Entropy and the Big Crunch

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Many cosmologists find the concept of a re-collapsing universe philosophically attractive.  Einstein and Wheeler among others were drawn to the idea of a universe that was infinite in both space and time.  Wheeler felt that a Big Crunch or the collapse of an earlier universe and its subsequent re-expansion would provide a pleasing symmetry to the history of one that began with a big bang. 

But many feel the symmetry imposed by a Big Crunch and its re-expansion would violate the second law of thermodynamics, which states the entropy or disorder of an isolated system either remains constant or increases with time.

However, this conclusion is not supported by observations.

For example if we take a quantity of gas concentrated in a small region, it will naturally tend to expand to fill a progressively larger volume of space.  This is an example of how the entropy of physical systems tends to increase while the reverse of this process does not.  In other words, the fact that we do not observed a dispersed quantity of gas spontaneously becoming concentrated into a smaller region is confirmation of the second law of thermodynamics

However, in the treatment of small quantities of gas, gravitational attraction is negligible, but for a sufficiently large quantity, it cannot be ignored.

For example, gravity causes the high entropy configuration of interstellar gas and dust particles to contract and form stars while at the same time redistributing its energy in the form of heat.

In other words, the effects of gravity appears to transform the disorganized high entropy configuration of interstellar gas into a more organized lower entropy configuration while recovering the energy stored in it in the form of heat. 

Many believe that it is not possible recover the energy of the big bang from the high entropy configuration of our present universe in such a manner as to cause its re-expansion.

However, the observation that the gravitational collapse of high entropy interstellar gas causes the initiation of nuclear reactions in stars that releases energy indicates otherwise.  Additionally the fact that the gravitational collapse of a star can cause it to supernova, and expand violently supports the conclusion the gravitational collapsed of the entire universe can result in a “Big Bang” or its violent expansion. 

Granted, cosmologist are not sure if the universe will experience a gravitational collapse, but if it did, as is shown in the article “Gravity verse Entropy” Nov. 15, 2010 these observations suggest that gravity can transform the increasing entropy associated with an expanding universe into the energy that could power its re-expansion.

Another criticism many cosmologists have regarding a cyclical scenario of expansions and contractions is that they believe a collapsing universe would end in the formation of a singularity similar to the ones found in a black hole and therefore, it could not re-expand.

However, if gravity’s ability to reduce the entropy or disorder a system and transform it to heat or radiation as the first law of thermodynamic says it must the universe would have to begin expanding before it reached a singularity because that law of states that energy in a closed system can neither be created or destroyed.

The universe is by definition an isolated system therefore; the energy generated by its gravitational collapse cannot be radiated to another volume but must remain within it.  This means the radiation pressure exerted by its collapse must eventually exceed momentum of its contraction and the universe would have to enter an expansion phase at a low entropy point and “bounce” towards a higher entropy future.  This is because its momentum will carry it beyond the equilibrium point were the radiation pressure equals the momentum of its mass.  This will cause the energy/mass of the universe to oscillate around a point in space. 

This would be analogous to the how momentum of a mass on a spring causes it spring to stretch beyond its equilibrium point resulting it osculating around it. 

There can be no other interoperation if one assumes the validity of the first law of thermodynamics and that the total energy of the universe is defined in terms of its energy or heat and momentum of its mass.  Therefore, when one decreases the other must increase and the universe must oscillate around a point in space if it does enter a contraction phase.

The reason a singularity can form in black hole is that it is not an isolate system is because the thermal radiation associated with its collapse can be radiated into the surrounding space.  Therefore, its collapse can continue because momentum of its mass can exceed the radiation pressure cause by its collapse in the volume of space surrounding a black hole.

The heat generated by the collapse of the universe would raise the temperature to a point where electrons would be strip off all matter and it would become ionized, making it opaque to radiation.  It would remain that way until it entered the expansion phase and cooled enough to allow matter to recapture and hold on to them.  This Age of Recombination, as cosmologists like to call it is when the Cosmic Background Radiation was emitted.

One could quantify this scenario by using the first law of thermodynamics to calculate when the radiation pressure generated by the gravitational collapse of the universe exceeds the momentum of that collapse to see if it could be associated with the Age or Recombination as it must to account for the observed properties of the Cosmic back ground radiation.

This show the existence of gravity and the laws of thermodynamics can provide the basis for the theatrical model Einstein and Wheeler were drawn to because it would define the origins of our present universe in terms of a Big Bounce or Bang caused by the gravitational collapse of a previously existing universe.

Later Jeff

Copyright Jeffrey O’Callaghan 2010

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