Space Emerging from Quantum Mechanics

The other day I was amused to find a quote from Einstein, in 1936, about how hard it would be to quantize gravity: “like an attempt to breathe in empty space.” Eight decades later, I think we can still agree that it’s hard.

So here is a possibility worth considering: rather than quantizing gravity, maybe we should try to gravitize quantum mechanics. Or, more accurately but less evocatively, “find gravity inside quantum mechanics.” Rather than starting with some essentially classical view of gravity and “quantizing” it, we might imagine starting with a quantum view of reality from the start, and find the ordinary three-dimensional space in which we live somehow emerging from quantum information. That’s the project that ChunJun (Charles) Cao, Spyridon (Spiros) Michalakis, and I take a few tentative steps toward in a new paper.

We human beings, even those who have been studying quantum mechanics for a long time, still think in terms of a classical concepts. Positions, momenta, particles, fields, space itself. Quantum mechanics tells a different story. The quantum state of the universe is not a collection of things distributed through space, but something called a wave function. The wave function gives us a way of calculating the outcomes of measurements: whenever we measure an observable quantity like the position or momentum or spin of a particle, the wave function has a value for every possible outcome, and the probability of obtaining that outcome is given by the wave function squared. Indeed, that’s typically how we construct wave functions in practice. Start with some classical-sounding notion like “the position of a particle” or “the amplitude of a field,” and to each possible value we attach a complex number. That complex number, squared, gives us the probability of observing the system with that observed value.

Mathematically, wave functions are elements of a mathematical structure called Hilbert space. That means they are vectors — we can add quantum states together (the origin of superpositions in quantum mechanics) and calculate the angle (“dot product”) between them. (We’re skipping over some technicalities here, especially regarding complex numbers — see e.g. The Theoretical Minimum for more.) The word “space” in “Hilbert space” doesn’t mean the good old three-dimensional space we walk through every day, or even the four-dimensional spacetime of relativity. It’s just math-speak for “a collection of things,” in this case “possible quantum states of the universe.”

Hilbert space is quite an abstract thing, which can seem at times pretty removed from the tangible phenomena of our everyday lives. This leads some people to wonder whether we need to supplement ordinary quantum mechanics by additional new variables, or alternatively to imagine that wave functions reflect our knowledge of the world, rather than being representations of reality. For purposes of this post I’ll take the straightforward view that quantum mechanics says that the real world is best described by a wave function, an element of Hilbert space, evolving through time. (Of course time could be emergent too … something for another day.)

Here’s the thing: we can construct a Hilbert space by starting with a classical idea like “all possible positions of a particle” and attaching a complex number to each value, obtaining a wave function. All the conceivable wave functions of that form constitute the Hilbert space we’re interested in. But we don’t have to do it that way. As Einstein might have said, God doesn’t do it that way. Once we make wave functions by quantizing some classical system, we have states that live in Hilbert space. At this point it essentially doesn’t matter where we came from; now we’re in Hilbert space and we’ve left our classical starting point behind. Indeed, it’s well-known that very different classical theories lead to the same theory when we quantize them, and likewise some quantum theories don’t have classical predecessors at all.

The real world simply is quantum-mechanical from the start; it’s not a quantization of some classical system. The universe is described by an element of Hilbert space. All of our usual classical notions should be derived from that, not the other way around. Even space itself. We think of the space through which we move as one of the most basic and irreducible constituents of the real world, but it might be better thought of as an approximate notion that emerges at large distances and low energies.

So here is the task we set for ourselves: start with a quantum state in Hilbert space. Not a random or generic state, admittedly; a particular kind of state. Divide Hilbert space up into pieces — technically, factors that we multiply together to make the whole space. Use quantum information — in particular, the amount of entanglement between different parts of the state, as measured by the mutual information — to define a “distance” between them. Parts that are highly entangled are considered to be nearby, while unentangled parts are far away. This gives us a graph, in which vertices are the different parts of Hilbert space, and the edges are weighted by the emergent distance between them.


We can then ask two questions:

  1. When we zoom out, does the graph take on the geometry of a smooth, flat space with a fixed number of dimensions? (Answer: yes, when we put in the right kind of state to start with.)
  2. If we perturb the state a little bit, how does the emergent geometry change? (Answer: space curves in response to emergent mass/energy, in a way reminiscent of Einstein’s equation in general relativity.)

It’s that last bit that is most exciting, but also most speculative. The claim, in its most dramatic-sounding form, is that gravity (spacetime curvature caused by energy/momentum) isn’t hard to obtain in quantum mechanics — it’s automatic! Or at least, the most natural thing to expect. If geometry is defined by entanglement and quantum information, then perturbing the state (e.g. by adding energy) naturally changes that geometry. And if the model matches onto an emergent field theory at large distances, the most natural relationship between energy and curvature is given by Einstein’s equation. The optimistic view is that gravity just pops out effortlessly in the classical limit of an appropriate quantum system. But the devil is in the details, and there’s a long way to go before we can declare victory.

