Hey folks! A couple of weeks ago I gave a talk at the Princeton Plasma Physics Labs as part of their “Science on Saturday” program. It was a lot of fun and a huge success. They tell me that 523 people came, including lots of high school and middle school students. Tons of great questions afterwards as well. They’ve posted the video (and my slides and abstract) on their archive along with a lot of other interesting talks.
For your convenience, you can check out the video here as well:
| Videography by Carl Scimeca, Media Services, PPPL |
Enjoy! And don’t forget to email me if you have any more questions.
-Dave
Primaries
This is primarily a blog about physics, astronomy, and science writing, but every so often, I like to dip my toe into discussions about politics or economics. I am not a political scientist or an economist, so you can take my opinion at face value. Besides, there are some good precedents for astronomers using their analytic skills to think about political questions.
I know the rate of astrophysics posts have gone down in recent months, but since I’m in the midst of writing my next book (“The Universe in the Rearview Mirror“), most of my science writing effort is going in that direction.
That said, I have a quickie today, and that is: Why is the primary calendar set up like it is. That is, consider the first three states in the primary calendar this year:
- Iowa (D +9.5%)
- New Hampshire (D +9.6%)
- South Carolina (R +9.0%)
Where the numbers in the parentheses are the margins of victory for each state in the 2008 cycle. It is clear to most observers that the field gets winnowed very early in the process so that states like Pennsylvania (where I live) get virtually no say in the process whatsoever.
Of course, it makes sense that there isn’t a single, one-day national primary. It would be ruinous financially to candidates from both major parties. At least in principle, having a slow winnowing of the process makes some sort of sense. But the order, at present, is ridiculous.
Certain states should almost certainly be ignored in the primary. California, for example, will almost certainly go Democrat, and has done so in every election since 1992. Obama won it by 24% in the 2008 election. Texas, on the other hand, will almost certainly go Republican, and has done so in every election since Reagan won it in 1980. It’s worth noting that both Iowa and New Hampshire have gone to both Democrats and Republicans in recent elections, but that they’re only worth a combined 11 electoral votes. South Carolina (worth eight) last went Democrat in 1976, and has gone Republican ever since.
My point is that there are a relatively small number of swing states, and that both parties should have it in their best interest to court the actual preference of those states from the outset. I propose that it makes sense to have primaries in order of the gap in the previous presidential race. In this case, it would be:
- Missouri (R +0.1%)
- North Carolina (D +0.3%)
- Indiana (D +1.0%)
Or, perhaps even better, the order could be determined by the difference in margin from the national average. In 2008, Obama won by 7.3%. A Republican would have to improve his numbers by that margin (on average) to win the race. So it would make more sense for the Republicans to run their primaries in states where Obama won by very close to the national average:
- Virginia (D +6.3%)
- Colorado (D +9.0%)
- Iowa (D+ 9.5%)
Or this could be tweaked still further, including a weighting for more compact states or something like that.
The point is discussion is simply that if both parties want to nominate a candidate who has the maximum probability of winning under the current rules (winner take all within a state) while minimizing their expenditures during the primary, the current system seems very ill-suited.
Discuss.
-Dave
Camille Flammarion, L’Atmosphere: Météorologie Populaire (Paris, 1888)
I’ve been inundating you with issues in symmetry, but I hope you don’t mind. I’m now in the midst of Chapter 4, which deals with (among much else) the homogeneity and isotropy of the universe and the related symmetries in physical laws. One of the starting points for this discussion is the Copernican Revolution.
You know the basic story. The ancients (and especially Aristotle and Ptolemy) thought the planets and sun revolved around the earth. Ultimately, Copernicus rediscovered the Heliocentric model of Aristarchus, and thanks to Kepler, Galileo, Newton, and others, we ultimately learned that we aren’t at the center of the universe.
That’s the condensed version, anyway. It’s tough to put a new take on the story since most people have heard variants of it so many times that it’s become stale. In the process of writing it, I was describing the Copernican Revolution to my wife, pointing out that Aristotle posited a spherical earth as obvious. She said something along the lines of, “Wait! Didn’t people used to believe that the earth was flat? Why did we learn that?”
