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.
April 26th, 2009 at 2:15 pm
I’ve always remembered that 25 m/s is very close to 55 miles/hour. That helps bring an abstract measurement to the familiar.
In computer science it’s sometimes useful to remember that 5 megabytes is roughly the size of War and Peace (uncompressed), or that the Encyclopedia Brittanica minus the images is about 300 MB, or about half the size of a CD-ROM (again, uncompressed). Not just to bring a data-size measurement into familiar terms, but also as a reminder of how little storage text actually requires. A picture may be worth a thousand words, but it costs far more than that.
April 26th, 2009 at 2:44 pm
I’m not sure how useful this is but an attoparsec per fortnight is to very good precision 1e-6 inch/second.
April 26th, 2009 at 2:48 pm
c = 1 ft/ns is sort of well known to computer types. The late Grace Hopper used to hand out nanoseconds (pieces of wire cut to slightly less than a foot on length) during her lectures. I still have one.
April 26th, 2009 at 3:29 pm
I got a degree in astronomy and we were expected to know and use the shortcut that there are roughly pi * 10 ** 7 seconds in an earth year.
April 26th, 2009 at 3:32 pm
I’ve always liked the approximation that 1 year is pi*10^7 seconds.
April 26th, 2009 at 3:55 pm
A microcentury is about 52.5 minutes, close to the standard length of an academic lecture. (Yes, they’re usually supposed to be 50 minutes, but professors can’t shut up.)
April 26th, 2009 at 4:16 pm
My summer’s are spent in music production, we work in 20′ fields of scope and vision. Stages are often 40′ X 80′ or other units divisible by 20. Thus most of us in the infrastructure production end use 20′ X 20′ as the base measure for almost everything: “That’s three 20s plus one caterpillar (or cat)” translates to 60 feet plus four feet. A caterpillar refers to lengths that most snake {electric/sound/video cable zipped together} protective covers [they are yellow and black and linked together look like a swallow tail caterpillar; and depending on what part of the country you live these are also ‘yellowjackets”) are available and thus would be the distance in front of a stage or other installation between that structure and the people barriers (called bike racks or chainlink). Bike rack fencing comes in 8′ lengths so we just use the number needed, and chainlink modular fencing comes in 10′ sections. After a while you get completely used to the jargon; and to an outsider your conversations make zero sense. Last example is a “booth” which is the space assigned to a vendor that is defined as a 10′ X 10′ footprint. Therefore, a box of booths would have a footprint of a 20 X 20 and is usually assigned to food vendors where as a line of X booths would be a row of 10′ X 10′s.
April 26th, 2009 at 5:04 pm
That 1 foot/ns trick was really useful when I did AMO for a sanity check on trigger or coincidence timing. On our laser tables, all the screws were six inches apart – so you could count holes and divide by two to find the time delay of any laser pulse.
April 26th, 2009 at 5:07 pm
Along with changing the units to imaginable ones I like order of magnitude comparisons with objects of experience. Like if an apple were the size of the earth the atoms would be the size of an apple.
April 26th, 2009 at 5:31 pm
I tend to think in metric, so for me that shortcut has always been c = 30 cm/ns.
April 26th, 2009 at 5:53 pm
A million seconds is about a week (or, to greater precision, eleven and a half days).
0 mag (“Vega”) is 1,000 photons per second per cm^2 per Å at 5500 Å, at the top of the atmosphere (now why would anyone want to try to remember that!?!).
April 26th, 2009 at 5:56 pm
Oh, and another one that I got from pendulum work is that pi^2 = g.
April 26th, 2009 at 5:59 pm
Grace Hopper (http://en.wikipedia.org/wiki/Grace_Hopper) when lecturing often used to pass out wires cut in about 1 foot lengths to represent nanoseconds.
April 26th, 2009 at 6:15 pm
I’ve always liked the way of describing the incredible sensitivity of neutron EDM experiments. If the neutron were blown up to the size of the Earth, the shift in the charge distribution would be less than about a micron.
