Sean Carroll

There's also questions about physics at super long times and low energies. We don't know the answer to. Both of them involve, among other things, is baryon number conserved, which is a way of saying, are protons stable, right? Maybe they are. We think that they're not. Most physicists think that they're not, but we've never seen one decay.

We think, among other things, if you just have ordinary matter, there is a possibility, a sort of probability per unit time, that if you waited long enough would always become real, that the ordinary matter collapses into a black hole. right? And then it would just evaporate away. And that's true for your impermeable barrier also.

We think, among other things, if you just have ordinary matter, there is a possibility, a sort of probability per unit time, that if you waited long enough would always become real, that the ordinary matter collapses into a black hole. right? And then it would just evaporate away. And that's true for your impermeable barrier also.

Even if that doesn't happen, the protons in your barrier could decay themselves, and that would be bad. So it's hard to imagine truly impermeable barriers. It's also hard to imagine small toy universes a few meters in diameter for exactly the reason that Einstein was shocked back in 1917 when he started thinking about cosmology. And he realized that in general relativity,

Even if that doesn't happen, the protons in your barrier could decay themselves, and that would be bad. So it's hard to imagine truly impermeable barriers. It's also hard to imagine small toy universes a few meters in diameter for exactly the reason that Einstein was shocked back in 1917 when he started thinking about cosmology. And he realized that in general relativity,

Universes tend to either expand or contract. You can't keep the universe fixed, in other words. So that's fine. I'm going to roll with the question. I know what you mean. But I just want people to know that in a world with physics as we currently know it, imagining a small universe that just sits there stationary forever is harder than you think. OK?

Universes tend to either expand or contract. You can't keep the universe fixed, in other words. So that's fine. I'm going to roll with the question. I know what you mean. But I just want people to know that in a world with physics as we currently know it, imagining a small universe that just sits there stationary forever is harder than you think. OK?

So we're going to do it anyway, but it's harder than you think. OK. So there's an apple. in our region, what happens to it? Well, again, what happens to the apple depends on laws of physics that we don't know the answer to. The apple, we think, has a probability per unit time of spontaneously collapsing to make a black hole. And then that black hole would gradually radiate via Hawking radiation.

So we're going to do it anyway, but it's harder than you think. OK. So there's an apple. in our region, what happens to it? Well, again, what happens to the apple depends on laws of physics that we don't know the answer to. The apple, we think, has a probability per unit time of spontaneously collapsing to make a black hole. And then that black hole would gradually radiate via Hawking radiation.

Even if that doesn't happen, the protons and neutrons in the black hole probably also have a probability of decaying into other things if baryon number is not conserved. So I think, as far as our best guesses about physics are concerned, that Aaron's theory is mostly correct.

Even if that doesn't happen, the protons and neutrons in the black hole probably also have a probability of decaying into other things if baryon number is not conserved. So I think, as far as our best guesses about physics are concerned, that Aaron's theory is mostly correct.

because either the protons and neutrons directly decay in the apple, or, and part of the decay, like when the proton decays, it will emit a positron, which will annihilate the electrons in the apple, and mostly you'll be ending up with photons. Now, if it does decay into a black hole and that black hole turns into photons, details are going to start to matter.

because either the protons and neutrons directly decay in the apple, or, and part of the decay, like when the proton decays, it will emit a positron, which will annihilate the electrons in the apple, and mostly you'll be ending up with photons. Now, if it does decay into a black hole and that black hole turns into photons, details are going to start to matter.

How small is this region of space that you have invented? Because it's always possible for those photons to recombine to make another black hole, right, which would then decay again. And in fact, there's going to be some equilibrium distribution where it's mostly photons. The vast majority of things are photons.

How small is this region of space that you have invented? Because it's always possible for those photons to recombine to make another black hole, right, which would then decay again. And in fact, there's going to be some equilibrium distribution where it's mostly photons. The vast majority of things are photons.

But there's a probability that a tiny little black hole pops into existence and then radiates away again. Okay. Okay. Now for Claudio's question, it's a little bit different. Claudio is asking whether or not you could do science in this region. Could you study the cosmological constant in questions such as the heat-death of the universe in the sealed-off sphere? Well, in principle, yes.

But there's a probability that a tiny little black hole pops into existence and then radiates away again. Okay. Okay. Now for Claudio's question, it's a little bit different. Claudio is asking whether or not you could do science in this region. Could you study the cosmological constant in questions such as the heat-death of the universe in the sealed-off sphere? Well, in principle, yes.

In practice, no. In principle, the cosmological constant, which is equivalent to the energy density of empty space, has an effect on the geometry of spacetime here in our solar system? If that's what you're getting at, then the answer is yes, it absolutely does.

In practice, no. In principle, the cosmological constant, which is equivalent to the energy density of empty space, has an effect on the geometry of spacetime here in our solar system? If that's what you're getting at, then the answer is yes, it absolutely does.

So for example, the orbit of Mercury, which famously was a test of general relativity, because general relativity predicts that Mercury's elliptical orbit precesses a little bit more than Newtonian gravity predicts. the cosmological constant adds a contribution to the predicted precession of the orbit of Mercury.