Posts Tagged ‘Physics’

You probably learned about projectile motion in introductory physics class. If you throw something (a baseball, say) then its horizontal motion will remain constant, whereas its vertical motion will change under the influence of Earth’s gravitational pull. The result is a parabolic arc, right?

Well, no. Saying that projectile motion is parabolic is only an approximation.

In class, I “prove” that the motion of the baseball is a parabola, but in order to do so, I make the (reasonable) assumption that the effect of gravity is a constant. That is, I assume that the vector g (the acceleration due to gravity) always points in the same direction all along the trajectory.

This is actually not quite true, however. I’ve neglected the curvature of the Earth.

Now, this isn’t really a big deal when throwing baseballs. Suppose you toss a ball to your friend 50 m away. The vector g for you does point in a slightly different direction then g for your friend, but the angular difference is miniscule…it’s about 50/637,000,000 radians, or 0.00045 degrees. This is so small that I am comfortable pretending that the two g’s are actually parallel, and the derivation thereby leads to a parabolic arc.

But what if you don’t make that approximation? What answer do you get?

You get an ellipse. You get an orbit. And here’s the point of my post:

Every time you throw an object, the object is (temporarily) in orbit until it hits the ground.

Here’s the orbit of a thrown baseball (not to scale):


Now suppose the Earth had the same mass, but was the size of the Little Prince’s home asteroid B-612, which is as big as a house. The orbit is the same, but this time the baseball doesn’t strike the surface:


The takeaway is that all projectile motion is really orbital motion. I find this fascinating: you don’t need a fancy rocket to launch something into orbit. Your arm will suffice. It’s just that you need the Earth to not be in the way.

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I suspect there are hundreds of physics classrooms across the country that have the following poster:

10314603This is the CENCO (Central Scientific Company) poster of the famous 1927 Solvay Conference. I’ve been to at least three universities that have this thing on the wall, including my own institution, Western Carolina University, and my alma mater, Wake Forest University. Strangely, I can’t date the poster, although if you read the descriptions of the 1927 Solvay attendees, the poster lists Dirac as being dead and De Broglie as being alive. Ergo, the posters were printed some time between 1984 and 1987. I suppose CENCO gave the posters away for free as a promotional during the Reagan administration, and I’d guess most of those freebies are still hanging on the wall today. (Physicists don’t update their décor very often.)

I’ve spent a fair amount of time looking at this poster (sometimes, the life of a lab instructor is dreary). And, in all my time staring at these giants of modern physics, I’ve formulated one burning question:

Which of these people was the dumbest?

[Note: I used this site for a listing of the attendees in the famous photo]

Don’t get me wrong; I’m not claiming anyone in the poster is dumb per se. And I would never compare myself to anyone on the list. But logic dictates that one of the people here was literally the dumbest attendee; I feel a moral obligation to identify this person for posterity.

Most of the names on the poster are familiar to physicists, and most of the attendees are therefore out of the running. No one would ever seriously consider Einstein, Curie, Dirac, Bohr, etc. as being the “dumbest.” On the other hand, some of the physicists aren’t so familiar, but they were obviously talented: Guye wrote over 200 papers; Knudsen had a bunch of crap named after him (Knudsen cell, Knudsen flow, Knudsen number, Knudsen layer and Knudsen gases). Piccard and Langmuir fall into this category as well.

And then there are the scrubs flanking Ehrenfest,


Henriot, Ehrenfest, and Herzen

and the scrubs flanking Schrödinger,


de Donder, Schrödinger, and Verschaffelt

These scrubs are so scrubby that the CENCO poster doesn’t even talk about them.

Surely one of these fools was the dumbest?

Let’s take them in order. Henriot was a chemist, so that’s a strike against him; he discovered that potassium is naturally radioactive, which is cool I guess, and figured out a way to make tops spin at high speeds. Woop-de-do. Herzen was a friend of Ernest Solvay, but didn’t really do anything else of note; I think we know how Herzen got an invite to the conference, don’t we?

Being a mathematician, de Donder probably gets a pass: he also wrote a shitload of books. The final scrub, Verschaffelt, is notable as having the shortest Wikipedia article of any Solvay attendee. Basically, all I can find out about him was that he was a physicist. Period.

Before we decide between Herzen and Verschaffelt, we should mention two other physicists in the poster. Compton once said, “the supernatural is as real as the natural world of Science,” so I’m tempted to list Compton amongst the scrubs. Anyone with so much woo in his veins can’t be listed amongst the top tier of physicists. Compton did win a Nobel prize though, and he was American…we have to disqualify him, then. America, fuck yeah! That leaves Ehrenfest, who was by all accounts a clever guy. But come on, the guy shot his own son and then killed himself. That’s hard to get past. I guess we’ll chalk that up to mental illness, not stupidity, but no one is ever going to make an Ehrenfest action figure.

