(light piano music) (light piano music) - So Chester, you and I both come from a non-scientific background.

- Yes.

- In your case, music and the flute.

In my case literature, especially dramatic literature.

And here we are at St. John's College, in which about probably half of our time we spend teaching mathematics and laboratory science, and we both love it.

We've done it together a number of times - Yeah.

- with much pleasure.

So right now you're working on quantum mechanics with your seniors.

- Yeah, we're just about coming to an end of the semester, yes.

- Yeah, so how does someone approach that subject for the first time, - [Chester] Yeah.

- from a non-scientific background?

I mean, can you recount what it was like for you to get into it initially, and how did you find your way in?

What opened the door for you?

- I think what started to attract me and once I'd had the job was that there were all these demonstrations and experiments.

And so, I was fascinated on trying to see how the experiments could go along with the readings.

And I have to say, you know, having been away from studying these things, I can't explain, but I fell in love with the readings.

And I especially fell in love with readings where when I couldn't figure something out and the language was accessible to me, such as French, I would start to translate.

And I think that was kind of the theme.

I would find something difficult, I knew there had to be something exciting about it, and then.

- [Louis] Yeah.

- So that allowed me to look at the laboratory more just as the speech of these amazing human beings.

And then, the practical part, yeah, how to make things work.

I mean, as anybody who knows me well knows that I 'm not the most practical human being in the universe, but it was just a lot of fun to work with students and other colleagues and try, you know, not just to make things work but to see how the so-called physical world - Oh, yeah, yeah.

- coincided with it.

- So what you were just saying, Chester, might be analogous to an experience I had in graduate school working on Shakespeare.

And, you know, reading plays and tons of criticism, and then discovering in the theater itself, the practical, you know, and the experimental where you have to actually get on your feet and give body and voice to these things.

And find the, as you were saying, find the way that makes it work given that particular group of people.

And that's what really captured me and made me, you know, wanna continue working on that for the rest of my life.

But maybe that's analogous to what you're describing with the lab, where you go from things on a page or written, to something real that you can get your hands on.

- Yeah, to condense the story a little bit.

The junior lab, it's a difficult tutorial, and- - It was once described to me as the most difficult thing we do.

- It's one of the ones.

I put down music as another one, but yeah.

Yes, but everything gets worked out in that year.

I mean, many things get worked out.

All the things we kind of take for granted, for force, energy, mass, motion, speed, all those things kind of are worked out, you know, with the new start from Galileo and Descartes.

- [Louis] Yeah.

- And then the senior year begins as if we already knew them, we were professionals at them.

- [Louis] That's right.

- The readings are, by people closer to our own time, you know, the 19th century who assume that we have done the junior lab, - [Louis] Indeed.

- but in fact, much more than the junior lab.

- That's why I think senior lab is the hardest because it presumes already the junior classical physics background.

- [Chester] Yeah.

- And then goes into a terrain, where, to go back to what we were saying a moment ago, where the picturable and the experiential - Yes.

- and the bodily aren't necessarily going to help you.

In fact, they might get in the way.

- That's absolutely right.

In fact, very soon in a year with Thomson, we look at cathode rays.

(chuckles) It's hard to even know what a cathode ray is.

Looks like a flash of light, now it turns out we'll be told, are streams of electrons, but we have no idea what the thing is.

But we're using the mathematics of Galileo, of the parabola, of bodies moving in a horizontal direction and bodies falling.

- [Louis] Yeah.

- So basically, we're using the tools from the junior lab and the forces that act upon the bodies that we know as bodies to act upon this stream.

- [Louis] Yeah.

- which, that wasn't the only interpretation of the cathode ray, as you know as well as I know.

But Thomson thought, well it would make more sense, or it could be if we could consider them as bodies, which are both going forward, therefore with mass, and also falling.

And so, that turns out to be experimentally successful.

We set up the apparatus and they go shooting through at a very fast pace, but they also fall a little bit.

And so, lo and behold, they go in a parabola, but they're also acted upon biomagnet.

So, those first readings in senior lab, where we're looking at, and this is gonna be a theme for both our conversation and for the senior lab, the very, very small.

- So I tell the students sometimes, "Don't get discouraged if you're drawing blanks on Planck.

