We find that this setup, built with massive mesoscopic particles, can potentially reveal the t 3 gravitational phase term and thus, the BMV effect. We can solve for k giving k sqrt ( (1+v/c)/ (1-v/c)) which is the relativistic Doppler shift formula. Thus the speed of B according to A is v D/t DA (R)/tA (R) c (kk-1)/ (kk+1). The idea that spacetime is distorted by motion, as in special relativity, is extended. We can now compute the distance of event R from As worldline and time of event R according to A, tA (R). The principle is described by the physicist Albert Einsteins famous formula. Gravity in general relativity is described in terms of curved spacetime. Gravitational field perturbations, including quantum gravity fluctuations and gravitational waves, introduce additional phase terms that decohere the entangled pairs used to build the quantum cryptographic key, with the result of coloring the white noise. In physics, massenergy equivalence is the relationship between mass and energy in a systems rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement. Hence, one cannot distinguish, with a local measurement, if the spacetime is flat or curved, or in a superposition of such spacetimes. Einstein’s general theory of relativity can be summed up in just 12 words: Space-time tells matter how to move matter tells space-time how to curve. In fact, an ideal quantum cryptographic key, built with the sharing of maximally entangled states of particles, is represented by a random sequence of uncorrelated symbols mathematically described by a perfect white noise, a stochastic process with zero mean and without correlation between its values taken at different times. To improve the sensitivity we propose to cumulate the effects of the gravitational field fluctuations in time on the outputs of a series of independent measurements acted on entangled states of particles, like in the building of a quantum cryptographic key, and extract from the associated time series the effect of the expected gravitational field fluctuations. The technique here proposed promise to reveal gravitational field fluctuations from the analysis of the stochastic noise associated to an ideal output of a measurement process of a quantum system. The equivalence principle implies (at least, suggests) that the action of gravity should be attributed to the curvature of space-time: it implies that there. We propose a new thought experiment, based on present-day Quantum Information Technologies, to measure quantum gravitational effects through the Bose-Marletto-Vedral (BMV) effect, ,, by revealing the gravitational t 3 phase term, its expected relationships with low-energy quantum gravity phenomena and test the equivalence principle of general relativity.
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