Essay Abstract

To 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 Bio

Sean Carroll is a research professor at the California Institute of Technology. Ashmeet Singh is a graduate student at the California Institute of Technology.

Download Essay PDF File

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.

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聽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.

    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

    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

    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.

    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.

    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,

    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

    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

    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 Essay

    Thank you

    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".

    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

    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

    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.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 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 Hq, the apparatus Ha and the environment (or the rest of the universe) He. 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 Hq and Ha 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 Hq 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

    7 days later

    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

    4 days later

    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