## The Speed of Light - A Fundamental Limit

There are situations in which it may seem that matter, energy, or information travels at speeds greater than c, but inspection shows this to be false. For example, if a laser beam is swept quickly across a distant object, the spot of light can move faster than c, but the only physical entities that are moving are the laser and its emitted light, which travels at the speed c from the laser to the various positions of the spot. The movement of the spot will be delayed after the laser is moved because of the time it takes light to get to the distant object from the laser.

In some interpretations of quantum mechanics, certain quantum effects may seem to be transmitted faster than c - and thus instantaneously in some frame – the EPR paradox is one, in which the products of a decay move apart. Until either of the particles is observed, they exist in a superposition of two quantum states. If the particles are separated and one particle's quantum state is observed, the other particle's quantum state is determined instantaneously (i.e., faster than light could travel from one particle to the other). However, it is impossible to control which quantum state the first particle will take on when it is observed, so information cannot be transmitted in this manner.

Many waves or particles can travel faster than light in many media, but not c, which remains an upper limit.

The rate of change in the distance between two objects in a frame of reference with respect to which both are moving (their closing speed) may have a value in excess of c. However, this does not represent the speed of any single object as measured in a single inertial frame, and any signal between them travels at speed at most c.

So-called superluminal motion is seen in certain astronomical objects, such as the relativistic jets of radio galaxies and quasars. However, these jets are not moving at speeds in excess of the speed of light: the apparent superluminal motion is a projection effect caused by objects moving near the speed of light and approaching Earth at a small angle to the line of sight: since the light which was emitted when the jet was farther away took longer to reach the Earth, the time between two successive observations corresponds to a longer time between the instants at which the light rays were emitted.

In models of the expanding universe, the farther galaxies are from each other, the faster they drift apart. This receding is not due to motion through space, but rather to the expansion of space itself. For example, galaxies far away from Earth appear to be moving away from the Earth with a speed proportional to their distances. Beyond a boundary called the Hubble sphere, this apparent recessional velocity becomes greater than the speed of light.