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All right, so are you ready to dive into some seriously mind bending physics?

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I think so.

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You wanted to understand quantum mechanics better, right?

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Yeah.

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Particularly that whole idea about objects exploring all possible paths.

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Oh yeah, definitely.

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Well, we've got this video and transcript from a physics expert that

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breaks it down into a really cool way using something called action.

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Action, huh?

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Yeah.

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And it's not always covered in like traditional physics classes,

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Yeah.

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But it turns out to be super important in understanding how the quantum world works.

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Okay.

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So our mission today is to try and unpack this complex concept.

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Sounds good.

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And see how it connects to the familiar world we experience.

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I am game.

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Excellent.

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I think you'll be surprised by how intuitive it can be once we kind of break it down.

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I hope so.

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I hope so.

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So the expert starts with this analogy about saving a friend in the water.

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Okay.

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Let's say they're struggling out in the ocean, right?

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Do you run straight towards them the shortest distance?

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Right.

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Or does there maybe a faster way?

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Oh, that's a, yeah, that's a great question because it gets right to the heart of optimization.

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You might instinctively want to run straight to them.

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Right.

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But remember, you run much faster on sand than you swim in the water.

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Oh, yeah.

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So sprinting down the beach a bit first, then swimming a shorter distance might

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actually be quicker.

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Right.

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You know.

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That makes total sense.

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It's like our brains are already doing these many physics calculations without

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us even realizing it.

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Yeah.

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And this light does the same thing.

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Really?

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It somehow knows the fastest path.

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Yeah.

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Just like we do in that beach scenario.

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Right.

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And for a long time, even physicists like myself assumed light just sets off in one

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direction and then adjusts as it encounters different mediums.

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Right.

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But there's a deeper principle at play here and that's where action comes in.

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Okay.

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So let's unpack action.

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Okay.

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It's a quantity that combines mass, velocity and distance.

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Yeah.

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I do.

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Got it.

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Okay.

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Think of it as a measure of how much effort a particle expands as it moves along

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a path.

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Okay.

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And it's not a new idea either.

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Right.

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It was first proposed way back in the 1700s by a scientist named Montpertuis.

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And later refined by Hamilton.

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Okay.

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Initially it was just seen as a convenient alternative to Newton's laws.

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Okay.

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So how did this concept of action become so central to quantum mechanics?

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Well, it all started with a puzzle that had physicists scratching their heads in

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the late 1800s.

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Okay.

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Picture Germany, the era of emerging electric lighting.

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Okay.

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Light bulbs were the hot new tech.

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Yeah.

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Fun intended.

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Okay.

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And scientists were obsessed with understanding how to maximize their light output.

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So they're trying to figure out how different materials emit light as they heat up.

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Mm-hmm.

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And I'm guessing this is where the black body comes in.

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You're exactly right.

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Okay.

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To simplify things, they imagined a black body.

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Okay.

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A hypothetical object that absorbs all light and it misradiation perfectly based on its temperature.

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So almost like a perfect absorber and emitter?

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Precisely think of it like a hole in a metal cube.

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Okay.

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Any light entering the hole gets trapped inside making it a perfect absorber and therefore a perfect emitter.

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Okay.

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I'm following so far.

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So they're using this idealized black body to study how light is emitted.

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Yeah.

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And they run into a problem.

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A big one.

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Oh no.

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Classical physics, which worked so well for so many things, completely failed to predict the radiation emitted by these black bodies.

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Mm-hmm.

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The theory predicted an infinite amount of energy at short wavelengths.

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Wow.

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That's like saying a light bulb would release more energy than the sun.

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It doesn't sound right.

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Clearly something was fundamentally wrong.

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So this is what they called the ultraviolet catastrophe, right?

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Yes.

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It was a major roadblock.

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So how did they resolve it?

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Enter Max Planck.

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Exactly.

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Planck was wrestling with this problem for years trying every approach imaginable and nothing worked.

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Oh wow.

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In a moment of desperation, he did something nobody had considered before.

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What was that?

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Classical physics said that the energy of an electromagnetic wave could take on any value.

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But Planck decided to try restricting it, allowing it only in multiples of the smallest possible amount of quantum.

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So he's saying energy isn't continuous.

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Right.

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But comes in these discrete packets.

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Yeah.

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That's a huge shift in thinking.

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It was a radical idea.

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And to connect this energy to the waves frequency, he came up with the equation E8, where H is a constant.

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And this H is what we now call Planck's constant, right?

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Exactly.

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But what does it have to do with action?

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That's the amazing part.

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It turns out that Planck's constant H has the units of action.

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Really?

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Planck realized that any change in nature might occur in multiples of this fundamental quantum of action.

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Wow.

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Wow. So this seemingly simple idea of quantized energy had profound implications for understanding action at a fundamental level.

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It did indeed.

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It was a hint that there was a deeper principle at play.

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Yeah.

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Something that connected energy frequency and this mysterious concept of action.

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OK.

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And it wouldn't be long before young Albert Einstein would take this idea even further.

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OK, this is getting really interesting.

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It is.

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But before we move on to Einstein, I just want to make sure I understand the key takeaway here.

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Sure.

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Planck's work on black body radiation essentially revealed that energy isn't continuous, but exists in discrete packets.

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And this realization is intimately tied to the concept of action.

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That's a fantastic summary.

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You've hit the nail on the head.

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All right.

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I'm ready for Einstein.

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What did he do with this quantum idea?

