字幕表 動画を再生する 英語字幕をプリント In the late 19-teens, Albert Einstein had a new hammer, and he was in search of nails to hit. He had just developed a new and more powerful mathematical description of gravity , and was using it to make predictions willy-nilly. First, Einstein checked that his new description matched up with the previous state-of-the-art description of gravity, newton’s law, for situations where newton’s law agreed with experiments. And it did. So far so good. Then Einstein plugged in the orbit of Mercury and got a prediction that correctly matched the experimental observations of the day; observations which had an anomaly that couldn’t be explained with Newton’s law of gravitation. He plugged in starlight passing by the sun and got a prediction that it should bend because of the sun’s gravity; this was later confirmed. He plugged in starlight leaving large stars and got a prediction that the spectrum of the light should be redshifted as it climbs out of the gravity well; this was later confirmed. He plugged in empty space and got a prediction that waves of gravitation should propagate through it; this, too, was later confirmed. And he plugged in the universe and got a prediction that it should be static and unchanging. Which was wrong. Now, the general understanding at the time was that the universe didn’t expand or contract, and while there were starting to be rumors that distant nebulas were consistently moving away from us , Einstein was firmly in the “static universe” camp. And it just so happened that when Einstein did his calculation about the universe, he made a small but significant technical mistake that implied that the universe couldn’t be expanding or contracting. I suspect Einstein probably didn’t catch the mistake for two reasons: because tensor calculus is hard and annoyingly subtle, and because he agreed with the result so had no reason to question it. This is all the more significant because the mistake ultimately meant that his equations predicted the universe couldn’t have anything in it at all, and Einstein had to find a totally different clever mathematical trick in order for his equations to describe a universe that did have stuff in it in spite of his mistaken calculation. Anyway a few years later, Russian physicist Alexander Friedmann plugged the universe into Einstein’s equations, and he didn’t make the mistake Einstein did. He got a prediction that the universe could either be expanding, or contracting, or static, depending on how much stuff there was in it and the balance of matter and energy. But Einstein still didn’t realize that he had made a mistake: instead, he published a criticism of Friedmann’s work, justifying his critique with the same erroneous calculation as before. So Friedmann wrote Einstein a private letter, graciously (but firmly) explaining to Einstein the correct calculation, and (again graciously) asking Einstein to either show him where HE was wrong, or publish a correction. And Einstein eventually saw that Friedmann was right - so he admitted it and published a retraction of his previous criticism. Turns out the equations of general relativity could describe an expanding or contracting universe after all. The scientific end to this story is that Friedmann died before the conclusive experimental data came in and showed that the universe is expanding, so he never knew which possible outcome of his equation was right. And Einstein died before the conclusive experimental evidence came in that showed that the mathematical trick he had used to adjust for his mistake turned out to be super useful and is now used to describe dark energy. So Einstein was famously upset about the whole episode; the story is typically written to suggest that he simply regretted being wrong. And maybe that’s the truth. But speaking as a physicist - and to be clear, this is purely my own personal speculation - I kind of wonder if Einstein also was kicking himself in the pants because if he hadn’t made that silly math error, maybe he could have arrived, years earlier, at the same equations as Friedmann (and which are now called the Friedmann equations, and are the foundation of our modern understanding of the large-scale structure of the universe). But I’m not entirely sure he would have been able to do what Friedmann did - because all people, even scientists, have biases, and biases tend to be held so strongly and so deeply that they not only blind us to alternatives, they blind us to their existence. The beauty of keeping an open, rational and scientific mindset is that when one of your biases is wrong, you’re more willing to look at the evidence, see that you’re wrong, and admit it. But that’s really hard to do, even - or maybe especially - for somebody like Einstein. And I wonder if Einstein would have been able to see past his bias about the static nature of the universe without outside help. Einstein, like all of us, was human after all. What we can take from Einstein’s actions in this story is this : we can understand that we can be wrong, and when we are, graciously admit it. This video is sponsored by a platform that’s all about understanding when you’re wrong and trying to improve: of course, it’s Brilliant.org. Brilliant has courses and quizzes and puzzles to master logic, math and science skills in whatever size dose you want, and they’re sporting a new look. What I like about their redesign is that it’s not just cosmetic - the interactive quizzes and problems are getting more and more interactive and animated! Do you know what the angles on the outside of a pentagon add up to? What about why solar panels are tilted, and how you pick the right angle? For something a little more in-depth, I’d recommend their “mathematical fundamentals” course. To sign up for free, go to brilliant.org/minutephysics - that lets Brilliant know you came from here, plus Brilliant is offering 20% off of a premium subscription to the first 200 people to go to that link. Again, that’s brilliant.org/minutephysics, and thanks to brilliant for supporting MinutePhysics.