entropy

[Sanford]

We physicists must be careful to insure that theories begin with correct principles. One basic principle is that all quantities must be capable of being observed or measured. If a theory uses a quantity that cannot be observed, then it is not a physics theory, but a hypothesis or a phenomenological explanation. These are important logical explanations, and possibly quite useful for proper applications, but not a proper theory. We must continue our efforts to find a proper theory.

 

An example of a theory that does not begin from basic principles is special relativity as originally expressed by Einstein. He postulated the speed of light is constant in all inertial frames. His mistake is that light is not fundamental, but a consequence of Maxwell's Equations, ME. The correct way to develop this theory is to postulate that ME is valid in all inertial frames.

 

Entropy is phenomenological, not a basic concept of physics, at the current state of physics. In statistical mechanics, SM, entropy is defined as the log of the number of possible arrangements of the molecules. This cannot be measured, and so current ideas about entropy are not part of a physics theory.

 

The idea is that we can move a molecule of a gas to a higher energy state, and simultaneously move a molecule at this higher energy state to a lower state, so that the total energy is constant. We can imagine performing this experiment using lasers. There are two issues. One is that there is no observable difference between these two states, and so to discuss the number of such states is not meaningful physics. Second, we cannot imagine performing this experiment. A principle of thermodynamics is that we cannot add energy to a system and remove the same energy.

 

Let us illustrate this with superfluid helium. The entropy is zero. We cannot picture this as individual helium atoms each having position and momentum, the way we picture helium gas, except to say the atoms are in the container. Since there is no possible way to rearrange the atoms, the entropy is zero. The concepts of position and momentum are not valid for the atoms of superfluid helium. By the way, this is a beautiful example of quantum mechanics on the macroscopic level.

 

Just as we cannot picture the position and momentum of an atom of superfluid helium, we cannot picture the rearrangement, at constant system energy, of atoms of helium gas. If we cannot picture this and cannot measure it, it cannot be a fundamental principle.

 

Entropy is a very useful concept in thermodynamics. In SM, we can define the probability of particles, p(i) with energy E(i). This is because in QM there are discrete numbers of energy levels. We can define the temperature of a system by measuring heat flow. The Boltzmann assumption is a meaningful statement as it involves meaningful quantities. We can define the partition function and energy U.

 

We would like to continue and derive the thermodynamics potentials, such as A and S (entropy). If we succeed in this derivation, we can then say entropy is a meaningful concept. We need to search for a derivation of entropy that starts with SM and not with the unphysical idea that entropy is the log of the possible rearrangements. Once we correctly derived entropy, we can then show, as a result of the theory's postulates, things like Gibbs' expression for entropy and say that this shows that entropy is the log of all possible rearrangements. This would be fine; it is not fine to start with this as the first step.

 

Here is a paper that started my thinking.

Entropy.pdf

[swansont]

We physicists must be careful to insure that theories begin with correct principles. One basic principle is that all quantities must be capable of being observed or measured. If a theory uses a quantity that cannot be observed, then it is not a physics theory, but a hypothesis or a phenomenological explanation. These are important logical explanations, and possibly quite useful for proper applications, but not a proper theory. We must continue our efforts to find a proper theory.

 

An example of a theory that does not begin from basic principles is special relativity as originally expressed by Einstein. He postulated the speed of light is constant in all inertial frames. His mistake is that light is not fundamental, but a consequence of Maxwell's Equations, ME. The correct way to develop this theory is to postulate that ME is valid in all inertial frames.

Why is that not covered by physics being the same in all inertial frames? You know, the first postulate of SR?

[Sanford]

Why is that not covered by physics being the same in all inertial frames? You know, the first postulate of SR?

Right. But A. Einstein wrote in his paper that constant light speed is a postulate.

[swansont]

Right. But A. Einstein wrote in his paper that constant light speed is a postulate.

Yes, the second postulate, and something that follows from Maxwell's equations. What's the problem?

[Ronald Hyde]

How soon would you like this document shredded sir, and into how many pieces?

 

I sometimes like to find 'slightly wrongheaded' papers and study them by faulting their reasoning. One that I remember very

clearly was an article in Analog Science Fiction magazine, titled Dimensions Anyone?, written by a medical doctor. Now it wasn't

really wrong in any big way, just enough to get the 'logical juices' flowing so to speak. But that article taught me so much

about how to think of and use Dimensional Analysis and how not to use it too.

 

The article you linked to is so wrong on some many levels, that it's hard to know where to start. And it begs to be thoroughly

taken apart and debunked because people might be easily fooled into thinking it has something important to say.