We'll be going at this four or five times through different authors - Yeah.

- to try and understand quantum mechanic."

Do you think that's right?

- I think that's dead right.

Can you indulge me in one kind of warm-up to that?

- [Louis] Yeah.

- Because once you know what's gonna happen, then you look back.

So we have even Rutherford who wants to know what the shape of the atom is, and basically it turns out that about what shape he means, how much space it's taking up.

And so it's still, he's using a Newton proposition.

- [Louis] Yes.

- The proposition which talks about how bodies work in the heavens.

- Very big bodies.

- Very big bodies to show how a very small particle called an alpha particle is deflected when it is shot into, well through gold foil.

Now even the set of these things, it turns out to be infinitely elaborate, but basically, he is throwing alpha particles at gold foil, and the alpha particles are going through.

Now what he discovers is that the atom itself is taking up an insanely small amount of space and it's mostly just so-called empty space and force.

But the alpha particle is curving, and now later our interpretation, once we see that small particles can also be thought of as waves.

When we get into quantum mechanics, even in wave mechanics, we will see that the very little alpha particle could be interpreted as a wave going through.

- [Louis] Yes.

- But, to really answer your question, I think it's when we get Planck.

- [Louis] We get Planck, yeah.

- So Planck, you know, many things can be said about Planck.

I don't really understand what he was up to, but I can say the following.

He was investigating the radiation of heat.

- [Louis] Yeah.

- And what he stumbles on, and kind of a popular but not too bad a way of saying is that energy is discontinuous of the smaller level.

- Yeah, it's discrete.

- It's discrete.

- So why is that a big deal?

Because we're used to discreteness just from the earliest age when we start counting.

- Yeah.

- One, two, three.

So that comes naturally to us.

- Right.

- So to say energy is discrete, it's countable, it comes in, you know, discrete particles.

Why is that a discrete amounts?

Why is that so, sometimes I think the students don't quite feel the force of that.

- Right.

So this cup would be discrete.

(Louis assents) Okay.

If I needed two cups, I just take yours.

But if I start to let the cup fall, which I won't do, (Chester chuckles) it would speed up and eventually we're gonna say, as it speeds up, its energy - [Louis] Its kinetic energy.

- is moving energy, it's as live as it says.

Its vis-viva is getting greater and greater.

- In a continuous fashion.

- In a continuous fashion.

Why would I not expect that to be the case?

- Yeah.

- And again, here's where experiment comes through.

So, there's much that we can say about Planck, but Planck comes up with a mathematical expression where on the left-hand side he says energy is equal to, on the right-hand side, he has the frequency.

Now, it's the frequency of a wave, which is the star player of continuity.

- Yeah.

- So energy is equal, is proportional to frequency, but with a constant, and that constant is 6.625 times 10 to the negative 27.

That's a very small number.

So we're gonna go towards the small.

- So that's what causes the energy to be quantized, - That's what it does.

- that constant.

- Yes, and this is something, I'm just so glad I get to say this, that that proportionality constant, Planck's constant, H, the units of it are the units of what Leibniz called (chuckles) moving action.

- [Louis] Oh yeah.

- Now, the only point of this is that hundreds of years ago, people not doing experiment- - Okay.

- Yeah.

Yeah.

- So hold on.

Does that mean that what we were previously thinking of as a continuous spectrum of energy, like a falling moving body, it's not continuous because moving action is discrete?

- Well, Leibniz example of moving action show you how one of the greatest geniuses of all time has simple examples.

If you were to walk across the room, you have a certain mass, and you were to walk across a certain distance of the room and we closed our eyes, we'd see you here and then see you there.

Then, you could either do it quickly or slowly.

So, I would say the formal effect was your mass times the distance.

He'd say the vigorous effect would be how fast you went.

He'd say you multiply those three quantities together and you get moving action.

And Leibniz would think this is at the heart of substance or being.

Now, we'll get out of that realm really quickly and back to the really important thing.

So when if I say E, energy is equal to H, that small constant, times the frequency, that leads into, let's talk about Einstein for a second, that that leads into the thought that, let's talk about a particular frequency.

Let's talk about blue light.

Blue light could has a frequency by the way, which is higher than red light.

