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| '''Bremermann's Limit''', named after [[Hans-Joachim Bremermann]], is the maximum computational speed of a self-contained system in the material universe. It is derived from [[Albert Einstein|Einstein]]'s mass-energy equivalency and the [[Heisenberg uncertainty principle]], and is ''[[speed of light|c]]''<sup>2</sup>/''[[Planck's constant|h]]'' ≈ 1.36 × 10<sup>50</sup> [[bits per second]] per kilogram. <ref>Bremermann, H.J. (1962) [http://holtz.org/Library/Natural%20Science/Physics/Optimization%20Through%20Evolution%20and%20Recombination%20-%20Bremermann%201962.htm ''Optimization through evolution and recombination''] In: Self-Organizing systems 1962, edited M.C. Yovitts et al., Spartan Books, Washington, D.C. pp. 93–106.</ref><ref>Bremermann, H.J. (1965) [http://projecteuclid.org/euclid.bsmsp/1200513783 Quantum noise and information]. 5th Berkeley Symposium on Mathematical Statistics and Probability; Univ. of California Press, Berkeley, California.</ref> This value is important when designing [[cryptography|cryptographic]] algorithms, as it can be used to determine the minimum size of [[encryption key]]s or hash values required to create an algorithm that could never be cracked by a [[brute-force search]]. | | <br><br>The other day I woke up and realised - Now I've been single for a little while and after much intimidation from friends I now find myself signed up for web [http://lukebryantickets.neodga.com Vip Tickets Luke Bryan] dating. They guaranteed me that there are lots of interesting, [http://www.dict.cc/englisch-deutsch/pleasant.html pleasant] and ordinary individuals to fulfill, so the pitch is gone by here!<br>My [http://www.britannica.com/search?query=buddies buddies] and fam are awesome and hanging [http://www.senatorwonderling.com luke bryan 2014] out together at pub gigs or meals is constantly imperative. As I find that you could never get a nice conversation against the sound I haven't ever been in to clubs. In addition, I got two unquestionably cheeky and very adorable canines who are consistently excited to meet up fresh people.<br>I try and keep as physically fit as potential coming to the fitness center several-times a week. I enjoy my sports and try to perform or watch since many a possible. I will frequently at Hawthorn matches being winter. Notice: Supposing that you would contemplated buying a hobby I don't mind, I have experienced the carnage of fumbling fits at stocktake sales.<br><br>Feel free to visit my page; luke bryan concert tour ([http://lukebryantickets.lazintechnologies.com just click the up coming website]) |
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| For example, a computer with the mass of the entire [[Earth]] operating at the Bremermann's limit could perform approximately 10<sup>75</sup> mathematical computations per second. If we assume that a cryptographic key can be tested with only one operation, then a typical 128 bit key could be cracked in under 10<sup>−36</sup> seconds. However, a 256 bit key (which is already in use in some systems) would take about two minutes to crack. Using a 512 bit key would increase the cracking time to approaching 10<sup>72</sup> years, without increasing the time for encryption by more than a constant factor (depending on the encryption algorithms used).
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| The limit has been further analysed in later literature as the maximum rate at which a system with energy spread <math>\Delta E</math> can evolve into an orthogonal and hence distinguishable state to another, <math>\Delta t = \pi \hbar / 2 \Delta E</math>. <ref name="Aharonov1961">{{Cite journal
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| | last1 = Aharonov | first1 = Y.
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| | last2 = Bohm | first2 = D.
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| | doi = 10.1103/PhysRev.122.1649
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| | title = Time in the Quantum Theory and the Uncertainty Relation for Time and Energy
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| | journal = Physical Review
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| | volume = 122
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| | issue = 5
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| | pages = 1649–1658
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| | year = 1961
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| | url = http://dieumsnh.qfb.umich.mx/archivoshistoricosmq/ModernaHist/Aharonov%20a.pdf
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| |bibcode = 1961PhRv..122.1649A }}</ref><ref name="Lloyd2000">{{Cite journal
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| | last1 = Lloyd | first1 = Seth
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| | title = Ultimate physical limits to computation
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| | journal = Nature
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| | volume = 406
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| | issue = 6799
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| | pages = 1047–1054
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| | year = 2000
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| | doi = 10.1038/35023282
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| | pmid = 10984064
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| | arxiv = quant-ph/9908043
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| }}</ref> In particular, [[Norman Margolus|Margolus]] and Levitin has shown that a quantum system with average energy E takes at least time <math>\Delta t = \pi \hbar / 2 E</math> to evolve into an orthogonal state.<ref name="Margolus1998">{{Cite journal
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| | last1 = Margolus | first1 = N.
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| | last2 = Levitin | first2 = L. B.
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| | doi = 10.1016/S0167-2789(98)00054-2
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| | title = The maximum speed of dynamical evolution
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| | journal = Physica D: Nonlinear Phenomena
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| | volume = 120
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| | pages = 188–195
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| |date=September 1998
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| | arxiv = quant-ph/9710043
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| |bibcode = 1998PhyD..120..188M }}</ref>
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| ==See also==
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| *[[Bekenstein bound]]
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| *[[Transcomputational problem]]
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| *[[Limits to computation]]
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| *[[Margolus–Levitin theorem]]
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| ==References==
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| {{reflist}}
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| [[Category:Cybernetics]]
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| [[Category:Theory of computation]]
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| {{comp-sci-stub}}
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| {{physics-stub}}
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