All physical laws are highly symmetric and cannot give rise to the observable and perceptible universe. The visible universe is far from being derivable from these laws. So there will never be any theory of everything as the high energy physicists and string theorists would like to believe. The universe is asymmetric, does not obey ergodicity and has an arrow in time. Are there any more fundamental ingredients? Please comment on my Friday afternoon world view.
I think these should be some important parts of the world view.
Most physical laws you mentioned I called as the first law physics, because they are simlar to the first law of thermodynamics, the symmetry of these laws is only the symmetry of the conserved quantities, not the phenomena themselves. In thermodynamics, there is another law, the second law.
Ergodicity and the equal a priori probability are considered as the fundamental postulates of statistical mechanics, unfortunately, these fundamental postulates cannot extend to all over the world around us. Because of this, statistical mechanics can noly work in its postulate boundary due to Universe Is Not a Gas In a Box.
The absence of antimatter in the universe is due to the symmetry breaking in the early universe.
On the entropy only
Misunderstandings in ideas about entropy
Many misunderstandings in understanding the problems of life and evolution from the standpoint of physics and physical chemistry are typically associated with misconceptions in understanding entropy. The term "entropy" coined Rudolf Clausius. According to his "model" of the world (universe), he presented a statement: "The energy of the world is constant. The entropy of the world tends to the maximum". Later this statement was chosen by JW Gibbs as an epigraph to the paper "On the Equilibrium of Heterogeneous Substances". These scientists have given this statement in relation to their model of the universe. This model corresponds to a simple isolated system of ideal gas, i.e. isolated system of ideal gas, energy and volume of this system are constant and in which only the work of expansion is performed. Entropy of such a system can only increase!
It should be noted that when we say on ideal model, which would correspond to the real universe, it would be necessary to accept the unreal assumption that any form of energy real universe will be transformed into thermal energy. Only in this case, also under additional unrealistic assumptions, the real universe "would turn" into the model of ideal system of Clausius - Gibbs.
However, lovers of science have applied representations on simple systems to systems of other types, in which the interactions takes place between particles of different nature (interactions of molecules or other objects of different hierarchies) and to systems which interact with the environment. Some scientists, who are not professionals in the relevant fields of knowledge, have not escaped such errors. This has led to unimaginable confusion. This has slowed down the development of science, more than on a century. There are thousands of publications in scientific journals and popular literature containing marked misunderstandings. To these were added incorrect ideas on the negentropy and on the dissipative structures in the living world.
The origin of life and its evolution can be easily explained from the standpoint of hierarchical near equilibrium thermodynamics of complex dynamic systems. This thermodynamics established on a solid foundation of equilibrium thermodynamics - thermodynamics of Rudolf Clausius, JW Gibbs and other great scientists.
http://www.membrana.ru/particle/17266
http://www.eoht.info/page/Entropy+%28misinterpretations%29 http://www.youtube.com/watch?v=CYr1G5TZO50
Detailing theories about the origin of life and evolution is presented in the new sites (Knol moved to Wordpress): Some work: http://gladyshevevolution.wordpress.com/
http://creatacad.org/?id=48&lng=eng
The entropy is certainly the most enigmatic thing. If the second law is valid then the early universe is expected to have small entropy and the present universe to have larger entropy and hence the arrow of time. But again we know that the early universe was uniform hot dense gas and therefore have very large entropy. So there is an apparent contradiction. Some cosmologists tried to resolve this contradiction by invoking gravitational degrees of freedom and gravitational entropy which makes the entropy of the early universe very small. But there are counter arguments and the whole topic is still controversial. Any comments regarding this point?
If gravitation does not contribute to entropy then how to get a low entropy for the early universe? If the early universe did not have a lower entropy than the present universe then we have a crisis in physics. The foundation of physics crumbles down.
Dear Tang Suye,
"In fundamental equation of thermodynamics, the term generalized force Y can be extended to gravity, Yx (dx is the generalized displacement) makes no contribution to entropy, the gravitational potential energy is the free energy, gravitational entropy is a misconception."
You are right !
Sure there is a correlation between entropy and symmetry and similarity. For informational entropy it is easier to relate them. High symmetry has less information content and has more entropy. But the case of early universe is more complex I suppose.
@Brajesh: Read "Correlation of Entropy with Similarity and symmetry", S.-K Lin, J. Chem. Inf. Comput. Sci. 36, 367 (1996).
Dear Georgi,
I read your articles, and I endorse the point of view “The origin of life and its evolution can be (easily) explained from the standpoint of hierarchical near equilibrium thermodynamics of complex dynamic systems.” G is a key factor, and “the standpoint of hierarchical” is a valuable idea.