 

The concept of Entropy was introduced by Rudolf Clausius, with additions by others, most notably Sadi Carnot and Claude Shannon,

both engineers by the way. Now it just so happens that the Second Law of Thermodynamcs is not meaningful in a classic sense, it

can not be applied to 'continuous systems', they must have discrete elements. So Entropy as a thermodynamic concept is only valid

for discrete systems. They must as it were 'be quantized' is some way. You can see where this is going already. Sadi Carnot applied it

to 'real world' systems, steam engines and such, he belonged to that era. The 'Age of Steam', a fascinating era if you enjoy the history

of technology, gives way to the 'Information Age' and a telephone company engineer named Claude Shannon develops something he

calls 'Information theory'. A very beautiful theory, when I first read and understood it, chills literally went up my spine because it had

such beauty and simplicity. Shannon used a concept that defined the information measure of a message or an ensemble of messages

and he called it Entropy. He clearly recognized that his Entropy was related to the thermodynamic version. Now to me Claude Shannon

is one of what I call the 'Golden People', every subject that he touched he bettered thereby. So if you want to study people who much

improve the life and understanding of the Human race, include him in, with a lot of others I might add.

 

Enter 'Johnny', not Jack Nicholson, but John von Neumann. Someone actually wrote that he was primarily a Logician and did not make

many contributions outside of that. I coulda punched da guy in da nose. Johnny was like this amazing space alien intelligence that

visited Earth and left many wonderful things that we do not yet fully understand. Imagine handing a pocket calculator to a South

American native and asking them to explain it. And in all of this he's a fun loving nice guy who treats others well, not like some I've

met.

 

Johnny gave us the next step in understanding thermodynamics and Entropy, because he wrote a seminal paper ( he didn't write any

other kind ) on Quantum Thermodynamics. Characteristic Johnny, clearly written, everything logically connected, just beautiful work.

So if you want to understand QT start with Johnny's paper and go from there.

 

I actually tell people this. Nature isn't like Lucy, she doesn't have any 'splainin' to do. We have to take our measurements and figure

it all out for ourselves. So when I see people saying 'Nature must do this, or must do that', I think 'what a fool', who thinks that

Nature must do things according to his viewpoints. So it's a very false premiss to say that Nature must not think that Entropy is

important. And another of my favorite people, Mark Twain, 'Never approach a Bull from the front, and Horse from the rear, or a Fool

from any direction'. I would not approach this paper from any direction.

[Sanford]

Yes, the second postulate, and something that follows from Maxwell's equations. What's the problem?

 

The point is that light is defined from Maxwell's equations. What are you saying?

 

How soon would you like this document shredded sir, and into how many pieces?

 

I sometimes like to find 'slightly wrongheaded' papers and study them by faulting their reasoning. One that I remember very

clearly was an article in Analog Science Fiction magazine, titled Dimensions Anyone?, written by a medical doctor. Now it wasn't

really wrong in any big way, just enough to get the 'logical juices' flowing so to speak. But that article taught me so much

about how to think of and use Dimensional Analysis and how not to use it too.

 

The article you linked to is so wrong on some many levels, that it's hard to know where to start. And it begs to be thoroughly

taken apart and debunked because people might be easily fooled into thinking it has something important to say.

 

The concept of Entropy was introduced by Rudolf Clausius, with additions by others, most notably Sadi Carnot and Claude Shannon,

both engineers by the way. Now it just so happens that the Second Law of Thermodynamcs is not meaningful in a classic sense, it

can not be applied to 'continuous systems', they must have discrete elements. So Entropy as a thermodynamic concept is only valid

for discrete systems. They must as it were 'be quantized' is some way. You can see where this is going already. Sadi Carnot applied it

to 'real world' systems, steam engines and such, he belonged to that era. The 'Age of Steam', a fascinating era if you enjoy the history

of technology, gives way to the 'Information Age' and a telephone company engineer named Claude Shannon develops something he

calls 'Information theory'. A very beautiful theory, when I first read and understood it, chills literally went up my spine because it had

such beauty and simplicity. Shannon used a concept that defined the information measure of a message or an ensemble of messages

and he called it Entropy. He clearly recognized that his Entropy was related to the thermodynamic version. Now to me Claude Shannon

is one of what I call the 'Golden People', every subject that he touched he bettered thereby. So if you want to study people who much

improve the life and understanding of the Human race, include him in, with a lot of others I might add.

 

Enter 'Johnny', not Jack Nicholson, but John von Neumann. Someone actually wrote that he was primarily a Logician and did not make

many contributions outside of that. I coulda punched da guy in da nose. Johnny was like this amazing space alien intelligence that

visited Earth and left many wonderful things that we do not yet fully understand. Imagine handing a pocket calculator to a South

American native and asking them to explain it. And in all of this he's a fun loving nice guy who treats others well, not like some I've

met.

