studiot

I find the explanation in terms of a lagrangian deeply circular and unsatisfactory. The lagrangian is defined in terms of energy! The honest truth is that we don't know what energy is, although we do know a great deal about it and how to process it mathematically. In all systems of rational thought we have to start somewhere. We start with some concepts that are taken for granted or given and the system of rational thought is then about the development of relationships between these concepts. We identify at least three types of concept: Definitions Axioms Rules All of which are stated without proof or much explanation. For example what is matter? Well, matter is made of molecules, molecules are made of atoms atoms are made of protons, neutrons, electons protons etc are made of quarks quarks are made of....? At the bottom of the heirarchy there is always something that we have to take on trust. Energy is just such an entity. What you are asking is a definition in terms of something 'more fundamental'. We don't have anything more fundamental at the present state of our knowledge. go well

Well in my version of R & H the page numbers are different, but I expect you are referring to the section in the relativity chapter entitled "A New Look at Energy" This section does indeed discuss the conversion of mass into energy, but in atomic (nuclear) reactions. It describes how to calculate the conversion of some of the mass of the particles involved into the energy that often accompanies nuclear reactions and explains why we do not observe this with ordinary chemical reactions. It also describes the relativistic increase in the kinetic energy of a particle as its speed increases. But nowhere does it say that the particle will 'become energy'. This is not the meaning of the term 'rest mass'. There is no more such a thing as absolute rest in the universe as there is absolute velocity so nothing is ever actually 'at rest'. What it means is that if we work backwards down the total energy v velocity curve described to the y intercept (zero velocity) we will find that this intercept is not zero on the energy axis. The actual value is known as the rest mass and is the energy equivalent we would recover if we could totally 'implode' that mass to energy. We would, of course, also recover any kinetic energy that accrued due to the motion of the mass. As described this caould be very considerable if the relative speed of the mass to its destruction target was large.

Under what circumstances do you think your scenario couls come about? How do you think the perceived differences in energy would show up? Hint energy is proportional to what property of a photon, given its speed is the same for all observers?

If the car was passing at 99.9c how long would you be near the car? If you were moving along with the car you would not see a relative motion of 99.9c

What a shame. Another attempted nit. I clearly stated to "a great many systems" not to all systems. Far better to have used my crystal example 7 to discuss the interesting fact that with this example we can make the system open or closed depending upon where we place our boundaries. By initially restricting the system to one block we have an open system. By initially including the movable block we have closed system.

When you are ready to discuss rather than preach we can take this further. Meanwhile I looked up Resnick et al (6th ed was all they had) in the library this afternoon but was unable to find any statement to the effect that a material body on achieving lightspeed would convert to energy. Nor was I able to find and reference to a 'frame of the universe'. So I would be grateful for some chapter and paragraph references. I did, however find conventional expositions of relativity and frames of reference, including detail about proper time, which I suggest you inquire into.

There are several more examples of plain nit picking argument instead of cooperative constructive discussion in the post this was selected from. But you have tripped your own self up here. I can readily define the system process as "adding 100 joules of heat" to the system before defining any system and know that I can apply this process to a great many systems. Chemical engineers do this daily for a living. @michel The answer to your dilemma is simple. The whole point of a system process and the laws of thermodynamics is to change the system in some way. The process may change the physical boundaries of the system as well as the energy content temperatuure or pretty well any parameter we choose. Obviously we home in on significant ones.

Unfortunately you have a basic misconception about frames of reference (the basis of relativity), which leads to this erroneous statement. There is no 'absolute frame of reference' or if you like 'relative to the rest of the universe'. Perhaps the discussion in this thread will help http://www.sciencefo...constant-value/ As a matter of interest the book you refer to is normally referred to by its original authors Resnick and Halliday It is very popular, although I have never liked it.

My apologies for my earlier imprecision. Whether the system in example 7 is and ever shall be or not one single crystal is not worth disputing. I'm sure you know that you cannot specify any system without also specifying the system process. In this case adding another block by pushing it across was the system process. Of course you also have to specify the boundary conditions. In the other examples the half full barrel was the system, the system process as described and the boundary conditions the refirgeration or insulation as appropriate. A final requirement for the full description of a system is to allow what is excluded. Very often if a quantity plays no part in the system process iot is excluded, although present. A good test of this is if the same quantity appears unchanged on both sides of an equation. So for instance the internal energy of molecular bonding is not included in any of my examples. It is not a good idea to keep repeating someone elses' statement (eg from a book) like a religous catechisim without critical examination. I have not seen your sources but, since they take a stat mech approach, would expect them to list the underlying assumptions of that discipline. Some are The system comprises an assembly of distinct independent particles that are weakly coupled. Each particle has access to a manifold of energy states. Conservation of number and total energy applies. If you feel that the internal energy rises by some other value in my examples 4 and 6 perhaps you would exhibit a calculation showing this?