April 26th, 2009 at 6:35 pm
- The sensitivity of the human eye is such that it can see a match flame from a mile away
- If you stick out your arm your thumb subtends rough 1 arcsec
April 26th, 2009 at 6:44 pm
hc = 1240 eV nm is often useful.
April 26th, 2009 at 7:47 pm
I’ve always heard that an ultra-high-energy cosmic ray has about the same energy as a good fastball.
April 26th, 2009 at 7:49 pm
1 km/s = 1 pc / million years.
1 arcsec @ 1 Mpc = 4.8 pc
1 gm = 20 Kiloton
rho_crit ~ one balloon of H per earth volume.
April 26th, 2009 at 8:26 pm
c/g = 1 year (within about 3%)
April 26th, 2009 at 9:10 pm
Yes but how many New York minutes are in a dog year?
April 26th, 2009 at 9:44 pm
60 mph is 88 fps. Came up a lot in high school physics for some reason.
And I also have a nanosecond wire.
April 26th, 2009 at 10:22 pm
@friend
/i If you stick out your arm your thumb subtends rough 1 arcsec/i
Mine subtends an angle of a bit over 2 deg so I expect you’ve got very long arms!
April 26th, 2009 at 10:34 pm
@Gareth: I always go with pi^2 = 10, though you’re right that pi^2 = g m/s is closer accuracy-wise. Anyway, whenever I need half an order of magnitude, I always use factors of pi.
April 26th, 2009 at 10:46 pm
Right-On Rock; There are almost exactly piE7 sec/yr (0.5% accuracy)
Dave: Better is h-bar*c =2E-7 ev-m.( 1.5%). Drop the cumbersome writing of `10^x for exponentials, as E+/-x is `computerese’, quicker to write, and easier to comprehend than “Ten to the whatever”.
My fave is 1 A.U. = 150 G-meters (within ~ 0.5 %).
Students make contact with solar system astronomy much quicker with this unit, since they KNOW what a Giga-anything is, and they sure know what a meter is. Plus, easy to remember.
Far-out: 1Ly is E16m (95% accuracy). Slighly farther out, but easier to express once familiarity is achieved, is 1 parsec out to the nearest star (alpha-centauri), and 1 Mega-parsec to the nearest galaxy (Andromeda).
Better to cut the cord to ft., miles, pounds, ad nauseam, ASAP, and demand students embrace the international standards. They ususally respond.
April 26th, 2009 at 10:57 pm
my favourite is always that the average density of the sun is that of water.
April 26th, 2009 at 11:46 pm
In my first quantum class, we were expected to use hbar c = 200 eV nm or 200 MeV fm whenever we had to calculate “actual” numbers.
Recently had to talk about heavy ion collisions/QGP, and all of the times were given in units of fm/c ~1e-23 seconds, or the time to cross a nucleus (roughly) at light speed. I’d seen 1e-23 seconds quoted as the “characteristic time” for strong interactions, but never really connected that to nuclear sizes, so seeing it as a fm/c was oddly somewhat enlightening.
Also, in high-frequency/RF circuitry, thinking of the speed of light as 30 cm*GHz can be really useful, since often your relevant design parameters are on the scale of cm and GHz, and c = 30 cm*GHz is pretty much exact to within design tolerances.
April 26th, 2009 at 11:46 pm
Theorists should take a cue from Hans Bethe. He never calculated any theoretical object without plugging human scale numbers at the end. In fact many of his calculations were order of magnitude dimensional analysis.
The famous example was the lamb shift, where he did some egregious (at the time) mathematical manipulations, but actually came out with a value that was pretty close to the correct number.
April 27th, 2009 at 12:05 am
“I think having a human-scale idea of uncommonly large physical numbers provides a very nice feel for the concep”
This means that you consider 10**-9 second a more “human-scale idea,” then 10**8 meters, in reality both amounts defy imagination imo, the better “feel” has probably more to do with the fact that nanosecond is more familiar due to technology then anything else.
