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FQXi Essay Contest - Spring, 2017
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TOPIC:
Mad-Dog Everettianism: Quantum Mechanics at Its Most Minimal by Sean M. Carroll and Ashmeet Singh
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Author Sean Carroll wrote on Jan. 25, 2018 @ 17:23 GMT
Essay AbstractTo the best of our current understanding, quantum mechanics is part of the most fundamental picture of the universe. It is natural to ask how pure and minimal this fundamental quantum description can be. The simplest quantum ontology is that of the Everett or Many-Worlds interpretation, based on a vector in Hilbert space and a Hamiltonian. Typically one also relies on some classical structure, such as space and local configuration variables within it, which then gets promoted to an algebra of preferred observables. We argue that even such an algebra is unnecessary, and the most basic description of the world is given by the spectrum of the Hamiltonian (a list of energy eigenvalues) and the components of some particular vector in Hilbert space. Everything else – including space and fields propagating on it – is emergent from these minimal elements.
Author BioSean Carroll is a research professor at the California Institute of Technology. Ashmeet Singh is a graduate student at the California Institute of Technology.
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sonali sengupta sengupta wrote on Jan. 25, 2018 @ 18:09 GMT
Thought provoking essay."Spectrum",sounds like a probability distribution of energy eigen values (scalars)and associated vectors. "Energy"could imply vibrations associated with a particular direction (vector)from which fields emerge, which get entangled to give rise to geometry of "space". Emergent space sounds mathematical.Thank You.
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David Brown wrote on Jan. 25, 2018 @ 19:53 GMT
"The simplest quantum ontology is that of the Everett or Many-Worlds interpretation, based on a vector in Hilbert space and a Hamiltonian." Is the preceding idea somehow related to the following?
"Connecting loop quantum gravity and string theory via quantum geometry" by Deepak Vaid, 2018, arXiv.org
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Member Matthew Saul Leifer wrote on Jan. 26, 2018 @ 04:48 GMT
This essay is an clear summary of your extreme Everett approach, which I think is very ambitious, even if I don't subscribe to it myself. One aspect of the construction was unclear to me:
"If we divide the entanglement into a small-scale ultraviolet term that determines the spacetime geometry, and a longer-scale infrared term characterizing matter fields propagating within that geometry, the change in one kind of entropy must be compensated for by a corresponding change in the other"
Presumably, the division between "infra-red" and "ultra-violet" degrees of freedom involves another tensor product decomposition of the Hilbert space or, more generally, a decomposition into "logical qubit" generalized subsystems and "the rest", as in a quantum error correcting code. My question is, how do you identify this decomposition in the first place? I can imagine it might be determined in part by the spectrum of the Hamiltonian, i.e. does a small change in the state of one component lead to a large or small change in the expectation of the energy, but I cannot see how one would go about doing that, and whether any procedure would be unique.
If you have such a decomposition, you can then attempt to divide the entropy into "ultra-violet" and "infra-red" components as you suggest, but what would happen if the "ultra-violet" and "infra-red" components were entangled with each other? Then the sum of the two components of entropy would not have to be conserved, so you wouldn't get the entropy balance and Einstein equations. Or perhaps the method you imagine for identifying the "infra-red" and "ultra-violet" degrees of freedom would ensure that there is very little entanglement between them for low-lying states. Any more details of this you can give would be appreciated.
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Author Sean Carroll replied on Jan. 27, 2018 @ 18:31 GMT
Matthew -- yes, this is a very good question; one that we're thinking a lot about right now. The answer isn't completely clear. The most straightforward idea is that there aren't actually separate UV & IR degrees of freedom, but just different amounts of entanglement between the existing degrees of freedom depending on whether they are "nearby" or "far away." That in turn can be directly fixed by the Hamiltonian (nearby factors are ones for which there is a nonzero interaction term in H).
But there may something more subtle or clever going on. In https://arxiv.org/abs/1712.02803 we suggest (following work by Dan Harlow in the AdS/CFT context) that it might be helpful to think in terms of quantum error-correcting codes. The rough idea is that the IR contribution can be identified with the entropy within a code subspace, while the UV piece comes from the physical space. But how to algorithmically construct that division is still a bit murky, at least to me.
