Theory of special

None of Einstein s first four papers published between 1901 and 1904 foreshadowed his explosive creativity of 1905, his annus mirabilis, in which he produced in March, his proposal of the existence of light quanta and the photoelectric effect, work for which in 1922 he received the Nobel Prize in April, a paper on the determination of molecular dimensions, which earned him his Ph.D. m Zurich m May, his theory of special relativity in September, a sequel to the preceding paper containing the relation E = mc. Any one of these papers would have made him greatly renowned their totality made him immortal. 

In the theory of special relativity the gauge factor a is a constant since there exists only one coordinate system for all space. The transformation17... 

A. Einstein Theory of special relativity in Selected Papers, edited by I.E. Tamm... 

The early years of the twentieth century saw giant advances in man s understanding of nature which must be mentioned in any synopsis of the scientific history of this era. Thus, in 1901, M. Planck (NLP 1918 ) published his first paper on the black-body radiation law which ushered in the era of quantum mechanics. In 1905, A. Einstein (NLP 1918 ) published his Anna Mirabilis Papers on the photo effect, on Brownian motion, and on the theory of special relativity and the equivalence of matter and energy. 

The power of the operational approach became strikingly evident in Einstein s theory of special relativity, with its analysis of the meaning of presumably absolute, intuitive concepts such as time or space. Newton defined absolute time as... 

LS Spin-Orbit Interaction. When a charge moves in an electric field, the theory of special relativity tells us that part of the electric field appears as a magnetic field to the electron. The magnetic moment of the electron interacts with this magnetic field giving rise to what is known as the spin-orbit interaction. From Dirac s theory of the electron, it can be shown (/) that this interaction takes the form... 

According to Einstein s theory of special relativity, at 60 percent the speed of light, gold s innermost electrons experience only 52 seconds for each i of our minutes. A diamond may be forever, but the innermost electrons of gold are 8 seconds per minute slow ... 

Generating functions occur in other contexts than moments and, in particular, the theory of special functions is full of them. Their use in deriving the solution to a whole family of equations is well illustrated in the reprint M, p. 337, Chapter 10. A simple example would be the ideal residence time tracer the chain of identical C s governed by... 

In this work, Einstein s theory of special relativity (SRT) is fully accepted, with the supposition that it is valid in the region of the spacetime where v < c is possible only. There are many experimental proofs that support the concepts of SRT, which justify the main postulate c = constant. However, none of the experimental proofs for the validity of the special relativity concepts have led to the fundamental postulate c = constant being accepted as a physical law. It still remains a postulate, that is, an assumption. It is a justified assumption for the theory of special relativity, but still an assumption only [1-3]. 

In 1916, Einstein published his work The fundamentals of general relativity [10], 11 years after he published his theory of special relativity [1,2]. Later, in 1954, he published a work to explain the differences and connections between special and general relativity [15]. In this work he gives the exact formulation of general relativity, with the following two postulates ... 

As already discussed at the end of Section 2.2.3, we derived a universal superposition principle from a complex symmetric ansatz arriving at a Klein-Gordon-like equation relevant for the theory of special relativity. This approach, which posits a secular-like operator equation in terms of energy and momenta, was adjoined with a conjugate formal operator representation in terms of time and position. As it will be seen, this provides a viable extension to the general theory [7, 82]. We will hence recover Einstein s laws of relativity as construed from the overall global superposition, demonstrating in addition the independent choice of a classical and/or a quantum representation. In this way, decoherence to classical reality seems always possible provided that appropriate operator realizations are made. 

If these research design features had been mandatory, this chapter would be exceedingly short. Thankfully, undaunted researchers have collected a substantial amount of data that, when pressed against the filter of scientific rigor, yields at least indirect evidence. Still, there are times when indirect evidence is quite ample and convincing (e.g., Einstein s Theory of Special and General Relativity). 

The conscious final decision to take the risk, with the current sequence, should be read as a personal conviction that the beauty of chemistry can never be fully appreciated unless viewed against the background in which all matter originates - space-time, or the vacuum. Not only matter, but all modes of interaction are shaped by the geometry of space, which at the moment remains a matter of conjecture. However, the theory of general relativity points the way by firmly demonstrating that the known material world can only exist in curved space-time. The theory of special relativity affirms that space-time has a minimum of four dimensions. Again, spaces of more dimensions are conjectural at present. 

The possibility of non-local interaction within quantum systems, so vividly illustrated here for a holistic electron, was first recognized by Einstein and others [46]. To avoid conflict with the theory of special relativity the effect was interpreted to mean that quantum theory was incomplete. More recently... 