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Well, Einstein was never one to shy away from radical ideas.

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In 1905, he took Planck's quantum theory and ran with it, arguing that light itself exists in these discrete packets, which we now call photons.

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Photons.

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Each photon carries energy equal to HFF, Planck's constant times its frequency.

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Wow.

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Yeah, it's pretty incredible.

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It is.

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Yeah.

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So Einstein took Planck's idea of quantized energy and applied it to light itself.

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Uh-huh.

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That's a huge leap.

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It is.

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What made him think that light could be made of these individual packets of energy?

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Well, Einstein was looking at something called the photoelectric effect, where light can knock electrons loose from a metal.

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OK.

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But here's the catch.

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It only works if the light's frequency is high enough.

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So it doesn't matter how bright the light is, how many waves are hitting the metal.

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If it's the wrong kind of light, nothing happens.

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Exactly.

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It's like each photon, each little packet of light needs a certain amount of energy to knock an electron loose.

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Right.

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And that energy, as Planck discovered, is directly related to the light's frequency.

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OK.

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I can see how that supports the idea of light being quantized.

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But what does all this have to do with atoms?

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Well, a few years after Einstein's work on the photoelectric effect,

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a Janish physicist named Niels Bohr was wrestling with a different problem.

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OK.

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The stability of atoms.

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Right.

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If electrons are negatively charged particles orbiting a positively charged nucleus,

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Yes.

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why don't they just spiral inward and crash?

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Exactly.

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Classical physics couldn't explain why atoms didn't collapse in on themselves?

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Yeah, that's a good point.

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Bohr, inspired by Planck's quantum idea, proposed a radical solution.

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OK.

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I like where this is going.

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What if the angular momentum of an electron in an atom could only exist in discrete values,

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multiples of Planck's constant, divided by 2 pi?

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Hold on.

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Angular momentum.

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Remind me what that is again.

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Of course, angular momentum is a measure of an object's tendency to keep rotating.

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OK.

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For an electron orbiting a nucleus.

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Right.

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It depends on its speed and distance from the nucleus.

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OK.

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And the interesting thing is the units of angular momentum are the same as action.

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So Bohr was basically saying that action at the atomic level is quantized too.

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It can only come in specific chunks.

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Exactly.

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And to represent Planck's constant, divided by 2 pi, we use the symbol H bar.

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H bar.

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Bohr proposed that the electron's angular momentum could only be multiples of H bar.

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OK.

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But why would quantizing angular momentum solve the problem of atomic stability?

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Well, think about it this way.

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OK.

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If the electron's angular momentum can only take on specific values,

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that means it can only exist at specific distances from the nucleus.

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OK.

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It's like there are only certain allowed orbits for the electron.

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So the electron can't just gradually spiral inward because it has to jump between these allowed orbits.

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Precisely.

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It's a bit like climbing a ladder.

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You can't stand between the rungs.

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Right.

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And this jumping between orbits is what explains how atoms emit and absorb light.

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When an electron jumps from a higher energy orbit to a lower one,

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the difference in energy is released as a photon of light.

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And Bohr actually calculated these energy jumps and found they perfectly matched the observed spectrum of light emitted by hydrogen.

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He did.

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It was a huge victory for the idea of chronization, even if nobody fully understood why it worked.

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Right.

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And that's where Louis de Broglie enters the scene with an even more radical idea.

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Oh.

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He thought.

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Here we go.

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If light, which we normally think of as a wave, can behave like a particle.

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Right.

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Why not the other way around?

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What if matter?

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OK.

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Things like electrons could behave like waves.

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Wait, matter as waves.

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I know.

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That's mind blowing.

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I thought waves were spread out.

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Yeah.

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And particles were but particle.

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It does seem counterintuitive, right?

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It does.

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But de Broglie proposed that every object, even you and me, has a wavelength associated with it.

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Really?

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And this wavelength is determined by Planck's constant divided by the object's momentum.

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OK.

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But if everything has a wavelength, why don't we see people diffracting through doorways like light does?

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That's a great question.

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The answer lies in the incredible smallness of Planck's constant for everyday objects like a baseball or a person.

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Yeah.

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The wavelength is so tiny, so incredibly minuscule that it's practically unmeasurable.

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OK.

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But for tiny particles like electrons.

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Right.

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The wavelength becomes significant.

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So how does this wave nature of matter explain Bohr's quantized atom?

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It provides a beautiful and intuitive explanation.

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Imagine the electron orbiting the nucleus not as a point particle, but as a wave.

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So like a wave rippling around a central point.

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Exactly.

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And just like a guitar string can only vibrate at certain frequencies to create standing waves.

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Yeah.

268
00:10:09,200 --> 00:10:13,800
An electron can only exist in orbits where its wave fits perfectly around the nucleus.

269
00:10:14,000 --> 00:10:14,400
OK.

270
00:10:14,400 --> 00:10:19,000
It has to form a standing wave, a whole number of wavelengths fitting around the circumference of the orbit.

271
00:10:19,200 --> 00:10:26,200
So Bohr's seemingly arbitrary quantization of angular momentum arises naturally from this wave nature of matter.

272
00:10:26,400 --> 00:10:26,800
Yes.

273
00:10:27,000 --> 00:10:28,200
It all starts to click into place.

274
00:10:28,400 --> 00:10:29,000
It does.

275
00:10:29,200 --> 00:10:34,200
And it leads to an even deeper understanding of one of the most iconic experiments in quantum mechanics.

