the separation of the space between the objects will exceed the speed of light. As Professor Möbius pointed out, this can be explained by the existence of a repulsive force, or by the explanation that space itself is loaded with energy that drives the universe apart.
The many worlds interpretation is one of several interpretations of quantum mechanics. Morgan then stated Heisenberg’s uncertainty principle that an object’s position and momentum cannot both be known precisely, that there is a minimum level of uncertainty to all measurements. She also used the example of Schrödinger’s cat to demonstrate uncertainty in quantum mechanics. Professor Möbius then explained Schrödinger’s cat paradox with the following explanation: A cat is locked in a box with a Geiger counter and a tiny amount of radioactive substance. The substance is so small that in some prescribed amount of time, say an hour, the substance will have equally probable chances of decaying or not decaying. If it decays, then the Geiger counter triggers an apparatus that opens a canister of poisonous gas that kills the cat. If it doesn’t decay, then the canister is left unopened and the cat lives. The question is after an hour, is the cat alive or dead? Until a measurement is made, there is no way to know. Therefore, until making a measurement, the cat has a 50% chance of being alive and a 50% chance of being dead, or taking the combination of the radioactive nucleus, the mechanism, and the cat as one quantum system with superposition the cat is both dead and alive. Once a measurement is made, then the cat can be determined to be alive or dead.
George stated that the ensemble theory of multiple universes states that any mathematically consistent universe may exist. Any mathematical description may exist in the physical world. Professor Möbius clarified this definition that any mathematical description can be included in the ensemble of possibilities. Professor deVries then interpreted this statement to mean that there cannot be mathematically inconsistent universes.
After describing the theories, George explained a two-dimensional image that contained multi-colored bubbles all branching from one common source. He said that the different colors denoted different physical laws and therefore different universes. He then went on to describe universal Darwinism. His explanation is that a black hole may exist within a universe and collapse to form a new universe with the genes of the universe from which the black hole came.
Morgan then described the possibility theorized by Linde that the bubbles may inflate into one another, and that physical laws will change if universes merge. In this way, Linde believed that eons into the future, bubble theory may be a testable theory. If the physical laws ever change, then he believes it is evidence of two universes inflating into one another.
Professor Möbius then stated that this has been refuted, at least up to now, because the physical constants have been determined to be constant to a high accuracy over the life of the universe.
Morgan explained the possibility that a zero energy universe could have arisen from nothing without violating the conservation of energy. Since gravity is an attractive force, it has negative energy, and if there is enough gravitational energy in the universe to negate all of the positive energy attributed to all the mass in the world, then our universe will have a total energy value of zero. She then went on to explain that bubble universes are created by quantum fluctuations in space-time foam. Once they reach a critical energy, they give birth to a new and different universe.
The question was asked why gravity provides for negative energy to balance out mass. Professor Möbius explained that a satellite requires energy to be sent away from earth and that at a location infinitely far from earth the gravitational energy due to earth is zero. Also, gravitational potential energy increases with distance (the higher an object is above the surface of the earth, the more potential it has). Since the gravitational energy is zero infinitely far away (the maximum distance away, therefore the maximum potential energy) gravitational potential energy must be less than zero at closer locations.
Professor deVries offered another explanation that at infinity the total energy of an object is zero and we know energy is conserved. As this object comes closer it travels faster and faster the nearer it gets. Since we know an object traveling with increasing speed has increasing (positive) kinetic energy, then the gravitational potential energy must become more negative at the same rate in order to produce a net energy of zero.
Professor Möbius defined Planck time as 10^-43 seconds, and that below a Planck length (the distance traversed by a photon traveling at the speed of light in one unit of Planck time) the universe could have spontaneously popped up from a vacuum. Professor Möbius then explained that Linde came up with a mathematical model that has a fast expansion at first that later settles down. With slow expansions, space-time must be flat. When the universe is expanding rapidly, space-time develops certain shapes that he can describe mathematically.
George then defended the theory of multiverses against the claim that it is bad science. He said that before we throw it out as a theory due to a lack of empirical evidence, we must wait for technology to catch up to be able to test the theory. Theories must have predictive powers, and string and bubble theory haven’t developed predictive powers yet, partly because these theories aren’t advanced enough and partly because our technology isn’t sophisticated enough to carry out experiments that would test these theories.
The Inverse Gambler’s Fallacy is an argument against multiverses. The fallacy would be that the existence of other universes doesn’t make our highly evolved universe more probable. If you flip a coin 10 times and get heads each time, the eleventh flip will still have a 50% chance of being heads even though one might think it is more probable that it will be tails.
Vasiliy asked how the number 10^(10^28) was found. Morgan replied that it was a back-of-the-envelope calculation.
Professor deVries then asked what the levels of multiverse theory are, and Morgan replied that they are a hierarchy of comprehensiveness starting with level I (the least comprehensive) and ending with level IV (the most comprehensive).