Joe Fisher wrote on Jan. 26, 2018 @ 17:12 GMT
Dear Professor Sean M. Carroll and Ashmeet Singh,
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.
Joe Fisher, Realist
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Wilhelmus de Wilde de Wilde wrote on Jan. 26, 2018 @ 17:51 GMT
Dear Sean
You are very right when you say “a relation to underlying reality, if any” the “if any” explains the position of the agents (us) in reality.
I also liked !“a classical limit emerges in the right circumstances” which is in concordance with “causal emergence”, meaning that there are multiple limits. Emergence is not only happening at the “if any” but also in the higher levels of emergent phenomena.
You say : “This is a version of the Everettian (ManyWorlds) approach to quantum mechanics”
In
my essay “Foundational Quantum Reality Loops” I propose a different way of explaining the problems that are solved by the MWI, NOT by the splitting up of realities, but through the “choice” of probability Loops. (I hope that you can spare some time to read and comment it.
Quote: “All of the additional elements familiar in physical theories, we will argue, can be emergent from the state vector”. Is it possible that these “state vectors” are comparable to my “Reality Loops” ?
“it seems plausible that the spacetime dynamics familiar from general relativity can arise in an emergent spacetime purely from generic features of the entanglement structure of the quantum state; finding gravity ....” If we perceive entanglement as a form of wormhole-connection (interconnection of emergent space in a reality-loop) as I argue then this argument is fully comprehensible.
I thank you very much for an essay that helped me evolving my own thoughts.
Best regards
Wilhelmus
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Colin Walker wrote on Jan. 26, 2018 @ 18:22 GMT
I have no comment, but I wonder if Sean has ever come across the criticism of general relativity presented in my essay,
A Tale of Two Relativities?
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Jochen Szangolies wrote on Jan. 27, 2018 @ 11:11 GMT
Dear authors,
to me, this is one of the most exciting essays in the contest so far (well, of those I've read, anyhow). There is some similarity, at least in spirit, to von Weizsäcker's old idea of 'ur-theory', which postulated that the phenomenology of the world, gravity, particles and all, should be derivable from an 'abstract quantum theory' of 'simple alternatives' (the urs---'ur'...
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Dear authors,
to me, this is one of the most exciting essays in the contest so far (well, of those I've read, anyhow). There is some similarity, at least in spirit, to von Weizsäcker's old idea of 'ur-theory', which postulated that the phenomenology of the world, gravity, particles and all, should be derivable from an 'abstract quantum theory' of 'simple alternatives' (the urs---'ur' meaning something like 'primordial' in German). (Incidentally, 'ur' is pronounced more like 'oor' than 'your', and it makes googling for the theory immensely hard, since all you're likely to get on a first attempt is cats claiming that 'ur theory sux', something I don't really believe they have the qualifications to confidently declare.)
But where the arguments of von Weizsäcker and his few followers often remained rather qualitative and somewhat arbitrary, you draw on modern developments in quantum mechanics to at least outline a plausible course for your program---which, I agree, has to be considered highly speculative at this point (but the payoff, in terms of getting a lot of explanation for very few assumptions one has to put in, certainly seems to justify the gamble of following this idea).
What I don't really get, however, is what's specifically Everettian about this approach. The essay mainly seems to deal with how observable physical phenomenology can be derived from very simple physical starting points, but it doesn't go too deeply into interpretational issues. Of course, you mention decoherence, but while decoherence may be important to Everettian QM, decoherence itself is quite independent of it.
There seems to be a guiding idea of simplicity in the essay, so maybe there's the connection: after all, Everettian QM is often alleged to be the 'most simple' interpretation of quantum mechanics. But I think one has to be careful here: the notion of 'simplicity' used in paring down the assumptions going into a physical theory, and the simplicity of a metaphysical interpretation, are two very different beasts, and ought not be conflated.