Here’s the abstract for our paper:

Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
ChunJun Cao, Sean M. Carroll, Spyridon Michalakis

We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space H into a tensor product of factors, we consider a class of “redundancy-constrained states” in H that generalize the area-law behavior for entanglement entropy usually found in condensed-matter systems with gapped local Hamiltonians. Using mutual information to define a distance measure on the graph, we employ classical multidimensional scaling to extract the best-fit spatial dimensionality of the emergent geometry. We then show that entanglement perturbations on such emergent geometries naturally give rise to local modifications of spatial curvature which obey a (spatial) analog of Einstein’s equation. The Hilbert space corresponding to a region of flat space is finite-dimensional and scales as the volume, though the entropy (and the maximum change thereof) scales like the area of the boundary. A version of the ER=EPR conjecture is recovered, in that perturbations that entangle distant parts of the emergent geometry generate a configuration that may be considered as a highly quantum wormhole.

Like almost any physics paper, we’re building on ideas that have come before. The idea that spacetime geometry is related to entanglement has become increasingly popular, although it’s mostly been explored in the holographic context of the AdS/CFT correspondence; here we’re working directly in the “bulk” region of space, not appealing to a faraway boundary. A related notion is the ER=EPR conjecture of Maldacena and Susskind, relating entanglement to wormholes. In some sense, we’re making this proposal a bit more specific, by giving a formula for distance as a function of entanglement. The relationship of geometry to energy comes from something called the Entanglement First Law, articulated by Faulkner et al., and used by Ted Jacobson in a version of entropic gravity. But as far as we know we’re the first to start directly from Hilbert space, rather than assuming classical variables, a boundary, or a background spacetime. (There’s an enormous amount of work that has been done in closely related areas, obviously, so I’d love to hear about anything in particular that we should know about.)

We’re quick to admit that what we’ve done here is extremely preliminary and conjectural. We don’t have a full theory of anything, and even what we do have involves a great deal of speculating and not yet enough rigorous calculating.

Most importantly, we’ve assumed that parts of Hilbert space that are highly entangled are also “nearby,” but we haven’t actually derived that fact. It’s certainly what should happen, according to our current understanding of quantum field theory. It might seem like entangled particles can be as far apart as you like, but the contribution of particles to the overall entanglement is almost completely negligible — it’s the quantum vacuum itself that carries almost all of the entanglement, and that’s how we derive our geometry.

But it remains to be seen whether this notion really matches what we think of as “distance.” To do that, it’s not sufficient to talk about space, we also need to talk about time, and how states evolve. That’s an obvious next step, but one we’ve just begun to think about. It raises a variety of intimidating questions. What is the appropriate Hamiltonian that actually generates time evolution? Is time fundamental and continuous, or emergent and discrete? Can we derive an emergent theory that includes not only curved space and time, but other quantum fields? Will those fields satisfy the relativistic condition of being invariant under Lorentz transformations? Will gravity, in particular, have propagating degrees of freedom corresponding to spin-2 gravitons? (And only one kind of graviton, coupled universally to energy-momentum?) Full employment for the immediate future.

Perhaps the most interesting and provocative feature of what we’ve done is that we start from an assumption that the degrees of freedom corresponding to any particular region of space are described by a finite-dimensional Hilbert space. In some sense this is natural, as it follows from the Bekenstein bound (on the total entropy that can fit in a region) or the holographic principle (which limits degrees of freedom by the area of the boundary of their region). But on the other hand, it’s completely contrary to what we’re used to thinking about from quantum field theory, which generally assumes that the number of degrees of freedom in any region of space is infinitely big, corresponding to an infinite-dimensional Hilbert space. (By itself that’s not so worrisome; a single simple harmonic oscillator is described by an infinite-dimensional Hilbert space, just because its energy can be arbitrarily large.) People like Jacobson and Seth Lloyd have argued, on pretty general grounds, that any theory with gravity will locally be described by finite-dimensional Hilbert spaces.

That’s a big deal, if true, and I don’t think we physicists have really absorbed the consequences of the idea as yet. Field theory is embedded in how we think about the world; all of the notorious infinities of particle physics that we work so hard to renormalize away owe their existence to the fact that there are an infinite number of degrees of freedom. A finite-dimensional Hilbert space describes a very different world indeed. In many ways, it’s a much simpler world — one that should be easier to understand. We shall see.

Part of me thinks that a picture along these lines — geometry emerging from quantum information, obeying a version of Einstein’s equation in the classical limit — pretty much has to be true, if you believe (1) regions of space have a finite number of degrees of freedom, and (2) the world is described by a wave function in Hilbert space. Those are fairly reasonable postulates, all by themselves, but of course there could be any number of twists and turns to get where we want to go, if indeed it’s possible. Personally I think the prospects are exciting, and I’m eager to see where these ideas lead us.

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70 Responses to Space Emerging from Quantum Mechanics

  1. Daniel Kerr says:

    I’m a bit confused on the hypothesis here. Is the claim that gravity is an emergent property of (finite) Hilbert space constructions of any quantum theory? Or is the claim that by solving the quantization problem in reverse we find an appropriate Hamiltonian by recognizing how it factors the overall Hilbert space?

  2. mgrinder says:

    Hello Sean,

    I just read your book “The Big Picture” and enjoyed it. Thanks for writing it.

