A poem for Stephen Hawking

Posted on March 14, 2018 by preskill

Everyone is talking
About Stephen Hawking.
My good friend
Explained how time can end.
And clued us in
On how time can begin.

Always droll,
He spoke about a hole:
“Now, wait a minute, Jack,
A black hole ain’t so black!”

Those immortal words he said,
Which millions now have duly read,
Hit physics like a ton of bricks.
Well, that’s how Stephen got his kicks.

Always grinning through his glasses,
He brought science to the masses,
Displayed a rare capacity
For humor and audacity.

And that’s why, on this somber day,
With relish we can gladly say:
“Thanks, Stephen, for the things you’ve done.
And most of all, thanks for the fun!”

And though there’s more to say, my friend,
This poem, too, must, sadly, end.

Zoe Saldana Answers the Quantum Call

Posted on December 16, 2016 by Jose M Gonzalez Jr

Stephen Hawking & Zoe Saldana try to save Simon Pegg’s cat

Watch Quantum Is Calling with Zoe Saldana, Stephen Hawking, Keanu Reeves, Paul Rudd, Simon Pegg, and John Cho.

We are on the verge of a quantum revolution. Like in the days of the space race, technology has brought an impossibly distant frontier to our doorstep. Just over 17 years ago Michael Crichton wrote a parallel universe-hopping adventure, Timeline, whose fundamental transportation technology required the advent of quantum computing – a concept that was still only theoretical at the time. Today, IBM’s five-quantum bit (or qubit) array is at the fingertips of anyone within reach of the cloud. Google is building a fifty-qubit array. Microsoft is bankrolling a brain trust that will build a quantum computer based on topological qubits. Intel is investing $50 million on spin qubit technology. The UK has announced a £270 million program, and the EU a €1 billion program, to develop quantum technologies. And even more quantum circuits are on the way; the equivalent of competing classes of space shuttles. Only these crafts aren’t meant to travel through space, or even time. They travel through the complete unknown. Qubits fluctuate between the infinite universes of possibility, their quantum states based inherently on uncertainty. And the best way to harness that seemingly unlimited computing power, and take the first steps into the quantum frontier, is through the elusive concept of entanglement.

So then, the quantum crafts are ready; the standby lights on their consoles blinking in a steady yellow cadence. What we’re missing are the curiosity-driven pilots willing to grapple with the uncertain and unpredictable.

The quantum mechanics property of entanglement was discovered by Albert Einstein, Boris Podolsky, and Nathan Rosen and soon after described in a famous 1935 paper. Einstein called it “spooky action at a distance.” Virtually all of his contemporaries, including Edwin Schrödinger who coined the term “entanglement”, and the entire subsequent generation of physicists would struggle with this paradox. Although their struggles would be necessary to arrive at this particular moment in time, this precipice, their collective and prodigious minds were, and remain to be, handcuffed by training and experiences rooted in a classical understanding of the laws of nature – derived from phenomena that can be seen or felt, either directly or indirectly. Quantum entanglement, on the other hand, presents a puzzle of a fundamentally abstract nature.

Paul Rudd & Stephen Hawking chatting it up

When Paul Rudd defeated Stephen Hawking in a game of quantum chess – a game built from the ground up with a quantum mechanical set of moves leveraging superposition and entanglement – our intent was to suggest that an entirely new generation of physicists can emerge with an intuitive understanding of entanglement, even before having to dip their toes in mathematics.

Language, Young Lady

Following up on Anyone Can Quantum, the challenges were to (1) further introduce and elaborate on quantum entanglement and (2) reach a wider audience, particularly women. Coming from a writer’s perspective, my primary concern was to make the abstract concept of entanglement somehow relatable. Popular stories, at their most basic, are told through interactions between people in relationships. Only through relational interactions can characters be challenged enough to affect a change in behavior, and as a result support a theme. Early story concepts evolved from the idea that any interaction with entanglement would result in a primary problem of miscommunication. Entanglement, in any form approaching personification, would be fully alien and incomprehensible. Language then, I decided, would become the fabric by which we could create a set of interactions between a human and entanglement.

