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. Ben Goren says:

    Sean, could you clarify what you mean by “observer” and “observation”? In the informal language you used above, it comes with the implication of a conscious intelligence as an integral part of the process, and I’ll bet that’s not actually the case — or, at least, not in the way it’s commonly understood.

    For example: “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 would seem to imply — incorrectly, I’m sure — that the human mind has the power to cause electrons to start fluctuating, merely by focussing one’s attention upon them.

    Thanks,

    b&

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  2. Sean Carroll says:

    Ben– It has nothing to do with consciousness or intelligence (of course). An “observation” in quantum mechanics happens whenever any out-of-equilibrium macroscopic system becomes entangled with the quantum system being measured. It will then decohere (become entangled with the wider environment), which causes a splitting of the wave function into separate branches.

    It’s key that the macroscopic device in question starts out far from equilibrium. Otherwise it would already be entangled with everything, and the measurement/splitting process couldn’t occur.

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  3. Bob Zannelli says:

    I haven’t read this yet, just the blog article. Interestingly the idea that quantum fluctuations make no sense absent a measurement process is an idea that has been bandied about on Dr Vic Stenger’s discussion list, even as long as few years ago. But if there is no measurement process in De Sitter space doesn’t this rule out any kind of vacua decay in inflation as well as the Carroll Chen proposal on the origin of universes? In fact wouldn’t it would rule out every possible model of the Universe’s origin . i.e. . Vilenkin, Linde, Hartle and Hawking, Atkatz and Pagel etc. How do you get from the quantum universe of the Wheeler De Witt equation , a static, timeless state , to the universe we actually live in? With the boundary as everything ( no boundary) there is no De Coherence process. If in De Sitter space nothing ever really happens, so much more the void of third quantization.

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  4. Ben Goren says:

    Thanks for the clarification, Sean.

    Your second paragraph makes me wonder: the state you describe there sounds awfully similar to the state of the de Sitter space you’re describing. If so, wouldn’t everything be entangled and in equilibrium? How, then, would such a space transition to the one we’re familiar with?

    b&

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  5. Sean Carroll says:

    Bob– Ordinary tunneling down from a false vacuum to a true one is perfectly allowed by our analysis, since it increases entropy and generates decoherence.

    Ben– If we are in a perfect de Sitter vacuum, we’re saying there will be no transitions to anything. But we’re probably not; it’s easy to imagine a landscape of many different approximate vacua.

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  6. John Barrett says:

    From my studies of pop physics, I was under the impression that “quantum fluctuation” was synonymous with random particle pair creation and annihilation (that would be a mouth full). So then there very well could be “quantum fluctuations”, because the mechanism behind random particle pair creation and annihilation are unknown. Then I thought that was the reason why Michio Kaku ask the question of why there is not enough antimatter in the universe, because if the “quantum fluctuations” are random particle pair creation and annihilation then the universe would have to be half antimatter. But then, from the “cosmology experiment” the universe is mostly matter, so then the “cosmology experiment” shows that was not the case, unless there was some unknown reason why the universe isn’t half antimatter.

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  7. Ben Goren says:

    Ah — I think I get it; it’s an approximation useful for certain scales. Just as it’s useful to approximate the Earth as flat when you’re spreading that street map out on the table.

    So, the Cosmos (perhaps, if you’re right) approximates a perfect de Sitter vacuum, and, in that context (which is at the same scale) Boltzmann Brains and the like aren’t relevant. But at different scales (where Boltzmann Brains aren’t relevant) it deviates enough from a perfect de Sitter vacuum for local dechoerence and all the rest — just as the Earth clearly isn’t actually flat if you’re floating by the window of the ISS.

    Thanks!

    b&

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  8. miller says:

    Sounds like a great paper, though I don’t think I quite understand it.

    So, during inflation, the inflaton field is at a higher potential, rolling down to a lower potential. That means it’s not in the lowest energy state, and not a vacuum state–maybe it’s a false vacuum state? Is that right?

    Another question, how does entropy figure into this? Fluctuations in the CMBR seem to represent huge amount of free energy. Where did that free energy come from? Why can’t that free energy go into creating Boltzmann brains?

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  9. Bob Zannelli says:

    I slogged through the paper, I will need to read it several times to get some decent degree of understanding. However, for what’s it worth, I think the basic premise, that you can’t have quantum fluctuations absent a measurement process ( De Coherence) is without doubt right. The rub will be whether or not a De Sitter space is really free of any measurement process. I hope this paper stimulates some responses from folk like Linde who are bound to approch these assertions very critically. This is a very interesting paper.

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  10. Hi Professor Carroll,
    What is the best explanation to quantum fluctuations? I mean why do Q. fluctuantions occur? Do We really do not have the ”cause” of it? Is it just a consequence of Heisenberg´s principle? (that is not the ”cause”?) I know the word “cause” is problematic.

    And about TIME, Do quantum fluctuations occur without time? I mean out of time. Not needing the influence of time. Without the existence of time.
    Could it be one reason to suspect the time is fundamental?

    Thank You.