It's too often forgotten what makes Occam's razor so powerful, and what underlies its application to empirical theories. Put briefly, parsimony guarantees predictivity: by choosing, from the infinite ensembles of possible theories accounting for a given set of data, the simplest one, we assure that we can make unique predictions, to either confirm or use to falsify the theory. Otherwise, we could always introduce ad-hoc hypotheses to derive any 'prediction' imaginable.
It's clear, however, that this justification can't work, if applied to metaphysical interpretations. After all, an interpretation makes no prediction; thus, we aren't on the same grounds to demand parsimony as we are in empirical matters. Simplicity then becomes rather an aesthetic constraint.
One might still think that it's a good thing to keep one's ontology minimal in some sense; but the grounds here are certainly not as ironclad as they are in the sciences.
Anyway, that probably takes us too far afield. I think that your program would benefit if you would more sharply delineate between its physical and interpretational content. Other than that, though, this is an almost perfect essay, and it should do well in this contest.
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Marcel-Marie LeBel wrote on Jan. 27, 2018 @ 21:21 GMT
Sean, Asmheet,
What is fundamental is what the universe is and does before we look or even think about it.
Quantum mechanics is our most ontological theory. It is possible to get the metaphysical equivalent. We have to match the probability of finding a particle with the equal probability for the particle to be there. There is a simple underlying rule that compels the particle to be there with a certain probability i.e. the “existing” of the particle much match our “finding” of the particle.
The causality is hidden in the wave function ..... and the background. My essay invites us to ask “why” instead of “how” in order to take us out of the equation and address the logical state of the underlying reality.
Best of luck,
Marcel,
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Member Tejinder Pal Singh wrote on Jan. 29, 2018 @ 05:58 GMT
Dear Authors,
Thank you for your essay.
I will be grateful if you could explain in brief the essence of your two Refs. on deriving the Born probability rule in this approach.
To me, the occurrence of probabilities in a theory is a signature of randomness, either in the initial conditions, or in the dynamics. How do we understand randomness in Everettianism?
Since quantum linear superposition of position states [cat states] has not been experimentally established for objects with masses larger than about 10,000 a.m.u. and since the apparent random breakdown of linear superposition occurs for masses larger than these, I feel there should be a major world-wide effort to confirm /rule out stochastic theories such as GRW, which predict departures from quantum theory in the macro-limit. [If GRW is ruled out, then one has a strong case for Everettianism, in my opinion. On the other hand I once heard a Bohmian say that if GRW is ruled out, that will prove Bohmian mechanics is right!. How do we choose between Bohm and Everett?]
It is puzzling to me that while such experiments are being carried out in Europe, there seems to be no such effort in North America, to the best of my knowledge. Is there a reason for that?
With regards,
Tejinder
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Andrew Beckwith wrote on Jan. 30, 2018 @ 10:17 GMT
https://arxiv.org/pdf/gr-qc/9703089.pdf
The following is an argument given in ARXIV against the Many worlds interpretation
quote
it is argued that frequency operator
theorems of Hartle and Farhi-Goldstone-Gutmann do not in themselves
provide a probability interpretation for quantum mechanics, and thus neither
support existing MWI nor would be useful in constructing new MWI. Comments
are made on papers by Geroch and Deutsch that advocate MWI. It is
concluded that no plausible set of axioms exists for an MWI that describes
known physics.
I would welcome your commentary on this article, and to see if you reject this articles premises.
You are welcome to review my essay as well as of December 21st
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adel sadeq wrote on Feb. 2, 2018 @ 17:20 GMT
Hi
It is really a big shame that this wonderful essay is being ignored or not appreciated. So I guess I should not be disappointed either if nobody is killing himself trying to understand mine.
I agree with your essay because it goes to the heart of the physics problem without the usual extra heavy philosophical gymnastics. Moreover, I think my essay is similar if not identical to your idea.
Please visit the
EssayThank you
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John Rider Klauder wrote on Feb. 3, 2018 @ 21:29 GMT
SC
Your essay deals with many topics. I have two comments.