Dr. Louise Banks (Amy Adams) & Ian Donnelly (Jeremy Renner) in Arrival

This particular dynamic was tackled in the recent movie Arrival. There, the fictional linguist Dr. Louise Banks is tasked with translating the coffee-ring-stain sign language of a visiting alien civilization before one of the world’s many nervous armies attacks them and causes an intergalactic incident. In the process of decoding the dense script, the controversial Sapir-Whorf theory is brought up introducing the idea that language shapes the way people think. While this theory may or may not hold snow, I am still impressed with the notion that a shared, specific, and descriptive language is necessary to collaborate and innovate. This impression is supported by my own experience in molecular and cell biology research in which communicating new findings always requires expending a tremendous amount of energy crafting a new and appropriate set of terms, or in other words, an expansion of the language.

Marvel To The Rescue

The Tesseract & Groot in Guardians of the Galaxy

To drive their building, multi-threaded Infinity Stones storyline, the Marvel Cinematic Universe (MCU) has been fortuitously bold in broaching quantum physics concepts and attempting to ground them in real science, taking advantage of the contacts available through the Science & Entertainment Exchange. Through these consultations, movies like Thor and Ant-Man have already delivered to a wide and diverse audience complex concepts such as Einstein-Rosen bridges (wormholes) and the Quantum Realm.

The Ant-Man consultation, in particular, resulted in a relationship between IQIM’s own Spyridon Michalakis (aka Spiros) and Ant-Man himself, Paul Rudd. This relationship was not only responsible for Anyone Can Quantum, but it was also the reason why Spiros was invited to be a panelist at the Silicon Valley Comic Con earlier this year, where he was interviewed by science journalist Zuberoa “Zube” Marcos of the global press outfit, El Pais, a woman who would end up playing a central role in getting Quantum Is Calling off the ground.

Leonard Susskind

Juan Maldacena

So the language of quantum physics was being slowly introduced to a wider, global population thanks to the Marvel films. It occurred to us that we had the opportunity to explain some of the physics concepts brought up by the MCU through the lens of quantum physics, and entanglement in particular. The one element of the MCU storylines that was most attractive to us was the Tesseract and its encased Space Stone. It was the first of the Infinity Stones introduced (in Captain America: The First Avenger) and the one that drove the plot of The Avengers, culminating in the creation of a wormhole over Manhattan. For Spiros, the solution was simple: In order to create wormholes, the exotic matter comprising the Space Stone would likely have to exploit entanglement, as described in a conjecture, dubbed “ER=EPR”, published by Leonard Susskind and Juan Maldacena in 2013.

The USS Enterprise (NCC-1701) in the Star Trek TOS episode “The Immunity Syndrome”

Finding Our Star

The remaining challenge was to find the right actress to deliver the new story. The earliest version of our story (back in June, 2016) was based on the crew of the Starship Enterprise encountering an alien creature that was the embodiment of entanglement (a.k.a The Flying Spaghetti Monster), a creature that attempted communication with Earthlings by reciting sound bytes originating from past Earth radio transmissions. In this story iteration, Chief communications officer Uhura would have used her skills to translate the monster’s message amidst rising tension (just like in Arrival).

Zoe Saldana as Lt. Nyota Uhura

In the subsequent revisions to the story we had to simplify the script and winnow down the cast. We opted to lean on Zoe Saldana’s Uhura. Her character could take on the role of captain, communications officer, and engineer. Zoe was already widely known across multiple sci-fi franchises featuring aliens (namely Star Trek, Guardians of the Galaxy, and Avatar) and her characters have had to speak in or translate those languages.

Zoe = Script

But before approaching Zoe Saldana – and at that point in time, we had no idea how to go about that – we needed to complete a script. Two other incredible resources were available to us: the voices of Dr. Hawking and Keanu Reeves; and we had to make all three work together in a unique comedy – one that did not squander the involvement of either voice, but also served to elevate the role of Zoe.

Stephen Hawking

Keanu Reeves

Even in the first version of the story it was my intent to have Keanu Reeves provide the voice for entanglement, expressed through the most alien sounding languages I could imagine. To compress the story to fit our budget we were forced to narrow the list of languages to two, and I chose Dothraki and Navajo. The role of Keanu’s character was to test, recruit, and ultimately invite Zoe Saldana to enter and experience entanglement in the Quantum Realm. Dr. Stephen Hawking would be the reluctant guide that helps Zoe interpret the confusing clues embedded within the Dothraki and Navajo to arrive at the ER=EPR conjecture.

