Theory of special relativity

While not unique, the Scluodinger picture of quantum mechanics is the most familiar to chemists principally because it has proven to be the simplest to use in practical calculations. Hence, the remainder of this section will focus on the Schrodinger fomuilation and its associated wavefiinctions, operators and eigenvalues. Moreover, effects associated with the special theory of relativity (which include spin) will be ignored in this subsection. Treatments of alternative fomuilations of quantum mechanics and discussions of relativistic effects can be found in the reading list that accompanies this chapter. 

The version of quantum mechanics we have developed so far does not satisfy the requirements of the special theory of relativity. We can see this by noting the form of the time-dependent Schrddinger equation for a single electron... 

It is a first-order differential equation in time, but second-order in the spatial variables. Space and time do not enter on an equal footing, as required by the special theory of relativity. 

However, one of the consequences of Einstein s special theory of relativity (in 1905) is that a photon has an energy that can be expressed as... 

It was only in 1905 that the reality of atoms was finally demonstrated. In that year, the same year that he published the first papers on his special theory of relativity, Albert Einstein published a paper on Brownian movement, the irregular motion of small particles suspended in a liquid. Einstein showed that the patterns of movement that were observed could be explained only by assuming that the particles are constantly buffeted by the molecules that make up the liquid. Thus, observations of Brownian movement provided evidence that molecules—and consequently atoms—are indeed real. 

The preceding is a result of special relativity precise to one part in 1023 [49]. Its explanation in standard special relativity is as follows. Let the tangential velocity of the disk be vi and the velocity of the particle be V2 in the laboratory frame [52]. When the particle and disk are moving in the same direction, the velocity of the particle is v2 v i = V3 relative to an observer on the periphery of the disk. Vice-versa, the relative velocity is v2 + v = V4. The special theory of relativity states that time for the two particles will be dilated to different... 

Fortunately for science, Einstein s deflection toward other problems ended productively, for the ensuing 1905 Annus Mirabilis witnessed publication of Einstein s three papers on the special theory of relativity, Brownian motion, and the quantum theory of the photoelectric effect.)... 

The finitencss of Planck s constant ft and its resulting implications laid the foundations of quantum theory. Quantum theory, like Hie special theory of relativity, was discovered through experiments on electromagnetic phenomena and their theoretical interpretations. 

The space-time coordinates (x,y,z,t) of a point in a stationary system are, according to the special theory of relativity, related to the space-time coordinates in a system moving along the x axis (x , /, z, t ) by the relations... 

To help construct his argument about the wavelike behavior of matter, de Broglie used the now-famous equation E = me2, which had been proposed in 1905 by Einstein as part of his special theory of relativity. 

Point 3, the assumption that Schriklinger s equation is exact, is very significant at a fundamental level. Einstein s Special Theory of Relativity proposed a modification of classical mechanics in a different direction from that of quantum mechanics. The corrections involved in Einstein s theory, which are not incorporated in Schrbdinger s equation, only become significant... 

Let us concentrate on the particle aspect only. The main issue is to identify an space (three- or four-dimensional ) where photons propagate with constant speed c. Einstein s second postulate of the special theory of relativity (STR) requires the speed of light in free space to be the same for all inertial observers. This postulate is conventionally interpreted as implying the non-existence of a preferred frame E. As discussed in section II, the exactly opposite view will be adopted here. 

Einstein s second postulate requires the speed of electromagnetic radiation in free space to be the same for all inertial observers. The special theory of relativity (STR) is conventionally interpreted as a prohibition for the existence of a preferred frame S. 

Actually, the preferred frame is undefined in special theory of relativity. 

The constancy of velocity of light attracted the whole scientific community since the publication of the paper on special theory of relativity by Albert... 

In Einstein s special theory of relativity [1,2], the Galilean transformation had to be replaced by the Lorentz transformation, so that the speed of light would be invariant or independent of the relative motion of the observers—in particular, because the assumption f t is no longer correct. In the Lorentz transformation the time is t / t. 

Brief mention of radioactivity is in order because it, along with quantum mechanics and relativity, transformed classical into modem physics. Radioactivity was discovered by Becquerel in 1896. However, an understanding of how materials like uranium and radium could emit, over the years, a million times more energy than would be permitted by chemical reactions, had to await Einstein s special theory of relativity (Section 4.2.3), which showed that a tiny, unnoticeable decrease in mass represented the release of a large amount of energy. 

The special theory of relativity (the one germane to chemistry, since gravity is irrelevant to our science) and its chemical consequences are nicely reviewed in Balasubramanian K (1997) Relativistic effects in chemistry, Parts A and B. Wiley, New York... 

The special theory of relativity states that the mass of a body is a measure of its energy E = me2, where c is the speed of light. That is, energy and mass are equivalent and interconvertible. Changes in mass are measurable only when changes in energy are considerable, which in practice commonly means for nuclear processes. 

The most attractive feature of the hydrodynamic model is that it obviates the statistical interpretation of quantum theory, by eliminating the need of a point particle. However, even Einstein, despite his famous insistence that "the old one does not play dice", and despite the convincing physical picture of the Schrodinger interpretation, remained convinced that an electron had to be a point particle. His first allegiance was, after all, with his own special theory of relativity that imposes an upper limit of c on the speed at which any signal can be transmitted. 

The special theory of relativity predicts effects such as enhancement of mass of fast moving particles. 

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