The Nobel prize in physics this year went to black holes.

Generally speaking.

Specifically it was shared by the astronomers who revealed  to us the Milky Way’s central black hole and by Roger Penrose, who proved that in general relativity, every black hole contains a place of   infinite gravity - a singularity.

But the true  impact of Penrose’s singularity theorem   is much deeper - it leads us to the limits Einstein’s  great theory and to the origin of the universe.

Black holes have haunted our  theories of gravity since the 1700s.

When John Mitchell and Pierre-Simon Laplace explored Newton’s law of universal gravitation,   they realized the possibility of a  star so massive that it would prevent   even light from escaping its surface.

Few people took these “dark stars” seriously - especially   when we learned that light didn’t really behave as Mitchell, Laplace, and even Newton assumed.

And then of course we figured out that not  even gravity worked as Newton had told us.

In 1915, Newtonian gravity was superseded by Einstein’s general theory of relativity.

But that wasn’t the end of black holes  or dark stars; it was their resurrection.

Karl Schwarzschild solved the equations of general relativity soon after Einstein published them,   revealing that a sufficiently dense ball of matter would be surrounded by a surface where time froze.

Beneath that “event horizon” all matter, light, space itself was doomed to fall inwards towards a central   point.

At that so-called singularity, the  gravitational field becomes infinite.

But   physicists tend to be dubious about infinities - more often than not they turn out to be a glitch   in the theory.

Einstein himself doubted that  the black holes could form in the real universe,   and even if they could, they certainly  shouldn’t harbor singularities.

After all, Schwarzschild’s solution  didn’t say anything about HOW   a clump of matter could reach the densities  high enough to produce an event horizon - nor   even whether such dense matter would  really contract into a single point.

It only showed that, once so-contracted,  the resulting black hole was stable.

But the intriguing and terrifying possibility  that black holes might really exist   inspired some of our greatest minds  to find ways they could exist.

In 1939 Robert Oppenheimer and Hartland  Snyder showed that a perfectly spherical,   perfectly smooth ball of dust could  collapse into a Schwarzschild black hole,   singularity and all.

Makes sense - if all  particles are falling directly towards each   other on a perfect collision course, the  math has to land them all in the center.

But this didn’t convince anyone - what in our universe is perfectly spherical or smooth?

It was assumed that normal, messy objects could  never collapse into a perfect point.

Surely any   tiny deviation from spherical symmetry would cause particles to miss each other at the last instant.

That might, for example, result in the infalling matter flying back outwards again.

So, for   example, a star that collapses at the end of its life might entirely rebound as a giant explosion.

And now we come to the mid 1960s.

Roy Kerr has just figured out how to describe a rotating black   hole in Einstein’s theory.

In it, the central point of infinite gravity is spun out into a   ring - but it was a singularity nonetheless.

The Kerr solution was still highly symmetrical,   so the same old arguments held against  these things forming in reality.

It took a young Camridge physicist named Roger Penrose to prove that black hole singularities   were utterly unavoidable in Einstein’s theory.

Penrose’s singularity paper is   deceptively short - just a couple of pages in Physical Review Letters   However that brevity is deceptive.

But some say this 1965 paper produced the first truly   new advances in general relativity, half  a century after the theory was published.

So what did Penrose discover?

How did he manage to peer into the mathematical heart of the black   hole?

And why did this deserve a Nobel prize?

Penrose set out to show that an event horizon   and a singularity would form for any distribution of matter, no matter how messy, as long as that   matter was compacted into a small enough volume of space.

At least according to general relativity.

And his singularity theorem succeeded in that - but it succeeded in so much more, as we’ll see.

Today I’m going to give you a sense  of Penrose’s breakthrough, and why it   revolutionized general relativity.

For a more complete picture I can refer you to a good grad   program in physics - but let’s see how much we can do in a handful of minutes.

Basically,   Penrose showed that according to Einstein’s theory plus a couple of assumptions,   black holes must contain singularities.

And this is true regardless of how the black hole formed.

He did it in a clever way - by showing that the grid of spacetime literally comes to an end inside   a black hole.

In general relativity we map the fabric of spacetime with gridlines that we call   geodesics.

These are the paths traveled by an object in free fall in a gravitational field.

The path traveled by a ray of light is  called a null geodesic.

They are the   gold-standard for gridding up spacetime.

Null geodesics traveling into or past any   gravitational field tend to be drawn  together - to converge, or be focused.

This is gravitational lensing.

Gravitational  fields produced by regular matter   always produce this convergence.

It would take negative mass or negative pressure   to cause light rays to diverge.

This focusing property of gravitational fields is called the   weak energy condition of general relativity, and it almost certainly holds in black holes.

So null geodesics traveling down into a  black hole are going to converge - no big   surprise there.

But the crazy thing about  black holes is that null geodesics beneath   the event horizon that are trying  to travel outwards also converge.

Actually, the whole idea of the event horizon is tricky here - there are multiple ways to   define an event horizon depending on where you sit compared to the black hole.

Penrose came up with a   more precise idea - that of the trapped surface.

