On the universality of free fall, the equivalence principle, and the gravitational redshift

Abstract

Through the contributions of Galileo, Newton, and Einstein, we recall the universality of free fall (UFF), the weak equivalence principle (WEP), and the strong equivalence principle (SEP), in order to stress that general relativity requires all test masses to be equally accelerated in a gravitational field; that is, it requires UFF and WEP to hold. The possibility of testing this crucial fact with null, highly sensitive experiments makes these the most powerful tests of the theory. Following Schiff, we derive the gravitational redshift from the WEP and special relativity and show that, as long as clocks are affected by a gravitating body like normal matter, measurement of the redshift is a test of UFF/WEP but cannot compete with direct null tests. A new measurement of the gravitational redshift based on free-falling cold atoms and an absolute gravimeter is not competitive either. Finally, we compare UFF/WEP experiments using macroscopic masses as test bodies in one case and cold atoms in the other. We conclude that there is no difference in the nature of the test and that the merit of any such experiment rests on the accuracy it can achieve and on the physical differences between the elements it can test, macroscopic proof masses being superior in both respects

A Unique Mathematical Derivation of the Fundamental Laws of Nature Based on a New Algebraic-Axiomatic (Matrix) Approach ‡

“…[44][45][46][47][48], in agreement with the recent astronomical data, we can directly establish a lower bound for a constant quantity which is equivalent to the constant α = (82) that is generated by a coupling torsion field of the type (79-3) of the background curved space-time.…”

“…Since the parameter m 4 has not appeared in the solution (46), it could be assumed that m 4 = 0, and the condition (47) is reduced to the following homogeneous quadratic equation, which is equivalent to the quadratic Equation (20) (corresponding to the system of linear Equation (28)):…”

“…Moreover, the trace part of torsion field Z τµν in (79-3) is obtained as: [17,39,[44][45][46][47][48]. However, in Section 3.15, we show that assuming the spin-1/2 fermion fields (describing generally by the field Equation (110-9) compatible with specific gauge symmetry group (110-12), as shown in Section 3.15, Formulas (110-9)-(110-12)) and their compositions as the source currents of the (1 + 3)-dimensional cases of general covariant massive field Equation (72) (describing the spin-1 boson field), then this field equation would be invariant under two types of gauge symmetry groups, including: SU(2) L ⊗U(2) R and SU(3), corresponding with a group of seven bosons and a groups of eight bosons (as shown in Section 3.15, Formulas (114-4)-(114-9)).…”

Quantum Formulation of the Einstein Equivalence Principle

“…Nearly any claim about it can find support in the scientific literature: that the EEP is violated in quantum mechanics [33,34]; that there is a tension between the very formulation of the EEP and quantum theory -and therefore EEP has to be suitably reformulated before its validity can be discussed in quantum mechanics [26] -but also that there is no difference between testing validity of the EEP in classical and quantum physics [35]. (The latter view is motivated by the fact that so far proposed reformulations still gave rise to the same quantitative conditions in the quantum and in the classical case.…”

Systematic errors in high-precision gravity measurements by light-pulse atom interferometry on the ground and in space

“…This value is only an approximation to the real one, expressed mathematically by the instantaneous second time derivative of the position or obtained experimentally with a large enough number of measurements per drop.Using the classical approach [1] we report the physical consequences of this fact when AIs are used to measure the absolute value of the gravitational acceleration g, for gravity gradiometry and for testing the Universality of Free Fall (UFF), both on ground and in space. Although the issue has been glossed over for quite a long time, the consequences are far reaching and deserve to be carefully addressed.Since AIs are used also for testing UFF we include since the beginning the possibility that the equivalence of inertial and gravitational mass may be violated for atoms of different species A, B in the field of Earth (violation of the Weak Equivalence Principle, WEP), hence violating UFF [5]. We therefore write the masses aswhere superscripts i, g refer to inertial or gravitational mass and the Eötvös parameters η A , η B , η ⊕ may not be exactly zero (although experiments prove that they must be smaller than 1 by many orders of magnitude [6,7]).…”