Touching The Limits Of Knowledge

Cosmology and our View of the World


Everything out of Nothing? Lead: Eberhard Möbius


Summary by Philip Fernandez

Everything out of Nothing? - The Story of the Universe

This lecture was intended to give a general overview of the history of the physical universe. It ensured that all members of the discussion have a solid foundation of background information regarding the evolution of our universe (as we understand it). The lecture began with a few anecdotes, which helped establish a genial atmosphere. The first was a cartoon with a pair of angels, with one commenting, “Ever since the big bang, God has had a hearing problem.” This was followed by this segment from the comic strip Non-Sequitur:

Link to "Non Sequitur" here!

Prof. Möbius then reflected on ideas that occurred to many of us as a child. What is the universe? Does it go on forever? If there is an edge, what does it look like? An analogy was made in which the universe was compared to the room of a building. A room has walls, which form a distinct edge. Those walls also serve as the edge of other rooms, which share walls with other rooms; the analogy can be expanded to imply an infinite number of rooms. Is this the nature of our universe? That we are but one universe in an infinite number of universes, without end?

The difficulty in determining this lies in the fact that we are unable to step out of our universe. Thus, we cannot compare our universe to others (if those others do indeed exist). The class was then shown this painting, “The Gallery” by M.C. Escher.

This painting, presented in the context of our discussion on cosmology, gives a possible portrayal of our universe. Perhaps in attempting to view the universe, we end up where we began – looking at ourselves. In science, typically one isolates the object being studied. You then figuratively step back, and study the object, without influencing the object’s behavior through your own actions. Cosmology differs from other physical sciences, because we cannot perform these actions with the universe. We cannot physically separate ourselves from the universe in which we live. It was also mentioned that one runs into very similar difficulties in studying consciousness. We cannot separate ourselves from our consciousness in order to study it – instead, we must study consciousness from within, just as we do with the universe.

Another idea compounds the problem of studying the universe: we have only one universe to study. There are billions of galaxies, stars, and planets, and in studying these objects, we can make comparisons to help us draw conclusions. Unfortunately, we are aware only of our universe, and hence we have nothing to compare it to. An identical problem arises in trying to study life or consciousness. Although there are millions of different species of life, we are only aware of one particular type of life – carbon-based life that has evolved on Earth. We have nothing to compare ourselves to. This is also true for consciousness. An individual knows only his/her own consciousness, and hence has nothing to compare it to. In practice, science requires multiple examples in order to establish scientific facts. Because our universe (from our view) is a singularity, the only way we can study it is by performing a series of independent tests, and construct a model of the universe that matches these test results.

This leads to an important point – science does not construct reality. Instead, science constructs a model that describes our observations of the universe. Through the aforementioned independent tests, we test this model, until the model becomes a theory. In the scientific community, the term theory has different meaning than its everyday layman usage. The American Heritage Dictionary gives the following definitions of a theory:

Scientific definition: a set of statements or principles devised to explain a group of facts or phenomena, especially one that has been repeatedly tested or is widely accepted and can be used to make predictions about natural phenomena.
Layman definition: a proposed explanation whose status is still conjectural, in contrast to well-established propositions that are regarded as reporting matters of actual fact.

At this point, the class departed from a lecture-style format as members became much more active in discussing the distinction between theory, law, and fact. Sam Meehan asked about the difference between a theory and a law. For example, why do Einstein’s equations for relativity constitute a theory, whereas Newton’s equations for gravity are known as the law of gravitation? An interesting point that was not actually brought up in discussion is that Einstein’s theory of relativity is actually more complete than Newton’s law of gravitation. Prof. deVries pointed out that theories are never black and white. Because of the rigorous testing that a scientific postulate must endure to become a theory, a theory is rarely completely wrong. Contrarily, there is a variation in the rightness of a theory. Newton’s gravity is a good theory, but it is not perfect. Einstein’s relativity is a better theory, because it is more complete. Returning to the argument of theory versus fact, Prof. Davis commented that a law is typically descriptive, whereas a theory is typically explanatory. In an e-mail following the class discussion, I (the author) asked Prof. Davis to elaborate on his comment. This was his reply:

You may have noted that Professors deVries and Moebius did not necessarily agree with my statement. Any lack of agreement on this point stems from the existence of different (although related) usages of the word "explanation. When I say that laws are descriptive, I mean that they do not explain the existence of the phenomenon to which they refer (although they may be used to explain its operation). For instance, Newton's law of gravitation is an equation that stipulates a certain relationship between two masses. The law can be used to predict how fast a dropped object will fall, but it does not explain why two masses are gravitationally attracted to each other. In contrast, Darwinian theory provides an extensive explanation of a mechanism (natural selection) by which evolution can occur.

Following Prof. Davis’ comments, Marcy Elliot pointed out that in science, postulates are always just a theory, because science is never absolute. Prof. Möbius was very quick to point out that although science is not completely absolute, we certainly are very sure about certain things. For example, the scientific community is quite sure that global warming exists, but is uncertain about the severity. Prof. deVries explained that the phrase “just a theory” is often misleading, because this implies theory versus fact. As explained above, it is not an elementary process for a scientific hypothesis to become a theory.

Here, the discussion took another abrupt turn as we moved from asking the “big” questions to a lecture-style period of instruction on the known history of our universe. Prof. Möbius discussed a few fundamental astronomical concepts, beginning with scaling the universe. He used a sphere approximately 15cm in diameter to represent the sun. The earth would then be the size of a pinhead, and would be located approximately 15m from the sun. This distance, the sun-earth distance, is 1 Astronomical Unit (AU) and is equal to approximately 149 598 000 kilometers (92 955 887.6 mi). Using our scale, Saturn would be located 150m away (10AU), which is approximately the distance from Morse Hall to Thompson Hall. The nearest star to our solar system, Alpha Centauri, lies 4.3 light-years from the sun. Using our scaled universe, this would be the distance from Durham, NH to San Francisco, CA. The Andromeda Galaxy is located 200 million light-years away, and the size of the universe itself is approximately 13.7 billion light-years. Note that the term “light-year” is a unit of distance, not time. It is the distance that light travels in one year, and is approximately 9.4605284 * 1012 kilometers (5.87849981 * 1012 mi). This is a very important concept in cosmology; when we look at the cosmos, we are looking back in time. The light we receive from the sun is light that left the sun 8 minutes ago. Likewise, we see the Andromeda Galaxy as it looked 200 million years ago.

How do we determine these distances? One method is through parallax, which you can easily demonstrate to yourself. Hold your thumb out at arm’s distance away, and look at your thumb with your left eye (close the right). Now, without moving your head or arm, open your right eye and close your left, and notice how your thumb moves relative to the background. This is parallax. With the use of geometry, this method can be used to determine the distances to objects that are relatively close to the earth. We also use Type 1a Supernovae in distant galaxies to determine that galaxy’s distance. This type of supernova is called a standard candle, because it always outputs the same amount of light. From its brightness, we can deduce distance using the 1/r2 relationship.

Prof. Möbius then presented a bit of history, both philosophical and scientific in nature. In the 19th century, it was believed that the universe was infinite in both age and size. But, a 19th century physician and an amateur astronomer named Olbers presented an argument that became known as Olbers’ Paradox. Olbers postulated that if the universe is infinite, then there must be an infinite number of stars. If there were an infinite number of stars, then the night sky should be completely filled with light.

In the early part of the 20th century, Edwin Hubble determined that the universe was indeed finite. He found that identical spectral lines from different galaxies had shifted. These spectral lines had shifted toward the red end of the spectrum, indicating a radial velocity away from the Earth. He also found that the radial speed of the galaxy was proportional to the galaxy’s distance from the earth. Mathematically, Hubble’s Law is expressed as v = Hd, where v is the radial velocity, d is the galaxy’s distance from the Earth, and H is Hubble’s constant. It turns out that the inverse of H, 1/H, is the age of the universe, because it is the time that it took the galaxies to separate. Currently, the age of the universe is estimated to be 13.7 billion years.