As for the riddle itself, I chose to use two poems from Through the Looking Glass (and What Alice Found There), The Walrus and The Carpenter as well as Haddock’s Eyes, as the reference material, so that those savvy enough to solve even half the riddle on their own would have a further clue pointing them to the final answer.

Simon Pegg’s cat, Schrodinger (not his actual cat)

The disappearance of Simon’s cat, Schrödinger, had a tripartite function of (a) presenting an inciting incident that urged Zoe to subject herself to the puzzle-solving trial, which we called the Riddle of the Tesseract, (b) to demonstrate the risk of touching the Tesseract and the gravity of her climactic choice, and (c) invoking Schrödinger’s famous thought experiment to present the idea that, in the Quantum Realm, the cat and Zoe are both dead and alive, an uncertainty.

The story was done. And it looked good on paper. But the script was just a piece of paper unless we got Zoe Saldana to sign on.

Zuberoa Marcos

Zoe = Zube

For weeks, Spiros worked all of his connections only to come up empty. It wasn’t until he mentioned our holy quest to Zube (from El Pais and Silicon Valley Comic Con) during an unrelated Skype session that he had the first glimmer of hope, even kismet. Zube had been working on arranging an interview with Zoe for months, an interview that would be taking place three days later in Atlanta. Without even a second thought, Spiros purchased a plane ticket and was on his way to Atlanta two days later. Watching the interview take place, he heard Zoe answer one of Zube’s question about what kind of technology interested her the most. It was the transporter, the teleportation machine used by the crew of the Enterprise to shift matter to and from surfaces of alien planets. This was precisely the kind of technology we were interested in describing at a quantum level! Realizing this was the opening we needed, Zube nodded over to Spiros and made the introductions.

It turns out Zoe had been fascinated by science fiction since her early childhood, being particularly obsessed with Frank Herbert’s Dune. Moreover, she was interested in playing the role of our lead character. In the weeks that followed, communication proceeded through managers in an attempt to nail down a filming date.

Mariel, Zoe, and Cicely Saldana

The Dangers of Miscommunication

I probably don’t need to remind you that Zoe Saldana is a core component of three gigantic franchises. That means tight schedules, press conferences, and international travel. Ultimately Zoe said that her travel commitments wouldn’t allow her to film our short. It was back to square one. We were dead in the water. The script was just a piece of paper.

However, for some reason, Spiros and Zube were not willing to concede. Zube found out about Zoe Saldana’s production company Cinestar and got in contact with coordinator Diego Gonzalez, to set up a lunch meeting. At lunch, Diego informed Zube and Spiros that Zoe really wanted to do this, but her team was under the impression that filming for our short video had to take place the week Star Trek: Beyond was to be released (Zoe was arguably busier than the POTUS during that week). Spiros informed Cinestar that we would accommodate whatever date Zoe could be available. Having that hurdle removed paved the way for a concrete film date to be set, October 25th. And now the real work began.

Simon Pegg in Shaun of the Dead

Finding Common Language

We had set the story inside Simon Pegg’s house and the script included voice-over dialogue for the superstar, but we had yet to even contact Simon. We had written in a part with Paul Rudd on a voicemail message. And we had also included a sixth character that would knock on the door and force Zoe to make her big decision. On top of that I had incorporated Dothraki and Navajo versions of century-old poems that had yet to be translated into those two languages. While Spiros worked on chasing down the talent, I nervously attempted to make contact with experts in the two languages.

David J. Peterson

I remember watching a video of Prof. David J. Peterson, creator of the Dothraki language for HBO’s Game of Thrones, speaking at Google about the process of crafting the language. Some unknown courage surfaced and I hunted down contact information for the famous linguist. I found an old website of his, an email address, and sent and inquiry at about midnight pacific standard time on October 14th, the day before my birthday. Within 45 minutes David had responded with interest in helping out. I was floored. And I couldn’t help geeking out. But more importantly this meant we would have the most accurate translation humanly possible. And when one is working on behalf of Caltech you definitely feel the pressure to be above reproach, or unsullied ;).

