The Planck length, denoted by <math>l_P \ </math>, 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. 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.
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Value
The Planck length equals:
- <math> l_P =\sqrt\frac{\hbar G}{c^3} \thickapprox 1.616 252 (81) \times 10^{-35}</math> meter,
per NIST's 2006 CODATA values. where:
- <math>\hbar </math> (pronounced h-bar) is Dirac's constant, Planck's constant divided by 2π ;
- <math>G</math> is the gravitational constant;
- <math>c</math> 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. 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.
Significance
Ignoring a factor of <math> \pi</math>, 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 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. 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.
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 <math>\hbar \ </math> 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.
References in Science Fiction
- In Hyperion by Dan Simmons, Planck length is referred to as "the shortest length possible".
- Many objects in Xenosaga are compressed to a 'planck-scale size'.
- A modified Planck length is used as a wish-fulfillment device in Rudy Rucker's Master of Space and Time.
See also
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."
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| Base Planck units | Planck time · Planck length · Planck mass · Planck charge · Planck temperature |
| Derived Planck units | Planck energy · Planck force · Planck power · Planck density · Planck angular frequency · Planck pressure · Planck current · Planck voltage · Planck impedance · Planck momentum |
