Probabilities Give Results, Not Reasons
March 21, 2015
Kent W Mayhew
Probabilities can be used to determine the results of many processes, such as:
1) The dealing of cards, there is a probability for getting a full house and another for getting a pair and still another for getting a pair of jacks.
2) Rolling of the dice, there is an equal probability for each dice to show 1 though six and there are different probabilities for the sum of the dice with seven holding the distinction of being the highest probability.
3) A drunkard walking in random directions, there is even a probability of him finding his rightful bed.
Of course there are too many processes to which probabilities apply to list here. In all cases the probability gives RESULTS and not the REASONS for the event. Many of us are taught to master these probabilities and the various distributions in thermodynamics. But as with anything, we walk very dangerous ground when we start thinking in terms of a given set of probabilities providing a reason rather than a result. Yet this is done all the time, and we physicists are as much to blame as anyone.
Too often we boldly state this or that based upon solutions that incorporate probabilities, when the reality is that our deduction can only be at best deemed, possibly correct. The only way to fully validate what we now believe is to find some constructive logic that gives the results without the necessity of using a probability. And even then an empirical result does not prove a given constructive logic, rather it can only disprove your theory, or at the very least make you rethink what your analysis.
In other words any given empirical result may have more than one theory, and if your theory is based upon probabilities then there is strong probably that something is amiss with your theory.
Nowhere in the history of mankind has this been more true than in thermodynamics. Herein we formulated entropy and the second law, then applied eigen values/energies onto the systemís molecules, construed probabilities, determined the number of possible states; And then set: TdS=dE+PdV.
Then we formulated traditional thermodynamics around the above stated probabilities and all of its accompanying mathematics. Surely a simpler approach would have been to realize that lost work is the work required to displace our atmosphere, that being: W=PdV.
Without a doubt, not only did the above led to the belief by too many in a complicated thermodynamics which was not based upon constructive logic, but it also wrongly reinforced some theorists beliefs in the powers of statistical physics/mechanics; namely its power in determining reasons rather than simply results.
In hindsight you should now realize that the reason for lost work is the upwardly displacement of our atmosphere. And the fact that statistical thermodynamics can determine all the possible results wherein; W=PdV just proves how powerful statistical physics/mechanics is as a mathematical entity.
Copyright Kent W. Mayhew