Marty Rowley asked “What is a singularity” and Morgan responded that a black hole exhibits a singularity because it has infinite density and infinitely small volume. Professor Möbius added that the gravitational potential energy of an object approaches infinity as its size approaches zero. Quantum mechanics saves the physical singularity because an object with zero volume cannot exist. Since gravitational force obeys an inverse-square law, as the radius of an object approaches zero, the force it provides approaches infinity because the denominator becomes zero. Therefore any law that behaves as an inverse-any-order relation will provide a singularity as the variable in the denominator approaches zero. Dr. Davis went on to explain that we’re in a universe where 1000 throws of a coin came up heads. He continued to say that we have no evidence to prove it had two sides that it could have been just a one-headed coin. He also stated that the constants could have other values and asked how we can test for these other values.
Vasiliy asked how new universes arise through black holes. Professor Möbius
explained that beyond the event horizon of a black hole we cannot retrieve any
information. Therefore, it is possible for a new universe to develop within
the event horizon of a black hole.
Marty Rowley asked if the theory of multiverses permit time travel. Morgan responded by saying that Stephen Hawking used to think that time travel into the past was possible through black holes.
The question was asked if black holes lose mass. Professor Möbius then
explained that black holes must emit radiation in order to obey the laws of
thermodynamics. A temperature can be assigned to a black hole, and the smaller
the black hole, the hotter the temperature. It is theorized that as the black
hole radiates and loses its mass, it becomes smaller and smaller and therefore
hotter and hotter until it evaporates. Black holes would theoretically explode
in a gamma ray burst. The gamma ray explosion of a black hole has not yet been
Becky asked for a clarification between parallel universes and multiverses. George said they are used interchangeably in the literature, but Professor Möbius said that the many worlds approach encompasses multiverses, but that multiple universes don’t necessarily imply that the universes are parallel.
Professor deVries asked about how time is affected with inflationary theory. With Einstein’s proof that space and time are inextricably intertwined, shouldn’t time be affected when space is expanding at an unusual rate? Professor Möbius said that he hasn’t seen a special treatment of time in the inflationary theories. He also stated that with space expanding during inflation, Einstein’s general theory of relativity must be employed; his special theory can’t be used to explain this epoch. His special theory of relativity states that nothing can travel faster than the speed of light, but the special theory of relativity applies to objects within space, and not to space itself.
The question was asked what lies between the multiverses in bubble theory. Professor Möbius replied that looking at the bubbles in three dimensions does not allow interpretation. String theory contains 10 dimensions and M-theory has 11. The “stuff” between multiverses exists in the higher dimensional theories. The three dimensional interpretation of a four dimensional hyper sphere begins with a point, then expands into a ball, then shrinks back down to a point and then disappears.
Neal asked if space isn’t a “thing” how can it expand. Professor Möbius responded by reiterating his raisin cake example that universe is represented by a model of a raisin cake and the raisins (galaxies) are receding from each other while the cake (space) is expanding. He also pointed out that the cosmic background radiation provides us with a reference frame for the original description of the space we are in. Space itself is defined by the mass contained therein (as shown by general relativity), and the shape of space is connected to the mass within it. Mass and space are always interconnected.
Professor deVries set up the empty conjecture that over night the universe and everything in it doubles in size. Would this change be theoretically detectable? Professor Möbius responded that ten years ago it wouldn’t be, but since the belief that dark energy is inherent in space has arisen, this change would in fact be detectable.
DJ asked if we can observe one or two dimensions, since our world is three dimensional. deVries stated that we can see the surface of objects and a surface is a two-dimensional abstraction from the three dimensions of the objects.
Cesar asked why there is always a probability in quantum mechanics, and not an absolute prediction. Professor Möbius explained that light has finite wavelengths and that detecting an object smaller and smaller requires shorter and shorter wavelengths, and therefore higher and higher frequencies, thus higher and higher energies. Eventually the wavelength is so small that the energy of the photon measuring the object is so high that it blows the object away. Professor deVries added that even if the speed of the receding object was measured and the energy of the photon was known, there would still exist a fundamental uncertainty due to the nature of quantum mechanics.
Professor deVries asked how hidden variable theories have been disproved. Professor Möbius responded that the Aspect experiment has proven there are no hidden variables. The Hidden Variable Theory says that nature is deterministic, but the Aspect experiment disproved this theory. Professor deVries noted that it drove Einstein mad that the world was inherently indeterministic. He also pointed out that measurement error is completely different from quantum indeterminism.
Neal asked if experiments were performed on a collection of particles and they used the probabilities to infer information about individual particles from the result of the experiment. Professor Möbius affirmed this statement, and Professor deVries added that the properties of either particle are indeterminate, or there exists non-local causation, which violates Einstein’s cosmic speed of light limit. Either way, Einstein doesn’t agree with the result.
With measurements, there exists an initial state and a final measured state. In between the two states there is a coupled state. Quantum mechanics says that the objects behave as waves in between the initial and final states, and upon measurement, the objects become particles. This is the wave-particle duality in quantum mechanics.