Squelching Boltzmann Brains (And Maybe Eternal Inflation)

There’s no question that quantum fluctuations play a crucial role in modern cosmology, as the recent BICEP2 observations have reminded us. According to inflation, all of the structures we see in the universe, from galaxies up to superclusters and beyond, originated as tiny quantum fluctuations in the very early universe, as did the gravitational waves seen by BICEP2. But quantum fluctuations are a bit of a mixed blessing: in addition to providing an origin for density perturbations and gravitational waves (good!), they are also supposed to give rise to Boltzmann brains (bad) and eternal inflation (good or bad, depending on taste). Nobody would deny that it behooves cosmologists to understand quantum fluctuations as well as they can, especially since our theories involve mysterious aspects of physics operating at absurdly high energies.

Kim Boddy, Jason Pollack and I have been re-examining how quantum fluctuations work in cosmology, and in a new paper we’ve come to a surprising conclusion: cosmologists have been getting it wrong for decades now. In an expanding universe that has nothing in it but vacuum energy, there simply aren’t any quantum fluctuations at all. Our approach shows that the conventional understanding of inflationary perturbations gets the right answer, although the perturbations aren’t due to “fluctuations”; they’re due to an effective measurement of the quantum state of the inflaton field when the universe reheats at the end of inflation. In contrast, less empirically-grounded ideas such as Boltzmann brains and eternal inflation both rely crucially on treating fluctuations as true dynamical events, occurring in real time — and we say that’s just wrong.

All very dramatically at odds with the conventional wisdom, if we’re right. Which means, of course, that there’s always a chance we’re wrong (although we don’t think it’s a big chance). This paper is pretty conceptual, which a skeptic might take as a euphemism for “hand-waving”; we’re planning on digging into some of the mathematical details in future work, but for the time being our paper should be mostly understandable to anyone who knows undergraduate quantum mechanics. Here’s the abstract:

De Sitter Space Without Quantum Fluctuations
Kimberly K. Boddy, Sean M. Carroll, and Jason Pollack

We argue that, under certain plausible assumptions, de Sitter space settles into a quiescent vacuum in which there are no quantum fluctuations. Quantum fluctuations require time-dependent histories of out-of-equilibrium recording devices, which are absent in stationary states. For a massive scalar field in a fixed de Sitter background, the cosmic no-hair theorem implies that the state of the patch approaches the vacuum, where there are no fluctuations. We argue that an analogous conclusion holds whenever a patch of de Sitter is embedded in a larger theory with an infinite-dimensional Hilbert space, including semiclassical quantum gravity with false vacua or complementarity in theories with at least one Minkowski vacuum. This reasoning provides an escape from the Boltzmann brain problem in such theories. It also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere while slow-roll inflation occurs, suggesting that eternal inflation is much less common than often supposed. On the other hand, if a de Sitter patch is a closed system with a finite-dimensional Hilbert space, there will be Poincaré recurrences and Boltzmann fluctuations into lower-entropy states. Our analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation, since reheating naturally generates a high-entropy environment and leads to decoherence.

The basic idea is simple: what we call “quantum fluctuations” aren’t true, dynamical events that occur in isolated quantum systems. Rather, they are a poetic way of describing the fact that when we observe such systems, the outcomes are randomly distributed rather than deterministically predictable. But when we’re not looking, a system in its ground state (like an electron in its lowest-energy orbital around an atomic nucleus) isn’t fluctuating at all; it’s just sitting there. And in de Sitter space — empty space with a positive cosmological constant — all of the fields are in their ground states. If we were to probe empty de Sitter space with a particle detector, it would certainly detect particles — but there are no particle detectors around, so in fact the quantum fields are sitting there quietly in a stationary state with no definite particle number. Therefore, these kinds of fluctuations aren’t “really happening.”

