Basic Physics Of Quantum Theory, The. Basil S Davis
sense of the term. This means they relied only on their observation in order to draw conclusions regarding the reality of objects in the visible universe, rather than the authority of priests or sacred books.
They observed that the sky was filled with different luminous objects that rose in the east and traveled slowly towards the west before disappearing below the horizon. These celestial objects included the sun, the moon, the stars, and a few star-like spots of light of differing brightness. The stars seemed to be fixed to an invisible hollow sphere, and it was as though this sphere rotated around the earth. The axis of rotation appears to pass through a star in the north which we call the North Star or the Pole Star. The sun and the moon and the other star-like objects seem to revolve round the earth with different speeds. There were five such star-like lights visible at different times in the night sky: Mercury, Venus, Mars, Jupiter and Saturn. These star-like objects — together with the sun and the moon — were called Wanderers or Planets (from the Greek for wanderer).
The ancient Greek philosopher Aristarchus (died 230 BCE) suggested that instead of imagining all these heavenly objects to be orbiting the earth, it is easier to imagine the earth rotating about its axis. But this idea was so revolutionary that it was rejected. It was hard to understand how such a massive object as the earth could be set in motion, and how birds which flew above the earth were not left behind due to the rotation of the earth. Moreover, a stone thrown vertically upwards came back vertically downwards, which seemed to suggest a static earth. Many discoveries had to be made before all these objections could be satisfactorily answered.
2.2Measurement of time
The seven-day week is probably traceable to the seven Planets seen in the sky.1 Each day of the week was dedicated to a particular one of these heavenly lights. We can see echoes of this in our English names: Saturday for Saturn’s day, Sunday for the sun’s day and Monday for the moon’s day. We also find this in the French names for the other days of the week, with the suffix di for day: Tuesday mardi (Mars), Wednesday mercredi (Mercury), Thursday jeudi (Jove = Jupiter) and Friday vendredi (Venus).
The pattern of the stars in the night sky changes gradually from night to night, but is repeated after a period of 365 days, or more accurately 365 and a quarter days. This was established by the ancient Egyptians who painstaking recorded the position of the bright star Sirius shortly after sunset night after night and found that Sirius returned to its original position after 365.25 days. This period of about 365 days also matched the climatic cycle of the seasons, which includes average temperatures, positions of the sun in the sky at noon, etc. So the idea that there is a natural period of time which we call a year was established in ancient Egypt, long before the year was associated with the earth’s motion round the sun.
The Egyptians also divided the day into 12 equal periods and the night into 12 equal periods. Each period was called an hour. Clearly, a day hour was in general different from a night hour. Moreover, the actual length of an hour also varied with the season, day hours being shorter in winter and longer in the summer, with the reverse holding for night hours.2 Later the hour was defined as a 24th part of a day-night duration, making it a constant measure of length at any time of day or night and all through the year. Today the scientific unit of time is the second, which is defined by an atomic clock.
As the moon orbits the earth its phase as seen from earth changes from new moon to crescent moon to half moon to gibbous moon to full moon and all the way back to new moon. So the lunar cycle also defines a period of time. This period was called a month, the word month being related to the word moon. This is not an invariant period, because the length of a lunar month varies slightly from cycle to cycle. The average length of a lunar month is a little less than 30 days. So there are 12 lunar months in a year, with a few extra days left over. These days are added (unevenly) to the months to make the sum of the days of the 12 months equal to 365. Now, since the year is closer to 365.25 days, if we were to limit the year to 365 days, after 4 years we would be behind by 1 day. So 1 day is added to the year every four years (leap year). If the last two digits of the year is a multiple of 4 then it is a leap year. But even this arrangement is not perfect. Every now and then a small further adjustment is needed. So the rule is that if the last two digits are 0, then we look at the next two digits and if this number is divisible by 4, then it is a leap year. If not, it is not a leap year. So 1900 was not a leap year, and 2100 will not be a leap year. But 2000 was a leap year, and the next leap year ending in two zeros will be 2400.
Exercise 2.1.
(a) How many seconds are there in a month of 30 days?
(b) How many seconds are there in a year (365.25 days)?
2.3Ptolemy’s model
Since the sun presents a circular face it seemed natural to assume that the sun is actually a sphere. Likewise, although the moon goes through phases, it made sense to assume that the moon is a sphere and the dark part of the moon represents the night regions. The shapes of the other planets could not be discerned with the human eye, but it seemed logical to assume they too are spheres. What about the earth? The earth looks more or less flat, but the early scientists figured out that the earth is actually a sphere.
The Greek philosophers came to this conclusion through careful observation and logical deduction. Chief among their observations were the following:
1. A ship dips below the horizon when it travels far from the shore, showing that the ocean surface is curved.
2. The noon day sun is seen further south in the sky in more northern climates.
3. The shadow of the earth on the moon’s surface during a lunar eclipse is circular.
So the earth and all the planets were known to be spherical. The sphere was therefore a perfect three-dimensional shape. It made sense to say that the circle was the perfect two-dimensional shape. This had major consequences for understanding the movement of the solar system.
Ptolemy (died 178 CE) was an Egyptian astronomer who studied the celestial objects with great precision. He concluded that the heavenly bodies all travel around the earth in circles — with each circle being called a deferent — with somewhat differing speeds. With the exception of the sun, the moon, and the stars, the celestial objects (i.e. the five planets) also move in a cyclic path — called an epicycle — about the main circular orbit or deferent. This dual motion was necessary to explain why these planets seem to backtrack their path in the sky every now and then instead of progressively moving along in a single direction.
Ptolemy’s model prevailed for over a thousand years and was the dominant model of the solar system used by scientists until it was seriously challenged by Copernicus.
2.4The Copernican revolution
Copernicus (died 1543) showed that it is easier to explain all the astronomical data of the movements of the heavenly bodies by assuming that the earth rotates on its axis and that it goes round the sun and that all the planets also orbit the sun, except that the moon orbits the earth and travels along with the earth in its orbit of the sun. Copernicus’ model is called the heliocentric — sun at the center — model, as opposed to the geocentric — earth at the center — model of Ptolemy. Because Copernicus’ theory brought about a major shift in our most basic understanding of the visible universe, any major change of generally accepted ideas has come to be called a Copernican shift.
But the Copernican revolution did not happen overnight. Copernicus was fully aware of the controversy that his theory would create, and so he published his thesis only on his deathbed. He was condemned by the Christian leaders of Europe, both Catholic and Protestant, on the charge that his model contradicted the Bible. Though the Bible has not changed, today no Christian leader claims any contradiction between the Bible and the Copernican model of the solar system. But the religious objection was not the most serious obstacle to the universal acceptance of Copernicus’ theory. Let us recall that the philosopher Aristarchus (died 230 BCE) had put forward a heliocentric model of the solar system several centuries earlier. The opposition to Aristarchus certainly did not come from religion