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 PollackWe 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.
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.
The Minkowski space vacuum state of a quantum scalar field (like a neutral Higgs) can be written as superposition of “shape states” of the field — states | f,t > which, at some definite time t, have a definite shape:
S(x,t) | f,t > = f(x) | f,t >
(where S is a scalar quantum field operator, x is a three-vector, and f(x) is any continuous function in function space).
In this basis, the vacuum state |0> can be written as a functional integral of shape states:
|0> = Integral [df] V[f] | f,t >
where the functional V[f] is given by:
V[f] = exp [(-1/4 pi) Integral dx dy dk f(x) f(y) exp {i k * (x – y) Sqr(k^2 + m^2)}]
where x, y, k are three-vectors.
(This functional V[f] is non-vanishing for all f, and can be shown to be the unique functional that yields a Poincare invariant vacuum.)
The time evolution of each of these shape states is rather explosive, but the above superposition of these shape states that constitutes the vacuum state |0> is stationary, as it must be. (Easy exercise.)
This can be (should be) interpreted as saying that the field is fluctuating in the vacuum, independent of whether it’s being measured. Just as the position of the election in the hydrogen ground state is fluctuating in non-rel QM. The hydrogen ground state can be expressed as a superposition of position eigenstates that each undergo a very non-trivial time-evolution. Just as we would say that the election’s position isn’t stationary in the hydrogen ground state, here we should say that the quantum field’s shape isn’t stationary in the vacuum. These vacuum fluctuations (e.g., of the scalar Higgs field) have real physical effects at the 1-loop and higher loop orders in QFT.
I don’t see how this is consistent with some of your statements, such as “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…”
Instead, these field fluctuations seem to be as real as any other quantum effect.
John Hagelin
Hi Sean,
One often encounters statements that a fluctuation up (down) the inflationary potential causes inflation to last longer (shorter) leading to a larger (smaller) value of the scale factor a(x,t) in any region, and that these scalar fluctuations give rise to density perturbations. I am wondering exactly how this would be rephrased. Would we instead say that the wave function for the metric perturbations evolves until reheating, and then when decoherence happens, observers will see spatial variation in the scale factor, but should not interpret this as spatial variation in the amount of inflation?
Also, would it be possible to recover the stochastic behavior during inflation with something like warm inflation, so there are additional degrees of freedom that can become entangled with inflaton modes when they cross the horizon, and induce decoherence at that point?
Thanks,
Elliot
You guys could tell me “who does the fluctuation”?
I’m not a scientist, but logically speaking it’s as if Sean is saying the fluctuation isn’t an intrinsic property, but generated by the interaction between two entities. So it’s produced by the “collision” of two objects (observer and observed) and their respective origin (what Sean called “a macroscopic system that is out of equilibrium”).
So it’s like I’m seeing the object a little different because it’s as if I look at it from a certain angle. If I change my angle of observation, then the object changes. So this “fluctuation” depends on the angle.
Is this correct or not?
What, if any, is the connection between this and Albrecht’s de Sitter Equilibrium cosmology?
@Bob Zannelli
I don’t get it. I don’t think dark energy and inflation have ever been shown to be related to each other even though they do similar things like expanding the universe. Dark energy is a present state of the universe problem, and inflation has more to do with times closer to the Big Bang. Then inflation caused expansion of the universe to be at different rates than what dark energy does today.
The state of equilibrium is interesting to me and a question forms, is L location in Lagrangian a case in point?
Also to see where the leading perspective in QGP arrives at a viscosity state as to imply such a equilibrium would allow information to move through without constraint? This is forward thinking, in terms of particle dispersal through cosmic particle collisions that would move in the medium of earth as ice(Cherenkov) to count as a measure of?
I am sorry if I cannot be much clearer, your points about what you have previously written did come to mind a lot.:) Your talk with David Albert comes to mind.
http://bloggingheads.tv/diavlogs/12123?in=NaN:NaN:NaN
Your points about arrow of time come into view for me and how you would have to contend with this in your paper. As you say this is very healthy aspect that I see you countering.
Best,
A man, in between the past and the future?
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John Barrett writes
I don’t get it. I don’t think dark energy and inflation have ever been shown to be related to each other even though they do similar things like expanding the universe. Dark energy is a present state of the universe problem, and inflation has more to do with times closer to the Big Bang. Then inflation caused expansion of the universe to be at different rates than what dark energy does today.
Dark Energy and inflation are both examples of exponential expansion of the universe because of an energy density that falls off slowly enough. They are virtually the same process , their energy scale is different.
John D says:
May 6, 2014 at 5:50 am
Interesting stuff, Sean. I’m not keen on talk of Boltzmann brains and the multiverse myself, but nevermind. IMHO yes, there were no quantum fluctuations. Because the energy density was so high the whole universe was subject to something similar to gravitational time dilation. Like a black hole event horizon is. And because the time dilation is infinite, it takes forever for a fluctuation to occur. So it never ever does. Which means Hawking radiation doesn’t occur either.