    I was interested in your comments about consciousness. In your book you basically say that any theory of consciousness cannot introduce something to physics that would contradict the laws of physics. I agree with this. You yourself seem to be an emergentist, if I may call you that. So I was wondering what you, as an emergentist, and a physicist, think of the following theory of the mind. It is an attempt to give consciousness a causal role in nature, and at the same time introduce something to the scientific picture of the world without contradicting any physical laws. I find emergentism implausible, so that is why I came up with this.

    The theory basically has two hypotheses:

    (1) Every time a fundamental particles, such as electrons or quarks (or bound combinations thereof: like protons, atoms, and molecules), change state, what will happen must be “calculated” (information must be processed in some manner, somehow) by the particle(s) (or something associated with the particles), and

    (2) A conscious experience (a “quale” (plural qualia)) aids in this “calculation”. After this “calculation via qualia” is complete, the particle then changes state, as when an electron jumps to a higher orbital after being hit by a photon.

    That’s the theory of consciousness in a nutshell. I agree it sounds weird, but it seems to generate a good theory, in my opinion of course. To try to describe it a bit more briefly:

    Instead of assuming that particles change state “automatically”, it is supposed that particles must first “calculate” what to do next, and use qualia to do it. Thus consciousness becomes a sort of universal calculation mechanism, used by all particles everywhere.

    Usually, of course, people assume that particles change state without any need for a “calculation” happening first, and indeed, this seems simplest on the face of it. However, this assumption seems to lead to a denial of consciousness existing at all in the scientific picture. If an assumption denies that part of reality exists, it is not the best assumtion. Occams razor does not support it. I would think you do not agree that the scientific picture denies that consciousness exists, but there are powerful arguments for this view, like Chalmer’s zombie argument. If the scientific picture of the world really does deny consciousness exists, it must be modified. Anyways, it seems to me that assuming this calcualtion mechanism exists should be no contradiction to the laws of physics. Particles will do what the laws of physics say they will do in this theory, but now we have an added detail that explains consciousness, and gives it a role in nature.

    This theory postulates that there are uncountable qualia (which are not much like our own human experiences, it is probably better to call them something like “primal” qualia) being generated in matter all the time, everywhere, as particles change state . However, certain of these qualia, associated with certain molecules interacting in living cells, account for the conscious experiences of living things. Basically, I suppose that large molecules interacting in living cells are complex enough, and contain enough information to reference memories, a sense of self, and sense data from bodily organs, such as our eyes and ears. All other particle interactions in the universe would not be able to reference past states (memories), or a sense of self, so would not be like our own experiences. More on this in my essay, if interested.

    In this theory, consciousness is more or less part of how the laws of nature work. Consciousness has a causal role in nature, it is the means by which particles calculate what to do next. It is a sort of “calculation mechanism”, a natural means of information processing. If true, this solves the “hard problem” of consciousness in a functional sense, i.e. the reason we have conscious experiences is because that is how some particles in our brains (as well as all particles everywhere) “figure out” what to do next. This also gives insight into answering the hard problem in a comparison sense, i.e. what are conscious experiences are compared to other things like mass and charge? In this theory it would appear to be some sort of “immaterial” calculation mechanism, whatever that means.

    Anyways, much more to be said, and the website which deveops this theory is linked to my name, if interested. Again, I am interested in your reaction to this theory of mind, which seems to me to be original.

  3. zarzuelazen says:


    Yes indeed, I too was dissatisfied with Sean’s comments on consciousness, and I had some similar thoughts as yourself. You might like to read all the comments for the last few posts on this blog, where I subjected Sean’s views to stern examination, and Ben Goran (another regular poster on the forums) put up a strong defence.

    After some further reflection, I think that Sean has made the mistake of conflating two different propositions:

    (a) Consciousness is *consistent* with the laws of physics and
    (b) Consciousness is *explained by* the laws of physics.

    I was persuaded by (a), however, I’m still not convinced by (b), because it is actually a separate proposition that doesn’t logically follow from (a) at all! The laws of physics are *constraints* on explanation, *not* total explanations in themselves. The laws of physics rule out many supernatural or magical explanations of consciousness , but this does not mean that they actually *explain* consciousness, which in my view still needs additional principles.

    David Deutsch is developing what he calls ‘constructor’ theory, which views the world in terms of ‘tasks’ (processes) rather than ‘things’. Incidentally, Deutsch’s theory takes ‘information’ to be fundamental. Alfred North Whitehead, a famous philosopher of the last century, also tried to explain consciousness through what he called ‘process theory’. Thermodynamics and ‘the arrow of time’ is a possible related line of attack; I don’t find Sean’s explanation for the arrow (in terms of the low entropy initial state of the universe) entirely convincing.

  4. Ben Goren says:


    (1) Every time a fundamental particles, such as electrons or quarks (or bound combinations thereof: like protons, atoms, and molecules), change state, what will happen must be “calculated” (information must be processed in some manner, somehow) by the particle(s) (or something associated with the particles), and

    Sean addresses exactly this in The Big Picture. Riffing off of the “philosophical zombie,” which posits entities that give all outward signs of consciousness but which aren’t actually conscious, Sean proposes considering two universes: one with conscious fundamental particles and ones without. Our universe behaves exactly the same way as one would expect one with unconscious particles to behave, so the zombies are left with absolutely nothing to do with their consciousness.