April 27th, 2009 at 12:13 am
A handy mnemonic for the pi-year relation earlier is:
” pi seconds is one nano-century “
April 27th, 2009 at 12:43 am
This means that you consider 10**-9 second a more “human-scale idea,” then 10**8 meters
No, neither of them is a human-scale idea. The “natural” scales of the problem are nanoseconds (typical lifetime of some elementary particles) and c (typical speed they are traveling in your experiment). The rule of thumb converts these hard-to-picture scales into a literally human-scale unit (feet).
April 27th, 2009 at 12:57 am
my favorite unit of volume is the Hubble-barn: Hubble’s constant (actually c/H, to get a rough size for the visible universe) times one barn is approximately ten liters.
(13.2 liters using the WMAP data)
April 27th, 2009 at 12:58 am
Of course, all VMS experts are familiar with the unit “microfortnight”.
April 27th, 2009 at 2:20 am
When you work in analogue broadcast TV, the colour subcarrier frequency is 4.43361875MHz for 625 line PAL (I’m in Australia). That makes one cycle (360 deg.) = approx 225nS. The delay through 75 ohm coax cable is about 5 nS/m, and this had to be taken into account in all equipment interconnections.
‘Course, now that I’m retired and it’s all digital, no-one gives a fig about that any more. Grump.
April 27th, 2009 at 4:41 am
To within 0.3 percent, the following ratios are the same:
inch/mile = AU/lightyear
April 27th, 2009 at 6:01 am
Roughly 1 in 10 working adults in a group won’t be there for the group, even if they are there physically. They’re thinking about family, another project, other allegiances, etc. Knowing this is normal helps me to understand national surveys where a percent of people take a very bizarre position. 10%’s about normal there. If that number is less than that, the issue is either something big or something is very wrong (vote fraud, etc.).
Also, out of 1000 people, assuming normal conditions, 25 are irrational at any time. Not necessarily harmful, just not working under any “normal” logical frame of thought.
I work out both numbers whenever I get a chance after some large project, emails to my website after a big day (million hits in one day), etc. They help to explain humanity as a whole. For me, at least.
April 27th, 2009 at 6:28 am
I learned in grad school that
the distance light traveled in
a nanosecond was called the
PHoton UniT, or “phut”.
April 27th, 2009 at 6:32 am
A pint’s a pound
)
The world around.
(Maybe I should work the Hubble-barn into this somehow!
The sun moves about one hand-width-at-arm’s-length per hour (if you’re not too close to the poles). Good for estimating how much time you have left before sunset.
April 27th, 2009 at 8:04 am
Sentences following the Pareto principle
http://en.wikipedia.org/wiki/Pareto_principle
can be roughly stated as “e out of pi…” since e/pi = 0.865256.
Example: “e out of pi people in our group are hopeless geeks.”
April 27th, 2009 at 8:49 am
From the middle ages :
Rumour has it that Shakespeare originally wrote
“I’ll put a gridle round the earth in twice forty minutes”,
then struck out the “twice” to make the line scan better
“A shout, milady, travels at thrice the speed of Agincourt’s arrows”
April 27th, 2009 at 8:51 am
@Charlie: Alas, in the UK, “A pint of water weighs a pound and a quarter” – we use 20 fluid oz in a pint rather than the 16 used in the US. So it’s not quite “the world around”. This also makes our gallons differ from yours.
It’s not quite as accurate as some of the factors quoted above, but x metres per second is *approximately* 2x miles per hour (12% low).
April 27th, 2009 at 9:23 am
your fist at arms length subtends 10 degrees
April 27th, 2009 at 10:08 am
A neutron star is about the size of a city, and its magnetosphere (light cylinder) ranges from just a couple of times that up to the earth-moon distance. Their surface magnetic fields have about the same energy density as lead’s rest mass density.
A solar-mass white dwarf is about the size of the earth. A typical density of the interstellar medium is about one particle per cubic centimeter.
