Abstract
The most exciting phrase to hear in science, the one that heralds new discoveries, is not ‘Eureka!’ but ‘That’s funny…’
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Notes
- 1.
As you can demonstrate by standing on your feet, in spite of Earth’s gravity.
- 2.
Or the “macroscopic scale” if you have no poetry in your soul.
- 3.
So named because they are cone-shaped (roughly).
- 4.
Many species of birds, reptiles, and fish have four cone cells. Apes (including people), some monkeys, and marsupials have three cones cells, but the vast majority of all other mammals have only one or two.
- 5.
“discern” = “make a good guess at”.
- 6.
Having three cone cells.
- 7.
It’s as dark as a witch’s anything-you-could-name; what is there to see?
- 8.
And that’s why water’s blue!
- 9.
So named because we can see it (visually).
- 10.
More accurately, it has some colors taken away more than others. Still, what remains is no longer white light.
- 11.
After the worst storm ever, by far.
- 12.
Seriously. Feynman did a lot of weird stuff.
- 13.
Pronounced “pie on”.
- 14.
When a physicist says “massive” they mean “it does not have zero mass” as opposed to the more common meaning “it has buckets of mass”.
- 15.
When a charge is placed in an electric field it accelerates. An MeV, “Mega Electron Volt”, is the amount of energy a charged particle (like protons or electrons) will have after being accelerated through an electric field of one million volts.
- 16.
For sound (a form of waves) coherence is the difference between a single clean tone and random noise.
- 17.
It has recently been discovered that neutrinos have mass, which makes them least massive particles (as of now). However, they’re basically “ghost particles” whipping around the universe and straight through everything in it at, or very near, the speed of light. So don’t worry about them.
- 18.
1951–1957.
- 19.
Radio waves can also bounce off of the ionosphere.
- 20.
This is actually a description of the electric field: the electric field of a photon points sideways relative to the direction of motion and switches back and forth sinusoidally (like a sine wave!). Photons don’t actually “wave back and forth”.
- 21.
Bosons have “integer spin”.
- 22.
Fermions have “half-integer spin”.
- 23.
Our experience of the world is that turning around 360∘ brings you back to where you started. Particles like electrons, which have “one half spin” have the bizarre property that they need to turn all the way around twice. If they turn around once, their wave function flips sign (so doing that twice brings them back to the original wave function). Feynman had a cute demonstration for why this has anything to do with exchanging particles. Hold a belt in front of you and, keeping the ends pointing in the same direction the whole time, switch them between your hands. You’ll find that the belt now has one full twist in it: exactly what you would have if you just turned one end in a full circle.
- 24.
See, for example, all of chemistry.
- 25.
The moment a physicist picks something up, it ceases to be a “toy” and begins its dramatically shortened life as “research equipment”.
- 26.
This remarkable property makes the “spark gap” a useful circuit element, although typically not in circuits where precision is needed.
- 27.
Not a real word.
- 28.
Especially clever readers may have noticed that adding a neutron to 14 N (seven protons, seven neutrons) leaves 15 N (seven protons, eight neutrons). But 15 N is stable, and will not decay into 14 C, or anything else. So why does the reaction n +14 N → p +14 C happen? The introduced neutron could be introduced gently or with great gusto. This extra energy can sometimes make the nucleus “splash”. It’s a little like pouring water into a glass. If you pour the water in slowly, then nothing spills out and the water-in-glass system is stable. But if you pour the same amount of water into the glass quickly, then some of it is liable to splash out. Similarly (maybe not that similarly), introducing a fast neutron to a nucleus can have a different result than introducing a slow neutron. Dealing with complications like this is why physicists love big computers.
- 29.
Dracula is dead, but he’s still part of the carbon cycle since he eats (or drinks at least). Therefore, we can expect that carbon dating would read him as “still alive”, since he should have about the same amount of carbon-14 as the people he imbibes.
- 30.
There are several different radioactive elements used for dating things. To date really old stuff, like the Earth itself, we’ve used zircon dating. Zircon crystals will happily incorporate uranium when they form, but never lead. But when uranium decays, it turns into lead. So, by comparing the amount of lead to uranium in a fleck of zircon, you can figure how long it’s been since that crystal formed.
- 31.
At most we have access to one Earth mass.
- 32.
