The predictability of randomness and the age of Earth

The uranium-lead transition isn’t the only one used. There’s also the rubidium-strontium transition (with a half-life of 49 billion years), the potassium-argon decay (1.3 billion years), and a handful of others. The key in all these cases is to have a rock — meteorite or otherwise — with enough atoms of the given types to perform measurements. One we don’t see in the list is “carbon dating”: carbon-14 has a half-life of about 5,700 years, so it’s useful for archaeology and dating the remains of animals from the relatively recent past, but utterly useless for measuring the age of Earth.

But why is a random process like radioactive decay useful as a clock?

Please Don’t Beam Me Up, Scotty

Visitor: It doesn’t transport. It disassembles your molecules and reassembles them on the other side. It annihilates you, and builds a perfect copy in a new location. It’s not a transporter, it’s a replacer. What results is a facsimile, a reproduction, a brand-new being with borrowed memories. The original creature—its consciousness—its soul—all gone.

This is funny, and mostly right. But there’s one physics error I spotted, and it’s a whopper. As you might guess, it ties in with the details of quantum teleportation. It’s unfortunate, too, because I think much of the story holds together without it.

Visitor: Think about it. It’s not the actual molecules being “transported,” just information about them. You could just as easily transmit that information—and build the new being—while leaving the old one perfectly intact. Couldn’t you? And if the old one persisted, wouldn’t it be obvious that the new copy is a different being altogether?

Spock: His analysis is not incorrect, Captain.

What Spock should have said was that the answer is “no”; i.e. there’s a superfluous “not” in there (a sign error, of sorts). Destruction of the state of the original is a requirement of quantum teleportation, which renders the rest of that section’s argument moot. Perfect copying while retaining the original is cloning and there is something called the no-cloning theorem in quantum mechanics: basically, you can’t make copies of an unknown quantum state (the wikipedia page on this gets technical pretty quickly). You can transfer that information from one particle to another, but the information in the original is destroyed.

The gory details of this bit of theory is tad outside of my wheelhouse, but as I understand it if you could clone, then you could measure the cloned state without disrupting the original. But there are a whole bunch of quantum effects that depend on a state being undetermined, rather than having some underlying reality — there must be more than one possible state in order to see interference. It’s a reason that classical explanations for entanglement fail, because in classical physics you can have an unknown state (a coin you’ve flipped) and then measure it (look at the coin, see it’s “heads”), and you will know that it was heads even before you looked at it. In QM, you don’t know that it was heads until the moment of measurement — it was in a superposition of heads and tails before that, and that superposition will behave differently than a state that was secretly heads (or tails) the whole time.

Ask Ethan #36: The Amazing Spinning Electron

Nice illustration of symmetric vs antisymmetric states and why one forms bonds while the other does not.

Even though we have no way of distinguishing one electron from another (because they’re identical), each atomic system is unique. In other words, if I have four different hydrogen atoms in the ground state, they’re not going to be required to occupy different energy states.

Indeed.

The Sacred, Spherical Cows of Physics

Oh, that fearful symmetry

Early in their training, many physics students come across the idea of spherical cows. Cows in the real world—even at their most plump and well-fed—are hardly spherical, and this makes it tricky to calculate things like, say, how their volume or surface area scales with their height. But students learn that these numbers are easy to calculate if they assume the cow is a perfect sphere, or in other words, that it has spherical symmetry. The lesson: Hard problems become easier when certain underlying (though approximate) symmetries are enforced.

It’s a very informative post, but it seems to me this introduction has little to do with the symmetry discussions that follow. A spherical cow approximation is less about applying symmetry than about physicists using approximations in an attempt at getting an answer that’s actually solvable and (one hopes) close enough to what nature says it is. An equation describing an actual cow shape would likely be exceedingly difficult to manipulate, for whatever problem you were trying to solve. So you approximate, and hope that whatever information is lost is negligible. That the shape is symmetrical incidental; the important point is that it’s simple — it’s also why we employ frictionless surfaces, perfectly elastic collisions and ignore numbers that are small compared to other numbers in a problem. I think the rest of the piece stands on its own without the spherical cow reference.

Hacking nature: loopholes in the laws of physics

I hope that the next time you encounter an inviolable law of nature, you’ll apply the hacker mentality and attempt to strip it down to its essence, isolate assumptions, and potentially find a loophole.

Tunneling: A Quantum Process

[T]he weirder thing is what happens if I have two traps, separated from one another, and I put the electron in one trap. Yes, the center of either trap is a good stable location for the electron. That’s still true… in the sense that the electron can stay there and won’t run away if you jiggle the trap.

However, if I put the electron in trap number 1, and walk away, sealing the room etc., there’s a certain probability (Figure 4) that when I come back the electron will be in trap number 2.