Sean Carroll: What is the Wave Function?
00:00:00.000 | - So what's a wave function?
00:00:03.680 | You said it's an interesting detail.
00:00:05.560 | - Yeah.
00:00:06.400 | - But in any interpretation,
00:00:09.280 | what is the wave function in quantum mechanics?
00:00:11.880 | - Well, you know, we had this idea from Rutherford
00:00:14.120 | that atoms look like little solar systems.
00:00:17.040 | But people very quickly realized
00:00:18.920 | that can't possibly be right.
00:00:20.520 | Because if an electron is orbiting in a circle,
00:00:23.220 | it will give off light.
00:00:24.400 | All the light that we have in this room
00:00:25.840 | comes from electrons zooming up and down and wiggling,
00:00:28.360 | and that's what electromagnetic waves are.
00:00:30.560 | And you can calculate how long would it take
00:00:32.440 | for the electron just to spiral into the nucleus.
00:00:34.800 | And the answer is 10 to the minus 11 seconds, okay?
00:00:37.440 | 100 billionth of a second.
00:00:39.000 | So that's not right.
00:00:40.120 | Meanwhile, people had realized that light,
00:00:44.380 | which we understood from the 1800s was a wave,
00:00:48.060 | had properties that were similar to that of particles, right?
00:00:50.800 | This is Einstein and Planck and stuff like that.
00:00:53.560 | So if something that we agree was a wave
00:00:57.380 | had particle-like properties,
00:00:59.840 | then maybe something we think is a particle, the electron,
00:01:02.720 | has wave-like properties, right?
00:01:05.360 | And so a bunch of people eventually came to the conclusion,
00:01:08.560 | don't think about the electron as a little point particle
00:01:11.640 | orbiting like a solar system.
00:01:13.960 | Think of it as a wave that is spread out.
00:01:16.640 | They cleverly gave this the name the wave function,
00:01:18.920 | which is the dopiest name in the world
00:01:20.420 | for one of the most profound things in the universe.
00:01:24.040 | There's literally a number at every point in space,
00:01:28.300 | which is the value of the electron's wave function
00:01:31.160 | at that point.
00:01:32.000 | - And there's only one wave function.
00:01:34.980 | - Yeah, they eventually figured that out.
00:01:36.460 | That took longer.
00:01:37.780 | But when you have two electrons,
00:01:39.860 | you do not have a wave function for electron one
00:01:42.100 | and a wave function for electron two.
00:01:43.980 | You have one combined wave function for both of them.
00:01:47.280 | And indeed, as you say, there's only one wave function
00:01:50.020 | for the entire universe at once.
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