Sean Carroll

Author: Sean Carroll

  • From Eternity to Book Club: Chapter Eight

    Welcome to this week’s installment of the From Eternity to Here book club. Finally we dig into the guts of the matter, as we embark on Chapter Eight, “Entropy and Disorder.”

    Excerpt:

    Why is mixing easy and unmixing hard? When we mix two liquids, we see them swirl together and gradually blend into a uniform texture. By itself, that process doesn’t offer much clue into what is really going on. So instead let’s visualize what happens when we mix together two different kinds of colored sand. The important thing about sand is that it’s clearly made of discrete units, the individual grains. When we mix together, for example, blue sand and red sand, the mixture as a whole begins to look purple. But it’s not that the individual grains turn purple; they maintain their identities, while the blue grains and the red grains become jumbled together. It’s only when we look from afar (“macroscopically”) that it makes sense to think of the mixture as being purple; when we peer closely at the sand (“microscopically”) we see individual blue and red grains.

    Okay cats and kittens, now we’re really cooking. We haven’t exactly been reluctant throughout the book to talk about entropy and the arrow of time, but now we get to be precise. Not only do we explain Boltzmann’s definition of entropy, but we give an example with numbers, and even use an equation. Scary, I know. (In fact I’d love to hear opinions about how worthwhile it was to get just a bit quantitative in this chapter. Does the book gain more by being more precise, or lose by intimidating people away just when it was getting good?)

    In case you’re interested, here is a great simulation of the box-of-gas example discussed in the book. See entropy increase before your very eyes!

    (more…)

  • Will Video Games Save the World?

    Jane McGonigal thinks they can help. She’s a game designer who gave a talk at the TED conference this year (although her talk isn’t up yet).

    McGonigal makes some good points in this short video, especially about how dealing with things in a video-game environment — like failure, or social interactions — can be greatly helpful when one eventually has to deal with them in the real world. She also helped put together Urgent Evoke, a large-scale multiperson game where you collect achievements by performing world-saving tasks.

    The kids these days, they love their gaming. So it makes sense to ask how that passion can be put to good use. Personally I’m fascinated by the prospects of using games to teach people science. Not just facts and features of the real world — although those are important — but the scientific method of hypothesis-testing and experiment. Games already feature exactly those features, of course; everyone who figures out the “laws of nature” in the game world is secretly doing science. It wouldn’t be that hard to tweak things here and there so that the techniques they were practicing connected more directly with science in the non-virtual reality.

  • Forget About Herding

    It’s walking cats that is truly problematic.

    Feel free to construct your own similes. (Via Cynical-C.)

  • Rules for Writers

    Everyone is linking to this Guardian article collecting advice from fiction writers. My favorite list comes from Richard Ford — not that I necessarily agree with every rule:

    1 Marry somebody you love and who thinks you being a writer’s a good idea.

    2 Don’t have children.

    3 Don’t read your reviews.

    4 Don’t write reviews. (Your judgment’s always tainted.)

    5 Don’t have arguments with your wife in the morning, or late at night.

    6 Don’t drink and write at the same time.

    7 Don’t write letters to the editor. (No one cares.)

    8 Don’t wish ill on your colleagues.

    9 Try to think of others’ good luck as encouragement to yourself.

    10 Don’t take any shit if you can ­possibly help it.

    There’s an entire blog devoted to listing the daily routines of writers. It’s a funny business — the people who do it can’t imagine doing anything else, but they still rely on all sorts of gimmicks to keep their work flowing smoothly. Maybe that’s part of the difference between styling one’s self as a writer and actually writing.

  • From Eternity to Book Club: Chapter Seven

    Welcome to this week’s installment of the From Eternity to Here book club. We next take a look at Chapter Seven, “Running Time Backward.” Now we’re getting serious! (Where “serious” means “fun.”)

    Excerpt:

    The important concept isn’t “time reversal” at all, but the similar-sounding notion of reversibility–our ability to reconstruct the past from the present, as Laplace’s Demon is purportedly able to do, even if it’s more complicated than simply reversing time. And the key concept that ensures reversibility is conservation of information–if the information needed to specify the state of the world is preserved as time passes, we will always be able to run the clock backward and recover any previous state. That’s where the real puzzle concerning the arrow of time will arise.

    With this chapter we begin Part Three of the book, which is the most important (and my favorite) of the four parts. Over the course of the next five chapters we’ll be exploring the statistical definition of entropy and its various implications, as well as the puzzles it raises.