Parents snub traditional action figures in favour of such as historical icons as Einstein and Van Gogh

None of these for Ehrenfest.

So who was dumber, Herzen or Verschaffelt?

Herzen wrote a book or two, and supposedly played a “leading role” in physics and chemistry. So I’ll give him the nod over Verschaffelt. Thus we can tentatively say:

Verschaffelt was the dumbest attendee of the 1927 Solvay Conference.


“I’m still smarter than you.”

You’re welcome.

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Physicist or not a physicist?

In the film Amadeus, Salieri wonders what Mozart looks like.  He knows Mozart by reputation, but has never met the man.  He says:

“As I went through the salon, I played a game with myself. This man had written his first concerto at the age of four; his first symphony at seven; a full-scale opera at twelve. Did it show? Is talent like that written on the face?”

Good question. Decide for yourself:

Is this genius?

Which brings me to a game we can play: Physicist or not a physicist?

Look at the following portraits, and see if you can see the spark of genius in them.  Which ones are as smart as Einstein?  And which ones are merely composers, economists, or chess players?  [Answers follow at the end of the post.]

























[A quick note on the formatting of this post.  Yes, I know it sucks.  And it took me 2.5 hours to get to this level of suckiness.  Thanks, WordPress, for forcing the broken Beep Boop Boop editor on me, and disabling classic mode!  In the Beep Boop mode, not only is everything slower, but (1) you can’t center text in picture captions, (2) the visual editor doesn’t accurately display what’s in the HTML editor, (3) the visual editor doesn’t accurately display what’s in preview mode, (4) if text is left justified, then it wraps around automatically, even if you didn’t choose this option, (5) you can’t change font size of the text, or caption, (6) you can’t even change the fucking FONT, (7) tags are now buried under several levels of drop-down menus, slowing things down immensely, and (8) there’s an annoying pop-up asking me after every edit if Hey! Do I want to Preview?  No, I don’t want a preview, WordPress, and your removing the “switch to classic mode” button was frankly just malicious.]

Answers [highlight to reveal]: #1 Physicist Emmy Noether.  #2 Composer Bela Bartok.  #3 Chess champion Mikhail Tal.  #4 Economist John Maynard Keynes.  #5 Physicist Shirley Jackson.  #6 Physicist Lise Meitner. #7 President John Tyler.  #8 Physicist Chen Ning Yang.  #9 Physicist Michael Faraday.  #10 Physicist Emilie du Chatelet.  #11 Swordsman Miyamoto Musashi.  #12 Physicist Michael Binger.

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I’ll start with a limerick:

The Becquerel has me morose;

These units I can’t diagnose.

The rads and the Grays

Don’t measure decays—

But what of equivalent dose?


1 Becquerel = 1 decay/s

There are at least seven units of radioactivity floating around out there, measuring at least three different kinds of things; a veritable zoo of scientific terms. Unfortunately, most people don’t know a rad from a Gray from a Becquerel. Here, then, is my attempt to sort out the confusion.

You’re welcome.

First, let me just say that most people (to my dismay) equate the terms “radioactivity” and “radiation”. There’s some disagreement on the meanings of these terms; I find myself in the conservative camp on this issue. To me, “radioactivity” refers to junk flying out of an unstable nucleus: alpha particles, gamma rays, and the like. “Radiation”, on the other hand, refers exclusively to electromagnetic radiation (anything from long-wavelength radio waves to ultra-short-wavelength gamma rays). By my fuddy-duddy standards, “radiation” is just light; it may or may not be biologically dangerous. Radiation is just one of the possible kinds of radioactivity.

Unfortunately, through the inevitable process of “language creep” (the same process by which the original four “collie” birds became four “calling” birds in the Twelve Days of Christmas, because people are just ignorant) the term “radiation” has come to encompass any ionizing junk from a nucleus.  So some people now call alpha particles and beta particles “particle radiation” to distinguish them from gamma rays, which is “electromagnetic radiation”. This usage bothers me, but I’ll get over it. Just note that I won’t use this terminology here.

So: unstable nuclei exist. They occasionally spit out things—a phenomenon I call radioactivity. These things can often knock electrons free from atoms (i.e. they can ionize atoms). Such ionization events can be detected by a Geiger-Müller tube (among other devices).

Activity. The first way to measure radioactivity is to measure these ionization events in a given amount of time, which in turn tells you how often decays are occurring. So we measure R, the “activity” of a nuclear sample. The metric system unit of activity is the Becquerel (Bq), which is defined to be one decay/second. (Note that 1 Bq is essentially equivalent to 1 Hz = 1 s–1.)