    In your particular case, it would help to consider the motions of the planets. Jupiter does not perform any calculation in order to decide whether or not to follow the essentially Newtonian path it takes around the Sun. If you want to predict what Jupiter will do, the best way is to perform a calculation — but Jupiter simply falls towards the Sun, but it had enough of an head start going sideways that its fall takes it back where it started.

    Now, consider your own case. When you trip and fall, do you perform a conscious calculation that determined your own parabolic trajectory towards the ground?

    (2) A conscious experience (a “quale” (plural qualia)) aids in this “calculation”. After this “calculation via qualia” is complete, the particle then changes state, as when an electron jumps to a higher orbital after being hit by a photon.

    The problem with this is that consciousness on Earth only arrived very recently in its history, yet we have overwhelming evidence that physics chugged along quite happily without any conscious observers. Further, we have all sorts of evidence that, even today, physics does the exact same thing whether or not any conscious observers are observing what’s going on.

    Even worse, you are proposing a means of interacting with electrons. We know all the ways it’s possible to interact with electrons — mostly, via electromagnetism, with a few footnotes. A physicist would call a way of interacting with something a “force.” And it’s a fact of nature that each force has particles associated with it. That means that you can smash two electrons together at the right energy and create the particle associated with the force…which we’ve done, and found no consciousness particles that carry your proposed consciousness force. (It might help to understand that “particles” aren’t actually bits of stuff, but rather waves in their associated fields, and a physicist would understand the previous description as really saying that the two fields are coupled in such a way that, at such-and-such an energy in the one, you create a wave in the other. That’s how you can smash electrons and create photons. Think of it as akin to the harmonic resonance that lets microphones record sounds.)

    You may also be interested to know that what you’re proposing very easily fits into the general category of philosophies known as “panpsychism.” zarzuelazen, who has already replied to you, is also a proponent of panpsychism.

    The fundamental problem of panpsychism is that, though you can propose a self-consistent universe that operates according to its principles, we know as surely as we know that the Sun rises in the East that that’s not how our universe operates.

    Sean addresses a number of the ways we know this in The Big Picture. For example, we have ways of measuring the degrees of freedom available to fundamental particles — with the charge and spin of an electron being two examples. The problem for panpsychism is that our accounting of those degrees of freedom is demonstrably complete, with no freedom left over for intelligence.

    …and we can also approach it from the other direction. We may have only a fuzzy picture of what consciousness is, but it’s more than clear enough to rule out any deep mysteries. Indeed, ever since the Egyptians refined the art of brewing beer, we’ve had overwhelming evidence that consciousness is a physical phenomenon that can be predictably altered through physical means. The sad case of Phineas Gage removed any remaining doubt, and modern neuroscience has filled in far more gaps than you imagine.

    Once upon a time we had to resort to something like elan vital to explain the mystery of life, or gods to explain the origins of species. But now we know it’s just chemistry and Evolution. Similarly, we also know that consciousness is ultimately no more mysterious than life — even if we do understand life rather better than we understand consciousness.



  5. zarzuelazen says:

    Insofar as consciousness interacts with the physical world, consciousness has to be physical yes.

    In the previous discussions I did manage to identify one possible remaining escape route for panpsychism…the arrow of time.

    David Deutsch is a certified genius; he’s a world class physicist and one of the world’s top researchers on quantum computing; he is not convinced that the arrow of time is explained by the ‘initial (low entropy) condition’ of the universe.:

    “According to Deutsch, current theories of physics based on quantum mechanics do not adequately explain why some transformations between states of being are possible and some are not. For example, a drop of dye can dissolve in water but thermodynamics shows that the reverse transformation, of the dye clumping back together, is effectively impossible. We do not know at a quantum level why this should be so.”

    Deutsch also says:

    “Information has the property that a given statement might have said something else, and one of these alternatives would not be true. The untrue alternative is said to be “counterfactual”. Conventional physical theories do not model such counterfactuals. However the link between information and such physical ideas as the entropy in a thermodynamic system is so strong that they are sometimes identified. For example, the area of a black hole’s event horizon is a measure both of the hole’s entropy and of the information it contains. ”

    Source: Wikipedia entry on ‘Constructor Theory’.

    Therefore, if Deutsch is correct, the ‘arrow of time’ introduces an extra unexplained degree of freedom into physics.

  6. Moe says:

    @Ben Goren

    “the quantum interpretation mystery seems to be a matter of figuring out why that one particle in the detector was the one to interact with the diffracted electron as opposed to some other particle in the detector.”

    This is indeed at the heart of the interpretation of quantum mechanics. This is the question about wave function “collapse”.

    If the ‘wave’ is moving out in all directions at the speed of light, why does it seem to collapse/interact at only a single point in space and time?

    I (and many others, including Sean) believe that this is an illusion, and that there is no one single interaction with a single particle in the detector. There is eventually an interaction with every particle, and not just those in the detector.

