Sean Carroll

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.

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But spatial locality was used to separate types of emergence. Couldn't the analogous thing be done for spatial locality, where knowledge about other locations is contained at each location, making the dynamic local? Is there some crucial difference between time and space that I am missing? Yes, there is a very crucial difference between time and space that you are missing. This is subtle.

But spatial locality was used to separate types of emergence. Couldn't the analogous thing be done for spatial locality, where knowledge about other locations is contained at each location, making the dynamic local? Is there some crucial difference between time and space that I am missing? Yes, there is a very crucial difference between time and space that you are missing. This is subtle.

You know, we all know that Einstein came along and said that in some sense, time and space are both part of a single underlying space-time. You want to say that, and you want to appreciate it, and you want to take it on board in your precious belief set. But you also want to understand that there are still differences between time and space.

You know, we all know that Einstein came along and said that in some sense, time and space are both part of a single underlying space-time. You want to say that, and you want to appreciate it, and you want to take it on board in your precious belief set. But you also want to understand that there are still differences between time and space.

The single biggest difference, I would say, there's a lot of differences, but the single biggest one is time. given information about the universe at one moment in time, you can, in principle, in classical mechanics, predict what it will be like at other moments of time, right? That's Laplace's demon that we were just talking about. There is no analogous statement for space, okay?