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Need a little more clarification for laymen: there's a bound for the amount of information in a finite region of space ( Bekenstein bound, which depends on the amount of energy-mass in that region. Does it mean if there's an infinite amount of energy in a region of space then there's an infinite amount of information? Should there be an upper bound for energy-mass if Pauli exclusion principle really holds true? Also, if that's the case then singularity is ruled out? Mastertek ( talk) 14:50, 23 October 2011 (UTC)
Would it be appropriate to state the maximum information density in bits per cubic meter (or cubic millimeter)? This looks like a straightforward calculation from the S = A/4 formula, but I don't know if there are gotchas in making this kind of comparison. I assume the applied kinds of densities in places like Computer storage density are many orders of magnitude from what is discussed here, but are there even deeper reasons why they are talking about two different things, or is it potentially comparable? (either a "yes" or a "no" might be good to add to the article). Kingdon 19:53, 25 May 2007 (UTC)
Fairandbalanced ( talk) 19:26, 16 September 2008 (UTC)
I am no expert, but when it says in the first paragraph, "... or the information necessary to perfectly describe that system, must be finite if the region of space or the energy is finite," doesn't the author actually mean 'AND', as in, "if the region of space AND the energy is finite?" The Berkenstein bound is proportional to both the radius, R, and the mass-energy, E, so if either quantity is unbounded, the resulting Berkenstein calculation will be without bound. Right? If I haven't misunderstood, would someone knowledgeable please fix this? Thanks. SJGooch ( talk) 10:40, 7 January 2011 (UTC)
15 cite notes on one sentence??? Too much. -- œ ™ 15:27, 7 November 2010 (UTC)
The number of significant digits in the examples is only silly. — Preceding unsigned comment added by 81.216.218.158 ( talk) 20:52, 14 October 2011 (UTC)
In the end of the section on the human brain, how can 2^(n*10^42) be LESS THAN 10^42 ??? (something x 10^41) I.e. the author claims the number of STATES a string of bits can assume is LESS THAN the number of BITS. This is nonsense! — Preceding
unsigned comment added by
98.222.62.231 (
talk)
23:01, 12 October 2012 (UTC)
8 bits can have 2^8, ie 256 states. N bits can have 2^N states. — Preceding unsigned comment added by 24.156.205.96 ( talk) 03:30, 8 September 2015 (UTC)
Bekenstein's bound implies that roughly spherical objects like stars collapse into black holes if too much mass is packed within too small a radius. But a Turing machine could have an infinite rod-like tape, with a finite-sized head crawling back and forth along it, without any part of it exceeding the Bekenstein bound. Does anyone know of any argument why an extended rod-like object must suffer gravitational collapse if it gets too long? An easy calculation shows that the compressive force in an infinite rod due to self-gravitation remains finite, so the rod would not even need to be particularly strong. Maybe it would need to be infinitely stiff to avoid buckling, but that is a harder calculation. However that may be, the assertion that the Bekenstein bound prevents infinite Turing machines from existing requires further demonstration or documentation. CharlesHBennett ( talk) 01:00, 11 April 2013 (UTC)
Agreed. Even if such as restriction exists, it is not implied by the bound itself. Added the "finite physical dimensions" qualification (that includes finite length, width, height, AND energy; I hope this meaning is clear, if not, the text should be reworded). Raven lv ( talk) 16:20, 25 May 2013 (UTC)
Agreed too. The point is that if any law of physics makes Turing machines impossible this does not seem to be the Bekenstein bound. What one needs i just a large enough universe to create a tape that is as long as needed. If there is a problem with this it does not seem to stem from the Bekenstein bound. Moreover, the sentence is obscurely phrased: what does 'with finite dimension and unbounded memory' mean? Does it mean that the head-read head is finite but the tape can be as long as wanted (but still finite)? If yes, it should be said more clearly and avoid suggesting that there are Turing machines with infinite dimension (of what? of the head? why would one want the head to be infinite?) User:Mbtnt\Mbtnt ( User talk:Mbtnt\Mbtnt) (11:46am Nov 7 2017) — Preceding unsigned comment added by Mbtnt ( talk • contribs) 16:47, 7 November 2017 (UTC)
Since this is included in Limits to computation, please include comparisons with the storage density of actual modern hardware, and with the theoretical maximum storage density of magnetic media — Preceding unsigned comment added by 71.167.67.219 ( talk) 20:38, 5 May 2013 (UTC)
At the end of the Examples section, we have the lines "The existence of Bekenstein bound implies that the storage capacity of human brain is finite, although very large. This implication has important consequences on mind uploading, making it theoretically possible, given that physicalism is true."