A Hilbert space and a quantum Hamiltonian H with its spectra determine your physical outcome. Take a classical Hamiltonian p^2+q^4 and, following conventional procedures, the quantum Hamiltonian is given by P^2+Q^4 and its spectra. Without further information we could also have chosen p^4+q^2 and also P^4+Q^2. These two operators have the same spectra which could cause confusion. To help the situation I choose q to represent how many steps I need to cross my room and I choose p to relate to the uniform speed I take to cross my room. It.seems that a full understanding of a given problem rests on the meaning of the variables that are chosen.
You have a short story about the Wheeler-DeWitt (WDW) equation written as H |psi>=0. The normal way to write the WDW as H(x)|psi>=0 where x is a spatial coordinate and int H(x) dx =H. It follows, however, that [H(x) , H(y) ] |psi> =/=0 because there are second class constraints that forbid an =0 result. (An example of second class constraints is. Q|phi> =0 and P|phi>=0 but [Q , P ] |phi>=/=0.)
Both Wheeler and DeWitt disowned this equation before they died. I even heard DeWitt say that “he wished his name had never been attached to that equation”.
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Member Paul Knott wrote on Feb. 5, 2018 @ 08:48 GMT
Hi Sean and Ashmeet,
Thanks for this fascinating essay. I got a little lost in some of the details, but really enjoyed reading it nonetheless, and I love the ambition of deriving everything from such basic principles.
Quick question: what does the "mad dog" refer to??
Recently I've been interested in showing how objectivity -- a central part of classicality -- can emerge from a quantum substrate. A really nice paper showed that, whenever the system of interest is connected to a sufficiently large environment, objectivity emerges (i.e. different observers will agree on their measurements) even when no assumptions are placed on the Hilbert space or the Hamiltonian (https://arxiv.org/abs/1310.8640). I've been extending their results to infinite dimensions (paper in preparation!).
This is probably a naive thought, but I wonder if some of the other aspects you covered (space-time, gravity, etc) are also an inherent part of the mathematical structure of quantum mechanics, rather than being properties of the specific Hamiltonian or Hilbert space?
All the best,
Paul
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Steven Andresen wrote on Feb. 6, 2018 @ 05:30 GMT
Dear Sean Carroll
I read your critique on crackpot theorists. Cant say that endeared you to me, but I wont let that effect my judgment of the work you present now.
Just letting you know that I am making a start on reading of your essay, and hope that you might also take a glance over mine please? I look forward to the sharing of thoughtful opinion. Congratulations on your essay rating as it stands, and best of luck for the contest conclusion.
My essay is titled
“Darwinian Universal Fundamental Origin”. It stands as a novel test for whether a natural organisational principle can serve a rationale, for emergence of complex systems of physics and cosmology. I will be interested to have my effort judged on both the basis of prospect and of novelty.
Thank you & kind regards
Steven Andresen
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Satyavarapu Naga Parameswara Gupta wrote on Feb. 6, 2018 @ 19:35 GMT
Respected Prof Sean Carroll
Dear Ashmeet Singh
You have very nicely interpreted that the "quantum mechanics" is one of the most fundamental things of the universe. ........ Many-Worlds interpretation, based on a vector in Hilbert space and a Hamiltonian vis a vis an algebra of preferred observables. You argue that even such an algebra is unnecessary, and even went for the most basic...
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Respected Prof Sean Carroll
Dear Ashmeet Singh
You have very nicely interpreted that the "quantum mechanics" is one of the most fundamental things of the universe. ........ Many-Worlds interpretation, based on a vector in Hilbert space and a Hamiltonian vis a vis an algebra of preferred observables. You argue that even such an algebra is unnecessary, and even went for the most basic description of the world...... the spectrum of the Hamiltonian ..... wonderful logic sirs.... 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 and hope for reciprocity ….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.h
tml
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 repliedBest
=snp
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Luca Valeri wrote on Feb. 8, 2018 @ 13:43 GMT
Dear Sean and Asmheet,
you gave a nice intuition on your research program. In fact given a wave function of the universe and a Hamiltonian governing the evolution, one should in principle be able to derive our observable universe. Of course the reverse engineering from our observable universe to the universal wave function is much more difficult.
My approach to the quantum measurement problem is similar to Everett’s relative state formulation of quantum mechanics, but with no branching and no external decoherence.