It won’t.
- 33.
It probably will.
- 34.
The “Large Hadron Collider” near Geneva, Switzerland, which is presently the most powerful particle accelerator ever built.
- 35.
Because they carry about 7,500 times as much kinetic energy as mass.
- 36.
This radiation is emitted from the tortured space above the event horizon (a black hole’s “point of no return”) and not from the black hole itself. This subtle distinction is why Hawking radiation doesn’t violate the “nothing escapes a black hole” rule.
- 37.
Hawking radiation is a prediction of some clever math involving quantum mechanics applied to the empty space just above the event horizon. The theoretical arguments are convincing enough (to the physicists who understand them) that frenemies Stephen Hawking and Kip Thorne have made and settled a series of public bets on the subject, without direct, physical confirmation of the existence of Hawking radiation.
- 38.
Explosion = energy released fast.
- 39.
The “worst case” is all of the 115 billion protons in each of the at-most 2,808 groups moving at full speed are all piled up in the same tiny black hole.
- 40.
That rivals the total output of the Sun for that second, so you wouldn’t want to be nearby.
- 41.
Colder than the Sun at least.
- 42.
Something like a 200 km ball of stone or bigger.
- 43.
That’s more remarkable than it sounds: matches won’t work anywhere else in the known-so-far universe.
- 44.
They’re in a specific, unlikely, and therefore low-entropy state: on top of a flagpole.
- 45.
It’s easy to get caught up in thinking that “positive” and “negative” have some objective meaning here. Evolution is not “survival of the fittest”, it is more accurately “whatever works, works”. Turtles move slowly so that they require less food and cheetahs move quickly so that they can get more food. One is not necessarily “fitter” than the other (although, given the option, being a cheetah seems like more fun).
- 46.
Technically, most plants need certain single-celled symbiotic critters to help them break stuff down around their roots, so this isn’t just a plants-only effort. No species is an island.
- 47.
Having an “effective temperature” of − 21∘ C means that the Earth radiates heat into space at the same rate as a − 21∘ C black-body sphere (something simpler and without air) of comparable size. The actual surface temperature is greater because we have the greenhouse effect, which is good when it keeps the Earth from being frozen, but is best in moderation.
- 48.
There are tiny oases surrounding “black smokers” (volcanic vents) on the ocean floor that include some organisms that can subsist on the “chemosynthesis” of materials from within the Earth. Technically, those few critters don’t necessarily need the Sun. In spite of that, not even anaerobic chemosynthesizing creatures are islands.
- 49.
\(\varepsilon _0=8.854\times 10^{-12}\frac {C^2s^2}{kg\,m^3}\) and \(\mu _0=4\pi \times 10^{-7}\frac {kg\,m}{C^2}\).
- 50.
This is safer than it sounds. Because of all those units, you’ll be reminded that you need to put some combination of ε 0 and μ 0 back when you’re done mathing, because otherwise your answer will have the wrong combination of Coulombs, meters, seconds, and kilograms.
- 51.
You’d expect “M” to be used for the magnetic field, but it’s already used for mass, so some genius decided “B” was a good letter for magnets and the notation stuck.
- 52.
In fact, that’s exactly what a mathematician means when they say “vector field”.
- 53.
Not for lack of trying. After a couple centuries of false hope and dead ends, it is now reasonable to say that “magnetic charges” do not exist in the way that electrical charges exist.
- 54.
You won’t see that on the SAT.
- 55.
In particular: “Stokes theorem” which, along with “Gauss’ integral theorem”, is one of the indispensable rules of vector calculus and, because they’re practically one and the same, electromagnetism as well.
- 56.
“Moving electrical charges”=“current”.
- 57.
Here I’ve made the presumption that you live in the Americas. Generally speaking, electricity in the Americas is distributed at 60Hz and distributed at 50Hz everywhere else.
- 58.
We could just as easily have solved for the magnetic field and gotten the same result. But since one determines the other in a vacuum, that would be redundant.
- 59.
I’m stretching the analogy a bit. There is an amount of kinetic energy that you can give, say, your arm, beyond which your shoulder will tear apart before it’s able to bring your arm to a halt. That’s the “binding energy” of your shoulder.
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Cottrell, S.S. (2018). In-Between Things. In: Do Colors Exist?. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-64361-8_3
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