Unfortunately, the Becquerel is a small unit—if we’re talking about radioisotopes used in medicine, for example, we might have to speak of billions of Becquerels. So there’s another unit of activity: the Curie (Ci). One Curie is defined to be the activity of 1 gram of 226Ra. If you want to convert, 1 Ci = 3.7 x 1010 Bq.

There is a problem with measuring activity: it doesn’t really tell you how dangerous a particular sample is. Not all radioactivity particles are the same. Getting hit with millions of weak particles might be preferable to being hit by only a few high velocity ones. One bullet is more dangerous than 500 rapidly-fired marshmallows.

Absorbed dose. To get a feel for the dangerousness of a sample, we talk about absorbed dose: a measure of energy absorbed per kilogram of target material. In metric units, the applicable unit is the Gray (Gy): 1 Gy = 1 Joule/kg. Other people use the rad, with the conversion 1 rad = 1 erg/g = 0.01 Gy. Use of the rad is discouraged by the international scientific community but is still common in (surprise surprise!) the United States.

There’s still a problem. Suppose I’m exposed to 1 Gy of radioactivity (meaning that I expect to absorb a joule of energy per kilogram of my mass). It matters whether I’m absorbing beta particles (say) or alpha particles, because the damage done by alpha particles is worse, pound-for-pound. That is, different kinds of radioactivity are more or less dangerous, depending on the predilection of the given particle(s) for causing genetic damage and possibly causing cancer. This leads us to introduce…

Equivalent dose. Equivalent dose is basically just absorbed dose, times a “fudge factor” that depends upon the kind of radioactivity involved. The unit we use is the Sievert (Sv) = 1 J/kg (weighted). X-rays, gamma rays, and beta particles are all in a sense “equally” dangerous and have a weight factor of 1. So for those kinds of particles, 1 Gy → 1 Sv. Alpha particles, though, are around 20 times as “dangerous”, so if we’re dealing with alpha particles then 1 Gy → 20 Sv.

Of course Americans are contrary when it comes to units, and so the rem is still in common use; 1 rem = 100 erg/g (weighted) = 0.01 Sv. If you’re a science writer, you’d be best served by eliminating rad’s and rem’s altogether; why perpetuate archaic units? You don’t use furlongs/fortnight to measure speed, do you?

I can’t help but mention a seventh unit of radioactivity: the Banana Equivalent Dose, or BED; 1 BED = 0.1 μSv, and so represents an equivalent dose. It (roughly) equates to the amount of radioactive exposure you would get if you ate a banana. (Bananas are naturally radioactive, as they contain significant amount of radioactive potassium, 40K.) This kind of unit helps people put the hobgoblin of “radioactivity” into perspective. “Oh my God! The nuclear plant let off some radioactive steam! Am I doomed?” “Well, your exposure was about 10 BED’s. So basically eat 10 bananas for the same effect.” (There are some issues with the BED as a unit; see this for more information.)


In summary:

Unit                                                     Symbol            Note


Becquerel: one decay/s                     Bq                   Same as 1 Hz

Curie: activity of 1g of 226Ra              Ci                    Not SI unit, 1 Ci = 3.7×1010 Bq

Absorbed dose

Gray: 1 J/kg                                         Gy

rad: 100 erg/g                                     rad                  Not SI unit; 1 rad = 0.01 Gy

Equivalent dose

Sievert: 1 J/kg                                     Sv

rem: 100 erg/g rem                             rem                 Not SI unit; 1 rem = 0.01 Sv

Banana equivalent dose                      BED                Not SI unit; 1 BED = 0.1 mSv

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Anyone who studies physics and/or mathematics has often encountered the following conundrum:

How do you distinguish 18th-century French mathematicians with surnames beginning with an “L”? (I call these E.C.F.M.W.S.B.W.A.L.’s)

For example, you might recall that an E.C.F.M.W.S.B.W.A.L. invented the calculus of variations, some time around 1760.  Was it Legendre?  Lagrange? Laplace?  Or maybe you remember that an E.C.F.M.W.S.B.W.A.L. was the father of probability theory, and worked on the Buffon needle problem.  Was that Laplace?  Legendre? Lagrange?

So as a public service, I’ve sorted this out for you.  I henceforth talk about these three great mathematicians, and hope to distinguish them in your mind.

Lagrange: perhaps the best mathematician of the 1700’s.

Lagrange is the oldest of the E.C.F.M.W.S.B.W.A.L.’s, born in 1736.  Some call him the greatest mathematician of the century, although I might give that title to Euler.  In any case, he’s responsible for a host of discoveries: he pretty much invented an entire branch of mathematics, the calculus of variations; he used this tool to reformulate classical mechanics (think L = T – V) making it suitable for non-Cartesian coordinates, such as polar; he invented Lagrange multipliers, an elegant way to deal with constraints in differential equations; and he introduced the f(x),f'(x),f”(x)…notation for derivatives.

