compost heaps and ten minutes

 

And at the end he'll blow your minds and it won't be computer science.

 

Thanks.  Nothing like being put on the spot.  I was giving a visiting lecture in a friend's class the other day when he did this to me.  

 

The lecture was going to be fun.  Last year we had talked about the value of deeply understanding failure.  Failure analysis is key to the game of science and experiments are designed in a way that it can be understand and quantified.   I brought up Pixar's post mortem process and he complained this has become rare in software engineering.  Usually the pressure to patch or rewrite is so great that the process can be a bit blind.  We agreed it   would be interesting to teach an updated version of one of my favorite classes  - Engineering Disasters of the 20^th Century.  He took it seriously and created a class -  Engineering Disasters of the 21^st Century - so far...   The end of the course had a few sessions with guest lectures on looming disasters of the 2020s.  

 

 I'm not a particularly fast thinker and I don't multitask well (as it happens no one does).  I finished the the chat  thinking maybe I could just sneak out and find lunch.  No such luck - about three quarters of them stayed put. I had to come up with something.   I decided to talk about a realization that startled me as a teenager.  It still inspires wonder.   That's the rest of the post:

 

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Neutrons are radioactive.  In a bit over ten minutes a bag of factory fresh neutrons will decay into three particles - a proton, an electron and a neutrino (specifically an electron anti-neutrino) by a process called beta minus decay.  Since neutrons make up more than half your mass this should be approximately alarming.  

 

In the twenties people knew about protons and electrons.  A theoretical particle called the neutron was conceived to help explain why the proton and electron didn't crash together.  It wasn't very satisfying and  swept too much under the rug.  Then, in the early 30s, neutrons were discovered and they didn't act like the models that had been proposed.  New physics was necessary.

 

The neutron has a bit more mass than a proton - about a tenth of a percent more.  A free-range neutron has enough energy to decay.  But consider a neutron deep inside an atom. Now it's tightly bound to the nucleus and you need a good deal energy to pull it out.  Enter E = mc². Einstein showed us the total energy of a particle is proportional to mass.  So the mass of a bound neutron is lower than its free-range cousin.   In this case just low enough that it can no longer decay into a proton.  Stable beyond hydrogen are possible. 

 

If not for this small difference and mass-energy equivalence, anything more complicated than hydrogen would decay quickly.  The universe would be entirely different.  No people, no planets, no stars ...  not an interesting place.    

 

It still amazes me.   The stability of a bound neutron is a necessary condition for a non-trivial universe.

 

Up until this time there were just two known forces in Nature:  gravity and electromagnetism.  Beta decay didn't fit and turned out to involve a third force known as the weak force.¹   

 

You've probably heard that nuclear fusion in the Sun turns hydrogen into helium.  The process has a bit of complexity, but for the Sun the major reaction has three main parts.  The first part of the reaction involves the weak force with another type of beta decay - beta plus decay where a proton is turned into a neutron plus a positron (positive charged version of an electron) and an electron neutrino.  The weakness of the force means the process proceeds slowly.    Very slowly - the mean time in the Sun's core in about a billion years.

 

Most of the Sun's fusion takes place inside the core - out to  20% or so of the Sun's radius.  At this distance the density of the Sun is about forty times higher than water and the temperature is way high - about ten million degrees Kelvin (or Centigrade for that matter:-)  Less than that and very little fusion takes place.

 

The power density - watts per cubic meter - is surprisingly low at this distance - about ten watts per cubic meter.  If you move towards to the center few percent of radius where most of the fusion takes place, the power density rises to about 275 watts per cubic meter.   This is surprisingly low!  The average human has a metabolic power density of about 1200 watts per cubic meter.  The core of the Sun is about the same as an average compost heap -- or a lizard.  Sort of  an issue if you want to build a fusion reactor.  You need temperatures and pressures much higher than in the core of the Sun and different reactions to get reasonable power densities

 

We're really lucky .. in fits and starts it took about four and a half billion years  from the time the Earth formed to get to us.  That requires a mostly constant output  slow burning star and we've got one.  Its power density isn't much, but there's a boatload of Sun, so we get enough energy to run the film of life that covers our little blue dot. 

 

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¹ a fourth force is the strong force - it's about a million times stronger than the weak force and holds protons and neutrons together.  Getting into any detail gets into the weeds quickly.