Quantum Mechanics Smackdown

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Greetings from the Big Apple, where the World Science Festival got off to a swinging start with the announcement of the Kavli Prize winners. The local favorite will of course be the Astrophysics prize, which was awarded to Alan Guth, Andrei Linde, and Alexei Starobinsky for pioneering the theory of cosmic inflation. But we should also congratulate Nanoscience winners Thomas Ebbesen, Stefan Hell, and Sir John B. Pendry, as well as Neuroscience winners Brenda Milner, John O’Keefe, and Marcus E. Raichle.

I’m participating in several WSF events, and one of them tonight will be live-streamed in this very internet. The title is Measure for Measure: Quantum Physics and Reality, and we kick off at 8pm Eastern, 5pm Pacific.

[Update: I had previously embedded the video here, but that seems to be broken. It’s still available on the WSF website.]

The other participants are David Albert, Sheldon Goldstein, and Rüdiger Schack, with the conversation moderated by Brian Greene. The group is not merely a randomly-selected collection of people who know and love quantum mechanics; each participant was carefully chosen to defend a certain favorite version of this most mysterious of physical theories.

  • David Albert will propound the idea of dynamical collapse theories, such as the Ghirardi-Rimini-Weber (GRW) model. They posit that QM is truly stochastic, with wave functions really “collapsing” at unpredictable times, with a tiny rate that is negligible for individual particles but becomes rapid for macroscopic objects.
  • Shelly Goldstein will support some version of hidden-variable theories such as Bohmian mechanics. It’s sometimes thought that hidden variables have been ruled out by experimental tests of Bell’s inequalities, but that’s not right; only local hidden variables have been excluded. Non-local hidden variables are still very viable!
  • Rüdiger Schack will be telling us about a relatively new approach called Quantum Bayesianism, or QBism for short. (Don’t love the approach, but the nickname is awesome.) The idea here is that QM is really a theory about our ignorance of the world, similar to what Tom Banks defended here way back when.
  • My job, of course, will be to defend the honor of the Everett (many-worlds) formulation. I’ve done a lot less serious research on this issue than the other folks, but I will make up for that disadvantage by supporting the theory that is actually true. And coincidentally, by the time we’ve started debating I should have my first official paper on the foundations of QM appear on the arxiv: new work on deriving the Born Rule in Everett with Chip Sebens.

(For what it’s worth, I cannot resist quoting David Wallace in this context: when faced with the measurement problem in quantum mechanics, philosophers are eager to change the physics, while physicists are sure it’s just a matter of better philosophy.)

(Note also that both Steven Weinberg and Gerard ‘t Hooft have proposed new approaches to thinking about quantum mechanics. Neither of them were judged to be sufficiently distinguished to appear on our panel.)

It’s not accidental that I call these “formulations” rather than “interpretations” of quantum mechanics. I’d like to see people abandon the phrase “interpretation of quantum mechanics” entirely (though I often slip up and use it myself). The options listed above are not different interpretations of the same underlying structure — they are legitimately different physical theories, with potentially different experimental consequences (as our recent work on quantum fluctuations shows).

Relatedly, I discovered this morning that celebrated philosopher Hilary Putnam has joined the blogosphere, with the whimsically titled “Sardonic Comment.” His very first post shares an email conversation he had about the measurement problem in QM, including my co-panelists David and Shelly, and also Tim Maudlin and Roderich Tumulka (but not me). I therefore had the honor of leaving the very first comment on Hilary Putnam’s blog, encouraging him to bring more Everettians into the discussion!

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The Meaning of Life

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I have been a crappy blogger, and I blame real life for getting in the way. (No, that’s not the meaning of life.) I keep meaning to say something more substantial about the BICEP2 controversy — in the meantime check out Raphael Flauger’s talk, Matias Zaldarriaga’s talk (slides), this paper by Mortonson and Seljak, or this blog post by Richard Easther.

At least I have been a productive scientist! One paper on the expected amount of inflation with Grant Remmen, and one on the evolution of complexity in closed systems with Scott Aaronson and Lauren Ouellette (no relation to Jennifer). Promise to blog about them soon.

But not too soon, as I’m about to hop on airplanes again: first for the World Science Festival, then for the Cheltenham Science Festival. (Cheltenham is actually part of the world, but the two festivals are quite different.) Note that at the WSF, our session on Quantum Physics and Reality (with Brian Greene, David Albert, Sheldon Goldstein, and Ruediger Schack, Thursday at 8pm Eastern) will be live-streamed. Maybe the Science and Story event (with Steven Pinker, Jo Marchant, Joyce Carol Oates, and E.L. Doctorow, Thursday at 5:30 Eastern) will be also, I don’t know.