Keanu Reeves, Jennifer Wheeler, a pumpkin, a highlighter & my left arm

Finding a Navajo translator was comparatively difficult. A couple days after receiving Dr. Peterson’s email, I was in Scottsdale, AZ with my brother. I had previously scheduled the trip so that I could be in attendance at a book-signing featuring two of my favorite authors, as a birthday gift to myself. The event was held at the Poisoned Pen bookstore where many other local authors would regularly hold book-signings. While I was geeking out over meeting my favorite writing duo, as well as over my recent interaction with David Peterson, I was also stressed by the pressure to come through on an authentic Navajo translation. My brother urged me to ask the proprietors of the Poisoned Pen for any leads. And wouldn’t you know it, they had recently hosted a book-signing for the author of a Code Talkers book, and she was local. A morning of emails led to Jennifer Wheeler. We had struck gold. Jennifer had recently overseen Navajo translations of Star Wars: A New Hope and Finding Nemo, complete with voice-overs. There was probably nobody more qualified in the world.

Keanu Reeves as Ted “Theodore” Logan in Bill & Ted’s Excellent Adventure

So it turns out that Navajo is a much more difficult language to translate and speak than I had anticipated. For instance, there are over a hundred vowel sounds. So even though the translation was in good hands, I would be imposing on Keanu Reeves one of the greatest vocal challenges he would ever undertake. Eventually I arranged to have Jennifer on hand during Keanu’s voice recording. Here’s what he had to record (phonetically):

Tsee /da / a / ko / ho / di / say / tsaa, / a / nee / di

aɫ / tso / n’ / shay / ch’aa / go

Echo Papa Romeo / do / do / chxih / da

Bi / nee / yay / bi / zhay / ho / lo / nee / bay / do / bish / go.

Alex Winter & Zoe Saldana hard at work

Filming Day

After months of planning and weeks of script revisions, filming finally happened at an opulent, palatial residence in the Hollywood Hills (big props to Shaun Maguire and Liana Kadisha for securing the location). Six cats. Three trainers. Lights. Cameras. Zube. Zoe Saldana actually showed up! Along with her sisters, Cinestar, and even John Cho! Spiros had gotten assurances from Simon Pegg that he would lend his name and golden voice so we were able to use the ridiculous “Simon’s Peggs” wood sign that we had crafted just for the shoot. Within a few busy hours we were wrapped. All the cats and props were packed and back in LA traffic, where we all seem to exist more often than not. Now the story was left to the fate of editing and post-production.

In Post

Unlike the circumstances involved with Anyone Can Quantum, for which there was a fast approaching debut date, Spiros and myself actually had time to be an active part of the post-production process. Alex Winter, Trouper Productions, and STITCH graciously involved us through virtually every step.

One thing that became quite apparent through the edits was the lack of a strong conclusion. Zoe’s story was designed to be somewhat open-ended. Although her character arc was meant to reach a conclusion with the decision to enter the Quantum Realm, it was clear that the short still needed a clear resolution.

What Seraph looks like as code in the Matrix Reloaded

Through much debate and workshopping, Spiros and I finally arrived at bookend scenes that took advantage of Keanu Reeve’s emblematic representation of, and inescapable entanglement with, The Matrix. Our ultimate goal is to create stories that reflect the quantum nature of the universe, the underlying quantum code that is the fabric from which all things emerge, exist, and interact. So, in a way, The Matrix wasn’t that far off.

Language Is Fluid

LIQUi|> (“liquid”), or Language-Integrated Quantum Operations, is an architecture, programming language, and tools suite designed for quantum computing that is being developed by the Microsoft team at Quantum Architectures and Computation Group (or QuArC). Admittedly taking a few liberties, on Spiros’s advice I used actual LIQUi|> commands to create a short script that established a gate (or data structure) that I called Alice (which is meant to represent Zoe and her location), created an entanglement between Alice and the Tesseract, then teleported the Tesseract to Alice. You’ll notice that the visual and sound effects are ripped right from The Matrix.

This set up the possibility of adapting Neo’s famous monologue (from the end of the original Matrix) so we could hint that Zoe was somewhere adrift within the quantum code that defines the Quantum Realm. Yes, both Spiros and I were in the studio when Keanu recorded those lines (along with his lines in Dothraki and Navajo). Have I mentioned geeking out yet? An accompanying sequence of matrix code, or digital rain, had to be constructed that could accommodate examples of entanglement-related formulas. As you might have guessed, the equations highlighted in the digital rain at the end of the short are real, most of which came from this paper on emergent space (of which Spiros is a co-author).

Keanu Reeves & Keanu

Listen To Your Friend Keanu Reeves. He’s A Cool Dude.