His greatest work was Mécanique analytique; all of the above achievements are found in this book.  Hamilton described the work as a “a scientific poem,” for its elegance is astounding.



Lagrange was rigorous and abstract: he bragged that the Mécanique analytique did not have a single diagram.  To Lagrange, math was an art; the aesthetics of a theory took precedence over utility.

Laplace: the “applied” mathematician

Laplace was seven years younger than Lagrange, born in 1749.  He also is associated with classical mechanics, but unlike Lagrange, he did not reformulate the field per se.  Rather, he took Newtonian mechanics to its “apex” with his work Mécanique céleste.  This work is brilliant, but it’s also clunky and difficult.  It analyzes the orbits of all known bodies in the solar system, and concludes that there is no need of God to keep the whole mess going.  In fact, Napoleon supposedly asked why Laplace didn’t mention God in the Mécanique céleste.  He reportedly said “I have no need for that hypothesis.”



Laplace didn’t place as much emphasis on “beauty” in mathematics.  To him, math was just a tool.  Not surprisingly, he contributed to the “applied” field of probability theory; in fact, he’s arguably the founder of probability theory as we know it today.

Legendre: the elliptic integral guy

Although highly regarded in his day, Legendre (b. 1752) is really a tier below the first two guys.  Basically, he worked out how to do some elliptic integrals, and he introduced the Legendre transformation, which is used in many branches of physics.  For example, you can go back and forth between the Hamilton and Lagrange approaches of classical mechanics by means of Legendre transformation.  Also, such transformations are ubiquitous in thermodynamics (think U → H → A → G).

Legendre is also know for the portrait debacle.  Only a single known image of Legendre exists, and that image is not flattering:



Every other supposed portrait of Legendre is actually the picture of some obscure politician, because of a mistake which has propagated forward for 200 years.

In summary:

Lagrange: the beauty of math; reformulated mechanics in the Mécanique analytique

Laplace: math as a tool; Newtonian mechanics reaches its zenith in Mécanique céleste; probability theory

Legendre: the creepy looking elliptic integral guy

Note: I have not mentioned Lavoisier (b. 1743) because he was a chemist.  But if you really need him:

Lavoisier: a chemist who was guillotined in the French Revolution.

[Note added Dec. 4, 2014]  I could have included L’Hopital (French, died 1704) but all he did was write a textbook.  Laguerre was French, but he was born in 1834;  Lebesgue was French, but he was born in 1875.

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As promised, the solutions…

1.   681472 [Um, Didn’t we answer this one earlier?]

2.   3927.27272… seconds This represents the amount of time it takes the minute hand of a clock to lap the hour hand.  For example, the hands coincide at midnight; they next coincide 3927.27272 seconds later, or at about 1:05:27 AM.

3.   23.14069… This is just e^π.

4.   2.1656 x 10^185 This is how many cubic planck lengths fit in the observable universe…basically, if our universe were a 3D computer, this is how many pixels you’d need.

5.   1.03 light year/year^2 This is the acceleration due to gravity g, in non-standard units.  It has the following interpretation: if you ignored relativity and accelerated at a rate of 1 g (reasonable for a starship), after a year you’d have reached the speed of light.

6.   133956 This is the number of possible combinations of two birthdays, since 133956 = 366^2.  If everyone on Earth had a significant other, there would be over 26,000 couples with the exact same two birthdays as you and your other.

7.   About 19.5 million people The number of people on Earth who share your birthday.

8.   0.739085… This is called the “Dottie number”…an irrational number that solves the equation cos x = x.

9.   1.72048 m^2 The area of a pentagon with sides of 1 m.

10.   0.004295 % This is what percent of Earth’s history homo sapiens has been around.

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Many Worlds Puzzle #3

Today there are really 10 puzzles. Can you figure out the significance of each number below? I’ve answered the first to get you started.

1.   681472

This number has a prime factorization of 2^9 x 11^3, which indicates that it equals 88^3. There are 88 keys on a piano…so one obvious interpretation is that the number 681472 is the number of possible three-note permutations that could start any piece on a piano (not counting rests, and ignoring duration). I wonder how many of the permutations have actually ever been played over the years?

2.   3927.27272… seconds

3.   23.14069…

4.   2.1656 x 10^185

5.   1.03 light year/year^2

6.   133956

7.   About 19.5 million people

8.   0.739085…

9.   1.72048 m^2

10.   0.004295 %

Because many of these problems are challenging, I will post hints in a week or so.

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