- #1
ianhoolihan
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Hi all,
A question about the Holographic Principle. I've recently started reading up about this, and watched Bousso's neat introductory video .
I thought, "Ah, this is so refreshingly simple!", and proceeded to write down my own notes. However here things revealed themselves to be not quite what they seemed.
Firstly I believe Bousso's argument for an entropy bound goes as follows:
By the uncertainty principle, the energy required to observe a "bit" of information is inversely proportional to its size. So if we try to make our bits smaller and smaller as such, we will need larger and larger amounts of energy to observe them. But as there is a limit on the energy inside a given volume - that is, so a black hole doesn't form - then there is a limit to how small we can have our bits, and hence there is a bound on the amount of information (entropy) which we can contain inside a given volume.
On thinking about this more, I've come across a few points that I'm not comprehending. It depends on what Bousso was saying. Either
1. The bit particle is very localised, so has a very large energy by the uncertainty principle.
2. The bit particle is very localised, so it takes a very high energy object to observe it (i.e. "read" the bit).
In the first case, I'm stumped by this logic (and have been for a while). For shouldn't point 1 read "The particle is very localised, so has a very uncertainty in its energy, by the uncertainty principle." For example, a particle can be inside a tiny box and still have zero energy...it's just you're extremely unsure about that! Is my interpretation correct here? If so, how can one recover Bousso's argument?
If Bousso was meaning the second case, then again I'm not sure where the need for a higher energy object comes from. I'm aware that this holds in practice...you need smaller wavelength photons/particles to observe smaller things. But what is the justification for this? And even if this does hold, am I not correct in saying that the energy of the observing particles has no relation to the energy of the particles actually inside the volume?
Those are my two main qualms about this talk given by Bousso. I believe there are much more rigorous derivations for an energy bound based on black holes and the generalised second law, but I have read that these only hold under certain assumptions, for example spherical geometry or weak (strong?) gravity. Is there any "conclusive" proof of an entropy bound, that follows from the generalised second law? Is Bousso's Covariant Entropy Bound an example of this?
I admit my reason for looking into this is to consider Verlinde's paper more thoroughly. I believe he starts with the Holographic Principle as an assumption however. Although I'd like to keep this thread focused on my issues with the Holographic Principle and the entropy bound, pertinent comments about Verlinde's results may be appreciated.
Regards.
A question about the Holographic Principle. I've recently started reading up about this, and watched Bousso's neat introductory video .
I thought, "Ah, this is so refreshingly simple!", and proceeded to write down my own notes. However here things revealed themselves to be not quite what they seemed.
Firstly I believe Bousso's argument for an entropy bound goes as follows:
By the uncertainty principle, the energy required to observe a "bit" of information is inversely proportional to its size. So if we try to make our bits smaller and smaller as such, we will need larger and larger amounts of energy to observe them. But as there is a limit on the energy inside a given volume - that is, so a black hole doesn't form - then there is a limit to how small we can have our bits, and hence there is a bound on the amount of information (entropy) which we can contain inside a given volume.
On thinking about this more, I've come across a few points that I'm not comprehending. It depends on what Bousso was saying. Either
1. The bit particle is very localised, so has a very large energy by the uncertainty principle.
2. The bit particle is very localised, so it takes a very high energy object to observe it (i.e. "read" the bit).
In the first case, I'm stumped by this logic (and have been for a while). For shouldn't point 1 read "The particle is very localised, so has a very uncertainty in its energy, by the uncertainty principle." For example, a particle can be inside a tiny box and still have zero energy...it's just you're extremely unsure about that! Is my interpretation correct here? If so, how can one recover Bousso's argument?
If Bousso was meaning the second case, then again I'm not sure where the need for a higher energy object comes from. I'm aware that this holds in practice...you need smaller wavelength photons/particles to observe smaller things. But what is the justification for this? And even if this does hold, am I not correct in saying that the energy of the observing particles has no relation to the energy of the particles actually inside the volume?
Those are my two main qualms about this talk given by Bousso. I believe there are much more rigorous derivations for an energy bound based on black holes and the generalised second law, but I have read that these only hold under certain assumptions, for example spherical geometry or weak (strong?) gravity. Is there any "conclusive" proof of an entropy bound, that follows from the generalised second law? Is Bousso's Covariant Entropy Bound an example of this?
I admit my reason for looking into this is to consider Verlinde's paper more thoroughly. I believe he starts with the Holographic Principle as an assumption however. Although I'd like to keep this thread focused on my issues with the Holographic Principle and the entropy bound, pertinent comments about Verlinde's results may be appreciated.
Regards.
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