The effect of these gravitational waves is to squeeze and stretch space. If you were floating near these black holes, you would literally be squeezed and stretched. If you were close enough, you would feel the difference between the squeezing and stretching on your face or your feet. We’ve even conjectured that your eardrum could ring in response, like a resonant membrane, so that you would literally hear the wave, hear it even in the absence of a medium like air. Even though we think that empty space is silent, in these circumstances you would hear the black holes collide but you wouldn’t see them; it would happen in complete darkness. The two black holes would be completely dark, and your only evidence of their collision would be to hear the spacetime ringing.SOUNDS OF THE SKIES
I’ve been very excited about the developments in gravitational wave astrophysics lately. I remember when I was a student and I would listen to Kip Thorne give these lectures about the upcoming gravitational wave observatories. They were still just an idea. They hadn’t been built. The first generation of machines weren't built until 2000, but the idea was to measure spacetime itself, to measure spacetime ringing. It was unlike anything that had ever been tried before.
If you think about it, almost everything we know about the universe comes to us from light. We have telescopes, satellites, and observatories, and they all collect different kinds of light. We have this silent movie of the universe, these frozen snapshots that we take so we can look deeper into space and see further back in time. We have this history of the universe in these frozen snapshots, and that’s extraordinary.
This was different. This ambition was to not collect light at all, not take pictures of the sky, but to record the ringing drum of spacetime. At the time that Kip would first start talking about it, drumming up enthusiasm in the community, it was, in the early days (before my days), extremely slow going. There was a lot of negativity about that ambition. People didn’t understand if there would ever be anything cataclysmic enough in the universe to ring spacetime loud enough.
My favorite example is black holes. Imagine two black holes collide. We know the standard lore that deep concentrations of masses like black holes curve space and time around them, and when we fall towards the Earth and we fall towards a black hole, what we’re really doing is falling along the natural curve in spacetime imprinted from this massive object. If you think about black holes orbiting each other, those curves have to move and adjust because the black hole is moving. They can’t move faster than the speed of light because that would violate the speed limit that exists, the cosmic speed limit. Nothing can travel faster than the speed of light—no information, not even information about space and time.
These waves in the shape of spacetime start to readjust around the moving black holes and travel outward at the speed of light. The effect of these gravitational waves is to squeeze and stretch space. Their effect is to squeeze and stretch space. If you were floating near these black holes, you would literally be squeezed and stretched. If you were close enough, you would feel the difference between the squeezing and stretching on your face or your feet. We’ve even conjectured that your eardrum could ring in response, like a resonant membrane, so that you would literally hear the wave, hear it even in the absence of a medium like air. Even though we think that empty space is silent, in these circumstances you would hear the black holes collide but you wouldn’t see them; it would happen in complete darkness. The two black holes would be completely dark, and your only evidence of their collision would be to hear the spacetime ringing.
At the time that people like Kip Thorne and Rai Weiss were first dreaming up these machines to detect this, people weren’t even sure black holes were real. Black holes as astrophysical objects were still contentious. People didn’t know if nature made black holes, and also people were still arguing about whether these waves themselves were real. It’s pretty tricky business. It’s pretty tough stuff. People knew that black holes were a mathematical possibility; Einstein knew this in 1916. As soon as he writes down the general theory of relativity, Karl Schwarzschild, from the trenches reading the proceedings about general relativity, writes down the solution that we now know as the black hole and sends it to Einstein. Einstein immediately accepts that it’s a correct solution; he just doesn’t think nature is going to allow this to happen. He doesn’t think there’s any way you’re going to crush matter dense enough for this to happen. And this goes on for a very long time.
Oppenheimer, interestingly enough, did some of the most important work on discovering black holes. He was thinking about nuclear physics and nuclear matter with some of his students under idealized conditions. They came to the conclusion that matter could not resist collapse if a star were to die and fall under its own weight, that it would necessarily form a black hole.
Johnny Wheeler, the granddaddy of relativity, who trained entire generations of relativists including Kip Thorne and people like Richard Feynman, really thought Oppenheimer was wrong and offended him by critiquing his work. Wheeler was also deeply invested in nuclear physics. He worked very hard on the bomb project. He was part of designing the plutonium reactors to separate plutonium, the first separation facilities in Hanford, Washington, which by coincidence is now the site of one of the LIGO Observatories (the gravitational-wave observatory).