To get into a bit more detail, there are two things going on here: a certain interpretation on the meaning of “quantum fluctuations,” and some claims about de Sitter space. As far as quantum fluctuations are concerned, we readily admit that our analysis relies heavily on the Everett/Many-Worlds formulation of quantum theory. In that view, there is nothing truly random and unpredictable about quantum dynamics. There is only the smooth, unitary evolution of the wave function according to the Schrödinger equation. Apparent unpredictability arises because that smooth evolution can take a quantum state from a single connected “world” into several distinct “branches,” each of which features certain entanglements between subsystems (like the spin of a particle and the readout of a measuring apparatus that just measured that spin). But such branching doesn’t happen willy-nilly; it’s crucial that the system undergoes decoherence. Roughly speaking, that’s when a macroscopic quantum system becomes entangled with an unobserved environment. Macroscopically different states of the system (like different readouts on a measuring apparatus, or alive/dead states of a cat in a box) become entangled with different environment states. Once that happens, the two states of the macroscopic system can never talk to each other again, and in particular cannot experience mutual quantum interference. It’s as if they have become part of two different worlds.

So in the Everett picture, a quantum system in its lowest-energy state (or in any state of precisely-defined energy) isn’t fluctuating at all. It’s just sitting there, until some nosy measuring device comes poking at it. From the point of view of any given observer, the outcome of those pokes is intrinsically random. Because our brains are wired for classical physics, we therefore sometimes speak as if the system is fluctuating around even when we’re not looking at it — as if an electron is actually bouncing around in the vicinity of the nucleus of an atom, and its orbital represents the likelihood of it being in one place or another. But that’s not right: the orbital (the wave function) is the electron, it doesn’t represent our knowledge of it. And when nobody is observing it, literally nothing is fluctuating.

What does this have to do with cosmology? We often contemplate situations in which space is completely empty other than for vacuum energy — perhaps during inflation in the very early universe, or perhaps in our own future once all the matter and radiation has been dispersed by the expansion of the universe. We’re left with de Sitter space. Back in the 70’s, Gibbons and Hawking showed that de Sitter space, just like a black hole, has a temperature. That’s because, just like a black hole, de Sitter space comes with an horizon. That horizon cuts off the degrees of freedom to which any observer has access, leaving them in a thermal state at a well-defined temperature. It’s as if — but, we are claiming, only as if! — the cosmological horizon is radiating into the interior, just as the black hole horizon radiates to the outside world.

de Sitter horizon

But this quantum-mechanical “thermal state” is different from our intuition, once again trained by classical mechanics, of a bunch of particles randomly bouncing around inside a box. Globally (including outside the horizon), the quantum state is static. It only appears thermal to an observer because the horizon cuts them off from the rest of the world. This gives us a mixed state, in which the local observer doesn’t know exactly what state they’re actually in — but all of the allowed possibilities are completely stationary. So once again, nothing is actually fluctuating.

My confidence in this story about quantum fluctuations and de Sitter space is extremely high, even though it does conflict with the way many cosmologists think about the situation. The less secure part of our story is when we move from the idealization of pure de Sitter space to the messy real world. In the real world, you might think you’re in de Sitter space once and for all, but you could actually be in a temporary false-vacuum state. If there is only one vacuum, we can appeal to a “cosmic no-hair theorem” (analogous to similar theorems for black holes) that says a universe with a cosmological constant will eventually dissipate all of its excitations and turn into de Sitter space. But when there are false vacua, the situation is admittedly tricker. We’ve thought about it, and decided that the story we told above for de Sitter space is the one that is usually right, even if you’re in a false vacuum. (There are some subtleties dealing with complementarity and the dimensionality of Hilbert space, but that’s the typical situation.)

The ramifications are very interesting. The idea that Boltzmann brains fluctuate into existence and should count as “observers” in a multiverse cosmology has been a troubling one, and now we’re saying it might not be nearly as severe as people have thought. Whereas before Boltzmann brains were hard to avoid if your cosmological model ever entered a de Sitter phase, now we think it’s quite hard to get them to appear in any appreciable abundance. This might mean that the last paper by Kim and me, asking whether the Higgs field could provide an escape from the BB problem in our actual universe, is addressing a non-problem (in at least some models).

