Planck scale

Encyclopedia

In particle physics

and physical cosmology

, the

(which corresponds by the mass–energy equivalence to the Planck mass 2.17645 × 10

breaks down (due to the non-renormalizability

of gravity). That is, although physicists have a fairly good understanding of the other fundamental interactions or forces on the quantum level, gravity is problematic, and cannot be integrated with quantum mechanics

(at high energies) using the usual framework of quantum field theory. For energies approaching the Planck scale, an exact theory of quantum gravity

is required, and the current leading candidate is string theory

, or its modernized form M-theory

. Other approaches to this problem include Loop quantum gravity

, Noncommutative geometry

, and Causal set theory

. At the Planck scale, the strength of gravity is expected to become comparable to the other forces, and it is theorized that all the fundamental forces are unified at that scale, but the exact mechanism of this unification remains unknown.

The term

or time scale.

The Planck length is related to Planck energy by the uncertainty principle

. At this scale, the concepts of size and distance break down, as quantum indeterminacy

becomes virtually absolute. Because the Schwarzschild radius

of a black hole

is roughly equal to the Compton wavelength

at the Planck scale, a photon with sufficient energy to probe this realm would yield no information whatsoever. Any photon energetic enough to precisely measure a Planck-sized object could actually

), thus completely distorting that region of space, and swallowing the photon. This is the most extreme example possible of the uncertainty principle, and explains why only a quantum gravity

theory reconciling general relativity

with quantum mechanics

will allow us to understand the dynamics of space-time at this scale. Planck scale dynamics is important for cosmology because if we trace the evolution of the cosmos back to the very beginning, at some very early stage the universe should have been so hot that processes involving energies as high as the Planck energy (corresponding to distances as short as the Planck length) may have occurred. This period is therefore called the Planck era or Planck epoch

.

, as it relates to a surprisingly broad range of topics. It may, in fact, be a fundamental aspect of the universe. In terms of size, the Planck scale is unimaginably small (many orders of magnitude smaller than a proton). In terms of energy, it is unimaginably 'hot' and energetic. The wavelength

of a photon

(and therefore its size) decreases as its frequency

or energy increases. The fundamental limit for a photon's energy is the Planck energy, for the reasons cited above. This makes the Planck scale a fascinating realm for speculation by theoretical physicists from various schools of thought. Is the Planck scale domain a seething mass of virtual black holes? Is it a fabric of unimaginably fine loops

or a spin foam

network? Is it interpenetrated by innumerable Calabi-Yau manifolds, which connect our 3-dimensional universe with a higher dimensional space? Perhaps our 3-D universe is 'sitting' on a 'brane' which separates it from a 2, 5, or 10-dimensional universe and this accounts for the apparent 'weakness' of gravity in ours. These approaches, among several others, are being considered to gain insight into Planck scale dynamics. This would allow physicists to create a unified description of all the fundamental forces.

, there possibly was a time when the universe itself achieved Planck scale energies, and we have measured the afterglow of that era with instruments such as the WMAP probe, which recently accumulated sufficient data to allow scientists to probe back to the first trillionth of a second after the Big Bang

, near the electroweak phase transition. This is still several orders of magnitude away from the Planck epoch

, when the universe was at the Planck scale, but planned probes such as Planck Surveyor

and related experiments such as IceCube expect to greatly improve on current astrophysical measurements.

Results from the Relativistic Heavy Ion Collider

have pushed back the particle physics frontier to discover the fluid nature of the quark-gluon plasma

, and this process will be augmented by the Large Hadron Collider

at CERN

, pushing back the 'cosmic clock' for particle physics still further. This is likely to add to the understanding of Planck scale dynamics, and sharpen the knowledge of what evolves from that state. No experiment current or planned will allow the precise probing or complete understanding of the Planck scale. Nonetheless, enough data have already been accumulated to narrow the field of workable inflationary universe

theories, and to eliminate some theorized extensions to the Standard Model

.

physics beyond or smaller than the Planck scale.

The Elegant Universe by Brian Greene

discusses briefly the strange world of the sub-Planck and how it "creates" the quantum universe by its averages. In his later work, The Fabric of the Cosmos

, Greene

states that "the familiar notion of space and time do not extend into the sub-Planckian realm, which suggests that space and time as we currently understand them may be mere approximations to more fundamental concepts that still await our discovery.”

Particle physics

Particle physics is a branch of physics that studies the existence and interactions of particles that are the constituents of what is usually referred to as matter or radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics...

and physical cosmology

Physical cosmology

Physical cosmology, as a branch of astronomy, is the study of the largest-scale structures and dynamics of the universe and is concerned with fundamental questions about its formation and evolution. For most of human history, it was a branch of metaphysics and religion...

, the

**Planck scale**is an energy scale around 1.22 × 10^{19}GeVGEV

GEV or GeV may stand for:*GeV or gigaelectronvolt, a unit of energy equal to billion electron volts*GEV or Grid Enabled Vehicle that is fully or partially powered by the electric grid, see plug-in electric vehicle...