Wheeler was very adamant about building a nuclear bomb. He was deeply invested in nuclear physics and realized he could use this same thinking to answer this question about whether or not stars would form black holes after they collapsed. He comes to the conclusion that they do, and he gives this lecture. He bounds onto stage where he is describing the end state of gravitational collapse. Interestingly, Oppenheimer was there, but I guess there were some bad feelings between Oppenheimer and Wheeler. Oppenheimer wouldn’t enter the auditorium; he sat outside—the story is—talking among friends, and seemed to not be interested anymore either in the question or in Wheeler’s resolution.
The term "black hole" wasn’t coined until shortly after Oppenheimer died. I heard the story that this happened in a seminar on Broadway up by Columbia, above Tom’s Restaurant. Wheeler was visiting Goddard Space Center there, and while he was giving the seminar he kept saying, "End state of gravitational collapse." He kept saying this incredibly unwieldy phrase that he was tiring of saying and somebody from the audience apparently shouts, "How about black hole?" And then Wheeler just imposes the term on the community, just begins using it in his fashion. He was famous for his Wheelerisms.
People knew that black holes theoretically were very likely by the late '60s, but there was no evidence that people recognized until later. You have to understand that while they began this campaign late '60s, early '70s to measure spacetime ringing, to literally record the sounds of spacetime, they were doing so without a guarantee that the astrophysics was even going to provide sources. They weren’t sure nature would even provide sources.
It was an extremely ambitious and daring thing to not only invest in but to invest in for fifty years. Even though later people start to acknowledge black holes exist, that they collide, that they’ll ring spacetime; stars explode, and that would ring spacetime; neutron stars, which are dead stars that don’t quite make it to become black holes, can ring spacetime with their imperfections like scraping and creating waves in the shape around them if there’s a little mountain—nobody knew if they were populous enough. Maybe it only happens once every 100 years that we would see such a thing.
So we’re building this instrument and we could just be sitting there, silently listening; it seemed insane to people. I call it a "Climbing Mt. Everest" story more than anything else, which is one of these remarkable scientific stories where the drive and the ambition was so powerful that they couldn’t turn away. They just couldn’t stop.
Rai describes building these little prototypes like the "plywood palace" at MIT, which was a makeshift structure that was thrown up during World War II to try to get scientists and engineers to work on things like radar. It was this ramshackle structure that was half falling apart, but somehow the shoddiness of the structure allowed them to do things that they couldn’t do in a normal building. They were punching holes in ceilings, breaking through walls, tapping pipes overhead. They just started these creative, free projects where they weren’t thinking about immediacy of outcome.
Rai’s first prototype of the LIGO machine, which is the instrument that just recently succeeded in making the first detection of gravitational waves—as announced on February 11th—is a remarkably exciting discovery. This idea of building a machine to record the skies starts in a few places, but Rai Weiss makes a very important first step: He dreams up this instrument, which would bob on the wave of changing spacetime and record the shape of it. It’s almost like a musical instrument, in some sense, recording the modulating shape of a drum and then playing it back to us as sound. He calls it a haiku. It’s just a crazy idea he starts to think about.
Rai says one of the big events comes when he meets Kip Thorne. Kip Thorne is a theoretical astrophysicist, a real dreamer. Already, at a very young age, he's a famous Caltech professor, a relativist. Kip and Rai come together and start to discuss the realities of bringing the experimental ambition to Caltech. And then it starts to grow. Then they hire Ron Drever at Caltech. Ron Drever is a Scottish physicist from a very different scientific and personal culture, but an ingenious dreamer of machines, a really great experimentalist. The three of them are the original architects of this instrument.
It’s over decades from the first time Rai dreams it up in the late '60s, early '70s that the machines are built (the year 2000). In that time, you have Kip making the scientific case; you have Rai doing everything he can to keep this alive for that many decades; and you have Ron Drever, with an ingenious approach to experimental physics, doing the design. They all give everything they have to this campaign. It takes a good part of their lives and their careers to do this and there’s no guarantee of success. Rai said to me, "I started life with one ambition: to make music easier to hear." When he was a kid he would build hi-fis; he wanted to make music easier to hear. There’s this direct relationship to what his ultimate scientific contribution was, which was to build this machine to record the skies, record the sounds of spacetime.
