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Lepton number and gravitational waves

When I was in college, Gerhard ‘t Hooft (a Nobel-prize winning physicist) came to speak, and gave a lecture on black hole evolution (I think based on this paper). I didn’t have the education to really understand it, and I still don’t, but what I got out of it was

  • Hawking radiation is a semiclassical approximation
  • A black hole in a box should be coherent, just like Schrodinger’s Cat
  • Therefore Hawking radiation is really just the stuff that went in to the black hole coming back out, after a lot of interactions

This felt right to me. Call it parsimonious: if you can explain all expected black hole behaviors within the existing laws of physics, then that’s probably the right answer. It does, however, force you to throw out the no-hair theorem, which states that black holes are a perfect billiard ball, smooth and free of history. That might be true in General Relativity, but it can’t be true in coherent quantum gravity.

One interesting side effect of this approach is that all the various conservation laws should apply: not just the classical ones like conservation of energy, momentum, and charge, but also quantum ones like color charge, weak isospin, baryon number (i.e. # of quarks), and lepton number (~# of electrons).

This is not normally a problem. We can simply demand that the Hawking radiation spit out the same proportions of stuff that went in in the first place. No Big Deal.

A few months ago, the first gravitational wave detection was announced. A billion light-years away, a 36-solar-mass black hole merged with a 29-solar-mass black hole, in a collision so dramatic that 3 solar masses of energy were radiated away as gravitational waves, leaving a 62-solar-mass black hole behind, spinning rapidly. Conservation of mass/energy, check. Conservation of angular momentum, check.

But what about baryon number? Ordinary matter falling into the black hole is almost entirely baryonic by mass, insofar as it’s mostly protons and neutrons. Five percent of the mass was lost to gravitational waves. That means the Hawking radiation would have to produce the same number of baryons, at a 5% discount on mass! If the Hawking radiation is protons and neutrons as seems natural, then this is simply impossible. The mass of a proton (or neutron) is a constant.

I can think of several ways to resolve this problem, all of which seem implausible.

The baryons could come out bound in low-mass configurations The lowest-mass configuration known is Iron-56, which has a 1% mass discount … not even close to enough. The only known way to pack more baryons into less mass is to spit out an entire gravitationally bound neutron star … which would be an awfully big piece of Hawking radiation!

We could assume that at least 5% of the mass was contributed by the kinetic energy of infalling particles. This is probably true … but it doesn’t seem like there’s any reason it has to be true. If we carefully fed two black holes with low-speed baryons, would they then not be able to radiate gravitational waves upon colliding? That would be extremely weird, a gross violation of general relativity.

It turns out that baryon number may not be conserved. However, most existing theories assume some similar conservation laws. Even if baryons can be converted into leptons, the finite mass of the lightest lepton (neutrinos) means that proton-fed black holes will still run into this problem if they radiate enough of their mass into gravitational waves. Sure, it’s unlikely, but it still doesn’t seem like an expected limit. Moreover, the validity of quantum coherence and general relativity shouldn’t depend on the fine details of high-energy conservation laws!

Finally, we could postulate that baryon number or other quantum numbers could be carried away by the gravitational waves themselves. If the wave were absorbed by another black hole, it could even transfer the quantum number into that black hole, for eventual re-emission. This is the most beautiful solution … but also the weirdest. Firstly, this is weird because all existing quantum gravity theories assume a simple massless graviton as the force carrier. How do you encode a baryon or lepton number into a graviton!? Secondly, this is weird because essentially all gravitational wave mass energy will radiate to infinity, dissipating and redshifting with expansion. Where did the baryons go? You can’t redshift the mass of a proton!

I must be misunderstanding ‘t Hooft, but I’m not sure how. (I certainly can’t decipher the paper!)

I wonder if anyone else has thought about this.

The Man Who Knew Something

I saw The Man Who Knew Infinity on opening night Friday. It’s a biopic of Ramanujan, ostensibly. Ramanujan’s mathematical genius has been a staple of the sort of pop science that I’ve been reading since I was a kid, so I was glad to see his story reaching a larger audience.

