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First to start, and to be clear, let's talk about a macroscopic string. Then we can talk about a quantum mechanical system. For the macroscopic string, the state is more than just the position of each infinitesimal piece of the string - it is also the momentum of each infinitesimal unit of the string. So when you are looking at the spot where there has ...

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Is there a minimum energy content of information? Carl Witthoft's answer gives us a key hint: in terms of energy efficiency one can't really do better than using photons to encode bits. A photon residing in a container of linear size $R$ has minimum energy $\Delta E \approx \hbar c / R$. By increasing the size $R$ one can reduce the energy per bit below ...

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This may not be the best way to look at the problem, but: Suppose you send one photon for a "1" and no photon for a "0" according to some prearranged clock. What's the lowest possible photon energy? The answer, of course, is "asymptotically approaching zero." Not that I'd like to build an antenna capable of detecting a photon with $\lambda > 1$ ...

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See e.g. Landauer's principle http://en.wikipedia.org/wiki/Landauer's_principle and capacity of noisy channels http://en.wikipedia.org/wiki/Channel_capacity. Not everybody agrees with these limits, but to me they seem fairly reasonable based on relatively straight forward noise arguments. In an ideal world (i.e. temperature T=0), there is no lower limit ...

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I'm no physicist, but I think that event horizon will form, but nothing will ever fall there. So no information is destroyed, just very inaccessible. See How can anything ever fall into a black hole as seen from an outside observer? "All the oblects close enough to the horizon remain "sticked" to it and follow all the changes of the BH form" Imagine two ...

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You have found an elaborate way of calculating $2\pi \alpha/ \ln 2 \approx 0.0661658$. Here, $\alpha \approx 1/137$ represents the fine-structure constant. The points to note is that: A) Bekenstein's bound defines the maximum number of nats of information that can be contained in a spherical region as the circumference of that region divided by the reduced ...

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One can't take results like that too seriously at the scale at which an electron would apply. In particular, the classical general relativistic model, applied naively to a point mass electron would tell you that the electron has too large a charge and angular momentum to have a black hole horizon, and would instead be the exotic type of object called a ...

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