Like any campaign to conquer nature, bodies are left along the side of the road at some point. There were real moments of strife and real moments where it was possible that the whole project would collapse. There were many people who came along the way and went. Robbie Vogt did an important job as one of the first directors, but ultimately was fired. Barry Barish came in, considered one of the finest leaders of big projects in the world, if not the finest, and saved the project at a crucial moment. Ron Drever was eventually fired from the project. There was a lot of drama that not everybody likes to talk about. A lot of people will refuse to discuss it. In the Caltech archives some of it is still sealed and inaccessible. Ultimately the project survived.
What’s amazing is the first generation of machines was technologically incredibly successful. The first prototypes that people were working on were 1.5 meters long with two mirrors suspended at either end measuring the distance between the mirrors basically. If the mirrors bob on the wave, it can tell that the mirrors have bobbed on the wave and it records the shape of the ringing—technological feat accomplished. But nothing. No detections. People started to get a little nervous. They always imagined that there would have to be a second generation of advanced machines, but this is already decades into it; it’s another fifteen-year project to develop the advanced machines, install the components, and get the machine working.
When I would hang around on the LIGO sites, go to the facilities, everyone told me there’s going to be no detections until 2018. No way. No detections. One of the experimentalists, Rana, apparently always said, "No, we’re about to detect something." But he said that he always says that. He’s just eternally optimistic. He has to say that.
The first science run ever of the advanced machine was scheduled for September 14, 2015, at 8 a.m. It had to be postponed for a week because the machines were ready, but the algorithms to analyze the data and trigger partners, which had telescopes that would point in the same direction—a kind of network of partners—those algorithms weren’t fully operational. So they were still doing an engineering run on September 14th. During an engineering run you do whatever you want to the machine: you disrupt it, you run tests, you knock it. You’re just playing around, just doing systems tests.
Rai says he was there that weekend noodling with radio interference, and he says, "Luckily, my wife told me I had to come home." So he puts down his tools and goes home. He was at the site in Louisiana. Apparently, students were still banging on the machine until one or two in the morning.
In Washington State where the other machine is—same thing: people were still running tests and disturbing the machine, I guess. Within the space of less than an hour, everyone puts down their tools and goes home. The machines are locked in observing mode, but it’s an engineering run, not a science run. Within an hour, from the southern hemisphere comes a gravitational wave from the collision of two black holes 1.4 billion light years away, hits Louisiana, rings the machines at about 4:50 a.m. Ten milliseconds later it skims across the continent and rings the Hanford site. Everyone’s asleep. The trigger pipelines aren’t fully automated yet, but they do make a note. The automated analysis of the data makes a note that there was an event at both machines.
People wake up in Europe and they see that there’s a candidate event. Now this happens from time to time. There are candidate events and they get thrown away, but there’s some chatter about this event. People start to wake up at the different sites, go into work, and there’s just a lot of chatter. Everyone thought it was what’s called a "blind injection." A blind injection is when fake data is intentionally injected into the instrument to simulate detection just to test operations. It's blind in that nobody knows it happened so that they do a serious job analyzing it, and do a hard test of the machine and the analysis.
At one point, one of the experimentalists Mike Landry from Hanford, Washington, says to one of the people responsible for the blind injections—this is 8:30 that morning—"Did you test the blind injections? Did you test injections of any type? Are we in a phase of injecting?" There are only certain questions that they’re allowed to answer, but the answer was "no" to all the questions. Mike suddenly realizes that this incredibly clear signal that is clearly louder than the noise that looks just like what you would expect from the sound of a collision is not a drill. And the excitement slowly builds as they spend the next couple of months analyzing the data.
I got a message mid-December from the director David Reitze and from Kip and Rai that read: Confidential Communication from LIGO, with the news. I was totally floored. At first I read Confidential Communication, and I couldn’t read on, I was too excited. And then: We want to let you know we have detected the collision of two about 30 solar mass black holes. It’s definitive. We’ve analyzed it for three months. It’s the first direct detection of not only two black holes, but of a gravitational wave. And then they told me not to tell anybody.
I love that not only did the detection come early, not in 2018, but almost exactly 100 years after Einstein first proposed the theory of general relativity. It came early so Rai, Kip, and Ron Drever didn’t have to suffer anymore. They got this great satisfaction of this detection. The fact that it was from black holes is huge. Rai kept saying to me, "I gotta tell ya, if we don’t detect black holes, this thing is a failure."
