Hawking & the Universe This is a supplement to the lecture given on Jan 26, 2015, by Dr. Mounib El Eid, Physics department, AUB. It may motivate the reader to explore some of the presented issues. There is no claim of being comprehensive, because this subject is too involved. 1. Geocentric model of the universe (Ptolemy, 100-170 A.D) This is also called Ptolemy model: Earth at center motionless, five planets, the Sun, and the Moon orbit the Earth in perfect circles. Explanation of the retrograde motion was done by introducing the so called epicycles. But this was an artificial explanation to keep the perfection of the circles. It was a philosophical bias to circles. Even Aristotle knew that the Earth was spherical. The Greek Astronomer Eratosthenes (276-194 B.C.) have used the curvature of the Earth to determine its equatorial diameter (see lecture). The geocentric model survived for more than thousand years, why? May be it was considered to represent reality. 2. Heliocentric model (Copernicus) Basic difference to the geocentric model: the Sun is in the center, but still motionless and planets including the Earth still performing circular orbits around the Sun. Copernicus (1473-1543) was able to determine the distance of the planet Venus to the Sun in terms of the distance between the Earth and the Sun (send e- mail to meid@aub.edu.lb to know how). The heliocentric model was a scientific and philosophical revolution, because it has proposed the Sun-centered solar system, and has displaced us from our centric view of ourselves that our planet is a focal point. Reality is now connected to experience. 3. Galileo, Kepler & Newton There were many discoveries by Galileo (see lecture): discovery of sunspots on the surface of the Sun, and the moons orbiting the planet Jupiter. This was possible, because Galileo has used a telescope for the first time. Reality became a matter of experience based on empirical facts. Kepler has discovered three laws describing the dynamics of the planets around the Sun (see lecture). Newton has explained the origin of the Kepler laws through his three laws and the force of gravity (see lecture). The profound achievement of these scientists was: The planets are not independent of each other as the Greeks have thought, they move according to basic physical laws. This was indeed a scientific and philosophical revolution.
4. Relativity The theory of special relativity formulated by Albert Einstein in 1905 is considered to be a milestone in the scientific development. It is based on two fundamental postulates: Universality of the speed of light: speed of light does not depend on the motion of the source. The laws of science are the same in all frames moving at constant speed, the so called inertial frames This theory has many profound consequences: a. It has removed the view of absolute space and time. Space and time are intertwined (twisted together). In other words, we deal with space-time when observing cosmic objects. Think about a galaxy like our own Galaxy. The light needs about 100,000 years to cross it. Thus, it takes more time to receive information from the far end than from the near end. In other word, one can observe a Galaxy only in space-time. b. Motion affects the measurement and therefore the reality. Think about measuring the length of a meterstick in a moving spaceship at a significant fraction of the speed of light (60%, say). Then you will measure the meter stick contracted, because you cannot measure both ends simultaneously like an observer at rest with the meter stick. This is not a physical shrinking, it is the result of a measurement. c. We can only see the past when observing cosmic objects. In the lecture is an illustration dealing with the time needed for the light to reach the Earth after leaving the Sun. Interesting to note that the asymmetry between past and future is ingrained in our experience 5. General relativity, Quantum mechanics and the Universe The theory of general relativity (TGR) is based also on two postulates: All laws of physics have the same form for observers in any frame In the neighborhood of any given point, a gravitational field is equivalent to an accelerated frame without a gravitational field (Principal of Equivalence between gravitational and inertial mass). The TGR is a classical field theory. It predicts the existence of black holes (see basic description in the lecture). If an observer crosses the event horizon of a black hole he/she is ultimately driven to the singularity (infinitely high density and temperature). It also predicts that the Big Bang started out from a singularity (mathematically: like dividing by zero). But this does not mean that the TGR is wrong, rather it cannot be applied to describe physical situations like early universe or inside black holes. Modern cosmology led to the view that the universe was a cataclysmic quantum event, because of the extremely small scales. To understand the beginning a combination between general relativity and quantum mechanics needed. But how does this work? Relativity wraps space, but how to wrap time? The problem is that we can separate space and time only in case low speed and weak gravity. But, in general space and time are intertwined. When quantum
mechanics is added, time becomes another dimension of space, and you see that the early universe is at least 4-dimensional. Here is a nice statement: When we talk about the beginning we look back in time beyond our Experience, but not beyond our imagination, we still have the Mathematics. If so, we stop talking about the beginning, we put it at zero time 5. Big Bang and the Expanding Universe The Big Bang was proposed by the Russian Alexander Friedmann after he solved the Einstein s equations. This was not accepted by many people. But, there are three experimentally verified indications of the Big Bang: (a) Microwave background radiation, an almost perfect black body described by a temperature, of T= (2.726 0.0013) K (result of the satellite WMAP) (b) The main production of Helium in the universe occurred during the first 3 min after Big Bang, since stars cannot produce more than about 4% of the abundances of this element. This fact is considered as argument of