Saturday, December 04, 2010

Grand Design by Stephen Hawking

The theory of everything is what this book is about. For hard core scientists, the book starts slow by reviewing alot of material that you would have studied in school before combining these ideas into the proposed 1o dimensional theory of everything 'M-Theory'.

The book does a great job of explaining Feynman's sum of histories concept, and how this impacts the way quantum systems behave - including our universe's origin.

I still don't get how Hawking radition causes black holes to evaporate to nothing (sadly the book doesn't really talk about that). Why doesn't the black hole just stay the same mass if an equal number of paired matter and anti-matter particles form at its event horizon and only one of the coupled pair falls in, leaving the other as a tell tale radiation? It would mean that an equal amount of matter and antimatter should fall in and radiate away; a net zero in change of mass of the black hole. Is there some preference for only antimatter to fall in and for matter to radiate away? It would seem for the black hole to radiate away this would have to be the case? Why should this be?

1000 years before Galileo and Coprenicus

Aristarchus (circa 310-230BC) used careful geometric analysis of the earth's shadow cast on the moon during a lunar eclipse to conclude that the sun must be much larger than the earth. Perhaps inspired by the idea that tiny objects ought to orbit mammoth ones, and not the other way around, he became the first person to argue that the earth is not the center of our planetary system, but rather that it and the other planets orbit the much larger sun. It is a small step from the realization that the earth is just another planet to the idea that our sun is nothing special either. Aristarchus suspected that this was case and believed that the stars we see in the night sky are actually nothing more than distant suns. P21

What a genius! Why don't we ever hear about poor Aristarchus? Robbed of his glory by Galileo, Corprenicus.

The illusion of free will

A study of patients undergoing brain surgery found that by electrically stimulating the appropriate regions of the brain, one could create in the patient the desire to move the hand, arm, or foot, or to move the lips and talk. It is hard to imagine how free will can operate if our behavior is determined by physical law, so it seems that we are no more than biological machines and that free will is just an illusion. P32

For example, we can't solve the equations governing the gravitational interactions of every atom in a person's body with every atom in the earth. But for all practical purposes the gravitational force between a person and the earth can be described in terms of just a few numbers, such as person's total mass. Similarily we can't solve the equations governing the behavior of complex atoms and molecules, but we have developed an effective theory called chemistry that provides an adequate explanation without accounting for every detail of the interactions. In the case of people, since we can't solve the equations that determine our behavior, we use the effective theory that people have free will. The study of our will, and of the behavior that arises from it, is the science of psychology. Economics is another effective theory, based on the notion of free will plus the assumption that people evaluate their possible alternative courses of action and choose the best. That effective theory is only moderately successful in predicting behavior because, as we all know, decisions are often not rational or are based on a defective analysis of the consequences of the choice. P33

A model is a good model if it:

  1. Is elegant

  2. Contains few arbitraty or adjustable elements

  3. Agrees with and explains all existing observations

  4. Makes detailed predictions about future observations that can disprove or falsify the model if they are not borne out p51

To paraphrase Einstein “A theory should be as simple as possible, but not simpler.”... Though added complexity could make the model more accurate, scientists view a model that is contorted to match a specific set of observations as unsatisfying, more of a catalog of data than a theory likely to embody any useful principle. P52

Feynmann was able to figure out why this happens

Firing electrons (or any other particle) at a double slit – one at a time – still produces an interference pattern. To physicists this was a startling revelation: If individual particles interfere with themselves, then the wave nature of light is the property not just of a beam or of a large collection of photons but of individual particles. P70

What happened before the big bang? Why not ask, what's south of the southpole?

Time can behave like another dimension... Suppose the beginning of the universe was like the south pole, with degrees of latitude playing the role of time. As one moves north, the circles of constant latitude, representing the size of the universe, would expand. The universe would start as a point at the south pole, but the south pole is much like any other point. To ask what happened before the beginning would become a meaningless question, because there is nothing south of the south pole. In this picture, spacetime has no boundary – the same laws hold at the south pole as in other places. In an analgous manner, when one combines the general theory of relativity with quantum theory, the question of what what happened before the beginning of the universe is rendered meaningless. The idea that histories should be closed surfaces without boundary is called the no boundary condition. P135

Inflate or die

A few of the possible universes will be like bubbles of steam. Many tiny bubbles (universes) will appear, and then disapper again. These represent mini-universes that expand but collapse again while still microscopic size. They represent possible alternative universes, but they are not of much interest since they don't last long enough to develop galaxies and stars, let alone intelligent life. A few of the little bubbles, however, will grow large enough so that they will be safe from recollapse. They will continue to expand at an ever increasing rate. These correspond to universes that inflate. P138

How the present changes history, according to Feynmann

There will be a quantum probability amplitude for every number of large space dimensions from zero to 10. The Feynman sum [of histories] allows for all of these, for every possible history for the universe, but the observation that our universe has 3 large space dimensions selects out the subclass of histories that have the property that is being observed. In other words, the quantum probability that the universe has more than or less than 3 large dimensions is irrelevant because we have already determined that we are in a universe with 3 large dimensions. So as long as the probability amplitude for the 3 large dimensions is not exactly zero, it doesn't matter how small it is compared to the probability amplitude of other numbers of dimensions. It would be like asking for the probability amplitude the present pope is Chinese. We know that he is German, even though there are far more Chinese than there are Germans. Similarly, we know our universe has 3 large space dimensions, and so even though other numbers of large dimensions may have a greater probability, we are interested only in histories with 3. p141

Be nice to your robot

How can we tell if an alien or robot has free will?... As we said earlier, we can't even solve exactly the equations for 3 or more particles interacting with each other. Since an alien the size of a human would contain a thousand trillion trillion particles, even if he were a robot or machine, it would be impossible to solve the equations and predict what it would do. We would therefore have to say than any complex being has free will – not as a fundamental feature, but as an effective theory, an admission of our inability to do the calculations that would enable us to predict its actions. P178

The big net zero

One requirement any law of nature must satisfy is that it dictates that the energy of the isolated body surrounded by empty space is positive, which means that one has to do work to assemble the body. That's because if the energy of an isolated body were negative, it could be created in a state of motion so that its negative energy was exactly balanced by the positive energy due to its motion. If that were true, there would be no reason that bodies could not appear anywhere and everywhere [at anytime, all of the time!]. Empty space would be unstable... If the total energy of the universe must be zero, and it costs positive energy to create a body, how can a whole universe be created from nothing? That is why there must be a force like gravity. Because gravity is attractive, gravitational energy is negative: one has to do work to separate gravitationally bound systems. This negative energy can balance the positive energy needed to create matter... Because there is a law like gravity, the universe can and will create itself from nothing in the manner we have described. P180

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