Don't be ridiculous. When you add mass to any system that it did not start out with you could say this, which could only mean that there is no such thing as an open system. Of course you can take a system and add mass. Then you have a system with more mass. I did this by adding a block to one system and pouring liquid into a barrel in another. Both are perfectly valid open systems. I'm sorry but this statement seems more meaningless than weird. I certainly don't understand it. Stating something without proof many times to does not increase its validity. In the barrel example that you so rudely ignored, the internal energy increases by exactly the heat content of the added liquid, thus completely satisfying your presentation of the first law. I provided variations on this example with the intention of introducing Gibbs paradox to the discussion, but my attempts to offer constructive comments seem to be falling on deaf ears. I am sorry about that.

Did you not take what I said seriously? I asked politely for the title and author of your textbook. I also offered a simple analogy that you clearly misunderstood. If you stand on 'the dock of the bay' watching a ship roll out to sea, you observe that ship pick up speed and move away. If instead you stood on the ship you might well gain the impresion that it was the dock that was receding. Indeed much poetry and literature has commented upon this phenomenon. Relativity demands that the observer and particle in my example have the same relationship. In the abstract: if A moves away from B at any speed v (including c) then it is exactly equivalent to say that B moves away from A at this speed. Consequently the Earth (and that part of the universe which is moving similarly) appears to my particle to recede at the same speed from the particle as the particle appears to move away from the Earth. It was known, long before Einstein, that there is no such a quantity as 'absolute velocity'. Today the earlier version of relativity is called Galilean relativity. This is still used at normal speeds. When c>>v Einstein's Special Relativity reduces to this.

It would be interesting to learn the title and author of your book. Does it mention 'proper time' ? It is not a matter of whether you 'believe me' or anyone else; my objective is for you to think about the subject for yourself and to inquire further into it. I am merely trying to point out fruitful lines of inquiry. So consider this. Let us imagine watching a particle which somehow has the power to reach the speed of light as it accelerates away from us. You claim that as it reaches the speed of light it transmogrifies into a puff of energy. Yet the principle of relativity tells us that from the point of view of the particle it is us, not the particle that has accelerated away in the other direction. So why did we not also disappear in a puff of energy?

If a system is defined as initially comprising one block and I add a second, by definition I have an open system. Why do you say it is closed? Why do you bother to reproduce my post without reply to the other questions? I think you are simply dodging the issue, which is that I have exhibited open and closed systems with zero change in U and in one case zero q and w as well.

No one actually knows what happens if and as a particle with mass achieves light speed. What your textbook should say is that multiplying the mass by the Lorenz factor implies that the apparent mass goes to +infinity as light speed is achieved. This is why I keep talking about asymptotes - do you know what an asymptote is? The reason behind this is because we include the factor (1-v2/c2) which becomes zero as v approaches c so implies division by zero. Edit:- factor corrected

I'm sorry I do not have access to your cited authors works. I would say that any textbook that states this as a basis for definition is a very poor textbook. It is true that one of the triumphs of 20th century thermodynamics has been the development of stat mech and demonstrating that this approach results in the same equations on average as the exact and rigorous definitions and analysis developed in the 19th century and further useful theory besides. However the earlier 19 century definitions and analysis still stand because thermodynamics must perforce cover all conceivable systems, including ones where stat mech does not apply. I think I've already said that the trick is in the definition/specification of a system and it is a point worth repeating. Again I preach the value of exhibiting examples over swopping opposing statements. It is instructive to revisit James Prescott Joule's original barrel in the light of modern knowledge. 1)Let us consider this barrel, first well insulated so that conditions approach adiabatic, and half full of fluid. Let the fluid be mechanically stirred, perhaps by a modern magnetic non contact stirrer, so that all the work input is converted to a fluid temperature rise. The first law tells us that all the mechanical energy appears within the system as an increase in internal energy. Without statistical variation. It does not describe fully the distribution of this increase in U however. Is this system open or closed? What is the heat flow in this situation? 2)Now let the barrel be well refrigerated so that conditions approach isothermal and again be stirred mechanically. Now there is no change in internal energy as all the mechanical energy supplied is carried away as heat. Is this system open or closed? What is the change in U? 3)Now let the barrel be well refrigerated so that conditions approach isothermal but this time instead of stirring the fluid let us pour in some fluid at identical temperature to that already in the barrel, very slowly and gently. Is this system open or closed? What is the change in U? 4)Now let the barrel be well refrigerated so that conditions approach isothermal but this time instead of stirring the fluid let us pour in some additional fluid at higher temperature to that already in the barrel, very slowly and gently. Is this system open or closed? What is the change in U? 5)Now let the barrel be well refrigerated so that conditions approach isothermal but this time instead of stirring the fluid let us pour in some fully miscible fluid that does not react chemically and is at the same temperature to that already in the barrel, very slowly and gently. Is this system open or closed? What is the change in U? 6)Now let the barrel be well refrigerated so that conditions approach isothermal but this time instead of stirring the fluid let us pour in some fully miscible fluid that does not react chemically and is at higher temperature to that already in the barrel, very slowly and gently. Is this system open or closed? What is the change in U? 7) Consider two flatt-topped blocks of perfect crystals standing side by side on a level table at absolute zero. Let there be a third block of perfect crystal standing on the left hand block and consider the solitary right hand block as the system. Now slide the upper left hand block across onto the right hand block and therefoe into the system. Is this system open or closed? What is the change in U?

