Entropy as a measure of Fundamentality by Ng Xin Zhao

Hello Xin,

A well-written essay. This is a unique thought that theories could be like entropy which would go on dividing from lower entropy theory. If I describe my essay in term of yours then 'Mathematics is lower entropy' or the lower entropy theory should be perfectly mathematical.

You have some views on Buddhism. Being born in a country where Buddha was born, I really appreciate your message and viewpoints. In fact, sometimes I try to relate science to religion. For instance: It is believed that doing sin result in bad future which correlates to Newtons Third law "To every action, there is an equal and opposite reaction."

Anyway, I enjoyed reading your essay and wish you a good luck in the competition.

Meanwhile, I invite you to my essay Is mathematics Fundamental? and discuss your viewpoints in my essay.

Kind Regards

Ajay Pokharel

Dear NG Xin Zhao, the fundamental must be simple, understandable and save our thinking, as you say to have a low entropy. This is the New Cartesian Physics, which is based on the identity of space and matter of Descartes, which wants to be the theory of everything. You write: If a fundamental theory means the theory that which all other theories can be derived from, it is the ultimate theory of everything (TOE), then certainly it should describe the Big Bang or if there is one at all or if there is anything before it. Look at my essay, FQXi Fundamental in New Cartesian Physics by Dizhechko Boris Semyonovich Where I showed how radically the physics can change if it follows this principle. Evaluate and leave your comment there. Then I'll give you a rating. Do not allow New Cartesian Physics go away into nothingness.

Sincerely, Dizhechko Boris Semyonovich.

Dear Ng Xin Zhao,

FQXi.org is clearly seeking to confirm whether Nature is fundamental.

Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

Only the truth can set you free.

Joe Fisher, Realist

The association of entropy with disorder is misleading. First, because it is based in the lack of distintion between the concept of physical entropy associated to thermodynamics and the several informational entropy concepts found in the theory of information. Second, because it gives rise to that belief that a system always evolves irreversible towards a more disordered state. Mix two inmiscible liquids until getting a homogeneous system and stop the mixing. The system will evolve irreversibly towards a final equilibrium state made of two phases. Has the system evolved towards a more ordered state? Here we would start debating what we mean by ordered and non-ordered and usually the debate consists on introducing some coarse-grained and totally arbitrary concept of "disorder".

This incorrect analogy is the cause for the misguided belief that irreversibility is a consequence of our ignorance: "Thus the second law seems to have emerged from using higher entropic theory to describe and view the world in the first place". The claim "we keep track of every molecules in two different gases intermixing using Newtonian dynamics, we never see increase of entropy because we don't have information hidden from us" is valid only if we replace thermodynamic entropy by informational entropy and we cherry pick the concept of "information".

Do physical systems evolve irreversibly because "higher entropy means losing track of information (coarse graining)"? No. Systems evolve irreversibly independently of the information that I track about them. I can only track the evolution of temperature with time or I can track the detailed trajectory of each molecule, and in both cases the system evolves exactly in the same way and towards the same final state, with the final value of the thermodynamic entropy being the same in both cases.

Moreover, entropy is not a fundamental property. We can discuss any irreversible process without introducing the concept of entropy in the equations. I can wrote anything like this for a chemical system

[math]\frac{d[A]}{dt}= k^{-} [B] - k^{}[A][/math]

and I can describe the irreversible evolution of the system towards a final equilibrium state, without even mentioning the word "entropy".

The idea that a "more fundamental theory corresponds to a theory which needs to keep track of more variables thus more information, have

more principles, and have wider range of validity" compared to a less fundamental theory is not at all correct. For instance, in classical mechanics we require position and momenta variables; exactly the same number of variables are required in the phase space formulation of quantum mechanics.

F=ma "is telling us how forces are the cause for accelerated motions" when we read it from left to right. If we read it from right to left we can say that accelerated motions cause forces. An equation does not introduce a unique cause effect relationship because both sides of an equation have to be treated in the same footing. X=Y is the same than Y=X.

Maxwell's equations do not describe "all of the classical electromagnetic phenomenon"; in a first step we have to complement them with the Lorentz force law and with the equations of mechanics. F=ma for a charded particle is not derivable from Maxwell equations. Maxwell's equations and the Lorentz force law have other deficiencies, and in subsequent steps we have to complement them to consistently describe classical electromagnetic phenomena.

Special relativity is not a covering theory of "Newtonian dynamics". In the one-particle limit one can show that special relativistic expressions reduce to Newtonian expressions in the low velocity limit (or when taking a formal [math]c\to \infty[/math] limit). But this equivalence is broken when one adds a second particle. There is no consistent and complete special relativistic theory for a multiparticle system of interacting particles. It is not possible to build a Lagrangian or a Hamiltonian for those systems. Fundamental theorems such as the no-interaction theorem prove that particles worldlines cannot satisfy the principles of special relativity when particles are interacting.