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  11. If the universe/multiverse is infinite, do you still get an infinite number of Boltzmann brains, as long as their probability is finite in an infinite number of finite patches? If so, is there a good way to calculate the ratio of Boltzmann brains to normal observers? Or are you thinking that it’s just Bang – us – de Sitter, end of story?

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  12. Charlie says:

    Doesn’t a Boltzmann Brain count as an observer? Or for that matter, a Boltzmann Bowl of Petunias (since intelligence isn’t really needed to be an observer)?

    Edit: oops! on rereading, I see the sentence ‘The idea that Boltzmann brains fluctuate into existence and should count as “observers”…has been a troubling one,’ which makes my question above seem lifted from the text. But my question isn’t about my worry that only empty space exists outside my office door. It’s about the concept: “there are no particle detectors around”. Don’t the Boltzmann Brains and Boltzmann Bowls of Petunias themselves count as particle detectors?

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  13. Sean Carroll says:

    miller– The kind of inflation that we think gave rise to density perturbations is “slow-roll” inflation, where a field is slowly rolling down its potential. So it’s not really in a vacuum state at all. Nevertheless, it can be very close to the vacuum state; in particular, not entangled with anything else.

    Alexandre– Quantum fluctuations occur because the universe is fundamentally quantum-mechanical, and observations typically probe quantities (like position or momentum) that are not precisely defined in a quantum state.

    Eric– We’re saying that the probability of fluctuating a Boltzmann brain goes to zero, so the integral over all time is finite (and likely quite small).

    Charlie– The informal notion of an “observer” requires a macroscopic system that is out of equilibrium. In de Sitter space, everything is in equilibrium.

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  14. Michael says:

    Hello Professor,

    I wonder how these new ideas of yours relate to your previous work on the arrow of time. The impression I get from this ( I’m just a layman,I’m no physicist, so I am most likely off) is that once the Universe expands enough to become the true De Sitter space, the universe is effectively dead. No more work can happen, and it is basically in a state of true heat death.

    In your previous work, you seem to indicate (again, I may be misinterpreting here) that there may not be a true final “end” to work in the universe, and that it can still achieve a low entropy state given enough time, random chance etc. Are you saying that the work that you have down and your thoughts that you wrote about in “From Eternity To Here” are now no longer valid according to you? If so, how do you now resolve the questions of how the universe started in a low entropy state, and how do you reconcile the ideas of time reversible laws of physics into your new view?

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  15. Robin Hanson says:

    This makes a lot of sense, and is now my default view of things. Good work! I’ll worry less about Boltzman brains and worry more about where inflation comes from, since it probably isn’t eternal.

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  16. Sean Carroll says:

    Michael– Your impression is correct, but only if de Sitter space is truly an equilibrium vacuum state. If it is unstable (for example, to nucleating baby universes, or to decaying to a lower-energy vacuum), then interesting things can still happen, including the scenario I discussed in FETH.

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  17. Bob Zannelli says:

    Let me ask the dumb question. If you have the Inflaton field slow rolling down the potential hill, how can we say we have a static unmeasured quantum state. Isn’t the value of the Inflaton field potential the result of a measurement process? This being the case how does this process evade “experiencing” quantum fluctuations.

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  18. T.E. Oakley says:

    Dr. Carroll,
    In your paper “DeSitter Space Without Quantum Fluctuations,” you and your co-authors state in Section 6, under “Conclusions”:
    “In stationary states, entropy is not generated, and the wave function remains fixed; therefore, there are no quantum fluctuations….” (p.28).
    The “nothing theorists,” including Dr. Stephen Hawking, Dr. Lawrence M. Krauss, and Dr. Alex Vilenkin all propose a Cosmic Origin scenario with reference to a “quantum fluctuation”:
    1.) “Absolute nothingness” phase transitions via 2.) a “quantum fluctuation” to 3.) Our Cosmos.
    “Absolute nothingness” is variously defined as a.) “a closed spherical spacetime of zero radius.” (Dr. Vilenkin); b.) “… no space, no time, no anything!” (Dr. Krauss); and c.) “…some peculiar non-geometric phase where we wouldn’t recognize it as ‘space’ at all.” (Dr. Sean M. Carroll).
    Using the above quote from your paper of 1 May 2014, can we now look at this “Nothingness Origin” scenario in the following way:
    (1.) “Absolute nothingness” is unquestionably a “stationary state.”
    (2.) “Entropy” is not generated; as a physicalist you must know that this “nothingness,” as defined, is a metaphysical construct: the “W” in L. Boltzmann’s formula for entropy (S=k log W) is, in “absolute nothingness,” ZERO, A NULL SET.
    (3.) The “wave function” remains fixed in this “nothingness state”—if we can talk at all in these quantum mechanical terms with reference to “absolute nothingness.” Therefore:
    (4.) “THERE ARE NO QUANTUM FLUCTUATIONS.”
    If there are no “quantum fluctuations” in this Origin scenario, a key transitional element is now lost in the “nothing” program of “A Universe From Nothing!”
    In your book “From Eternity to Here,” in note 232 on page 405, you reference the Gottfried Wilhelm Leibniz existential question “Why is there something rather than nothing;” and you declare the classical ontological definition of nothing as a genesis “state,” “neither…warranted by either experience or logic.” My question to you Dr. Carroll is twofold:
    (A.) Are not the above quoted definitions of “absolute nothing” really EQUIVALENT to the classical ontological definition of nothing? and
    (B.) In the conceptual perspective of your post “DeSitter Space Without Quantum Fluctuations” paper, do you find, now, the above described Origins scenario from “absolute nothing” as “neither…warranted by either experience or logic?”
    T.E. Oakley

    Sent from my iPhone

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  19. Ian says:

    How does this sit for virtual particles and the Casimir effect?