    This is the ‘Many Worlds’ idea.

    It appears that interactions occur only with a single particle in the detector, but that is just from your limited perspective, looking backwards in time from your only possible vantage point.

    In a broader ‘reality’, there are multitudes of “you” who have each observed the interaction at each of the possible locations, according to the Born Rule.

  7. Moe says:

    @Ben Goren

    “For me, the big unknown, the big mystery, is what is actually happening when one particle interacts with another.”

    From your comments, you seem like you have read and studied this stuff for some time. In my opinion, this situation is the least mysterious.

    I won’t get into any equations, but if you just imagine that all ‘particles’ are in some way actually ‘waves’ in some medium, then the interaction makes sense.

    Particles can transform into different particles, because they are all just vibrations of the same thing.

    An ‘interaction’ occurs when there is a new resonance to either recreate the same wavelength, break it into seperate waves with the same energy, or combine different waves into one with the same energy.

    You can see things like this occur on the surface of a pool of water when the energy of some stones are flung in.

    The thing about reality and quantum mechanics is that (unlike in a pond), you can only observe things from a blurry line from your position back in time. You can never see the entire pond.

    If a wave that seemed to earlier steer off in it’s own direction later meets back up with a wave within your ‘past’, then you have quantum inteference.

    Entanglement is a bit different, because it requires standing waves and the aknowledgement that time is not a one way street. Many people have trouble with this.

    Most of the ‘paradoxes’ of quantum physics have to do with people not even trying to imagine the same situation with the clock running backwards.

    I would encourage everyone that encounters a ‘paradox’ or otherwise ‘difficult to understand situation’ in quantum mechanics to try and look at it from the understanding that time is running in both directions. The speed of light is only a description of a distance that is somehow coupled to moving a distance in one of the other three directions.

    No matter how strange it seems, this will give you a much better grasp on what we can consider reality.

  8. Fred says:

    Objects traveling at high velocities create their own gravity, their own spatial geometries, so why shouldn’t confined quantum “objects,” waves, do the same? Makes sense to me given no real understanding of the subject.

  9. mgrinder says:

    Thanks for your comments Zarzulean and Ben Goren.

    Zarzulean: I like how you phrase that there is a difference between consciousness being consistent with physics and consciousness being explained by physics. It’s hard to phrase all this philosophical jumbo jumbo, and that puts it well. It’s interesting how you got the idea right away. And,

    Ben Goren: in contrast, you don’t seem to get the idea very well. Jupiter would not make a calculation in this theory to go around the sun because (1) It’s in free fall around the Sun, and it’s not changing state. As I understand it, unless something disturbs Jupiter as it orbits, it does not change state. (2). It is the collections of bound particles , like molecules, or atoms in a solid of diamond, that are changing state in Jupiter that need to calculate what to do before they change state. For instance, if there is a molecule of methane on Jupiter that encounters another molecule of something, and they bond, then before this bonding can happen, a “calculation” (information processing) must occur. That is the theory. In contrast, Jupiter is a vast collection of molecules and bound atoms. These individual entities (molecules and atoms) would calculate before they change state, but Jupiter itself would not, unless Jupiter can be regarded as having its own wavefunction. Even if you can regard Jupiter as having its own wavefunction, the calculations that Jupiter itself would experience are not calculations that you’d write home about. All these “calculations” that occur on Jupiter involve qualia (that is the theory) but not qualia that reference memories or a sense of self as they occur, so they are not like our human, animal, experiences.

    Further, I do not experience a “calculation” before I fall on the ground, yes, as you point out. But in this theory, the particles in my body joined to other ones , like a molecule in one of my muscle cells, would experience a “calculation” of sorts as they change state because of my body flexing as it stumbles and falls on the ground. None of these “calculations” in my body reference memories or a sense of self as they happen. So I don’t experience them. The only ones I experience are those that occur in some of my neurons as molecules that actually DO reference memories and my sense of self as they change state. The theory is that some of these molecules have enough information content, and are set up correctly, that they reference memories and my sense of self as they bond with other molecules. It is these “special” interactions which constitute my human experience, my conscious life. Note that the vast majority of particle interactions that occur in these very neurons where my human experiences occur do not contribute to my human experience, my conscious life, at all, even though they are changing state and undergoing “calculations” as they change state. Why do I not experience these? Because they reference none of my memories or my sense of self as they occur, only certain, “special” molecules in my neurons do. Why do I not experience your thoughts? Because they do not refence my memories or sense of self as they occur, they reference yours. That is the theory, anyways.

    Hope that is comprehensible. Please try reading my essay, linked to my username for more details.

    Also, I am very , very, aware that this theory is similar to panpsychism, thank you. However it is a bit different as well. This theory postulates that, in addition to all the particles, forces, and space time out there, there is also a universal calculation mechanism of sorts (that Is “immaterial” – whatever that means, and seems to use no energy) that all particles must use before they change state. Panpsychism postulates that all particles have mental properties in addition to things like charge and mass. However, in panpsychism these mental properties are epiphenomenal, they are useless. In this theory, this universal calculation mechanism does not produce any new behaviour of particles, but is not epiphenomenal at all. It does something in nature, and it’s not an additional property to particles, it’s an additional property of nature itself, with a very similar role to the role that physical laws play in nature. In many ways, this universal calculation mechanism is part of the laws of nature, can even be said to be the laws of nature (roughly). Hence this is a new theory, and does not fit into the pigeonhole of panpsychism, dualism, emergentism, materialism, or any other previous theory of the mind.

