Black hole Lasers: The science of "Interstellar" revisited

The movie "Interstellar" has not only fascinated moviegoers: it also has created a discussion among scientists whether any and all of the science discussed in the movie is accurate. To be sure, this is not the fate that befalls your average Sci-Fi movie where the laws of physics are routinely (and often egregiously) broken over an over again. I'm sure you can find a list simply by googling appropriately. Try "physics violations in sci-fi movies", for example. 

But this movie is different. This move has famed theoretical physicist (and newly-minted Nobel laureate) Kip Thorne as an executive producer. 

Kip Thorne (source: Wikimedia)

Not only did Kip advise director Christopher Nolan about the science (including talking him out of using time travel as a plot device), but he also spent time to calculate what a black hole event horizon should look like. He is quoted as saying, for example: 

"For the depictions of the wormholes and the black hole, we discussed how to go about it, and then I worked out the equations that would enable tracing of light rays as they traveled through a wormhole or around a black hole—so what you see is based on Einstein's general relativity equations." 

This is certainly unusual for a Sci-Fi movie. Indeed, the renderings of the equations Kip provided have have been published in two papers: one aimed at the general relativity crowd, and one aimed at the SIGGRAPH audience. 

To boot, Kip Thorne not only is an advisor: he co-wrote the initial script of the movie (that originally had Steven Spielberg attached as director). But according to Kip, the final story in "Interstellar" only bears a fleeting resemblance to his initial script.   

So if "Interstellar" is so infused with Kip's science, why would there be a need to go "revisit the science of 'Interstellar', as this blog post titillatingly promises.

Black holes, that is why! 

"Interstellar" has black holes front and center, of course. And having Kip Thorne as an advisor is probably as good as you can get, as he is co-author of the magnum opus "Gravitation", and also wrote "Black Holes and Time Warps" for the less mathematically inclined. I have both volumes, I should disclose. I believe my copy of "Black Holes" is signed by him.

Having said all this, and granted my admiration with his science and his guts (he defied federal funding agencies by writing proposals on closed time-like loops) I have a bone to pick with the science depicted in the movie.

Lord knows, I'm not the first one (but perhaps a tad late to the party). So just give this long moribund blog post a chance, will you?

This is no time to worry about spoilers, as the movie came out a while ago. The story is complex, but a crucial element of the story requires traveling into, and then somewhat miraculously out of, a black hole.

When you get past the event horizon, as our hero Joseph Cooper (played by Matthew McConaughey) does, could there be any way back (as depicted in the movie)? At all? Without breaking the laws of physics and therefore credulity at the same time?

This blog post will tell you: "Yes actually, there is", but it is not an answer that Kip Thorne, or anyone else involved with the Interstellar franchise, might cozy up to. It is possible, but it involves making a people-Laser. Read on if that's not immediately obvious to you.

I am going to ask and answer the question: "If something falls into a black hole, and that black hole is connected to another black hole for example by a wormhole, can you come out on "the other side"?

But I have to issue a quantum caveat: I'm going to assume that the two black holes are connected via quantum entanglement as well. Black holes that are connected this way have been considered in the literature before (Google "ER=EPR" if you want to learn more about this).

Two black holes connected by a wormhole (Source: Wikimedia).

The main point for us here is that the two "mouths" of the "Einstein-Rosen bridge" (that's what the two black holes that are connecting two different regions of spacetime are called) are quantum coherent. And of course, you figured out that "ER" stands for "Einstein-Rosen", and "EPR" abbreviates "Einstein-Podolski-Rosen", the three authors that investigated quantum entanglement and its relation to quantum reality in the famous 1935 paper. Now, previously people had argued that the wormhole connecting the two black holes would not be stable (it would collapse), and that anyway it could not be traversed. But later on it was shown (and Kip Thorne was involved in this work) that wormholes could be stabilized (maybe using some exotic type of matter), and possibly could also be traversable. So I'm not going to debate this point: I'll stipulate that the wormhole is indeed stable, and traversable. What I'm concerned with is the escape. Because remember: "What goes on inside of a black hole stays inside the black hole"?

"So what's this about a people-Laser?"

Hold your horses. Let me get some preliminaries off my chest first. You've been to my blog pages before, right? You've read about what happens to stuff that falls into black holes, no? If any of your answers is "Umm, no?", then let me gently point your browser to this post where I explain to you the fate of quantum information in black holes. In the following, I will shamelessly assume you have mastered the physics in that post (but I will gently issue reminders to those whose memory is as foggy as mine own).

So what you the reader of my pages know (that, alas, most of the people working in the field have yet to discover) is that when you throw something in a black hole, several things happen. The thing (and we usually think of a particle, of course) is either absorbed or reflected (depending on the particle's angular momentum). Let's say it is absorbed. But Einstein taught us in 1917 that something else happens: the vacuum makes a copy of what you threw in, along with an anti-copy.