With only a few days left before our debut date, Simon Pegg, Stephen Hawking and Paul Rudd all came through with their voice-over samples. Everything was then stitched together and the color correction, sound balancing, and visual effects were baked into the final video and phew. Finally, and impossibly, through the collaboration of a small army of unique individuals, the script had become a short movie. And hopefully it has become something unique, funny, and inspiring, especially to any young women (and men) who may be harboring an interest in, or a doubt preventing them from, delving into the quantum realm.

Quantum Chess

Posted on February 15, 2016 by Chris Cantwell

Two years ago, as a graduate student in Physics at USC, I began work on a game whose mechanics were based on quantum mechanics. When I had a playable version ready, my graduate adviser, Todd Brun, put me in contact with IQIM’s Spiros Michalakis, who had already worked with Google to design qCraft, a mod introducing quantum mechanics into Minecraft. Spiros must have seen potential in my clunky prototype and our initial meeting turned into weekly brainstorming lunches at Caltech’s Chandler cafeteria. More than a year later, the game had evolved into Quantum Chess and we began talking about including a video showing some gameplay at an upcoming Caltech event celebrating Feynman’s quantum legacy. The next few months were a whirlwind. Somehow this video turned into a Quantum Chess battle for the future of humanity, between Stephen Hawking and Paul Rudd. And it was being narrated by Keanu Reeves! The video, called Anyone Can Quantum, and directed by Alex Winter, premiered at Caltech’s One Entangled Evening on January 26, 2016 and has since gone viral. If you haven’t watched it, now would be a good time to do so (if you are at work, be prepared to laugh quietly).

So, what exactly is Quantum Chess and how does it make use of quantum physics? It is a modern take on the centuries-old game of strategy that endows each chess piece with quantum powers. You don’t need to know quantum mechanics to play the game. On the other hand, understanding the rules of chess might help [1]. But if you already know the basics of regular chess, you can just start playing. Over time, your brain will get used to some of the strange quantum behavior of the chess pieces and the battles you wage in Quantum Chess will make regular chess look like tic-tac-toe [2].

In this post, I will discuss the concept of quantum superposition and how it plays a part in the game. There will be more posts to follow that will discuss entanglement, interference, and quantum measurement [3].

In quantum chess, players have the ability to perform quantum moves in addition to the standard chess moves. Each time a player chooses to move a piece, they can indicate whether they want to perform a standard move, or a quantum move. A quantum move creates a superposition of boards. If any of you ever saw Star Trek 3D Chess, you can think of this in a similar way.

Star Trek 3D Chess

There are multiple boards on which pieces exist. However, in Quantum Chess, the number of possible boards is not fixed, it can increase or decrease. All possible boards exist in a superposition. The player is presented with a single board that represents the entire superposition. In Quantum Chess, any individual move will act on all boards at the same time. Each time a player makes a quantum move, the number of possible boards present in the superposition doubles. Let’s look at some pictures that might clarify things.

The Quantum Chess board begins in the same configuration as standard chess.

All pawns move the same as they would in standard chess, but all other pieces get a choice of two movement types, standard or quantum. Standard moves act exactly as they would in standard chess. However, quantum moves, create superpositions. Let’s look at an example of a quantum move for the white queen.

In this diagram, we see what happens when we perform a quantum move of the white queen from D1 to D3. We get two possible boards. On one board the queen did not move at all. On the other, the queen did move. Each board has a 50% chance of “existence”. Showing every possible board, though, would get quite complicated after just a few moves. So, the player view of the game is a single board. After the same quantum queen move, the player sees this:

The teal colored “fill” of each queen shows the probability of finding the queen in that space; the same queen, existing in different locations on the board. The queen is in a superposition of being in two places at once. On their next turn, the player can choose to move any one of their pieces.

So, let’s talk about moving the queen, again. You may be wondering, “What happens if I want to move a piece that is in a superposition?” The queen exists in two spaces. You choose which of those two positions you would like to move from, and you can perform the same standard or quantum moves from that space. Let’s look at trying to perform a standard move, instead of a quantum move, on the queen that now exists in a superposition. The result would be as follows:

The move acts on all boards in the superposition. On any board where the queen is in space D3, it will be moved to B5. On any board where the queen is still in space D1, it will not be moved. There is a 50% chance that the queen is still in space D1 and a 50% chance that it is now located in B5. The player view, as illustrated below, would again be a 50/50 superposition of the queen’s position. This was just an example of a standard move on a piece in a superposition, but a quantum move would work similarly.

