Gravity verse Entropy

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On page 297 of Sean Carroll’s book from “Eternity to Here” he discusses the difficulty in interrogating gravity with the second law of thermodynamics.

The second law of thermodynamics states the entropy or disorder of an isolated system either remains constant or increases with time and that no usable energy can be obtained from a high entropy configuration.

However, observations of the effects gravity has on interstellar environments appear to contract it.

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 a dispersed quantity of gas will not spontaneously become concentrated into a smaller region confirms the second law of thermodynamics

However, in regions of interstellar space where there exist large quantities of gas (of sufficient density) it will naturally contract due to the mutual gravitational attraction of the molecules thereby decreasing their entropy.

Additionally the observation that the gravitational collapse of high entropy interstellar gas causes the initiation of nuclear reactions in stars that releases useable energy appears to be a violation of the postulate contained in the second law of thermo dynamics that no usable energy can be obtained from a high entropy system.

Some physicists try to rescue it by pointing out that the gravitational collapse of interstellar gas does not occur in a closed environment and that the heat and usable energy generated from its collapse is offset by the heat radiated out into space thereby increasing the overall entropy of the universe.

However, that argument cannot be applied to the universe as a hole because by definition it is a closed system.  This means the heat and useable energy caused by its gravitation collapse could not be offset by energy being radiated to another environment.

This also beings up the question as to why the second law of thermodynamics held in such high esteem by many physicists.

For example Sir Arthur Stanley Eddington, implied it is the most important law in physics when in “The Nature of the Physical World” when he said “The second law that entropy always increases holds, I think, the supreme position among the laws of Nature.  If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations — then so much the worse for Maxwell’s equations.  If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes.  But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.”

However, observations of gravity’s effect on our local environment, when extrapolated to a cosmic scale can have a profound effect on our understanding of the origins of our universe.

Granted science has not yet determined with certainty if the universe will continue to expand or will enter a contraction phase.

However, if it did it would present a serious problem for the second law of thermodynamics because the loss of entropy and generation of heat by the total gravitational collapse of our universe could not be radiated to another environment.  Therefore, the radiation pressure caused by this heat and loss of entropy would result in its reexpansion.  Hence the argument that the heat and usable energy (usable in the sense that it powered its expansion) generated by the gravitational collapse of the universe is offset by the heat radiated out into space would not apply to the gravitational collapse of the universe.

Even if the universe does not enter a contraction phase this presents a strong theoretical challenge to the universality of the statement “The second law that entropy always increases holds, and that it is the supreme position among the laws of Nature”

However, this also means that we may be able to quantifiably derive the origins of our present universe, as was suggested by Robert Dicke in 1964 in terms of cyclical expansion and contraction of previous ones.

As was shown in the article “Entropy and the Big Crunch” Sept 15, 2010 the heat generated by the gravitationally collapse of the universe could raise its temperature to a point where all matter would become ionized, while the radiation pressure generated by its increasing temperature would eventually halt its contraction and cause it to enter an expansion phase. 

There are many objections to scenario however they are based on applying the second law of thermodynamic to local environment such as the collapse of interstellar gas to form stars.

For example many dismiss this idea because they believe that the “engine” powering the universe’s cycle of expansions and contractions would eventually slow down and stop because according to the second law of thermodynamic there is no such thing as a totally efficient engine. 

However, that assumption is not based extending the validity of that law to a scale which encompasses the entire universe, which as was just shown is invalid when you consider the effects of gravity.

One reason a perfectly efficient engine cannot exist is because energy, usually in the form of heat escapes from its environment.  However, as mentioned earlier because the universe is by definition a closed environment no energy can escape from it therefore, it would be a perfectly efficient with respect to the energy associated its gravitational contraction and thermodynamic expansion.

Another aspect of the second law of thermodynamics many use to invalidate the concept of a cyclical universe, is that it dictates that as the number of cycles increases the entropy or randomness of its components and structures must also increase and therefore after infinite number of cycles there should be no organized structures such as galaxies remaining.

However, this would only be true if the heat generated by the gravitational collapse of the universe was not great enough to completely break matter down to its constituent parts.

As mentioned earlier the article “Entropy and the Big Crunch” showed the energy associated with its gravitational collapse would be great enough to completely break matter down into it fundamental components thereby each cycle would start at the same point with respect to randomness or entropy of its matter component.

In other words the matter component of the universe would be reset or reinitialized to their previous configuration at the beginning of each cycle thereby making the randomness of its components, such as galaxies consistent through each success cycle.

This scenario gives just as logical and consistent explanation of the Cosmic Background Radiation as the current Big Bang Model because it assumes it is a result of the universe cooling to a point, due to its expansion where its matter component has become  de-ionized enough to make it transparent to radiation. 

However, in the model suggest above the heat generated by the collapse of the universe would ionize all matter while the radiation pressure caused by its contraction will eventually result in it entering an expansion phase.  Therefore, the universe would be opaque to radiation until it entered an expansion phase and cooled enough to allow its matter component to become de-ionized.

Therefore, both of these theoretical models make the same predications as to the origin and the properties of the Cosmic Background Radiation.

A cyclic universe like the one Robert Dicke proposed would also answer several of the questions nagging modern science.  It would allow us to understand and predict what came before the Big Bang in terms of a collapse and the subsequent expansion of a previous universe.  It would also eliminate the fine-tuning required to make the present Big Bang model fit modern observational data regarding the abundances of the light elements by allowing one to predict them based on what occurred before its expansion.

For example, the Big Bang model accurately predicts the abundances of the light elements.  However, each prediction requires at least one adjustable parameter unique to that element prediction.  When you take away these degrees of freedom, no genuine prediction remains.  The best the Big Bang can claim is consistency with observations using the various ad hoc models to explain the data for each light element.

However, if it is true that our present universe is a result of its collapses and reexpansion one could use the first law of thermodynamics to predict and quantify the properties of the environment when the lighter elements were formed based on the energy supplied to it by the momentum of its collapse.  One could then determine if their observed abundances could be predicted based on the properties of that environment.

Additionally a cyclical model like the one suggest by Robert Dicke has an advantage over the big bang model in that it would allow one to quantify the origins of our present universe by observing the way it is now and to extrapolative it backwards in time to determine if they could predict its reexpansion in its present form.  Additionally this would give science the ability to quantify the properties of the environment where the light elements were formed based on observations of the present universe instead on the random selection of different parameters.

Later Jeff

Copyright Jeffrey O’Callaghan 2010

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