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

Hi James,

You are correct when you say that we should use only length and time but we can go even further and use just length !

Have a look at my theory (3D Universe Theory), I derive most empirical constants with just the Planck Length and a simple expression 8Pi-1. I know that most people will dismiss these formulae as pure numerology but there is a chance you might have a different opinion.

Cheers,

Patrick

    • [deleted]

    • Post #24

    Patrick Tonin,

    Hi. Thank you for reading my essay. That point about using length (meters) and time (seconds) only applies to themacroscopic world for convenience. Other units that are more fundamental, i.e. Planck length and Planck time, could be used instead. I don't use those because meters and seconds work conveniently enough for me down to atomic dimensions. There is another reason for not adopting Planck units yt and that is that those units are formed from combinations of units which I do not need. I need only the units of empirical evidence and they are length and time. This is not a strange thing to do.

    My argument is that every mechanical dimension should be rooted in empirical evidence if possible. I find it is quite possible to do, and, is the key to learning what fundamental unity is. Fundamental unity is immediate and I feel is convincing evidence that returning the equations of physics to their empirical roots, by ensuring that all units of properties are expressible in the same units as is the empirical evidence from which is existence is inferred, is the most accurate and most useful form of physics equations.

    It is through the units that ideas are made concrete parts of physics equations. It is the units that make equations either empirical or theoretical. Since all units are reducible to those of mass, distance and time, it is the case that mass must be made right. Mass must be expressed in the same terms a is its empirical evidence. The units of that empirical evidence are only those of distance and time. All of my work involves that change. This essay is just one part of my work.

    Your essay uses planck length and time. Your cubit uses length only. Your layers are traversed one at a time every Planck unit of time. You do mention that your dimension in the radial direction represents space-time. Your layers consist of length only and they are your present one after the other. I assume that your statement that we only need length is based upon your idea that the present only has dimensions of length. There is though the matter of change. All empirical evidence of physics occurs as patterns in changes of velocity. How do you account for change in equations. Calculus equations are equations of change. Physics need extensive use of calculus in order to express its ideas. You may answer this message in you own forum. I will look for it there.

    Thanks again,

    James Putnam

    5 days later

    Dear James

    I have skimmed your paper, quickly realizing that to understand it and make intelligent comments requires many readings and lots of time learning not only what is standanrd thermodynamic theory, but also your version of it if that is what you are proposing.

    So for now just a few questions - who is Gibbs? Is the paradox related to Maxwell's demon ? And also about your Appendix B can you explain in a bit more detail about Boltzman's number and the concept of mass in your theory - is it based on some physical image or model that you have? Relating mass to acceleration is an extension to Einstein's basic concept about gravity in GR, but how does it 'work'?

    Thanks and best wishes

    Vladimir

    11 days later

    James,

    Interesting reading, and good thinking. It's on a subject I'm certainly no expert on, so it was enlightening, and I liked your approach. I found some correlation with my own in terms of Gibbs assumption that "The gases were either distinguishable or they weren't." This then ignores and excludes the 'middle' between 0 and 1, which I also identify as a mistake when dealing with nature. I also like your use of fundamental units, which I identify as relevant to wavelength, not the derived abstract 'frequency' that then confounds logic leading to paradox.

    I then also like your 'quantized' time increment (3). your other postulates appeared very radical (rich coming from me I suspect!!) and I couldn't rationalise them at first read. I hope I'll get a chance to read again with them in mind, but if you can help here (I know length is always an issue) please do.

    I wish you luck.

    Peter

    12 days later

    Dear James

    Sympathy for me first, but I do not understand you are "accounting" for what is that ?

    http://fqxi.org/community/forum/topic/1802

    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

      Dear James Putnam,

      I have down loaded your essay and soon post my comments on it. Mean while, please, go through my essay and post your comments.

      Regards and good luck in the contest.

      Sreenath BN.

      http://fqxi.org/community/forum/topic/1827

      Dear James,

      I thought you might be interested in chengxi guo's essay, specifically in his discussion of force:

      "Force is not an entitative concept. It is designed as an intermediary virtual parameter in processing physical problems. The force is said to be intermediary, because when we use the concept of force, it always appears in the interaction manner. The virtual property of force is that it does not have objective substantiality, can not exist alone in breaking away from entities.

      In Newton's law of motion, the two concepts of force and mass are defined in one equation. The mass here is usually considered as inertial mass, confusion also arising from the relationship between inertial and gravitational mass. Aside from the confusion, from a logical point of view, force and mass in the second law played a role of mutual definition logically out of place, this can not be satisfied."