This provoked a variety of questions from the class. Mike Dunn asked if Hubble’s findings gave any indication that the universe is expanding. Erica Westerman questioned about whether or not we could determine if a galaxy was moving parallel to us. Prof. deVries then asked for elaboration regarding the Doppler shift, and its relation to the time it takes for the light from a galaxy to reach us. Prof. Möbius explained that Hubble’s Law relates a galaxy’s distance to its radial velocity (as opposed to tangential velocity) and that it gives no evidence for or against an accelerating universe. Because galaxies’ velocities are determined by the Doppler shift (the shift of spectral lines), we are only able to determine the radial component of its velocity; the Doppler shift is unable to show us if a galaxy is moving parallel to our own. He also noted that the Doppler shift measures the velocity of the galaxy when that light left the galaxy. Hence, the radial velocity that we measure for the Andromeda Galaxy was its velocity 200 million years ago.

Prof. Möbius resumed his lecture, introducing the class to the cosmological principle. The cosmological principle states that the universe is the same in all directions. It is helpful to explain this idea using the analogy of raisin dough. As the dough expands, each raisin moves further apart from all other raisins. This means that you can view the expansion from any raisin, and all others will appear to be moving away from you. Hence, there is no “center” of the universe, because it looks the same regardless of where you are viewing it. Similarly, the further the raisin from your viewing point, the faster it is moving away from you. Applying this analogy to the universe leads to a key point in cosmology: the recession of galaxies is not due to the galaxies’ motion through space. Contrarily, it is the space itself between galaxies that is expanding. As we look further away from our own galaxy, we see that galaxies’ radial velocities increase. Because of the linearity of Hubble’s Law, this implies that at some point, galaxies are traveling away from us at faster than the speed of light. But surely, this is a violation of Einstein’s relativity, which state that nothing can travel faster than the speed of light! These galaxies do not violate any physical laws, because it is the space itself that is expanding faster than the speed of light. This conclusion is the first answer to Olbers’ Paradox. Although the universe is infinite, we cannot see the light from galaxies that are receding at speeds faster than the speed of light.

According to the cosmological principle, because the universe is the same everywhere, there must be galaxies even beyond those receding at the speed of light. Therefore, augmenting our first answer to Olbers’ Paradox, we conclude that the light from these galaxies would therefore take longer than the age of the universe to reach us. This introduces a new conundrum – we live in an infinite universe which is expanding. This concept is difficult, if not impossible to wrap one’s mind around. Adding to the difficulty, Chris asked if eventually, all particles in the universe will be infinitely far apart. If the universe is expanding, then yes indeed all particles will be infinitely far apart, in an infinite universe that continues to expand.

The current expansion of the universe necessarily implies that the early universe was very compressed. This theory is incorporated by the big bang theory. This theory is widely accepted by most scientists, and states that the early universe was extremely massive and high in density. The universe then began expanding in following an event similar to an explosion. In direct opposition to the big bang theory is the steady state theory, which claims that the universe has always been as it appears now (hence has been forever expanding). Unfortunately for supporters of the steady state theory, evidence acquired over the last 60 years points very strongly toward the big bang theory.

Because the early universe was very compressed, it must have been extremely high in temperature. Prof. Möbius gave a demonstration on just how much thermal energy can be released by compression. The demonstration used a glass tube with a plunger at one end, and a piece of cotton on the other. The tube was situated so that pressing down on the plunger caused the air inside to compress. Rapidly compressing the air caused the cotton to ignite in a small, bright burst of flame. It is approximated that the universe was 3000K when it was 300,000 years old. The universe has since expanded 1000 times, so there should be a left over temperature of ~ 3K. In 1965, at Bell Labs, two employees were working with a new antenna. They heard a continuous background noise which they could not explain. After taking extensive action to resolve the noise (including cleaning pigeon droppings off the antenna) it was determined that this noise was the Cosmological Microwave Background (CMB), the background radiation left over from the big bang. In 2006, the Nobel Prize for Physics was awarded for the data acquired by COBE (Cosmic Background Explorer), which helped solidify the validity of the big bang theory. Along with CMB, the big bang theory is also supported by the expansion of the universe, as well as the elemental rations (mainly the ratio of Hydrogen to Helium).

