Bill,
Without imposing my thinking on the subject on yours, may I just ask some leading questions...
1. IF (in capitals), space is expanding and entropy is increasing, might this not suggest a common production process for the two, since both are in the same direction of time? Or at least a relationship, since Mother Nature is usually very frugal in her ways.
2. What is the meaning of the equation
dS = dE/T?
Given a system of low entropy, how can you quantitatively increase the entropy in the system?
3. If the second law of thermodynamics is correct for our universe and has been correct for all time, meaning the more you look to the past, the lower the entropy of the universe will be and therefore at the beginning, S = 0. If we add the third law of thermodynamics, which guides us what the temperature would be at the lowest possible value of entropy, would the very beginning at time zero be hot or cold?
4. Ludwig Boltzmann has the equation S = k log W inscribed on his tombstone, where S is entropy, k is Boltzmann's constant, log stands for natural logarithm and pay attention here, W stands for the NUMBER OF WAYS the system can be realized by assigning different positions and momenta to the various participants. If space is not infinitely divisible into positions because of a limit at the Planck length ~ 10-35m, in a system of given small size, are there a maximum number of positions and momenta available or is the number infinite?
5. Following from 5., if the thermodynamic equations are infallible, what will physically happen if entropy has to be further increased after the maximum, W for that system size is attained?
6. If your opinion to 6. is that system size will be compelled to increase in obedience to thermodynamic law, is this an explosive mechanical process at high pressure à la Big Bang?
7. Have you calculated what the temperature of the universe will be if it contained all the matter,~ 1052kg (1068J) at the very beginning, say about Planck size before 'inflationary scenario' complication? Do you obtain 1047K or 1032K that fits the model?
8. What really is energy? We use the term often in physics, but what exactly is it? Is it something or a much ado about nothing in the final analysis?
Now, this is speculative and tentative. We know that energy is consumed (-ve) to increase radius and thus potential energy, and such energy is released (+ve) as heat, gravitational waves (for GR people) and electromagnetic radiation when radius and potential energy is reduced. In other words,
Eq.1. increase (+) in potential energy and radius of system = (-)decrease in energy in form of heat, radiation.
Eq.2. decrease in potential energy and radius of system = increase in energy in form of heat, radiation.
So these two 'energy types' appear to be OPPOSITE each other, but both energies all the same.
If we put all the energy terms on one side, can I suggest that if the mathematics is not flawed we could write Eq.1 as:
increase (+) in potential energy and radius of system + increase in energy in form of heat, radiation = 0,
since (-) changes to (+) and decrease changes to increase?
If I am correct, then for a system whose balance sheet was initially ZERO, and which must remain so, ANY increase from zero radius MUST be accompanied by an increase in energy in the form of heat, radiation, etc. This energy balancing must continue always till current era.
I think Edward Tryon reasoned in similar way some 40 years ago.
This may satisfy the condition given by those who do not like to eat free lunch. If the increase in energy from zero is simultaneously accompanied and balanced by increase of radius from zero, then perhaps no free lunch after all and no contravention of energy conservation law as the net energy change is zero.
Well let me pause here for now.
Regards,
Akinbo