I think you’re jumping to unwarranted conclusions. A black hole at absolute zero temperature would be strange indeed. Black holes are not isolated stationary quantum states, nothing in Carroll’s paper suggest that black holes are this strange as far I can see. I think it’s important to understand, that a proposal that predicts that a whole lot of generally agreed upon physics is wrong is probably wrong.
Sean,
1. In what way(s) does your scenario change for Copenhagen Interpretation instead of MWI?
2. If one considers everything is pretty much already entangled, naturally (cup of coffee not spilling by itself), how can there be any “out-of-equilibrium macroscopic system” left to do any measurement? Related question: Are all entanglements accompanied by dis-entanglements?
3. It would be much appreciated if you could kindly give a review on the topic of Inflation/Unruh/Hawking and the role played by space expanding at faster than the speed of light.
Thanks.
@Bob Zannelli
Maybe you missed the part I said about the density in inflation theory does not change. I just saw a video about it the other day on Netflix where Alan Guth himself was saying so. I think it would be naive to think that inflation and dark energy are just the same thing. Inflation had rapid periods of burst multiple times and dark energy has remained mostly constant. The expansion of the universe due to dark energy doesn’t remain at a constant density as well. Then they would have to be due to different things, and inflation would have to be a result of special conditions close to the moment of the Big Bang. Otherwise, finding the secret of dark energy and inflation could be as simple as finding what has changed since then to make it act so differently.
Then inflation avoids the problem of black holes or the singularity by saying that not all the matter in the universe started out being there at the moment of creation. It gains it’s mass by transferring energy from the inflation field. Then the inflation field is really just something that Guth just made up and doesn’t really exist or is known to be in one form of existence or another in any other part of physics. Nothing tangible can be prescribed to it.
On another note, Einstein discovered that all of physics was wrong, but then he made a slight correction to fix all of it. Discovering something new is more like figuring out how something could have been there unknowingly all along.
John Barret writes
‘Maybe you missed the part I said about the density in inflation theory does not change. could be as simple as finding what has changed since then to make it act so differently.”
I shouldn’t have been so flip. I didn’t mean that inflation and dark are the same thing, rather that they share the general process. If you’re concern is that we don’t know what the Inflaton field is, I agree we don’t. We don’t have a particle physics description of inflation. The same BTW can be said for dark energy. We have lots of intriguing ideas but that’s all. On the other hand we do have lots of evidence for the existence of dark energy and that inflation really happened, especially if the BICEP 2 data holds up to scrutiny . So as I see it, we are pretty sure dark energy exists and inflation occurred but we don’t have a definitive model in either case.
@Bob
It’s fine. This blog really kind of took me back to where I was thinking before about all the crazy things I thought about the Big Bang. Then it is crazy, because if there is really no such thing as an inflation field that can transfer energy, then there would have to be some way energy could be created. Then most of modern physics was founded on the classical idea of conservation of energy. Then a part of me doesn’t really think it is that crazy at all when we are talking about the creation of the universe here. Then if it was true, like Sean Carroll say, that nothing would be able to fluctuate. Then he would have effectively took away all the spark out of the Big Bang. Then I don’t think this problem is really nothing new in a way, because like I said before, in other uses of the word “fluctuation” there just wasn’t enough anti-matter in the universe. Then if they are both wrong. We shouldn’t be here chatting right now, or that would violate the laws of physics. That would mean that there would have to be another way.
http://xkcd.com/1365/
Don’t forget to mouseover!
It would seem that if QM was an incomplete theory in most any way, that this idea runs aground. In other words this idea relies heavily on QM working perfectly in areas that are to put it lightly untested.
But all physical theories have been proven wrong, or are waiting to be proved wrong. Or is QM a case of ‘this time it’s different’?
Gravity for instance. The Newton formulation is very accurate, but if one takes it to the limit we can generate instant communication and other absurdities.
In the case of QM theory, the cases of ‘too good to be true’ seem to piling up. QM computation is another program that relies on the formulation to work exactly across huge regimes.
The thought that the wave function of every particle being nonzero everywhere in the universe is preposterous.
Tom Andersen writes
“The thought that the wave function of every particle being nonzero everywhere in the universe is preposterous.”
)))))))))))))))
Tom what does this mean?
Bob Zannelli
Sean:
Boltzmann Brains, as far as I have understood, are a manifestation of thermal fluctuations not quantum mechanical fluctuations. After all that’s why it is named after “Boltzmann” because of his contributions to statistical mechanics that predate quantum physics.
Is there a confusion here?