I have a general conclusion: “the second law itself contains the building mechanisms” (“The total entropy production always increases monotonically, but the partial differential of which can be less than zero”). Life and its evolution are the great achievements of the second law (the building mechanisms). “We tend to regard the second law as the law of building, and the entropy production as the spending of the building process.”
@Tang Suye: I am sure that your statement "For primordial gas, high temperature, high pressure, high density and high quantum states is a state of low entropy" must be true. Can you prove it or it is just a plausible statement supported by the second law of thermodynamics.
I’d discussed this question, but did not strictly prove it. A qualitative proof is not too difficult. The photon gas, plasma gas, the production of matter and chemical elements, gravity …, the spontaneous processes are the objects of thermodynamics. Some conclusions are already there, such as the expansion of a photon gas.
I wish to see an analytical proof of the statement "For primordial gas, high temperature, high pressure, high density and high quantum states is a state of low entropy" . Do you know any reference that I can read.
Dear Tang Suye,
Thank you.
Entropy production is interesting to study only for simple (ideal systems). We should use the changing of Gibbs free energy for investigation of complex real systems.
Misunderstandings in ideas about entropy
Many misunderstandings in understanding the problems of life and evolution from the standpoint of physics and physical chemistry are typically associated with misconceptions in understanding entropy. The term "entropy" coined Rudolf Clausius. According to his "model" of the world (universe), he presented a statement: "The energy of the world is constant. The entropy of the world tends to the maximum". Later this statement was chosen by JW Gibbs as an epigraph to the paper "On the Equilibrium of Heterogeneous Substances". These scientists have given this statement in relation to their model of the universe. This model corresponds to a simple isolated system of ideal gas, i.e. isolated system of ideal gas, energy and volume of this system are constant and in which only the work of expansion is performed. Entropy of such a system can only increase!
It should be noted that when we say on ideal model, which would correspond to the real universe, it would be necessary to accept the unreal assumption that any form of energy real universe will be transformed into thermal energy. Only in this case, also under additional unrealistic assumptions, the real universe "would turn" into the model of ideal system of Clausius - Gibbs.
However, lovers of science have applied representations on simple systems to systems of other types, in which the interactions takes place between particles of different nature (interactions of molecules or other objects of different hierarchies) and to systems which interact with the environment. Some scientists, who are not professionals in the relevant fields of knowledge, have not escaped such errors. This has led to unimaginable confusion. This has slowed down the development of science, more than on a century. There are thousands of publications in scientific journals and popular literature containing marked misunderstandings. To these were added incorrect ideas on the negentropy and on the dissipative structures in the living world.
The origin of life and its evolution can be easily explained from the standpoint of hierarchical near equilibrium thermodynamics of complex dynamic systems. This thermodynamics established on a solid foundation of equilibrium thermodynamics - thermodynamics of Rudolf Clausius, JW Gibbs and other great scientists.
http://www.membrana.ru/particle/17266
http://www.eoht.info/page/Entropy+%28misinterpretations%29 http://www.youtube.com/watch?v=CYr1G5TZO50
Detailing theories about the origin of life and evolution is presented in the new sites (Knol moved to Wordpress): Some work: http://gladyshevevolution.wordpress.com/
http://creatacad.org/?id=48&lng=eng
Dear Tapan,
I’d verified the second law for cosmological and astrophysical processes, and found that they are in conformity well with the second law (I don't believe "heat-death”) , so I have not paid attention to the reference (too many misunderstandings for the second law), you can verify it by yourself.
For a generalized thermodynamic system,
1) dS=dU/T-Ydx/T-μdN/T+pdV/T
You can see Ydx and μdN make no contribution to entropy, so called as “the free energy”. Define the function that
2) dq= dU-Ydx-μdN
Name as “the internal heat energy”, such that
dS=dq/T+pdV/T
S=q/T+pV/T
The higher T, the smaller dS or S, for an expansion, pdV >0, so high pressure and high density correspond to small V and dS or S.
The generalized force Y can be extended to gravity, thermodynamic analysis in the production of matter and chemical elements are similar to chemical reaction (μN).
The intensive quantity T (temperature) of heat q is a scalar, so the degrees of freedom in heat q make sense. Gravity is a vector, and it is also a long-range force, so the gravitational degrees of freedom make no sense, gravitational entropy is a misconception.
For the entropy of the early universe just after the big bang we must not only include the effect of gravity but we must consider the huge amount of radiation. If gravity does not make any contribution then does the radiation contribute to the entropy of early universe?
I listened to the Newton lecture of Roger Penrose (2005) on the same subject in the web. It seems that he has some ideas but he assumes a lot of knowledge on general theory of relativity and topology of space-time and it is not easy to understand all his arguments.
@Tang Suye. I don't understand your argument: "the higher T, the smaller dS or S".
Even If dS is small, S can be very large.
