An Example of a "Learning Process" Journal (using the 2 colored box format)

"Time Travel in Einstein's Universe" by Richard Gott (Chap. 4, pp. 131-199)

• "... an accelerating astronaut firing his rocket ship into empty space with a normal vacuum will, surprisingly, detect photons. This thermal radiation is called Unruh radiation. ... The energy the astronaut 'borrows' from the vacuum therefore makes him observe a vacuum with an energy density below zero - a vacuum state called the Rindler vacuum.The Rindler vacuum has negative energy density and negative pressure. ... The astronaut detects photons; you do not. You and he disagree about what the vacuum state is and whether any photons are present, but you both agree on the total energy density." [p. 141]
• "... the front and back walls in the Misner space must approach each other at a velocity of 99.9993 percent of the speed of light. This was a beautiful solution." [p. 142]
• "Thus Einstein's universe model included a prediction that was proved false. In Einstein's model, galaxies would forever remain the same distance from one another - they would not be moving apart. ... Alexander Friedman ... solved Einstein's original equations exactly - without the cosmological constant - by making an important assumption: there were no 'special' points in space. ... any point in space was as good as any other. That meant that as far as the curvature of space was concerned, no locations were special, and the amount of curvature must be the same everywhere." [p. 151]
• "The simplest of Friedman's big bang models is the closed three-sphere universe that starts with a big bang and ends with a big crunch. Its spacetime geometry resembles a football." [p. 154]
• "As we trace time back toward the initial singularity, following the laws of Einstein's theory of general relativity, we first reach an epoch in which the density becomes so large that quantum effects cause the laws of general relativity to break down. ... spacetime is no longer smooth but instead becomes a complicated spongelike spacetime-foam." [p. 162]
• "We do not currently have a theory of quantum gravity or an all-encompassing theory-of-everything. ... we have to admit that before a certain time, we do not know what happened. ... We cannot say exactly how our universe formed." [p. 162]
• "Our paper, 'Can the Universe Create Itself?' was published in Physical Review D (the premier journal for particle physics) in May 1998. It has 155 equations and 187 references, yet its key idea can be summaarized by Figure 27 [which shows 4 'horns', one of which has a time loop near the bottom]". [p. 189]

The first point about negative energy is analogous to the statements about agreement on total timespace differences. But I must admit it still seems to me to be more examples of trying to interpret some mathematics in terms of 'reality', and this doesn't always seem to make much sense.

The comment on Misner space also seems a bit far-fetched.

The idea that any point in space was as good as any other is an important idea when considering comological models.

I have another book on quantum gravity, called "Three Roads to Quantum Gravity". It might be worth a glance after I finish these notes.

I want to find the article 'Can the Universe Create Itself?' and see what a scholarly paper in this field looks like.

"Time Travel in Einstein's Universe" by Richard Gott (Chap. 5, pp. 200 - 242)

• "Quantum mechanics tells us that in principle all predictions we make about the future must be stated in terms of probabilities of outcomes of future observations. ... these probability estimates can be extremely useful and may tell us all we can really know." [p. 204]
• "If you observe something at a random time, there is a 50 percent chance you will catch it in the middle two quarters of its period of observability. ... the future is between one third and 3 times as long as the past." [p. 208]
• "In a 1994 paper in Nature, I was aable to show that a Bayesian treatment using Jeffrey's methods gave exactly the same 95 percent confidence level limits as the Copernican results did." [p. 229]

The idea that the future is between one third and 3 times as long as the past permits one to estimate how long the future of a situation is likely to be, if one can estimate how long it has already occurred. Beautiful! One can also change the level of confidence from 50% to any value (such as 95%). The 95% confidence interval is between 1/39th and 39 times its past longevity.

The confidence intervals for various events such as the longevity of humans, or the United States, or Oxford University are ridiculously long.

The agreement between Bayesian and Copernican systems (where every point in time is considered equally likely) is interesting. This is another paper I would like to find.

This was a fascinating book. The diagram of a self-creating universe will remain with me for some time.

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