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Trick or Truth: The Mysterious Connection Between Physics and Mathematics
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It From Bit or Bit From It
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Juan Ramón González Álvarez: on 2/27/18 at 20:42pm UTC, wrote I forgot the attachment with the general spectral decomposition of the...

Juan Ramón González Álvarez: on 2/27/18 at 20:10pm UTC, wrote Everett's work was debunked many time ago, both in physical and...

Cristinel Stoica: on 2/22/18 at 15:51pm UTC, wrote Dean Sean and Singh, This was very impressive. This program seems to me...

Steven Andresen: on 2/22/18 at 8:35am UTC, wrote Dear Sean If you are looking for another essay to read and rate in the...

jason Roy: on 2/20/18 at 5:09am UTC, wrote Such a great place where you play stickman games free online games...

Avtar Singh: on 2/20/18 at 1:57am UTC, wrote Hi Sean and Ashmeet: Enjoyed your well-written and enlightening essay,...

Peter Jackson: on 2/15/18 at 15:57pm UTC, wrote Sean, Asmheet, I think that's the best description of Many Worlds I've...

Luca Valeri: on 2/8/18 at 13:43pm UTC, wrote Dear Sean and Asmheet, you gave a nice intuition on your research program....


Zeeya Merali: "Viviana Fafone is a member of the VIRGO collaboration that detects..." in Micro and macro-physics...

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Building Agency in the Biology Lab
Physicists are using optogenetics techniques to make a rudimentary agent, from cellular components, which can convert measurements into actions using light.

Think Quantum to Build Better AI
Investigating how quantum memory storage could aid machine learning and how quantum interactions with the environment may have played a role in evolution.

Outside the Box
A proposed quantum set-up that could predict your game-playing strategy resurrects Newcomb’s classic quiz show paradox.

The Quantum Agent
Investigating how the quantum measurement process might be related to the emergence of intelligence, agency and free will.

First Things First: The Physics of Causality
Why do we remember the past and not the future? Untangling the connections between cause and effect, choice, and entropy.

June 5, 2020

CATEGORY: FQXi Essay Contest - Spring, 2017 [back]
TOPIC: Mad-Dog Everettianism: Quantum Mechanics at Its Most Minimal by Sean M. Carroll and Ashmeet Singh [refresh]
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Author Sean Carroll wrote on Jan. 25, 2018 @ 17:23 GMT
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

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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,

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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 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.

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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


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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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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,


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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,


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Andrew Beckwith wrote on Jan. 30, 2018 @ 10:17 GMT

The following is an argument given in ARXIV against the Many worlds interpretation


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

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

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John Rider Klauder wrote on Feb. 3, 2018 @ 21:29 GMT

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 ( 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,


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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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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 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


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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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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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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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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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