Reading Notes of "The New World of Mr. Tompkin
2012-02-06
✓ Chapter 2
✓ The transformation of time into space is obvious to us, because we can move at a speed fast enough to create an interval of space perceptible to us in a time interval also perceptible to us. In other words, if our speed is very very low, say the train is moving at 1mm per decade, we will then not be able to tell the interval of space in a perceptible and acceptable amount of time (in fact, this situation actually happens everyday, since the continent is moving at a very low rate. Thus, the saying that "I will stay at the same spot for five seconds" is meaningless, since no matter how still you can be, you will be at a different place five seconds later thanks to the motion of the ground under your feet). However, the transformation of space into time is very difficult to perceive, because our perception of time is too slow, or that of space is too limited, in terms of what the speed of light is capable of. Say we can discern the time interval of 0.000000003 second, then we, who are observing the whole event from the roadside, can tell that two people, sitting separately, holding a cup of coffee to their mouths, which would be seen as simultaneously on the train they are traveling with, is not happening at the same time. The reason is that the information of those two actions reaches our eyes in an order: the person sitting closer to us has the information reach us earlier than the other. The time interval of the arrivals of the two pieces of information is very small, if the distance between us and the people on the train is not significant to the speed of light. Yet we can tell it now, since our presumption is that we can perceive 0.00000003 second. But it is impossible for us to have such an acute perception. Thus it is also very hard to observe the transformation of space into time directly on Earth. Yet, the vastness of the universe provides another outlet: the immensity of space to compensate our dullness in time perception. Therefore, events that happen at a reasonable speed can demonstrate the transformation of space to time due to the distance between the events and we observers.
✓ Chapter 3
✓ Acceleration creates gravity. Therefore, if gravity has an effect on time, so does acceleration. For the one subjected to acceleration, he sees the person not being accelerated having time faster than his own. The evidence is that atom particle vibrates faster on top of a tower (lower gravity) than its counterpart at the bottom (higher gravity). For this evidence, it can be seen as that the particle at the top is stagnant, while the one at the bottom is undergoing acceleration. From the bottom-particle's perspective, during the interval of his vibration, the top-particle can vibrate multiple times, which means the top-particle is living at a faster speed than he does. In other words, the twin on the train will calculate that his brother at the station lives slower during his light-speed travel but much faster when he is being accelerated. And the overall effect is that the hastening of time during acceleration overwhelms its dilation. Therefore, the brother at the station would appear much older than the one who just comes back.
✓ The regulation in the book of instruction revealed by the police officer actually means that if, within the time period of 2d/c, a person is seen remaining at the same spot, he is really at that spot unaltered (the minimum time interval required for him to go there and return, that is covering a distance of 2d, is 2d/c). Therefore, if the clerk was seen within 2d/c not holding a gun, he really was NOT holding a gun.
✓ Chapter 4
✓ No matter how complicatedly we fold a piece of paper, the resultant "curved" structure does NOT represent a mathematical "curved surface". The best example of a curved surface is that of the surface of a sphere. The surface of a cylinder (the top and bottom not included) is not a curved surface, though it seems to us curved.
✓ The situation of Observer B is hard for me to comprehend. It seems that even if she cannot sense the motion of the table, she is still able to note odd things happening on the table, such as the pushing away of objects towards the periphery and the slobbering of the clock on the periphery. But isn't she static relative to the table? If she does not observe the motion, how can she notice the effects of relativity?
✓ Ok, the whole pointing of bringing out a rotating table is to create an acceleration or gravity, so that to make the explanation for the following information easier.
✓ I think special relativity means the relativity effect caused by high speed, while general relativity gravity (acceleration). The formal can be created and terminated by us in our own system, but the latter exists throughout our system and cannot be terminated by us. General relativity is the intrinsic feature of the world we are aware of. Even though we are inside the system and thus unaware of its acceleration, we are still capable of observing the effects of relativity (slowing of time due to difference in gravity, curvature of light beam). Therefore, this is a different effect from the one produced by moving close to the speed of light.
✓ Chapter 8
✓ When doing an observation of small particle, if one uses light with short wavelength for illumination, one can measure the position of the particle but its momentum will be altered due to the collision of high energy photons. On the other hand, if one uses light with long wavelength for illumination, thus lowering down the effect of altering the momentum of the particle due to collision with photons, then he cannot accurately measure the position of the particle since the wavelength is too long. This is why one can never accurately measure both the momentum and position of a particle simultaneously.
✓ Chapter 9
✓ The uncertainty in quantum mechanics indicates the trade-off of momentum and wavelength. In our world, since the Plank's constant is very very small, the quantum effect is not observable in daily life--even a fairly small momentum still produces quite negligible wavelength. However, if such constant is large, in order to reduce the wavelength--that is to localize an object and not make it spread out, one needs a large momentum. And if the object is not supposed to move at a high speed, the only way to increase the momentum is by increasing the mass. That's why the the guide suggested them renting an elephant instead of a donkey.
✓ Chapter 10
✓ I think the foolproof gambling system can work, as long as one only bets 1 pound after a previous victory and the game has a fifty-percent probability of winning. In that case, the probability of a losing streak is as small as that of a winning streak. Therefore, it is very unlikely that one would keep losing and build up an amazingly high debt. The more likely scenario is an alternation of winning and losing. Provided that one has a backup fund that could sustain for a 10 losing streak, he can bet each time after a previous victory 1 pound. If he loses, he bets 2 the next time. Since the losing streak would not likely to last more than 10 times, he would eventually win one game before his backup found is exhausted. And that victory could guarantee him with 1 pound bonus. Then he simply has to restart everything again, with betting 1 pound in the beginning. In this manner, he can keep winning 1 pound after a couple of games, and as long as he plays the game long enough, he will have accumulated a fortune, though it is fairly small considering the gain of 1 pound each time.
✓ The problem for people carrying out this foolproof gambling system is not with the system itself, but rather with people's greed and its efficiency. Normally people are not satisfied with winning 1 pound each victory, especially when that victory happens after several losses. They naturally want to raise the steak by, say, betting 2 pounds after a victory. However, one of the secrets in this system is that the gain increases much much slower than the lost. The more one bets, the more he will lose if he keeps to the rule of the system. And eventually what happens is that the person's backup fund is drawn up before he could strike his next chance to win it all back. On the other hand, the extremely low efficiency of gaining in this system also encourages people to take risks and ruin themselves. In fact, it is actually of no use to carry out the system--what is the point of gambling if one can only win a couple of pounds after doing it for several months!
✓ One more thing to note is that, in the real world, the probability of winning is much lower than that of losing (there is only one winning horse but probably a dozen losers). So the probability of a losing streak is not that uncommon. All in all, the foolproof gambling system is of no practical use and extremely dangerous to a normal person, but quite an entertainment and really foolproof for a bizarre guy.
✓ Chapter 13
✓ The repulsion force among protons is overall weaker than the short range interaction. Therefore, according to the classical mechanics, it is impossible for any atom to radiate any particles. However, the reality is that radiation takes place, though at a very low rate. The reason is that the escape of the "inescapable" alpha particles is due to the quantum effect, one that allows a particle to go across a wall at a certain probability. Though the probability of an alpha particle to overcome a higher energy barrier is very small, it can happen after a considerable number of trials and a long time. That's why the half life of the radioactive element is normally very long, ranging from hundreds to millions of years--alpha particles are actually defeating the unfavorable probability!