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

"Simply Einstein" by Richard Wolfson (Chap. 9, Star Trips and Squeezed Space. pp. 109 - 126)

• "Would you be aware, while traveling, that you're aging more slowly than usual? Would you feel your heartbeat slow down and notice your hair growing more slowly? Absolutely not! To you, in your spaceship, everything seems perfectly normal. It must! Why? Because you're in a perfectly good frame of reference for exploring physical reality. The laws of physics work just as well for you as they do on Earth." [p. 112 - 113]
• "... measures of space, as well as of time, are different in different reference frames." [p. 115]
• "If the distance between two objects is d in a frame of reference where the two are at rest, then in a reference frame moving at speed v relative to the objects, the distance will be contracted by this same factor, giving d' = d x (square root(1 - v*2)). [p. 115]
• "... one's relationship with an object like a ruler is certainly simplest in a frame of reference at rest with respect to the object. For that reason the length measured when one is at rest with respect to an object is called the object's proper length. Here 'proper' doesn't mean 'correct' as much as it does 'proprietary' - in the sense of 'belonging' to the object ... Observers in different reference frames will measure different lengths for an object, and they'll all be correct. Measures of space and time just aren't absolute. An object is longest in a reference frame where it's at rest and shorter in any other frame." [p. 116]
• "The further you go in space, the further you can jump into the future. A round-trip to the center of our galaxy, 30,000 light-years distant, takes a minimum of just over 60,000 years in the Earth's frame of reference. But on a spaceship making that trip, the round trip could take a few years, a day, an hour, or even less, depending on how close v (ratio of v' to c) is to 1. So with a trip to the galactic center you can jump 60,000 years into the future. ... But you can't go back." [p. 126]

The first quote addresses perfectly a question that has long bothered me. The key insight is the last sentence of the quote.

I am not yet ready to do the maths to derive the equation for distance contraction, but I want to be able to do this before I am finished with this topic. As an aside, this is when the web becomes frustrating - it's inability to handle math symbols. I will have to do this in Word and then copy the results as an image.

This leads naturally to Mathematica (perhaps I should try to obtain a copy, to Wolfram's "A New Kind of Science" and to Papert's claim that doing comes before understanding. It might be interesting to pursue the ideas in "The Computational Beauty of Nature" using Mathematica.

"Simply Einstein" by Richard Wolfson (Chap. 10, The Same Time? pp. 127 - 138)

• Consider the case of a spaceship travelling very fast as it passes earth. From an observer on earth, the clocks on the spaceship appear to be slow. But since one can equally view the situation as the earth is travelling very fast as it passes the spaceship, for a person on the spaceship, clocks on earth are travelling slow.
• "What does it mean to say that two events occur at the same time? If the two events also occur at the same place, then there's no question." [p. 129]
• "... events that are simultaneous in one reference frame may not be simultaneous in another reference frame moving relative to the first." [p. 132]

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