The Planck length, denoted by , is the unit of length approximately 1.6 × 10⁻³⁵ metres, 6.3 × 10^-34 inches, or about 10^-20 times the diameter of a proton. It is in the system of units known as Planck units. The Planck length is deemed "natural" because it can be defined from three fundamental physical constants: the speed of light, Planck's constant, and the gravitational constant. For other uses of this word, see Length (disambiguation). ... Mid-19th century tool for converting between different standards of the inch An inch is an Imperial unit of length. ... In physics, Planck units are physical units of measurement defined exclusively in terms of the five universal physical constants shown in the table below in such a manner that all of these physical constants take on the numerical value of one when expressed in terms of these units. ... In physics, natural units are physical units of measurement defined in terms of universal physical constants in such a manner that some chosen physical constants take on the numerical value of one when expressed in terms of a particular set of natural units. ... In physics, fundamental physical constants are, in the strictest sense, physical constants that are independent of systems of units and hence are dimensionless numbers. ... The speed of light in vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ...

The physical significance of the Planck length is unclear. Because it is the only length (up to a constant factor) obtainable from the constants G, h, and c, it is expected to play some role in a theory of quantum gravity. In some forms of quantum gravity, it is the length scale at which the structure of spacetime becomes dominated by quantum effects, giving it a discrete or foamy structure. In other forms of quantum gravity there are no such effects. If there are large extra dimensions, the measured strength of gravity may be much smaller than its true (small-scale) value; in this case the Planck length would have no physical significance, and quantum gravitational effects would appear at much larger scales. This article does not cite any references or sources. ... This article needs to be cleaned up to conform to a higher standard of quality. ... In particle physics, the ADD model, also known as the model with old large dimensions, is a scenario inspired by string theory to explain the weakness of gravity relatively to other forces in which the fields of the Standard Model are confined to a higher-dimensional membrane but gravity can...

Value

The Planck length equals:

meter,

per NIST's 2006 CODATA values. The metre, or meter (symbol: m) is the SI base unit of length. ... CODATA (Committee on Data for Science and Technology) was established in 1966 as an interdisciplinary committee of the International Council of Science (ICSU), formerly the International Council of Scientific Unions. ...

where:

• (pronounced h-bar) is Dirac's constant, Planck's constant divided by 2π ;
• G is the gravitational constant;
• c is the speed of light in vacuum.

The two digits between the parentheses denote the uncertainty (standard deviation) in the last two digits of the value. Plancks constant, denoted h, is a physical constant that is used to describe the sizes of quanta. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... The speed of light in vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum. ... For technical reasons, :) and some similar combinations starting with : redirect here. ... In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. ...

In SI units, the Planck length is approximately 1.6 × 10⁻³⁵ meters. The estimated radius of the observable universe (4.4 × 10²⁶ m or 46 billion light-years) is 2.7 × 10⁶¹ Planck lengths. The International System of Units (symbol: SI) (for the French phrase Système International dUnités) is the most widely used system of units. ... See universe for a general discussion of the universe. ... This article is about the unit of length. ...

Significance

Ignoring a factor of π, the Planck mass is roughly the mass of a black hole with a Schwarzschild radius equal to its Compton wavelength. The radius of such a black hole would be, roughly, the Planck length. The Planck mass is the natural unit of mass, denoted by mP. It is the mass for which the Schwarzschild radius is equal to the Compton length divided by Ï€. ≈ 1. ... For other uses, see Black hole (disambiguation). ... The Schwarzschild radius (sometimes inappropriately referred to as the gravitational radius[1]) is a characteristic radius associated with every mass. ... The Compton wavelength of a particle is given by , where is the Planck constant, is the particles mass and is the speed of light. ...

The following thought experiment illuminates this fact. The task is to measure an object's position by bouncing electromagnetic radiation, namely photons, off it. The shorter the wavelength of the photons, and hence the higher their energy, the more accurate the measurement. If the photons are sufficiently energetic to make possible a measurement more precise than a Planck length, their collision with the object would, in principle, create a minuscule black hole. This black hole would "swallow" the photon and thereby make it impossible to obtain a measurement. A simple calculation using dimensional analysis suggests that this problem arises if we attempt to measure an object's position with a precision to within a Planck length. In philosophy, physics, and other fields, a thought experiment (from the German Gedankenexperiment) is an attempt to solve a problem using the power of human imagination. ... Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ... The wavelength is the distance between repeating units of a wave pattern. ... Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ...

This thought experiment draws on both general relativity and the Heisenberg uncertainty principle of quantum mechanics. Combined, these two theories imply that it is impossible to measure position to a precision greater than the Planck length, or duration to a precision greater than the time a photon traveling at c would take to travel a Planck length. This suggests that in a theory of quantum gravity combining general relativity and quantum mechanics, traditional notions of space and time break down at distances shorter than the Planck length or times shorter than the Planck time. For a less technical and generally accessible introduction to the topic, see Introduction to general relativity. ... Werner Karl Heisenberg (December 5, 1901 – February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics and acknowledged to be one of the most important physicists of the twentieth century. ... In quantum physics, the outcome of even an ideal measurement of a system is not deterministic, but instead is characterized by a probability distribution, and the larger the associated standard deviation is, the more uncertain we might say that that characteristic is for the system. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... This article does not cite any references or sources. ... In physics, the Planck time (tP), is the unit of time in the system of natural units known as Planck units. ...

History

Max Planck was the first to propose the Planck length, a base unit in a system of measurement he called natural units. By design, the Planck length, Planck time, and Planck mass are such that the physical constants c, G, and all equal 1 and thus disappear from the equations of physics. Although quantum mechanics and general relativity were unknown when Planck proposed his natural units, it later became clear that at a distance equal to the Planck length, gravity begins to display quantum effects, whose understanding would seem to require a theory of quantum gravity. “Planck” redirects here. ... In physics, natural units are physical units of measurement defined in terms of universal physical constants in such a manner that some chosen physical constants take on the numerical value of one when expressed in terms of a particular set of natural units. ... In physics, the Planck time (tP), is the unit of time in the system of natural units known as Planck units. ... The Planck mass is the natural unit of mass, denoted by mP. It is the mass for which the Schwarzschild radius is equal to the Compton length divided by π. ≈ 1. ... In physics, a physical constant is a physical quantity of a value that is generally believed to be both universal in nature and not believed to change in time. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... For a less technical and generally accessible introduction to the topic, see Introduction to general relativity. ... For a less technical and generally accessible introduction to the topic, see Introduction to quantum mechanics. ... This article does not cite any references or sources. ...

References in Science Fiction

• In Hyperion, the novel of Dan Simmons, Planck length is referred as "the shortest length possible".
• Many objects in Xenosaga are compressed into a 'planck-scale size'; generally they're in actually placed into the higher domain of U-DO.

Hyperion is a Hugo Award-winning 1989 science fiction novel by Dan Simmons. ... It has been suggested that List of Xenosaga cast members be merged into this article or section. ...

See also

• Planck units
• Planck scale

In physics, Planck units are physical units of measurement defined exclusively in terms of the five universal physical constants shown in the table below in such a manner that all of these physical constants take on the numerical value of one when expressed in terms of these units. ... In physics, Planck units are physical units of measurement originally proposed by Max Planck. ...

External links

• NIST, "Planck's Length", NIST's published CODATA constants.
• John Baez, "Length Scales in Physics: The Planck length."
• John Baez, "Higher-Dimensional Algebra and Planck-Scale Physics: The Planck Length."