276
00:10:34,400 --> 00:10:34,600
Yeah.

277
00:10:34,800 --> 00:10:35,800
The double slit experiment.

278
00:10:36,000 --> 00:10:36,400
Exactly.

279
00:10:36,600 --> 00:10:40,800
That's the one where you shine light through two slits and get an interference pattern on a screen.

280
00:10:41,000 --> 00:10:41,600
Yes.

281
00:10:41,800 --> 00:10:43,400
Showing that light acts like a wave.

282
00:10:43,400 --> 00:10:44,400
Exactly.

283
00:10:44,600 --> 00:10:46,600
But it's actually much deeper than that.

284
00:10:46,800 --> 00:10:51,800
Richard Feynman, a brilliant physicist, took this experiment to the next level.

285
00:10:52,000 --> 00:10:52,400
OK.

286
00:10:52,600 --> 00:10:57,200
He imagined adding more and more slits until the screen with slits essentially disappears.

287
00:10:57,400 --> 00:10:57,800
OK.

288
00:10:58,000 --> 00:11:03,000
The math then forces you to consider every possible path a particle could take.

289
00:11:03,200 --> 00:11:05,800
Not just through the slits, but through all of space.

290
00:11:06,000 --> 00:11:06,400
Whoa.

291
00:11:06,600 --> 00:11:08,200
That's a lot of paths to consider.

292
00:11:08,400 --> 00:11:09,200
It is.

293
00:11:09,200 --> 00:11:14,600
And this led Feynman to develop what we call the path integral formulation of quantum mechanics.

294
00:11:14,800 --> 00:11:15,200
Oh, wow.

295
00:11:15,400 --> 00:11:18,800
Instead of thinking about a particle taking a single defined path,

296
00:11:19,000 --> 00:11:22,200
you consider the contribution of every conceivable path.

297
00:11:22,400 --> 00:11:22,600
Right.

298
00:11:22,800 --> 00:11:28,200
Even the seemingly absurd ones to calculate the probability of a particle going from point A to point B.

299
00:11:28,400 --> 00:11:30,600
So we're not just talking about waves interfering anymore.

300
00:11:30,800 --> 00:11:31,000
Right.

301
00:11:31,200 --> 00:11:33,600
We're talking about all these different paths interfering with each other.

302
00:11:33,800 --> 00:11:34,600
That's right.

303
00:11:34,600 --> 00:11:39,400
Each path is assigned a phase related to the action along that path.

304
00:11:39,600 --> 00:11:40,000
OK.

305
00:11:40,200 --> 00:11:47,200
As a particle traverses a path, its phase increases and this phase determines the amplitude of the wave associated with that path.

306
00:11:47,400 --> 00:11:47,800
OK.

307
00:11:48,000 --> 00:11:52,400
Now, Planck's constant or H bar is incredibly tiny, remember?

308
00:11:52,600 --> 00:11:52,800
Right.

309
00:11:53,000 --> 00:11:53,800
Incredibly tiny.

310
00:11:54,000 --> 00:12:00,600
And that means the phase of macroscopic objects like a baseball changes incredibly rapidly as it moves.

311
00:12:00,800 --> 00:12:01,200
Oh, wow.

312
00:12:01,200 --> 00:12:07,000
For all practical purposes, the phases of most paths cancel each other out through destructive interference.

313
00:12:07,200 --> 00:12:08,400
So they just disappear.

314
00:12:08,600 --> 00:12:09,400
In a way, yeah.

315
00:12:09,600 --> 00:12:09,800
OK.

316
00:12:10,000 --> 00:12:13,800
We only observe the paths where the phases align constructively interfering.

317
00:12:14,000 --> 00:12:15,800
So it's like all these crazy paths are happening?

318
00:12:16,000 --> 00:12:16,200
Yes.

319
00:12:16,400 --> 00:12:18,200
But we only see the ones that reinforce each other.

320
00:12:18,400 --> 00:12:19,000
Exactly.

321
00:12:19,200 --> 00:12:20,400
And here's the kicker.

322
00:12:20,600 --> 00:12:20,800
OK.

323
00:12:21,000 --> 00:12:26,000
Those paths of constructive interference correspond to the paths of least action.

324
00:12:26,200 --> 00:12:26,800
Wow.

325
00:12:26,800 --> 00:12:32,600
It's the principle of least action governed by quantum mechanics that determines the paths we see in the classical world.

326
00:12:32,800 --> 00:12:33,600
That's incredible.

327
00:12:33,800 --> 00:12:34,000
Yeah.

328
00:12:34,200 --> 00:12:39,600
So even though we don't see it directly, everything is constantly exploring all these possibilities.

329
00:12:39,800 --> 00:12:40,200
Yes.

330
00:12:40,400 --> 00:12:41,800
It's a mind-blowing concept.

331
00:12:42,000 --> 00:12:42,400
It is.

332
00:12:42,600 --> 00:12:48,600
And this principle of least action, this minimization of effort, is what shapes the reality we perceive.

333
00:12:48,800 --> 00:12:49,200
Wow.

334
00:12:49,400 --> 00:12:56,200
From the trajectory of a baseball to the orbits of planets, it's all a delicate dance of quantum possibilities,

335
00:12:56,200 --> 00:12:58,200
guided by this fundamental principle.

336
00:12:58,400 --> 00:12:59,200
That's amazing.

337
00:12:59,400 --> 00:12:59,600
Yeah.

