UNCERTAINTY > Implications The Heisenberg relations do not reflect a practical limitation of our measuring devices. Rather, they express an intrinsic feature of quantum observables. The uncertainty relations are at odds with the deterministic description of nature provided by classical mechanics, i.e. the description in terms of bodies which are characterized at any instant by well-defined kinematical properties (position and momentum values), which can be predicted – in principle - with infinite accuracy. Position and momentum are well-defined observables in quantum mechanics too. However, as pointed out by Heisenberg, ‘if one wants to be clear about what is meant by ‘position of an object’, for example of an electron [...], then one has to specify definite experiments by which the ‘position of an electron’ can be measured [...].’

We know very well how to measure the velocity or the position of a quantum particle. But, in this case, we can hardly think of position and velocity as having a well-defined value independently of the precise context of their observation. (See complementarity and superpositions for further discussion.)

Besides their deep philosophical implications, the Heisenberg relations are a far-reaching empirical principle. They explain for example why the search for minuscule particles demands huge accelerators: a small size being coupled with large momentum, particles must be accelerated up to enormous energies in order to explore infinitesimal length scales.

Among the fundamental implications of the position/velocity uncertainty relations, we can mention the diffraction of particle beams (see experimental evidence) and the indiscernibility of quantum particles.

Time/energy uncertainty relations have important empirical implications too. One example is provided by the impossibility of determining simultaneously, with arbitrary accuracy, the phase which characterizes the wavelike aspect of a light field and the photon number which characterizes its corpuscular aspect. This is because time enters in the definition of the field's phase, whereas the photon number determines the field's energy. Analogously, when considering the photon emitted in the decay of an excited atom, it is impossible to predict both when the photon will be emitted and what will be its frequency (the photon's energy and frequency are linked by de Broglie's relations). This is why the atom life-time , i.e. the average time the atom remains excited before radiating, is linked to the natural width of spectral lines, i.e. the width of the frequency distribution of the emitted photons.

Quantum fluctuations are responsible for a number of fundamental effects. We mention two, which play a key role in electronics and astrophysics respectively: quantum tunneling (particles ‘passing through’ a potential barrier that they could by no means overwhelm according to classical mechanics) and the evaporation of black holes (from which, by definition, no energy should escape: leaks are due to quantum fluctuations).

Virtual particles are widely used in quantum field theory as a helpful concept to visualize elementary (subatomic) interactions and carry out the related computations. Some effects observed at the atomic scale can be explained by models that involve virtual particles (an example being the Casimir effect, i.e. the attraction between two uncharged mirrors facing each other).