<Dd> ħ (\ displaystyle \ hbar) is the reduced Planck's constant (Planck's constant divided by 2 π (\ displaystyle \ pi)). </Dd> <P> Heisenberg originally explained this as a consequence of the process of measuring: Measuring position accurately would disturb momentum and vice versa, offering an example (the "gamma - ray microscope") that depended crucially on the de Broglie hypothesis . The thought is now, however, that this only partly explains the phenomenon, but that the uncertainty also exists in the particle itself, even before the measurement is made . </P> <P> In fact, the modern explanation of the uncertainty principle, extending the Copenhagen interpretation first put forward by Bohr and Heisenberg, depends even more centrally on the wave nature of a particle: Just as it is nonsensical to discuss the precise location of a wave on a string, particles do not have perfectly precise positions; likewise, just as it is nonsensical to discuss the wavelength of a "pulse" wave traveling down a string, particles do not have perfectly precise momenta (which corresponds to the inverse of wavelength). Moreover, when position is relatively well defined, the wave is pulse - like and has a very ill - defined wavelength (and thus momentum). And conversely, when momentum (and thus wavelength) is relatively well defined, the wave looks long and sinusoidal, and therefore it has a very ill - defined position . </P> <P> De Broglie himself had proposed a pilot wave construct to explain the observed wave - particle duality . In this view, each particle has a well - defined position and momentum, but is guided by a wave function derived from Schrödinger's equation . The pilot wave theory was initially rejected because it generated non-local effects when applied to systems involving more than one particle . Non-locality, however, soon became established as an integral feature of quantum theory (see EPR paradox), and David Bohm extended de Broglie's model to explicitly include it . </P>

Electromagnetic radiation can behave both as a wave and as a particle