338
00:12:59,800 --> 00:13:07,200
So in a way, our everyday world is built on this underlying quantum weirdness, where things explore all paths.

339
00:13:07,400 --> 00:13:08,000
It really is.

340
00:13:08,200 --> 00:13:10,000
It's like the universe is always optimizing for efficiency.

341
00:13:10,200 --> 00:13:10,800
It is.

342
00:13:11,000 --> 00:13:15,000
But if everything is exploring all these paths, how do we actually see this happening?

343
00:13:15,200 --> 00:13:19,600
Well, it's hard to directly observe these quantum effects for macroscopic objects.

344
00:13:19,800 --> 00:13:22,200
Remember, the wavelengths are so small that it's practically impossible.

345
00:13:22,400 --> 00:13:22,800
Right.

346
00:13:22,800 --> 00:13:30,600
But I actually have a demo that can visually demonstrate how manipulating these paths can reveal the underlying quantum reality.

347
00:13:30,800 --> 00:13:31,800
Oh, a demo.

348
00:13:32,000 --> 00:13:33,200
I love demos.

349
00:13:33,400 --> 00:13:34,200
Tell me more.

350
00:13:34,400 --> 00:13:38,400
It involves a mirror, a light source, and a special piece of foil.

351
00:13:38,600 --> 00:13:43,200
This foil acts as a diffraction grating covered in thousands of tiny lines.

352
00:13:43,400 --> 00:13:43,600
Okay.

353
00:13:43,800 --> 00:13:47,200
By strategically covering portions of the mirror with this foil.

354
00:13:47,400 --> 00:13:47,800
Okay.

355
00:13:48,000 --> 00:13:52,000
We can actually manipulate the interference pattern of light reflecting off the mirror.

356
00:13:52,000 --> 00:13:55,000
So you're saying you can make light reflect in directions it normally wouldn't?

357
00:13:55,200 --> 00:13:55,800
Exactly.

358
00:13:56,000 --> 00:14:03,600
We can make the light take paths that seem impossible from a classical perspective, proving that it's really exploring all possible paths.

359
00:14:03,800 --> 00:14:04,200
Wow.

360
00:14:04,400 --> 00:14:05,600
We even did it with a laser.

361
00:14:05,800 --> 00:14:06,200
Really?

362
00:14:06,400 --> 00:14:15,600
By shining the laser next to the foil covered mirror, we could make the laser beam reflect off the mirror, even though the laser was pointed in a completely different direction.

363
00:14:15,800 --> 00:14:16,400
No way.

364
00:14:16,600 --> 00:14:18,400
It's pretty mind blowing to see it in action.

365
00:14:18,600 --> 00:14:19,200
That's awesome.

366
00:14:19,400 --> 00:14:20,000
Yeah, it is.

367
00:14:20,000 --> 00:14:30,000
Okay, so we've gone from this everyday idea of finding the quickest way to rescue someone to this mind blowing concept of objects exploring all possible paths.

368
00:14:30,200 --> 00:14:30,600
Right.

369
00:14:30,800 --> 00:14:35,200
But it all comes back to this idea of action being this underlying principle that governs everything.

370
00:14:35,400 --> 00:14:35,600
Right.

371
00:14:35,800 --> 00:14:38,400
And it's not just some abstract mathematical tool.

372
00:14:38,600 --> 00:14:39,800
Action is fundamental.

373
00:14:40,000 --> 00:14:40,200
Okay.

374
00:14:40,400 --> 00:14:41,400
Help me connect the dots here.

375
00:14:41,600 --> 00:14:42,000
Sure.

376
00:14:42,200 --> 00:14:48,000
How does action relate to the actual laws of physics that we use to describe the universe?

377
00:14:48,000 --> 00:14:56,400
Well, the laws of physics can actually be derived from finding the correct Lagrangian, which is a mathematical expression related to the action of a system.

378
00:14:56,600 --> 00:15:01,400
So Lagrangian is like a blueprint for how a system will evolve over time.

379
00:15:01,600 --> 00:15:02,200
Exactly.

380
00:15:02,400 --> 00:15:07,400
And this is what theoretical physicists are really searching for when they talk about a theory of everything.

381
00:15:07,600 --> 00:15:08,400
A theory of everything?

382
00:15:08,600 --> 00:15:10,400
They're looking for the ultimate Lagrangian.

383
00:15:10,600 --> 00:15:11,000
Wow.

384
00:15:11,200 --> 00:15:14,400
The one that can explain all the forces and particles in the universe.

385
00:15:14,400 --> 00:15:18,800
So it's like a quest to find the deepest, most fundamental level of reality.

386
00:15:19,000 --> 00:15:19,400
It is.

387
00:15:19,600 --> 00:15:23,200
And the principle of least action is a key part of that journey.

388
00:15:23,400 --> 00:15:24,400
It really is.

389
00:15:24,600 --> 00:15:33,800
It's this incredible idea that the universe at its core is always optimizing, always seeking the most efficient path, the path of least effort.

390
00:15:34,000 --> 00:15:41,000
It's amazing to think that this seemingly simple idea of minimizing effort is woven into the fabric of reality.

391
00:15:41,200 --> 00:15:41,800
It is.

392
00:15:42,000 --> 00:15:43,800
So what does this all mean for us non-physicists?

393
00:15:43,800 --> 00:15:49,200
How should we think about the world differently after learning about action and quantum mechanics?

394
00:15:49,400 --> 00:15:52,600
I think it encourages us to look beyond the surface of things.