Thanks,
Farhâd
Bob: re “I think you’re jumping to unwarranted conclusions. A black hole at absolute zero temperature would be strange indeed…”. I’ve been thinking about this a lot recently, and about the original “frozen star” black hole concept. Don’t think a proposal must be wrong because agreed-upon physics can’t be. That’s how scientific progress works. The conclusion I come to is IMHO where Sean should end up when he says “there are no quantum fluctuations”. OK not in this paper, but maybe in the next. And it is this: Hawking radiation does not exist.
Could you expand a bit on why you think of a theory having Boltzmann brains as a problem? I agree that it’s a disturbing consequence, but that’s a bad reason to favor theories that don’t have them. Nature is how it is, not how we want it to be.
Boltzmann brains have an anthropic cherry picking thing going on, where your expectations are the same when you condition on “and I live”, that prevents Bayesian inference from working. So I wouldn’t expect us to know about it, except indirectly via the laws of physics…
John D Writes
The conclusion I come to is IMHO where Sean should end up when he says “there are no quantum fluctuations”. OK not in this paper, but maybe in the next. And it is this: Hawking radiation does not exist.
)))))))))))
Sorry but saying there are no quantum fluctuations is like saying there are no mountains in India. I don’t think Sean is trying to suggest the uncertainty principle is wrong. As for black holes and Hawking radiation, I think the prediction of a non zero temperature for black holes is pretty robust, based on what we know about gravity and quantum mechanics. But nothing is written on stone tablets.
@Bob Zennelli
I think the point Sean was really trying to make here is that Boltzmann Brains cannot really exist. That seems to be an ongoing theme to this blog. Then he is just saying that the uncertainty principle as we know it in quantum physics that gives rise to effects due to acts of observations doesn’t allow for quantum fluctuations that would provide the necessary ends for Boltzmann Brains and some inflationary models.
Then I had thought that the Higgs Field could provide the means necessary for a Boltzmann Brain to exist. All there would really have to be is a force that works against symmetry in quantum physics to be broken. Then it takes a required amount of energy to create a Higgs Boson. Then the Boltzmann Brain wouldn’t have to consist of the particles themselves, and it would work in between the lines so to speak of the Standard Model. I really wouldn’t be that surprised if Boltzmann Brains became a standard way to try to unlock and unravel deeper mysteries about the Higgs Field and how it operates. Then unlocking how a Boltzmann Brain in the Higgs Field thinks, one could derive how those thought processes arrived from natural laws of temporal asymmetry.
Since Boltzmann brains are on the table here, let me offer this. This is the first few paragraphs of a post I did on physics discussion list. The paper mentioned suggest the prediction that Boltzmann brains are more numerous than universes fluctuation into existence is because Susskind and co authors simply did the calculation wrong. In my opinion, this paper by Andreas Albrecht and Lorenzo Sorbo does not get enough attention.
Boltzmann’s Brains and Eternal De Sitter Space
In 2002 Dyson, Kleban and Susskind (DKS) wrote a land mark paper which investigated the problem associated with an eternal De Sitter space. (Hep-th/0208013]
Based on current astronomical data and the predictions of Holographic Dark energy model (Which I have posted on in detail) our own Universe is on a straight trajectory to just such a condition. Therefore understanding the implications of an eternal De Sitter space is important. Even accepting that a non zero vacuum energy condition itself is not eternal does not give us a surefire way to avoid an eternal De Sitter space condition. Only if the decay constant were relatively large with respect to the efold time of the De Sitter space could we avoid this state. Given the age of Universe of 13.7 billion years, it seems unlikely any possible decay constant is large enough to prevent an Eternal De Sitter space.
In their study DKS investigated the relative probabilities of a Quantum fluctuation that produced an inflating Universe and a Quantum fluctuation that produced a Universe similar in broad outline to our Universe. This calculation also relates to the Boltzmann Brain problem, the concern here being the relative probabilities of a Quantum fluctuation producing an isolated brain and an inflating Universe.
The problem deals with the relative decrease in entropy for each possibility. A tunneling even to inflation requires a fluctuation to a very low entropy state, while the two aforementioned events can occur at higher entropy states. In this post I will look at a simplified version of the DKS argument and then relate, what I think is a satisfactory solution proposed by Andreas Albrecht and Lorenzo Sorbo in 2004. [hep-th/0405270v2]
Tom Andersen:
You do know the name of this blog, right? 🙂
@Tom Andersen: more seriously, there’s no reason why physics should make intuitive sense to anyone absent training. In the 20th century physics moved well beyond the environment in which humans evolved; that is, well beyond anything that has any right to make intuitive sense. We developed science precisely to overcome our cognitive weaknesses, through a combination of experiment and mathematical theory. There’s a reason I tell my students to literally trust science more than their own senses in tricky situations.
Also, Sean explicitly says that a hidden variables theory would indeed undermine this work.