Topic 12 - The Big Bang

 

The Space/Time Continuum - Finite or Infinite?

The General Theory of Relativity changed our view of the Universe for it stated that the Universe is a curvilinear space/time continuum and best described by a non-Euclidean (Riemannian) geometry. But other questions of Universe remained. Is the Universe infinite in size? Has it always been here?

One key question was 'is the curvature of the Universe positive or negative?' If the curvature is positive (like the surface of a ball), then one can imagine the Universe closing back on itself to form a finite but very large continuum. But if the curvature is negative (like a horse saddle), then the Universe goes on and on and is infinite in size.

This can be tested by measuring the number of stars per unit area. In order to do that we need to go back to Astronomy and think about how we measure distance to stars.

 

Star Distances

The distances to nearby stars can be measured directly by parallax with good quality telescopes. One can also measure the brightness of these stars and from a knowledge of brightness and distance determine their actual luminosity. Luminosity is a measure of the amount of light an object gives off per unit time - sort of like a 75-watt versus brighter 100-watt light bulb.

A better knowledge of stars and how they evolve also suggested that one type of star always have the same luminosity. If this type of star can be seen and its brightness measured, then one can determine its distance. In this way, the distances to many more distant stars was determined.

Out of this came the view that our Galaxy is about 100,000 light years across and that there are other galaxies many millions of light years away. Hubble identified the first galaxy other than our own in 1924

 

Our current best view is that the curvature of the Universe is positive! Thus it is a closed finite Universe.

 

Red Shift/Big Bang

As distances to stars were being determined and the brightness of each star measured, the light spectrum of each star was also measured. The light spectrum (light intensity as a function of frequency) helps to tell us what elements are prevalent in each star.

It was noticed that the frequencies of light for each element were shifted a bit in frequency. This was interpreted to indicate that the star was moving relative to the Earth as the light was given off. It turns out that almost all stars have a shift toward lower frequency (red shift) and that means that the stars are all moving away from us.

We interpret this to mean that the Universe in expanding. We can calculate when it should have started expanding and get a number on the order of 20 billion years ago. This is the Big Bang - start of the Universe. Hawking proved that the Big Bang is a natural consequence of the General Theory of Relativity!

 

Nature of Time and Causality in the Universe

Hawking describes the effects of having a finite speed of light in the Universe. The light we see at night coming from the stars is light that left them millions to billions of years ago. There is no way that we can tell if the stars really exist today because information cannot travel faster than the speed of light.

 

Mr. Tompkins Takes a Holiday - Chapter 3

In world of relativity, if one boils an egg by moving pan back and forth as water is heated, the egg will take longer to boil. Time slows down for objects in a state of acceleration.

Mr. Tompkins and the Professor witness a murder (station master with a porter nearby reading a paper) as their train is going past a station. They stop the train and tell the police what they saw. The police arrest the porter and tell the two train riders that they cannot tell who did or did not shoot the station master, because they have a different sense of simultaneity. But causality still holds and porter reading a paper was seen close to station master at (whatever) time he was shot. So he could not have done it.

Quantum constant went scewy for a short period of time and Mr. Tompkins sees many women all looking like Maud. When constant goes back to normal, only one Maud exists.

 

The Pulsating Universe - Chapter 5

Mr. Tompkins finds himself on a small planet in a different world of relativity. One that has universe expansion/contraction going on in days rather than billions of years and a size on the order of 10's of km (kilometers) rather than >>billions of km.

MT firsts observes planet early in its formative period with lots of dust and meteoroids nearby and occasionally slamming into it. There are no stars because no objects have enough mass to provide pressures needed to start fusion.

Professor's book goes flying away from him and MT thinks it is forever lost. Professor notes that it will continue in straight line, but finite size and curvilinear nature of universe will make it come back in short period of time. They watch book recede through binoculars. It first gets smaller, then bigger even though it is still going away from them. Professor explains that as due to convergence of light rays at opposite edge of universe. Its like converging longitude lines at poles of Earth. Once past opposite side of universe, the book starts to look smaller again until they look the opposite way and see the book coming back.

Later, MT notes less dust and meteors and small planets are farther apart. Universe is getting older and expanding. Objects are glowing pink due to red shift as they move away.

Finally, objects start to look violet as universe reaches maximum size and starts to collapse under gravity pull. Objects now have blue shift. Later, universe collapses around MT, everything gets hotter, and he awakes in his bed with covers suffocating him.

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