Sean Carroll

But much better informed people than me believe in the holographic principle where something like that happens. Can you help me understand where my intuition has gone wrong here? No, I think that your intuition is completely fine. It's absolutely the case. Everyone knows that there are fewer Planck areas on the surface of a sphere than there are Planck volumes in the volume of a sphere.

But much better informed people than me believe in the holographic principle where something like that happens. Can you help me understand where my intuition has gone wrong here? No, I think that your intuition is completely fine. It's absolutely the case. Everyone knows that there are fewer Planck areas on the surface of a sphere than there are Planck volumes in the volume of a sphere.

That's very well known. The whole point of the holographic principle is those Planck volumes in the volume of the sphere are not independent from each other. right? That's the whole point of a hologram. A real-world hologram is a two-dimensional thing that if you shine light on it in the right way, you see a three-dimensional image.

That's very well known. The whole point of the holographic principle is those Planck volumes in the volume of the sphere are not independent from each other. right? That's the whole point of a hologram. A real-world hologram is a two-dimensional thing that if you shine light on it in the right way, you see a three-dimensional image.

But the different parts of the three-dimensional image are not independent from each other. They're all derived from only two dimensions worth of information. So that's the whole trick in the holographic principle. You don't, in holography, have the ability to separately choose what is going on everywhere within the volume of spacetime.

But the different parts of the three-dimensional image are not independent from each other. They're all derived from only two dimensions worth of information. So that's the whole trick in the holographic principle. You don't, in holography, have the ability to separately choose what is going on everywhere within the volume of spacetime.

Now, how does that actually play out in practice is a little bit unclear, but people are working on it. It's clearest in the ADS-CFT correspondence, but even there, it's not 100% clear. So still work in progress. Yeah. Sandro Stucki says, in your January solo on the existence of time, you sketch an argument for why Boltzmann brains are not a problem once one considers quantum physics.

Now, how does that actually play out in practice is a little bit unclear, but people are working on it. It's clearest in the ADS-CFT correspondence, but even there, it's not 100% clear. So still work in progress. Yeah. Sandro Stucki says, in your January solo on the existence of time, you sketch an argument for why Boltzmann brains are not a problem once one considers quantum physics.

You said that this is because thermal quantum states are static, but I could not quite follow how that solves the problem. How can the universe settle into a static state if Hilbert space is finite? Doesn't recurrence forbid that? Yeah, no, you're absolutely 100% correct. So I don't know whether maybe I mumbled through it and wasn't clear.

You said that this is because thermal quantum states are static, but I could not quite follow how that solves the problem. How can the universe settle into a static state if Hilbert space is finite? Doesn't recurrence forbid that? Yeah, no, you're absolutely 100% correct. So I don't know whether maybe I mumbled through it and wasn't clear.

The whole point is that this scenario where the universe settles down and asymptotes to a static state and there are no fluctuations and no Boltzmann brains, that only works if Hilbert space is infinite dimensional. Now you have to be careful because we think that the Hilbert space of our observable universe is finite dimensional. But that's okay.

The whole point is that this scenario where the universe settles down and asymptotes to a static state and there are no fluctuations and no Boltzmann brains, that only works if Hilbert space is infinite dimensional. Now you have to be careful because we think that the Hilbert space of our observable universe is finite dimensional. But that's okay.

Maybe there's something outside our observable universe and maybe there's infinite more Hilbert space out there. That's what you would need to make this scenario work. We don't know if that's true or not. So if it turns out to be true that Hilbert space is truly finite dimensional, then this argument is off the table.

Maybe there's something outside our observable universe and maybe there's infinite more Hilbert space out there. That's what you would need to make this scenario work. We don't know if that's true or not. So if it turns out to be true that Hilbert space is truly finite dimensional, then this argument is off the table.

Then indeed you would expect recurrences, fluctuations, Boltzmann brains, all of that stuff going on. Kirsten Johnson says, do you think the holographic principle might have anything to say about why neural networks work as well as they do? I guess that depends on what you mean by the holographic principle.

Then indeed you would expect recurrences, fluctuations, Boltzmann brains, all of that stuff going on. Kirsten Johnson says, do you think the holographic principle might have anything to say about why neural networks work as well as they do? I guess that depends on what you mean by the holographic principle.

The holographic principle, strictly speaking, is supposed to be a statement about quantum gravity. It's not supposed to be a statement about anything else. It's not, you know, a principle that is widely extendable to all sorts of different circumstances.

The holographic principle, strictly speaking, is supposed to be a statement about quantum gravity. It's not supposed to be a statement about anything else. It's not, you know, a principle that is widely extendable to all sorts of different circumstances.

It's something that becomes evident when you have quantum mechanics plus gravity, and in particular, when you have pretty strong gravity, like a horizon or something like that, when... you have black hole, or you have anti-de Sitter space, de Sitter space, a cosmological horizon, then holography becomes relevant.

It's something that becomes evident when you have quantum mechanics plus gravity, and in particular, when you have pretty strong gravity, like a horizon or something like that, when... you have black hole, or you have anti-de Sitter space, de Sitter space, a cosmological horizon, then holography becomes relevant.