395
00:15:52,800 --> 00:15:53,000
Yeah.

396
00:15:53,200 --> 00:15:56,600
We live in a world where objects seem to follow definite paths.

397
00:15:56,800 --> 00:15:57,200
Right.

398
00:15:57,400 --> 00:16:02,000
But beneath that apparent certainty, there's this incredible quantum dance of possibilities.

399
00:16:02,200 --> 00:16:02,600
Wow.

400
00:16:02,800 --> 00:16:12,600
Even a simple act like throwing a ball is at its core a symphony of quantum interactions guided by this principle of least action.

401
00:16:12,600 --> 00:16:19,400
You know, it's like our intuition about the world is based on this classical view where things are predictable and follow a single path.

402
00:16:19,600 --> 00:16:19,800
Yeah.

403
00:16:20,000 --> 00:16:25,200
But quantum mechanics reveals this hidden layer of reality where things are far more complex and fascinating.

404
00:16:25,400 --> 00:16:27,000
And that's the beauty of it, isn't it?

405
00:16:27,200 --> 00:16:31,800
The more we learn about the universe, the more we realize how much we still don't know.

406
00:16:32,000 --> 00:16:33,000
I completely agree.

407
00:16:33,000 --> 00:16:43,200
So to wrap things up, I think the key takeaway here is that we live in a world where objects explore all paths guided by this principle of least action.

408
00:16:43,400 --> 00:16:46,800
But it's quantum mechanics that shakes the reality we perceive.

409
00:16:47,000 --> 00:16:52,200
It makes you wonder what other hidden actions might be shaping our reality that we haven't even discovered yet.

410
00:16:52,400 --> 00:16:53,000
I love that thought.

411
00:16:53,200 --> 00:16:55,400
There's so much more to explore and uncover.

412
00:16:55,600 --> 00:16:56,000
Right.

413
00:16:56,200 --> 00:17:00,000
The universe is full of wonder and the quest to understand it is never-ending.

414
00:17:00,200 --> 00:17:01,400
And that's what makes it so exciting.

415
00:17:01,600 --> 00:17:01,800
Yeah.

416
00:17:01,800 --> 00:17:04,600
So keep questioning, keep exploring, keep diving deep.

417
00:17:04,800 --> 00:17:08,000
Who knows what other mind-blowing discoveries await us out there?

418
00:17:08,200 --> 00:17:09,600
Definitely keep exploring.

419
00:17:09,800 --> 00:17:10,000
All right.

420
00:17:10,200 --> 00:17:14,400
That's it for this deep dive into the world of quantum mechanics and the principle of least action.

421
00:17:14,800 --> 00:17:15,400
Thanks for having me.

422
00:17:15,600 --> 00:17:16,200
Absolutely.

423
00:17:16,400 --> 00:17:18,600
Until next time, keep those brains budding.

424
00:17:18,800 --> 00:17:19,200
Bye.

425
00:17:19,400 --> 00:17:19,800
Bye.

426
00:17:21,200 --> 00:17:21,600
Okay.

427
00:17:21,800 --> 00:17:26,200
So Einstein took Planck's idea of quantized energy and applied it to light itself.

428
00:17:26,400 --> 00:17:27,600
It's a huge leap.

429
00:17:27,800 --> 00:17:31,400
What made him think that light could be made of these individual packets of energy?

430
00:17:31,400 --> 00:17:34,400
Well, Einstein was looking at something called the photoelectric effect,

431
00:17:34,600 --> 00:17:37,600
where light can knock electrons loose from a metal.

432
00:17:37,800 --> 00:17:38,800
But here's the catch.

433
00:17:39,000 --> 00:17:41,600
It only works if the light's frequency is high enough.

434
00:17:41,800 --> 00:17:45,200
So it doesn't matter how bright the light is, how many waves are hitting the metal.

435
00:17:45,400 --> 00:17:48,000
If it's the wrong kind of light, nothing happens.

436
00:17:48,200 --> 00:17:48,800
Exactly.

437
00:17:49,000 --> 00:17:54,000
It's like each photon, each little packet of light needs a certain amount of energy to knock an electron loose.

438
00:17:54,200 --> 00:17:59,200
And that energy, as Planck discovered, is directly related to the light's frequency.

439
00:17:59,400 --> 00:17:59,800
Okay.

440
00:17:59,800 --> 00:18:03,200
I can see how that supports the idea of light being quantized.

441
00:18:03,400 --> 00:18:05,200
But what does all this have to do with atoms?

442
00:18:05,400 --> 00:18:09,000
Well, a few years after Einstein's work on the photoelectric effect,

443
00:18:09,200 --> 00:18:15,600
a Danish physicist named Niels Bohr was wrestling with a different problem, the stability of atoms.

444
00:18:15,800 --> 00:18:16,200
Right.

445
00:18:16,400 --> 00:18:20,800
If electrons are negatively charged particles orbiting a positively charged nucleus,

446
00:18:21,000 --> 00:18:23,200
why don't they just spiral inward and crash?

447
00:18:23,400 --> 00:18:24,000
Exactly.

448
00:18:24,200 --> 00:18:27,400
Classical physics couldn't explain why atoms didn't collapse in on themselves.

449
00:18:27,600 --> 00:18:28,200
Yeah, I think that point.

450
00:18:28,200 --> 00:18:32,400
Bohr, inspired by Planck's quantum idea, proposed a radical solution.

451
00:18:32,600 --> 00:18:33,000
Okay.

