Doctor Who "Heaven Sent" and Astrophysics

 

[Peter Capaldi as The Doctor]

One of the most disturbing episodes of the Capaldi era of Doctor Who has to be "Heaven Sent." The Doctor is imprisoned in his confession dial by the Time Lords, and is faced with a wall of Azbantium, a mineral that is harder than diamond. Being the Doctor, he recognizes that there is a similarity between his situation and that of the eponymous shepherd boy in the Brothers Grimm tale; but instead of a bird chiseling a mountain of diamond with his beak, the Doctor must punch his way through the Azbantium wall in order to escape. But to make the seemingly impossible task even more daunting, the Doctor is continually killed and must make another copy of himself using a teleportation chamber in order to continue with his hopeless attempt at escape.

Of course, the Doctor does succeed, after beating his head against the wall - metaphorically of course, since it was his fist - for about 4.5 billion years. And Prometheus thought *he* had it bad!

What, you ask, does this have to do with astrophysics?

Thursday morning, during my 8 AM Astrophysics class, we were discussing how the sun creates its energy using nuclear fusion. Basically, hydrogen nuclei collide at very high energies, and through a chain of different steps, eventually create a helium nucleus and energy via 

(thank you Dr. Einstein!)

However, hydrogen nuclei are nothing more than protons, and as you learned in high school science, protons have a positive electric charge, and like charges repel (and opposites attract). So when you try to slam protons together, they resist it - very strongly! In fact, it takes a force stronger than the electromagnetic repulsion - a force literally called the Strong Force - to overcome this and start the fusion cycle. But in order to allow the Strong Force to take over you must get the protons very close indeed, which is very unlikely. The process is likened to trying to walk through a wall. 

[Ouch - too soon!]

While you and I (and Rose and the Doctor) can't walk through a wall, in the realm of subatomic particles like protons, the laws of quantum mechanics demonstrate that there is a tiny (but not zero!) chance that the particle can get through the barrier despite the fact that it doesn't have the energy to climb over it. We call this quantum tunneling.

[Imagine if Sisyphus could manage this]

Each pair of protons in the sun's core lacks enough energy to get over the energy barrier associated with the repulsion of the protons' like electric charges. However, there is a very tiny chance that one can "tunnel" through the energy barrier and find itself close enough to the other for the Strong Force to kick in and for fusion to start. But the probability is very, very, very tiny (about 1 in 300 million - similar to winning the lottery). It's a really good thing that the sun has LOTS of protons in its core, all trying to slam into each other, every second of every day, and enough succeed to power the sun. 

It's an unlikely task, but not impossible, if you are very, very, very patient, like the Doctor.

The connection between fusion and "Heaven Sent" came in the middle of my lecture, while we were calculating how long, on average, an individual proton in the sun's core has to bang against the energy barrier before it breaks through. The answer: 5.4 billion years. I stopped, suddenly remembered the episode, and told the students about the connection (I had remembered the length of time as 5 billion years). 

Of course, the 4.5 billion year sentence was probably chosen by Steven Moffat to align with a different astronomical timing: the current age of the sun and earth.

[And Amelia Pond thought *she* had to wait a long time - snort!]