This implies that the Bekenstein bound has relevance for the human brain which is manifestly false. Human brains, indeed all matter, doesn't come even remotely close to approaching the bound. No matter what the bound is or indeed whether a bound exists at all has, I think, no relevance to human brains or to mind uploading. Is it ok with everyone if I delete the lines in question? Tmfs10 ( talk) 21:47, 3 June 2013 (UTC)
Disagree. The mind uploading article explicitly mentions Bekenstein bound. At the same time, the brain example was removed from the Bekenstein bound page earlier, citing absence of justification as the reason. I readded the example and provided justification. I support that a clarification may be added, citing current research results about the estimated information storage capacity in brains and its comparison with the bound. However, perhaps the bound is more relevant to simulated reality hypothesis, and mentioning it would provide better justification. Raven lv ( talk) 20:55, 18 June 2013 (UTC)
Listen what Connection Machine designer says recalls
The game of Life is an example of a class of computations that interested Feynman called "cellular automata". Like many physicists who had spent their lives going to successively lower and lower levels of atomic detail, Feynman often wondered what was at the bottom. One possible answer was a cellular automaton. The notion is that the "continuum" might, at its lowest levels, be discrete in both space and time, and that the laws of physics might simply be a macro-consequence of the average behavior of tiny cells. Each cell could be a simple automaton that obeys a small set of rules and communicates only with its nearest neighbors, like the lattice calculation for Lattice QCD. If the universe in fact worked this way, then it presumably would have testable consequences, such as an upper limit on the density of information per cubic meter of space.
. Why do I post it here? Might be we include this into the origins, referencing the Digital Physics?-- Javalenok ( talk) 18:13, 31 October 2014 (UTC)
Does the Bekenstein limit only apply to computing power, or does it describe physical information, as in the disposition and energy states of the atoms within, say, a cubic millimeter? In terms of actual, physical entities (such as atoms) expressed in terms of various equations, and not an idea described by a series of 1s and 0s dictated by an electron's spin state, what would be the Bekenstein limit for a cubic millimeter? — Preceding unsigned comment added by 96.2.91.78 ( talk) 19:30, 16 January 2015 (UTC)
Since quantum data is measured in qubits rather than bits, shouldn't that be the unit used in this article? Storing n bits takes n qubits, but the converse is exponentially false. MvH ( talk) 16:24, 23 April 2015 (UTC)MvH
The comment(s) below were originally left at Talk:Bekenstein bound/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Comments on article assessment. I think the article deserves a "low" status because 1. in the scientific community, the bound is still somewhat of a conjecture (perhaps proven for some matter contents, etc) and is a bit "hypothetical" (compare an article, on say, "atom") 2. it's generally of mostly specialist interest. I go for "start" class since there is a dead link or two (eg, "Planck area") and I think the article could do with a little more background, explanation for the non-expert reader, and perhaps links to other areas to help explain arguments -- especially in the last paragraph. The article could also be organized a little more: for example, a header followed by section(s). Wesino 00:45, 29 November 2006 (UTC) |
Last edited at 00:45, 29 November 2006 (UTC). Substituted at 09:21, 29 April 2016 (UTC)
In the revision of 11 April 2018, user Boundarylayer inserted the text:
This finds parallels with the concept of a kugelblitz, a concentration of light or radiation so intense that its energy forms an event horizon and becomes self-trapped: according to general relativity and the equivalence of mass and energy.
The reason that this concept is worth noting on Wikipedia is that it is possible for gravitational collapse to occur from sources that are massless (this is even possible with gravitational radiation; see e.g. Abrahams and Evans (1993)).
However, this does not warrant inclusion in the present article on the Bekenstein bound. The Bekenstein bound is interesting in light of the black hole information problem. The origin of the black hole in question is completely irrelevant.
In particular, whether the black hole was generated by gravitational collapse by massive or massless fields is irrelevant.
In the revision of 1 August 2018, I ( Leo C Stein) removed the aforementioned sentence, for the above reason.
In the revision of 2 August 2018, user Boundarylayer reverted my edit and reinstated their earlier edit.