a hot Big Bang, because the helium production needs at least 100 million degrees. (c) The expansion of the universe firstly observed by Edwin Hubble back to the twenties of the last century has shown that the Galaxies are receding from each other. This expansion is understood as follows: Circle a galaxy on a balloon s surface, the circle will not expand as the balloon is inflating. This means the space between the galaxies is expanding, and there is no fixed center of the expansion. This is important to know, because we can detect the expansion only if our measuring instruments have fixed sizes. Otherwise, if everything changes size we would not notice the difference 6. Cosmic inflation The cosmic inflation was proposed in 1980 by the Russian Alexander Starobinsky and the American Alan Guth. As a possible explanation of why the cosmic microwave background radiation (CMBR) is isotropic and also to understand the so called flatness problem. Inflation has more consequences as we shall see below. But a complete theory of inflation is still outstanding, because it goes beyond the TGR and must include quantum mechanical effects, In other words, it needs quantum gravity, which is still developing. Despite of the enormous expansion of the space by a factor of 50 order of magnitude (see Figure in the lecture), the inflation was not completely uniform, since minuscule variation of the temperature of the CMBR has been discovered by the COBE and WMAP satellites. For the inflation to work, the initial state of the Universe must have been very special and highly improbable (Hawking in Grand Design). A question arises whether the expansion during inflation violates relativity which limits the speed of moving objects in space to the speed of light. However, that speed limit does not apply to the expansion of space itself
7. Fundamental forces and the evolution of the Universe There are four fundamental forces that explain the interactions in the Universe: the gravitational force, the electromagnetic force, the strong nuclear force, and the weak nuclear force. Gravitational force: long range, dominates the universe on astronomical time scales Galaxies, stars). Electromagnetic force: long range, stronger than the gravitational force by a Factor of 10 38. It is responsible for holding the electrons in orbits about nuclei, so that atoms can be formed. Interesting to note that the long-range effect of this force is not observed, because there is always a negative charge for every positive charge, and there is a south magnetic for each north magnetic pole, and no monopoles exist, Thus, over a volume of space the effects of the electromagnetism cancel out. This is not the case for the gravitational force, since there is no negative mass around. It is then understandable why the only force holding the Earth in orbit around the Sun is the gravitational. Strong nuclear force: holds the neutron and protons together in nuclei. It is a short-range force with a scale of order of 10-15 m indicating the size of nuclei. Note that since the protons and neutrons are made of elementary particles called quarks, these are hold by the strong force also. Weak nuclear force: extremely short range (10-18 m), weaker than the strong force by a factor of 10-9. It is responsible for transforming a neutron to a proton of vice versa. This is called weak interaction, and is a fundamental process for the fusion of protons in stars. Evolution of the fundamental forces Referring to the Figure in the lecture, here are some explanations. (a) From the time t=0 to 10-43 sec (Planck time), all four forces described above were unified (supersymmetry). This period is not understood, since the theory of everything (TOE) is not yet visible. (b) The expansion and cooling after the Planck period lead to a first spontaneous symmetry breaking. When the gravitational force decouples from the other forces. Or gravity was frozen out. The temperature at this stage was 10 32 K. (c) At t=10-35 sec, the temperature fell down to 10 27 K, and the strong force froze out. This is a second symmetry breaking, and it seems that the inflation epoch started near this time. (d) At t=10-12 sec, the temperature dropped to 10 15 K, and a third and last spontaneous symmetry breaking occurred when the electromagnetic and weak force decoupled. All forces became separated to enable life in the universe.
8. Anthropic principle Some questions: Why the Early Universe so hot? Why the Universe so uniform on large scale? Why does it look the same in all directions and having the same emperature? We have Galaxies and stars owing to density fluctuations. What is their origin? All the above, and the initial amazing conditions of the Big Bang initiated a stream of thinking by many researchers. Many physicists brought this in connection with the Anthropic Principle. There are two versions of this principle: weak an strong Weak version: In a Universe that is large or infinite in space and/or time the conditions necessary for the development of intelligent life will occur in certain regions limited in space & time. No surprise. It is like a rich person living in a wealthy area not seeing poverty Strong version: Either many different universes, or many different regions in a single universe. Our own universe would have the right conditions for the development of intelligent life. The strong statement is: Asking: Why the universe is the way we see it? Answer: if it were different we would not exist. Well, we know that the fundamental constants (strength of the forces) are fine-tuned. Still there are objections to the strong version. In what sense can many universes exist? We cannot know what happened in them. We tend to remove them from the theory If they are different regions of the same universe, the law of sciences would be the same in each region, so that we can move from one to the other. But the initial conditions would be different, and we are back to the weak version Another argument against the strong version is: It runs against the tide of the history of science. All what we have discovered from the geocentric model to the modern picture and all what is existing, hundred billion of galaxies is for our sake? End of the flysheet