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

"Simply Einstein" by Richard Wolfson (Chap. 11, Past, Present, Future ... and Elsewhere. pp. 139 - 148)

• "... the time order of events may depend on one's reference frame ..." [p. 139]
• "There are, in fact, events that are unambiguously in the past - meaning that they occurred at a time before the present event. ... the relativity of simultaneity precludes my talking about a universal present instant." [p. 139 - 140]
• "The past of a given event consists of all those events that are capable of influencing the given event. ... I'm talking about the past and future in relation to a specific event." [p. 140 - 141]
• "Are there events that have not occurred but that cannot be influenced by what I'm doing right here and now?" [p. 141]
• "... the speed of light is the maximum possible speed in the Universe ... information cannot be communicated at speeds faster than c. ... [example of] a pair of events that just cannot be causally related, because no information can travel between them. They're too far apart in space and too close in time for even light to be present at both events. ... Nothing we do at our present moment [on Earth] can influence what happens on Mars 5 minutes from now." [p. 142 - 143]
• "Events that aren't in the past or the future of a given event are in its elsewhere. They're events that cannot communicate with the given event, so the two cannot be causally related." [p. 143]
• "... what are you? On a spacetime diagram, you're a path, called a worldline.

The idea of an 'elsewhere' is very timely at the moment, with the two Mars rovers in action. Yet the media has not taken advantage of this to provide a brief introduction to spacetime.

Mention of an elsewhere brings to mind Stepen Hawking's description of the same situation. He used the phrase 'light cone' which I found very appealing.

I must force myself to think in terms of light cones and worldlines. Can a worldline have any shape - for example, can it have a loop? I don't think so, since that would imply going backward in time. Unless spacetime itself has a loop. Richard Gott suggests that may be a possibility.

"Simply Einstein" by Richard Wolfson (Chap. 12, Faster Than Light? pp. 149 - 163)

• E = mc*2: "... a better name is mass-energy. The total amount of mass-energy remains the same, but how much of it is in the form of mass and how much is in the form of energy can change." [p. 156]
• It is possible that there are objects that move with speeds greater than light (called tachyons) or other objects (called luxons) besides light that move with speed c, but so far they have not been detected. [p. 160]
• "Recently there's been considerable interest in a strange phenomenon in quantum physics whereby two objects are somehow 'entangled' in such a way that they seem to communicate instantaneously even when they're far apart." [p. 161]

Using a label like 'mass-energy' changes the entire way that one thinks about mass and energy. Psychologically this is very powerful. Are there other instances where our present labels act as inhibitors to thought?

"Simply Einstein" by Richard Wolfson (Chap. 13, Is Everything Relative? pp. 164 - 173)

• What are the absolutes (i.e. values that don't change with one's frame of reference)?
  - space-time interval
  - c
  - momenergy (the 4-dimensional analog of momentum and energy)
  - the 4-dimensional analog of electric charge and current

Once again, being able to conceptualize in 4-dimensions (at least mathematically) is the way to go.

"Simply Einstein" by Richard Wolfson (Chap. 14, A Problem of Gravity. pp. 174 - 202)

• "Einstein knew that Newton's theory of gravity could not be consistent with special relativity. ... In Newton's view, that influence from Earth to Moon is instantaneous. ... that implies instantaneous transmission of information from Earth to Moon, which is inconsistent with relativity's assertion that information cannot be transmitted faster than the speed of light." [p. 175]
• "Another problem with Newtonian gravitation is that the gravitational force depends on the distance between massive objects. We've learned that 'the distance between ...' is not an absolute quantity; it differs from one reference frame to another." [p. 175]
• "In the field picture, the proton creates an electric field in the space around it, and the electron responds to the field in its immediate vicinity. Suppose the proton were suddenly to disappear. In electromagnetism, news of that disappearaance moves outward as an electromagnetic waave, travelling at the speed of light. Ahead of the wave, the electric wave is just as it was before. Behind it, there is no electric field. The region of no field expands outward, from the site of the vanished proton, at the speed of light. Eventually the electron learns of the proton's disappearance as the no-field region reaches it and it ceases to feel an electric force." [p. 176]
• "Apollo 15 astronaut David Scott dropped a hammer and a feather on the Moon; with no air resistance, they hit the ground at exactly the same time." [p. 182]
• "... spacetime curvature is gravity. Gravity is not some force that affects objects in spacetime." [p. 192]
• "We can call such effects 'gravitational', but we could equally well call them 'geometrical' " [p. 193]
• "How does spacetime acquire its curvature? ... it is ... the presence of matter or energy that curves spacetime. ... The so-called field equations of general relativity tell quantitatively what curvature results from a given distribution of matter and energy ... Where matter is densely concentrated, spacetime is more curved." [p. 199]

The description of field theory is the clearest I have seen.

I wonder if there is a tape of Scott's experiment? (check NASA web site)

"Simply Einstein" by Richard Wolfson (Chap. 15, Into the Black Hole. pp. 203 - 228)

• "... an object so dense that not even light could escape. That's a black hole." [p. 218]
• "Strong gravity exists where escape speed is an appreciable fraction of the speed of light, c. Weak gravity means escape speed is far less than c. ... Gravity everywhere in our Solar System is weak." [p. 218]
• "... quasars ... emit more energy than an entire galaxy comprising hundreds of billions of stars." [p. 224]
• "What's a ripple in spacetime? Simply a change in the curvature of spacetime - a change that moves outward from the disturbance that initiates it. ... the're called gravitational waves ... travel at the speed of light." [p. 225]

Strong and weak gravity are new terms for me, as is a gravity wave.

"Simply Einstein" by Richard Wolfson (Chap. 16, Einstein's Universe. pp. 229 - 240)

• "What is the large-scale curvature of space-time? Because matter is what warps spacetime, giving it curvature, the answer lies in the amount of matter present in the Universe. There's a critical density. ... Remarkably, the real Universe seems close enough to the dividing case of critical density that the answer isn't obvious from observations." [p. 232]

Although this book stays away from mathematics and equations, it does provide a clear conceptual description of the ideas inherent in special and general relativity. I think I am now in a much better position to try a couple of more books on the same subject.

Here are three I borrowed from the Library, that I may want to look at later, after I have had a look at a few that I have bought in the last couple of years:

• Walter Scheider (2000). A Serious but not Ponderous Book About Relativity. [QC 173.55 S44]
• Bertel Laurent (1994) Introduction to Spacetime: A First Course in Relativity. [QC 173.55 L365]
• Arthur Miller (1981). Albert Einstein's Special Theory of Relativity. [QC 173.52 M54]

Science Index