And the obvious: an object at one parsec has a parallax of one arcsecond. For some reason all the astronomers I talk to use parsecs rather than lightyears, so it’s easy to take a guess at how feasible it will be to get a parallax distance.
April 27th, 2009 at 10:21 am
The neutral hydrogen line at 1420 MHz is observed a lot by radio astronomers.
For converting Doppler shifts in the spectral line to a radial velocity, its handy to
remember that a shift in frequency of 1 MHz corresponds to a radial velocity of about
200 km/s.
April 27th, 2009 at 11:05 am
Plate tectonics pushes the plates around at about the speed your fingernails grow. Every time you trim your fingernails, Europe and North America have moved that much further apart.
April 27th, 2009 at 11:40 am
Humans embryos implant when they are about 1 Planck mass.
April 27th, 2009 at 12:13 pm
As for the extended arm and thumb, that is an old nautical estimator that tracks approximately one hour of sun movement near the plane of the horizon (it really doesn’t work so well overhead). All sorts of those nautical proverbs still exist in some form: Red sky in the morning sailors take warning and so forth.
Generators and amplifiers usually cost about one dollar ($1.00) per watt of power output. It takes about 100 watts to move 100 dBs a meter from a mid-range (5.7″) speaker into an outdoor space. For 19″ subwoofers that requirement is multiplied by 10 to 1000 watts.
April 27th, 2009 at 12:14 pm
The mass of the sun in geometrized units (G=c=1) is 1.4 km.
April 27th, 2009 at 3:42 pm
Planck’s constant divided times the speed of light light (i.e. the constant to convert a photon wavelength to an energy) is pretty close to 1 eV * 1 micron. (Within 20% or so, anyway.)
Kepler’s Third law is P^2 = A^3 if you measure P in years and A in AU.
April 27th, 2009 at 3:43 pm
oops… take “divided” out of my last comment. (Brain fart)
April 27th, 2009 at 4:50 pm
hc = 1240 eV nm
This makes it easy to calculate the energy of photons, given their wavelength, or vice versa, because E = hc/lambda. So a red photon of 620 nm is about 2 eV in energy.
April 27th, 2009 at 4:52 pm
Here’s another water one. One cubic meter of water has 1000 liters, each of which is a kilogram. Therefore a cubic meter of water is 1 metric ton. There are one million milliliters in that ton, each with a mass of 1 gram.
April 27th, 2009 at 5:10 pm
1000 km/s is approximately 1 Mpc/Gyr.
A dime at a distance of one mile subtends an arcsecond.
April 27th, 2009 at 6:08 pm
One that hasn’t come up yet: the average thermal energy of a particle in a gas at room temperature is 1/40 of an electron volt.
One that I remember because it was part of a question at my thesis defense is that the de Broglie wavelength of an atom at the single-photon recoil velocity is equal to the wavelength of the light.
One that I remember because it came up in one of my rare attempts to do theory is that h-bar is 2255 if you measure time in microseconds, mass in atomic mass units, and length in units of 100 Bohr radii.
April 27th, 2009 at 6:17 pm
I always liked kT = 4.1 pN*nm = 25 meV at room temperature.
The first form is really useful for example if you want to have an idea of the work a molecular motor or similar is able to perform (ie. can pull 4 nm with 1 pN force).
The second is handy to estimate the occupancy of excited states or similar.
April 27th, 2009 at 8:02 pm
1 meter/sec is approximately 2 knots (1.944)
or 1 km/sec is approximately 2000 knots
1 nautical mile is approximately 2000 yards (2025.37)
April 28th, 2009 at 1:11 am
36 Km per hour = 20 metres per second
A New York second = the time between the traffic lights turning green & the car behind honking! (Terry Pratchatt)
April 28th, 2009 at 1:20 am
In M-Theory, the size of a string to the size of a proton, is roughly the size of a tennis ball to the size of our galaxy.
I think that is “true” to within an order of magnitude.
Anyhow, it helps me understand just how small the strings of M-Theory are!