I pause here for those readers that just struggled with an onset of what feels like an aneurysm.

To those readers: please read the post on the "Cloning Wars", which explains that, yes, this happens, and no, this does not violate the no-cloning theorem.

A copy and an anti-copy? Well, yes, if you're gonna create a copy and you don't feel like violating conservation laws (like, pretty much all of them) then you have to create a copy and an anti-copy. If you throw in an electron, an electron-positron pair will be created (Einstein says: "stimulated"), where the positron is the anti-copy. If you throw in a proton, Einstein's stimulated emission process near the black hole will create a proton-anti-proton pair. The copy stays outside of the black hole, and the anti-copy now finds itself inside of the black hole, alongside the original that the black hole just swallowed. 

So let's just keep a count, shall we? Inside the black hole we have the original and the anti-copy, outside we have the copy. You can use the outside copy to make sure the laws of information conservation aren't broken, as I have argued before, but today our focus is on the stuff inside, because we imagine we threw Cooper into the wormhole. The black hole dutifully responds by stimulating a Cooper clone on the outside of the black hole, while the original Cooper, alongside an anti-Cooper, is traveling towards the singularity, which in this case connects this black hole to another one, far far away. Here's a handy diagram to keep track of all the Coopers.

A Cooper is absorbed at horizon \(H_1\) (black), stimulating the emission of a Cooper pair (red)

At this point I feel I should have a paragraph arguing that the vacuum could really produce something as complex as a Cooper-pair (see what I did there?) via stimulated emission. This is not a terrible question, and I'm afraid we may not really be able to answer that. It sure works for elementary particles. It should also work on arbitrary pure quantum states, and even mixed ones. We don't have an apparatus nearby to test this, so for the sake of this blog post I will simply assume that if you can somehow achieve coherence, then yes the vacuum will copy even macroscopic objects. Just take my word for it. I know quantum.

But this interlude has detracted us from Cooper and his anti-twin traveling through the suitably stabilized wormhole, towards the event horizon on the other black hole that the entry portal is connected with, in both an ER and an EPR way. They are now inside of a black hole, yearning to be free, and let's imagine they have the time to ponder their existence. (They are not holding hands, by the way. That would be utter annihilation).

What is it like inside of a black hole, anyway? It's a question I have been asked many times, be it on a Reddit AMA or when giving presentations called "Our Universe" to elementary school children. (Black holes always come up, because, as I like to say, they are like dinosaurs.)

If you can ignore the crushing gravity (which you can if the black hole you inhabit is big enough, and you are far enough away from the center) then the black hole doesn't look so different from the universe you are used to. But there is a very peculiar thing that happens to you. Now, if you happened to inhabit a decent-sized planet like Earth (not a black hole), then if you shoot a small rocket up into the sky, it falls back down somewhere far away. If you can make a much more powerful rocket, it may go up but, when coming back down, will miss the surface of the planet. And keep missing it: it is actually in orbit. But if your rocket is even more powerful, it could leave your planet's gravitational field altogether.

But when you live inside of a black hole, gravity is so strong that no rocket is powerful enough to leave orbit. So you decide to fire a ray-gun instead because light surely goes faster than any rocket, but you then realize that gravity also bends light rays. And because you're in a black hole, the best you can do is that your light ray (after going up and up) basically goes in orbit around the black hole. Just about where Schwarzschild said the event horizon would be.

So you see, when you are inside a black hole, nothing can go out. Everything you shoot out comes back at you (so to speak). There is actually a word for something like that: an area of space-time that you cannot penetrate: it is called a white hole.

So basically, if you are inside a black hole the rest of the universe looks to you like a white hole.

I've mentioned this before in the last paragraph of a somewhat more technical post, so if you want to revisit that, please go ahead, because it has some interesting connections to time-reversal invariance.

But now we understand the Cooper-pair's predicament. No Cooper can escape the black hole, because the horizon they are looking at is a white-hole horizon. Everything is lost, right?

Well, not so fast. In the move Interstellar, some Deus-Ex-Machina extracts Cooper from the black hole, but how could this work in a world where the laws of physics aren't just mere suggestions?

The answer is obvious, isn't it? You hurl anti-Cooper at the White Hole Horizon.

Stimulated emission was able to breach the horizon in the first place, by creating a Cooper-pair. Can anti-Cooper do the same thing from the inside? We now treat the horizon that separates the black hole interior from the outside as a white-hole horizon. And if you do the math right (and I did in the cloning paper) the anti-clone that is hurled into the white-hole horizon will create an anti-anti-clone on the other side. That anti-anti-clone is, of course, a clone: it is Cooper himself, resurrected on the outside. Somewhat stunned, we assume. Here's what this would look like:

The anti-Cooper that was produced at horizon \(H_1\) stimulates the production of a Cooper-anti-Cooper pair as it reflects off of the White Hole Horizon \(H_2\)

This is great: the wormhole resident anti-Cooper has stimulated a Cooper outside horizon \(H_2\), which is how Cooper can see the light of day once more. The anti-Cooper that is stimulated at the same time annihilates the Cooper that was absorbed initially.  But hold on.