Note that the condition r>,u — rK(f) — (f M/c2) follows from the definition of p. Quantum conditions further yield r> 2/z. Note the incompatibility between the force defined in Eq. (50) and the energy law defined by the theory of special theory of relativity. One should note here that Einstein, in his studies of the general theory of relativity, started from the force law... 

If we use the potentials derived above in our molecular Hamiltonian, they are open to the further serious objection that they refer only to an electron moving with uniform velocity, a situation which is not very realistic in the context of the molecular problem. However, the theory of special relativity does not provide a means of describing the motion of a rapidly moving and accelerating particle exactly. An approximate treatment is possible, but since the effects of the non-uniform motion of an electron on its vector and scalar potentials give terms with higher powers of 1 /c than we require in the final expansion of our Hamiltonian, we can ignore them. 

Not only the laws of Nature but also all major scientific theories are statements of observed symmetries. The theories of special and general relativity, commonly presented as deep philosophical constructs can, for instance, be formulated as representations of assumed symmetries of space-time. Special relativity is the recognition that three-dimensional invariances are inadequate to describe the electromagnetic field, that only becomes consistent with the laws of mechanics in terms of four-dimensional space-time. The minimum requirement is euclidean space-time as represented by the symmetry group known as Lorentz transformation. 

The experimental basis of the theory of special relativity provides another example of such a dimensional effect (T 4.3.3). Within Galilean relativity the line element r2 is invariant under rotation. The observation that this line element is not Lorentz invariant shows that world space has more dimensions than three. The same effect in 2 and 3 dimensions is demonstrated diagram-matically in figure 2. The norm of the two-dimensional vector is seen to be... 

Now Tm going to tell you about a strange concept that s necessary for understanding radioactivity and other nuclear reactions. That concept is the equivalence of mass and energy. Mass can transform into energy, and vice versa. This is part of Einstein s theory of special relativity and is the source of that famous equation E = m. Let s apply the theory to the activities you did in the previous section. When the two magnets are apart, we say that they have potential energy due to... 

At about the same time that Einstein was performing his analysis of the photoelectric effect, he was also constructing the theory of special relativity. In connection with this work Einstein derived the famous equation... 

Recall that Einstein postulated in his theory of special relativity in 1905 that the mass (m) of a moving object increases with its velocity (v) ... 

In 1887 two American scientists, physicist Albert Michelson and physical chemist Edward Morley, performed an experiment that was designed to detect the motion of Earth through a hypothetical medium known as the luminiferous ether, which was thought to be present throughout space. They made their measurements with a very sensitive optical instrument now called a Michelson interferometer. Their observations showed no indication of movement through the predicted ether. This outcome was unexpected and has become one of the fundamental experimental results in support of the theory of special relativity, developed by Albert Einstein in 1905. 

The Michelson-Morley experiment is a perfect example of a null experiment, one in which something that was expected to happen is not observed. The consequences of their observations for the development of physics were profound. Having proven that there could be no stationary ether, physicists tried to advance new theories that would save the ether concept. Michelson himself suggested that the ether might move, at least near the Earth. Others studied the possibility that rigid objects might actually contract as they traveled. But it was Einstein s theory of special relativity that finally explained their results. 

M. Guillen, Five Equations That Changed the World The Power and Poetry of Mathematics, Hyperion, New York, 1995. The five equations Guillen includes are Newton s law of gravity, Bernoulli s law of hydrodynamic pressure, Faraday s law of electromagnetic induction, Clausius s second law of thermodynamics, and Einstein s theory of special relativity. 

While, even accepting discrepancies by a factor of O 2, the fulfillment of Eqs. (l)-(7) does not constitute proof of Planck-power input, it at least seems suggestive. Could Planck-power input, if it exists, be a classical process independent of quantum effects, if not absolutely then at least via opposing quantum effects canceling out, as h cancels out in the division Ppianck = Planck / Planck Note that perhaps similar canceling out obtains with respect to the Planck speed /pianck/f Planck = c c is the fundamental speed in the classical (nonquantum) theories of Special and General Relativity. 

The set of transformations of the spacetime coordinates that project the laws of electrodynamics from any observer s reference frame to any other (continuously connected) inertial frame such that the laws remain unchanged is the symmetry group of the theory of special relativity. It was discovered that this is... 

The idea of covariance is then that the same set of spacetime transformations that leave the differential metric (13) in special relativity, or (14) in general relativity, unchanged (invariant) also leave all the laws of nature covariant (unchanged in form) under these transformations between reference frames. The metric (13) in special relativity, or (14) in general relativity, then guides one to the forms of the covariant laws of nature, in accordance with the theory of (special or general) relativity. This is the role of the differential metrics—they are not to be considered as observables on their own ... 

---