So, in lieu of original content, here is seven minutes of me pronouncing sonorously on the meaning of life. This is from a debate I participated in with Michael Shermer, Dinesh D’Souza, and Ian Hutchinson (not the Greer-Heard Forum debate with William Lane Craig, as I originally thought). I talked about how naturalists find meaning in our finite lives, without any guidance from the outside world.

SEAN CARROLL - The Meaning of Life

I had nothing to do with the making of the video, and I have no idea where the visuals are from. It’s associated with The Inspiration Journey group on Facebook.

When I extend an kind of olive branch to believers, I do so in all sincerity. I unambiguously disagree with religious people on matters of fundamental ontology; but I recognize that we’re all just tiny little persons in a very big universe, trying our best to figure things out. And I’m firm in my conviction that we’re making progress.

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Arrrgh Rumors

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Today’s hot issue in my favorite corners of the internet (at least, besides “What’s up with Solange?”) is the possibility that the BICEP2 discovery of the signature of gravitational waves in the CMB might not be right after all. At least, that’s the rumor, spread in this case by Adam Falkowski at Résonaances. The claim is that one of the methods used by the BICEP2 team to estimate its foregrounds (polarization induced by the galaxy and other annoying astrophysical stuff, rather than imprinted on the microwave background from early times) relied on a pdf image of data from the Planck satellite, and that image was misinterpreted.

culprit

Is it true? I have no idea. It could be. Or it could be completely inconsequential. (For a very skeptical take, see Sesh Nadathur.) It seems that this was indeed one of the methods used by BICEP2 to estimate foregrounds, but it wasn’t the only one. A big challenge for the collaboration is that BICEP2 only observes in one frequency of microwaves, which makes it very hard to distinguish signals from foregrounds. (Often you can take advantage of the fact that we know the frequency dependence of the CMB, and it’s different from that of the foregrounds — but not if you only measure one frequency.) As excited as we’ve all been about the discovery, it’s important to be cautious, especially when something dramatic has only been found by a single experiment. That’s why most of us have tried hard to include caveats like “if it holds up” every time we wax enthusiastic about what it all means.

However. I have no problem with the blog rumors — it’s great that social media enable scientists to examine and challenge results out in the open, rather than relying on being part of some in-crowd. The problem is when this perfectly normal chit-chat gets elevated to some kind of big news story. To unfairly single someone out, here’s Science NOW, with a headline “Blockbuster Big Bang Result May Fizzle, Rumor Suggests.” The evidence put forward for that fizzling is nothing but the Résonaances blog post, which consists in turn of some anonymous whispers. (Including the idea that “the BICEP team has now admitted to the mistake,” which the team has subsequently strongly denied.)

I would claim that is some bad journalism right there. (Somewhat more nuanced stories appeared at New Scientist and National Geographic.) If a reporter could talk to an actual CMB scientist, who would offer an informed opinion on the record that BICEP2 had made a mistake, that would be well worth reporting (along with the appropriate responses from the BICEP2 team itself). But an unsourced rumor on a blog isn’t news (not even from this blog!). As Peter Coles says, “Rational scepticism is a very good thing. It’s one of the things that makes science what it is. But it all too easily turns into mudslinging.”

We’re having a workshop on the CMB and inflation here at Caltech this weekend, featuring talks from representatives of both BICEP2 and Planck. I was going to wait to talk about this until I actually had some idea of what was going on, which hopefully that workshop will provide. Right now I have no idea what the answer is — I suspect the BICEP2 result is fine, as they did things other than just look at that one pdf file, but I don’t pretend to be an expert, and I’ll quickly change my mind if that’s what the evidence indicates. But other non-experts rely on the media to distinguish between what’s true and what’s merely being gossiped about, and this is an example where they could do a better job.

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Afterlife Aftermath

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Video from Wednesday’s debate over “Death Is Not Final” is now up.

You’ll be happy to hear that the good guys “won.” In scare quotes because helping the world’s population understand that naturalism is the right way to view the universe is a long-term project that won’t be settled with a single debate. But Intelligence Squared does a fun thing where they ask people to vote before the debate starts, and then again afterward. We started out the night slightly behind in the polls, and by the time we were done we were slightly ahead. Mostly by peeling away the undecideds, as any savvy politician strives to do. [Update: oops, not right. See below.] So that counts as a victory — especially when the topic is one where many people (not all!) have fairly fixed opinions.

death-results

death-pies

It was a pleasure to have Steve Novella as a partner. The man knows his neuroscience, as well as his debating. He did a great job making the single most important point for an issue like this: the mind is the brain, full stop. It’s hard to hear the case he makes and hold on to any contrary view.

