Blogs / Cosmic Variance

There should be some government program that forces scientists to watch dystopian science-fiction movies, so they can have some idea of the havoc their research is obviously going to cause. I just stumbled across an interview with Nobel Laureate Gerald Edelman, that has been on the site for a couple of months. (Apparently the Discover website is affiliated with some sort of magazine, to which you can subscribe.)

Edelman won the Nobel for his work on antibodies, but for a long time his primary interest has been in consciousness. He believes (as all right-thinking people do) that consciousness is ultimately biological, and is interested in building computer models of the phenomenon. So we get things like this:

Eugene Izhikevitch [a mathematician at the Neurosciences Institute] and I have made a model with a million simulated neurons and almost half a billion synapses, all connected through neuronal anatomy equivalent to that of a cat brain. What we find, to our delight, is that it has intrinsic activity. Up until now our BBDs had activity only when they confronted the world, when they saw input signals. In between signals, they went dark. But this damn thing now fires on its own continually. The second thing is, it has beta waves and gamma waves just like the regular cortex—what you would see if you did an electroencephalogram. Third of all, it has a rest state. That is, when you don’t stimulate it, the whole population of neurons stray back and forth, as has been described by scientists in human beings who aren’t thinking of anything.

In other words, our device has some lovely properties that are necessary to the idea of a conscious artifact. It has that property of indwelling activity. So the brain is already speaking to itself. That’s a very important concept for consciousness.

Oh, great. We build giant robots, equip them with lasers, and now we teach them how to gaze at their navels, and presumably how to dream. What can possibly go wrong?

Mary Roach, author of Bonk, gives a TED talk about Ten Things You Didn’t Know About Orgasm. All based on stuff that appeared in highly reputable scientific journals, but still I find the story about the brushing-teeth woman hard to credit.

(Aimed at adults, or at children who live in families who don’t think sex is dirty.)

Via Rebecca Skloot’s Twitter feed, so there’s no reason to take it seriously. (Because it’s from Twitter, I mean, not because it’s from Rebecca.)

With the new Star Trek out, it’s long past time (as it were) that we laid out the rules for would-be fictional time-travelers. (Spoiler: Spock travels to the past and gets a sex change and becomes Kirk’s grandfather lover.*) Not that we expect these rules to be obeyed; the dramatic demands of a work of fiction will always trump the desire to get things scientifically accurate, and Star Trek all by itself has foisted half a dozen mutually-inconsistent theories of time travel on us. But time travel isn’t magic; it may or may not be allowed by the laws of physics — we don’t know them well enough to be sure — but we do know enough to say that if time travel were possible, certain rules would have to be obeyed. And sometimes it’s more interesting to play by the rules. So if you wanted to create a fictional world involving travel through time, here are 10+1 rules by which you should try to play.

0. There are no paradoxes.

This is the overarching rule, to which all other rules are subservient. It’s not a statement about physics; it’s simply a statement about logic. In the actual world, true paradoxes — events requiring decidable propositions to be simultaneously true and false — do not occur. Anything that looks like it would be a paradox if it happened indicates either that it won’t happen, or our understanding of the laws of nature is incomplete. Whatever laws of nature the builder of fictional worlds decides to abide by, they must not allow for true paradoxes.

1. Traveling into the future is easy.

We travel into the future all the time, at a fixed rate: one second per second. Stick around, you’ll be in the future soon enough. You can even get there faster than usual, by decreasing the amount of time you experience elapsing with respect to the rest of the world — either by low-tech ways like freezing yourself, or by taking advantage of the laws of special relativity and zipping around near the speed of light. (Remember we’re talking about what is possible according to the laws of physics here, not what is plausible or technologically feasible.) It’s coming back that’s hard.

2. Traveling into the past is hard — but maybe not impossible.

If Isaac Newton’s absolute space and time had been the correct picture of nature, we could simply say that traveling backwards in time was impossible, and that would be the end of it. But in Einstein’s curved-spacetime universe, things are more flexible. From your own personal, subjective point of view, you always more forward in time — more technically, you move on a timelike curve through spacetime. But the large-scale curvature of spacetime caused by gravity could, conceivably, cause timelike curves to loop back on themselves — that is to say, become closed timelike curves — such that anyone traveling on such a path would meet themselves in the past. That’s what respectable, Einstein-approved time travel would really be like. Of course, there’s still the little difficulty of warping spacetime so severely that you actually create closed timelike curves; nobody knows a foolproof way of doing that, or even whether it’s possible, although ideas involving wormholes and cosmic strings and spinning universes have been bandied about.