Some of you might have noticed the quantum move basically gives you a 50% chance to pass your turn. Not a very exciting thing to do for most players. That’s why I’ve given the quantum move an added bonus. With a quantum move, you can choose a target space that is up to two standard moves away! For example, the queen could choose a target that is forward two spaces and then left two spaces. Normally, this would take two turns: The first turn to move from D1 to D3 and the second turn to move from D3 to B3. A quantum move gives you a 50% chance to move from D1 to B3 in a single turn!

Let’s look at a quantum queen move from D1 to B3.

Just like the previous quantum move we looked at, we get a 50% probability that the move was successful and a 50% probability that nothing happened. As a player, we would see the board below.

There is a 50% chance the queen completed two standard moves in one turn! Don’t worry though, things are not just random. The fact that the board is a superposition of boards and that movement is unitary (just a fancy word for how quantum things evolve) can lead to some interesting effects. I’ll end this post here. Now, I hope I’ve given you some idea of how superposition is present in Quantum Chess. In the next post I’ll go into entanglement and a bit more on the quantum move!

Notes:

[1] For those who would like to know more about chess, here is a good link.

[2] If you would like to see a public release of Quantum Chess (and get a copy of the game), consider supporting the Kickstarter campaign.

[3] I am going to be describing aspects of the game in terms of probability and multiple board states. For those with a scientific or technical understanding of how quantum mechanics works, this may not appear to be very quantum. I plan to go into a more technical description of the quantum aspects of the game in a later post. Also, a reminder to the non-scientific audience. You don’t need to know quantum mechanics to play this game. In fact, you don’t even need to know what I’m going to be describing here to play! These posts are just for those with an interest in how concepts like superposition, entanglement, and interference can be related to how the game works.

The Science that made Stephen Hawking famous

Posted on November 5, 2014 by shaunmaguire

In anticipation of The Theory of Everything which comes out today, and in the spirit of continuing with Quantum Frontiers’ current movie theme, I wanted to provide an overview of Stephen Hawking’s pathbreaking research. Or at least to the best of my ability—not every blogger on this site has won bets against Hawking! In particular, I want to describe Hawking’s work during the late ‘60s and through the ’70s. His work during the ’60s is the backdrop for this movie and his work during the ’70s revolutionized our understanding of black holes.

(Portrait of Stephen Hawking outside the Department of Applied Mathematics and Theoretical Physics, Cambridge. Credit: Jason Bye)

As additional context, this movie is coming out at a fascinating time, at a time when Hawking’s contributions appear more prescient and important than ever before. I’m alluding to the firewall paradox, which is the modern reincarnation of the information paradox (which will be discussed below), and which this blog has discussed multiple times. Progress through paradox is an important motto in physics and Hawking has been at the center of arguably the most challenging paradox of the past half century. I should also mention that despite irresponsible journalism in response to Hawking’s “there are no black holes” comment back in January, that there is extremely solid evidence that black holes do in fact exist. Hawking was referring to a technical distinction concerning the horizon/boundary of black holes.

Now let’s jump back and imagine that we are all young graduate students at Cambridge in the early ‘60s. Our protagonist, a young Hawking, had recently been diagnosed with ALS, he had recently met Jane Wilde and he was looking for a thesis topic. This was an exciting time for Einstein’s Theory of General Relativity (GR). The gravitational redshift had recently been confirmed by Pound and Rebka at Harvard, which put the theory on extremely solid footing. This was the third of three “classical tests of GR.” So now that everyone was truly convinced that GR is correct, it became important to get serious about investigating its most bizarre predictions. Hawking and Penrose picked up on this theme most notably.The mathematics of GR allows for singularities which lead to things like the big bang and black holes. This mathematical possibility was known since the works of Friedmann, Lemaitre and Oppenheimer+Snyder starting all the way back in the 1920s, but these calculations involved unphysical assumptions—usually involving unrealistic symmetries. Hawking and Penrose each asked (and answered) the questions: how robust and generic are these mathematical singularities? Will they persist even if we get rid of assumptions like perfect spherical symmetry of matter? What is their interpretation in physics?

I know that I have now used the word “singularity” multiple times without defining it. However, this is for good reason—it’s very hard to assign a precise definition to the term! Some examples of singularities include regions of “infinite curvature” or with “conical deficits.”