I was slightly disappointed in the folks on the other side. Eben Alexander basically relied on two things. One was his personal story of having a Near-Death Experience while in a coma. Anyone who accepts that people can experience dreams or hallucinations will not be overly persuaded by that alone. The other was to throw up ideas like “quantum mechanics” and “the hard problem of consciousness” in an obfuscatory way, to give people license to believe that science doesn’t understand everything. Which is true! Science doesn’t understand everything. Which doesn’t change the fact that no serious researcher in quantum mechanics or the hard problem thinks that those ideas provide an excuse for believing in life after death.

Ray Moody was a very pleasant gentleman, someone you’d be happy to have a beer with and talk philosophy. But he did almost nothing to defend the proposition. I was expecting him to broaden the evidence from Alexander’s own case to many others, but instead he spoke in generalities about science and philosophy and logic, concluding essentially that it’s “conceivable” that a realm exists where souls can persist after death. Indeed it is. Many things are conceivable.

At the end of my opening talk I said that the choice here basically comes down to two options we can believe:

  1. Everything we think we understand about the behavior of matter and energy is wrong, in a way that has somehow escaped notice in every experiment ever done in the history of science. Instead, there are unknown mechanisms allow information in the brain to survive in the form of a blob of spirit energy, which can then go start talking to other blobs of spirit energy, but only after death, except sometimes even before death.
  2. Physics is right. And people under stress sometimes have experiences that seem real but aren’t.

In the light of the evidence, the choice is pretty clear. We’ll get there, a couple of percentage points at a time.

Update: I was too hasty in presuming that most of our increase came from swaying undecided voters. Here are the actual data:

death-crosstabs

As you can see, the undecideds actually broke almost equally for the two sides. Our glorious victory actually came from a combination of factors, including persuading some of the “For” voters to switch.

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Is There Life After Death? A Debate

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No, there’s not. In order to believe otherwise, you would have to be willing to radically alter our fundamental understanding of physics on the basis of almost no evidence. Which I’m not willing to do. But others feel differently! So we’re going to have a debate about it tonight — to be live-streamed, see below.

death-debate

This is an Intelligence Squared debate, which is a series of Oxford-style formal debates that are held around the world, often with quite impressive participants. Four people, two on each side of a resolution. Seven-minute opening statements, round-table discussion, then two-minute closing statements. No slides or other visual aids; just bare-knuckle combat in the gladiatorial arena of ideas.

The resolution simply reads “Death Is Not Final,” and it will be affirmed by Eben Alexander and Raymond Moody, both of whom have written best-selling books along these lines. Alexander, in particular, is a neurosurgeon who had a near-death experience and now claims to have proof of the existence of Heaven. (For a skeptical take on Alexander, see this Esquire profile.) I’ll be negating the resolution, along with my partner Steven Novella. Steve is a practicing neuroscientist who is also active in the skeptic movement, blogging at Neurologica and leading the Skeptic’s Guide to the Universe podcast.

Festivities begin at 6:45pm Eastern Time. It will be broadcast on various NPR stations around the US, but you should also be able to see it live-streamed right here:

If you can’t catch the live-stream but still want to watch, I presume it will go on YouTube eventually, but I don’t know for sure.

To get a feeling for how an Intelligence Squared debate goes, you might check out Stephen Fry and Christopher Hitchens persuading a large group of people that the Catholic Church has harmed the world.

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Squelching Boltzmann Brains (And Maybe Eternal Inflation)

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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. …

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Help Wanted: Moving Naturalism Forward

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Update: This request received an amazing response! I had to make a tough choice, but I’ve picked someone to do the paid work of making a careful outline and suggesting possible excerpts. Thanks for everyone who sent a query.

Following ideas mentioned in the comments, however, there’s no reason why anyone cannot simply volunteer their own suggestions for parts of the videos that would make good excerpts. So, if anyone is so motivated, feel free to leave suggestions in the comments to this post. We might not be able to take all of them, but anything sensible will be considered. Thanks!