The plot of the movie is almost indistinguishable from Ramanujan’s Wikipedia entry, with the exception of some extremely fishy subplots involving an almost comically evil mother-in-law, and his young beautiful bride (who in reality was 10 years old when she was married to the 22-year-old Ramanujan. Yikes.).

Ramanujan is the title character, but in the century-long cult of Ramanujan he is always described as unknowable, far beyond ordinary minds, and focused entirely on mathematics to the exclusion of all else. The movie doesn’t really try to resolve this, mostly leaving Ramanujan as an exotic object to be run through a social and academic wringer.

Instead, the movie becomes a biopic of G. H. Hardy, the relatable (if curmudgeonly) British mathematician who becomes Ramanujan’s mentor. By word count, it’s more a biopic of Hardy than of Ramanujan. Luckily, Jeremy Irons plays a subtle and wonderfully entertaining Hardy.

I might wish for some real insight into the soul of Ramanujan, something deeper than just wondering at the mystery of his amazing results. Instead, what I got was a decent portrait of Cambridge University in the midst of World War I, as measured by the reflections of Ramanujan’s splash.

I’ll take it.

James Webb Space Telescope Live!

You can watch the assembly of the James Webb Space Telescope live:

This week they’re taking off the mirror covers.

I don’t really know much about Webb, but a super-cooled origami-folding space telescope the size of a badminton court seems like it’s worth a look.


I just saw Adam Green’s Aladdin, and I encourage all and sundry to at least see the trailer. It might be the weirdest light comedy ever made. To me it feels a lot like an Adult Swim cartoon run through an animation to live action transmogrifier, only to come out half-melted, untranslatable.

The film is chock-full of references to the tip of tech pop culture: the CIA, bitcoin, 3D printers, government transparency, internet folklore, wifi toxicity myths, surveillance drones, binary data and non-binary gender, the works. But none of the references make any sense. In the dreamworld of this movie, a 3D printer is a 5-dimensional guy with an attitude, drones are actual bumblebees, anti-government protests demand that the gods go home, and when someone’s arm is cut off by the CIA, feathers fly out.

Everyone and everything are as insubstantial as a pillow. It feels like a parody of commentary.

I saw the film at The Hole, a downtown art gallery now showing the many cartoon-brought-to-life props and sets used in the filming. I would never have seen a movie like this if the producer weren’t a friend, and I might have enjoyed it more if the room had been a little less echoey, the better to hear the unpredictable dialog, which includes long strings of non-sequiturs, but overall … amazing.


The last time I tried to make something interesting with tahini, some sort of crazy chemistry happened, and I ended up with a substance that could have been used as tile grout, or maybe an atmospheric re-entry heat shield.

I had the bright idea to try another tahini experiment today, and the results were just as weird. Attempting to make a tahini-based salad dressing, I poured the tahini into a bowl, and stirred in maybe half as much balsamic vinegar. The mixture blended … and then froze into a dark wine-colored dough, with a shortbread consistency. Mix two liquids, get a solid!

Then I added water, and stirred some more. The solid melted back into a liquid … and turned back to the golden color of tahini! Even with quite a bit of water it was still more viscous than tahini, more like peanut butter (the natural kind, not the peanut-flavored hydrogenated palm oil that we’ve all been sold).

As salad dressing it actually worked, so all’s well that ends well. Still, I’m totally mystified. So is the rest of the world: I haven’t found any explanation on the internet.

Building a Wahl

I have a Wahl Peanut beard trimmer, which I use to maintain my consistently unkempt appearance. It’s the best trimmer I’ve ever had … and actually the only electric shaving implement I’ve ever owned that didn’t self-destruct within a few months. I’ve had it for over a year, and it’s been working great … until last month.

I brought the trimmer with me to Spain, and plugged it in (with an adapter) in my hotel room. Maybe I thought it was a special shaver outlet. Maybe I’d just forgotten that not all appliances have auto-voltage switching power supplies. Anyway, I figured out my mistake pretty fast when there was a loud bang, a spark, a puff of magic smoke, and all the lights went out. Having embarrassed myself and broken my trimmer, I then had to hunt in the dark for the hotel room’s circuit breaker box.