It was a very bold thing to say before it succeeded. "We want pure spacetime coalescence," he said, "and if we don’t get that we’ve led this country down a garden path." He really stuck his neck out saying that. The fact that it was the first, not three or four years, into advanced LIGO operating, and it just rang the machines in this beautiful and unexpected way, I think was incredibly fortuitous, a real gift. I was very excited for them. Kip said he had a moment of profound satisfaction. He was very reserved.
Einstein, right after [1915], in a correspondence with Schwarzschild who wrote down the black hole solution—even though it wasn’t called that yet—starts to talk about gravitational waves right away. He calls gravitational waves his top priority. It’s this deep part of the theory. Will these waves in spacetime carry energy away? He doesn’t imagine at all that they would be detectable. If you figure, 100 years later there’s this final piece in the puzzle in some sense, which is deeply fundamental to understanding curved spacetime. Gravitational waves are deeply fundamental to the whole business in a way that maybe even Einstein didn't fully appreciate.
In some sense, gravitational waves are why we know that the sun is there. The sun moves or settles down and these waves, propagate out from the sun, and eventually create the curved spacetime around the sun where we stably fall along our orbit. We are slowly emitting gravitational waves ourselves, and very slowly falling into the sun (barring other solar system influences). It takes a very, very long time. This is fundamental to how gravity, in some sense, is communicated across the universe. It’s absolutely at the core of the theory. Obviously, on this centenary, which everyone was aiming for, to have confirmed this is very thrilling.
On the other hand, everyone expected this was true. There was indirect evidence that gravitational waves existed. We see things spiraling into other things. We famously see a pulsar, which is a neutron star with like a lighthouse beacon on it, and we see this pulsar falling into its companion ever so slowly, exactly as predicted by the energy loss to gravitational waves. So nobody’s like, "Wow, I didn’t see that coming." In that sense, it’s not quite like the Higgs where maybe it really wasn’t there and we were way off base. But what is more exciting is what we can do with astronomy with the gravitational-wave observatory.
The challenge moving forward after this first detection, is for the gravitational-wave observatories to start doing astronomy in the conventional sense the way a radio telescope is accumulating astronomical information all the time. Tons of scientists work on the data and study the data from radio telescopes. We’re learning things that, I don’t know, maybe the general public won’t be as excited about with some of these instruments: How much hydrogen is there, or how much dust is there between us and quasars. But all of this stuff contributes to this extraordinary story we end up telling about the universe, which is that it was born 14 billion years ago with not much in it, and that it slowly evolved to have stars, galaxies, heavy elements, planets, and people who build these things to reconstruct that whole history.
The challenge for LIGO will be to start to discover things that we absolutely could have not discovered any other way. The black hole/black hole collision is a step because we can’t see two dark black holes any other way. They, by definition, are dark. They don’t emit light or reflect light unless they’re cannibalizing another star or tearing down a lot of material. So we do see that; we see them destroying things around them. But if there are two bare black holes with no debris then they’re dark, truly. This is already a discovery that couldn’t be made solely with a telescope. The hope moving forward is that there will be this rich and profitable era of accumulating information about the cosmos.
When Kip started talking about potential sources in the early days, even before 2000, he would talk about the wild stuff too, stuff we’ve never thought about. What else could be out there that we know nothing about? We know that there are really dark components to the universe; there’s dark matter and dark energy, which are just proxies for things that we can’t see with telescopes. We already know there are things that we can only detect indirectly from their effect on the space and time around them. It would be thrilling if there was even more out there that we hadn’t yet foreseen.
The dark matter and the dark energy are not light interacting, by definition. They’re not sending light our way, they’re not scattering light our way—we have to see them indirectly. We weigh the universe, in some sense, by looking at the effect on spacetime. Dark energy has a very specific effect on spacetime causing it to grow at an accelerated rate getting faster and faster. That’s what we measure, and we deduce how much dark energy there is, but we actually have no idea what it is. There are only theories out there.
When I’m not working on black holes I do dream about stuff like this, think about stuff like this. We wonder if there are extra spatial dimensions and they’re dark, could they trap a kind of quantum energy that would explain the dark energy? That’s a really interesting viable idea. Maybe we’re already seeing extra dimensions in the dark energy, but we’re a long way from determining that experimentally.
