quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

, the u-bit or ubit is a proposed theoretical entity which arises in attempts to reformulate wave functions using only

real number In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...

s instead of the

complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form ...

s conventionally used.

Description

In order to discover the real probability of a given quantum event occurring, the conventional calculation carries out an operation, analogous to squaring, on an associated set of complex numbers. A complex number involves the use of the

square root of minus one The imaginary unit or unit imaginary number () is a solution to the quadratic equation x^2+1=0. Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition an ...

, a number which is described as " imaginary" in contrast to the familiar " real" numbers used for counting and describing real physical objects. Because the computed result is required to be a real number, information is lost in the computation.The Ubit Model In Real-Vector-Space Quantum Theory
(2012) Lecture by William Wootters at the Institut Périmètre de Physique Théorique , Canada. Accessed Jan 2014 This situation is regarded as unsatisfactory by some researchers, who seek an alternative formulation which does not involve the square root of minus one. Bill Wootters, of

Williams College Williams College is a Private college, private liberal arts colleges in the United States, liberal arts college in Williamstown, Massachusetts. It was established as a men's college in 1793 with funds from the estate of Ephraim Williams, a col ...

Williamstown, Massachusetts Williamstown is a town in the northern part of Berkshire County, in the northwest corner of Massachusetts, United States. It shares a border with Vermont to the north and New York to the west. It is part of the Pittsfield, Massachusetts Metropolit ...

, and colleagues have derived such a model. This model requires the presence of a universal entity which is quantum-entangled with every quantum wave and which he calls the u-bit. Mathematically the u-bit may be represented as a vector rotating in a real two-dimensional plane. It has no known physical representation in the real world.

References

{{reflist Quantum mechanics Real numbers Fringe physics