452
00:18:33,200 --> 00:18:34,200
I like where this is going.

453
00:18:34,400 --> 00:18:39,400
What if the angular momentum of an electron in an atom could only exist in discrete values,

454
00:18:39,600 --> 00:18:42,400
multiples of Planck's constant divided by 2 pi?

455
00:18:42,600 --> 00:18:43,000
Hold on.

456
00:18:43,200 --> 00:18:45,200
Angular momentum remind me what that is again.

457
00:18:45,400 --> 00:18:51,600
Of course, angular momentum is a measure of an object's tendency to keep rotating for an electron orbiting a nucleus.

458
00:18:51,800 --> 00:18:54,400
It depends on its speed and distance from the nucleus.

459
00:18:54,400 --> 00:18:59,000
And the interesting thing is the units of angular momentum are the same as action.

460
00:18:59,200 --> 00:19:03,400
So Bohr was basically saying that action at the atomic level is quantized too.

461
00:19:03,600 --> 00:19:04,800
It can only come in specific chunks.

462
00:19:05,000 --> 00:19:05,400
Exactly.

463
00:19:05,600 --> 00:19:09,600
And to represent Planck's constant divided by 2 pi, we use the symbol H bar.

464
00:19:09,800 --> 00:19:10,200
H bar.

465
00:19:10,400 --> 00:19:10,600
Okay.

466
00:19:10,800 --> 00:19:15,200
Bohr proposed that the electron's angular momentum could only be multiples of H bar.

467
00:19:15,400 --> 00:19:15,600
Okay.

468
00:19:15,800 --> 00:19:21,400
But why would quantizing angular momentum solve the problem of atomic stability?

469
00:19:21,600 --> 00:19:22,800
Well, think about it this way.

470
00:19:22,800 --> 00:19:26,800
If the electron's angular momentum can only take on specific values,

471
00:19:27,000 --> 00:19:30,200
that means it can only exist at specific distances from the nucleus.

472
00:19:30,400 --> 00:19:33,200
It's like there are only certain allowed orbits for the electron.

473
00:19:33,400 --> 00:19:38,400
So the electron can't just gradually spiral inward because it has to jump between these allowed orbits.

474
00:19:38,600 --> 00:19:39,000
Precisely.

475
00:19:39,200 --> 00:19:40,400
It's a bit like climbing a ladder.

476
00:19:40,600 --> 00:19:42,000
You can't stand between the rungs.

477
00:19:42,200 --> 00:19:50,200
And this jumping between orbits is what explains how atoms emit and absorb light when an electron jumps from a higher energy orbit to a lower one.

478
00:19:50,200 --> 00:19:53,200
The difference in energy is released as a photon of light.

479
00:19:53,400 --> 00:19:59,800
And Bohr actually calculated these energy jumps and found they perfectly matched the observed spectrum of light emitted by hydrogen.

480
00:20:00,000 --> 00:20:00,400
He did.

481
00:20:00,600 --> 00:20:05,600
It was a huge victory for the idea of quantization, even if nobody fully understood why it worked.

482
00:20:05,800 --> 00:20:06,000
Right.

483
00:20:06,200 --> 00:20:09,800
And that's where Louis de Broglie enters the scene with an even more radical idea.

484
00:20:10,000 --> 00:20:16,000
He thought if light, which we normally think of as a wave, can behave like a particle, why not the other way around?

485
00:20:16,200 --> 00:20:19,000
What if matter, things like electrons, could behave like waves?

486
00:20:19,000 --> 00:20:20,400
Weight matter is waves.

487
00:20:20,600 --> 00:20:21,600
That's mind blowing.

488
00:20:21,800 --> 00:20:24,800
I thought waves were spread out and particles were well, particles.

489
00:20:25,000 --> 00:20:26,600
It does seem counterintuitive, right?

490
00:20:26,800 --> 00:20:31,400
But de Broglie proposed that every object, even you and me, has a wavelength associated with it.

491
00:20:31,600 --> 00:20:35,400
And this wavelength is determined by Planck's constant divided by the object's momentum.

492
00:20:35,600 --> 00:20:36,200
OK.

493
00:20:36,400 --> 00:20:42,600
But if everything has a wavelength, why don't we see people diffracting through doorways like light does?

494
00:20:42,800 --> 00:20:44,200
That's a great question.

495
00:20:44,200 --> 00:20:50,200
The answer lies in the incredible smallness of Planck's constant for everyday objects, like a baseball or a person.

496
00:20:50,400 --> 00:20:55,800
The wavelength is so tiny, so incredibly minuscule that it's practically unmeasurable.

497
00:20:56,000 --> 00:20:59,800
But for tiny particles like electrons, the wavelength becomes significant.

498
00:21:00,000 --> 00:21:04,200
So how does this wave nature of matter explain Bohr's quantized atom?

499
00:21:04,400 --> 00:21:07,200
It provides a beautiful and intuitive explanation.

500
00:21:07,400 --> 00:21:11,800
Imagine the electron orbiting the nucleus, not as a point particle, but as a wave.

501
00:21:11,800 --> 00:21:14,400
So like a wave rippling around a central point.

502
00:21:14,600 --> 00:21:15,200
Exactly.

503
00:21:15,400 --> 00:21:19,400
And just like a guitar string can only vibrate at certain frequencies to create standing waves,

504
00:21:19,600 --> 00:21:23,800
an electron can only exist in orbits where its wave fits perfectly around the nucleus.