It’s been a year and a half since the Moving Naturalism Forward workshop, which featured a great line-up of thinkers: Jerry Coyne, Richard Dawkins, Terry Deacon, Simon DeDeo, Dan Dennett, Owen Flanagan, Rebecca Goldstein, Janna Levin, Massimo Pigliucci, David Poeppel, Alex Rosenberg, Don Ross, and Steven Weinberg. Fortunately we got the whole thing on video, so the conversations are preserved for posterity. Unfortunately, that amounts to ten videos, each about an hour and a half long. Not a quick watch for someone who just wants the highlights!

Moving Naturalism Forward: Day 1, Morning, 1st Session

So ever since the workshop, I’ve been wanting to go through the entire video record and make it more organized and digestible. That basically amounts to two things:

  1. Create a semi-detailed listing of who says what, when. So someone who wanted to hear Dan Dennett’s defense of free will could just skip right to that part of the relevant video — and could also see who mounted a challenge to it.
  2. Edit the long videos into much shorter highlights. Some very short bits of rhetorical brilliance, and/or some medium-length exchanges of separate interest.

I’ve been meaning to re-watch all the videos myself and do the above tasks, but it’s pretty clear that other obligations are in the way and it’s not going to happen. I have someone who will do the actual video editing, so really it’s about watching all the videos and making some intellectual/artistic decisions about what snippets might be good on their own.

So — anyone want to do it? This would be a paid gig, although it’s nothing you’d earn a living on, I promise you. I’m looking for a person with some kind of background both in science and philosophy, who can follow all the discussions and sensibly dissect them. Maybe about a week’s worth of work or a bit less, although it wouldn’t all have to be done within a week.

If you’re interested, shoot me an email (not a comment here), explaining a bit about what your background is. It’s not an enormous rush, although I’d like to get it done sooner rather than later. Could be fun!

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A Leap in Energy

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The discovery by BICEP2 of the signature of gravitational waves in the cosmic microwave background — if it holds up! — is not only good evidence for inflation in the very early universe, it’s a fairly precise indication that inflation occurred at a very high energy scale. I thought of a vivid way to emphasize just how high that energy is.

Particle physicists like to keep things simple by characterizing all physical quantities in terms of a single kind of unit — typically energy, and typically measured in electron volts. That’s part of the magic of natural units. We live in a world governed by relativity, so the speed of light c provides a natural unit of velocity. We also live in a world governed by quantum mechanics, so Planck’s constant ℏ provides a natural unit of action. And we live in a world governed by statistical mechanics, so Boltzmann’s constant k provides a natural conversion between energy and temperature. We therefore set these quantities equal to unity, ℏ = c = k = 1. Once that’s done, mass and temperature have the same units as energy. Time and distance have units of 1/energy. Energy density is energy per unit spatial volume, which works out to (energy)4. This kind of reasoning makes particle physicists happy, since they like to think of everything in terms of energy scales.

So, thinking about everything in terms of energy scales, what’s the energy of everyday life? It makes sense to choose room temperature, about 295 Kelvin. That works out to about 0.02 electron volts, which we can call the temperature of everyday life:

E_{\rm everyday} = 2 \times 10^{-2}\, {\rm eV}.

One way of thinking about the progress of fundamental physics is to track the progress of our understanding to higher and higher energy scales. The highest energies we’ve ever probed in experiments here on Earth are those at the Large Hadron Collider. The last run of the LHC reached energies of 8 TeV, or 8×1012 eV. But it would be an exaggeration to say that we really understand those energies; when protons collide at the LHC, their energies are distributed among a number of particles in each event. That’s why the heaviest particles we’ve ever found are the Higgs boson and the top quark, both with masses a bit under 0.2 TeV. So let’s call that the highest energy we’ve understood through experiments here on Earth:

E_{\rm understanding} = 2 \times 10^{11}\, {\rm eV}.

Thus, the progress of science has extended our understanding a factor of 1013, thirteen orders of magnitude, above our everyday experience:

E_{\rm understanding}/E_{\rm everyday} = 10^{13}.

Not too shabby, for a species of jumped-up apes with only an intermittent dedication to the ideals of rationality and empiricism.

Now let’s turn to inflation. The great thing about detecting gravitational waves in the CMB is that, in contrast with the density perturbations we’ve known about for some time, the gravitational wave amplitude depends solely on the expansion rate during inflation, not on any details about the scalar-field potential. And the expansion rate is directly related to the energy density (energy to the fourth power) by general relativity itself. So measuring the amplitude, as BICEP2 did, tells us the inflationary energy scale directly. And the answer is:

E_{\rm inflation} = 2 \times 10^{25}\, {\rm eV}.

For comparison, the reduced Planck energy (where “reduced” means “including the factor of 8π where it should be”) is 2×1027 eV, a mere stone’s throw away.