So that means that Einstein has to reason to or think or come up with this beautiful notion that there's a unit of blue light which will give it a number, which happens to be its frequency.

So already you can see there's a kind of, we're using a wave property to talk about the unit or discrete particle, the quantum of blue light.

So, blue light comes in units and now it's second unit would be two times that amount, then three times that amount.

There's nothing in between.

- Nothing in between.

- Nothing in between.

And so just to finish, put the nail into the coffin, red light has a smaller frequency.

So it comes into one unit of red light, two units of red light, three units of red light.

So three units of red light have less energy than three units of blue light.

- Okay.

- Now that, it's not too hard to go back to Maxwell, the man who just gave us all we'd ever wanna know about light as a wave to show that there's a discrepancy between that.

For Maxwell, light is continuous.

- So yeah.

So what's the connection between what we're talking about earlier, the size question, big and little, and what we're now talking about the quantization or the discreteness of energy?

- Yeah.

So this is why it would be important.

So Planck and his studies, which had really not that much to do with this, did discovered the following thing.

When you heat a body (Louie assents) and it gives off heat, Planck discovered that if energy did not come in discrete units, it would almost instantaneously give off all of its heat.

And the popular of this is called the ultraviolet catastrophe.

- The ultraviolet catastrophe.

- We'll all be incinerated, yeah.

- But it's really deep.

Meaning that, you know, people talk about ovens, but it's just, Planck talks about black body.

So imagine painting a body black.

It absorbs up a lot of heat, once it comes to equilibrium, if energy is continuous, in an argument which can be understood by liberal arts students, the math simply doesn't work out and the energy is instantly given off.

- Infinite amounts - Infinite amounts.

- according to the classical equations.

- According to everything that we studied in the junior year.

- Okay.

- And that's the beginning- - That's the beginning of- - That's the beginning of the end.

And so, I guess the argument is, but energy is not given off instantaneously or in infinite amounts, therefore we have to start to think about energy at the small level as being discrete.

But in our daily lives- - We don't notice that, no.

- Because the unit of energy is so small.

So we would not know.

- So that unit, that Planck's constant, it's very smallness as a constant.

- Yes.

- It's like 6.67 times 10 to the negative 27.

- That's right.

- Yeah, very, very small.

That smallness translates into, is this right?

Translates into a limit on what we can know about small things.

- That's right, yeah.

Yeah, that's right.

- [Louis] Okay.

- And so the next move is- - And that limit is not, just to clarify, that's not in principle overcomeable.

That is, we can't get over, get smaller than that limit by getting better equipment or better experiments, or anything like that.

- Right, and that takes a little while to come out.

But once we, I guess, we go through Schrodinger.

I guess we need to talk about matter and radiation, or matter and waves.

- So if we pick this thread up that the discreteness of energy, as shown by this new constant of nature, means there's a limit to what we can know about small things.

What exactly are we talking about in terms of what we want to know and what we can't know?

And then the implications of that, of that limit on our knowledge?

- Yeah.

I mean, I guess to really answer that, we'd have to go to the end of the senior lab, where in a certain way quantum mechanics has been developed and its predictions come true.

But because of this factor H, it's impossible to have simultaneous knowledge of, for example, where somebody is or where a body is and how fast it's moving.

- [Louis] Yeah.

- Now we assume.

- It's what every parent wants to know about their child.

(Chester laughs) Where are you and what are you doing?

- Right.

- And now we can't know that about little particles.

- For example, we would all say that this cup is on the table.

We could give it some kind of spatial coordinates.

We could say where it is, we can give its location, and we could also say give it speed.

In this case we would say it's at rest with respect to you and myself.

And now it's in motion.

What quantum mechanics can't get beyond is that when we actually, as the particles get smaller and smaller, is this particle is now at the smallest level?

My measuring its position, where it is, with precision, the more precise I make that measurement, the less precise I know how fast it's going.

In fact, the extreme cases to know exact within a very small amount where it is, I've lost it for all time.

That's the same.

My looking at it cause it to go away.

But it's a lot more complicated than it's just a subjective kind of thing or an objective kind of thing.

This kind of, or to put it more succinctly, H is now a factor of all the physical expressions for both matter and waves, or the matter that we're composed of, the atoms that we're composed of.

