Light, speed/velocity

The possible existence of faster-than-light objects has a long history, which, since the early 1900s, can be traced back in pre-relativistic times) to J. J. Thomson and A. Sommerfeld (see the excellent review in Ref. 1 by Recami for a full historical account). After the advent of special relativity in 1905, light speed (the speed of light) in vacuum was considered as the maximal causal speed, as an upper limit for any velocity. Such a common belief lasted for about half a century, when the problem of faster-than-light particles was reconsidered... 

Consider a source that emits light of velocity c and which moves relative to an observer with velocity v. The observed speed of the light ray, according to the addition formula follows from ... 

Due to the specific character of this refraction tensor, which correlates the propagation of the electromagnetic waves in vacuum - ( ) with that of a crystalline environment - (Z)), the last statement can be written also for the propagation speeds in vacuum, represented by the scalar of the light speed c, respecting the velocity of the system in cause, represented by the vector (v). Thus, the tensor of the refraction index will not be of second order, but of the first order, to satisfy the contracting relation ... 

Modem elementary-particle physics is founded upon the two pillars of quantum mechanics and relativity. I have made little mention of relativity so far because, while the atom is very much a quantum system, it is not very relativistic at all. Relativity becomes important only when velocities become comparable to the speed of light. Electrons in atoms move rather slowly, at a mere one percent of light speed. Thus it is that a satisfactory description of the atom can be obtained without Einstein s revolutionary theory. 

Free-Electron Lasers. The free-electron laser (EEL) directly converts the kinetic energy of a relativistic electron beam into light (45,46). Relativistic electron beams have velocities that approach the speed of light. The active medium is a beam of free electrons. The EEL, a specialized device having probably limited appHcations, is a novel type of laser with high tunabiHty and potentially high power and efficiency. 

Spaceships capable of reaching stars other than the sun are expected to be more directly involved with plasmas than are contemporary spacecraft, in terms of their motion through the interstellar plasmas and their propulsion. Very high velocities are expected to be required for travel to other stars, eg, Proxima Centauri, which is 4.3 light years distant and would require 43 years at one-tenth the speed of light. 

The various solutions to Equation 3 correspond to different stationary states of the particle (molecule). The one with the lowest energy is called the ground stale. Equation 3 is a non-relativistic description of the system which is not valid when the velocities of particles approach the speed of light. Thus, Equation 3 does not give an accurate description of the core electrons in large nuclei. 

The energy of a Is-electron in a hydrogen-like system (one nucleus and one electron) is —Z /2, and classically this is equal to minus the kinetic energy, 1/2 mv, due to the virial theorem E — —T = 1/2 V). In atomic units the classical velocity of a Is-electron is thus Z m= 1). The speed of light in these units is 137.036, and it is clear that relativistic effects cannot be neglected for the core electrons in heavy nuclei. For nuclei with large Z, the Is-electrons are relativistic and thus heavier, which has the effect that the 1 s-orbital shrinks in size, by the same factor by which the mass increases (eq. (8.2)). 

The properties of natural gas are dominated by those of methane, notably a low maximum flame speed of 0.33 m/s. This strongly influences burner design, which must ensure that the mixture velocity is sufficiently low to prevent blow-off. Light-back , on the contrary, is very unlikely with such a low flame speed. 

In the first of these methods, the reduction in air mass flow is limited by considerations of distribution velocities within the rooms, so at light load more air may need to be used, together with more re-heat, to keep air speeds up. Within this constraint, any proportion of sensible and latent heat can be satisfied, to attain correct room conditions. However, full humidity control would be very wasteful in energy and a simple thermostatic control is preferred. 

For a typical sodium atom, the initial velocity in the atomic beam is about 1000 m s1 and the velocity change per photon absorbed is 3 crn-s. This means that the sodium atom must absorb and spontaneously emit over 3 x 104 photons to be stopped. It can be shown that the maximum rate of velocity change for an atom of mass m with a photon of frequency u is equal to hu/lmcr where h and c are Planck s constant and the speed of light, and r is the lifetime for spontaneous emission from the excited state. For sodium, this corresponds to a deceleration of about 106 m s"2. This should be sufficient to stop the motion of 1000 m-s 1 sodium atoms in a time of approximately 1 ms over a distance of 0.5 m, a condition that can be realized in the laboratory. 

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