3. Traveling through time is like traveling through space.

I’m only going to say this once: there would be no flashing lights. At least, there would only be flashing lights if you brought along some strobes, and decided to start them flashing as you traveled along your closed timelike curve. Likewise, there is no disappearance in a puff of smoke and re-appearing at some other time. Traveling through time is just like traveling through space: you move along a certain path, which (we are presuming) the universe has helpfully arranged so that your travels bring you to an earlier moment in time. But a time machine wouldn’t look like a booth with spinning wheels that dematerializes now and rematerializes some other time; it would look like a rocket ship. Or possibly a DeLorean, in the unlikely event that your closed timelike curve started right here on Earth and never left the road.

Think of it this way: imagine there were a race of super-intelligent trees, who could communicate with each other using abstract concepts but didn’t have the ability to walk. They might fantasize about moving through space, and in their fantasies “space travel” would resemble teleportation, with the adventurous tree disappearing in a puff of smoke and reappearing across the forest. But we know better; real travel from one point to another through space is a continuous process. Time travel would be like that.

4. Things that travel together, age together.

If you travel through time, and you bring along with you some clocks or other objects, all those things experience time in exactly the same way that you do. In particular, both you and the clocks march resolutely forward in time, from your own perspective. You don’t see clocks spinning wildly backwards, nor do you yourself “age” backwards, and you certainly don’t end up wearing the clothes you favored back in high school. Your personal experience of time is governed by clocks in your brain and body — the predictable beating of rhythmic pulses of chemical and biological processes. Whatever flow of time is being experienced by those processes — and thus by your conscious perception — is also being experienced by whatever accompanies you on your journey.

5. Black holes are not time machines.

Sadly, if you fell into a black hole, it would not spit you out at some other time. It wouldn’t spit you out at all — it would gobble you up and grow slightly more corpulent in the process. If the black hole were big enough, you might not even notice when you crossed the point of no return defined by the event horizon. But once you got close to the center of the hole, tidal forces would tug at you — gently at first, but eventually tearing you apart. The technical term is spaghettification. Not a recommended strategy for would-be time adventurers.

Wormholes — tunnels through spacetime, which in principle can connect widely-separated events — are a more promising alternative. Wormholes are to black holes as elevators are to deep wells filled with snakes and poisoned spikes. The problem is, unlike black holes, we don’t know whether wormholes exist, or even whether they can exist, or how to make them, or how to preserve them once they are made. Wormholes want to collapse and disappear, and keeping them open requires a form of negative energies. Nobody knows how to make negative energies, although they occasionally slap the name “exotic matter” on the concept and pretend it might exist.

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What is the Secretary of Energy doing submitting papers to the arxiv when he’s supposed to be solving the world’s energy problems? I have enough trouble getting papers written when it’s my actual job.

Atom interferometry tests of local Lorentz invariance in gravity and electrodynamics
Authors: Keng-Yeow Chung, Sheng-wey Chiow, Sven Herrmann, Steven Chu, Holger Mueller

Abstract: We present atom-interferometer tests of the local Lorentz invariance of post-Newtonian gravity. An experiment probing for anomalous vertical gravity on Earth, which has already been performed by us, uses the highest-resolution atomic gravimeter so far. The influence of Lorentz violation in electrodynamics is also taken into account, resulting in combined bounds on Lorentz violation in gravity and electrodynamics. Expressed within the standard model extension or Nordtvedt’s anisotropic universe model, we limit twelve linear combinations of seven coefficients for Lorentz violation at the part per billion level, from which we derive limits on six coefficients (and seven when taking into account additional data from lunar laser ranging). We also discuss the use of horizontal interferometers, including atom-chip or guided-atom devices, which potentially allow the use of longer coherence times in order to achieve higher sensitivity.

We kid the Energy Secretary, but this is a very cool experiment. (I presume this is the interferometer?) Basically, you throw an atom up in the air, and catch it as it comes down. But you actually split the wave function of the atom into two different beams, depending on when it absorbs and emits a pulse of laser light. The beams leave the same place and are collected at the same place, but travel on slightly different paths; you can use interferometry to see whether these different paths have evolved differently.

Which lets you test all kinds of things, from measuring the fine structure constant to looking for new forces to testing Lorentz invariance, as is happening here. But if it helps free us from dependence on foreign oil sources, I’d be surprised.

