Temperature History of the Universe
JOB 6: WHAT HAPPENED in the YEAR 500,000?
-- and how did it happen?



      The world has not always been transparent. We take it for granted that we can look in every direction in the sky, and here on earth, and see as far as there is anything to see. This hasn't always been so. Are you surprised? .... But we're getting ahead of ourselves. How long ago are we talking about?

      We are told that about 14 billion years ago the universe exploded from a miniscule space and began to expand into the enormous size it is now. This event is called the "Big Bang." In the previous job (Job 5) you saw how Hubble's observations first led astronomers to draw that idea.

      There is something else that astronomers have discovered. They have figured out that about 500,000 years after the Big Bang, the universe experienced a very big change. The whole universe - everything that was -- had been in a thick fog of particles, through which light could not travel because it would immediately be absorbed. Then, almost overnight, so to speak, the universe became transparent.

Just what gave astronomers the clue that this transformation occurred at that time? After all, 500,000 years after the Big Bang is still almost 14 billion years ago!

       Would you like to know? The answer is part of the story of this Job. It's kind of a round-about story, so come and take the journey with us, one step at a time.


(1)    BOILING TEMPERATURE

Water boils at 100o (Celsius).
   This means that below 100o, water is liquid. The water molecules stick together. They are held by "bonds" -- forces between one water and another.
   Above 100o water has boiled and is called steam.
   The random motion of the water molecules becomes so vigorous, that it breaks the bonds between the molecules. In steam each water molecule is separate.

"Boiling temperature" in general is the temperature at which the heat motion is vigorous enough to break some particular bond.
   In the simplest atom, hydrogen, the electron and the proton are held together by a bond caused by the electric force of attraction between them.
   The boiling point of that bond is about 10 million degrees (10,000,000o). Scientists know this because they have been able to break those bonds in the laboratory (not by heat, but by zapping with electricity.)



(2)    "WHAT HAPPENS WHEN "ELECTRONS BOIL?"

   When electrons zoom about free of their bonds to atoms, they quickly absorb any light that comes their way. For anyone who would like to see what is going on around them, it is like being in a thick fog -- no light can reach your eyes. It was like that in the first 500,000 years of the universe. No one could see anything, because of the fog of free electrons. Of course no one was around who wanted to see what was happening!

   It was hotter than 10,000,000o, and, just then, as the universe gradually cooled, the temperature dipped below 10,000,000o, and a wonderful thing happened. All of a sudden bonds formed between electrons and protons in hydrogen, and in atoms in general,and the bonds were able to hold fast. There was not enough kick in the heat motion to break those bonds anymore. All electrons were trapped in atoms. There were no longer a lot of free electrons, and light was able to travel about the universe. The universe had become transparent. One could see from one place to another.


(3)     LOOK-BACK TIME -- Seeing into the Past

   No, you can't go back in time. Time travel is science fiction.
   But you can LOOK back in time. You do it all the time. When you take a picture of the sun, (don't look at the sun! it would hurt your eyes) your picture shows you the sun as it was eight minutes earlier, because it takes 8 minutes for light to travel here from the sun. When you look at the Andromeda galaxy in the sky, you see it not as it is now, but as it was 2,000,000 years ago, because that is how long it takes light to travel here from Andromeda. This is called "look-back" time.

   Our telescopes can see quasars whose light took over 12 billion years to reach us. These quasars tell us what the universe was like 12 billion years ago.

   When we look back just a couple of billion years longer than that, we don't see any objects, because there were not yet any stars or galaxies that far back in time. But, our radio telescopes do "see" light from that period in time, only it is just a general blur, because there were no objects, just the universal soup that was the early universe. The farthest back in time that we will ever be able to SEE with light is that blur from all directions (called the universal background radiation) that has just the right wave lengths for a hydrogen gas glowing at 10,000,000 degrees. It is the oldest light that can be seen, because before that the electrons were all boiled out of their atoms, and light did not survive to come to our telescopes.


(4) How do astronomers know WHEN the universe became transparent?

    The universe started out very hot and as it expanded, it cooled, until now it is quite cold (except near a star, like the sun). As the universe cooled, there came a time when its temperature passed from being hotter than 10,000,000o to being colder than that. This is when free electrons partnered with protons to become atoms, and the world became transparent.

    We can model the cooling process, because we know what caused it to cool. As the universe expanded, everyhting got got farther away from everything else. This spreading apart is, in principle, not much different from what happens when you throw a ball upward. The gravitational potential energy goes up as the ball gets farther from the earth. The increase is most rapid at first, the gravitational potential energy increasing as the ball slows down and its kinetic energy decreases. As long it is going up, it still has kinetic energy to give up, and it will go higher. When it has no more kinetic energy left, it can not go farther up, and it stops, and begins to fall.

   As it falls, it re-enacts its rise, only backward. As it falls, it goes faster and faster, feeding the increase in kinetic energy from the decrease in potential energy.

Our universe at present consists of galaxies far apart, which is like a ball that has been projected upward reaching a great height. We can conclude that the ball, like the stuff of the universe, must have been projected with a great deal of kinetic energy, going very fast.

   If we wish to determine the ball's "speed" history as it rose, we can solve equations dealing with the upward projection. We can equally well determine the history by solving the equations of the ball's descent downward, and this is a bit easier on the imagination as well as the algebra.

   Although the universe is billions of galaxies, and the distances are enormous, its expansion is governed by gravity, much as the ball's rise is. We can solve some equations to give us a speed history of the expansion of the universe, or we can get the same information by studying the collapse that would occur if the expansion were reversed, the galaxies stopped in their tracks and allowed to fall back upon each other over billions of years.

