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

"Time Travel in Einstein's Universe" by Richard Gott (Chap. 2, pp. 55-75)

• "In 1919 Theodor Kaluza discovered that if one generalized Einstein's theory of gravity into a world with four dimensions of space and one dimension of time, one would obtain normal Einstein gravity plus Maxwell's equations for electrodynamics. Electromagnetism was just due to the action of gravity in an extra spatial dimension. [p. 62-63]
• "In 1926 Oskar Klein ... worked out the idea that the extra dimension could be curled up like the circumference of a soda straw. ... with a circumference so small (8 x 10-31cm) that we would not notice it." [p. 63]
• "In this universe, positively charged particles like the proton would circulate counterclockwise around the straw, whereas negatively charged particles like the electron would circulate clockwise. Neutral particles (like the neutron) would not circle the straw. The wave nature of particles would allow only an integer number (1, 2, 3, 4, and so on) of wavelengths to wrap around the tiny circumference, and therefore charges should come in multiples of a fundamental charge like those carried by the proton and electron. Kaluza-Klein theory unified the forces of gravity and electromagnetism, explaining both in trms of curved spacetime - a step toward Einstein's goal of a grand unified field theory." [p. 63-64]
• "Recently, however, superstring theory has revived the idea of extra dimensions. ... Superstring theory (or M theory, as it is sometimes called) suggests that our universe actually has 11 dimensions - with one macroscopic dimension of time, three macroscopic dimensions of space, and seven curled-up dimensions of space each of order 10-33 centimeters in circumference." [p. 64]
• "The exact shape of this space, whether like a higher dimensional sphere or donut or pretzel, would determine the nature of the particle physics we observe." [p. 64]

I am feeling very refreshed and relaxed this morning (5:45 am) as I begin making a few more notes. It is a good time of day for learning.

This is the first time I have really read something about superstring theory. The idea of tiny dimensions that are curled up as exemplifying sub-atomic particles is new to me, but I think I have a grasp of the basic idea. I wonder if this provides an explanation for the 2-slit interference experiment where photons act like both a particle and a wave. I should reread David Deutsch's explanation of this again (in his book The Fabric of Reality).

"Time Travel in Einstein's Universe" by Richard Gott (Chap. 3, pp. 76-130)

• "Do you want to see yourself in the past? Stand five feet in front of a mirror." [p. 77]
• "... but light travelling just outside a black hole can be bent by 180 degrees and return to Earth. ... In principle, a photon emitted from Earth in 14,000 B.C.E. could have travelled out to that black hole, whipped around it, executing a U-turn, and headed back to Earth for arrival in the year 2000. ... Unfortuantely, the black hole is very small, so the fraction of all photons emitted by Earth that come close to the black hole is tiny, and the fraction of those that actually return to Earth is also extremely tiny. Doing the calculation, one finds it likely that not even a single photon emitted from Earth has ever returned to Earth by this black hole during their mutual history." [p. 79]
• "But according to Einstein's theory of gravity - known as general relativity - under certain conditions, spacetime can curve in ways that permit shortcuts through spacetime, allowing you to beat a light beam and journey back into the past." [p. 83]
• "Kip Thorne of Caltech ... traveling quickly through a wormhole - a theoretical tunnel that cuts straight across an area in which space curves."
• "Einstein proposed that mass and energy cause spacetime to curve. It took him 8 years of hard work to derive the equations governing this. ... He had to learn about the Riemannian curvature tensor - a mathematical monster with 256 components telling how spacetime could be curved." [p. 87]
• "Ever since Einstein announced his equations of gravitation in 1915, people have been exploring 'solutions' to them. ... such a solution would give both a mathematical description of the geometry involved, how the spacetime would look, and the distribution of mass and energy required to produce it. Many of these solutions have remarkable properties" [p. 90]
• "Another exact solution to Einstein's equations ... the geometry around a cosmic string. This term refers to thin strands of high-density material left over from the early universe. ... Scientists figure that cosmic strings should have a width narrower than an atomic nucleus and a mass of about 10 million billion tons per cnetimetre. Strings are also under tension, like stretched rubber bands, which causes infinite strings to straighten out with time and whip around at velocities that should typically be over half the speed of light." [p. 92-93]
• "... Stephen Hawking's famous question: 'Why haven't we been overrun by tourists from the future?' " [p. 109]
• a warpdrive is a deformation caused by 'poking' deeply into a crved surface, which then permits 'shortcuts', much like a wormhole. [p. 119]

I love the first quote! I had never thought of that, even though I was familiar with the idea of stars being light from the past.

I wonder what the calculations for computing a return trip to the black hole would look like?

I had no idea that general relativity involved tensors with 256 components. (8 dimensions?)

This book is becoming stranger and stranger. I am new to the concept of a cosmic string. Sometimes I have the suspicion that this is mathematics run amok. The math may be sound, but that does not imply the acual existence of such entities (nor does it preclude the possibility).

New concepts for me:

• cosmic string
• wormhole
• warpdrive.

Science Index