I started thinking about it, and realized that this is one of many misconceptions people have about what people did or didn’t believe at various times. As Stephen Jay Gould put it:
there never was a period of ‘flat earth darkness’ among scholars (regardless of how the public at large may have conceptualized our planet both then and now). Greek knowledge of sphericity never faded, and all major medieval scholars accepted the earth’s roundness as an established fact of cosmology.
And while the geocentric universe was generally accepted, it wasn’t uncontested. As I mentioned above, Aristarchus was among the first to posit that the sun was at the center of the universe. It is simply wrong that no-one had thought of a heliocentric universe before Copernicus.
So a couple of questions to you folks:
- What are some other examples of historical misconceptions about misconceptions that you’d like to see discussed?
- Anything you’d like to see about the Copernican Revolution that doesn’t get discussed in the standard treatment?
—————–
Talk Announcement!
Oh, and speaking of our place in the universe, I’m giving a free public talk next weekend. Here are the details:
- What: “‘What is the Universe Expanding into?’ and other perfectly reasonable questions.”
This is a general talk that covers much of the material that we discuss in Chapter 6 of the User’s Guide. It will be aimed at a lay audience, and there will be lots of time for questions.
- When: Saturday, January 14, 2012. 9:30am. Doors open at 8:15, and the Q&A typically ends at 11:15.
- Where: Princeton Plasma Labs as part of their Science on Saturday program. Directions are here.
Hope to see you there.
-Dave
I was listening to Tim Harford’s More or Less podcast last week in the wake of all of the excitement over the possible detection of the Higgs boson. More or Less is a show all about statistical abuses in the news and in life, and I strongly recommend it. In this episode, they had Robert Matthews, a physicist from Aston Universities talking about the nature of statistical significance. He did a good job, but his discussion was oddly lacking any reference to the Reverend Thomas Bayes.
This post will be a little bit technical (but nothing on the level of what we’ve seen in some of our relativity discussions), so you may want to get a bit of scratch paper out. It deals with how we actually discover new things, and in particular, how we assess the uncertainty of things that we can’t possibly know.
I should also add that while I will throw around a few example numbers, and that these resemble the real numbers put out by the ATLAS and CMS experiments at the LHC and the Tevatron at Brookhaven, this is really meant to be an overview.
What 
Take the plot at the top of the page. That’s a measurement of the signal and noise from the ATLAS collaboration. They were, as you know, looking for the Higgs Boson. The idea of the plot is that if there is no Higgs than the signal (the solid line) should appear within the green curve approximately 68% of the time (so-called 
This “68% of the time” or “95% of the time” needs some explanation. An experiment is going to be noisy. Sometimes the noise is going to produce an uptick, and sometimes a downtick. If there were no Higgs, and if you ran the same experiment thousands of times, you’d expect to find yourself within the yellow 95% of the time, above the yellow 2.5% of the time, and below the yellow 2.5% of the time.
In other words, a
There are other complications that I’m going to ignore here, since they don’t change the basic picture. One is that in searching for the Higgs, you get to look at lots of different possible masses. If you could look at 40 different masses, and all of them are independent, 1 of them is likely to be a
For our purposes, we want to only take into account the data around 125GeV, and ask what we can say about whether a Higgs at that mass is likely or not. Taking all of this into account, the ATLAS result is at 
If there is no Higgs, the odds of finding a signal this far above the expected background level is about 1%
This does not mean that the probability that the Higgs is real is 99%. That was Matthews’s point. To figure out how likely the Higgs is, we need to say a bit about Bayesian inference.
Bayes Theorem
Suppose I told you that I had a magic genie that grants wishes. I could prove it. I wish for a coin that comes up heads every time. To test my conjecture, I flip a coin 5 times in a row and get heads every time. That’s only a 1 in 32 probability (about 3%)!
Would you assume that I really did have a genie?
- My argument (following the same logic that we applied to the Higgs) might be that the probability of the genie is 97%.