Singularity theorems applied to cosmology: Hawking’s first major results, starting with his thesis in 1965, was proving that singularities on the cosmological scale—such as the big bang—were indeed generic phenomena and not just mathematical artifacts. This work was published immediately after, and it built upon, a seminal paper by Penrose. Also, I apologize for copping-out again, but it’s outside the scope of this post to say more about the big bang, but as a rough heuristic, imagine that if you run time backwards then you obtain regions of infinite density. Hawking and Penrose spent the next five or so years stripping away as many assumptions as they could until they were left with rather general singularity theorems. Essentially, they used MATH to say something exceptionally profound about THE BEGINNING OF THE UNIVERSE! Namely that if you start with any solution to Einstein’s equations which is consistent with our observed universe, and run the solution backwards, then you will obtain singularities (regions of infinite density at the Big Bang in this case)! However, I should mention that despite being a revolutionary leap in our understanding of cosmology, this isn’t the end of the story, and that Hawking has also pioneered an attempt to understand what happens when you add quantum effects to the mix. This is still a very active area of research.

Singularity theorems applied to black holes: the first convincing evidence for the existence of astrophysical black holes didn’t come until 1972 with the discovery of Cygnus X-1, and even this discovery was wrought with controversy. So imagine yourself as Hawking back in the late ’60s. He and Penrose had this powerful machinery which they had successfully applied to better understand THE BEGINNING OF THE UNIVERSE but there was still a question about whether or not black holes actually existed in nature (not just in mathematical fantasy land.) In the very late ‘60s and early ’70s, Hawking, Penrose, Carter and others convincingly argued that black holes should exist. Again, they used math to say something about how the most bizarre corners of the universe should behave–and then black holes were discovered observationally a few years later. Math for the win!

No hair theorem: after convincing himself that black holes exist Hawking continued his theoretical studies about their strange properties. In the early ’70s, Hawking, Carter, Israel and Robinson proved a very deep and surprising conjecture of John Wheeler–that black holes have no hair! This name isn’t the most descriptive but it’s certainly provocative. More specifically they showed that only a short time after forming, a black hole is completely described by only a few pieces of data: knowledge of its position, mass, charge, angular momentum and linear momentum (X, M, Q, J and L). It only takes a few dozen numbers to describe an exceptionally complicated object. Contrast this to, for example, 1000 dust particles where you would need tens of thousands of datum (the position and momentum of each particle, their charge, their mass, etc.) This is crazy, the number of degrees of freedom seems to decrease as objects form into black holes?

Black hole thermodynamics: around the same time, Carter, Hawking and Bardeen proved a result similar to the second law of thermodynamics (it’s debatable how realistic their assumptions are.) Recall that this is the law where “the entropy in a closed system only increases.” Hawking showed that, if only GR is taken into account, then the area of a black holes’ horizon only increases. This includes that if two black holes with areas $A_1$ and $A_2$ merge then the new area $A*$ will be bigger than the sum of the original areas $A_1+A_2$ .

Combining this with the no hair theorem led to a fascinating exploration of a connection between thermodynamics and black holes. Recall that thermodynamics was mainly worked out in the 1800s and it is very much a “classical theory”–one that didn’t involve either quantum mechanics or general relativity. The study of thermodynamics resulted in the thrilling realization that it could be summarized by four laws. Hawking and friends took the black hole connection seriously and conjectured that there would also be four laws of black hole mechanics.

In my opinion, the most interesting results came from trying to understand the entropy of black hole. The entropy is usually the logarithm of the number of possible states consistent with observed ‘large scale quantities’. Take the ocean for example, the entropy is humungous. There are an unbelievable number of small changes that could be made (imagine the number of ways of swapping the location of a water molecule and a grain of sand) which would be consistent with its large scale properties like it’s temperature. However, because of the no hair theorem, it appears that the entropy of a black hole is very small? What happens when some matter with a large amount of entropy falls into a black hole? Does this lead to a violation of the second law of thermodynamics? No! It leads to a generalization! Bekenstein, Hawking and others showed that there are two contributions to the entropy in the universe: the standard 1800s version of entropy associated to matter configurations, but also contributions proportional to the area of black hole horizons. When you add all of these up, a new “generalized second law of thermodynamics” emerges. Continuing to take this thermodynamic argument seriously (dE=TdS specifically), it appeared that black holes have a temperature!