 

Johnny gave us the next step in understanding thermodynamics and Entropy, because he wrote a seminal paper ( he didn't write any

other kind ) on Quantum Thermodynamics. Characteristic Johnny, clearly written, everything logically connected, just beautiful work.

So if you want to understand QT start with Johnny's paper and go from there.

 

I actually tell people this. Nature isn't like Lucy, she doesn't have any 'splainin' to do. We have to take our measurements and figure

it all out for ourselves. So when I see people saying 'Nature must do this, or must do that', I think 'what a fool', who thinks that

Nature must do things according to his viewpoints. So it's a very false premiss to say that Nature must not think that Entropy is

important. And another of my favorite people, Mark Twain, 'Never approach a Bull from the front, and Horse from the rear, or a Fool

from any direction'. I would not approach this paper from any direction.

 

Sorry, but you lost me. Talk to me in physics. I mentioned several points about entropy. Where do you disagree?

[md65536]

The point is that light is defined from Maxwell's equations. What are you saying?

Sorry to butt in as an uneducated slob, but...

I don't see the difference. It is a postulate either way. It is known that the reasoning or clue behind Einstein's postulate comes from Maxwell's equations (and is backed by experimental evidence), so it's not like it would have made a revolutionary difference in SR. And it's not like replacing one postulate with another would reduce the number of assumptions made.

 

If Einstein chose to use Maxwell's equations as a postulate, he would then have had to explain why that implies an invariant speed of light ---- which was what is important to SR. Why not skip right to what is important? Using Maxwell's equations would be just an extra step, and not really useful if he never referred to them again.

 

 

[swansont]

The point is that light is defined from Maxwell's equations. What are you saying?

And why is this a problem for relativity? Einstein took these concepts and applied them to mechanics, because there is an impact of Maxwell's Equations being invariant under a Lorentz transformation.

[Ronald Hyde]

The point is that light is defined from Maxwell's equations. What are you saying?

 

Sorry, but you lost me. Talk to me in physics. I mentioned several points about entropy. Where do you disagree?

 

Not to be impolite but the entire thesis of the paper, and your question, is just plain wrong.

The thesis: That we should only describe Nature using QM observables.

 

This is just like those people who say we can describe Nature using only:

Electricity

Magnetism

Electricity and Magnetism together.

 

The more knowledgeable of us know that this is not true, and disregard these 'theories', and rightly so.

 

The only reason I replied to this topic was this paper was presented in such a way as to lead people to

believe that it had a legitimate basis.

 

I'm going to comment on something swansont has replied to, his reply is perfectly good but I see that

you still don't quite understand it. And I'll overexplain as usual, just my style, I hate to be miunderstood.

 

I've seen some people say 'Well, Einstein wasn't a mathematician, he was a physicist and learned math

later'. Nonsense, he was a mathematician and a darned good one. He used math terminology in his SR

paper but it wasn't required in his other papers, they were more about the results of simple experiments.

 

The term 'postulate' is a math concept, it represents something that you wish to prove in the process of

reasoning. And Einstein was very good at reasoning, as his paper shows. That is the only meaning that

attaches to the word 'postulate' in Einsteins paper, period.

 

I'm not going to explain this in physics or math because the faulty premiss, another math term, will cause

all of that to fail. No only would I not approach that paper from any direction, I would ( conceptually ) throw

it as far away from me as I possibly could. Or you could do the community a service and simply shred it to

pieces by reasoning through it. I'm too busy and have other things to do, they involve the concept of Entropy.

[Sanford]

Summary of my position: A mathematical system starts with arbitrary consistent statements, and concludes with the logical conclusions. A physical theory is a mathematical system along with empirical verifications. All quantities must start with observable quantities or the conclusions from observable quantities. Do you disagree with any of this?

[Ronald Hyde]

I can see that you still don't quite get this, but I'm not making statements just for you, I'm making them for anyone who might be 'taken in'

by that paper.

 

A physical theory must start with observations, measurements, etc.. This 'data' let's call it, represents a set of related observation. A mathematical

model, what you call a physical theory, must connect all these observations among themselves and if possible predict new relations and sets of data that

can be verified by further experiments. Now one of my very firm beliefs is that Nature is in a very deep sense, just made of mathematical relations. I've

had that belief since I was fifteen years old.

 

A physical theory of itself does not have to satisfy any conditions but the one described. It doesn't have to satisfy any philosophical, religious, cultural

etc. conditions. If you want to draw philosophical conclusions from the theory, fine with me, but do not impose them on the theory. I do not know of any

valid physical theory that was constructed without very close attention to the 'physical picture'. NONE! Believe me, I stay as close to the physical picture

as I possibly can.