Unfortunately, the big bang theory is incomplete. There are a few important characteristics of our universe that are unexplained by the big bang. For example, we know through general relativity that mass distorts space. For the universe to be uniform (as it appears today), the early universe must have been extremely flat. There is also a problem referred to as the horizon problem. In short, the universe looks the same in every direction, yet there is no way that areas of the universe in opposite directions could have communicated (i.e. transferred energy) across the vast differences. The third contradiction is known simply as the matter problem. Why didn’t all matter and antimatter cancel out and become energy? Why is there any matter at all?

The proposed solution for these examples is known as the inflation model. The early universe inflated very rapidly, causing it to become very flat (very small curvature). This is similar to the flat appearance of the Earth’s surface, though we know that its surface is curved. Inflation also resolves the horizon problem, as all parts of the universe were initially in contact. Likewise, the matter problem is resolved by the inflation model. As the universe cooled, it lost its symmetry (just as water freezing into ice loses its structural symmetry). This loss of symmetry allowed energy to be converted into matter.

Even with the addition of the inflation model, we still lack a complete cosmological theory. Until recently, it was believed that the rate of expansion of the universe should be decreasing due to the effects of gravity. But, data shows that the expansion of the universe is accelerating! It is believed that this acceleration is due to a type of energy known as dark energy. Very little is known about this hypothetical dark energy – only that it should make up approximately 70% of all mass in the universe. This dark energy supplies the force causing the universe’s accelerating expansion. 27% of the mass in the universe is believed to be dark matter, which holds galaxy clusters together. The remaining 3% of the mass is all of the known mass and energy in the universe. In other words, we really don’t know what the universe is made of!

This again sparked discussion within the seminar as students began asking questions or giving their insight on the topics covered throughout the class. Prof. Möbius introduced John Archibald Wheeler’s concept of the self-reflecting universe, which claims that the universe looks back at the big bang through our eyes. This is similar to the idea of the Möbius strip (no relation to Prof. Möbius). Mike asked if we can pinpoint a specific center of the universe. All we know is that we are at the center of the known universe – we are just a small bubble in the infinite universe. Sam then asked if we travel to another star, does our known universe shift? Indeed it does, but when we travel back to Earth, our known universe would then shift back to be again centered on the Earth. Mike then proposed a question regarding the speed of gravity – when a supernova occurs, do we first notice the light or the gravitational effect of the event? Gravitational waves travel at the speed of light, so we actually notice the gravitational effects first, because they leave the source before the waves of light do. Unfortunately, we have not yet developed the technology to detect gravitational waves from astronomical objects. We theorize that gravitational waves are produced by the motion of an object through space-time. These waves are difficult to detect because they are extremely weak. However, scientists believe that the sensitivity of detectors coming on line in the next few years will be good enough to make these detections.

The final topic discussed during this lecture is the anthropic principle of the universe. The anthropic principle is typically divided into the strong and weak anthropic principles. In essence, the anthropic principle claims that the universe started with the necessary conditions in order for life to develop. For example, if gravity were just slightly stronger, the universe would have collapsed in the first 100 million years. There would have been no development of heavy elements, and life could not have evolved. Were gravity stronger in relation to the strong nuclear force, than all Hydrogen in the universe would have fused to become Helium in the first 100s of our universe’s existence. It is important to realize that the anthropic principle gives no scientific explanation about or existence; it merely discusses possibilities regarding necessary conditions of life. We did not delve deeply into the details of the anthropic principle as this will be the primary focus of a future lecture.