This year's Nobel Prize in Physics went to three researchers

for major breakthroughs in understanding the strange quantum behavior

of very, very cold materials.

Half of the near one million dollar prize was awarded to David Thouless,

and the other half split between collaborators Michael Kosterlitz and Duncan Haldane.

These theoretical physicists pioneered work in the understanding of phase transitions

of materials at temperatures close to absolute zero.

The familiar phase transitions happen due to heating or cooling of a material.

For example: going from a gas to a liquid to a solid as temperature drops,

and the motion of individual particles in the material gets slower and slower.

However, at extremely cold temperatures, this thermal motion

is so small that quantum effects can dominate the behavior of certain materials.

Thouless, Kosterlitz, and Haldane massively advanced our understanding of these quantum phases

by showing how topology drives this weird behavior.

In particular, in very thin films or strands of these materials.

Topology studies the geometry of shapes under what we call "continuous deformation."

So, changes in the shape that don't break any connected neighboring points.

In topology, holes are very important.

Two objects with the same number of holes are topologically similar.

So a bagel is closer to a coffee mug -- both having one hole -- than it is to a three-holed pretzel.

At extremely low temperatures, the spins of a material's particles tend to line up,

but you get these little twists at certain points:

a vortex around which the spin flips.

These vortices occur in pairs and have some amazing behaviors that resemble the behavior of elementary particles.

Vortices are essentially holes in the spin distribution, and so define the topology of the material.

Haldane and Kosterlitz showed how this topology led to superconductivity in thin materials

and how the splitting of vortex pairs destroyed superconductivity at higher temperatures.

Thouless later demonstrated how differences in topology were the culprit behind

a strange quantized magnetic field observed in the mysterious "quantum hole effect."

These findings will lead to some spectacular applications in the future,

improving our understanding of superconductors and superfluids,

and providing new ways to move charge, spin, and even information around materials.

New advanced electronic components are very likely, and it may even be possible to build a topological

quantum computer that uses entanglement between vortices.

Okay, on to the answer to our Galactic Civilization Challenge Question.

I asked you to figure out some probabilities

regarding the existence of other technological civilizations in our galaxy.

The first question asked you to follow the method used by astrophysicists Adam Frank

and Woodruff Sullivan to answer the following:

if humanity is the only technological civilization to have ever arisen within 100 light years of Earth,

what would that tell us about the chance of such a civilization arising on any one planet?

To answer this, you used Frank and Sullivan's modified version of the Drake Equation

which says that the number of civilizations that will develop in any given region of the universe --

that's this "A" number -- is equal to the number of habitable planets in that region --

that's "N (sub) ast" for "astrophysical factor" -- times the probability that a technological civilization

will form on any given habitable planet -- that's "f (sub) bt" for "bio-technical factor."

And it's that last factor that we want to estimate.

So we're being pessimistic when we say that humanity is the only such civilization to have formed within 100 light years.

This might be wrong, but given the fact that we don't see any evidence for such civilizations, then it can't be too far off,

unless they all wiped themselves out before even making the slightest dent in the local interstellar region.

So let's set "number of tech civilizations" to 1.

If you want to be pedantic, let's say that's the number of civilizations

that are currently detectable or left large scale evidence.

There are a few different ways to get the number of habitable planets within 100 light years.

Let's use the website "solstation" that I linked in the description.

It tells us the number of stars of each given type within a certain distance.

For 100 light years, we have 512 G-Type stars: that's the same type as our sun.

The Frank and Woodruff (Sullivan) paper estimates that around 1 in 5 stars has a terrestrial planet in the habitable zone.

So, in the distance from the star where water can exist as a liquid.

So that means there are around 100 such planets orbiting stars like the sun within 100 light years.

So, in the pessimistic assumption that we are the only technological civilization in the neighborhood,

and that others could only form on planets similar to the Earth,

we get that there's a 1 in 100 chance of this happening on any given planet.

So I'd take that as a very crude estimate of the maximum probability for Earth to have developed us.

No more likely than a 1 in 100 shot. Lucky Earth?

Probably it's lower, though. Frank and Sullivan low-balled the probability and set the "A" value as 0.01, instead of 1.

So that would indicate we're at most a 1 in 10,000 shot.

If you allow that more star types can produce planets with life, then this number just gets smaller.

Now there are several bio-technological factors that seem important in making technologically-capable life.

You need the initial abiogenesis, you need a few important steps in evolution,

you need the conditions to be right for one species to have a runaway growth in brain capacity,

and then you need it to survive long enough to become spacefaring.

So 1 in 100, or even 1 in 10,000 seems reasonable,

but Frank and Sullivan's estimate of 1 in 60 billion for the entire Milky Way seems low.

That tells me that we may be the only advanced-ish civilization to have emerged in the local region,

but probably not within the whole galaxy.

Okay, let's do the extra credit answer.

I asked you to figure out how close the nearest Type II, Dyson Swarm-capable civilization should be,

under the assumption that the weird dimming seen in Tabby's Star is due to a Dyson Swarm

and that it hosts the only such Type II civilization in the Kepler Sample.

There are a few ways to approach this, but let's keep it simple.

There are 100,000 stars in the Kepler Sample.

The Kepler Observatory points only in one direction,

so those stars are spread along a column a few thousand light years long.

So we instead need to ask, "How large a sphere centered on the sun would also contain 100,000 stars?"

There should be, on average, around one Dyson Swarm in those 100,000 stars, also.

Again, using the "solstation" website, we get that there are around 5,000 stars total

per 100 light year radius sphere.

So you'd get 100,000 stars in a 270 light year sphere.

That's a ballpark guess at how close the nearest Type II civilization would be

if Tabby's Star is also a Type II civilization.

Now we've studied all the non-red dwarf stars in that volume pretty thoroughly,

and none of them show any signs of having Dyson Swarms.

Also, if you extend that estimate to the entire Milky Way,

then you get something like 100,000 Type II civilizations in our galaxy.

That's something we probably would have noticed.

Ergo, Tabby's Star probably isn't aliens. Sorry!

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Please e-mail us at pbsspacetime@gmail.com with your name, address, and US t-shirt size

(small, medium, large, etc),

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See you guys next week on Space Time!