    Anyways, please feel free to read my essay, and if you know of a way to get Sean Carroll to, please tell me. 🙂

  10. Ben Goren says:


    Jupiter would not make a calculation in this theory to go around the sun because (1) It’s in free fall around the Sun, and it’s not changing state. As I understand it, unless something disturbs Jupiter as it orbits, it does not change state.

    But that’s just it.

    Jupiter is changing state — its position is in constant change. Not only its position, but its direction as well; it is in a state of neverending acceleration.

    And the other half is that we know that all Jupiter is doing is “falling down” the local gravitational potential as described by the gravity field…which is exactly what happens in all the rest of physics.

    To understand why your example of a methane molecule bonding to something else is of the same nature of event as Jupiter orbiting the Sun, you would need an introductory-level understanding of Quantum Field Theory. Sean has some videos out there that give such an introduction…but the super-short version is that, just as there is an universal gravitational field with a value at every point in space, all the other particles and forces have their own universal fields. An electron, for example, is most emphatically not a particle; it is, instead, a fluctuation in the electron field — and the strength of the fluctuation can be observed as the likelihood that you’d detect an individual electron. The different fields can couple and interact in specific ways at certain energies and so on, with our macroscopic perspective of the world emerging from the fields the same way that the ellipse of Jupiter’s orbit emerges from (essentially Newtonian / Laplacian) gravitation.

    So, when the electrons and quarks of that methane molecule interact with the electrons and quarks of some other molecule, they really are simply “falling down” their local gradients in the electron and quark fields. They no more need to “calculate” their trajectories than does Jupiter.

    You can, right now, perform some trivial experiments that should give you reason to accept that this “falling down” analogy applies to all of physics. You can, of course, do the standard high school physics experiments that derive all of Newtonian Mechanics, especially gravity. You can then do the other standard high school physics experiments involving magnets and magnetism — and then tie those together with electricity and electromagnetism. You can do optics experiments, including the optical double slit experiment and games with lasers and diffraction gratings. In all cases, you’ll see that there’s no need for the individual phenomena to “calculate” what they’re doing; they’re just following the path of least resistance, or “falling down” in the same way that Jupiter does when it orbits the Sun.

    Extending those observations into the microscopic realm would require a bit more equipment and expertise than most people can muster on a lazy Sunday afternoon, but they’re well within reach of amateurs. And the pattern continues, all the way to the LHC at CERN — whose researchers would be delighted to share their findings with you, even if they won’t let you push any of the buttons.

    Or, a shorter way of putting it…what you propose is that electrons in a wire (presumably) don’t need to do any calculation in order to create the electromagnetic field that lights the bulb when connected to the battery, but they do need to do some magic conscious calculation when they’re in your brain. And that’s nowhere near consistent enough to form a reliable scientific theory — never mind that it’s contradicted by observation.



  11. Ben Goren says:


    Your description of the interaction of particles matches mine. And it’s a big part of why I’m not so sure that there’s a deep mystery to understand.

    If my fuzzy understanding is correct — and, believe me, I can’t overemphasize how little confidence I have in my understanding — then the mystery of collapse seems to resolve itself once (in the case of the double-slit experiment) you stop thinking of the detector as a monolithic classical (or even Platonic) entity and instead consider it as a collection of a mind-boggling number of waves.

    Let’s pretend non-existent godlike powers of observation and prediction. We know ahead of time that, of all the brazilian-and-one electrons in all the atoms of all the phosphors of the detector, this one particular electron is going to be the one to interact with the incoming diffracted electron. As you describe and as I previously understood, that means that there’s going to be some variation on the theme of constructive interference between the two.

    We know that the incoming diffracted electron has a state that evolves with time. At one moment, it’s at the emitter; a bit later the wavefront reaches the slits; some time after that it reaches the detector.

    We should also therefore know that each of the electrons-waves in the detector are themselves evolving with time. However, by the design of the person who made the instrument, these electron-waves are tightly confined to their respective, point-like, locations. But they are not themselves static! They’re just, effectively, going ’round and ’round in circles. But still evolving with time, even if, macroscopically, they seem to be standing still.

    So, at the point in time when the wavefront from the diffracted electron reaches the detector, it’s not arriving at a perfectly-smooth plane of whatever; instead, it “sees” the full resolution of all the individual electrons in whatever state they happen to be in at that moment. And so the detector-electron that’s superficially geometrically closest to the slit may well be cresting on the back side of the atom at the instant that the diffracted electron reaches it — so no interaction is possible. Its neighbor atom’s electron is cresting somewhere on the side, still not in a position to interact. It’s only when you get to our divinely divined electron closer to the dark region of the interference pattern that the two are perfectly aligned, goldilocks-style, and the waves can therefore constructively interfere.