Statistical mechanics is not "less fundamental" than Newtonian dynamics. Statistical mechanics is not derivable from Newtonian dynamics. Statistical dynamics relies on mechanics plus some postulates, which are not derivable from Newtonian dynamics.

Quantum electrodynamics is not "more fundamental compared to quantum theory". As already stated by Dirac, quantum electrodynamics and quantum mechanics are two "disjoint theories". Just as in the classical clase, quantum electrodynanics cannot fully describe a many-particle system, unless we perform approximations, as is made in particle physics. There are other difficulties with quantum electrodynamics are exclusive to the well-known incompatibility of special relativity with quantum mechanics, as for instance that there is no longer position operator or valid associated wavefunctions in quantum electrodynamics.

Concepts as simple and elegant are subjective, and cannot be used to clasify theories into more fundamental and less fundamental. Do the Einstein (& Hilbert) equations in general relativity look "simple and elegant"? They look terribly unelegant and uneeded complex to me, when we move beyond the usual concise notation. And even if we accept the redundancies and difficulties of the equations and label them as "simple and elegant", we find tons of adittional difficulties when we apply those equations to certain galactic systems, and then we have to add ad hoc procedures and assumptions on top of previous add ad hoc procedures and assumptions to fit the equation to the empirical data, and finally we recover a modern version of the old epicycles.

Simmetries work fine for idealized systems, but they cannot even be taken as foundations --I recall the funny joke about physicists and spherical cows--. The example about Minkowski spacetime is just relevant. The simmetries that generated the concept of Minkowski spacetime are only valid when one considers that the whole universe is made of a single particle. Then all spacetime around the particle is symmetric and special relativity works fine. The problem arises, as mentioned above, when one adds a second particle. Then the direction connecting both particles is not equivalent to any other direction. The original symmetry is broken and consequences as the Lorentz transformations are no longer valid; indeed the no-interaction theorem proves that Lorentz transformations are only valid when we ignre the second particle.

Concepts as "ultimate TOE" are best left for philosophers. But even if we were to admit the concept into science, string theory and M-theory could not be more far from an "ultimate TOE".

The idea that quantum mechanics is unitary and "we do not see unitary in classical levels" is not correct at all. In general an electron in a watter molecule does not evolve unitarily. On the other hand certain classical system evolve unitarily.

Equations looked ok in the preview. Both are broken in the final post. Weird!

I try a second time (both look ok in the preview)

[math]\frac{d[A]}{dt}= k^{-} [B] - k^{}[A][/math]

and

[math]c \to \infty[/math]

entropy -> information -> it=(bit, it) -> a "non-wellFounded set"

Dear Xin Zhao Ng

It is wonderful that you are trying to combine Physics with ancient Buddism..."A viewpoint of entropic measurement of a theory as it's measure of fundamentality is proposed. This idea came about from philosophical musing with Buddhist fundamental principle of dependent origination. Information being kept track of by the theory, the principles which compacts the form of the theory, and the range of validity of the theory are examined with examples in Physics. These form the basis of measuring a theory's entropy." Hats off to your work and best wishes...

I hope you will not mind that I am not following main stream physics...

By the way...Here in my essay energy to mass conversion is proposed................ yours is very nice essay best wishes .... I highly appreciate hope your essay ....You may please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

Some of the Main foundational points of Dynamic Universe Model :

-No Isotropy

-No Homogeneity

-No Space-time continuum

-Non-uniform density of matter, universe is lumpy

-No singularities

-No collisions between bodies

-No blackholes

-No warm holes

-No Bigbang

-No repulsion between distant Galaxies

-Non-empty Universe

-No imaginary or negative time axis

-No imaginary X, Y, Z axes

-No differential and Integral Equations mathematically

-No General Relativity and Model does not reduce to GR on any condition

-No Creation of matter like Bigbang or steady-state models

-No many mini Bigbangs

-No Missing Mass / Dark matter

-No Dark energy

-No Bigbang generated CMB detected

-No Multi-verses

Here:

-Accelerating Expanding universe with 33% Blue shifted Galaxies

-Newton's Gravitation law works everywhere in the same way

-All bodies dynamically moving

-All bodies move in dynamic Equilibrium

-Closed universe model no light or bodies will go away from universe

-Single Universe no baby universes

-Time is linear as observed on earth, moving forward only

-Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

-UGF (Universal Gravitational Force) calculated on every point-mass

-Tensors (Linear) used for giving UNIQUE solutions for each time step

-Uses everyday physics as achievable by engineering

-21000 linear equations are used in an Excel sheet

-Computerized calculations uses 16 decimal digit accuracy

-Data mining and data warehousing techniques are used for data extraction from large amounts of data.