The next great step in exploring the physics of the early universe through the cosmic microwave background radiation (CMB) - the Planck Surveyor Satellite - launches one week from today! You can prepare by watching this handy primer

and watch the launch streamed live from the European Space Agency (ESA). You can also follow the mission using any number of those newfangled methods the young folk seem to be getting into - see Andrew Jaffe’s post over at Leaves on the Line for more details.

Here’s hoping it all goes off smoothly!

Since no one is blogging around here, and I’m still working on my book, I will cheat and just post an excerpt from the manuscript. Not an especially original one, either; in this section I steal shamelessly from the nice paper that Ted Bunn wrote last year about evolution and entropy (inspired by an previous paper by Daniel Styer).

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Without even addressing the question of how “life” should be defined, we can ask what sounds like a subsequent question: does life make thermodynamic sense? The answer, before you get too excited, is “yes.” But the opposite has been claimed – not by any respectable scientists, but by creationists looking to discredit Darwinian natural selection as the correct explanation for the evolution of life on Earth. One of their arguments relies on a misunderstanding of the Second Law, which they read as “entropy always increases,” and then interpret as a universal tendency toward decay and disorder in all natural processes. Whatever life is, it’s pretty clear that life is complicated and orderly – how, then, can it be reconciled with the natural tendency toward disorder?

There is, of course, no contradiction whatsoever. The creationist argument would equally well imply that refrigerators are impossible, so it’s clearly not correct. The Second Law doesn’t say that entropy always increases. It says that entropy always increases (or stays constant) in a closed system, one that doesn’t interact noticeably with the external world. But it’s pretty obvious that life is not like that; living organisms interact very strongly with the external world. They are the quintessential examples of open systems. And that is pretty much that; we can wash our hands of the issue and get on with our lives.

But there’s a more sophisticated version of the argument, which you could imagine being true – although it still isn’t – and it’s illuminating (and fun) to see exactly how it fails. The more sophisticated argument is quantitative: sure, living beings are open systems, so in principle they can decrease entropy somewhere as long as it increases somewhere else. How do you know that the increase in entropy in the outside world is really enough to account for the low entropy of living beings?

As we mentioned way back in Chapter Two, the Earth and its biosphere are systems that are very far away from thermal equilibrium. In equilibrium, the temperature is the same everywhere, whereas when we look up we see a very hot Sun in an otherwise very cold sky. There is plenty of room for entropy to increase, and that’s exactly what’s happening. But it’s instructive to run the numbers.

The energy budget of the Earth, considered as a single system, is pretty simple. We get energy from the Sun, via radiation; we lose the same amount of energy to empty space, also via radiation. (Not exactly the same; processes such as nuclear decays also heat up the Earth and leak energy into space, and the rate at which energy is radiated is not strictly constant. Still, it’s an excellent approximation.) But while the amount is the same, there is a big difference in the quality of the energy we get and the energy we give back. Remember back in the pre-Boltzmann days, entropy was understood as a measurement of the uselessness of a certain amount of energy; low-entropy forms of energy could be put to useful work, such as powering an engine or grinding flour, while high-entropy forms of energy just sat there.

The energy we get from the Sun is of a low-entropy, useful form, while the energy we radiate back out into space has a much higher entropy. The temperature of the Sun is about twenty times the average temperature of the Earth. The temperature of radiation is just the average energy of the photons of which it is made, so the Earth needs to radiate twenty low-energy (long-wavelength, infrared) photons for every one high-energy (short-wavelength, visible) photon it receives. It turns out, after a bit of math, that twenty times as many photons directly translates into twenty times the entropy. The Earth emits the same amount of energy as it receives, but with twenty times higher entropy.

The hard part is figuring out just what we mean when we say that the life forms here on Earth are “low-entropy.” How exactly do we do the coarse-graining? It is possible to come up with reasonable answers to that question, but it’s complicated. Fortunately, there is a dramatic shortcut we can take. Consider the entire biomass of the Earth – all of the molecules that are found in living organisms of any type. We can easily calculate the maximum entropy that collection of molecules could have, if it were in thermal equilibrium; plugging in the numbers (the biomass is 10¹⁵ kilograms, the temperature of the Earth is 255 Kelvin), we find that its maximum entropy is 10⁴⁴. And we can compare that to the absolute minimum entropy it could have – if it were in an exactly unique state, the entropy would be precisely zero.