You might worry that our dismissal of quantum fluctuations is too sweeping — after all, don’t we see their effects in the cosmic microwave background? Fortunately, no. The standard story says that the inflaton field undergoes quantum fluctuations, which then get imprinted as fluctuations in density. What we’re saying is that the inflaton doesn’t actually “fluctuate,” it’s just in some calculable quantum state. But there’s nothing “observing” it, causing decoherence and branching of the wave function. At least, not while inflation is going on. But when inflation ends, the universe reheats into a hot plasma of matter and radiation. That actually does lead to decoherence and branching — the microscopic states of the plasma provide an environment that becomes entangled with the large-scale fluctuations of the inflaton, effectively measuring it and collapsing the wave function. So in our picture, all of the textbook predictions for inflation perturbations remain unchanged.

Eternal inflation is a different story. The idea there is that the inflaton field slowly rolls down its potential during inflation, except that quantum fluctuations will occasionally poke the field to go higher rather than lower. When that happens, space expands faster and inflation continues forever. Like Boltzmann brains — and unlike density perturbations — this story relies on the idea that the “fluctuations” are actual events happening in real time, even in the absence of measurement and decoherence. And we’re saying that none of that is true. The field is essentially in a pure state, and simply rolls down its potential. Clearly a lot more careful analysis has to be done here, and we’ve started thinking about it. The stakes are substantial: the fact that inflation is eternal is a key part of its motivation in the minds of many cosmologists. (Note that we’re not saying eternal inflation is impossible; if you are stuck in a false vacuum with a very tiny decay rate, you can stay there for an arbitrarily long time. But the set of models in which inflation is eternal might be much tinier than was previously believed.) As with the Higgs and Boltzmann brains, this might be another case where I am undermining one of my own previous papers. So be it — in science you have to be willing to change your mind when faced with new data or better ideas. (I think that both the Higgs paper and the out-of-equilibrium paper are perfectly correct, given their working assumptions; I just think that the assumptions are much less likely to apply than I used to.)

Finally, it’s interesting to note the role of “interpretations of quantum mechanics” in this story. (I don’t like that term, since we’re not discussing “interpretations,” we’re comparing manifestly different physical theories.) In the Everett formulation, the wave function is a direct reflection of reality; when it is stationary, so is the quantum system. Other approaches take a very different tack. There are formulations of quantum mechanics where collapse of the wave function is truly random and unpredictable; there are others with hidden variables, in which the true state of the universe isn’t defined by the wave function. In any of those cases, our analysis is completely beside the point. It’s interesting to think — but perhaps unsurprising in retrospect — that the correct formulation of quantum mechanics might have crucial implications for the evolution of the universe.

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67 Responses to Squelching Boltzmann Brains (And Maybe Eternal Inflation)

  1. Void Walker says:

    I know little of physics, but does this mean that there is zero motion in the states described, no activity at all unless we actually observe it?

  2. John Ragin says:

    Sean Carrolls “Squelching” theory is interesting. Although I wonder about his use of TIME here. On one hand, Sean says it is not true that “fluctuations” are actual events happening in real time”. But on the other hand, he says – “The field is essentially in a pure state, and simply rolls down its potential.” But if the field is “rolling down its potential” isn’t “real time” required? If the wave function was truly static – (i.e, Sean says: “so in fact the quantum fields are sitting there quietly in a stationary state with no definite particle number. Therefore, these kinds of fluctuations aren’t “really happening”) – then I don’t see how the field can “roll down its potential” to ever get to reheating. But since we apparently do, then time must have passed during inflation; which for me means only that “measuring” (i.e. “decohering” was happening); which means the wavefunction was not in a pure state but was already decohering during inflation and thus causing real fluctuations. Or no? – I am just a philosopher so be gentle. :)

  3. Ignacio says:

    Sean

    Just because the Copenhagen interpretation can’t be applied to the Universe without invoking external observers and the like doesn’t mean that you can ignore quantum mechanical fluctuations. It only means that this interpretation was tailored to lab experiments.

    You seem to have your own interpretation for the dictum that “unperformed experiments have no results”, which is a mantra of QM practitioners such as David Mermin.

    But I do not believe one can be dogmatic as to what constitutes an experiment. The universe can certainly be thought of as a recording device. You can imagine allowing the possibility of eventual observers if it helps, but it really does not depend on that or happenstance of the sort you seem to argue for.