    But before getting to entropy, and the arrow of time that depends on it, we first have to understand life without an arrow of time. The only reason the Second Law is puzzling is because the rules of fundamental physics don’t exhibit an arrow of time on their own — they’re perfectly reversible. In this chapter we discuss what “reversible” really means, and contrast it with “time reversal invariance,” which is related by not quite the same. If a theory is both reversible and time-translation invariant (same rules at all times), it’s always possible to define time reversal so that your theory is invariant under it. (E.g. in most quantum field theories, “CPT” does the trick.)

    Reversibility is a very deep idea; it implies that the state of the universe at any one moment in time is sufficient (along with the laws of physics) to precisely determine the state at any other time, past or future. But not many popular physics books spend much time explaining this idea. So we reach all the way back to very simplified models of discrete systems on a lattice (“checkerboard world”). What we’re after is an understanding of what it really means to have “laws of physics” in the first place — rules that the universe obeys as it evolves through time. That lets us explore different kinds of rules, in particular ones that are and are not reversible.

    Along the way we talk about time-reversal invariance in the weak interactions of particle physics, and emphasize how this is not related to the thermodynamic arrow of time that is our concern in this book. Which gives me a good excuse to quote a touching passage from C.S. Wu. This chapter has everything, I tell you.

  • Energy Is Not Conserved

    I’ve been meaning to link to this post at the arXiv blog, which is a great source of quirky and interesting new papers. In this case they are pointing to a speculative but interesting paper by Martin Perl and Holger Mueller, which suggests an experimental search for gradients in dark energy by way of atom interferometry.

    But I’m unable to get past this part of the blog post:

    The notion of dark energy is peculiar, even by cosmological standards.

    Cosmologists have foisted the idea upon us to explain the apparent accelerating expansion of the Universe. They say that this acceleration is caused by energy that fills space at a density of 10-10 joules per cubic metre.

    What’s strange about this idea is that as space expands, so too does the amount of energy. If you’ve spotted the flaw in this argument, you’re not alone. Forgetting the law of conservation of energy is no small oversight.

    I like to think that, if I were not a professional cosmologist, I would still find it hard to believe that hundreds of cosmologists around the world have latched on to an idea that violates a bedrock principle of physics, simply because they “forgot” it. If the idea of dark energy were in conflict with some other much more fundamental principle, I suspect the theory would be a lot less popular.

    But many people have just this reaction. It’s clear that cosmologists have not done a very good job of spreading the word about something that’s been well-understood since at least the 1920’s: energy is not conserved in general relativity. (With caveats to be explained below.)

    The point is pretty simple: back when you thought energy was conserved, there was a reason why you thought that, namely time-translation invariance. A fancy way of saying “the background on which particles and forces evolve, as well as the dynamical rules governing their motions, are fixed, not changing with time.” But in general relativity that’s simply no longer true. Einstein tells us that space and time are dynamical, and in particular that they can evolve with time. When the space through which particles move is changing, the total energy of those particles is not conserved.

    (more…)

  • Many Roads to Science

    We’ve collected enough data in our What Got You Interested in Science? poll to draw some conclusions. Not very firm conclusions, of course, as the whole process was wildly non-scientific, and there’s no reason to expect that the respondents were a representative sample in any sense. (The numbers were not bad; the smallest category, “the internet,” received 62 votes so far.) But conclusions, nonetheless!

    And the main conclusion is: there are many different things that get young proto-scientists interested in the field. Books, both non-fiction and fiction, play an important role, but no one thing really stands out.

    sciencepie

    That’s interesting, and not really what I would have expected. Given that there certainly are many things that could get someone interested in science, I wouldn’t have been surprised if there was a dominant source for the pipeline, but instead it’s quite a diverse porfolio.

    If we think getting people interested in science is a good thing, the lesson is: there aren’t any magic bullets. A broad-based strategy seems appropriate. Interesting books, educational classes, encouraging relatives, engrossing hobbies and school activities, inspiring movies and TV shows. I approve.

  • Violating Parity with Quarks and Gluons

    Hey, nobody told me that having a blog would involve homework. But here’s Jerry Coyne, nudging me into talking about a story in this morning’s New York Times. Fortunately it’s interesting enough to be worth taking a swipe at.