First of all- - This sounds like some kind of law of compensation that, you know, various poets and writers have talked about.

That is you do good with your left hand, you're simultaneously doing something bad with your right - Right.

- in some other part of the world.

That there's this kind of balancing act.

So you can't know simultaneously position and momentum.

- Right.

- The better you do at one, the worse you do at the other.

- Right.

- So that sounds like written into nature.

There's this sense of, this is Emerson's term, compensation, - Right.

- We're speaking of it morally, but you're just talking about it physically.

- Niels Bohr by the way, who's one of the people we read, who is also a huge person because he just, there was a high school teacher who looked at, excited at hydrogen gas and saw a spectrum.

He saw some discrete lines.

So the gas, let it be kind of a pinkish color, gave off a red and a green and a couple blue lines.

Basically, something that anybody could do by heating up a gas.

Nobody could explain it.

Bohr takes a look at it and it can only be explained if the hydrogen atom we all learned about in high school has a nucleus, say, here, and the electron around here- - Like a solar system model.

- Like a solar system.

It turns out this solar system has all unique places for the electron.

The electron cannot exist in between those unique places.

- Well, that's the thing that has always given me wonder and a sense of almost of the mystical.

How does an electron go from one orbit to another orbit without passing in between, and while doing so giving off a continuous spectrum of energy?

'Cause as we're saying, it's just discrete chunks.

That means there's a jump, a leap, and nothing in between.

- Right, and with someone like Niels Bohr in the beginning, he would say, you cannot give the kind of account that we've been assuming that we can give in, not only natural science but as you pointed out in the poetry of Emerson in our day-to-day life.

We assume, for example, that this cup has a location, has a speed, has an energy.

I could do it a little more generally.

That we as bodies have, or our souls even have properties that are inherent with us.

It might be difficult to get to know them, but quantum mechanics is telling us that these things, they exist in a different mode.

Now the technical term is a state, and you could start to get at it by potentials.

Like I have the potential to be this or that.

- State, okay, but does nature make leaps?

That word occurs in Dirac, - Yeah.

- or jump.

When he's talking about a photon, which we'll hope talk about in a moment, you know, leaping into a certain state of polarization or of translation.

But that word leap suggests again, something like what Kierkegaard calls a leap of faith, or what, you know, Pascal talks about as a leap that one's soul has to perform in order to, well, to know God.

So why is that word turning up in the study of nature?

- Yeah, because- - Because, you know.

- Yeah, well back to our solar system, a planet couldn't go from one location to another one.

It would have to do it instantaneously.

And even if it did it, in so far as it would be giving off so much energy, that it would immediately crash into the sun.

But these kinds of things, so I guess what the study of the very small shows us is that we need new kinds of laws.

- Well, maybe new kinds of language.

- New kinds of law- - Maybe the word leap is just misleading.

- Yeah.

- We can't talk about quantum mechanics using words like that, even though they're descriptively helpful, because they mislead us.

- Yeah, and I wanna say one more thing along the lines of the practical and why we care.

We would not be having this conversation that is to say our atoms could not hold together, the physical universe could not stay together.

It's kind of a spinoff of the thing I was talking about with the ultraviolet catastrophe.

Only quantum mechanics gives us physical stability.

Now, this is building from the very small to the very large.

- So if you want to hold together over time, you have to give up knowing certain things?

- Or there's a new way.

I mean, that maybe can get us into Dirac.

That's the last thing we studied.

It's a recent thing at the college.

I mean, there have been people who've known about Dirac for a long time.

- I mean, for me, the Dirac is so wonderful because, and the experiments that go with it, because you are counting individual photons of light.

- Right.

- And that's mind-boggling.

- Yes.

- Photon doesn't have mass, doesn't have size.

And one thinks of it as this continual beam of something continuous.

- Well, we should get to this quickly.

- Yeah, so let's look at the top of what you put on this board.

- Okay.

We do this in the St. John's lab now.

We are able to do it through a very generous grant from the Hodson Trust.

- The equipment is quite impressive.

- Equipments, it's impressive.

And I wanna give credit to Enrique Galvez at Colgate University.

He and about four or five other people 20 years ago started working on experiments that undergraduate physics majors could do.

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