    Thanks to Sean, I’m now cool with derivations of the Born Rule from Many-Worlds. But I’m now left with a paradox…if I’m understanding correctly that interactions are constructive interference (or whatever), then Many-Worlds either has a problem with solidity or conservation.

    That is, Many-Worlds would say that the incoming diffracted electron interacts with the geometrically-closest electron in the detector, and it also does so with all the other electrons. But if it’s constructively interfered with the first, what’s left of it to do so with its neighbors? If it’s constructively interfering with all of them, what’s keeping all those interactions (Worlds) separated?

    I would encourage everyone that encounters a ‘paradox’ or otherwise ‘difficult to understand situation’ in quantum mechanics to try and look at it from the understanding that time is running in both directions. The speed of light is only a description of a distance that is somehow coupled to moving a distance in one of the other three directions.

    Thanks for this. I’m definitely going to have to think it through long and hard. It certainly superficially fits with everything else I’ve heard from Sean…as he might put it, if I “take seriously” that the macroscopic arrow of time is due entirely to the low entropy of the Big Bang, and if I also “take seriously” that there’s no such arrow of time at the microscopic level, then, yes, there are going to be some profound and, presumably, difficult-to-understand consequences.

    Also…this round of back-and-forth has given me some ideas for experiments I myself might be able to design and perform. I’m overwhelmingly expecting them to tell me that my idea is worng…but they also give me the excuse to fantasize as much about winning the Nobel as buying a lottery ticket gives me the excuse to fantasize about becoming a millionaire.



  12. mgrinder says:

    Ben Gordon:

    Sorry, I was just reading about GR and how things in free fall are actually the only things that are *not* accelerating. I’m getting this from Brian Greene’s “Fabric of the Cosmos”. Since when you are sitting at rest, there is the force from the chair stopping you from going through the floor, you are not force free. When you fall from a cliff, according to GR, you are force free. This provides the ultimate standard to say something is “at rest”, at least according to the book I am reading. That is why I said Jupiter is not changing state while it is in free fall around the sun. The things that are actually accelerating in GR are things like people sitting “at rest” on a chair. THey are actually accelerating upwards.

    If my interpretation of what I am just reading about GR is not correct, sorry, I’m still digesting the knowledge.

    ANyways, it’s not all that important for the theory I am presenting, which you still don’t seem to understand. The point is that Jupiter changing state as a whole in this theory is fine. The theory would say that, if all of Jupiter can be represented as a single wavefunction, and that wavefunction collapses, then before it changes state, it needs to calculate via qualia. As usual, that is not a conscious experience that we humans have, because it does not reference any memories or sense of self as it occurs.

    About electrons in a wire, in this theory, if they are changing state, then yes, they have a sort of “primal” conscious experience as they change state. As I keep saying, this is not the sort of experience we humans have. I hope this makes sense to you. It made sense to Zerzuleazan.

    Further, even if particles are vibrations in a quantum field, that’s OK for this theory, as long as they change state in some manner, as long as wavefunctions collapse, this theory is OK.

  13. Moe says:

    @Ben Goren

    “That is, Many-Worlds would say that the incoming diffracted electron interacts with the geometrically-closest electron in the detector, and it also does so with all the other electrons. But if it’s constructively interfered with the first, what’s left of it to do so with its neighbors? If it’s constructively interfering with all of them, what’s keeping all those interactions (Worlds) separated?”

    I think you are starting to think about it more correctly, but you are very limited by thinking that there is only a single interaction of the electron or photon (or whatever particle) with the detector.

    Take some time to think about diffraction of x-rays from a crystal lattice. This is very similar to the double slit experiment, but with millions of slits in three dimensions. Disregard what you know about the detector also being made up of particles, and pretend it is some perfect non-existent recording device.

    Even when the x-ray beam intensity is lowered to being single photons spaced out by minutes, eventually you can detect and record the EXACT SAME diffraction pattern as if you had sent billions of photons per femto-second.

    This means that the diffraction occurs from single photons interacting with themselves. There is no doubt about this.

    So. Whenever a single photon enters the crystal lattice, it actually interacts in every single possible way (arrording to physical laws of interaction) with every single particle in the crystal.

    Every single electron that could be bumped into a higher energy state actually does get bumped into a higher energy state. Every high energy electron that could fall into a lower energy state, while releasing a photon of the same energy that it had adsorbed, does release that photon.

    These billions of imaginary photons, traveling in all directions from every particle in the crystal lattice, interfere to somehow leave only a single interaction with one particle on the detector.

    Actually, this is just part 1.

    Between emmision and detection, a single particle can be split into an enormous, nearly infinite, number of equally real particles, which can interfere with themselves, and interact with the rest of the particles in the universe, as if each of them were waves.

  14. Moe says:

    @Ben Goren

    Now for part 2.

    As long as you understand diffraction of single photons from a crystal lattice, the next part should be easier. Let’s talk about the detector.

    You are thinking that the photon only interacts with one particle on the detector. That is what you said you believe. That is what you always seem to OBSERVE. This is making you wonder why that is the case. How can that be possible? Where is the collapse? Where do the other particles go? What about the conservation of energy?