    The news is an interesting result from RHIC, the Relativistic Heavy Ion Collider at Brookhaven Lab on Long Island. RHIC has been quite the source of surprising new results since it turned on in 2000. It’s not the highest-energy collider in the world, nor did it ever aim to be; instead, it creates novel conditions by smashing together the nuclei of gold atoms. Gold nuclei have lots of particles — 79 protons and 118 neutrons — so the collisions make a soup known as the quark-gluon plasma. (We ordinarily think of a proton or neutron as consisting of three quarks, but those are just the “valence” quarks that are always there. There are also large numbers of quark-antiquark pairs popping in and out of existence, not to mention scads of force-carrying gluons that hold the quarks together. So you are actually create a huge number of quarks and gluons in each collision.)

    qgp

    We think we understand the basic rules of quarks and gluons very well — they’re described by the theory of quantum chromodynamics (QCD), and Nobel prizes have already been handed out. But knowing the basic rules is one thing, and knowing how they play out in reality is something very different. We understand the basic rules of electrons and electromagnetism very well, but chemistry and biology (not to mention atomic physics) are still surprising us. Likewise with quarks and gluons: the results at RHIC have yielded quite a few surprises. Most interestingly, in the aftermath of the collisions the hot plasma of quarks and gluons seems to behave more like a dense fluid than a bunch of freely-moving individual particles. Still much to be learned.

    (more…)

  • From Eternity to Book Club: Chapter Six

    Welcome to this week’s installment of the From Eternity to Here book club. Chapter Six is entitled “Looping Through Time.” It’s about both the logical paradoxes presented by time travel, and some of the obstacles to actually building a time machine (closed timeline curves) in general relativity.

    Excerpt:

    Everyone knows what a time machine looks like: something like a steampunk sled with a red velvet chair, flashing lights, and a giant spinning wheel on the back. For those of a younger generation, a souped-up stainless-steel sports car is an acceptable substitute; our British readers might think of a 1950s style London police box. Details of operation vary from model to model, but when one actually travels in time, the machine ostentatiously dematerializes, presumably to be re-formed many millennia in the past or future.

    That’s not how it would really work. And not because time travel is impossible and the whole thing is just silly; whether or not time travel is possible is more of an open question than you might suspect. I’ve emphasized that time is kind of like space. It follows that, if you did stumble across a working time machine in the laboratory of some mad inventor, it would simply look like a “space machine”—an ordinary vehicle of some sort, designed to move you from one place to another. If you want to visualize a time machine, think of launching a rocket ship, not disappearing in a puff of smoke.

    There might not be too much new to say about this chapter, as part of it appeared as an excerpt in Discover and we’ve already talked about that. But maybe you weren’t reading that post, in which case, it’s new to you!

    There were three main goals in this chapter. The first was to explain what time travel would and would not be, in the context of general relativity — in particular, it would be just another form of travel through spacetime, not involving any disappearing and rematerializing at some other point in the past. The second was to go through some of the possible ways to make closed timelike curves (with wormholes or cosmic strings) and see how difficult it really was.

    But the third and most interesting goal was to connect time machines to the arrow of time and entropy. At this point in the book we’ve only introduced these concepts somewhat casually — the careful exploration of entropy is in Part Three, which begins next week — so one could argue that a more logical presentation would have delayed this discussion for later. But sometimes there are considerations beyond logic; in particular, once we built up momentum with the entropy discussion, a digression on time travel would have seemed like wandering too far afield. That was my feeling at the time, anyway.

    This is a really interesting aspect of time travel, which I think is dramatically under-emphasized in discussions about it: the real reason why traveling backwards in time makes us nervous is that it becomes impossible to define a consistent arrow of time. The arrow is very ingrained in how we think about the world, including the sense that the past is set in stone while we can still make choices that affect the future. In the presence of a time machine part of our personal “future” is already in the “past,” which seems to compromise our free will.

    So be it! Our free will was always an approximation, if we are good materialists who believe in the laws of physics. But it’s a highly useful approximation. It’s always worth emphasizing, when you start talking about the paradoxes of time travel: the simplest and most plausible way out is to imagine that the universe doesn’t (and won’t ever) actually have any time machines.

  • Nothing Says “I Love You” Like a Non-Orientable Surface

    Feeling like Valentine’s Day is a little too cutesy for an intellectual heavyweight such as yourself? Nonsense; the heart may have its reasons, but reason can certainly figure them out, given sufficient grant funding and some diligent graduate students. Jennifer Ouellette points to a talk by Mary Roach that is safe for TED but arguably not safe for work, and shares some brain scans to prove that love is really blind.

    6a00d8341c9c1053ef0120a89d40b8970b-500wi

    fourthheartcurveIf all that biology is a bit too squishy, Sarah Kavassalis does the math. Here you will find the right functions to use to draw hearts — my favorite is the fourth heart curve from Wolfram|Alpha, shown at right — and how to construct topologically nontrivial versions out of construction paper and scissors. Who says mathematicians aren’t practical? Nor are they above venturing into the realm of the literary.

    Roses are red.
    Violets are approximately blue.
    A paracompact manifold with a Lorentzian metric,
    can be a spacetime, if it has dimension greater than or equal to two.

    Shakespeare, maybe not. But the course of true science never did run smooth.