- The argument against is that while 5 heads in a row (especially if I called it ahead of time) is unlikely, the odds of genies are even more unlikely.
All of this can be formalized in a relation known as Bayes Theorem, which says that if I have two events, A & B, their probabilities can be related with the expression:
Don’t be scared off by the notation. It’s more straightforward than you might think. 
In this case:
-
= There really is a genie with the properties I described.
-
= I flip 5 heads in a row.
is “The probability of A given that B has already occurred.” In our case,
-
= The probability that we flip 5 heads if there really is a genie. = 100%. (That’s the rule for a genie.)
Computing the other terms are a bit more complicated. For one thing, we don’t really know ahead of time what the a priori probability of having a genie is (
At one extreme, I might say that there is literally zero chance of genies, or I might pick an incredibly small number, perhaps 1 in a million. At the other extreme, I might say that I’ve seen and interacted with genies before, so the chance is 100%. We really don’t know.
The good news, though, is that once we pick this number, we can compute everything else. The a priori probability is simply:
Put into words, this is simply the probability of flipping 5 heads on a fair coin (with no genie) added to the probability that there’s a genie.
From this, we can compute the “posterior probability” of there being a genie given that I’ve just flipped 5 heads, by plugging into Bayes theorem:
Naturally, if we already knew that there was a genie, our certainty was 100% before and after we did the experiment.
On the other extreme, if we really don’t believe in genies, this experiment isn’t going to help very much. If we thought that particular type of genies were a one in a million chance (a rather generous assumption) then even after seeing this “proof” we would only raise that belief from 0.0001% to 0.0032%.
And the Higgs
The calculation is very similar for the Higgs. We’re assuming that everything else has been ruled out and the “look elsewhere” effect has already been taken into account. We’re just asking about a Higgs at or near 125 GeV.
In this case, our two events might be:
-
-
We already know one of these terms, the probability of getting such a large amount of noise if there really is no Higgs
The number we don’t know, of course, is
which can then be plugged in to compute
where I’ve assumed (not entirely accurately) that if there really were a Higgs, then we’d see a
Just to make this clear. The idea is that we’ll only get a signal this large in the 5% probability that there is a Higgs plus the 95% probability of no Higgs times the 1% chance of getting the level of noise that we see. That adds up to 6%.
Plugging in the numbers, we’d get:
Or in other words, even if you believed with 95% confidence ahead of time that there shouldn’t be a Higgs, after conducting this experiment, your posterior probability is more like 16%. The likelihood of a Higgs is therefore 84%.
More generally, we can look at the posterior probabilities for any prior we like:
Note that the y-axis has a log scaling, and that it represents the probability of no Higgs (after seeing the data from ATLAS).
Some things to remember
- I picked my prior probability of the Higgs rather arbitrarily. If you think it 99.99% probable that there’s no Higgs (or any probability you like) then it’s going to be that much harder to convince you.
- ATLAS isn’t the only experiment in town. CMS detected something like a
result, and the Tevatron had something like a
result. Combined, these are at the
level (about 0.1% probability by pure chance). Using our 5% prior likelihood of the Higgs really being in this range, we get about a 98% posterior probability. This is why I’m so confident that Higgs will ultimately be officially detected.
- The particle physics community usually relies on a
result to “detect” a particle — less than 1 part in a million for
Apologies for the fairly technical post, and to the statistics community, apologies for playing fast and loose with some terminology.
In either case, I hope this helps to explain why there are some people who aren’t quite ready to believe the Higgs is real (yet) and why others (like me) are.
-Dave
My latest column is up on io9. Yesterday, I asked for questions related to the possible early detections of the Higgs, and today I’ve collected the most popular questions in one place. I’m sure there will lots of good discussion in the comments in the comments section.
And, as always, feel free to send me any questions you might have about the universe.
-Dave
Higgs!
I’m sure most of you have already seen the announcement. The LHC announced some preliminary results regarding the Higgs Boson this morning. Here’s the upshot:
- Both the ATLAS and CMS experiments (which are ostensibly independent) see something consistent with a Higgs with relatively high significance (3.6
- Even combining the results, this still falls shy of 5
- The mass of the Higgs is very consistent with what we expected from the Standard Model.