(which corresponds by the mass–energy equivalence to the Planck mass 2.17645 × 10

^{−8}kg) at which quantum effects of gravity become strong. At this scale, the description of sub-atomic particle interactions in terms of quantum field theoryQuantum field theory

Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...

breaks down (due to the non-renormalizability

Renormalization

In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities....

of gravity). That is, although physicists have a fairly good understanding of the other fundamental interactions or forces on the quantum level, gravity is problematic, and cannot be integrated with quantum mechanics

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

(at high energies) using the usual framework of quantum field theory. For energies approaching the Planck scale, an exact theory of quantum gravity

Quantum gravity

Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

is required, and the current leading candidate is string theory

String theory

String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...

, or its modernized form M-theory

M-theory

In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...

. Other approaches to this problem include Loop quantum gravity

Loop quantum gravity

Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...

, Noncommutative geometry

Noncommutative geometry

Noncommutative geometry is a branch of mathematics concerned with geometric approach to noncommutative algebras, and with construction of spaces which are locally presented by noncommutative algebras of functions...

, and Causal set theory

Causal sets

The causal sets programme is an approach to quantum gravity. Its founding principle is that spacetime is fundamentally discrete and that the spacetime events are related by a partial order...

. At the Planck scale, the strength of gravity is expected to become comparable to the other forces, and it is theorized that all the fundamental forces are unified at that scale, but the exact mechanism of this unification remains unknown.

The term

**Planck scale**can also refer to a length scaleLength scale

In physics, length scale is a particular length or distance determined with the precision of one order of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot affect each other and are said to decouple...

or time scale.

Quantity | SI equivalent |
---|---|

Planck time Planck time In physics, the Planck time, , is the unit of time in the system of natural units known as Planck units. It is the time required for light to travel, in a vacuum, a distance of 1 Planck length... |
5.39121 × 10^{−44} s |

Planck mass | 2.17645 × 10^{−8} kg |

Planck length (ℓ_{P}) |

The Planck length is related to Planck energy by the uncertainty principle

Uncertainty principle

In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...

. At this scale, the concepts of size and distance break down, as quantum indeterminacy

Quantum indeterminacy

Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics...

becomes virtually absolute. Because the Schwarzschild radius

Schwarzschild radius

The Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...

of a black hole

Black hole

A 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...

is roughly equal to the Compton wavelength

Compton wavelength

The Compton wavelength is a quantum mechanical property of a particle. It was introduced by Arthur Compton in his explanation of the scattering of photons by electrons...

at the Planck scale, a photon with sufficient energy to probe this realm would yield no information whatsoever. Any photon energetic enough to precisely measure a Planck-sized object could actually

*create*a particle of that dimension, but it would be massive enough to immediately become a black hole (a.k.a Planck particlePlanck particle

A Planck particle, named after physicist Max Planck, is a hypothetical particle defined as a tiny black hole whose Compton wavelength is comparable to its Schwarzschild radius. Its mass is thus approximately the Planck mass, and its Compton wavelength and Schwarzschild radius are about the Planck...

), thus completely distorting that region of space, and swallowing the photon. This is the most extreme example possible of the uncertainty principle, and explains why only a quantum gravity

Quantum gravity

Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

theory reconciling general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

with quantum mechanics

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

will allow us to understand the dynamics of space-time at this scale. Planck scale dynamics is important for cosmology because if we trace the evolution of the cosmos back to the very beginning, at some very early stage the universe should have been so hot that processes involving energies as high as the Planck energy (corresponding to distances as short as the Planck length) may have occurred. This period is therefore called the Planck era or Planck epoch

Planck epoch

In physical cosmology, the Planck epoch , named after Max Planck, is the earliest period of time in the history of the universe, from zero to approximately 10−43 seconds , during which, it is believed, quantum effects of gravity were significant...

.

## Theoretical ideas

The nature of reality at the Planck scale is the subject of much debate in the world of physicsPhysics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, as it relates to a surprisingly broad range of topics. It may, in fact, be a fundamental aspect of the universe. In terms of size, the Planck scale is unimaginably small (many orders of magnitude smaller than a proton). In terms of energy, it is unimaginably 'hot' and energetic. The wavelength

Wavelength

In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

of a photon

Photon

In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

(and therefore its size) decreases as its frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

or energy increases. The fundamental limit for a photon's energy is the Planck energy, for the reasons cited above. This makes the Planck scale a fascinating realm for speculation by theoretical physicists from various schools of thought. Is the Planck scale domain a seething mass of virtual black holes? Is it a fabric of unimaginably fine loops

Loop quantum gravity

Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...

or a spin foam

Spin foam

In physics, a spin foam is a topological structure made out of two-dimensional faces that represents one of the configurations that must be summed to obtain a Feynman's path integral description of quantum gravity...

network? Is it interpenetrated by innumerable Calabi-Yau manifolds, which connect our 3-dimensional universe with a higher dimensional space? Perhaps our 3-D universe is 'sitting' on a 'brane' which separates it from a 2, 5, or 10-dimensional universe and this accounts for the apparent 'weakness' of gravity in ours. These approaches, among several others, are being considered to gain insight into Planck scale dynamics. This would allow physicists to create a unified description of all the fundamental forces.

