Gibbs Paradox Solution by James A Putnam

Concerning changing the units of physics into the forms used in my essay:

The change made is not one of introducing new types of units. For example, the units used include meters and seconds. They remain as before. The actual change made is far more radical. It involves returning the equations of physics back to their empirical roots. In other words, removing all units that are not necessary for expressing empirical evidence. Empirical evidence consists of patterns in changes of velocities. The units used to express changes of velocity include just the two units of meters and seconds. Those are the only two units that should be necessary to express the equations of physics in their empirical forms.

An example of an empirical form for an equation of physics is f=ma before deciding about how to interpret mass and force. The empirical evidence for f=ma makes clear that there are four properties involved. They are: distance, time, force and resistance to force. Both distance and time are naturally indefinable properties and their units of meters and seconds are indefinable units.

Being definable means that a property can be expressed solely in terms of pre-existing properties. There are no properties pre-existing distance and time. There are no units pre-existing meters and seconds. However, both force and mass have been learned of and inferred by the patterns of empirical evidence. Everything we are to know about them is rooted in that empirical evidence.

Both force and resistance to force should be fully expressible in terms of the pre-existing properties of distance and time. The units of force and resistance to force should be fully defined by the pre-existing units of meters and seconds. This is the practice followed in my use of units.

The units are the two old units of meters and seconds. Both force and mass must have units that are formed from conbinations of meters and seconds. There are several possible combinations. The choice for mass, that is both logical and proves to be successful is for mass to have units of inverse acceleration. Those units are seconds^2/meters. Force, as a ratio of two accelerations is unit free.

From this point on all other units of higher level properties are definable in terms of those of mass, distance and time. All of them consist of combinations of meters and seconds. For example, energy as the product of force and distance has units of meters. Actually, in long form it has [(units of accleration)/(by units of acceleration )][units of meters].

James Putnam

The reason for using meters and seconds only, the units of empirical evidence:

Properties are defined by their empirical evidence. That empirical evidence tells us all that we will ever know about each property. Theory is the intrusion of guesses onto physics equations. The guesses cannot be more informative than is the empirical evidence. The guesses can be less informative. They are more often than not restrictive to the extent that important empirical meaning is lost. It is artificially hidden from our view by the added-on theory. Those theoretical guesses become permanent restrictions on the usefulness of the equations.

In the case of mass, getting the units right based upon the natural guidance of the empirical evidence means knowing what mass is right from the start. It means knowing that theory that is in contradiction to the meaning set by the empirical evidence cannot be correct. Mass is the most important property to get right. The degree of usefulness of the rest of theory depends upon getting mass right.

There is another very critical property that must be gotten right or unity will be lost. That property is 'electric charge'. There were two unknown terms in Coulomb's equation, often represented by the letter 'q'. It was guessed that those two terms represented a new property that was the cause of electro-magnetic effects. That guess became the theory of electric charge.

The best suited empirical units of mass are those of inverse acceleration. The use of those units leads to the recognition that the units of those two unknowns in Coulomb's equations have to be seconds. Putting this claim up against the long adopted theory of electric charge is difficult to make convincing. The chance to be convincing comes from putting forth the results that occur due to aaccepting seconds as the units for electric charge.

It is the case that the magnitude of fundamental electric charge with the units of seconds becomes key to achieving unity. That magnitude represent a universally constant increment of time. That increment of time placed consistently throughout the equations of physics brings those equations into compliance with always present fundamental unity.

In my essay, I included appendix A for the purpose of emphasizing that that is the case. The two expressions for the fine structure constant are shown to be derivable one from the other. That is just one of numerous examples that could have been chosen and that do exist ready for presentation. Several have been included in my previous essay contests entries. This present essay uses that immensely useful fundamental increment of time to explain what is thermodynamic entropy.

James Putnam

Eckard,

Thermodynamics pertains to macroscopic systems. The properties of temperature, pressure and volume are macroscopic quantitites that pertain to the internal energy of a system. The system could be the universe. The development of entropy began with Clausius discovering a new property of the system, the system being the 'It'.

Boltzmann's definition of entropy broke away from the macroscopic perspective and introduced a new kind of entropy that described a condition of microstates. His definition introduces the 'Bit' into a definition of entropy. One of the points of my essay was to show that Boltzmann's entropy is not a thermodynamic entropy. It is an introductory form of statisitical entropy. It did not include distinguishability.

Gibb's mixing entropy is also an anaylsis of microstates but introduced distinguishability. The example given in my essay involves two gases that are distinguisable. The mathematical solution for his mixing entropy has a form that is seen repeated in the rest of the entropy definitions up to and including Shannon's information entropy. I consider each of the microstate based entropies to represent the 'Bit'.

So, my essay begins by recognizing that the development of entropy is usually presented as if it followed logically connected steps. Yet, the aim of my essay was to demonstrate that the perceived connection between Clausius' entropy and Boltzmann's entropy does not logically follow. The meaning of Clausius' entropy was not explained nor understood by physicsts. It was skipped passed without adequate explanation in favor of jumping directly to statistical entropy. Statistical entropy was understandable.