We now have two Coopers. The one stimulated at horizon \(H_1\), and the one stimulated at horizon \(H_2\). Doesn't this violate the no-cloning theorem? I'll tell you in a minute that the answer is no, but not before I have to let you in on a secret: it's getting much worse for the Coopers.

You see the anti-Cooper that is reflected at the White Hole horizon \(H_2\)? It is on its way back to Horizon \(H_1\). And guess what happens if anti-Cooper is reflected there? You're right, it stimulates another Cooper-pair!

Reflection at horizon \(H_1\) creates another Cooper-pair

Now there are two Coopers at horizon \(H_1\) and one at horizon \(H_2\)! And, there are now two anti-Coopers on their way to \(H_2\). You can guess what happens from here on out.

Internal reflection of anti-Coopers stimulates Coopers at both horizons, giving rise to a Cooper-Laser

As long as anti-Coopers can reflect without loss at the horizons, the wormhole is going to produce beams of Coopers at both horizons. And if these Coopers are coherent (as we have assumed here), then these are Cooper-Lasers!

Now, to answer all the questions that are racing through your head:

1. No, we are not violating the no-cloning theorem, for the same exact reason why the no-cloning theorem is not violated by standard Lasers. Of course you know that Laser stands for "Light-Amplification via Stimulated Emission of Radiation". So the process that saves information conservation in black holes is the same that is responsible for Lasers, and if we were to connect two black holes via a wormhole, then you have created a black hole laser. The reason why Lasers do not violate the no-cloning theorem is that spontaneous radiation is also formed at the interface (I've omitted those in the depictions here for clarity, but the math has them, as do the diagrams in the original post on information-conservation in black holes). This spontaneous emission is, of course, just Hawking radiation. A tiny amount of this radiation is random Cooper pairs. 

2. The energy to produce all these Coopers is donated by the black holes that form the wormhole in the first place. All this stimulation of Coopers just makes it evaporate much faster than via the ordinary spontaneous emission of pairs (Cooper and non-Cooper alike). For standard Lasers, you actually have to provide this energy by creating an "inversion" that puts the atoms in the gas within the reflecting cavity into excited states. That's not needed for black hole Lasers: they come with their own energy source! 

3. Is there a paper that describes black hole Lasers? The answer is, for once, no. While it is obvious that wormholes that are connected coherently would make a black hole Laser, I also don't think referees would buy it. Such is the state of publishing in this area. After all, the community is still ignoring the fact that stimulated emission gives rise to a non-vanishing information-transmission capacity, seven years after the paper that showed this appeared (and seventeen years after this appeared as preprint). 

4. Could we observe black hole lasers? I don't know the answer to this. Black holes sure do spew out all kinds of stuff, but we mostly assume that these are jets that are fed from an accretion disk. To test whether this is instead stuff that is stimulated from inside a black hole, we would have to test whether there is some coherence in these beams. I suppose this could be done in principle, by taking advantage of the Hanbury-Brown-Twiss effect. I doubt anyone has tried it, or will. 

Remembering Stephen Hawking

The passing of the great physicist Stephen Hawking today at the age of 76 fills me with sadness for many different reasons. On the one hand, it was inspiring to witness that, seemingly, the power of will and intellect can hold such a serious illness at bay for so long.  On the other hand, I am also sad that I never got to talk to him, and perhaps explain to him my take on his great body of work.

Stephen Hawking (1942-2018)
Source: Wkimedia

I ran into Stephen several times when I was at Caltech (which Hawking visited regularly), but a situation never developed in which we could “chat”, as it were. One day in 1992 I was walking with Gerry Brown, a nuclear theorist who also visited Caltech each year in the Spring, together with Hans Bethe, Brown’s collaborator on the theory of binary neutron stars, along the lovely paths in Arcadia’s Arboretum. 

Hans Bethe and Gerry Brown, at Caltech in 1992

From afar, both Gerry and I spotted Hawking being pushed by his nurse along the path. Realizing that our paths will cross, Gerry and I both tried to get Hans to stop and engage Hawking, imagining that Hawking would be delighted to meet the eminent Bethe, winner of the Nobel Prize in Physics in 1967 for his discovery of how stars generate the energy to shine.  However, Bethe curiously demurred. Later I asked Gerry why Hans did not take this opportunity, and he answered: “You’d be surprised how shy Hans can be.”

Hans passed away thirteen years ago, Gerry left us almost eight years later, and now Stephen is gone too. For me, it is always difficult to imagine that these great minds could simply cease to be. But after all, Hawking is known to have said “I regard the brain as a computer which will stop working when its components fail”, and in that he was surely correct. But of course, these great minds have left a legacy that is immortal, and we will keep them in our memory as long as we think about the stars, black holes, and the vastness of the universe.