## Experiments probing the Planck Scale

Experimental evidence of Planck scale dynamics is difficult to obtain, and until quite recently was scant to non-existent. Although it remains impossible to probe this realm directly, as those energies are well beyond the capability of any current or planned particle acceleratorParticle accelerator

A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

, there possibly was a time when the universe itself achieved Planck scale energies, and we have measured the afterglow of that era with instruments such as the WMAP probe, which recently accumulated sufficient data to allow scientists to probe back to the first trillionth of a second after the Big Bang

Big Bang

The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in...

, near the electroweak phase transition. This is still several orders of magnitude away from the Planck epoch

Planck epoch

In physical cosmology, the Planck epoch , named after Max Planck, is the earliest period of time in the history of the universe, from zero to approximately 10−43 seconds , during which, it is believed, quantum effects of gravity were significant...

, when the universe was at the Planck scale, but planned probes such as Planck Surveyor

Planck Surveyor

Planck is a space observatory of the European Space Agency and designed to observe the anisotropies of the cosmic microwave background over the entire sky, at a high sensitivity and angular resolution...

and related experiments such as IceCube expect to greatly improve on current astrophysical measurements.

Results from the Relativistic Heavy Ion Collider

Relativistic Heavy Ion Collider

The Relativistic Heavy Ion Collider is one of two existing heavy-ion colliders, and the only spin-polarized proton collider in the world. It is located at Brookhaven National Laboratory in Upton, New York and operated by an international team of researchers...

have pushed back the particle physics frontier to discover the fluid nature of the quark-gluon plasma

Quark-gluon plasma

A quark–gluon plasma or quark soup is a phase of quantum chromodynamics which exists at extremely high temperature and/or density. This phase consists of asymptotically free quarks and gluons, which are several of the basic building blocks of matter...

, and this process will be augmented by the Large Hadron Collider

Large Hadron Collider

The Large Hadron Collider is the world's largest and highest-energy particle accelerator. It is expected to address some of the most fundamental questions of physics, advancing the understanding of the deepest laws of nature....

at CERN

CERN

The European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...

, pushing back the 'cosmic clock' for particle physics still further. This is likely to add to the understanding of Planck scale dynamics, and sharpen the knowledge of what evolves from that state. No experiment current or planned will allow the precise probing or complete understanding of the Planck scale. Nonetheless, enough data have already been accumulated to narrow the field of workable inflationary universe

Cosmic inflation

In physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 1078 in volume, driven by a negative-pressure vacuum energy density. The inflationary epoch comprises the first part...

theories, and to eliminate some theorized extensions to the Standard Model

Standard Model

The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...

.

## Sub-Planck physics

**Sub-Planck**refers to conjecturalConjecture

A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds...

physics beyond or smaller than the Planck scale.

The Elegant Universe by Brian Greene

Brian Greene

Brian Greene is an American theoretical physicist and string theorist. He has been a professor at Columbia University since 1996. Greene has worked on mirror symmetry, relating two different Calabi-Yau manifolds...

discusses briefly the strange world of the sub-Planck and how it "creates" the quantum universe by its averages. In his later work, The Fabric of the Cosmos

The Fabric of the Cosmos

The Fabric of the Cosmos: Space, Time, and the Texture of Reality is the second book on theoretical physics, cosmology, and string theory written by Brian Greene, professor and co-director of Columbia's Institute for Strings, Cosmology, and Astroparticle Physics .- Introduction :Greene begins with...

, Greene

Brian Greene

Brian Greene is an American theoretical physicist and string theorist. He has been a professor at Columbia University since 1996. Greene has worked on mirror symmetry, relating two different Calabi-Yau manifolds...

states that "the familiar notion of space and time do not extend into the sub-Planckian realm, which suggests that space and time as we currently understand them may be mere approximations to more fundamental concepts that still await our discovery.”

## See also

- Planck unitsPlanck unitsIn physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units elegantly simplify...
- Planck epochPlanck epochIn physical cosmology, the Planck epoch , named after Max Planck, is the earliest period of time in the history of the universe, from zero to approximately 10−43 seconds , during which, it is believed, quantum effects of gravity were significant...
- Planck particlePlanck particleA Planck particle, named after physicist Max Planck, is a hypothetical particle defined as a tiny black hole whose Compton wavelength is comparable to its Schwarzschild radius. Its mass is thus approximately the Planck mass, and its Compton wavelength and Schwarzschild radius are about the Planck...
- Quantum gravityQuantum gravityQuantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
- Max PlanckMax PlanckMax Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...

## External links

- The Planck scale: relativity meets quantum mechanics meets gravity from 'Einstein Light' at UNSW
- The Planck Era from U of Tennessee Astrophysics pages
- Higher-Dimensional Algebra and Planck-Scale Physics by John C. BaezJohn C. BaezJohn Carlos Baez is an American mathematical physicist and a professor of mathematics at the University of California, Riverside in Riverside, California. He is known for his work on spin foams in loop quantum gravity. More recently, his research has focused on applications of higher categories...