    But actually this is where the conservation of energy and the Born rule emerge, and it is because of the complexity of large systems and particularly our own bodies and brains. We are made up of a huge number of particles.

    Going back to the crystal diffraction, why is it that the emitted photon is able to interact as a wave with every single particle in the crystal (and show diffraction to prove that is actually the case), yet it interacts as a singular particle when hitting the detector?

    The answer should be obvious. It does interact in exactly the same way, as a wave, with every particle in the detector! Yet we only observe one outcome. Why?

    This is where the ‘Many Worlds’ come in. All of the interactions do occur. But, you are only able to see a unique one of them in your own personal past from your own personal position in the present.

    There are many ways to think about this, but it won’t be hard to understand once you get the diffraction part down.

    The next ‘tricky’ thing is entanglement of particles. It actually isn’t that tricky, though. Just think about all particles being able to move equally the same forward and backward in time. The counter-intuitive part emerges from entropy and the arrow of time.

  15. Moe says:

    “A finite-dimensional Hilbert space describes a very different world indeed. In many ways, it’s a much simpler world — one that should be easier to understand. We shall see.”

    Won’t this help to understand the Born rule as well?

    Most of the suggested problems with the Many Worlds idea come from there being infinite worlds, and so how could you get the statistical outcomes that are actually observed?

    If everything actually has finite boundaries, even if they are enormous, then problems associated with infinity are no longer really problems at all.

  16. zarzuelazen says:


    I definitely like your thinking, yes, if there’s any opening for consciousness, it has to be in ‘state changes’ and the forward arrow of time – I suggest you look into thermodynamics and the arrow of time stuff. Things have ‘propensities’ (tendencies) to act in certain ways – some state changes are more likely than others, and perhaps these propensities just *are* consciousness (qualia) in some sense.

    The problem with the idea of equating consciousness with ‘abstract rules’ is that it is hard to see how you could avoid epiphenomenalism. Abstract rules (like ‘laws of physics’) are supposed to be timeless and unchanging, whereas consciousness is dynamic. So abstract things in themselves can’t interact with physical reality. Ben’s point was a good one… insofar as consciousness can affect physical reality, consciousness has to *be* physical.

    A possible way to develop your idea is to postulate that consciousness has a ‘double-aspect’ – perhaps consciousness has *both* a physical aspect (the measurable processes going on in the brain) *and* an abstract/informational/computational aspect – the abstract rules governing the state changes.

  17. IdPnSD says:

    “So here is a possibility worth considering: rather than quantizing gravity, maybe we should try to gravitize quantum mechanics.” – Why can you not quantize the gravity? Gravity is the result of every physical object, like earth, moon, sun etc. All these physical objects are composed of particles. Therefore gravity is composed of some forces originated by such quantum particles.

    On the other hand the foundational elements of QM are not satisfactory. (1) How can you prove that a particle is a wave? Double slit experiment cannot send one particle at a time, because we do not have such a technology. (2) Probability is not there in engineering and nature. (3) Probability is defined by infinity, and infinity is not there in nature and in engineering. (4) If you replace infinity by any finite number, large or small, the characteristics of the corresponding theory, like Fourier Transform (FT), will completely change. (5) Hilbert space is also inconsistent with nature because it requires infinity. (6) Uncertainty Principle is based on FT, which in turn uses infinity. Etc.

  18. Benny Pendentes says:

    Your talks and books are exceptionally clear and you seem to have a knack for homing in on the appropriate content-bandwidth for each target audience… you don’t leave the lay reader eating your dust, but also don’t bore people who already *do* know the science. So I don’t know why I was so surprised to find that your site (in general) and posts like this one (in particular) are remarkably informative and clear to a level that many scientists can’t be bothered to waste their time reaching.

    Some science-y sites read like ‘moogly moogly moogly’; reading this page (and others like it on your site) every time I encounter a new concept that I feel I need to (re-)familiarize myself with to be able to understand what comes next, there is a handy link seamlessly embedded in the text that takes me right where I need to go to get up to speed.

    For all of *that*: thank you.

  19. mgrinder says:

    Thanks for your comments again.

    I think I agree with the “double aspect” possibility. Though I am not sure that a “physical change” in necessary to have a calculation via qualia, if it is required, I think it could be accounted for by wavefunction interference. It seems reasonable that whenever wavefunctions interfere, information is processed, and hence a “calculation” of sorts must be performed. If information is processed, then the “physical” part (whatever that means) of the calculation mechanism would be the wavefunction interference. The idea is that, as wavefunctions interfere, a “calculation” occurs. The physical mechanism is the wavefunction interference.
    IF this is right, then the “calculation via qualia” part would be associated with the wavefunction deciding what to do, based on all the information it has, as it collapses. This raises the intriguing possibility that perhaps the calculation via qualia is associated with processing the non local information that the wavefunction has access to. That’s just speculation of course.

    AS always, my website is where I do my best to develop this idea is linked to my username here.

  20. Space=gravitized quantum fields. Consciousness=gravitized electromagnetic interactions between the living brain and environment. Gravitize=giving body/weight to.