In tomorrow’s “Ask a Physicist” column, I’ll be doing a Higgs roundup. People should ask any and all questions about the discovery (the comments section below is as good a place as any), and I’ll answer as many as possible in the column.
Exciting times!
-Dave
Entropy, Time, and Maxwell’s Demon
Credit: Peter MacDonald, Edmonds UK.
While I don’t plan on giving a complete rundown of every sentence in my new Symmetry book every now and again, I figured I’d run some ideas by you and see if you have any followup questions. At the moment, I’m working on Chapter 2, with the working title, “Does Entropy Increase with Time or does it Make Time?” (Rest assured, there’s a lot of material that wasn’t in the original io9 article, but I like the title.)
Apropos of this, I’ve spent the weekend reading fellow Pennsbury High School alum and Dutton author Sean Carroll’s book, “From Eternity to Here,” who addresses this very question is a fair amount of detail. It’s a very well-reasoned book and has a very good tone, but in the end, I remain unconvinced. I still fall in the “time makes entropy” camp (which, to be fair, is the orthodox view, which is presumably one of the reasons why Sean wrote his book).
As you may know, the 2nd law of thermodynamics says, colloquially, that entropy always increases with time. Practically speaking, this means that energy will flow from hot materials to cooler ones in the form of heat.
Is there any loophole that could allow us to get around the Second Law? In the 19th century, James Clerk Maxwell devised a cool thought experiment to cheat entropy. Maxwell was no slouch. He unified all of electromagnetism into a single theory, combining a number of very disparate looking ideas into “Maxwell’s Equations,” which served as the principle inspiration for Einstein’s theory of Special Relativity.
Maxwell imagined a box filled with air molecules, some moving faster, and some moving slower than one another, but thoroughly mixed. In the middle of the box was a partition, separation the left from the right with a little hole and a trap door in front of it.
Maxwell’s idea was that whenever a “cold” molecule (one moving slower than average) approached the trapdoor from the left side of the box, a very clever demon would open the door and let the molecule through to the right side of the box. Likewise, whenever a “hot” molecule approached from the right, the demon would open the door and let the molecule go into the left side of the box. Otherwise, the door would remain closed.
That’s it, but it this has profound implications. Assuming the trapdoor is one of those no friction, the demon is basically making the left side of the box hot and the right side of the box cold. And he’s doing it without breaking a sweat.
Image Credit Science Photo Library
This is exactly the opposite of what’s supposed to happen in thermodynamics. Remember how it’s supposed to work. The takeaway about how the 2nd Law works is that heat should generally flow from hot regions to cooler ones. It’s probably not too much of a stretch to suppose that you didn’t even need a popular physics book to tell you that.
What gives? I admit that I first saw this problem when I was an undergraduate and was profoundly unimpressed with it. Who cares about a few atoms here and there? Besides, if the 2nd law is really only statistical in nature, does it really matter if we can circumvent it?
Yes, younger me. It does.
The 2nd law is supposed to be a hard and fast law of the universe, and a back door would be amazing. Why do we need to continuously burn coal, petroleum, or natural gas? Because most of the energy used by our machinery gets wasted as heat. If we could somehow employ a few million of Maxwell’s demons to recover the heat into useful energy, we’d be pretty much set.
It was until nearly a century after Maxwell came up with his demon that we really understood why the 2nd law remained inviolate. In 1948, Claude Shannon, a research scientist at Bell Labs, founded a branch of research known as “Information Theory.” Just as quantum mechanics made all of modern computing physically possible, information theory revolutionized cryptography, communication, and made innovations like the Internet possible.
One of the major results of information theory is that information and entropy are more or less the same thing. Suppose I send a message that is exactly two characters long. How many different messages can I send? I could in principle send you 26×26=676 different “words,” but most of those letter combinations are completely meaningless. Only a few (the Scrabble dictionary lists 101) are actual words.