So, you can do the math yourself. Inflation was going on at energy scales that exceed those we explore here on Earth by a factor of about

E_{\rm inflation}/E_{\rm understanding} = 10^{14}.

In other words, BICEP2 has extended our experimental reach, as measured by energy scale, by an amount (1014) slightly larger than the total previous progress of all of science (1013).

We don’t, of course, understand everything between LHC energies and inflationary energies, not even close. But we (the royal “we”) have been able to make an enormous extrapolation, using scientific reasoning, and get the right answer. It’s a big deal.

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I’m Not Sure That’s How Probability Works, Walter

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Tonight marks the debut of John Oliver’s Last Week Tonight on HBO. JenLuc Piquant reminds us of one of the former Daily Show correspondent’s finest moments: confronting Walter Wagner on why he thought black holes from the LHC were a threat to the existence of the Earth.

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Guest Post: Max Tegmark on Cosmic Inflation

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Max TegmarkMost readers will doubtless be familiar with Max Tegmark, the MIT cosmologist who successfully balances down-and-dirty data analysis of large-scale structure and the microwave background with more speculative big-picture ideas about quantum mechanics and the nature of reality. Max has a new book out — Our Mathematical Universe: My Quest for the Ultimate Nature of Reality — in which he takes the reader on a journey from atoms and the solar system to a many-layered multiverse.

In the wake of the recent results indicating gravitational waves in the cosmic microwave background, here Max delves into the idea of inflation — what it really does, and what some of the implications are.

Thanks to the relentless efforts of the BICEP2 team during balmy -100F half-year-long nights at the South Pole, inflation has for the first time become not only something economists worry about, but also a theory for our cosmic origins that’s really hard to dismiss. As Sean has reported here on this blog, the implications are huge. Of course we need independent confirmation of the BICEP2 results before uncorking the champagne, but in the mean time, we’re forced to take quite seriously that everything in our observable universe was once smaller than a billionth the size of a proton, containing less mass than an apple, and doubled its size at least 80 times, once every hundredth of a trillionth of a trillionth of a trillionth of a second, until it was more massive than our entire observable universe.

We still don’t know what, if anything, came before inflation, but this is nonetheless a huge step forward in understanding our cosmic origins. Without inflation, we had to explain why there were over a million trillion trillion trillion trillion kilograms of stuff in existence, carefully arranged to be almost perfectly uniform while flying apart at huge speeds that were fine-tuned to 24 decimal places. The traditional answer in the textbooks was that we had no clue why things started out this way, and should simply assume it. Inflation puts the “bang” into our Big Bang by providing a physical mechanism for creating all those kilograms and even explains why they were expanding in such a special way. The amount of mass needed to get inflation started is less than that in an apple, so even though inflation doesn’t explain the origin of everything, there’s a lot less stuff left to explain the origin of.

If we take inflation seriously, then we need to stop saying that inflation happened shortly after our Big Bang, because it happened before it, creating it. It is inappropriate to define our Hot Big Bang as the beginning of time, because we don’t know whether time actually had a beginning, and because the early stages of inflation were neither strikingly hot nor big nor much of a bang. As that tiny speck of inflating substance doubled its diameter 80 times, the velocities with which its parts were flying away from one another increased by the same factor 2^80. Its volume increased by that factor cubed, i.e., 2^240, and so did its mass, since its density remained approximately constant. The temperature of any particles left over from before inflation soon dropped to near zero, with the only remaining heat coming from same Hawking/Unruh quantum fluctuations that generated the gravitational waves.

Taken together, this in my opinion means that the early stages of inflation are better thought of not as a Hot Big Bang but as a Cold Little Swoosh, because at that time our universe was not that hot (getting a thousand times hotter once inflation ended), not that big (less massive than an apple and less than a billionth of the size of a proton) and not much of a bang (with expansion velocities a trillion trillion times slower than after inflation). In other words, a Hot Big Bang did not precede and cause inflation. Instead, a Cold Little Swoosh preceded and caused our Hot Big Bang.

Since the BICEP2 breakthrough is generating such huge interest in inflation, I’ve decided to post my entire book chapter on inflation here so that you can get an up-to-date and self-contained account of what it’s all about. Here are some of the questions answered:

  • What does the theory of inflation really predict?
  • What physics does it assume?
  • Doesn’t creation of the matter around us from almost nothing violate energy conservation?
  • How could an infinite space get created in a finite time?
  • How is this linked to the BICEP2 signal?
  • What remarkable prize did Alan Guth win in 2005?

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