505
00:21:24,000 --> 00:21:29,000
It has to form a standing wave, a whole number of wavelengths fitting around the circumference of the orbit.

506
00:21:29,200 --> 00:21:36,200
So Bohr's seemingly arbitrary quantization of angular momentum arises naturally from this wave nature of matter.

507
00:21:36,400 --> 00:21:37,800
It all starts to click into place.

508
00:21:38,000 --> 00:21:38,400
Yes.

509
00:21:38,400 --> 00:21:45,400
And it leads to an even deeper understanding of one of the most iconic experiments in quantum mechanics, the double slit experiment.

510
00:21:45,600 --> 00:21:45,800
Right.

511
00:21:46,000 --> 00:21:51,800
That's the one where you shine light through two slits and get an interference pattern on a screen showing that light acts like a wave.

512
00:21:52,000 --> 00:21:52,400
Exactly.

513
00:21:52,600 --> 00:21:59,000
But it's actually much deeper than that Richard Feynman, a brilliant physicist, took this experiment to the next level.

514
00:21:59,200 --> 00:22:04,800
Imagine adding more and more slits until the screen with slits essentially disappears.

515
00:22:04,800 --> 00:22:12,800
The math then forces you to consider every possible path the particle could take, not just through the slits, but through all of space.

516
00:22:13,000 --> 00:22:15,600
Oh, that's a lot of paths to consider.

517
00:22:15,800 --> 00:22:16,200
It is.

518
00:22:16,400 --> 00:22:20,800
And this led Feynman to develop what we call the path integral formulation of quantum mechanics.

519
00:22:21,000 --> 00:22:33,000
Instead of thinking about a particle taking a single defined path, you consider the contribution of every conceivable path, even the seemingly absurd ones, to calculate the probability of a particle going from point A to point B.

520
00:22:33,000 --> 00:22:35,400
So we're not just talking about waves interfering anymore.

521
00:22:35,600 --> 00:22:38,200
We're talking about all these different paths interfering with each other.

522
00:22:38,400 --> 00:22:39,000
That's right.

523
00:22:39,200 --> 00:22:43,400
Each path is assigned a phase related to the action along that path.

524
00:22:43,600 --> 00:22:51,200
As the particle traverses a path, its phase increases and this phase determines the amplitude of the wave associated with that path.

525
00:22:51,400 --> 00:22:56,200
Now, Planck's constant, or H-bar, is incredibly tiny.

526
00:22:56,400 --> 00:22:57,600
Right, incredibly tiny.

527
00:22:57,600 --> 00:23:05,400
And that means the phase of macroscopic objects like a baseball changes incredibly rapidly as it moves for all practical purposes.

528
00:23:05,600 --> 00:23:10,400
The phases of most paths cancel each other out through destructive interference.

529
00:23:10,600 --> 00:23:11,400
Oh, they just disappear.

530
00:23:11,600 --> 00:23:16,800
In a way, yeah, we only observe the paths where the phases align constructively interfering.

531
00:23:17,000 --> 00:23:20,800
So it's like all these crazy paths are happening, but we only see the ones that reinforce each other.

532
00:23:21,000 --> 00:23:21,400
Exactly.

533
00:23:21,600 --> 00:23:22,400
And here's the kicker.

534
00:23:22,600 --> 00:23:27,000
Those paths of constructive interference correspond to the paths of least action.

535
00:23:27,000 --> 00:23:32,800
It's the principle of least action governed by quantum mechanics that determines the paths we see in the classical world.

536
00:23:33,000 --> 00:23:33,600
That's incredible.

537
00:23:33,800 --> 00:23:38,200
So even though we don't see it directly, everything is constantly exploring all these possibilities.

538
00:23:38,400 --> 00:23:48,200
Yes, it's a mind-blowing concept and this principle of least action, this minimization of effort, is what shapes the reality we perceive from the trajectory of a baseball to the orbits of planets.

539
00:23:48,400 --> 00:23:53,200
It's all a delicate dance of quantum possibilities guided by this fundamental principle.

540
00:23:53,400 --> 00:23:54,000
That's amazing.

541
00:23:54,000 --> 00:24:01,600
So in a way, our everyday world is built on this underlying quantum weirdness where things explore all paths.

542
00:24:01,800 --> 00:24:04,200
It's like the universe is always optimizing for efficiency.

543
00:24:04,400 --> 00:24:08,400
But if everything is exploring all these paths, how do we actually see this happening?

544
00:24:08,600 --> 00:24:12,800
Well, it's hard to directly observe these quantum effects for macroscopic objects.

545
00:24:13,000 --> 00:24:15,800
Remember, the wavelengths are so small that it's practically impossible.

546
00:24:16,000 --> 00:24:22,800
But I actually have a demo that can visually demonstrate how manipulating these paths can reveal the underlying quantum reality.

547
00:24:23,000 --> 00:24:23,600
A demo.

548
00:24:23,600 --> 00:24:24,200
I love demos.

549
00:24:24,400 --> 00:24:24,800
Tell me more.

550
00:24:25,000 --> 00:24:29,000
It involves a mirror, a light source and a special piece of foil.

551
00:24:29,200 --> 00:24:36,200
This foil acts as a diffraction grating covered in thousands of tiny lines by strategically covering portions of the mirror with this foil.

552
00:24:36,400 --> 00:24:39,800
We can actually manipulate the interference pattern of light reflecting off the mirror.

553
00:24:40,000 --> 00:24:43,200
So you're saying you can make light reflect in directions it normally wouldn't?

