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## Main Question or Discussion Point

Dear all ---

This question raises concerns already expressed in

https://www.physicsforums.com/threads/the-bekenstein-bound.671770/

but in a more specific form --- so that, hopefully, a more specific answer may be given.

With the Bekenstein-bound-saturated-by-BH argument, we have that a sphere of radius R can have at most a.k.R^2/4 information inside.

Now, let me imagine the following scenario.

Let us say I have some very light physical device able to store one bit of data. It could be anything, perhaps a piece of mirror oriented in one direction or another --- something stable, localized in empty space, optically readable.

Now, very, very far away, perhaps a light year away, I place another one. And then another one. And so on, arranging all of this bits of information in an evenly spaced, infinite, _cubic_ grid, laid in almost flat space.

It seems to me that the attraction between each of these one-bit storage devices is perfectly negligible. Moreover, each device is evenly attracted by the others, so it won't "move". Therefore, we run no risk of them colliding into a BH.

Now, consider taking a subset of these physical devices. For instance, center on one of them, and draw an imaginary ball of radius R. Clearly, the information storage capacity of this ball grow in R^3. This information storage is accessible: I can always send a lightray, or even a spaceship if that is necessary, go and read some device inside: it will take a while but this is doable.

My main question is: does this contradict the Bekenstein-bound-saturated-by-BH argument?

Subquestions:

- do the agree that this will not collapse into a BH?

- do we agree that the information storage capacity grows in R^3, and so even if the information density is rather low, it will eventually exceed the a.k.R^2/4 bound?

- has this been discussed and fixed in any way that someone could explain?

Many thanks.

This question raises concerns already expressed in

https://www.physicsforums.com/threads/the-bekenstein-bound.671770/

but in a more specific form --- so that, hopefully, a more specific answer may be given.

With the Bekenstein-bound-saturated-by-BH argument, we have that a sphere of radius R can have at most a.k.R^2/4 information inside.

Now, let me imagine the following scenario.

Let us say I have some very light physical device able to store one bit of data. It could be anything, perhaps a piece of mirror oriented in one direction or another --- something stable, localized in empty space, optically readable.

Now, very, very far away, perhaps a light year away, I place another one. And then another one. And so on, arranging all of this bits of information in an evenly spaced, infinite, _cubic_ grid, laid in almost flat space.

It seems to me that the attraction between each of these one-bit storage devices is perfectly negligible. Moreover, each device is evenly attracted by the others, so it won't "move". Therefore, we run no risk of them colliding into a BH.

Now, consider taking a subset of these physical devices. For instance, center on one of them, and draw an imaginary ball of radius R. Clearly, the information storage capacity of this ball grow in R^3. This information storage is accessible: I can always send a lightray, or even a spaceship if that is necessary, go and read some device inside: it will take a while but this is doable.

My main question is: does this contradict the Bekenstein-bound-saturated-by-BH argument?

Subquestions:

- do the agree that this will not collapse into a BH?

- do we agree that the information storage capacity grows in R^3, and so even if the information density is rather low, it will eventually exceed the a.k.R^2/4 bound?

- has this been discussed and fixed in any way that someone could explain?

Many thanks.

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