    Murray Gell-Mann has been saying sensible things about this for quite a while. But I suspect he is running out of steam.

    It seems to me Gell-Mann has been the voice of reason about very many controversial topics for a very long time now. I have always been impressed by his willingness to state his position in a straightforward and clear manner.

    I do not see how your statements in this blog can be justified.

    Best
    Ignacio

  4. Bob Zannelli says:

    John Ragin writes

    ean Carrolls “Squelching” theory is interesting. Although I wonder about his use of TIME here. On one hand, Sean says it is not true that “fluctuations” are actual events happening in real time”. But on the other hand, he says – “The field is essentially in a pure state, and simply rolls down its potential.” But if the field is “rolling down its potential” isn’t “real time” required? If the wave function was truly static – (i.e, Sean says: “so in fact the quantum fields are sitting there quietly in a stationary state with no definite particle number. Therefore, these kinds of fluctuations aren’t “really happening”) – then I don’t see how the field can “roll down its potential” to ever get to reheating. But since we apparently do, then time must have passed during inflation; which for me means only that “measuring” (i.e. “decohering” was happening); which means the wavefunction was not in a pure state but was already decohering during inflation and thus causing real fluctuations. Or no? – I am just a philosopher so be gentle.

    )))))))))))))))

    This was my question too.

  5. Andy Charman says:

    Dear Professor Carroll,

    I would wholeheartedly agree that what are conventionally called “quantum fluctuations” are not “really happening.” But this point of view does not require or presuppose the Everett interpretation, only a careful distinction between fluctuations — actual variations in a physical quantity over space and/or time, and uncertainties — the limited ability of an agent to predict the value of a measurement.

    Strictly speaking, a literal reading of the quantum formalism suggest that what are usually called “quantum fluctuations” or “zero-point” motions reflects uncertainty, not any real fluctuation. Fluctuations require something to actually be changing in space and time. In quantum mechanics, I would agree that fluctuations require measurement, and in fact, repeated measurement. A divergent uncertainty in the value of the electromagnetic field in some region should not mean that there is actually infinite energy in the zero-poimnt motions of the field, but rather that we are completely unable to predict the value of the field. The amount of uncertainty can then of course differ from the level of fluctuations, and can be greater or less depending on the reasons for the uncertainty and the nature and resolution scales of the measurements.

    This was all spelled out by E.T. Jaynes with his usual crystalline clarity in his article, “Where Do We Stand on Maximum Entropy.”

    But this distinction can be maintained in virtually any sensible interpretation of quantum mechanics, except perhaps some hidden variable theories. It can lead to some puzzles concerning certain semiclassical theories, where we blithely use QM expectation values as source terms in classical equations of motion.

  6. Bob Zannelli says:

    Andy Charman writes

    strictly speaking, a literal reading of the quantum formalism suggest that what are usually called “quantum fluctuations” or “zero-point” motions reflects uncertainty, not any real fluctuation. Fluctuations require something to actually be changing in space and time. In quantum mechanics, I would agree that fluctuations require measurement, and in fact, repeated measurement.

    ))))))))))))))))

    Measurement is not just something done in a lab or by a human instrument. It’s what entanglement does to create the classical universe, which BTW doesn’t need human observation to exist.

  7. phayes says:

    I agree with Andy Charman that it’s hard to see why Many Worlds would be necessary for this, and the implication –

    But that’s not right: the orbital (the wave function) is the electron, it doesn’t represent our knowledge of it. And when nobody is observing it, literally nothing is fluctuating.

    – that psi-epistemicism would be what was responsible for a mistaken belief in real, dynamical fluctuations, even seems rather ironic:

    Arnold Neumaier on misinterpreting vacuum fluctuations
    Stephen Gull on a classical analog

  8. Andy Charman says:

    Dear phayes,

    Indeed, some do try to imbue the wave function with more reality than the electron it is meant to describe, and then of course are faced with certain difficulties (what is collapse, and does it happen instantaneously, or at all? why does the many-particle wavefunction live in configuration space rather than real space?, etc.) Carleton Caves, Chris Fuchs, and their colleagues have done a nice job critiquing this from a quantum Bayesian perspective.

