Okay, so let me welcome you again to the lectures on the foundations of quantum mechanics and

I first want to give you a brief overview of what we'll be doing in this lecture. And

actually, the first chapter will just be a reminder, a refresher of the Schrödinger equation.

How do we go about deriving the Schrödinger equation from simple principles?

And then I want to discuss a few aspects of the Schrödinger equation that you may have

learned in your standard quantum mechanics lectures, such as what happens when you do

a measurement, people talk about collapse of the wave function, or people talk about wave-particle

duality.

And the point of this brief overview will just mention all these aspects, which actually

will be the open questions, and then the rest of the lecture series will be about really

addressing those open questions.

So that's the idea, recount all those open issues.

And then in the second chapter I will go right away to attack what is probably the most important

achievement in the foundations of quantum mechanics in the past half a century, which

is Bell's inequalities.

And they are quite unique in the history of physics, because Bell's inequalities and the

experimental results rule out a complete large class of infinitely many theories that you

could try to cook up in order to understand quantum mechanics, and all of those theories

are ruled out at once.

So this is pretty unique, and so it's very important, and we will spend some time on

discussing Bell's inequalities.

And then we'll go back to standard quantum mechanics, not ask about the interpretation

so much, but apply quantum mechanics to issues such as measurement and decoherence.

And so for measurement we will learn that there is much, much more to be said than just

there's a collapse of wave function.

And it is possible nowadays to say much more about these topics, but it's also necessary

to say much more, because nowadays there are many experiments where you can actually learn

in detail and where you have to describe in detail what goes on when you actually do a

measurement.

And so much of this is really driven by new experiments.

And then there is another topic which is actually related to measurement, which will be decoherence.

And that has to do with wave-particle duality, because decoherence is about how you start

with wave effects such as interference, and then these wave effects are destroyed, for

example because there are interactions between particles or there are fluctuations in the

environment, and then gradually you go from these wave effects to particle-like behavior

like of classical particles.

So that will be decoherence.

So there are these two chapters, measurement and decoherence, and they are very tightly

related.

And then we'll go back to the meaning of it all.

We'll discuss the interpretations of quantum mechanics.

We will learn there are several possible interpretations of quantum mechanics.

And when I say interpretations, what I mean are theories that try to explain sort of what

goes on when you apply the formalism of quantum mechanics, but they keep the same results.

So they don't make any different predictions.

They keep the same results.

They keep the same predictions for experiments.

And so in that sense, they are interpretations.

And then on top of that, people have come up with what I would call extensions of quantum

mechanics.