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Register a new userGetting the Lorentz transformations without requiring an invariant speed
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The structure of the Lorentz transformations follows purely from the absence of privileged inertial reference frames and the group structure (closure under composition) of the transformations---two assumptions that are simple and physically necessary. The existence of an invariant speed is textit{not} a necessary assumption, and in fact is a consequence of the principle of relativity (though the finite value of this speed must, of course, be obtained from experiment). Von Ignatowsky derived this result in 1911, but it is still not widely known and is absent from most textbooks. Here we present a completely elementary proof of the result, suitable for use in an introductory course in special relativity.
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Quantum decoherence can arise due to classical fluctuations in the parameters which define the dynamics of the system. In this case decoherence, and complementary noise, is manifest when data from repeated measurement trials are combined. Recently a number of authors have suggested that fluctuations in the space-time metric arising from quantum gravity effects would correspond to a source of intrinsic noise, which would necessarily be accompanied by intrinsic decoherence. This work extends a previous heuristic modification of Schr{o}dinger dynamics based on discrete time intervals with an intrinsic uncertainty. The extension uses unital semigroup representations of space and time translations rather than the more usual unitary representation, and does the least violence to physically important invariance principles. Physical consequences include a modification of the uncertainty principle and a modification of field dispersion relations, in a way consistent with other modifications suggested by quantum gravity and string theory .
The properties of Lorentz transformations in de Sitter relativity are studied. It is shown that, in addition to leaving invariant the velocity of light, they also leave invariant the length-scale related to the curvature of the de Sitter spacetime. The basic conclusion is that it is possible to have an invariant length parameter without breaking the Lorentz symmetry. This result may have important implications for the study of quantum kinematics, and in particular for quantum gravity.
This work presents an experimental test of Lorentz invariance violation in the infrared (IR) regime by means of an invariant minimum speed in the spacetime and its effects on the time when an atomic clock given by a certain radioactive single-atom (e.g.: isotope $Na^{25}$) is a thermometer for a ultracold gas like the dipolar gas $Na^{23}K^{40}$. So, according to a Deformed Special Relativity (DSR) so-called Symmetrical Special Relativity (SSR), where there emerges an invariant minimum speed $V$ in the subatomic world, one expects that the proper time of such a clock moving close to $V$ in thermal equilibrium with the ultracold gas is dilated with respect to the improper time given in lab, i.e., the proper time at ultracold systems elapses faster than the improper one for an observer in lab, thus leading to the so-called {it proper time dilation} so that the atomic decay rate of a ultracold radioactive sample (e.g: $Na^{25}$) becomes larger than the decay rate of the same sample at room temperature. This means a suppression of the half-life time of a radioactive sample thermalized with a ultracold cloud of dipolar gas to be investigated by NASA in the Cold Atom Lab (CAL).
The paper aims to introduce a new symmetry principle in the space-time geometry through the elimination of the classical idea of rest and by including a universal minimum limit of speed in the subatomic world. Such a limit, unattainable by particles, represents a preferred reference frame associated with a universal background field that breaks Lorentz symmetry. Thus the structure of space-time is extended due to the presence of a vacuum energy density, which leads to a negative pressure at cosmological scales. The tiny values of the cosmological constant and the vacuum energy density shall be successfully obtained, being in good agreement with current observational results.
We expand the IST transformation to three-dimensional Euclidean space and derive the speed of light under the IST transformation. The switch from the direction cosines observed in K to those observed in K-prime is surprisingly smooth. The formulation thus derived maintains the property that the round trip speed is constant. We further show that under the proper synchronization convention of K-prime, the one-way speed of light becomes constant.
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