xhac (![[info]](http://p-stat.livejournal.com/img/userinfo.gif){kind=small} xhac) wrote,@ 2006-12-27 00:44:00 |
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symmetric marvels
It's been many years since I've seen the movie Doppelganger [1] but it left me with a lingering question that I finally got answered this week.
The plot of the movie is that a planet is accidentally (duh) discovered in the exact same orbit as the earth, only rotated by 180 degrees [2], so they send a man out to investigate. The spaceman ends up crash landing on the strange planet which is actually a mirror earth, where everything that happens on our earth, happens on the other earth as well, the only difference being that everything is reflected, just like looking at a mirror. Right is left and left is right. So when the spaceman disappears behind the sun, another "reflection" spaceman appears. Of course nobody believes him, even though they see that his internal organs are set up the wrong way.
So the question: Could this movie plot happen. I'm looking for "possible" not "probable".
So the other day I was listening to a lecture by Richard Feynman which was about exactly that problem. Only he didn't mention the movie. He was more concerned about whether the laws of physics are valid when you look at them in the mirror. As he puts it "can we describe 'left' to an alien over the phone?".
I will answer the original question first (could this movie happen) which is easy. No, it couldn't happen because of the parallax view the reflection earth would have of the universe. Astronomers would have placed their telescopes a tad differently to inspect close-up objects. Another problem I can think of are meteorite collisions (the dinosaurs could still be alive even it weren't for those). These didn't concern Feynman.
Here's another one: could life be sustained on a reflection earth? Feynman says that yes but not exactly. It seems that proteins and stuff are not symmetrical in that way and left-handed life could eat only life that evolved with left-handed life around it. So life could be there but the spaceman that landed there wouldn't be able to survive [3].
How about the physics. Is there a physical law that cares about left and right? A variation to this question is "If we were to substitute every occasion of the word 'left' with 'right' (within the relevant context) and vice versa in every physics book ever printed, would the books still make sense?"
You would be surprised to know that it wouldn't. Ok they actually would make sense but I said they wouldn't so that you would be a bit surprised and perhaps thought about it a little. In another twist, they actually wouldn't make sense if you didn't change some other stuff there as well, such as "north" and "south" (this also explains how come all those "right hand rules" in electro-magnetism, like in Laplace force could remain in place). This is getting really silly, but north and south are arbitrary also, so in case we don't care to be compliant with geography it's fine to leave everything as is.
So there, just as you have imagined all along. The symmetry holds. Wrong! And this isn't just a half lame technicality like "north" and "south". There are honest to goodness real phenomena that actually do define a certain "right" and a certain "left". You can do as I did and file it into the "under a strong magnetic field the products of some tiny particle's decay tends to go more to the left than the right" category, or you can look up CP-violations.
So there you have it. Contrary to what anyone would reasonably believe and to what everyone believed until the 60s, there _is_ a difference between right and left in the physical world, so reflection-earth could not exist.
I am really sorry about this but there is a final (?) twist to the story. It turns out that if matter spins to the left, antimatter spins to the right. Reflection earth would work the same as ours if only it was made out of antimatter. Now how cool is that. A seemingly obvious perfect symmetry that has tiny quantum flaws, which can be fitted in an even larger symmetry.
Feynman concludes with the rather poetic:
"So our problem is to explain where symmetry comes from. Why is nature so nearly symmetrical? No one has any idea why. The only thing we might suggest is something like this: There is a gate in Japan, a gate in Neiko, which is sometimes called by the Japanese the most beautiful gate in all Japan; it was built in a time when there was great influence from Chinese art. This gate is very elaborate, with lots of gables and beautiful carving and lots of columns and dragon heads and princes carved into the pillars, and so on. But when one looks closely he sees that in the elaborate and complex design along one of the pillars, one of the small design elements is carved upside down; otherwise the thing is completely symmetrical. If one asks why this is, the story is that it was carved upside down so that the gods will not be jealous of the perfection of man. So they purposely put an error in there, so that the gods would not be jealous and get angry with human beings. We might like to turn the idea around and think that the true explanation of the near symmetry of nature is this: that God made the nature laws only nearly symmetrical so that we should not be jealous of His perfection!”
I say that long before the spaceman hits reflection earth with 8.1 x 10^17 Joules of energy freshly converted from his mass, various chunks of space debris and solar winds would no doubt have eaten away the whole planet.
[3]: To be fair, I'm not sure he survived, though I'm not sure it was the food that killed him.
[1]: Or I might have saw it with the title "Journey to the Far Side of the Sun". Actually I'm not even sure if that's even the movie I saw, since I had to google for the plot to find it.