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  20. Abalieno says:

    Err, please excuse the completely non-scientist question, but I’d like Sean to explain this in simple terms…

    In the comments you seem to say that the macroscopic system has a kind of “imprint” that defines “where it comes from”. Like in science fiction usually is defined as a “vibration”, with parallel words having different vibrations or phases. So it seems you say that when an observation occurs, the entanglement happens because it’s the fingerprint of the macroscopic system that gives a peculiarity to the thing observed.

    In other words, the thing observed wasn’t originally moving, but it is moved through the act of observation and fixed in a position. Or, it’s the interaction between the thing and what was observing that produces the result.

    But if this isn’t a totally incorrect simplification, why are even we aware of this quantum theory if as an observing system we are always tied to “our way of seeing”? What’s the theoretical external observer that tells us there is more than one possible state?

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  21. BobC says:

    Does the de Sitter space for this paper include the Goldstone Theorem?

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  22. John Barrett says:

    One thing I found peculiar about inflation is that it assumes that there wasn’t that much matter/energy close to the Big Bang, but the inflation field consisted of something that was unable to change density. Then what was able to expand with the universe but not change in density was a mystery, but that was how Alan Guth was able to discover inflation. Then I thought if there was a free energy mechanism involved that resulted in the Big Bang, then the creation of energy could then act like a field that didn’t change in density. It could just create more particles as it grew, so that the total density would remain unchanging even though it had grew in size. It would be kind of funny if that was one of the skeletons hiding in inflation’s closet.

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  23. Bob Zannelli says:

    John Barret writes:

    “One thing I found peculiar about inflation is that it assumes that there wasn’t that much matter/energy close to the Big Bang, but the inflation field consisted of something that was unable to change density. Then what was able to expand with the universe but not change in density was a mystery, but that was how Alan Guth was able to discover inflation. Then I thought if there was a free energy mechanism involved that resulted in the Big Bang, then the creation of energy could then act like a field that didn’t change in density. It could just create more particles as it grew, so that the total density would remain unchanging even though it had grew in size. It would be kind of funny if that was one of the skeletons hiding in inflation’s closet.”

    Two words, Dark Energy.

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  24. Bob Zannelli says:

    Abalieno writes

    “(A.) Are not the above quoted definitions of “absolute nothing” really EQUIVALENT to the classical ontological definition of nothing? and
    (B.) In the conceptual perspective of your post “DeSitter Space Without Quantum Fluctuations” paper, do you find, now, the above described Origins scenario from “absolute nothing” as “neither…warranted by either experience or logic?”

    If we truly live in a quantum universe where the classical reality we observe is the product of wave function reduction, then there exists a quantum state of everything that is not time dependent. What we observe is highly coarse grained view of this, so time dependence is emergent.

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  25. John D says:

    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.

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  26. John Hagelin says:

    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

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  27. 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

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  28. Abalieno says:

    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?

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  29. What, if any, is the connection between this and Albrecht’s de Sitter Equilibrium cosmology?

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  30. John Barrett says:

    @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.

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  31. Platohagel says:

    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,

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  32. Platohagel says:

    A man, in between the past and the future?

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  33. Pingback: » Crackpot theories Looping Wor(l)d

  34. Bob Zannelli says:

    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.

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  35. Bob Zannelli says:

    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.

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  36. KC says:

    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.

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  37. John Barrett says:

    @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.

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  38. Bob Zannelli says:

    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.

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  39. John Barrett says:

    @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.

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  40. http://xkcd.com/1365/

    Don’t forget to mouseover!

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  41. Tom Andersen says:

    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.

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  42. Bob Zannelli says:

    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

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  43. Farhad Keyvan says:

    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

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  44. John D says:

    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.

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  45. Craig Gidney says:

    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…

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  46. Bob Zannelli says:

    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.

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  47. John Barrett says:

    @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.

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  48. Bob Zannelli says:

    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]

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  49. Charon says:

    Tom Andersen:

    The thought that the wave function of every particle being nonzero everywhere in the universe is preposterous.

    You do know the name of this blog, right? :)

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  50. Charon says:

    @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.

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  51. 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?

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  52. 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. :)

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  53. 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

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  54. 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.

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  55. 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.

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  56. 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.

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  57. 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

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  58. 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.

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  59. 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.

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  60. 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.

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  61. Vlad says:

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

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  62. 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.

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  63. 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.

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  64. 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.

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  65. 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.

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  66. 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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