To the computer scientists among you, this means that while in principle it would require about 10 bits (the 1’s and 0’s that are used to store data) to differentiate between every possible 2 letter combination, if you know that you’re transmitting a word, you only need about 7 bits. What a savings!
Communications can be significantly compressed by noticing that certain letters are used less frequently than others. E’s, for example, show up way more often than Z’s in the English language. This is why the former is worth only 1 point in Scrabble and the latter is worth 10. It also explains why “E” in Morse code is:
•
while Z is:
— — ••
Z takes far longer to tap out, but that’s okay, because you’re going to do it far less frequently. Another way of thinking about this is that the more complicated (or unlikely) a message is, the more information it carries, and the more bytes of data you’d need to store it on a computer.
What does all of this have to do with Maxwell’s Demon? Every time the demon has to decide whether or not to let an atom through his trap door, he takes a measurement and makes a recording of the speed of the atom. The very existence of that recording (whether in the brain of the demon, on a pad of paper, or in a computer) adds information to the universe, and information and entropy are the same thing.
The demon doesn’t really decrease entropy by playing his gas games; it’s just that the increased entropy goes in large part to creating his measurements and memories.
Your own memories, then, are in some sense a testament to the fact that the entropy of your brain is increasing with time. The fact that you remember the past and not the future really does just seem to be a testament to the increasing entropy of your brain.
———
Followup questions are appreciated.
-Dave
Greetings True Believers!
Work is well underway on “The Universe in the Rearview Mirror,” and I thought it would be fun to do a core dump of some of the more interesting symmetry quotes that I’ve come across. At very least, they’ll give you an idea of why symmetry is such a big deal. Feel free to use these to spice up your Christmas party conversations.
Herman Weyl, on what symmetry is (from “Symmetry”):
A thing is symmetrical if there is something you can do to it so that after you have finished doing it, it looks the same as before.
Why is this important? As Weyl added:
My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful.
Nobel Laureate Phil Anderson on the significance of symmetry in Physical Laws:
It is only slightly overstating the case to say that physics is the study of symmetry.
I found this quoted in “First Philosophy: A Theory of Everything” by Spencer Scolar. This isn’t the original source, of course, but he also gives a lot of other good symmetry quotes.
I particularly liked this one from John Wheeler:
There is no law of physics that does not lend itself to most economical derivation from a symmetry principle. However, a symmetry principle hides from view any sight of the deeper structure that underpins that law and therefore also prevents any immediate sight of how in each case that mutability comes about.
And one from his student, the great Richard Feynman:
So our problem is to explain where symmetry comes from. Why is nature so nearly symmetrical? No one has any idea why.
Feynman also has a great thought experiment concerning symmetry in his lectures:
Suppose we build a piece of equipment, let us say a clock, with lots of wheels and hands and numbers; it ticks, it works, and it has things wound up inside. We look at the clock in the mirror. How it looks in the mirror is not the question. But let us actually build another clock which is exactly the same as the first clock looks in the mirror – every time there is a crew with a right hand thread in one, we use a screw with a left-hand thread in the corresponding place on the other… If the two clocks are started in the same conditions, the springs wound to corresponding tightnesses, will the two clocks tick and go round, forever after, as exact mirror images?
PROTIP: If you have a budding (and extremely sophisticated) young scientist in your life and can’t figure out what to get them for the holidays, get them the Feynman Lectures. Do it now!
These common sense thought experiments in symmetry go back a long way, at least to Galileo:
I am certain you both know that an oak two hundred cubits high would not be able to sustain its own branches if they were distributed as in a tree of ordinary size; and that nature cannot produce a horse as large as twenty ordinary horses or a giant ten times taller than an ordinary man unless by miracle or by greatly altering the proportions of his limbs and especially his bones, which would have to be considerably enlarged over the ordinary.