So the largest conceivable change in entropy that would be required to take a completely disordered collection of molecules the size of our biomass and turn them into absolutely any configuration at all – including the actual ecosystem we currently have – is 10⁴⁴. If the evolution of life is consistent with the Second Law, it must be the case that the Earth has generated more entropy over the course of life’s evolution by converting high-energy photons into low-energy ones than it has decreased entropy by creating life. The number 10⁴⁴ is certainly an overly generous estimate – we don’t have to generate nearly that much entropy, but if we can generate that much, the Second Law is in good shape.

How long does it take to generate that much entropy by converting useful solar energy into useless radiated heat? The answer, once again plugging in the temperature of the Sun and so forth, is: about one year. Every year, if we were really efficient, we could take an undifferentiated mass as large as the entire biosphere and arrange it in a configuration with as small an entropy as we can imagine. In reality, life has evolved over billions of years, and the total entropy of the “Sun + Earth (including life) + escaping radiation” system has increased by quite a bit. So the Second Law is perfectly consistent with life as we know it; not that you were ever in doubt.

For the last few months there’s been some excitement among particle-astrophysicists about intriguing results from the PAMELA satellite experiment and the ATIC balloon experiment. (We also blogged about it here and here.) PAMELA claimed to see an excess in the number of high-energy cosmic positrons (anti-electrons) over what you would expect from conventional astrophysical sources, while ATIC (which can’t distinguish between positrons and electrons) saw an overall rise in the number of positrons and electrons combined, more or less consistent with what PAMELA saw. One dramatic but plausible explanation for this result is that the positrons are produced when dark matter particles and antiparticles annihilated with each other, which would certainly be exciting. But it wasn’t quite a home run, because there was no evidence for the corresponding excess of anti-protons you would probably also expect. (Although that is not a deal-breaker; with a little ingenuity, particle physicists are able to come up with models that produce positrons but not anti-protons.) There was also some controversy when theorists wrote papers trying to fit the data before the data were even published, by snapping pictures of plots shown at conferences with their cell-phone cameras. More than enough drama for a TV movie, I would say.

A tinfoil-hat conspiracy theorist might imagine that all the excitement was intentionally manufactured, just so people would pay more attention to the first measurement from the new Fermi (formerly GLAST) gamma-ray telescope. And now those results are in! (Other Fermi results have already appeared, but not about this particular question.)

Sadly, the results are “in” in the sense of being published in Physical Review Letters, which helpfully charges $25 if you’re not a subscriber. (Presumably it will be on arxiv soon, probably tonight.) The best summary of the results, although somewhat technical, is by Bruce Winstein and Kathryn Zurek at Physics, the American Physical Society’s in-house journal that highlights interesting results.

And here are those results.

Fermi is more like ATIC than like PAMELA, in that it also cannot distinguish between electrons and positrons, so this graph shows both. The blue line is a simple model that you might expect in the absence of any dark-matter annihilations, and the red points are the Fermi results. If you look very closely, you can see the grey squares representing the ATIC data, which peak way up there between 100 GeV and 1000 GeV of energy.

So: hmm. Sadly it’s not a completely definitive result, either way. (This is reflected in the coverage in the popular press, where, unlike the physicists, they need to come to a conclusion: Ron Cowen at Science News says “Another Clue in the Case for Dark Matter,” while Adrian Cho at ScienceNow says “Lights Out for Dark Matter Claim?” Both do a good job in the body of their articles.) The Fermi data are clearly lower than the ATIC data were — but they’re not quite as low as the simple model would predict. The energy resolution of Fermi also isn’t quite as good — it’s harder for them to pinpoint the energy of each particle — so it’s conceivable that there is a sharp peak that simply gets smeared out by their instrument. But I completely agree with Winstein and Zurek’s take:

These results, as precise as they are, do not definitively confirm or rule out a DM source. Although the large ATIC excess, which had been consistent with PAMELA, is ruled out, because of uncertainties from charge-dependent modulation in the flux from the solar wind, the Fermi and PAMELA data do remain consistent as having the same source. Since several natural astrophysical explanations can generate the Fermi and PAMELA spectra, the likely course is that one will be found there. It may simply be, as the Fermi paper points out, that the primary electron spectrum in the cosmic-ray source, predicted to fall as ~E^-3.3 (where E is the particle energy), does not fall as steeply as thought in the energy range observed by Fermi.

