The hijacking of the Big Bang

The Big Bang theory was invented in 1931 by the Belgian priest Georges Lemaître, through the backward application in time of the Hubble-Lemaître law, discovered by Lemaître in 1927 and independently by Hubble in 1929. Indeed, if most galaxies are moving away from one another, because of the expansion of the space separating them, billions of years ago they must have been much closer, and at the limit all the visible universe would have shrunk to a point. We believe today that this happened about 13.8 billion years ago.

In 1948, George Gamow, Ralph Alpher and Robert Herman made two predictions that should be fulfilled if the Big Bang theory were true: the mass of the universe should consist of about 75% hydrogen and 25% helium; and there should exist a cosmic background radiation with a temperature of about 5º Kelvin. Other cosmologists, however, took this theory as a joke, and to make fun of it they gave it the name Big Bang, which although not quite appropriate, has remained fixed, perhaps forever.

The weak anthropic principle: Are we alone in the galaxy?

Allen Telescope Array in the SETI project

In its initial formulation, the weak anthropic principle says that, although the appearance of intelligent life on a planet may be very unlikely, the Earth must meet all the conditions, since we exist. We know that the Milky Way contains about 10¹¹ stars. At least one (the sun) has a planet populated by intelligent life. It looks like the probability of this happening should be equal to or greater than 10^-11. Note that the weak anthropic principle does not say what the value of that probability might be.

Copyright and e-books

In other posts I spoke about the chaos of copyright rules and about e-books, pirated or not, that can be downloaded for free from the Internet. In this post I am going to add a few of my ideas in this regard.

• Just now, the European Union and the United States apply the rule that copyright lasts up to 70 years after the author's death, or almost three generations. As authors often die now at quite advanced ages, that means that the rights to their books last until the fourth or fifth generation after their own. I doubt that great-great-grandchildren and their children should continue to collect royalties for what their remote ancestor did?
• It is clear that the objective of such long duration is not to benefit authors, but publishers, many of which are very powerful, dominate mass media, and use them to pressure governments to extend the duration of copyright to their benefit, up to about a century. I think this is an abuse; governments should not have given in to these pressures. In my opinion copyright should disappear, at the latest, 25 years after the death of the author.

The best years of our lives

I have taken the title of this post from a famous film directed by William Wyler and released in 1946 (the year I was born). But in this post I am not going to deal with films, but with the different types of years.

Like the day, the year is a natural cycle, defined by the movement of the Earth around the sun. Unlike the day, which varies continuously and for which we must use the average duration, the solar year is fairly constant, as two different years are almost the same duration, although not exactly, so the concept of mean solar year is also used.

As with the hours, days and months, there are also several types of years, which differ slightly from each other, depending on the reference point considered (see the attached table).

Thirteen months in one year?

After talking about days and hours, this is the turn of the month. Like the day, it corresponds to a natural cycle: the revolution of the moon around the Earth. As we know, seen from the Earth, the moon does not seem to rotate around its axis and always shows us the same face. However, if we take as a reference point a star or the sun, a rotation can be seen. An observer located on the sun would see successively all the points on the surface of the moon, therefore would see it rotating around itself. It could also be observed that its period of rotation is the same as its revolution around the Earth. This is why it always shows the same face towards our planet.

The 24th hour

Melting Clock
Sculpture by Dalí

I have tweaked the title of the well-known novel by the Romanian writer Constantin Virgil Gheorghiu (The 25th hour), because in this post I am going to talk about the hours. As with the days, which we talked about in the previous post, there are different types of hours.

Each type of time is defined by dividing the length of the corresponding day by 24. Thus there are as many types of hours as there are days: lunar hour, sidereal hour and mean solar hour. But in addition to these three, there are two more: the true solar time and the official time (see the attached table). The first is a consequence of the fact that the true solar day differs from the mean solar day by up to a quarter of an hour, approximately. For that reason, when ship captains wanted to calculate the geographical longitude of their position by observing the moment when the sun passed through the meridian, they had to apply correction tables based on the date. If we divide the length of each true solar day by 24, we will get the true solar hour, which of course is equal to 60 minutes just a few times a year.

Works and Days

I have taken the title of this post from Hesiod's book. Although I won’t talk about works here, I will talk about days. The word day has two different meanings: the whole day (24 hours) and the part of the day when there is sunlight. Thus, it could be said that

day = day + night

which seems absurd, for a mathematician could deduce that the night does not exist. Instead of that equation, and to make it clear that there are two kinds of days, we should use this expression:

day₁ = day₂ + night

Here, day₁ is a natural cycle, the period of the Earth's rotational motion around its axis. But then a problem arises: when can we say that the Earth has made one complete rotation around its axis? The problem is, to define the period of a moving object, it is necessary to have a reference point. The results will be different depending on which point is chosen.