Gibbs Paradox Solution by James A 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

To all who have contributed messages to this forum:

Thank you for your messages. I have been sick for over three weeks. Very little stamina. I did participate in some discussions with Tom and Lev but those were easy. The hardest part was typing accurately. Now I want to put my time into addressing the concerns of others about my essay. Here is a first part to be followed by others:

The were two purposes for my essay. One was to point out, as I have done so many times to no avail, physicists do not know what thermodynamic entropy is. They give evasive answers such as: Thermodynamic entropy is a measure of energy unavailable to do work; or it is a measure of the degree of disorder. Each time an answer is given for any property in the form of: It is a measure of this or that, then, the writer is making known that they do not know what the property really is.

One knows what a property is when one describes it by its uniqueness. In other words, thermodynamic entropy does not have the units of Joules nor does it lack units such as 'disorder' does. It has units of joules per degree kelvin. The problem for physicists is made clear by the presence of the degrees kelvin. Those are the units of temperature. They are unique units. They are what I refer to as arbitarily indefinable units.

There are only two naturally indefinable units. Those are the units of empirical evidence. The units of empirical evidence are meters and seconds. There are no units existing before meters and seconds by which to define either one of them. Units are indefinable if they cannot be defined in terms of pre-existing units. Degrees were introduced because it was not known what temperature was. Temperature is an indefinable property. It is the fourth indefinable property. The third is mass.

Both mass and temperature are arbitrarily made into indefinable properties and are assigned indefinable units because it was not known how to define either of those properties in terms of pre-existing properties or their units. The dilemma for this kind of arbitary action is that neither degrees nor kilograms are units of empirical evidence. They are made up as human inventions. That act of invention is removed in my essay. All units, and therby their associated properties, are defined in terms of the units of empirical evidence.

The reason for going to this trouble is that: Thermodynamic entropy, and its type of analysis such as 'it increases for a closed system', is the beginning of the path that was historically followed leading to statistical analysis such as is done with the idea of 'bits'. Yet, this path is not realy there. What I mean is that physicists do now know what thermodynamic entropy is. I show what it is. But, because thermodynamic entropy is an unknown property, the pathway to statistical analysis must be reconstructed based upon knowing the properties involved.

So, before I could address the issue of analysis of 'bits', I needed to show how to establish the corrected pathway between the macroscopic world of thermodynamics, the 'it' world, and the microscopic world of 'bit's.

Next I will explain the method I used to remove the need for inventing arbitarily and artificially indefinable properties and indefinable units. Then I will explain what is thermodynamic entropy. I will use that explanation to make clear what Boltzmann's entropy is. Then, the subject of this essay, I explain what is mixing entropy. The importance of explaining mixing entropy has to do with the fact that Gibbs' work on mixing entropy laid part of the foundation for the mathematics of quantum physics and for information entropy. Both of these anaalyses involve statistical treatments of 'bits'.

James Putnam

There should be no need for theoretical inventions in the fundamentals of physics. Those inventions fill voids left due to lack of fundamental knowledge. In other words, when a property is not understood, the theorist fills in the gap in knowledge with their guess about what they think might be the missing knowledge. The difference between knowledge and theoretical substitutions for it is made apparent by the role that empirical evidence plays. If the knowledge is real, then it will be directly supported by empirical evidence. The theoretical substitutions will instead include inventions that are not dictated by empirical evidence.

For example, the equation f=ma results from mathematically modeling patterns of changes of velocity of objects. Empirical evidence directly supports this formula because patterns in changes of velocities are what empirical evidence consists of. The acceleration term is that which is empirical evidence. change in velocity with respect to time is acceleration. The other two properties, force and resistance to force (mass), are inferred from variations in the patterns. That inferrence is directly supported by the empirical evidence of acceleration.

The equations f=ma presents the first encounter with lack of knowledge by physicists. The knowledge that is lacking is: What are force and mass? The answers should be fully supported by the empirical evidence. That is the way the knowledge should be obtained, but it is not obtained in that way. Physicists do not rely upon empirical evidence to learn how to proceed. They resort to theorizing about the natures of force and mass.

Here is how that problem occurs: Both force and mass should be defined in the same terms as is the empirical evidence from which their existence is inferred. Everything we know about both force and mass is made known to us by the empirical evidence. It should not be necessary to invent a solution for either force or mass. Yet, physicists failed to define both force and mass from the properties of their empirical evidence. It was believed that neither force nor mass could be defined using only the properties of distance and time. It is those two properties alone from which all empirical evidence is obtained.

It was decided, due to lack of knowledge, that either force or mass needed to be made an invented property. By invention, I mean that one or the other was to be declared to be a third naturally indefinable property joining with the empirically natural indefinable properties of distance and time. The decision to make mass a fundamentally indefinable property was a theoretical invention introduced for the purpose of filling in a void in knowledge. This practice of filling voids in knowledge with guesses is the stuff from which theory is made. It should never be allowed to occur if there exist other possibilities of interpretation that are dictated by the empirical evidence.