That’s any closed surface that has this property   that null geodesics - and so any light - pointed outwards from the surface actually move downwards.

Any closed surface “inside” the black  hole is considered a trapped surface.

Penrose showed that at least some of  the parallel null geodesics leaving any   trapped surface, either up or down, had  to converge.

Had to cross each other and   come to a focus.

And he also showed that, for rays departing a trapped surface,   it’s meaningless to continue to track  the progression of space and time   beyond one of these focal points.

In other  words, space and time end at the focus.

I can only give you a vague sense of why this is the case.

Penrose proves it by showing that   impossible contradictions arise otherwise.

Imagine a pair of light rays emerging from the same point   and then focused back towards each other.

Both are equally the shortest path between those points.

Now imagine extending one of those paths just a little.

The distance from the starting point   to the end of that extension is still the  same whether we take the left or right arc.

But now we can find an even shorter path  - one obtained by smoothing out this kink.

And that has to be shorter  than both original paths.

So there’s the contradiction - we found a shorter path than the supposedly shortest paths.

This   tells us that the null geodesic does not continue past the focal points AS a null geodesic.

Null   geodesics terminate at these focal points within a black hole.

We call this geodesic incompleteness.

Because they are the grid we use to map space and time, geodesic incompleteness means space   and/or time end at these termination points.

It doesn’t just freeze, they literally cease.

Let’s try an analogy - the geodesics we  use to map the surface of the earth are   longitude and latitude.

Lines of longitude  come to a focus at the north and south poles.

A line of longitude is the shortest distance  to the north pole - the quickest way for you   to increase your “northness”.

But if you  travel past the north pole you’re no longer   on the shortest path to any new point that you reach, and at the same time you reached the end   of north - maxed your northness - and started traveling south again.

Well, in a black hole you   don’t reach the end of north, you reach the end of time or space.

They are dead-ends to reality.

So yeah, geodesic incompleteness is pretty freaky.

Prior to Penrose it was generally   held that geodesics could be traced  indefinitely into the past and future.

All of spacetime should be a smooth, if  curved structure - a manifold - cleanly   defined everywhere.

Penrose showed that  space and time could have holes in it.

These holes tend to be associated with infinite spacetime curvature - infinite gravity.

In other   words, singularities.

Penrose didn’t actually show what type of singularity would form in a   black hole - just that some type was inevitable.

In a Schwarzschild black hole, time ceases at the   point-like central singularity, while in Kerr  black holes space ends at the ring singularity.

With Roger Penrose’s discovery, black holes and the singularities within had to be taken more   seriously.

But the true utility of his singularity theorem went well beyond black holes.

Just after   Penrose published his paper, a young graduate student was inspired to apply the singularity   theorem in a very different way.

That student was Stephen Hawking.

In his PhD thesis Hawking   showed that you could use the same arguments to investigate the behavior of geodesics traced   backwards through our entire universe towards the Big Bang.

Now at this point we’d known for 40   years that the universe is expanding, and probably started in a much denser state.

In fact the latter   had been verified by the detection of the cosmic microwave background just the prior year in 1964.

We knew that geodesics converge towards each other looking backwards in time, but doesn’t mean they   had to all meet.

They could, for example, miss and weave past each other in an insanely dense but not   infinitely dense knot.

This might be the case if the universe underwent cyclic big bounces.

Hawking showed that Penrose’s arguments  about black holes also applied to the   universe - that geodesics traced backwards in an expanding universe had to truly meet - to   form a singularity, which meant they had to terminate.

Time itself could not be traced   beyond this point - which suggested that time really started at the Big Bang.

Hawking and   Penrose further developed these ideas together, publishing a clean proof in 1970.

We now call the   combined proofs of geodesic incompleteness the Penrose-Hawking Singularity Theorems.

This is probably the right time to tell you how the singularity theorems must be wrong - or at   least point to wrongness.

They give us the  predictions of pure general relativity,   and assume the various energy conditions.

We know that general relativity is not the entire   picture - and this might be the most powerful result of the singularity theorems.

Remember,   we should be dubious when we see infinities and singularities in our theories.

Penrose   showed us that singularities are unavoidable in general relativity, and so GR must break down at   those points.

The resolution must be the union of general relativity and quantum mechanics - a   theory of quantum gravity, from which both quantum mechanics and relativity are just approximations.

Such a theory may tell us what really happens to geodesics when they approach and merge.

And even,   hopefully, what geodesics - and space and time - really are.

Penrose’s singularity   theorem is a big part of what set us on the path to this yet-undiscovered greater theory.

Roger Penrose won this year’s Nobel prize  in physics for his contributions to our   theoretical understanding of black holes.

He shared it with Andrea Ghez and Reinhard Genzel,   who proved to us the existence of the Milky Way’s central supermassive black hole by monitoring the   crazy orbits of stars in the galactic core.

The work of Ghez and Genzel and other astronomers   have guaranteed the existence of black holes, which means their are places in the universe where   general relativity must break down or produce singularities.

Nobel-worthy insights, and all from   some bright ideas about how light rays travel and terminate at the singular dead ends of spacetime.