Limits to computation
Encyclopedia
There are several physical and practical limits to the amount of computation
or data storage
that can be performed with a given amount of mass, volume, or energy:
Several methods have been proposed for producing computing devices or data storage devices that approach physical and practical limits:
Computation
Computation is defined as any type of calculation. Also defined as use of computer technology in Information processing.Computation is a process following a well-defined model understood and expressed in an algorithm, protocol, network topology, etc...
or data storage
Data storage device
thumb|200px|right|A reel-to-reel tape recorder .The magnetic tape is a data storage medium. The recorder is data storage equipment using a portable medium to store the data....
that can be performed with a given amount of mass, volume, or energy:
- The Bekenstein boundBekenstein boundIn physics, the Bekenstein bound is an upper limit on the entropy S, or information I, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximum amount of information required to perfectly describe a given physical system down to the...
limits the amount of information that can be stored within a spherical volume to the entropy of a black hole with the same surface area. - The temperature of the cosmic microwave background radiationCosmic microwave background radiationIn cosmology, cosmic microwave background radiation is thermal radiation filling the observable universe almost uniformly....
gives a practical lower limit to the energy consumed to perform computation of approximately 4kT per state change, where T is the temperature of the background (about 3 kelvinKelvinThe kelvin is a unit of measurement for temperature. It is one of the seven base units in the International System of Units and is assigned the unit symbol K. The Kelvin scale is an absolute, thermodynamic temperature scale using as its null point absolute zero, the temperature at which all...
s), and k is the Boltzmann constant. While a device could be cooled to operate below this temperature, the energy expended by the cooling would offset the benefit of the lower operating temperatureOperating temperatureAn operating temperature is the temperature at which an electrical or mechanical device operates. The device will operate effectively within a specified temperature range which varies based on the device function and application context, and ranges from the minimum operating temperature to the...
. - Bremermann's limitBremermann's limitBremermann'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 Einstein's mass-energy equivalency and the Heisenberg uncertainty principle, and is c2/h ≈ 1.36 × 1050 bits per second per...
is the maximum computational speed of a self-contained system in the material universe, and is based on mass-energy versus quantum uncertainty constraints.
Several methods have been proposed for producing computing devices or data storage devices that approach physical and practical limits:
- A cold degenerate star could conceivably be used as a giant data storage device, by carefully perturbing it to various excited states, in the same manner as an atom or quantum wellQuantum wellA quantum well is a potential well with only discrete energy values.One technology to create quantization is to confine particles, which were originally free to move in three dimensions, to two dimensions, forcing them to occupy a planar region...
used for these purposes. Such a star would have to be artificially constructed, as no natural degenerate stars will cool to this temperature for an extremely long time. It is also possible that nucleonNucleonIn physics, a nucleon is a collective name for two particles: the neutron and the proton. These are the two constituents of the atomic nucleus. Until the 1960s, the nucleons were thought to be elementary particles...
s on the surface of neutron starNeutron starA neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...
s could form complex "molecules" which some have suggested might be used for computing purposes, creating a type of computroniumComputroniumComputronium is a material hypothesized by Norman Margolus and Tommaso Toffoli of the Massachusetts Institute of Technology to be used as "programmable matter," a substrate for computer modeling of virtually any real object....
based on femtotechnologyFemtotechnologyFemtotechnology is a hypothetical term used in reference to structuring of matter on a femtometer, which is 10-15 m. This is a smaller scale in comparison to nanotechnology and picotechnology which are 10-9 m and 10-12 m respectively...
which would be faster and denser than computronium based on nanotechnologyNanotechnologyNanotechnology is the study of manipulating matter on an atomic and molecular scale. Generally, nanotechnology deals with developing materials, devices, or other structures possessing at least one dimension sized from 1 to 100 nanometres...
. - It may be possible to use a black holeBlack holeA black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
as a data storage and/or computing device, if a practical mechanism for extraction of contained information can be found. Such extraction may in principle be possible (Stephen HawkingStephen HawkingStephen William Hawking, CH, CBE, FRS, FRSA is an English theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity...
's proposed resolution to the black hole information paradoxBlack hole information paradoxThe black hole information paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could disappear in a black hole, allowing many physical states to evolve into the same state...
). This would achieve storage density exactly equal to the Bekenstein BoundBekenstein boundIn physics, the Bekenstein bound is an upper limit on the entropy S, or information I, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximum amount of information required to perfectly describe a given physical system down to the...
. Professor Seth LloydSeth LloydSeth Lloyd is a professor of mechanical engineering at the Massachusetts Institute of Technology. He refers to himself as a "quantum mechanic"....
calculated the computational abilities of an "ultimate laptop" formed by compressing a kilogram of matter into a black hole of radius 1.485 × 10−27 meters, concluding that it would only last about 10−19 seconds before evaporating due to Hawking radiationHawking radiationHawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...
, but that during this brief time it could compute at a rate of about 5 × 1050 operations per second, ultimately performing about 1032 operations on 1016 bits. Lloyd notes that "Interestingly, although this hypothetical computation is performed at ultra-high densities and speeds, the total number of bits available to be processed is not far from the number available to current computers operating in more familiar surroundings."