The generalized uncertainty principle (GUP) is a proposed extension of the

Heisenberg uncertainty principle The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position a ...

that incorporates potential effects of gravitational interactions into quantum mechanical systems. It emerges from several approaches to

quantum gravity Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics. It deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the v ...

, including

string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...

loop quantum gravity Loop quantum gravity (LQG) is a theory of quantum gravity that incorporates matter of the Standard Model into the framework established for the intrinsic quantum gravity case. It is an attempt to develop a quantum theory of gravity based direc ...

, and

quantum geometry In quantum gravity, quantum geometry is the set of mathematical concepts that generalize geometry to describe physical phenomena at distance scales comparable to the Planck length. Each theory of quantum gravity uses the term "quantum geometry" ...

, and suggests the existence of a minimum measurable length, typically associated with the

Planck scale In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: '' c'', '' G'', '' ħ'', and ''k''B (described further below). Expressing one of ...

. A commonly used formulation of the GUP is: :

\Delta x \Delta p \geq \frac + \beta \Delta p^2

, where

\Delta x

and

\Delta p

represent the uncertainties in position and momentum,

\hbar

is the reduced Planck constant, and

\beta

is a parameter related to the minimal length scale. This modification implies that position measurements cannot be made with arbitrary precision, as there exists a fundamental lower bound to spatial resolution. The concept is motivated by the expectation that classical notions of

spacetime In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...

may break down at extremely small scales, such as the Planck length. Several forms of the GUP have been proposed in the literature, varying in mathematical structure and underlying theoretical assumptions, depending on the specific model of quantum gravity being considered.

Observable consequences

The GUP's phenomenological and experimental implications have been examined across low and high-energy contexts, encompassing atomic systems, quantum optical systems, gravitational bar detectors, gravitational decoherence, and macroscopic harmonic oscillators, further extending to composite particles, and astrophysical systems.

References

{{Reflist Quantum gravity String theory Unsolved problems in physics