Sean Carroll

If you put the elect—so here, let me say what I think is true, and then we can decide what you meant by the question. When you have an atom— that has an electron. Let's just take a hydrogen atom, right? Let's make it very simple. So you have one proton, which is the nucleus. You have one electron. And there are energy levels, okay? And there is a bottom energy level.

If you put the elect—so here, let me say what I think is true, and then we can decide what you meant by the question. When you have an atom— that has an electron. Let's just take a hydrogen atom, right? Let's make it very simple. So you have one proton, which is the nucleus. You have one electron. And there are energy levels, okay? And there is a bottom energy level.

There's the ground state energy, the minimum energy state of the electron. And as far as ordinary quantum mechanics goes, so we're ignoring... baryon number violation, proton decay, all that stuff, right? All that crazy stuff.

There's the ground state energy, the minimum energy state of the electron. And as far as ordinary quantum mechanics goes, so we're ignoring... baryon number violation, proton decay, all that stuff, right? All that crazy stuff.

In ordinary undergraduate quantum mechanics, if you have a hydrogen atom with its electron in the ground state and you ignore the rest of the world, then it will stay there forever, okay? It's a stable state. It's not going to do anything. It just sits there. If you excite it, so you send a photon in and you prod the electron to a higher energy state, the higher energy states are unstable.

In ordinary undergraduate quantum mechanics, if you have a hydrogen atom with its electron in the ground state and you ignore the rest of the world, then it will stay there forever, okay? It's a stable state. It's not going to do anything. It just sits there. If you excite it, so you send a photon in and you prod the electron to a higher energy state, the higher energy states are unstable.

They just are. You can predict, this is a classic undergraduate homework set, You can predict, based on what that energy is, the probability per unit time of the electron decaying back down to the ground state and emitting a photon. So if you wait arbitrarily long, the probability approaches one, that that electron will go back down to its ground state.

They just are. You can predict, this is a classic undergraduate homework set, You can predict, based on what that energy is, the probability per unit time of the electron decaying back down to the ground state and emitting a photon. So if you wait arbitrarily long, the probability approaches one, that that electron will go back down to its ground state.

If you want to ask why that happens, why is it necessary, why can't the electron just stay there, then there are many possible answers, depending on what kind of answer you're looking for. My favorite answer, which is not the one anyone else gives, but it's because entropy increases. Why is that?

If you want to ask why that happens, why is it necessary, why can't the electron just stay there, then there are many possible answers, depending on what kind of answer you're looking for. My favorite answer, which is not the one anyone else gives, but it's because entropy increases. Why is that?

Well, because you go from a system that has one proton and one electron to a system that has one proton, one electron, and one photon. There are more ways to have that system arranged than just the one proton and the one electron. So emitting more and more photons increases the entropy of the universe in general. So that's likely to happen and unlikely to unhappen.

Well, because you go from a system that has one proton and one electron to a system that has one proton, one electron, and one photon. There are more ways to have that system arranged than just the one proton and the one electron. So emitting more and more photons increases the entropy of the universe in general. So that's likely to happen and unlikely to unhappen.

It cannot happen because you can aim a photon, right? It's just the numbers are small enough that you can control what's going on. But in general, the way to think about it is the electron will want to dissipate any extra energy it has to go down to the ground state, and it does that dissipation by emitting photons, either single or more than one photon sometimes.

It cannot happen because you can aim a photon, right? It's just the numbers are small enough that you can control what's going on. But in general, the way to think about it is the electron will want to dissipate any extra energy it has to go down to the ground state, and it does that dissipation by emitting photons, either single or more than one photon sometimes.

A lot of us start the new year saying that we will learn a new language, but it's hard to actually commit to it. Babel makes it easy to learn one in less time than you think. Babbel's quick 10-minute lessons, handcrafted by over 200 language experts, get you to begin speaking your new language in three weeks or whatever pace you choose.

A lot of us start the new year saying that we will learn a new language, but it's hard to actually commit to it. Babel makes it easy to learn one in less time than you think. Babbel's quick 10-minute lessons, handcrafted by over 200 language experts, get you to begin speaking your new language in three weeks or whatever pace you choose.

And because conversing is the key to really understanding each other in new languages, Babbel is designed using practical, real-world conversations. What I love about Babbel is you can either dive in deeply and truly get fluent, or you can just master some of the basics before going on a trip. So let's get more of you talking in a new language.

And because conversing is the key to really understanding each other in new languages, Babbel is designed using practical, real-world conversations. What I love about Babbel is you can either dive in deeply and truly get fluent, or you can just master some of the basics before going on a trip. So let's get more of you talking in a new language.

Babbel is gifting our listeners 60% off subscriptions at babbel.com slash mindscape. Get up to 60% off at babbel.com slash mindscape, spelled B-A-B-B-E-L dot com slash mindscape. That's babbel.com slash mindscape. Rules and restrictions may apply. Thomas DeWitt says, Memories could be introduced at a given time step that have information about the past, while the system remains Markovian.

Babbel is gifting our listeners 60% off subscriptions at babbel.com slash mindscape. Get up to 60% off at babbel.com slash mindscape, spelled B-A-B-B-E-L dot com slash mindscape. That's babbel.com slash mindscape. Rules and restrictions may apply. Thomas DeWitt says, Memories could be introduced at a given time step that have information about the past, while the system remains Markovian.