If you try to keep your speculation on track it might lead somewhere, but I fear this is a wrong turning.

Perhaps you would like to explain this amazing claim further?

I don't see why a cloud of gas, small or large, has very high entropy. What is high entropy? Would a better measure be specific entropy?

Yes your definitition of a closed system as one which does not allow mass flow across its boundary is standard. Your one with dE strictly not equal to zero is not. The point is that it is one of the conditions of equilibrium that no energy flows between systems that are in equilibrium. That is dE = 0. Unless I am misunderstanding your dE? It would help if you would comment on the meaning of your terms. I have guessed several times here, without feedback.

Sorry if I didn't make myself clear. Your sketch didn't look like an asymptote, it looked more like a square law (from v2?). A square law is asymptotic nowhere. If it is meant to be a (relativistic?) asymptote, what equation are you using?

Thanks both, I'm beginning to get the hang of this. Could the Gif i had to resort to in post #8 be replaced to save memory space?

Thank you DH, for the helping hand; this post is by way of trying it out. I lost a considerable amount of typing yesterday after I found the sub and superscript buttons, but could not find how to exit the mode so all my subsequent typing ended in subscript mode. The return, esc ctrl keys did not help. Thinking about it I now wonder if Juan is mixing up the formulations, introduced by Gibbs and later called the 'canonical equations of state' by Plank, with the total energy of an assemblage af particles as calculated by statistical mechanics. [math]U = U(S,V,{N_1},{N_2},{N_3}........)[/math] [math]S = S(U,V,{N_1},{N_2},{N_3}........)[/math] for gibbsian classical themodynamics and The total energy of a system of particles in stat mech. [math]E = {\varepsilon ^a} + {\varepsilon ^b} + {\varepsilon ^c}....... = \sum {{\varepsilon ^i}} [/math] Which leads to the 'conservation' laws for number and energy [math]N = \sum {{n_i}} [/math] [math]E = \sum {{n_i}{\varepsilon ^i}} [/math] However both systems ( and they are compatible) are constrained by their underlying conditions of validity. Yeah I got formulae working. Now I've solved that can anyone tell me how to resolve the times shown on posts in my view and with my clock so that SF timeand mine coincides? I have the settings option set to (my) London time.

Hello tip, Should your E-V graph not be asymptotic to your (Einstein's) limit? I understood that was one justification for gainsaying FTL travel. I like, however, your acknowledgement in that graph of the areas beyond our (present) knowledge and understanding. That shows an open mind. There are several functions in mathematics & physics that veer off to plus infinity at some limit, but return in the other direction beyond that limit from minus infinity. In pure maths the tangent function comes to mind, in physics the specific energy function of a flowing fuid. go well and develop your idea further.

Do you really call this an explanation, in support of your statement? I cannot accept your definition of a closed system since it effectively disbars the existence of equilibrium along with the establishement of the thermodynamic temperature scale. I repeat the observation that the heat added and the work done are not functions of a non isolated system but may be impressed arbitrarily by the surroundings. Yes there are internal results (effects) within the system but I can heat a thermometer as little or as much as I please or even not at all.

Juan it is a pity you addressed my aside, rather than my important points. I simply wondered if your cited authors were developing Gibbs canonical equation, which has similar form and notation. You complained that these authors stated mass as constant. Well this is a requirement or restriction built into the small print as the GCE applies to unit or constant mass. That aside I do not see why you criticise DH for using different notation. The truth should be the same in all. He talks of the law of conservation of energy in the form: "What goes in is not lost but must be somewhere within the system." You have however introduced few errors. 1) The only system with constant energy is an isolated one. I did offer some comments for discussion about isolated systems. 2) If you add heat to a thermometer you increase its internal energy. 3) I offered to work through with you an example of how to apply the first law to open systems so it is disappointing to be told flatly it doesn't apply. I am, however, glad to see that you have got rid of that stuff about differentials. Internal energy can be a total differential because depends only upon system properties. Heat and work exchanged and total energy can be influenced by external agents. the first two are complete quantities not differences and in my view should not be written as differentials, deltas etc. The heat added to a system is the heat added to a system. There is no such quantity as the difference of heats added - large or small. As, I'm sure you know, Gibbs alleviated this by replacing q by TdeltaS in the first law in appropriate circumstances. go well