Edited September 27, 2012 by Ronald Hyde

[studiot]

A physical theory must start with observations, measurements, etc

 

I can't agree with you there. You are using a device right now that came of someone asking 'what if?'

 

The transistor and its associated physical theory was not invented by physical observations but by the simple idea as posed above.

[Ronald Hyde]

I can't agree with you there. You are using a device right now that came of someone asking 'what if?'

 

The transistor and its associated physical theory was not invented by physical observations but by the simple idea as posed above.

How would they know that semiconductors even existed without making observations? Galena and Pyrite are common mineral

semiconductors. There are others, just about any 'shiny' sulfide ore is a semiconductor. The semi-metal elements are also

semiconductors, Selenium rectifiers were in use before there was a theory of semiconductors. It was discovered that Silicon was a

semiconductor, during the War it was used in Radar detector diodes, even though there was no theory of it. Look up 1N21 diode.

 

The telephone company ( I don't remember which one off the top of my head ) thought that semiconductors might replace the

high maintenance 'electron tubes'. so after the War they set up a research group. They did not immediately discover the transistor

after constructing the theory, the 'transistor effect' only works with very lightly doped material. Silicon and Germanium had a

simpler crystal structure so they were tried first. At first Germanium had the lead because it was much easier to handle and

purify. Bu in the end Silicon took over because it is much more rugged during processing and more durable in service.

 

There are actually several types of transistors, the ones in your computer are very different from the ones in a transistor radio.

There were a lot of 'what ifs' and a lot of experimentation, 'cut and try'.

Edited September 27, 2012 by Ronald Hyde

[studiot]

There were a lot of ........

 

Words in this case but they didn't prove anything.

 

Just because you have semiconductors, and even simple semiconductor devices such as diodes, doesn't mean that you can casually 'observe a transistor happening'.

Someone (Shockley and Brittain) had the idea to place two junctions in close proximity which is required for transistor action.

 

I will grant you that many (probably most) theory in physics has been developed by observing something physical and wondering why.

The fact that the internal energy of an ideal gas depends solely on temperature (Joules experiment) is one such good example.

Another is the observation of matter leading eventually to the electron.

 

However antimatter was a postulate or hypothesis before any experimental evidence appeared to require it.

The positron was the first antiparticle discovered.

 

There have been several particles since postulated as a result of group theory or symmetry, searched for and finally discovered.

 

So physical theory has two sources of inspiration and development. That surely is better than one?

[Ronald Hyde]

Words in this case but they didn't prove anything.

 

Just because you have semiconductors, and even simple semiconductor devices such as diodes, doesn't mean that you can casually 'observe a transistor happening'.

Someone (Shockley and Brittain) had the idea to place two junctions in close proximity which is required for transistor action.

 

I will grant you that many (probably most) theory in physics has been developed by observing something physical and wondering why.

The fact that the internal energy of an ideal gas depends solely on temperature (Joules experiment) is one such good example.

Another is the observation of matter leading eventually to the electron.

 

However antimatter was a postulate or hypothesis before any experimental evidence appeared to require it.

The positron was the first antiparticle discovered.

 

There have been several particles since postulated as a result of group theory or symmetry, searched for and finally discovered.

 

So physical theory has two sources of inspiration and development. That surely is better than one?

What do you mean, the words don't prove anything? It's all History, just read the History, History doesn't need to be 'proven'.

The first type of transistor made was the point contact. It was pretty inevitable that all sorts of combinations of junctions

would be tried, so all sorts of things would be invented. The SCR is a 4 layer device invented by GE in 1955.

 

And I even know about Gell-Mann 'inventing' SU(3), he went through all the representations until he got to the 8-dimensional one.

A funny story you can tell your grand kids.

 

I'm not unaware of the interplay of theory and experiment, I'm just cautioning the original poster that Nature will not respect

his notion that a theory be based on purely 'philosophical' considerations, especially wrong-headed ones.

[Sanford]

Let us not confuse physics with a physics theory.

[studiot]

I'm not unaware of the interplay of theory and experiment,

 

So you have moved from your original categorical position that observation must precede theory and/or speculation.

 

That is good.

[pantheory]

Sanford,

 

.....An example of a theory that does not begin from basic principles is special relativity as originally expressed by Einstein. He postulated the speed of light is constant in all inertial frames. His mistake is that light is not fundamental, but a consequence of Maxwell's Equations, ME. The correct way to develop this theory is to postulate that ME is valid in all inertial frames.....