We should avoid an edit war, so let us discuss whether or not this sentence is relevant for the present article. -- Leo C Stein ( talk) 16:26, 3 August 2018 (UTC)
Is there some reason why the equations for entropy and information use "2π / ħ" instead of simplifying this to simply "1 / h"? It seems to me that using the un-reduced constant would slightly simplify these equations. — Preceding unsigned comment added by 67.166.118.104 ( talk) 07:01, 13 January 2020 (UTC)
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Need a little more clarification for laymen: there's a bound for the amount of information in a finite region of space ( Bekenstein bound, which depends on the amount of energy-mass in that region. Does it mean if there's an infinite amount of energy in a region of space then there's an infinite amount of information? Should there be an upper bound for energy-mass if Pauli exclusion principle really holds true? Also, if that's the case then singularity is ruled out? Mastertek ( talk) 14:50, 23 October 2011 (UTC)
Would it be appropriate to state the maximum information density in bits per cubic meter (or cubic millimeter)? This looks like a straightforward calculation from the S = A/4 formula, but I don't know if there are gotchas in making this kind of comparison. I assume the applied kinds of densities in places like Computer storage density are many orders of magnitude from what is discussed here, but are there even deeper reasons why they are talking about two different things, or is it potentially comparable? (either a "yes" or a "no" might be good to add to the article). Kingdon 19:53, 25 May 2007 (UTC)
Fairandbalanced ( talk) 19:26, 16 September 2008 (UTC)
I am no expert, but when it says in the first paragraph, "... or the information necessary to perfectly describe that system, must be finite if the region of space or the energy is finite," doesn't the author actually mean 'AND', as in, "if the region of space AND the energy is finite?" The Berkenstein bound is proportional to both the radius, R, and the mass-energy, E, so if either quantity is unbounded, the resulting Berkenstein calculation will be without bound. Right? If I haven't misunderstood, would someone knowledgeable please fix this? Thanks. SJGooch ( talk) 10:40, 7 January 2011 (UTC)
15 cite notes on one sentence??? Too much. -- œ ™ 15:27, 7 November 2010 (UTC)
The number of significant digits in the examples is only silly. — Preceding unsigned comment added by 81.216.218.158 ( talk) 20:52, 14 October 2011 (UTC)
In the end of the section on the human brain, how can 2^(n*10^42) be LESS THAN 10^42 ??? (something x 10^41) I.e. the author claims the number of STATES a string of bits can assume is LESS THAN the number of BITS. This is nonsense! — Preceding
unsigned comment added by
98.222.62.231 (
talk)
23:01, 12 October 2012 (UTC)
8 bits can have 2^8, ie 256 states. N bits can have 2^N states. — Preceding unsigned comment added by 24.156.205.96 ( talk) 03:30, 8 September 2015 (UTC)
Bekenstein's bound implies that roughly spherical objects like stars collapse into black holes if too much mass is packed within too small a radius. But a Turing machine could have an infinite rod-like tape, with a finite-sized head crawling back and forth along it, without any part of it exceeding the Bekenstein bound. Does anyone know of any argument why an extended rod-like object must suffer gravitational collapse if it gets too long? An easy calculation shows that the compressive force in an infinite rod due to self-gravitation remains finite, so the rod would not even need to be particularly strong. Maybe it would need to be infinitely stiff to avoid buckling, but that is a harder calculation. However that may be, the assertion that the Bekenstein bound prevents infinite Turing machines from existing requires further demonstration or documentation. CharlesHBennett ( talk) 01:00, 11 April 2013 (UTC)
Agreed. Even if such as restriction exists, it is not implied by the bound itself. Added the "finite physical dimensions" qualification (that includes finite length, width, height, AND energy; I hope this meaning is clear, if not, the text should be reworded). Raven lv ( talk) 16:20, 25 May 2013 (UTC)
Agreed too. The point is that if any law of physics makes Turing machines impossible this does not seem to be the Bekenstein bound. What one needs i just a large enough universe to create a tape that is as long as needed. If there is a problem with this it does not seem to stem from the Bekenstein bound. Moreover, the sentence is obscurely phrased: what does 'with finite dimension and unbounded memory' mean? Does it mean that the head-read head is finite but the tape can be as long as wanted (but still finite)? If yes, it should be said more clearly and avoid suggesting that there are Turing machines with infinite dimension (of what? of the head? why would one want the head to be infinite?) User:Mbtnt\Mbtnt ( User talk:Mbtnt\Mbtnt) (11:46am Nov 7 2017) — Preceding unsigned comment added by Mbtnt ( talk • contribs) 16:47, 7 November 2017 (UTC)
Since this is included in Limits to computation, please include comparisons with the storage density of actual modern hardware, and with the theoretical maximum storage density of magnetic media — Preceding unsigned comment added by 71.167.67.219 ( talk) 20:38, 5 May 2013 (UTC)
At the end of the Examples section, we have the lines "The existence of Bekenstein bound implies that the storage capacity of human brain is finite, although very large. This implication has important consequences on mind uploading, making it theoretically possible, given that physicalism is true."