Dark matter, similarly, we know is heavy like regular matter, but otherwise doesn’t interact with light. That’s less shocking. We know some things that don’t interact with light. Neutrinos are a kind of particle that have mass that don’t interact with light very much. Technically, they’re a form of dark matter, but we don’t know what this particular kind of dark matter is. We weigh it by looking at how heavy the galaxies are. We can tell how heavy they are by the effect it has on spacetime around it, and bending the path of light from other distant galaxies, or keeping stars in orbit, so we know it’s there.
It would be interesting if in the gravitational-wave experiments we would have some direct way of hearing things that we can’t see. It’s hard to know how dark matter or dark energy might do that, but maybe there are other things out there. That might sound wild to people, but if you think about the first time people were using telescopes, nobody dreamt of quasars or jets a million light years across or even entire galaxies, for that matter. Nobody imagined entire galaxies.
The idea that in doing something completely different we would discover wildly unknown stuff, is a reasonable idea. It’s very reasonable based on past experience, and that’s why people talk about the new window. This is a totally new window on the universe. Maybe we’re just—like in the early phases of the telescope—we’re just starting to pick up stuff that we know about. What would be most exciting is if we start recording things or unambiguous sounds from space and we have no idea what they are. Everybody would love that.
I was thinking about the Big Bang and the early universe long before I ever considered science. I don’t even think I recognized it as scientific thinking. I was midway through college before I discovered physics, so I came quite late to the realization that this was something a person could do, and that math was not only the language but it was this unbelievable way into the secret code.
Thinking about spacetime, you’re naturally eventually led to black holes. Black holes are very special objects. I got very into the whole spacetime relativity thinking; it’s my favorite domain. I love teaching it, I love thinking about it, I love doing research that’s very formal relativity. Black holes are special because they’re not actually things. People often will say something like, "Oh, a black hole is an incredibly dense crush of matter." That’s not true; that’s how they’re formed, but that’s not what the black hole is.
If I take a star and I turn off its nuclear fuel at the end of its life, and it has has no more pressure to keep it aloft, it starts to collapse under its own weight. And it’s true, that makes an incredibly dense crush of matter. The whole argument was, Is the gravitational force strong enough to push past quantum forces and crush it all the way? But once that matter crushes to the point that the spacetime around it is so strongly curved that not even light can escape—that’s the formation of what we call the event horizon or the shadow of the black hole—once that happens, that crush of matter continues to fall. It’s gone. It’s not sitting there at the event horizon. It continues to fall to the center and then, honestly, we don’t know what happens to it. What we know is that it’s not sitting there at the edge of the shadow. What we call the black hole is really a place; it’s a region where spacetime is so strongly curved that there’s a shadow cast, not even light can escape. If you were to fall across that line, there’s nothing there; there’s no matter from the star that formed it. Nor could you stay there once you cross. Once you cross, you’re forced to fall further forward towards the center of the singularity, which may or may not really exist, but at least you’re forced towards that area as surely as you’re forced forward in time. You can’t not do it.
The singularity is definitely in Einstein’s theory. There is a prediction that there will be an infinite region of curvature and an infinitely strong area where there is almost literally a cut in spacetime. That’s kind of catastrophic. A lot of people think that quantum forces will somehow amend that in some very interesting way. But that’s the final story. The rest of this, you know, falling towards the center, is all very solid.
The point is that the black hole is not a thing; it’s a place. That makes it very special. It’s a fundamental particle of gravity in some sense. All black holes of a certain mass, a certain electric charge, and a certain spin are absolutely identical to all others with those same properties. In that sense, it’s a fundamental object and it makes them very special.
They’re special not only in terms of their spacetime, but they provide a terrain to study the deepest theories of the universe, gravity and quantum theory coming together. This is where people like Lenny Susskind, Stephen Hawking, and Roger Penrose have made these very interesting contributions. They’re thinking about the black hole not as the dead state of a star but as a fundamental terrain to study what the ultimate laws of physics are, even beyond Einstein’s theory and quantum mechanics. It continues to be incredibly productive as a setting for that.
Hawking’s amazing observation was that even though not even light can escape from a black hole, it finds this clever way to evaporate, and it does this by stealing quantum fluctuations from empty space. It steals some and releases some and, in this very tricky way, the black hole evaporates. This caused not only excitement, because it was a fascinating idea, but a kind of crisis. If the black hole evaporates but still doesn’t let anything out, what did happen to all that matter that fell in when it originally formed a star? Where does it go? Hawking said that it’s just gone. It’s obliterated.