[2]: that's not an 180 degrees phase shift, mind you. Distances from the sun are (presumably) the same
It's been many years since I've seen the movie Doppelganger [1] but it left me with a lingering question that I finally got answered this week.
The plot of the movie is that a planet is accidentally (duh) discovered in the exact same orbit as the earth, only rotated by 180 degrees [2], so they send a man out to investigate. The spaceman ends up crash landing on the strange planet which is actually a mirror earth, where everything that happens on our earth, happens on the other earth as well, the only difference being that everything is reflected, just like looking at a mirror. Right is left and left is right. So when the spaceman disappears behind the sun, another "reflection" spaceman appears. Of course nobody believes him, even though they see that his internal organs are set up the wrong way.
So the question: Could this movie plot happen. I'm looking for "possible" not "probable".
So the other day I was listening to a lecture by Richard Feynman which was about exactly that problem. Only he didn't mention the movie. He was more concerned about whether the laws of physics are valid when you look at them in the mirror. As he puts it "can we describe 'left' to an alien over the phone?".
I will answer the original question first (could this movie happen) which is easy. No, it couldn't happen because of the parallax view the reflection earth would have of the universe. Astronomers would have placed their telescopes a tad differently to inspect close-up objects. Another problem I can think of are meteorite collisions (the dinosaurs could still be alive even it weren't for those). These didn't concern Feynman.
Here's another one: could life be sustained on a reflection earth? Feynman says that yes but not exactly. It seems that proteins and stuff are not symmetrical in that way and left-handed life could eat only life that evolved with left-handed life around it. So life could be there but the spaceman that landed there wouldn't be able to survive [3].
How about the physics. Is there a physical law that cares about left and right? A variation to this question is "If we were to substitute every occasion of the word 'left' with 'right' (within the relevant context) and vice versa in every physics book ever printed, would the books still make sense?"
You would be surprised to know that it wouldn't. Ok they actually would make sense but I said they wouldn't so that you would be a bit surprised and perhaps thought about it a little. In another twist, they actually wouldn't make sense if you didn't change some other stuff there as well, such as "north" and "south" (this also explains how come all those "right hand rules" in electro-magnetism, like in Laplace force could remain in place). This is getting really silly, but north and south are arbitrary also, so in case we don't care to be compliant with geography it's fine to leave everything as is.
So there, just as you have imagined all along. The symmetry holds. Wrong! And this isn't just a half lame technicality like "north" and "south". There are honest to goodness real phenomena that actually do define a certain "right" and a certain "left". You can do as I did and file it into the "under a strong magnetic field the products of some tiny particle's decay tends to go more to the left than the right" category, or you can look up CP-violations.
So there you have it. Contrary to what anyone would reasonably believe and to what everyone believed until the 60s, there _is_ a difference between right and left in the physical world, so reflection-earth could not exist.
I am really sorry about this but there is a final (?) twist to the story. It turns out that if matter spins to the left, antimatter spins to the right. Reflection earth would work the same as ours if only it was made out of antimatter. Now how cool is that. A seemingly obvious perfect symmetry that has tiny quantum flaws, which can be fitted in an even larger symmetry.
Feynman concludes with the rather poetic:
"So our problem is to explain where symmetry comes from. Why is nature so nearly symmetrical? No one has any idea why. The only thing we might suggest is something like this: There is a gate in Japan, a gate in Neiko, which is sometimes called by the Japanese the most beautiful gate in all Japan; it was built in a time when there was great influence from Chinese art. This gate is very elaborate, with lots of gables and beautiful carving and lots of columns and dragon heads and princes carved into the pillars, and so on. But when one looks closely he sees that in the elaborate and complex design along one of the pillars, one of the small design elements is carved upside down; otherwise the thing is completely symmetrical. If one asks why this is, the story is that it was carved upside down so that the gods will not be jealous of the perfection of man. So they purposely put an error in there, so that the gods would not be jealous and get angry with human beings. We might like to turn the idea around and think that the true explanation of the near symmetry of nature is this: that God made the nature laws only nearly symmetrical so that we should not be jealous of His perfection!”
I say that long before the spaceman hits reflection earth with 8.1 x 10^17 Joules of energy freshly converted from his mass, various chunks of space debris and solar winds would no doubt have eaten away the whole planet.
[3]: To be fair, I'm not sure he survived, though I'm not sure it was the food that killed him.
[1]: Or I might have saw it with the title "Journey to the Far Side of the Sun". Actually I'm not even sure if that's even the movie I saw, since I had to google for the plot to find it.
[2]: that's not an 180 degrees phase shift, mind you. Distances from the sun are (presumably) the same
Mood: awed
