Dear Sean

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

Dean Sean and Singh,

This was very impressive. This program seems to me very difficult, but you made it look very natural and the advances are impressive. I don't believe in MWI, but I am sure that in a parallel world you convinced me :)) (just kidding!)

There's something that bothers me for some time. You said that the Hilbert space of a compact region of space is finite-dimensional. This is something I hear, also in relation to black hole entropy, but can it work without imposing some additional constraints, like the wavefunctions having the support either included in the region or completely outside? And I think this condition is not justified, because: (1) the electron in an atom is spread in the entire space, (2) a wavefunction which is confined to a compact region immediately after spreads everywhere, (3) the Feynman diagrams include unlimited number of particles, so the Fock space on that region has to include the subspaces of any dimension. Consequently, it seems to me that the wavefunctions of the particles inside the region should have tails outside and vice-versa, resulting in an infinite-dimensional Hilbert space. The collapse into a black hole doesn't happen in this case because most particles are outside. If we impose the condition which leads to finite dimensional Hilbert space, I expect indeed that this will impose a cut-off on the Feynman graphs, but what justifies such a condition? On the other hand I agree that atoms can be located in regions of space, so maybe there is a weaker conditions and the tails are allowed to be outside, but in this case what makes the Hilbert space finite-dimensional?

Thank you in advance for any clarification of the above.

I was very skeptical few years ago that one can get a universe like the one we observe just out of psi, H, and the Hilbert space, mainly because the unitary symmetry seemed to me to remove any difference between the positions and other observables. I realized that the interaction Hamiltonian has to be local, and that by finding the symmetries of the Hamiltonian and psi we can recover spacetime, elementary particles, and all that. I am still suspicious about the classical level, it seems to me that it requires to find new laws which impose constraints on the wavefunction or interactions which remove the Schrödinger cats. The alternative is to prove that decoherence solves it, which is another ambitious program (which I see as a subprogram of MWI and other interpretations like Bohm's as well). To me a solution of the measurement problem and the emergence of classicality via decoherence seems sometimes trivial, sometimes impossible, so maybe the truth is in between.

There's something I saw in your essay which made me think that you may enjoy, at leisure time, this sci-fi short story called Quantum God (spoiler: is not religious :)) )

Congratulations and thanks again for this excellent essay!

Best wishes,

Cristi Stoica, Indra's net

5 days later

Everett's work was debunked many time ago, both in physical and mathematical grounds. Alternative attempts presented in the last 50 years by Graham, DeWitt, Geroch, Deuthch,... have been debunked as well.

Not only Many-Worlds isn't a valid interpretation of QM, but its proponents disagree. E.g. Deuth's Many-Worlds is not Everett's Many-Worlds. Next link contains rebuttal of early Everett ideas

http://www.mat.univie.ac.at/~neum/physfaq/topics/manyworlds

"Quantum theory describes the evolution of a state vector in a complex Hilbert space, but we populate our theories with ideas like "spacetime", "particles," and "fields"." That is a very narrow conception of quantum theory because, for instance, the quantum state of an unstable system isn't given by any state vector in a Hilbert space. We populate our theories with concepts as particles because they are the basic building blocks of Nature.

Equation (1) is an approximation. It doesn't apply to system in mixed states, neither to irreversible phenomena. The notation used is also inadequate. If the state vector is only a function of time, then a partial derivative makes little sense; a total derivative would be used.

"The lesson we draw from this is that Nature at its most fundamental is simply described by a vector in Hilbert space". As mentioned above, this isn't true. What is more, even for those systems adequately described by ordinary state vector theory, it is possible to find alternative formulations without Hilbert spaces or vectors. A well-known example is the Wigner-Moyal formulation of quantum mechanics. Hilbert space and state vectors are replaced by non-commutative phase space and Wigner function W(p,q). One evident advantage of the Wigner-Moyal formulation is that is also works for quantum systems for which the Hilbert formulation doesn't work.

"Classical concepts must emerge from this structure in an appropriate limit". It has been rigorously demonstrated that classical systems aren't contained in a Hilbert space structure. And that is the reason why many physicists and mathematicians are working in extensions of quantum theory. The old theory is being extended at two levels: generalized spaces beyond Hilbert space, and nonlinear extensions of Schrödinger equation.

Eq (3) is only valid for quantum systems with discrete spectrum. The complete spectral decomposition of the Hamiltonian operator is given in the attachment.

"One might ask why, if the fundamental theory of everything is fixed by the spectrum of some Hamiltonian, we don't simply imagine writing the state of the universe in the energy eigenbasis, where its evolution is trivial?" Because we know a spectral decomposition of the Hamiltonian doesn't fix "everything".

"Consider the classical theory of N particles moving under the influence of some multi-particle potential in 3 dimensions of space. The corresponding phase space is 6N-dimensional, and we could simply think of the theory as that of one point moving in a 6N-dimensional structure. But by thinking of it as N particles moving in a 3-dimensional space of allowed particle positions, we gain enormous intuition; for example, it could become clear that particles in uence each other when they are nearby in space, which in turn suggests a natural way to coarse-grain the theory". This class of reasoning is what confused Boltzmann and a several generations of physicists. The classical state is given by a point in the 6N phase-space. A model of N particles moving in a 3-dimensional space (really 6-dimensional) fails to consider subtle elements of the full dynamics, such as the existence of long-range correlations. Coarse graining the the theory over distances larger than the range of the interactions will erase the correlations that are needed to drive systems to stable equilibrium.

Similar remarks about (8) and (9).

"This procedure is crucial to the Everettian program, where the interaction of systems with their environment leads to decoherence and branching of the wave function [...] The Born Rule for probabilities, p(i) = |Psi_i@|2, isn't assumed as part of the theory; it can be derived using techniques such as decision theory [12] or self-locating uncertainty [13]". The Born rule isn't compatible with the kind of unitary evolution this Essay is assuming. So it cannot be derived. At best, the rule can be introduced ad hoc as an additional postulate, but then we have the same dual-evolution inconsistency than in the traditional Copenhagen treatment.

"The former condition is ultimately cosmological -- the universe started in a low-entropy state, which we won't discuss here". But equation (1) conserves entropy, and cannot describe evolution to current state.

"The essential observation is that, if quantum behavior is distinguished from classical behavior by the presence of entanglement, classical behavior may be said to arise when entanglement is relatively unimportant". Another old argument has been refuted again and again in the literature. Eliminating the entanglement simply provides a mixture with only diagonal elements in the density matrix, but this is not the classical state; reason why the founding fathers of QM introduced an additional postulate to complement the postulate about Schrödinger evolutions.

Next section is based in many assumptions and unproven statements, some of them explicitly assumed "although it's unclear how to achieve this at this time".

WdW equation is incorrect. In fact one of his authors even renounced to it considering it "a very bad equation". Further attempts to extract a valid concept of time from it are condemned to failure. The problem is not the "clock ambiguity", the real problem is that time is an evolution parameter, not an observable one can get from a spectrum.

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