With regard to Ritz and Einstein, my only resource for that is the Internet. I do have a paper I printed off sometime ago. It is titled: Ritz, Einstein, and the Emission Hypothesis by Alberto A Martinez.

James Putnam

Hi Jacek,

I don't have any quick links to offer. It is something that is usually referred to simply as being 'well known'. That which I have said about it involves only ideal gases. I just gave some of my opinion about Boiltzmann's entropy and Gibb's mixing entropy in the message above addressed to Eckard.

I do say that foce is unit free. A consequence of taking that position is that one force can be the product of two other forces. If you look back at my essay titled 'The Variability of the Speed of Light' in the last essay contest, you will find that I used this new view of force to calculate the universal gravitational constant. It involved using one force as the product of two forces.

This essay contest is my fifth one. Each of my essays involved deriving results using my new approach to the units of physics. I hope you find something helpful to you. I haven't yet read the other essays. I look forward to reading yours. Good luck with it.

James Putnam

So that readers are not mislead by Joe Fisher. My essay is not about abstractions. Even the use of ideal gases refers to a very close approximation of what actually happens to gas as its pressure approaches zero. The properties can be and have been observed experimentally as anyone with at least an introductory level of physics would know. The constants used are not abstractions. They each result from experimental results as anyone with at least an introductory level of understanding physics would know. Even though Joe is able to copy words back at the author while spouting his egotistical disdain, it is clear from his response that he did not understand the steps in the essay. For example Planck's constant was not 'somehow' involved, it was clearly put to use for real physical reason as anyone with even an introductory level of physics would have easily recognized.

James Putnam

Joe Fisher,

I suggest that you return to your numbers and snowflakes.

James Putnam

Eckard,

"Are you aware of On the So-Called Gibbs Paradox, and on the Real Paradox?"

The Author Arieh Ben-Naim briefly mentions, as a side issue, the real papradox but does not address it except to say that examples of real world discontinuity are observed.

The 'real' paradox has to do with the mathematical derivations of entropy and getting them right. is isolated in the ideal gas example that I gave. The author moves from one type of circumstance to another without connecting them. One example is when he states that "However, for ideal gases, the mixing, in itself, does not play any role in determining the value of the so-called entropy of mixing. Once we recognize that it is the expansion, not the mixing, which causes a change in the entropy, then the puzzling fact that the change in entropy is independent of the kind of molecules evaporates." He has to state clearly that all examples are of the adiabatic type.

The example of two distinguishable ideal gases, as I gave in my essay, does not cause a change in entropy whether one refers to mixing or expansion. I fail to see how he see a difference in expansion versus mixing in this same type of example. Mixing entroy cannot be dismissed as lightly as he thinks. It is an important theoretical foundation statistical mechanics and quantum theory. Its mathematical form repeats itself in derivations of entropy up to and including Shannon's information entropy.

I wondered how to respond with details of my own but couldn't see how to address all of the shortcomings that I feel exists in that article. I am thinking that I could write a few messages in my forum here that address some of the issues without direct reference to his article. There are many articles written to address the Gibb's Paradox. I could combine the major issues raised in these articles and address them myself. I think that in my essay I chose the best example for representing the paradox. It was not one chosen by the author to address in detail.

James Putnam

Eckard,

I see that a few words didn't make it into the final message. If you need clarification please let me know and I will rewrite those few parts. Thank you.

James Putnam

Thermodynamic entropy was defined by Clausius. It is the beginning of the concept of entropy. He discovered a thermodynamic property that joined with temperature, pressure and volume. His definition is the only thermodynamic definition. Even Boltzmann's definition is not thermodynamic.

Boltzmann's entropy was the first of statistical entropies. His definition carried the name entropy and by this act introduced confusion about how to connect non-thermodynamic entropies to thermodynamic properties. Boltzmann's entropy, along with the others that followed his lead, involved counting cells or microstates. Thermodynamic properties do not include counting molecules or microstates.

Clausius discovered a new property using only macroscopic thermodynamic properties. He arrived at a definition of entropy that was directly proportional to the ratio of heat to temperature, both thermodynamic properties. The difficulty faced by the non-thermodynamic entropies is that their non-thermodynamic definitions must give correct answers for actual thermodynamic entropies.

As one might expect, their results will be haphazzard. Yet, those incorrect results help to expose the parts of the definitions of non-thermodynamic entropies that are themselves non-thermodynamic. In this way, those definitions can be distinguished from thermodynamic entropy and given recognition for what they actually represent. They represent statistical definitions of things such as microstates or anything else that the theorist wishes to count.

The name entropy no longer belongs exclusively to thermodynamic properties. It hasn't done so since Boltmann gave his definition. The confusion that has followed results in part from his retention of his constant in his definition. Other definitions have retained that constant. The constant does have a thermodynamic connection to thermodynamic entropy. So, those definitions that choose to retain Boltzmann's constant do have a loose partial connection to thermodynamic entropy.

James Putnam