554
00:24:43,400 --> 00:24:44,200
Exactly.

555
00:24:44,400 --> 00:24:53,000
We can make the light take paths that seem impossible from a classical perspective, proving that it's really exploring all possible paths.

556
00:24:53,000 --> 00:24:57,400
We even did it with a laver by shining the laser next to the foil covered mirror.

557
00:24:57,600 --> 00:25:02,600
We could make the laser beam reflect off the mirror, even though the laser was pointed in a completely different direction.

558
00:25:02,800 --> 00:25:05,000
It's pretty mind-blowing to see it in action.

559
00:25:05,200 --> 00:25:07,200
That laser demo sounds incredible.

560
00:25:07,400 --> 00:25:13,000
It's amazing how you can actually see these quantum effects in action with something as simple as a mirror and a piece of foil.

561
00:25:13,200 --> 00:25:21,800
Yeah, it really highlights how even though we don't perceive these quantum paths directly, they're always there subtly shaping the world around us.

562
00:25:21,800 --> 00:25:29,600
So we've gone from this everyday idea of finding the quickest way to rescue someone to this mind-blowing concept of objects exploring all possible paths.

563
00:25:29,800 --> 00:25:34,400
But it all comes back to this idea of action being this underlying principle that governs everything.

564
00:25:34,600 --> 00:25:37,400
Right, and it's not just some abstract mathematical tool.

565
00:25:37,600 --> 00:25:38,600
Action is fundamental.

566
00:25:38,800 --> 00:25:40,600
Okay, help me connect the dots here.

567
00:25:40,800 --> 00:25:45,800
How does action relate to the actual laws of physics that we use to describe the universe?

568
00:25:45,800 --> 00:25:53,800
Well, the laws of physics can actually be derived from finding the correct Lagrangian, which is a mathematical expression related to the action of a system.

569
00:25:54,000 --> 00:25:58,000
So the Lagrangian is like a blueprint for how a system will evolve over time.

570
00:25:58,200 --> 00:26:03,200
Exactly, and this is what theoretical physicists are really searching for when they talk about a theory of everything.

571
00:26:03,400 --> 00:26:04,600
A theory of everything.

572
00:26:04,800 --> 00:26:09,400
They're looking for the ultimate Lagrangian, the one that can explain all the forces and particles in the universe.

573
00:26:09,600 --> 00:26:13,600
So it's like a quest to find the deepest, most fundamental level of reality.

574
00:26:13,600 --> 00:26:16,600
And the principle of least action is a key part of that journey.

575
00:26:16,800 --> 00:26:17,600
It really is.

576
00:26:17,800 --> 00:26:26,800
It's this incredible idea that the universe at its core is always optimizing, always seeking the most efficient path, the path of least effort.

577
00:26:27,000 --> 00:26:34,600
It's amazing to think that this seemingly simple idea of minimizing effort is woven into the fabric of reality.

578
00:26:34,800 --> 00:26:37,800
So what does this all mean for us non-physicists?

579
00:26:38,000 --> 00:26:41,600
How should we think about the world differently after learning about action and quantum mechanics?

580
00:26:41,600 --> 00:26:44,600
Well, I think it encourages us to look beyond the surface of things.

581
00:26:44,800 --> 00:26:52,800
We live in a world where objects seem to follow definite paths, but beneath that apparent certainty, there's this incredible quantum dance of possibilities.

582
00:26:53,000 --> 00:27:01,000
Even a simple act like throwing a ball is at its core a symphony of quantum interactions, guided by this principle of least action.

583
00:27:01,200 --> 00:27:08,200
You know, it's like our intuition about the world is based on this classical view where things are predictable and follow a single path.

584
00:27:08,200 --> 00:27:14,200
But quantum mechanics reveals this hidden layer of reality where things are far more complex and fascinating.

585
00:27:14,400 --> 00:27:15,400
And that's the beauty of it, isn't it?

586
00:27:15,600 --> 00:27:19,600
The more we learn about the universe, the more we realize how much we still don't know.

587
00:27:19,800 --> 00:27:20,800
I completely agree.

588
00:27:21,000 --> 00:27:30,000
So to wrap things up, I think the key takeaway here is that we live in a world where objects explore all paths guided by this principle of least action.

589
00:27:30,200 --> 00:27:33,200
But it's quantum mechanics that shapes the reality we perceive.

590
00:27:33,200 --> 00:27:38,200
It makes you wonder what other hidden actions might be shaping our reality that we haven't even discovered yet.

591
00:27:38,400 --> 00:27:39,400
I love that thought.

592
00:27:39,600 --> 00:27:41,600
There's so much more to explore and uncover.

593
00:27:41,800 --> 00:27:45,800
The universe is full of wonder and the quest to understand it is never ending.

594
00:27:46,000 --> 00:27:48,000
And that's what makes it so exciting.

595
00:27:48,200 --> 00:27:51,200
So keep questioning, keep exploring and keep diving deep.

596
00:27:51,400 --> 00:27:54,400
Who knows what other mind-blowing discoveries await us out there?

597
00:27:54,600 --> 00:27:56,600
Absolutely. Keep those brains buzzing.

598
00:27:56,800 --> 00:28:01,800
All right, that's it for this deep dive into the world of quantum mechanics and the principle of least action.

599
00:28:01,800 --> 00:28:03,800
Thanks for listening.

600
00:28:03,800 --> 00:28:32,800
We'll see you in a bit.