   An exact solutions for the whole universe, in three-dimensions is quite complicated. But, I have a better idea: There is a greatly simplified model that is still good enough to give us a lot of insight into what happens, whjen it happens, and why.


(5). The "Better Idea" model

    The "better idea" model of the universe illustrates several important features of the history of the universe beautifully. It does not claim to be "like" the universe in detail. No model this simple could be that perfect.

The features that this model demonstrates well are the following:
1. The universe began extremely small and extremely hot, about 14 billion years ago.
2. A great deal happened in a very short time at the beginning.
3. Its expansion was ruled primarily by the force of gravity.
4. As it expanded, its kinetic energy decreased as its gravitational potential energy increased.

     It is possible to determine the course of the cooling of the universe with time more accurately from a more exact model.

    The model we are using consists of two galaxies, behaving as if they were two objects. It follows their motion in one dimension in the place of a three dimensional universe with billions of galaxies. It counts the kinetic energy of the galaxies as they fall toward each other as an equivalent amount of heat kinetic energy, from which one can calculate a "temperature-equivalent" history. This is not as bad an approximation as might be thought, because in the real universe this kinetic energy was originally "heat" energy, that is, kinetic energy of particles. In the "reverse time" of the model, the kinetic energy gained by the galaxies as single objects is destined to become particle kinetic energy when the galaxies collide and merge.

The limitations of this model are these:
1. It can not correctly represent the very early universe, because after the model galaxies collide, they no longer act as if they were single objects.
2. The times and temperatures revealed by this model are approximate. See "/phys/howfar/T_Hist_actual.pdf" (from the download) for the results from more elaborate calculations based on a more exact model.

The "better idea" model
    Imagine a large galaxy that suddenly explodes, sending its two halves, each a moderate sized galaxy, in opposite directions at great speed, or, better yet, imagine the process in reverse:
    Stop two average sized galaxies when they are separated by a distance equal to the average distance between galaxies in today's universe, and let gravity pull them toward each other.
    Let these two galaxies go, and calculate how fast they approach each other as time goes on. The history of the imaginary galaxies falling toward each other is this model's solution to the forward-in-time history following a "big bang" explosion, just reversed.
    The temperature-equivalent of the two galaxies is calculated from their kinetic energy, as if it were "heat" energy. The result is what we call a "Temperature history." To get our model's temperature history of the expanding universe we reverse the time scale.

    This history (when calculated using a more exact model based on the same idea) gives us an estimate of the temperature of the universe at any time since the Big Bang. The time at which the temperature was 10,000,000o in turn tells us when the universe became transparent.
    More than that, the temperature history tells us at what time in the past the boiling temperatures of various other important bonds were crossed. It tells us, for example, when the universe became cold enough for the nuclear bonds to grab hold, allowing the formation of the nuclei of all the chemical elements of the periodic table.

    Modeling the universe with just two galaxies is a very crude approximation. Besides, it is not yet clear whether gravitation is the only force that controlled the playing out of the large scale history of the universe. Yet, this model is surprisingly informative.

    In the next section we will show you how to calculate such a Temperature History. It will take you perhaps a couple of hours of calculations using a hand-held calculator to do. Hundreds of ordinary high school students have done these calculations; seeing the temperature history revealed before your eyes, and by your own hand, is something you won't want to miss!



Your instructor will provide you with a printed set of instructions, data, and a copy of the table below for you to use.

If you are working from the web site, here is the same information:

Initial separation (d) between galaxies: 2 Million light years = 2.00 E+22 meters
Initial velocity = 184 m/s (This is an artificial number, to generate a reasonable starting temperature.) Temperature (deg K) = v2 / 12400
Mass of each galaxy: M = mass of 230 Billion stars the size of our sun = 4.6 E+41 kg
Time (conversion from Billion Years (BY) to seconds): 1BY = 3 E+16 sec
Force between galaxies: F = G*M*M/d2
(Law of gravitation) acceleration of each galaxy toward their center of mass : a = F/M
(Newton's Law of motion F=ma) decrease in distance between galaxies: d = 2*(v t + ½a(t)2)
new distance (move this result to column 4 in the next row): d'=d-d
new velocity (move this result to column 5 in the next row): v'=v+at

To get the Temperature history, fill in the table below. Work from left to right in each row, moving the new values for distance and velocity to columns 4 and 5 in the next row.



1234567891011 12
Time
interval
t
real time
after
bigbang
reverse
time
before
present
distance
(meters)
from col 11
prev row
velocity
(m/sec)
from col 12
prev row
  Temp  
(deg K)
  Force  
Newtons
accel-
eration
  (m/s2)  
time
interval
t
(sec)
decrease
in
distance
d
(meters)
new
distance
(meters)
(to col 4
next row)
new
velocity
(m/sec)
(to col 5
next row)
2 BY14 BY02.00E+221843 deg3.53E+287.67E-146E+162.761E+201.972E+224,602
2 BY12 BY2 BY1.97E+224,6021,711  6E+16    
2 BY10 BY4 BY     6E+16    
2 BY8 BY6 BY     6E+16    
2 BY6 BY8 BY     6E+16    
1 BY4 BY10 BY     3E+16    
1 BY3 BY11BY     3E+16    
1 BY2 BY12 BY     3E+16    
½ BY1 BY13 BY     1.5E+16    
***½ BY13.5 BY   ******************
xx            
xx            
xx            

Permission is hereby granted to reproduce the contents of this section for use in teaching, provided no charge or fee is accepted and provided credit is given to Cavendish Science Organization

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