As a quick aside, a deep and interesting question is what degrees of freedom contribute to this black hole entropy? In the late ’90s Strominger and Vafa made exceptional progress towards answering this question when he showed that in certain settings, the number of microstates coming from string theory exactly reproduces the correct black hole entropy.

Black holes evaporate (Hawking Radiation): again, continuing to take this thermodynamic connection seriously, if black holes have a temperature then they should radiate away energy. But what is the mechanism behind this? This is when Hawking fearlessly embarked on one of the most heroic calculations of the 20th century in which he slogged through extremely technical calculations involving “quantum mechanics in a curved space” and showed that after superimposing quantum effects on top of general relativity, there is a mechanism for particles to escape from a black hole.

This is obviously a hard thing to describe, but for a hack-job analogy, imagine you have a hot plate in a cool room. Somehow the plate “radiates” away its energy until it has the same temperature as the room. How does it do this? By definition, the reason why a plate is hot, is because its molecules are jiggling around rapidly. At the boundary of the plate, sometimes a slow moving air molecule (lower temperature) gets whacked by a molecule in the plate and leaves with a higher momentum than it started with, and in return the corresponding molecule in the plate loses energy. After this happens an enormous number of times, the temperatures equilibrate. In the context of black holes, these boundary interactions would never happen without quantum mechanics. General relativity predicts that anything inside the event horizon is causally disconnected from anything on the outside and that’s that. However, if you take quantum effects into account, then for some very technical reasons, energy can be exchanged at the horizon (interface between the “inside” and “outside” of the black hole.)

Black hole information paradox: but wait, there’s more! These calculations weren’t done using a completely accurate theory of nature (we use the phrase “quantum gravity” as a placeholder for whatever this theory will one day be.) They were done using some nightmarish amalgamation of GR and quantum mechanics. Seminal thought experiments by Hawking led to different predictions depending upon which theory one trusted more: GR or quantum mechanics. Most famously, the information paradox considered what would happen if an “encyclopedia” were thrown into the black hole. GR predicts that after the black hole has fully evaporated, such that only empty space is left behind, that the “information” contained within this encyclopedia would be destroyed. (To readers who know quantum mechanics, replace “encylopedia” with “pure state”.) This prediction unacceptably violates the assumptions of quantum mechanics, which predict that the information contained within the encyclopedia will never be destroyed. (Maybe imagine you enclosed the black hole with perfect sensing technology and measured every photon that came out of the black hole. In principle, according to quantum mechanics, you should be able to reconstruct what was initially thrown into the black hole.)

Making all of this more rigorous: Hawking spent most of the rest of the ’70s making all of this more rigorous and stripping away assumptions. One particularly otherworldly and powerful tool involved redoing many of these black hole calculations using the euclidean path integral formalism.

I’m certain that I missed some key contributions and collaborators in this short history, and I sincerely apologize for that. However, I hope that after reading this you have a deepened appreciation for how productive Hawking was during this period. He was one of humanity’s earliest pioneers into the uncharted territory that we call quantum gravity. And he has inspired at least a few generations worth of theoretical physicists, obviously, including myself.

In addition to reading many of Hawking’s original papers, an extremely fun source for this post is a book which was published after his 60th birthday conference.

Stephen Hawking wins $3M Milner Prize

Posted on December 10, 2012 by preskill

The official announcement won’t come until tomorrow, but The New York Times is reporting that Stephen Hawking will receive a “special” $3M Prize from Yuri Milner’s Fundamental Physics Prize Foundation.

This is fantastic news! I assume the Prize recognizes Stephen’s great discovery that black holes radiate, one of the most transformative developments in theoretical physics during my lifetime. That’s just one of Stephen’s many important contributions. And of course his supreme skill as a popularizer and the unparalleled courage he displays in response to his disability have made him the most famous living scientist in the world. Congratulations, Stephen!

Stephen has a long-standing relationship with Caltech. He spent a sabbatical year here during 1974-75, when he wrote his famous paper formulating the black hole information paradox, and he has made more or less annual extended visits to Caltech since the 1990s. Stephen and I had many memorable discussions about black holes over the years, culminating when he conceded a bet, for which I received far more attention than I deserved. I’ve been proud to be Stephen’s friend for the past 30 years, and we’ve shared a lot of laughter.

With Kip Thorne and Stephen Hawking, 2005.

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Stephen Hawking wins $3M Milner Prize

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