April 28th, 2009 at 7:27 am
I like this one
http://xkcd.com/526/
April 28th, 2009 at 8:19 am
The speed of sound in air is approximately one foot per millisecond.
I first learned this as five seconds per mile–I sort of instinctively start counting seconds whenever I see a lightning flash, waiting for the thunderclap, to estimate how far away it is.
April 28th, 2009 at 1:01 pm
88 ft/sec = 60 mph USED to be on most driver’s exams in the u.s. but apparently is no longer as NONE of my students know this. Thumb at arms length is close to one arc-minute (not one arc-second).
Here’s one I haven’t seen: 1 cubic meter of hydrogen at sea level gives about 1 kg of lift.
April 28th, 2009 at 1:02 pm
oops: I did it too! thumb at arms length is close to ONE DEGREE!
April 28th, 2009 at 3:35 pm
Here are two rules of thumb that I’ve used in the last week or so (though not, I hasten to add, for anything very important):
– Most chemical reactions yield about an eV per bond, so typically a few eV per molecule. This is useful for calculating the energy density of all kinds of things (like, say, gasoline), particularly if you remember that 1 eV is about 1.6×10^-19 Joules, and that a mole is about 6×10^23 whatevers. A mole of carbon weighs about 12 grams.
– Less generally useful, but interesting: the flux of solar radiation at Earth’s distance is about 1400 Watts per square meter. Fifteen lightbulbs.
April 28th, 2009 at 6:11 pm
The weight of an average apple is about 1 Newton.
April 29th, 2009 at 4:51 am
Another shortcut from astronomy: 1 km/sec is roughly 1 parsec/million years. (Useful because typical motions of stars are measured in km/sec and distances are measured in parsecs.)
Example: how long does it take the Sun to make one complete Galactic orbit, given that its orbit is roughly circular with a radius of 8 kiloparsecs (kpc) and a velocity of about 200 km/s? Circumference of orbit = 2 pi x 8 kpc = 50,000 parsecs; divide this by 200 and you get 250, so the answer is “about 250 million years”.
April 29th, 2009 at 11:17 am
i like hc~1234 ev nm
a megaparsec-barn is about the volume of your fingertip.
pi squared is ~10 (or as mentioned above, g)
April 29th, 2009 at 12:53 pm
60 miles an hour is also a mile a minute, or 88 ft/second.
April 29th, 2009 at 6:41 pm
oops!
“36 Km per hour = 20 metres per second”
should be
“36 Km per hour = 10 metres per second”
does no one check these approximations???
May 3rd, 2009 at 12:20 pm
A barn is 10 fm by 10 fm.
An erg is about 600 GeV and the Planck mass is of order 10 nanograms.
The local density of dark matter is about one WIMP [of 100 GeV] per coffee cup [300 mL].
May 3rd, 2009 at 12:22 pm
(a) kT = 1 electron volt at a temperature of just over 10^4 Kelvin
(b) 1g (acceleration) * 1 year = approximately the speed of light
(c) 2^10 = 1024 = approximately 10^3 (useful for quicly converting powers of 2 to powers of 10)
(d) another astronomy one: 1 arcsecond = 1/206265 radians,
or equivalently, 1 parsec = 206265 AU
(e) and one more astronomy one, 1AU (= radius of Earth’s orbit around sun)
= 149 million km (but astronomers tend to write things like 10^13 cm,
which always makes me stop and convert to meters then kilometers than AU)
May 3rd, 2009 at 8:29 pm
A billion seconds is about 30 years.
May 12th, 2009 at 10:16 pm
3db is approximately double.
1 bit of information at room temperature is about 1/55th of an electron volt. At liquid nitrogen temperature, its about 1/200th .
To cycle through all values of a 128-bit key at liquid nitrogen temperatures will need about 10^19.6 J, about 2.5 seconds of the total amout of solar radiation hitting the earth.
Roughly. Of course, you’ll need one mother of a heatsink to keep that comfy liquid nitrogen temperature. And that’s simply to cycle through the values. If you want to do some computations as well, that’ll cost you more.