As in your essay a quantum measurement is described as consisting of 3 systems: the quantum system H
q, the apparatus H
a and the environment (or the rest of the universe) H
e. The time evolution is given such, that all the 3 systems can get entangled. However contrary to the decoherence program I assume, that the environment must be in a very special symmetric state, such that the environment does not get entangled with the H
q and H
a subsystem. Such states of the environment exists. The evolution on the subsystem can be described by a unitary evolution. This is a condition that the properties of H
q can be measured or defined. The (from within the system) unobservable absolute quantities can be averaged out, which reduces the density matrix of the subsystem. This reduction is objective and immune against Wigner’s friend type objections because if Wigner (the environment) would like to observe the system it must get entangled with the subsystem. But then the conditions of a successful measurement would be broken.
I would love, if you find the time to comment on my essay
The quantum sheep - In defence of a positivist view on physics.
Best regards
Luca
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Peter Jackson wrote on Feb. 15, 2018 @ 15:57 GMT
Sean, Asmheet,
I think that's the best description of Many Worlds I've read. Very interesting, well written and explained.
However. I do derive a finding in my essay which suggests that either you may
"..have just gone mad.", or more likely that NO 'interpretation' beyond classical mechanics may be needed!! (I was conservative with the exclamation marks). Which is exactly as John Bell believed and stated.
Few are qualified to analyse the sequence of ontological mechanisms reproducing QM's predictions, I hope you are; I've just written a short outline on John Klauders string which will assist.
Declan Traill's short essay confirms the matching code gives the CHSH >2 Cos^2 plots as well as the steering >1 closing the detector loophole. My top scored 2015 'red/green sock trick' essay started the construction (as a test of a rational SR solution). Shockingly if correct there is no 'non-locality' and QM and SR unify!
I look forward to questions.
Well done for your excellent essay anyway.
Peter Jackson
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Avtar Singh wrote on Feb. 20, 2018 @ 01:57 GMT
Hi Sean and Ashmeet:
Enjoyed your well-written and enlightening essay, especially the discussion regarding the fundamental ontology of QM.
It is intriguing that while quantum theory describes the evolution of a state vector in a complex Hilbert space, I present a simple relativity based model that describes the universal physical reality as a set of relativistic mass/energy/space/time states in various frames of observer references with varying velocity V. Using this model, we can bridge the gap between quantum and relativistic ontology without the need of uncertainty and statistical nature of quantum mechanics. My model shows that the fundamental reality is relativistic and not quantum. Heisenberg’s uncertainty is shown to be an artifact of the measurement error caused by measuring a dominantly relativistic (commonly labelled as quantum, V close to C) phenomenon with dilated space-time in a classical fixed space-time.
In my paper– “
What is Fundamental – Is C the Speed of Light”, I propose the missing physics of spontaneous mass-energy conversion (as observed in wave-particle behavior) that bridges QM and relativity while resolving the paradox of the missing dark energy that is revealed as the relativistic kinetic energy and the model derives a physics based mathematical equation (no more a fudge constant) for the Cosmological Constant . It also resolves the paradox of the collapse of the wave function that is explained via transition to the classical space-time from the fully dilated space-time when a measurement is made, the black hole singularity of GR eliminated via mass dilation at small R, and solution is obtained to other current inconsistencies as well as weirdness (QM) of mainstream theories as described in my book.
I would greatly appreciate your time and feedback on my paper?
Thanking you in advance,
Best Regards
Avtar Singh
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jason Roy wrote on Feb. 20, 2018 @ 05:09 GMT
Such a great place where you play
stickman games free online games completely free of cost.
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Steven Andresen wrote on Feb. 22, 2018 @ 08:35 GMT
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...
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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
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Cristinel Stoica wrote on Feb. 22, 2018 @ 15:51 GMT
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...
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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
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Juan Ramón González Álvarez wrote on Feb. 27, 2018 @ 20:10 GMT
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...
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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/manywo
rlds
"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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Juan Ramón González Álvarez replied on Feb. 27, 2018 @ 20:42 GMT
I forgot the attachment with the general spectral decomposition of the Hamiltonian
attachments:
Spectral_decomposition.png
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