People like Lenny Susskind said that’s not tolerable because that means that information is being lost from the universe, and that’s not tolerable because everything we understand about the laws of physics has to do with tracking information. If information can suddenly be obliterated then, in some sense, we don’t have laws of physics. It was a big crisis. And this has been going on since the '70s as well. The debate is still pretty interesting.
Because black holes are fundamental objects, it means we should be able to create them by smashing atoms together just like we create electrons or the Higgs particle. If I smash particles together and they have enough energy that I can make something heavy, I should be able to also make a microscopic black hole. Stellar collapse is not the only way to make a black hole. What energies are high enough to make a black hole? Right now, we think that the energies are about 10 million billion times higher than the Large Hadron Collider can reach. Really high. The Large Hadron Collider is probing a fraction of a second after the Big Bang and it’s still not high enough energy.
Other people have thought that maybe if there are extra spatial dimensions and cosmology is a little bit different than we think, maybe that scale is much lower. Maybe we can make black holes at the LHC. In truth, they look for black holes in the collisions of the protons. So far, none have been seen. There was a scare that the black holes would destroy the universe if we were to make them, which would have been unfortunate. Black holes evaporate, as Hawking said, and so these little microscopic black holes evaporate extremely quickly; they vaporize. The bigger the black hole, the slower the evaporation; the smaller the black hole, the quicker. They basically just explode or vaporize. There was no theoretical expectation that you could make a stable black hole that would destroy the universe. People don’t like the kinds of statistics physicists deal with because nobody would say it’s 100 percent impossible, they would just say it’s very, very, very unlikely, which made some people anxious.
Even before Rai and Kip and Ron got interested in this program to build a gravity observatory like this, there was this one lone pioneer: Joe Weber. In the '60s, he built a very different kind of instrument much cheaper and much more immediate called a Weber Bar. It was like an aluminum cylinder, a guitar string, in a sense, or a part of a tuning fork. The idea was that when a gravitational wave struck it, it would resonate like a tuning fork and that you could measure the resonant vibrations and thereby detect the gravitational wave.
Joe Weber became instantly one of the most famous scientists in the world because he claimed he had evidence for gravitational waves, which caused this incredible excitement. In this sense, he absolutely launched the field. He was the pioneer who started this whole business, and people all over the world started building Weber Bars.
Unfortunately, nobody else heard a thing. After a few years things turned against Weber very badly, very aggressively, and he spends the next twenty-five or thirty years defending himself and his claims. He falls into disrepute. That created a cloud over the initial LIGO inventors. They were working not only against the possibility that nature wouldn’t provide any sources, but against community opinion. Community opinion was very much soured. I feel that Joe Weber deserves credit for being very ingenious and visionary. Now if you look at the LIGO papers they talk about Joe in the opening paragraphs as the pioneer who started the field, and I think that’s a great respect to pay to him.
I do a lot of this dreamy stuff about the Big Bang or extra spatial dimensions. Who knows in my lifetime if that stuff will ever be resolved. That’s why I like to spend time on black holes. For me that’s being concrete, down to earth. Even though I’ve harked on how dark black holes are, we have some good ideas about black holes lighting up in the final fraction of a second before they swallow either another black hole or a neutron star, that you can make a kind of electronic circuit, a giant astrophysical electronic circuit. We’re pretty excited about this. We’ve been making a lot of predictions and hoping telescopes will confirm.
My research world is a pretty small group of scientists that I work with. I work at Barnard and at Columbia with a lot of research scientists at Columbia. I have postdocs like Sean McWilliams who is now a professor, or Dan D’Orazio who is one of my students, Gabe Perez-Giz, Rebecca Grossman, a few students that have gotten PhDs and have moved on. Sometimes I begin to collaborate with faculty. Honestly, the faculty is so busy and we’re all pursuing our own ideas. Sometimes that’s the hardest, to work with other professors. It’s this beautiful way of operating. We operate very mathematically on my side. It is proof driven and math driven. We don’t proceed until we have a calculation that we think is very convincing and where we feel we understand all the steps and can solve a problem analytically. That’s not how everybody operates.
There’s a collaboration that gets handed off where there are people who build very complex computer simulations and they can, in some sense, do experiments just on the computer. We can’t do that with our mathematical tools. In some ways there’s a handoff where there are numerical experiments. Of course, now, with the actual detectors, there’s a whole relationship. Each thing feeds into the other; it’s a kind of scientific ecosystem.