I understand your point but think that any approach or derivation could have problems concerning derivation based upon "basic principles" aka "first principles."

For instance Maxwell's equations may not be valid in all inertial frames in all circumstances, and therefore may not necessarily be justifiable as a "first principles" derivation of SR. I agree that this assumption might be more acceptable as being of first principles than the postulate of the constancy of the speed of light.

 

Concepts from "first principles": "The idea for the physicist is to see where such a relationship comes from, beginning with "basic physics" principles—Newton's Laws or Maxwell's Equations, for example. Such first principles are generally well-established and ubiquitously accepted within the physics community, and are sometimes thought of as the most basic concepts in physics, from which all the other laws of physics can be derived."

 

http://www.niceneguys.com/science/fi...entific-limits

 

The point, I think, is that nothing in physics is based upon a certain foundation of validity.

 

(Physics) is not, however, self-sufficient as a field, in that its own foundations— (even) those first principles upon which it depends—are insecure without a few (more basic) assumptions. Perhaps these assumptions will some day be measured and quantified, but those measurements will surely rely on even more assumptions. In the meantime, and perhaps as an inherent restriction, these assumptions themselves cannot ultimately be answered by physics without appeals to philosophy.

(parenthesis added)

 

First Principles and Scientific Limits | The Nicene Guy

 

Maxwell's equations and Newton's Mechanic's equations are most often given as examples of equations from "first principles." But even they have "soft assumptions" that someday might be proven to be wrong under certain circumstances.

 

While Maxwell's equations are consistent within special and general relativity, there are some quantum mechanical situations in which Maxwell's equations are significantly inaccurate: including extremely strong fields (see Euler–Heisenberg Lagrangian) and extremely short distances (see vacuum polarization). Moreover, various phenomena occur in the world even though Maxwell's equations predicts them to be impossible........

http://en.wikipedia....l%27s_equations

 

Edited September 28, 2012 by pantheory

[Ronald Hyde]

So you have moved from your original categorical position that observation must precede theory and/or speculation.

 

That is good.

 

No, I haven't changed my view. I reason things through, here is an example of my reasoning. A long time ago I realized

that even if you developed a physical theory from 'whole cloth', from first principal you would need to know how it fits

into the observational picture, in other words how it describes things from our space-time viewpoint. So you would still

need to make observations.

 

If you read my signature you will understand exactly who should be the first and last arbiter in what is valid theory.

I repeat, do not tell Nature how she should build her house, do not impose your philosophy on her, develop the theory

however you wish, if it works, then find any philosophy in it.

 

Pantheory has many good points, some I would have made but don't need to now. But I will say something about SR

and how Einstein arrived at it. More History, every idea in Physics has a history. When he was fifteen he wondered what

it would be like to ride along with a light beam. I'm not going to go through all the steps here, I don't even know exactly

how he arrived at his final conclusion, but later on he realized that if one accepted the Lorentz transformation as a

general law of Nature and not just applicable to Maxwell's Equations, that this notion was a physical impossibility. Now

when he wrote his paper he used the format that mathematicians use to prove concepts, they postulate something, then

by 'reasoning among the facts' in this case, he shows it to be true. He was very good a reasoning, first rate.

[Sanford]

Newtonian gravitation is a valid theory of physics. The mathematical basis is clear and consistent. There is agreement with observations. Special relativity is also a valid theory. SR agrees with observations more than Newtonian, such as the Mercury orbit. Stat mech and entropy is not a valid theory. We cannot speak about the number of possible arrangements of molecules in a gas as we cannot observe this. Second law of thermo prohibits adding energy to a gas and extracting the same energy. However, this imaginary processes is behind imagining possible arrangements of the molecules. We must not discuss impossible things. An example is that even God does not know the positions of the atoms of superfluid helium except to say they are in the container.

[swansont]

Newtonian gravitation is a valid theory of physics. The mathematical basis is clear and consistent. There is agreement with observations. Special relativity is also a valid theory. SR agrees with observations more than Newtonian, such as the Mercury orbit. Stat mech and entropy is not a valid theory. We cannot speak about the number of possible arrangements of molecules in a gas as we cannot observe this. Second law of thermo prohibits adding energy to a gas and extracting the same energy. However, this imaginary processes is behind imagining possible arrangements of the molecules. We must not discuss impossible things. An example is that even God does not know the positions of the atoms of superfluid helium except to say they are in the container.

We cannot observe a system in a superposition of states, yet QM is a valid and useful theory. The superposition has implications that can be tested. Direct observation is not a requirement for a theory to be valid.

[Sanford]

Okay, then entropy is an intermediate quantity, like the wave function.