      You can read his paper for his specific treatment. I mentioned your approach in a comment on his page.

      Hope you are recovering well.

      Best,

      Edwin Eugene Klingman

        Hi Edwin,

        I feel fine. My strength is back. Thank you for mentioning my work at another's forum. I don't think that I will be following through on it. I have written and discussed enough here to have an accurate assessment of the value others here placed on my work. I don't say this because of the asinine effort by Tom to discredit my work. The combination of that display along with looking at my placement in the current contest are symptoms that I am wasting my time.

        I never have done well in these contests and allowed for the expected resistance to my ideas. However, looking at some of the essays that I have been placed below clarifies the situation more than enough for me to understand that it is definitely not only Tom's attitude that so violently rejects my ideas.

        I have turned my attention to trying to complete a paper I submitted to that conference I have mentioned. I submitted a draft yesterday. It was a day late. Yet it was accepted and I was invited to present an improved finalized version personally for the conference in a few weeks. My immediate problem is not this contest. It is that fixing and rewriting my draft is not going well at all. It needs to be done today and it looks like I have no chance of completing it.

        Even if I managed to squeeze a comprehensible version into the required ten pages, it is not anywhere near being in their required form. I thought I would be reformatting the paper today. Instead upon re-reading it this morning, it reflects the disjointed piecing together that I did to complete it quickly. Even the newly written sections were rough. I am impressed that the representative of the conference could recognize the intended purposes of the paper.

        It is not a one or two day fix. Then it would still remain to put it into its proper form. So perhaps I should relax this year, follow more peaceful interests of mine, and enjoy being retired. I do have other interests. :)

        Good luck to you in the contest. I did re-read your essay and gave you a 10 a while back. I would like to see your work given serious consideration by other physicists. I can't see for myself that that has yet happened. Maybe it will this time. I don't think that I will be reading or rating any more essays. Well back to work so that I at least know that I really tried to finish.

        James

        James,

        I'm sorry to hear about the deadline. I know how hard it is and how much time it takes to whip our ideas into presentable shape.

        There are many aspects at play in the FQXi scoring, and quality of thinking is far from the top. I believe that those who believe in magic are not happy to read arguments that expose this, and score accordingly. Also, by posting the scores, FQXi almost guarantees last minute jockeying to knock the lowest scores out of the winners category so that others may move in to replace them. And there are even grudges that have built over the last few years. So I would not put too much emphasis on the scores. I know that I could have written a different essay that would score more highly than my current one. But I am writing, like Phil Gibbs and others, to get my ideas recorded in as permanent a medium as I can. I believe that's what you are doing also. It *is* worthwhile.

        I did want to alert you to the fact that Lee Smolin (as noted in earlier comment) and now chengxi guo share your unhappiness with the way force and mass are defined. And I am still examining effects in various equations of replacing mass with inverse acceleration. I've been too busy lately to do much, but I have yet to encounter problems when I perform this replacement. At some point in the future I'll try to provide you details of what I'm doing.

        When it reaches the point of depressing you, it's time to back off and get perspective. You are retired and live in a beautiful part of the country. Enjoy your life; it's the best revenge!

        Your friend,

        Edwin Eugene Klingman

        James,

        I normally use the 'submission date' ordering, to try to keep track of what's new. But I just ordered the essays by community ranking, and was amazed. You note that several poor essays are ahead of you. I agree. There are also at least three exceptional essays far below you!

        The scoring is so screwed up in this contest I don't think you should even pay attention to it. I don't.

        Edwin,

        Well, I kept at it and improved the paper immensely. It was re-submitted late today but on time for the deadline. I don't know yet it its form is fully acceptable, but, the conference representative seemed appreciative of having received it. I was assigned to make a remote presentation at 9:30 AM Eastern time. Unfortunately, I will be in a small village on the ocean in Oregon. It will be 6:30 AM for me. There is no cell phone service, but, there is wi-fi. I think I will set myself up outside on the beach with the ocean behind me. There are huge picturesque rock formations out in the water. I will have to find out first how far the wi-fi reaches from the old cabin that I will be staying in. It is almost on the beach itself. I think it sounds like it could be a fun experience.

        I did a remote presentation last year and could see myself as I did it. I come across looking even older than I am; and, with my mannerisms, I appear to be something of a character. A lot of smiling and head moving. Also, I learned that my progressive lenses cause me to raise my head up to see the computer screen. So, a camera located on the computer picks me up with my nose and chin sticking somewhat upward. It added to the character look. It was humorous to see myself doing the presentation. There was nothing I could do but just go along with it and keep smiling. :)

        James