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. 33-55)

• "Do you want to visit Earth 1,000 years from now? Einstein showed how to do it. All you have to do is get in a spaceship, go to a star a bit less than 500 light-years away, and return, travelling both ways at 99.995 percent of the speed of light. When you come back, Earth will be 1,000 years older, but you will be only 10 years older. Such speed is possible. ..." [p. 33]
• "Maxwell developed a set of four equations governing electromagnetism. In these equations, there is a constant, c, a velocity that describes the relative strengths of the electric and magnetic forces between charged particles." [p. 37-38]
• "Maxwell knew the velocity of light, and when in 1873 he calculated the speed of his electromagnetic waves and found them to be traveling at 300,000 kilometers per second, he suddenly realized that light must be electromagnetic waves. It was one of the great discoveries in the history of science." [p. 39]
• "... in 1905 Einstein came up with two astonishing postulates. First, the effects of the laws of physics should look the same to every observer in uniform motion ... and second, the velocity of light through empty space should be the same as witnessed by every observer in uniform motion." [p. 41]
• "Einstein proceeded to prove numerous theorems based on these two postulates, and experiments have since confirmed their accuracy many times." [p. 42]
• "One of the first theorems Einstein proved from his two postulates showed that if an astronaut were to pass me at high speed, I should see his clocks ticking slowly relative to mine." [p. 44]
• "The astronaut could use his heartbeat as another kind of clock. ... When I not see his light clock ticking 3 times for every 5 times my light clock ticks, but his heart should appear to beat more slowly than mine by the same factor. Therefore Ishould see him age more slowly than I do." [p. 46]
• "Time travel to the future is made possible by the fact ath observers who are moving relative to each other have different ideas of time." [p. 47]
• "Einstein concluded that nothing can travel faster than the speed of light." [p. 53]
• "E=mc2 is another result Einstein proved from the two postulates." [p. 53]
• "The speed of light is a 'magic' velocity, a velocity everyone can agree on, so it can be used to compare separations in space with separations in time." [p. 54]
• Two people who differ by a uniform velocity will disagree on the separation of events in both space and time. "But we can agree on the square of the separation in space minus the square of the separation in time. ... If this quantity is negative, we say that the two events have a timelike separation ... when this quantity is positive, we say they have a spacelike separation ... when the quantity is zero, we say the two events have a lightlike separation." [p. 55]

Travelling to a star is irrelevant. The issue is only one of travelling to a location 500 light-years away.

I am beginning to feel a bit uneasy about this book, and others like it, that describe the implications of various equations without giving any sense of what the equations might be or how they were derived.

I really must do more reading about Maxwell and his four equations!

• http://scienceworld.wolfram.com/physics/MaxwellEquations.html

Typing Maxwell electromagnetism equations gives numerous web sites, but most are genuinely too technical for me. One of the difficulties was that the equations mentioned involved tensors. I am not sure what they are. I can recall some math majors discussing a course they were taking on tensor analysis, but I never took that course. A little more work with google and I Learned that a tensor is a multi-dimensiional vector. Simple!

While googling "Albert Einstein 1905" I found a reference to a book that is supposed to provide a line by line analysis of Einstein's 1905 paper on special relativity. A quci check of the U of L library indicates we have it. Now to see what it looks like!

I disagree with Gott on page 46. I agree that an astronaut's heart should appear to beat more slowly on a fast moving spaceship (as viewed by me, not on the spaceship) but if I carry this to a very very fast spaceship then the heart would almost come to a halt and this is not biologically possible without dying. The relativity equations are fine for inanimate objects, but I do not think they apply to living objects. Interesting!! This means that all of our interpretations about space/time travel are hooey! Or I am missing some critical point.

I would like to see all of the theorems that have been derived from Einstein's two postulates laid out in a manner similar to Euclid's Elements.

The idea of an invariant square of separation is a new one for me.

6:05 am I think I need a break and want to mull some of this over. It is a bit overwhelming. But very exciting.

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