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We called all glider pilots, surfers, physicists, and those who are interested in any of these fields of endeavor. Allan took a break from the sky to answer your questions.

## Q: Jim Chappell

Hi Allan,

A question that has puzzled me for a long time. If a black hole composed of “ordinary” matter coalesced with a black hole derived from “anti-matter” would there be any observable difference from the case of two “ordinary” matter black holes combining?

## A: Allan Adams

That’s a deep question.

in general relativity, the answer is a resounding “no!” in fact, this is elevated to a mathematical theorem called, no kidding, the “no hair theorem”, which says that two black holes with the same mass but built out of different stuff are perfectly indistinguishable (you can’t tell them apart by how they comb their hair — they’re all bald). this isn’t just a good idea, it’s a law! so can you tell whether a black hole was built by collapsing atoms or anti-atoms? by the no hair theorem, no!

quantum mechanics, however, throws a wrench in the gears. one of the most basic postulates of quantum mechanics is that information does not just disappear. this is called “unitarity” for technical reasons, but we might as well call it “unforgetfulness”. again, this isn’t just a good idea, it’s a fundamental law without which the universe would look nothing like the world around us. to physicists, unforgetfulness is as close to bedrock as theory ever gets. and what it says is that the universe can’t possibly forget that we built our black hole out of matter rather than anti-matter, so we must be able to tell the difference.

this conflict is one of the deepest problems in physics. unforgetfulness is a well-demonstrated observed fact about the world and lies at the heart of quantum mechanics. the no-hair theorem is a mathematical fact in general relativity, a theory which is also fabulously well tested (eg, the gps in your phone would never work without including corrections form general relativity). and they directly disagree! so what are we supposed to believe?

the short answer is this: general relativity is wrong. mind you, it’s not stupid — it fits all the data we have, in every regime where we’ve ever tested it, so it’s clearly right about those things. more precisely, it’s an excellent description in many contexts. but it’s not a reliable description in every context — in particular, when quantum effects and gravity are both important, we know from the above that general relativity must not tell the whole story. hence physicists’ interest in understanding quantum gravity.

sadly, building experiments where both gravity and quantum effects are important (eg, forming a black hole with the energy of a mosquito flying at top speed, or, alternatively, colliding two mosquitos traveling at very close to the speed of light) remains beyond current technology by rather a lot. so quantum gravity in any guise remains essentially a theoretical endeavor — with the notable exception of cosmology, where quantum gravity effects in the early universe may prove observable in details of the cosmic microwave backgrounds. time will tell!

so: coming back to your question — is there any observable difference? we know that the answer must be yes! but precisely how we would notice tell remains an interesting open question.

## Q: Marq Love

Hi, Allen. Thanks for taking questions! I have more than I could possibly post here to be feasible, but I would like to ask – How is the best way to get into physics? I’m very interested in Quantum and Astrophysics. I’ve been studying the history of mathematics, which is more than a little tedious. I also have a large book on algebra. Am I going in the right direction? I have a lot of theories of my own, but I understand that you can’t really get into physics without a firm understanding of Math and Algebra. Is that correct?

## A: Allan Adams

Math is the the language of physics, and you need to become fluent to hold a sophisticated conversation. that’s not to say physics is about math, any more than polish literature is about the polish language. but if you want to study polish literature, it’s pretty important to learn the language.

(nb, math, like polish, it’s full of beautiful poetry that simply does not translate.)

now, you can certainly do a lot without fancy math! you don’t need to know algebraic K-theory to understand waves on the ocean. but the greater your command of math, the easier it is to understand more abstract physics.

## Q: Casner

Have you analyzed the physics of thermalling? It would be nice to have an equation for the strength of the thermal, the performance numbers for the glider etc. to produce the optimum bank angle.

## A: Allan Adams

Interesting question. not in detail, but other people certainly have. the problem with a simple equation is that different thermals, and even different sections of the same thermal, can have very different properties, all of which are hard to detect without flying through them. apart from some basic rules of thumb about speed to fly and bank angle (45 is your friend), it would be hard for even a fairly fancy formula to beat a minimally experienced pilot flying by the seat of their pants. experience is invaluable. that said, with an apollo-era supercomputer in the cockpit (aka a smartphone), you can do some nice real-time analysis to help core and optimize a thermal (several software packages do this, eg win-pilot, seeyou, etc).

nb, way more important than computing the exactly optimal bank angle is holding a steady bank angle. ditto airspeed. if you let those fluctuate, you’re not flying a circle, and that makes it very hard to stay in the core of the thermal. precision is huge.