    I agree completely with Stephen Gull — this passage is an excerpt from a very nice book “Maximum Entropy in Action” by Brian Buck and Vincent Macaulay — but I would go even further than Neumaier: the Casimir effect does not provide evidence for the reality of vacuum fluctuations, or zero-point energy, because it can be described perfectly well as a properly retarded interaction between the actual electric charges in the plates.

  9. Bob Zannelli says:

    Once you start arguing if virtual particles exist or not, you’re down the rabbit hole. You could just as reasonably ask if electrons exist. ( They are quasi particles in solid state physics) All we have are models which if they good , will be predictive. It’s pointless to argue about what’s real and what’s not.

  10. Vlad says:

    @Andy Charman
    @phayes
    Sorry but the Vacuum energy is still a reality and so is the zero-point energy.
    Also over an infinite time variation can occur in the vacuum energy.

  11. Vlad says:

    @Robin Hanson
    @Void Walker
    Over an infinite time low probability event can still occur such as inflation from vacuum energy.

  12. Vlad says:

    @Michael
    Well again over an infinite time even improbable events can happen and of course it can come back to “us” with the Poincaré recurrence theorem.

    @Sean Carroll
    Even if De Sitter space is in truly equilibrihum, we are still left with electromagnetic radiation, vacuum energy and quantum tunneling.
    Over an infinte time the Poincaré recurrence theorem shows that we will return to our previous state.
    There is still quantum tunneling or change in vacuum energy (or zero-point energy) or vacuum polarization who can happen even in a spaceless/timeless universe.

  13. phayes says:

    @Vlad
    Why are you so sure? The ‘argument’ from the reality of the Casimir effect was always a non sequitur, psi-epistemicists can see a more fundamental problem with the cosmologists’ belief/assumption that it’s real and now, thanks to Sean and his colleagues, (some of) the psi-ontologists can too.

  14. Andy Charman says:

    Vlad,

    I am in agreement with phayes. On what grounds do you assert:
    “Sorry but the Vacuum energy is still a reality and so is the zero-point energy”? What experimental evidence do we have for such a claim? Or even what theoretical motivation?

    None of the usual arguments (Casimir effect, Lamb shift, spontaneous emission) are cogent, because these phenomena can be described using models or calculations which do not make use of vacuum fluctuations, or do not attach ontological significance to vacuum fluctuations.

    Logically speaking, if we are to assert the reality of something, it ought to be the case that simpler theories or models which omit that element of reality cannot predict the phenomena in question.

    The situation is somewhat analogous to the case for the existence of photons prior to Alain Aspect’s pioneering experiments involving anti-correlations in single-photon states. None of the usual textbook arguments for the necessity of photons (i.e., for quantizing the electromagnetic field) actually proved anything of the kind, because the Planck blackbody spectrum, the photoelectric effect, and the Compton effect could all be explained using a semiclassical model, where the matter was quantized but the radiation field was not.

  15. Bob Zannelli says:

    Sean and co authors assertion have made it to “New Scientist” which is always looking for ideas that shake up the prevailing consensus. Guth is writing a paper in response to Sean’s paper. Unfortunately Guth is a terrible procrastinator, we might have a wait. Nonetheless it will surely be worth the wait. My own view on this, for what it’s worth ( probably not much but I can’t resist) is that Sean is correct about the need for some measurement process to have quantum fluctuations, but I am not sure if he made the case for there being no measurement process in a De Sitter space. This may well just reflect my own confusion, but it’s how I see it.

  16. Vlad says:

    @Andy Charman
    @phayes

    The article is interesting and you have a point about the statistical/observer bias when measuring quantum fluctuation.
    However then the “real” existence of a lot of physical concept must be put in question (like your exemple of the photon). Also there is the totalitarian principle who state that at the quantum level everything wich is not forbidden WILL happen and in this case with quantum fluctuation without observator since over infinity of time low probability event can happen.

    Even without zero-point energy, vacuum energy is here thanks to higgs field and electromagnetic radiation.

    Sorry for my bad english.

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