- Many predictions of Dynamic Universe Model came true....Have a look at

http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.html

I request you to please have a look at my essay also, and give some of your esteemed criticism for your information........

Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.

In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from "http://vaksdynamicuniversemodel.blogspot.in/ "

I request you to please post your reply in my essay also, so that I can get an intimation that you replied

Best

=snp

Dear Ng Xin Zhao

If you are looking for another essay to read and rate in the final days of the contest, will you consider mine please? I read all essays from those who comment on my page, and if I cant rate an essay highly, then I don't rate them at all. Infact I haven't issued a rating lower that ten. So you have nothing to lose by having me read your essay, and everything to gain.

Beyond my essay's introduction, I place a microscope on the subjects of universal complexity and natural forces. I do so within context that clock operation is driven by Quantum Mechanical forces (atomic and photonic), while clocks also serve measure of General Relativity's effects (spacetime, time dilation). In this respect clocks can be said to possess a split personality, giving them the distinction that they are simultaneously a study in QM, while GR is a study of clocks. The situation stands whereby we have two fundamental theories of the world, but just one world. And we have a singular device which serves study of both those fundamental theories. Two fundamental theories, but one device? Please join me and my essay in questioning this circumstance?

My essay goes on to identify natural forces in their universal roles, how they motivate the building of and maintaining complex universal structures and processes. When we look at how star fusion processes sit within a "narrow range of sensitivity" that stars are neither led to explode nor collapse under gravity. We think how lucky we are that the universe is just so. We can also count our lucky stars that the fusion process that marks the birth of a star, also leads to an eruption of photons from its surface. And again, how lucky we are! for if they didn't then gas accumulation wouldn't be halted and the star would again be led to collapse.

Could a natural organisation principle have been responsible for fine tuning universal systems? Faced with how lucky we appear to have been, shouldn't we consider this possibility?

For our luck surely didnt run out there, for these photons stream down on earth, liquifying oceans which drive geochemical processes that we "life" are reliant upon. The Earth is made up of elements that possess the chemical potentials that life is entirely dependent upon. Those chemical potentials are not expressed in the absence of water solvency. So again, how amazingly fortunate we are that these chemical potentials exist in the first instance, and additionally within an environment of abundant water solvency such as Earth, able to express these potentials.

My essay is attempt of something audacious. It questions the fundamental nature of the interaction between space and matter Guv = Tuv, and hypothesizes the equality between space curvature and atomic forces is due to common process. Space gives up a potential in exchange for atomic forces in a conversion process, which drives atomic activity. And furthermore, that Baryons only exist because this energy potential of space exists and is available for exploitation. Baryon characteristics and behaviours, complexity of structure and process might then be explained in terms of being evolved and optimised for this purpose and existence. Removing need for so many layers of extraordinary luck to eventuate our own existence. It attempts an interpretation of the above mentioned stellar processes within these terms, but also extends much further. It shines a light on molecular structure that binds matter together, as potentially being an evolved agency that enhances rigidity and therefor persistence of universal system. We then turn a questioning mind towards Earths unlikely geochemical processes, (for which we living things owe so much) and look at its central theme and propensity for molecular rock forming processes. The existence of chemical potentials and their diverse range of molecular bond formation activities? The abundance of water solvent on Earth, for which many geochemical rock forming processes could not be expressed without? The question of a watery Earth? is then implicated as being part of an evolved system that arose for purpose and reason, alongside the same reason and purpose that molecular bonds and chemistry processes arose.

By identifying atomic forces as having their origin in space, we have identified how they perpetually act, and deliver work products. Forces drive clocks and clock activity is shown by GR to dilate. My essay details the principle of force dilation and applies it to a universal mystery. My essay raises the possibility, that nature in possession of a natural energy potential, will spontaneously generate a circumstance of Darwinian emergence. It did so on Earth, and perhaps it did so within a wider scope. We learnt how biology generates intricate structure and complexity, and now we learn how it might explain for intricate structure and complexity within universal physical systems.

To steal a phrase from my essay "A world product of evolved optimization".

Best of luck for the conclusion of the contest

Kind regards

Steven Andresen

Darwinian Universal Fundamental Origin

"... the Big Bang as singularity is a conundrum for physics ..." According to Fredkin, singularities, infinities, infinitesimals, perfectly continuous variables, and local sources of randomness are false hypotheses contrary to nature's reality. Do Einstein's field equations need at least 3 corrections? (1) Is prevention of the Big Bang singularity necessary? (2) Is prevention of infinite time necessary? (3) Is it necessary to modify the field equations to explain Milgrom's MOND? Google "kroupa milgrom" and "mcgaugh milgrom".