Monday, 17 March 2014

Einstein

Einstein is the hero genius of all humanity. For people like me, who study black holes, Einstein is even more of a hero; without him, the topic we've devoted our entire adult lives to simply would not exist. I have a little Einstein shrine in my office, where I pay thanks every day in the only way a working scientist knows how. "O great Einstein, how privileged I am to exist within your future light cone! As a humble token of my deep thanks, I vow to cite you three times today."

That makes it easy to forget that just like everyone else, Einstein both screwed up and covered up. A few years ago I heard a story that shrunk the Einstein myth to normal proportions. In 1936 he wrote a paper with Nathan Rosen, in which they demonstrated that gravitational waves are physically meaningless. Gravitational waves turned up in my crystal-clear explanation of Einstein's general relativity: they're wobbles in the shape of space and time itself, washing across the universe, signalling how objects have been zooming around. They're a crucial and natural part of the theory. Einstein and Rosen had considered what they thought would be a simple example of a long sheet of a gravitational-wave ripple, just like a dying ocean wave coming into shore, which you can see coming in all the way up and down the beach. The trouble with their example was that at some places along the beach, the dying wave exploded into a tsunami: the equations blew up in their faces. No matter what they did, the problem wouldn't go away. It was like pushing down an embarrassingly large bubble in a wall of wallpaper. Wherever they pushed it down, it popped up again somewhere else. Such things must be impossible, and so gravitational waves must not exist after all.

By that time Einsein was living in the United States (he had left Germany over a minor political disagreement that we need not go into), working at the Institute for Advanced Study in Princeton. He and Rosen sent their paper to the leading US physics journal and men's fitness magazine, Physical Review. The journal sent the paper to another scientist to referee. The anonymous referee then had the rare privilege to point out that Einstein had made a mistake. The journal had no choice but to return Einstein's work to him.

Einstein was furious. He wrote back, "I didn't send you the paper to check, I sent it to you to publish!" And with a charming petulant schoolboy flourish, added, "I'm never publishing in your journal again!" He then resubmitted the paper to the Journal of the Franklin Institute of Philadelphia, which treated the great man's work with the proper respect it deserved.

Now, the next bit is even better. It turns out that the referee was one Howard Percy Robertson, who was at Princeton University, which is entirely within prank-making distance of the Institute for Advanced Study. Robertson was no slouch himself, and was one of the people whose solution to Einstein's equations for the entire universe is what modern cosmologists spend all of their time failing to improve on.

Resplendent from having just given the world's most famous scientist the academic equivalent of a good slap, Robertson was strolling the corridors of Princeton soon afterwards. He ran into Leopold Infeld, who had just been hired as Einstein's new assistant. Robertson casually asked Infeld, "How's old Albert these days?"

"Furious!" replied Infeld. "Some scoundrel at the Physical Review has had the nerve to tell him his paper on gravitational waves is wrong."

"No! Surely not!" exclaimed Robertson. "And what paper would this be, exactly?"

Infeld proceeded to explain his new master's latest work of genius, and Robertson played dumb and listened, and then tried to make sense of the explanation.

"You see," explained Infeld, "in this solution he's found, singularities keep popping up, which just can't be. It's a contradiction. So gravitational waves must not exist!"

Robertson did some frowning and scratching of his head. "I'm confused. Isn't this just a trick of the coordinates? That's always a problem in Einstein's theory."

"Great Scott, you're right!" cried Infeld, or whatever it is that you exclaimed in 1936 when you realised that Einstein had botched up. It wasn't the gravitational waves that were nonsensical, but Einstein and Rosen's choice of coordinates; they needed to cut their wallpaper better.

Infeld scurried back to Einstein, and told him what he'd learned from Robertson.

Einstein was a professional, and he knew how to handle this. "Well done, my dear Infeld. I was just now looking for you to tell you precisely the same thing. I was considering my result in more detail last night, and reached the same conclusion."

Infeld was thoroughly relieved. "What a wonderful coincidence Herr Doctor Professor Einstein!"

"I must congratulate you on being only one day behind my own calculations."

"Thank you very much, Herr Doctor Professor!"

"Now you must excuse me, I am scheduled to give a seminar on my proof of the nonexistence of gravitational waves."

Then, without a hint of hesitation, Einstein delivered an impromptu lecture on why his original proof was wrong, and chuckled over what a tricky phenomena these little gravitational waves were.

Afterwards Einstein returned to his office. It was clear what he had to do. He innocently asked his secretary, "Miss Dukas, do you happen to know where that referee report went?"

"The one you threw in the trash and set alight?"

"Um, yes."

"After I put out the fire in your office, I used the ashes to fertilise my roses. Would you like me to try and reconstitute it?"

"No, thank you. I expect I can reproduce the results more quickly myself."

He set to work, and managed to resolve the problems in his calculation just in time for the article's proofs to arrive from the Journal of the Franklin Institute. He crossed out the title, "Do gravitational waves exist?", and replaced it with, "On gravitational waves." He also replaced the conclusions ("No") with a wonderful new solution of the Einstein equations, which predicted an entirely new class of gravitational waves, from a cylindrical source. When he returned the proofs he included a small note apologising for the minor changes. The journal duly published the modified paper.

Robertson was tickled pink to see the published result, but did not have long to bask in his smugness. The Physical Review had just sent him another thorny paper to referee.


Postscript:

If you read Daniel Kennefick's Physics Today article, you may be surprised by how much of this story is actually true. It is more likely that you will be shocked at what terrible liberties I have taken with such venerable characters in the illustrious history of my field.

As for gravitational waves themselves, they were tricky to clear up in the theory, and they have proved even harder to verify experimentally. However, their reality was implied by observations from Hulse and Taylor in 1974, which earned them a Nobel Prize in 1993. And if the rumours are true, later today (yes, today!) there will be an announcement of new readings of that great cosmological cave painting, the CMB, that infer the existence of an especially fancy class of gravitational waves, which were produced in the aftermath of the Big Bang. (Update: the rumours were true.)

Beyond that, direct measurements of the little buggers are much harder. But we are working on it.


Another postscript:

The BICEP-2 results turned out to be less convincing than originally reported, but roughly eighteen months later gravitational waves were directly measured for the first time by the Advanced LIGO detectors.

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