THE AGE OF THE UNIVERSE

( Here follows a mathematical proof of the age of the universe )

It has been found that the bodies comprising the Solar System accreted somewhere about 4,6 milliard years ago (4,6 x 10⁹ ) from the material spewed out by the last maximum of supernova explosions which, according to D N Schramm in his "The Age of the Elements" took place 5 milliard years ago (5 x 10⁹ ). From this material the Sun and the stars in its neighbourhood (the third generation of stars) together with their planets, including the Earth and everything on it were formed and life originated and developed and evolved until today the Earth can boast a technological civilisation, a civilisation which has the capability of destroying all life on the planet. We are therefore supernova material! We once had a temperature of hundreds of millions of degrees!

Schramm also found that a first maximum of supernova explosions took place 9 milliard (9 x 10⁹ ) years ago. He worked this out by research on the ages of radioactive elements such as uranium, thorium, radium, etc. These elements undergo spontaneous disintegration whereby they eject particles such as nuclei of helium as well as protons, electrons and gammarays. The rates of decay of these elements are not in the slightest affected by external conditions such as temperature and pressure. Each of these radioactive elements has a fixed half-life period - the time required for half of its atoms to decay, e.g. uranium has a half-life period of 4,56 x 10⁹ years; thorium 1,34 x 10⁹ years, radium 1590 years, according to J D Stranathan in "The Particles of Modern Physics". Since these half-life periods are constant, the ages of the deposits of radioactive ores can be very accurately measured, by measuring the amounts of decayed products (in all cases base lead) found in the ores. Uranium in the Lunar rocks dated the material from the Maria as 4,6 .x 10⁹ years and that of the Lunar Highlands as 3,9 x 10⁹ years. The greatest age that has been found for Earth rocks is 3,9 x 10⁹ years, as old as the Lunar Highlands. The Lunar Maria have a greater age because their surfaces consist of lava which welled up when massive bodies crashed on to the Moon, thereby flooding the surrounding highlands and submerging them.

By means of the redshift of the spectral lines the distances of far-off galaxies and quasars have been determined. If the distance of a quasar is, for example 5 x 10⁹ light-years, then that quasar must be at least 5 x 10⁹ years old. When the redshift of the spectral lines has been determined, the distance can be calculated by using Einstein's equation and Hubble's Law. Einstein's equation gives the speed of recession of the far-off object. All distant objects are receding from us and Hubble's Law states that the speed of recession is proportional to the distance.

The redshift can be easily determined because it is the fraction by which the spectral lines have been shifted to the red end of the spectrum. If the spectrum line shows a wavelength of whereas the wavelength at rest is then the redshift is given simply by:

If quasar 3C 273, for example has a redshift z = 0,16, then Einstein's equation gives:

where c is the speed of light (300 000 km per sec.) and v is the speed of recession of the body.  The redshift of quasar 3C 273 is 0,16. Therefore

, i.e.. Therefore 0.3456 c = 2.3456 v. Thus: 14.7% of the speed of light.

Quasar 3C 273 therefore has a speed of recession of 14,7 percent of the speed of light i.e. 0,147 x 300 000 km per sec.

 Hubble's Law states V = H_o D where V the is speed of recession and H_o is the Hubble constant. Various values have been found for the for the Hubble constant, from 55 to 100 km per sec. per megaparsec. Let us use a good average of 75 km per sec. per megaparsec.

, \ where V = 0.147 x 3000 000 and H_o = 75 km per sec. per megaparsec.

We have to multiply by 3,26 to convert parsecs into light years and divide by 1000 to obtain milliards. Therefore:

milliard light years. Distance divided by speed is equal to time, i.e. the time that the light has been on the journey from the quasar to us.

The age of the quasar therefore CANNOT BE LESS THAN THIS AMOUNT OF TIME.

So we have 1,917 + 0,147 = 13,04 milliard years. We see that this value is obtained for all the quasars listed in the table and this value 13,04 is therefore the age of the universe in milliards of years (10⁹).

If we use H_o = 55 we obtain an age of 17,78, and if we use H_o equal to 100 we obtain an age of 9,78 milliard years. This latter value allows very little time for the first stars to develop to the supernova stage which took place 9 x 10⁹ years ago. The most reasonable value for the age of the universe is therefore 13 milliard years (13 x 10⁹).

From the table we see that the speed of recession increases as the redshift increases. Also that the distance gets nearer and nearer to the value 13,04. When the speed of recession equals the speed of light, the distance will be 13,04 milliard light years!

Jan Eben van Zyl