It is the case that the empirical evidence of patterns in changes of velocities of objects does give information about how both force and mass can be defined in the same terms as is the empirical evidence from which their existence is inferred. The possible solutions are limited by that which is learned from (f/m)=a. This form of the equations shows that if one is to define both force and mass in the same terms, and their units, as is the empirical evidence from which their existence is inferred; then, those units of force divided by the units of mass must reduce to the units of acceleration. The units of acceleration are meters divided by (seconds ^2).

James Putnam

From the three properties of mass, distance and time, all other properties of mechanics can be defined. All other units of mechanics besides kilograms, meters and seconds are definable in terms of kilograms, meters and seconds. There remains a property of thermodynamics that is not definable in terms of mass, distance and time; nor are its units definable in terms of kilograms, meters and seconds. That property is temperature.

The purpose of removing the theoretical guess to make mass a fundamentally indefinable property is to, make all properties, including temperature definable in the terms of empirical evidence. There should be no need for units other than meters and seonds. That is the cirucmstance that should result from rooting all physics equations firmly in their empirical evidence.

The equation (f/m)=a allows for a few choices of possible units for force and mass. One of those choices is to give the units of inverse acceleration to mass. Force would then be unit free. That is the choice that I used. It is the choice that worked and continued making good sense as higher level theory was developed. Not only was mass made a definable property, but, so was temperature.

Both properties are defined using only that which is learned from empirical evidence and without injecting invented properties or definitions in the form of theoretical guesses. The nature of mass is not guessed into existence nor is the nature of temperature guessed into existence. The benefit of defining temperature instead of making it indefinable is that thermodynamic entropy is made known.

I use my essay to introduce the empirically dictated definition of thermodynamic entropy. From that point on, my essay deals with explaining Boltzmann's entropy, statistical entropy, and Gibb's mixing entropy. In this manner, the pathway from the macroscopic world to the microscopic world is made no longer theoretical, but is rather firmly established depending directly upon the dictates of empirical evidence.

There is, due to fixing the definition of mass, an automatic transition from the macroscopic world of 'it' into the microscopic world of 'bit', and, that transistions occurs due to temperature. When temperature is correctly defined, as it is in my essay, it connects thermodynamics to the mechanics of the microscopic world.

James Putnam

If the foundation is flawed, as in the case of using thermodynamic entropy as if it were disorder, then the value of predictions will be adversely affected. In the case of the Gibb's paradox, the paradox appears to exist because thermodynamic entropy was not understood in its true nature. The faulty prediction was that there shoud be a significant predictable change in temperature due to the mixing of two disimilar ideal gases.

The gases were both at the same temperature before mixing. There was no change in temperature due to the mixing process. Knowing what is thermodynamic entropy, as made known in this essay, contradicts the prediction of change in temperature. The corrected prediction is that there will be no change in any thermodynamic property, including temperature, due to mixing two dissimilar ideal gases.

The unknown nature of thermodynamic entropy was made known in this essay because I corrected the interpretation of temperature first. Temperature is no longer an indefinable property requiring indefinable units. I define temperature in terms of energy and time. the units of temperature become those of energy per time. The initial act of making mass and force both definable properties with definable units is what leads to defining energy in units of meters. That conclusion will not be understood by reading this message. It is explained in this essay.

With the clarification of what is thermodynamic entropy, Boltzmann's entropy, and mixing entropy, the pathway between the macroscopic 'it' world and the microscopic 'bit' world is made firm. The mathematics and the properties, with their units, included in those equations are corrected in definitions and in form.

James Putnam

Why change the definition of mass? This is a property that is used throughout physics equations. Changing the interpretation and units of mass will affect the interpretations and units of almost everything else. It is a property that is so integral to theoretical physics that no change will receive serious consideration without giving a very strong reason for the change. Even then, resistance will remain due to the prevailing opinion: Why change what has worked so well?

Theoretical physics is very successful at making predictions. Any erroneous change in mass and its units could be expected to immediately and persistently foul up theory yielding results that make no sense and are incapable of reproducing those successful predictions. Should the change to mass not harm physics equations. Should it reproduce the successful predictions and even improve on them, then that makes a very strong case for seriously evaluating its potential correctness.

That correctness would be immensely bolstered when comparing it to current theory, if it also produced clear, always present fundamental unity. That is what occurs as a result of redefining mass using only empirical evidence for direction. Any other direction allows theorists to mix their imaginings into physics equations. It is that infiltration of theoretical inventions into physics equations that can immediately and permanently cause the loss of fundamental unity. The new work that I have presented on several occasions shows that fundamental unity does exist and is incompatable with retaining theoretical inventions.

The change in the definition of mass, as indicated by empirical evidence, is that mass is the inverse of acceleration. That acceleration is the evidence for a fundamental property that remains a major part of physics theory. It reveals itself as the unifying cause for all effects. That is why my many examples of results given here in essays for all five contests are successful in producing unifying connections between all effects. I included for a second time a result that would seem to be unrelated to thermodynamic entropy. That result is the demonstration of how the two expressions for the fine structure constant are unified. They become unified for the same reasons that thermodynamic entropy becomes a known property.

James Putnam