He also described the motivation for what became known as “Galilean Relativity“:
Shut yourself up with some friend in the largest room below decks of some large ship and there procure gnats, flies, and other such small winged creatures. Also get a great tub full of water and within it put certain fishes; let also a certain bottle be hung up, which drop by drop lets forth its water into another narrow-necked bottle placed underneath. Then, the ship lying still, observe how those small winged animals fly with like velocity towards all parts of the room; how the fish swim indifferently towards all sides; and how the distilling drops all fall into the bottle placed underneath. And casting anything toward your friend, you need not throw it with more force one way than another, provided the distances be equal; and leaping with your legs together, you will reach as far one way as another. Having observed all these particulars, though no man doubts that, so long as the vessel stands still, they ought to take place in this manner, make the ship move with what velocity you please, so long as the motion is uniform and not fluctuating this way and that. You will not be able to discern the least alteration in all the forenamed effects, nor can you gather by any of them whether the ship moves or stands still. …in throwing something to your friend you do not need to throw harder if he is towards the front of the ship from you… the drops from the upper bottle still fall into the lower bottle even though the ship may have moved many feet while the drop is in the air …
Einstein (whose work on both Special and General Relativity were very consciously founded on symmetry) had this to say about the C (Charge) symmetry in the universe:
I used to wonder how it comes about that the electron is negative. Negative-positive—these are perfectly symmetric in physics. There is no reason whatever to prefer one to the other. Then why is the electron negative? I thought about this for a long time and at last all I could think was “It won the fight!”
There’s also his classic:
Everything should be made as simple as possible, but not simpler.
And, to finish, a rather romantic quote from Marcus Du Sautoy’s “Symmetry: A Mathematical Journey”:
…only the the fittest and healthiest individual plants have enough energy to spare to create a shape with balance. The superiority of the symmetrical flower is reflected in a greater production of nectar, and that nectar has a higher sugar content. Symmetry tastes sweet.
Like any blog post, this is a fishing expedition, and a lazy way to try to crowdsource research. Send me links to some of your own favorite symmetry quotes, and I’ll be eternally grateful.
-Dave
New Column! Also, a few announcements.
Hi, everybody! I realize that it’s been much a fairly long interruption in your regular “Ask a Physicist” service, and for that, I apologize. I hope we’re back on track now. Today’s column at io9 was all about how neutrino oscillation works (or rather why we’d expect it at all), and if you haven’t already done so, please check it out.
Better yet, ask me some good questions (preferably things that have genuinely been nagging at you, rather than things that you just assume other people might want to know).
Also, I have a few announcements!
- Book Title
As you may have seen in my previous post, I have a new book on symmetry in the works. Dutton will be publishing my next book in 2013. And my editor and I have finally converged on a final title:
THE UNIVERSE IN THE REARVIEW MIRROR
A High Speed Tour of Antimatter, Evil Twins, and Other Hidden Symmetries
- Polish Translation
Action continues with the User’s Guide. Our agent, Andrew, just sold the Polish rights to Proszynski Media. This will join Traditional and Simplified Chinese, Korean, Turkish, Russian, and Italian. Cover images when they become available.
- Upcoming Talk
I will be giving a talk on January 14 at Princeton Plasma Labs as part of their “Science on Saturdays” program. My talk will be entitled:
“The Dark Side of the Universe.”
Come! Ask questions!
That’s all for now. Sorry for the radio silence.
-Dave
Symmetry is on the way (in 2013)!
Good news, everyone! Those of you who don’t follow me on twitter or facebook will be pleased to learn that there is a new book officially on the way. The tentative title (always prone to change) is “The Why of it All: Antimatter, Evil Twins and how Symmetry Rules the Universe.” We’ve accepted an offer from Dutton with a planned Summer, 2013 publication date. Of course, if you can’t wait that long, I could always recommend some other reading.
Topics will range from questions about why we exist and all and weren’t destroyed in a giant conflagration of matter-antimatter annihilation, why time flows the way it does, why there are 3 dimensions of space and 1 of time, what the hell “symmetry” has to do with it all. The outline is in pretty good shape, but particularly interesting questions may yet find their way into the book, or at very least into my column.
Thanks for everybody’s support, and for all of the great questions so far. I’ll keep you updated.
-Dave
Buy the book on amazon!
Become a fan on facebook!
Follow us on twitter!
Buy Merch!
Write to us!