I can argue that the second equation is the integral form of the firts one and therefore it gives you only variations in entropy, not an absolute value
How do you explain that Nernst theorem is required to have absolute values for entropy?
I'm just trying to understand your argument that in the limit of T -> infinite entropy should be small. In the Euler equation you wrote, for example taking into account just the first term, if T is tendent to infinite, also the internal energy tends to infinite
Dear Paplo,
S=q/T+pV/T is an original sense, where S has an absolute value, due to entropy is a homogeneous function of degree 1. The differential expression usually means that dq and dV correspond to different T and p，so the absolute value need to be integrated, the two are similar to dQ/T and Q/T.
In addition, if we take the early Universe as an insulated system, Q is zero by definition, and in your equation we have just the term pV/T, with pressure tending to infinite when V->0. I'm not saying you are wrong stating that early Universe should have a small entropy, I'm just saying that your argument is not a proof.
Dear Paplo,
My equation is
dS=dq/T+pdV/T
where q is “the internal heat energy”, it is a new concept, a state function, the physical meaning of “the internal heat energy” is the heat energy within the system, not heat in transfer (different from Q).
“if we take the early Universe as an insulated system, Q is zero by definition”, but “the internal heat energy” of the insulated system is not zero. Please see my article
https://www.researchgate.net/publication/236983852_Internal_Heat_Energy_Entropy_and_The_Second_Law_A_New_Approach_to_Theoretical_Thermodynamics_(v4)
For example, the entropy of the radiation of early universe can be analyzed qualitatively by the photon gas, please see Eqs.(40) and (41).
Data Internal Heat Energy, Entropy and The Second Law: A New Pers...
Dear Tang.
Whatever. Let us put the question in these simple terms. Entropy is dimensionally an energy divided by a temperature. If I understood properly your argument, you are stating that when T-> infinite, then S->0. Now, for that to be true, it is necessary that the denominator (which is broadly speaking an energy) does not tend to infinite. Could you prove that?
Thanks Tang and Paolo for the illuminating discussion about entropy but I am yet to see a quantitative calculation of the entropy of the early universe from which we convince ourself that the entropy of the early universe was very small compared to the entropy it has now.
Now how about symmetry and ergodicity breaking? Can someone comment please?
The laws of physics can in some sense be deduced from symmetry arguments plus, say, the principle of least action. Hence we can say that the UNDERLYING laws are NOTHING BUT the symmetries and action principles. The symmetry breaking gives rise to complexity . The values of various coupling constant among the entities of the complex system are a feature of the symmetry breaking. , and hence specify the characteristic identity of a given universe out of the possible universes. The symmetry breaking gives also the direction of time etc. Effectively, a high symmetry state has less entropy than a low symmetry state.
I have explained many of these matters like time, irreversibility etc in my recent book A physicist's view of matter and Mind published by World Scientific- & Imperial College Press, June 2013.
http://www.amazon.com/A-Physicists-View-Matter-Mind/dp/9814425419
or
http://www.worldscientific.com/worldscibooks/10.1142/8594
Other books (e.g., by Kerson Huang on Gauge theories), or the book by Leon Lederman, also express similar views, although they do not treat complex systems, determinism, free will, and such questions in any detail, as I have done, as the scope of their books is more limited.
Chandre Dharma-wardana
The world around us is far too complex to understand from all the high-symmetric (especially time symmetric) basic theories. Symmetryand ergodicity must be broken and time flow needs a arrow. This is the basic message. But how do these happen? That's what we are out to discuss.
As I have discussed in my book ( and several others have done so in their works), the time symmetry of Mechanics (classical or quantum) HOLDS ONLY for the differential equations that express `laws of physics'.
These differential equations re-express the basic gauge symmetries and least action principles .
The perceptible world is given by OBSERVED SOLUTIONS of those differential equations. These require the application of boundary conditions that define the domain of observation, and then solving the differential equations SUBJECT TO THOSE BOUNDARY CONDITIONS. This process renders the solutions irreversible, both in the quantum and classical domains and vehemently so in statistical physics, as discussed in many chapters of my book.
If you ignore boundary conditions, obviously, the differential equations are, and have to be reversible. All discussions of reversibility ignore boundary conditions, and discuss time evolution of operator relations.
The role of quantum uncertainty, Poincare's work on classical many-particle systems and their extreme sensitivity to boundary conditions, the role of de Broglie thermal wavelength of a particle, and how they all complement and consistently mesh with one another also becomes clear, especially when the boundary conditions on the differential equations are re-written as Bohm quantum potentials that give clear irreversible time evolution.
See the first chapter, the last chapters of part-I (dealing with matter), and part-ii (dealing with complex systems like cells), of the previously referred to book, namely:
http://www.amazon.com/A-Physicists-View-Matter-Mind/dp/9814425419
Chandre Dharma-wardana
@Dharma-wardana: I shall read the book as soon as I get a copy of the book from our library.