This implies that the Bekenstein bound has relevance for the human brain which is manifestly false. Human brains, indeed all matter, doesn't come even remotely close to approaching the bound. No matter what the bound is or indeed whether a bound exists at all has, I think, no relevance to human brains or to mind uploading. Is it ok with everyone if I delete the lines in question? Tmfs10 ( talk) 21:47, 3 June 2013 (UTC)
Disagree. The mind uploading article explicitly mentions Bekenstein bound. At the same time, the brain example was removed from the Bekenstein bound page earlier, citing absence of justification as the reason. I readded the example and provided justification. I support that a clarification may be added, citing current research results about the estimated information storage capacity in brains and its comparison with the bound. However, perhaps the bound is more relevant to simulated reality hypothesis, and mentioning it would provide better justification. Raven lv ( talk) 20:55, 18 June 2013 (UTC)
Listen what Connection Machine designer says recalls
The game of Life is an example of a class of computations that interested Feynman called "cellular automata". Like many physicists who had spent their lives going to successively lower and lower levels of atomic detail, Feynman often wondered what was at the bottom. One possible answer was a cellular automaton. The notion is that the "continuum" might, at its lowest levels, be discrete in both space and time, and that the laws of physics might simply be a macro-consequence of the average behavior of tiny cells. Each cell could be a simple automaton that obeys a small set of rules and communicates only with its nearest neighbors, like the lattice calculation for Lattice QCD. If the universe in fact worked this way, then it presumably would have testable consequences, such as an upper limit on the density of information per cubic meter of space.
. Why do I post it here? Might be we include this into the origins, referencing the Digital Physics?-- Javalenok ( talk) 18:13, 31 October 2014 (UTC)
Does the Bekenstein limit only apply to computing power, or does it describe physical information, as in the disposition and energy states of the atoms within, say, a cubic millimeter? In terms of actual, physical entities (such as atoms) expressed in terms of various equations, and not an idea described by a series of 1s and 0s dictated by an electron's spin state, what would be the Bekenstein limit for a cubic millimeter? — Preceding unsigned comment added by 96.2.91.78 ( talk) 19:30, 16 January 2015 (UTC)
Since quantum data is measured in qubits rather than bits, shouldn't that be the unit used in this article? Storing n bits takes n qubits, but the converse is exponentially false. MvH ( talk) 16:24, 23 April 2015 (UTC)MvH
The comment(s) below were originally left at Talk:Bekenstein bound/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
Comments on article assessment. I think the article deserves a "low" status because 1. in the scientific community, the bound is still somewhat of a conjecture (perhaps proven for some matter contents, etc) and is a bit "hypothetical" (compare an article, on say, "atom") 2. it's generally of mostly specialist interest. I go for "start" class since there is a dead link or two (eg, "Planck area") and I think the article could do with a little more background, explanation for the non-expert reader, and perhaps links to other areas to help explain arguments -- especially in the last paragraph. The article could also be organized a little more: for example, a header followed by section(s). Wesino 00:45, 29 November 2006 (UTC) |
Last edited at 00:45, 29 November 2006 (UTC). Substituted at 09:21, 29 April 2016 (UTC)
In the revision of 11 April 2018, user Boundarylayer inserted the text:
This finds parallels with the concept of a kugelblitz, a concentration of light or radiation so intense that its energy forms an event horizon and becomes self-trapped: according to general relativity and the equivalence of mass and energy.
The reason that this concept is worth noting on Wikipedia is that it is possible for gravitational collapse to occur from sources that are massless (this is even possible with gravitational radiation; see e.g. Abrahams and Evans (1993)).
However, this does not warrant inclusion in the present article on the Bekenstein bound. The Bekenstein bound is interesting in light of the black hole information problem. The origin of the black hole in question is completely irrelevant.
In particular, whether the black hole was generated by gravitational collapse by massive or massless fields is irrelevant.
In the revision of 1 August 2018, I ( Leo C Stein) removed the aforementioned sentence, for the above reason.
In the revision of 2 August 2018, user Boundarylayer reverted my edit and reinstated their earlier edit.
We should avoid an edit war, so let us discuss whether or not this sentence is relevant for the present article. -- Leo C Stein ( talk) 16:26, 3 August 2018 (UTC)
Is there some reason why the equations for entropy and information use "2π / ħ" instead of simplifying this to simply "1 / h"? It seems to me that using the un-reduced constant would slightly simplify these equations. — Preceding unsigned comment added by 67.166.118.104 ( talk) 07:01, 13 January 2020 (UTC)