The maximal acceleration, extended relativistic dynamics and Doppler type shift for an accelerated source

Abstract

Based on the generalized principle of relativity and the ensuing symmetry, it has been shown that if the Clock Hypothesis is not true, there is a universal maximal acceleration am. We present here an extension of relativistic dynamics for which all admissible solutions will have have a speed bounded by the speed of light c and the acceleration bounded by am. An additional Doppler type shift for an accelerated source is predicted. The formulas for such shift are the same as for the usual Doppler shift with v/c replaced by a/am.The W. Kündig experiment of measurement of the transverse Doppler shift in an accelerated system was also exposed to a longtitudal shift due to the acceleration. This experiment, as reanalyzed by Kholmetskii et al., shows that the Clock Hypothesis is not valid. Based on the results of this experiment, we predict that the value of the maximal acceleration am is of the order 10 19 m/s 2 . Moreover, our analysis provides a way to measure experimentally the maximal acceleration with existing technology. Transformation between uniformly accelerated systemsThe Lorentz transformations of special relativity can be derived from the principle of special relativity alone, without assuming the constancy of the speed of light (see [1], ch. 1). It was also shown in [1] that the relativistic dynamic equation can be derived from Newton's second law and the boundedness of the speed by the speed of light. This derivation uses the Locality Hypothesis, formulated in [12] and [13], that an accelerated observer is at each instant physically equivalent to an otherwise identical momentarily comoving inertial observer.In [2], we applied the generalized principle of relativity and the ensuing symmetry to derive the transformations between two uniformly accelerated systems. To define uniform acceleration, recall that the proper velocity u of an object is the derivative of the object's displacement with respect to the proper time. In other words, u = γv, where v is the object's velocity and γ(v) = 1/ 1 − v 2 /c 2 . A system K is called uniformly accelerated if it moves parallel to an inertial system K and its origin O moves with constant acceleration a = du/dt (see [3] and [4]). In [2], it is shown that uniform acceleration is a Lorentz invariant property in the one-dimensional case.To describe the transformation between the inertial system K and the uniformly accelerated system K at some given time t * , we use a comoving frame K v . Suppose that at time t * , the velocity of O in K is v. Let K v be an inertial frame whose velocity in K is v and whose origin O v coincides with O at t * . The transformation between K and K is the product of the Lorentz transformation between the two inertial systems K and K v and the transformation between K v and K . For the transformation between K v and *

Novel Mössbauer experiment in a rotating system and the extra-energy shift between emission and absorption lines

“…In section 3 we present possible explanations of the extra energy shift between emission and absorption lines, which, to the accuracy c -2 , is added to the shift caused by the relativistic dilation of time. In sub-section 3.1 we criticize a recent attempt to explain the inequality k>0.5 with the hypothesis about the existence of a universal maximal acceleration [15][16][17][18], and concurrently show that recent attempts to re-interpret the Mössbauer experiments in rotating systems [18,19] are, in fact, erroneous. In sub-section 3.2 we present a possible explanation of eqs.…”

Testing Einstein's time dilation under acceleration using Mössbauer spectroscopy

“…By acceleration, we mean the proper acceleration defined [12] as g = d 2 x/dtdτ , where τ is the proper time. In this case, it was shown in [13] that a Doppler type shift for an accelerated source will be observed. This Doppler type shift is similar to the Doppler shift due to the velocity of the source.…”

“…In W. Kündig experiment the absorber was exposed to a significant acceleration. In [13] it was indicated that the deviation of the shift in the experiment may be due to a longitudinal Doppler shift caused by the acceleration of the absorber. It led to an estimate of a universal maximal acceleration of order 10 19 m/s 2 and an indication of non-validity of the Einstein Clock Hypothesis [11].…”

“…Thus we recommend Mössbauer spectroscopy scientists to perform an accurate experiment measuring the shift of the absorption line for a fast rotating absorber which may reveal a new fundamental law [13], with a monumental effect on whole of physics.…”

Thomas Precession by Uniform Acceleration and Gravity

“…Different approach used Friedman et al [23] in 2010. Concerning the Čerenkov radiation, it is based on the fact that the speed of light in the medium with the index of refraction n is c/n.…”