In other words, it’s not too hard to imagine an astrophysical explanation that doesn’t require new physics beyond the Standard Model (which would still be interesting). But more data would be nice. We’ll keep looking.

CERN announced today that the final replacement LHC magnet was lowered into the tunnel, and is making its way to Sector 3-4 (between collision points 3 and 4). Last September’s incident led to 53 magnets - about half a kilometer of the 27-km ring - having to be removed, repaired or cleaned, and replaced. Check out the video of the final dipole going in on April 16.

New systems are being installed to better detect incipient magnet quenches, and the helium pressure relief systems are being upgraded. My understanding is that this will be done on the greater part of the LHC magnets this year, but not all of them.

The plan is to complete the installation of the replacement magnets, and then cool down all sectors. At present, half the machine is being held at liquid nitrogen temperatures, and the other half is at room temperature. It will take a couple months, once they start, to cool the whole machine down to superconducting temperature, about 2 degrees K.

So, by late summer the LHC commissioning can begin where it left off last September. Assuming all goes well, physics collisions are foreseen at 10 TeV by late fall. The machine will not run at the design energy of 14 TeV at least until the entire machine is retrofit with the new quench detection and pressure relief systems. And, the beam intensity (and hence collision luminosity) will not be anywhere near the ultimate goal during the first physics run.

The usual running pattern at CERN is to start in the spring, and collide beams through the late fall, and do machine maintenance, etc. during the winter when electric power is more expensive in Europe (they heat with nukes, basically; we burn fossil fuel in the US in winter).

But a decision was reached earlier this year to run the LHC through next winter, with only a brief two-week shutdown for Christmas and New Year.

What we can reasonably expect is that if all goes well, we can accumulate something like 100 inverse picobarns of collisions by spring 2010, and perhaps 200 pb^-1 by the end of the run in fall, 2010. Now, pb^-1 this is a strange unit - it has dimensions of inverse area. Formally we call it integrated luminosity. Basically it tells you how many collisions you’ve had, in essence. To get the number of some type of interesting events, you need to know the cross section - which has units of area - for producing that type of event. Then you simply multiply the cross section times the integrated luminosity.

Once the machine shuts down in late 2010, and if we do have a sample of about 200 pb^-1, there will ensue a long shut down in 2010-2011 to complete the magnet retrofit. The LHC will then not run until late 2011.

This means that the lower-energy, relatively small sample of physics data is all we will have to analyze until 2012, three years from now! The experiments have already been simulating collisions at the lower energy and retuning analyses.

Though everyone is waiting breathlessly for the LHC to discover the Higgs boson, with lower energy and a smaller sample, I would not bet on the LHC finding it any time before 2012. In fact, a full analysis of the Higgs sensitivity at 10 TeV is yet to be done in ATLAS and CMS. This is a huge task, and will take months, but there is no question that it is more difficult at the lower energy, and it’s already very hard for the LHC to see, say, a 120 GeV Higgs boson. As I wrote in my post in March, this is also very hard for the Tevatron in the same time period. Those of us looking for a standard model Higgs boson have to exercise a bit of patience while working very hard toward the ultimate goal!

Neverheless, there is a ton of new physics that *could* emerge from even the first LHC physics sample from the 2009/10 run. If nature has new high-mass particles giving observable pair-production resonances at energies not accessible at the Tevatron, they could stand out in sharp relief above the standard model. Similarly if there are extra dimensions of space time, we may see excess pair production of standard model particles. If supersymmetry exists, and the experiments manage to understand well the apparent missing momentum transverse to the beam direction (a big challenge) then a first observation of the presence of supersymmetric particles might be possible.

At this point, all you can do is admire the wisdom of the great Zen master Yogi Berra, who said “If this was easy it wouldn’t be so hard!” But then, maybe we’ll get lucky.

A couple of years ago I got to hear Geoffrey West, one of Time magazine’s 100 Most Influential People, give a talk on his research at a meeting of the American Association for the Advancement of Science. It was a fantastic talk, and I immediately had the idea to ask him to come to Caltech at some point and give it as a colloquium. So tomorrow he’ll be here, and anyone in the neighborhood interested in a semi-technical account of complex systems from physics to biology is welcome to stop by. He might be angling for the record for the longest talk title ever:

The Complexity, Simplicity, and Unity of Living Systems from Cells to Cities: A Physicist’s Search for Quantitative, Unified Theories of Biological and Social Structure and Organization