I was looking for a quantiative calculation of the entropy of the early universe and physical explanation of why the early universe had a small or zero entropy.
Thank you very much. As you know, these questions are not easy to answer briefly or satisfactorily, and that is why I referred to the book. What we assume as the entropy of the early universe is also a boundary condition that we put into our differential equations. If the conclusions drawn from it agree with astrophysical observations, that is satisfying, but of course not definitive.
To think about the Dark Matter., Black Hole and Quantum Physics . I think there is a requirement for new theory such as Universal Universe Physics etc
High symmetry means less information content and high entropy. Is that right? I thought that the early universe was highly symmetric. Is that right too? If so then I do not understand how the early universe could have small or zero entropy. Can anyone explain this to me?
Assume that the high symmetry state is in some state C. Then, if you act on it with any symmetry transformation T, the result TC=C because of its absolute symmetry.
Hence there is just one configuration, and log 1=0
Consider a low symmetry state D.
TD is not necessarily D.
When operators act on it, it can transform to other states D_i. with a total of N possible configurations
The entropy is proportional to logN > Log 1
That is all there is to it.
See Chapter 9 of my book where I work out some simple but illustrative examples, Boltzmann's original form, information-theory interpretations, Maxwell's demon, philosophical implications etc.
@M. Dharma-Wardana: there is something I don't understand in your argument: if we a take a spherical container uniformly filled with gas, we have a high symmetry state which corresponds to the maximum of entropy. On the contrary, if the density of the gas is not uniform, the state is of low entropy and the symmetry is lower as well. How can this can be understood in terms of your argument?
If you are allowing for hidden structure you have to carefully sit down and formulate your calculation.
Perhaps the above answer is not clear enough. When you say "uniformly filled" , the uniformity is expressed to within a certain length scale. So you tacitly change the length scale to shorter values where there is granularity, enabling you to create density changes. (This misuse length scales is discussed in most chapters of my book and indicated as a pitfall, or the basis of new physical theories). A true 'uniform distribution' with no hidden structure' has a zero value for space derivatives at ALL length scales.
Do we know more about the past than the future?
For short time scale (for example one day) we do know more about the past than the future. But for a long time scale (for example billion years), we do not know more about the past than the future.
We know quite a lot about the past from the cosmic background radiation, the remaining signature of the big bang. Admittedly this is an indirect information but so are many other knowledge of physics. This is all about very long past. We know that there was also an inflation in expansion. We know about the element synthesis and star and galaxy formation. We know about the synthesis of heavier elements in star. We know that atoms that constitute our body was synthesized in stars in the past. We know about the life cycle of stars and galaxies. Now what do we know about future for certain? Will the cosmic expansion will go on forever or there will be a big crunch? Will the big crunch will be followed by a big bang? We know very little about the future indeed. Whatever we know is just an extension of our knowledge about the past. Now coming to the life of an individual we know a lot of our past (not just about yesterday) but about the future we know only one thing for certain that we will all die someday: earth to the earth, ash to the ashes!!
We know not a lot about the formation of our earth and geological evolution of the earth and the eventual appearance of life and their evolution but we definitely have some information based on scientific evidence and we know the timing of all these. We do not know a dam thing about the future of humanity and other forms of life even within a span of few hundred years. Will we screw up ourselves and our earth or rather have we already done it without really realizing it?
I have a few points:
Any theory on our world or The Universe is based on limited time scale. Therefore no theory would be guaranteed suitable when be used in unlimited time scale.
1. Outcome of the development of the universe will be a circle but there are two ( may be more ?) possible circle: the closing stages is extract the same as the starting stage or the starting stage is different to the closing stages. But there will never be the end. the universe will be continued forever.
2. Any current theory or new theory in limit time period will not be suitable for the period between the closing stages and the starting stage for current life circle of our universe
The longer the time, the closer we near unknow The longer the time, the closer we have the truth(Baoliang Zhang)
A concept that shows Fermat's principle of least action, Planck's mathematical description of temperature-energy-distance and the Heisenberg uncertainty principle are invalid is a necessary condition to validate by experiment what you have in mind.
Entropy: A concept that is not a physical quantity
https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity
There are (i) properties of elementary constituents such as conservation laws etc. which are governed (via Noether's theorem) by underlying symmetries, spontaneous breaking and so on, and then again there are (ii) properties of the world we see around us, which is macroscopic and which has macroscopic parameters such as pressure, temperature, volume, entropy etc. As you have rightly said, quite often the connection between such microscopic and macroscopic descriptions remains quite obscure to most of us, and we hope that this bridge will be made through the study of statistical mechanics.
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