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Spatial variation of the speed of light in a gravitational potential as measured against a distant observer's time reference is implicitly present in general relativity. [3] The apparent speed of light will change in a gravity field and, in particular, go to zero at an event horizon as viewed by a distant observer. [4]
A pulse with different group and phase velocities (which occurs if the phase velocity is not the same for all the frequencies of the pulse) smears out over time, a process known as dispersion. Certain materials have an exceptionally low (or even zero) group velocity for light waves, a phenomenon called slow light. [74]
In this example the time measured in the frame on the vehicle, t, is known as the proper time. The proper time between two events - such as the event of light being emitted on the vehicle and the event of light being received on the vehicle - is the time between the two events in a frame where the events occur at the same location.
Slow light is a dramatic reduction in the group velocity of light, not the phase velocity. Slow light effects are not due to abnormally large refractive indices, as will be explained below. The simplest picture of light given by classical physics is of a wave or disturbance in the electromagnetic field.
for virtually any well-behaved function g of dimensionless argument φ, where ω is the angular frequency (in radians per second), and k = (k x, k y, k z) is the wave vector (in radians per meter). Although the function g can be and often is a monochromatic sine wave, it does not have to be sinusoidal, or
A more intuitive characteristic of exponential decay for many people is the time required for the decaying quantity to fall to one half of its initial value. (If N(t) is discrete, then this is the median life-time rather than the mean life-time.) This time is called the half-life, and often denoted by the symbol t 1/2. The half-life can be ...
In addition to the light clock used above, the formula for time dilation can be more generally derived from the temporal part of the Lorentz transformation. [28] Let there be two events at which the moving clock indicates t a {\displaystyle t_{a}} and t b {\displaystyle t_{b}} , thus:
Light-time correction can be applied to any object whose distance and motion are known. In particular, it is usually necessary to apply it to the motion of a planet or other Solar System object. For this reason, the combined displacement of the apparent position due to the effects of light-time correction and aberration is known as planetary ...