Although Life is very likely the most complex phenomenon in the Universe, many of it’s most fundamental and complex phenomena scale with size in a surprisingly simple fashion. For example, metabolic rate scales approximately as the 3/4-power of mass over 27 orders of magnitude from complex molecules up to the largest multicellular organisms. Similarly, time-scales (such as lifespans and growth-rates) and sizes (such as genome lengths, RNA densities, and tree heights) scale as power laws with exponents which are typically simple multiples of 1/4. The universality and simplicity of these relationships, together with emergent “universal” invariants, suggest that fundamental constraints underly much of the coarse-grained generic structure and organisation of living systems. It will be shown how these 1/4 power scaling laws follow from underlying principles embedded in the dynamical and geometrical structure of space-filling, fractal-like, hierarchical branching networks, presumed optimised by natural selection. These ideas lead to a general quantitative, predictive theory that potentially captures the essential features of many diverse biological systems. Examples will include vascular systems, growth, cancer, aging and mortality, sleep, cell size, genome lengths, and DNA nucleotide substitution rates. These ideas will be extended to social organisations: to what extent are cities or corporations an extension of biology? Are they “just” very large organisms? Analogous scaling laws reflecting underlying social network structure point to general principles of organization common to all cities, but, counter to biological systems, the pace of social life systematically increases with size. This has dramatic implications for growth, development and particularly for sustainability: innovation and wealth creation that fuel social systems, if left unchecked, potentially sow the seeds for their inevitable collapse.

We’ve talked before about the difficulty in defining “life,” although one safe criterion is that a living organism is going to be pretty complex. What about the other way — when you have an undeniably complex system like a city or a university or a galaxy, at what point does it become useful to think of it as a “living organism”? Those are hard questions, but one angle is to investigate the similarities that complex systems demonstrate as they are manifested at different sizes. That’s the idea of “scaling laws” — measuring a feature common to a set of complicated systems (number of parts, speed of motion, etc.) and see how they change as a function of scale.

You might have imagined that complexity comes in a variety of completely different forms, and there would be no simple relationship that included viruses, house cats, and sprawling urban centers. But the data reveal a remarkable degree of regularity — many complex systems share certain basic features, just scaled up or down in ways appropriate to their size.

Here is one startling example: every living being on Earth gets about a billion heartbeats worth of lifespan. Larger organisms live longer, but their hearts (or other analogous rhythmic processes) beat more slowly. Use those heartbeats wisely!

The next challenge, of course, is to understand why. A few stabs have been taken in that direction using ideas about hierarchical networks of smaller systems — about which I shouldn’t say much, at least until I’ve heard the talk.

Those of you who can’t make it to LA on short notice can enjoy this video, or check out Blake Stacey’s live-blog of a previous talk.

This week I served on an oral exam committee for a thesis proposal in experimental particle physics (nice job Elisabetta). All went extremely well, and I was able to ask a few (I hope useful) questions, and also witness the way in which the people closer to the subject matter - the experimentalists - questioned their candidate. One thing I took away from this experience was a renewed admiration for the extremely hands-on way in which experimentalists, particularly those working in a subject that continually challenges one’s intuition, understand the concepts and quantities they deal with.

As a specific example, one question concerned how far various particles traveled from a primary interaction vertex in a detector. Obviously, a correct answer to this question requires the knowledge of an awful lot of physics. However, there are rough estimates one can do knowing a few simple facts such as the speed of light. Of course, we all know the speed of light, which we denote as c. Most of us physicists first learned that c is about 3 times 10⁸ meters per second. If you are in my field you are more likely to use different units; namely those in which c=1. However, neither of these choices of unit is particularly suited to calculating something useful for a collider experiment or, indeed, to making an on the fly estimate of a human-sized quantity.

The experimentalists in the room all use, of course, standard sets of units familiar to us all. However, they keep in their heads a bunch of handy human-sized versions, that just aren’t part of my (and I suspect many theorists’) usual way of thinking. In the case above, the relevant example is that light travels one foot per nanosecond (not metric, I know, but one meter per 3.3 nanoseconds somehow doesn’t have the same ring to it). I know the conversion takes hardly any time, and I know this isn’t a particularly scientifically deep piece of knowledge, but I think having a human-scale idea of uncommonly large physical numbers provides a very nice feel for the concept that just isn’t captured by the ways in which we normally, abstractly, think of them.

So I’m interested to know what other common sense statements of uncommonly large or small physical quantities our wise and worldly readers might have at their fingertips. Feel free to chime in in the comments.