When I got home, I disassembled the trimmer and was shocked to see how simple it was: just a 120V DC motor, a W04M rectifier, and an RF choke inductor, which had exploded. All through-hole soldered, old school. Replace the inductor, I figured, and everything should be fine.

I called my dad, a real electrical engineer, to ask about this, and without a pause he corrected me: it had to be a short in the rectifier. I took it back to the workshop and sure enough, the rectifier was shorted. It seems that transients when plugging in can exceed the 400 V limit on a W04M rectifier.

I bought a replacement rectifier for about $0.50 plus $12 shipping (sigh), desoldered the old parts and soldered in the new … and it worked!

I think this makes me an even bigger fan of Wahl. I now have empirical proof that some household appliances are still truly repairable.

Three Body

The Three-Body Problem is the first Chinese-language science-fiction novel to win English-language awards in translation. I don’t read as much sci-fi as I used to, mostly because I spend my commute standing up, but while traveling to Morocco and Spain I had plenty of time to read, so I brought a copy along.

Although the plot was inventive, I was principally interested in Three-Body because I’d heard conflicting assessments of whether it contained critical commentary on Chinese government policies. Three-Body was a major popular success in the original Chinese, so it must fall within the Chinese publishing industry’s limits on acceptable content.

Chapter 1 is titled “The Madness Years”, and like much of the novel, it is set in the violent midst of the Cultural Revolution, starting in 1967. In the opening scene, two factions of heavily armed teenagers, in slightly different variations on Red Guard uniforms, are fighting to the death for no discernible reason. In the course of the subsequent chronicle, professors are bludgeoned to death by children for perceived crimes against the revolution, and daughters are ordered to sign false confessions on their parents’ behalf. In short, it is the most direct and sweeping indictment of the Cultural Revolution that I have ever read.

One of the main characters is a scientist driven to nihilism by the evil she has experienced. At a critical moment, she renders a verdict — “our civilization is no longer capable of solving its own problems” — and sets in motion a doomsday process, the end of humanity as we know it.

The book’s other subplot takes place more or less in the present day, dealing with this apocalyptic crisis. In this era, all the world’s governments are working hand in hand, with secret high-level meetings and daring joint clandestine operations. If one of the members of this cabal is less than unimpeachable, it’s only because he’s overzealous in the pursuit of the public good, not corrupt, lazy, or deranged.

The book’s title refers to solar systems that are described as experiencing Stable Eras, when the motions of the planets are reasonably predictable, and Chaotic Eras, when nothing can be predicted. Thematically, then, the Cultural Revolution was an unfortunate Chaotic Era, but today China is experiencing a Stable Era, and no one can say just how long it will last.

I can see why the Chinese establishment might be accepting of this novel, despite its damning history of the Cultural Revolution. From where I stand, it seems to reflect the position of the Chinese Communist Party today. The Chinese government defends its repressive policies as necessary to ensure the maintenance of social and economic stability, and prevent the emergence of any disorder that risks tipping the whole society back into chaos.

Well, that’s just the first book. Turns out, it’s a trilogy. I have no idea what happens next.

Acela seats are not that great.

I traveled to Boston for the weekend on business, and the only appropriate train back was an Acela, the “high speed” trains that shave about 35 minutes off the Boston to New York transit time. (The train is rated to 160 MPH, but only averages 70 MPH between NYC and BOS.) The Acela trains have some nifty tricks, like active gimballing to take turns faster without spilling your coffee.

All Acela seats are “business class”, which in practice seems to mean “not so great”. I’m convinced that the normal Amtrak train seats are nicer: softer, wider, better upholstered, better tables. I can’t explain why this is. Acela cars are actually wider than the standard “Amfleet” cars, according to Wikipedia.

Hey Amtrak: why don’t you just put your normal squishy cloth-covered seats in the Acela?