A new test theory for describing tests of fundamental principles of special and general relativity is presented. Using a generalized Pauli equation which may be based on a generalized Dirac equation, possible violations of local Lorentz invariance and local position invariance on the quantum level are described. On the quantum level there are more possibilities to violate these principles than on the classical level. The corresponding terms can be tested by Hughes-Drever-type experiments or by atom interferometry. It is proposed that an atom interferometric test of local position invariance will give a three orders of magnitude improvement over existing estimates. PACS numbers: 0480C, 0375D, 0365
A new test theory for describing tests of fundamental principles of special and general relativity is presented. Using a generalized Pauli equation which may be based on a generalized Dirac equation, possible violations of local Lorentz invariance and local position invariance on the quantum level are described. On the quantum level there are more possibilities to violate these principles than on the classical level. The corresponding terms can be tested by Hughes-Drever-type experiments or by atom interferometry. It is proposed that an atom interferometric test of local position invariance will give a three orders of magnitude improvement over existing estimates. PACS numbers: 0480C, 0375D, 0365
A new test theory for describing tests of fundamental principles of special and general relativity is presented. Using a generalized Pauli equation which may be based on a generalized Dirac equation, possible violations of local Lorentz invariance and local position invariance on the quantum level are described. On the quantum level there are more possibilities to violate these principles than on the classical level. The corresponding terms can be tested by Hughes-Drever-type experiments or by atom interferometry. It is proposed that an atom interferometric test of local position invariance will give a three orders of magnitude improvement over existing estimates.
A new test theory for describing tests of fundamental principles of Special and General Relativity is presented. Using a generalised Pauli equation which may be based on a generalised Dirac equation, possible violations of local Lorentz invariance and local position invariance on the quantum level are described. On the quantum level there are more possibilities to violate these principles than on the classical level. The corresponding terms can be tested by Hughes–Drever type experiments or by atom interferometry. It is proposed that an atom interferometric test of Local Position Invariance will give a three order improvement of existing estimates. 1
Atomic- and neutron-beam interferometry offer a sensible technique for tests of the space-time structure. One important ingredient of the space-time structure is given by the null cones, which are related to local Lorentz invariance. A possible deviation from this structure described as splitting of the null cones gives rise to non-Lorentz invariance effects. It is shown that in the nonrelativistic limit this typically amounts to a new type of spin-momentum coupling. Starting from a generalization of the Dirac equation, based on fundamental principles, reasons are given for this special kind of coupling. The outcome of this model theory is taken to propose experiments which use atomic-beam interferometry and give improved upper limits on possible non-Lorentz invariance parameters.
The search for a fundamental, self-consistent theoretical framework to cover phenomena over all energy scales is possibly the most challenging quest of contemporary physics. Approaches to reconcile quantum mechanics and general relativity entail the modification of their foundations such as the equivalence principle. This corner stone of general relativity is suspected to be violated in various scenarios and is therefore under close scrutiny. Experiments based on the manipulation of cold atoms are excellently suited to challenge its different facets. Freely falling atoms constitute ideal test masses for tests of the universality of free fall in interferometric setups. Moreover, the superposition of internal energy eigenstates provides the notion of a clock, which allows to perform tests of the gravitational redshift. Furthermore, as atom interferometers constitute outstanding phasemeters, they hold the promise to detect gravitational waves, another integral aspect of general relativity. In recent years, atom interferometers have developed into versatile sensors with excellent accuracy and stability, and allow to probe physics at the interface of quantum mechanics and general relativity without classical analog. In this thesis, various aspects regarding tests of general relativity with atom interferometry have been theoretically investigated. This includes the analysis of fundamental effects as well as feasibility studies of experimental configurations. The work is partially focussed on a space-borne mission scenario for a dedicated quantum test of the universality of free fall beyond state-of-the-art by dropping matter waves of different elements. To enable the target accuracy at the level of 10^(−17), a compensation scheme has been developed and discussed, mitigating the detrimental effects of imperfect test mass co-location upon release and relaxing the requirements on the source preparation by several orders of magnitude. In addition, it was demonstrated that the careful design of quantum degenerate sources is indispensable for these experiments, requiring tailored schemes to prepare miscible binary sources. The possibility to test the gravitational redshift with atom interferometers has also been examined in this thesis and connected to the ideas of clock interferometry. With the proof that closed light pulse atom interferometers without transitions between internal internal states are not sensitive to gravitational time dilation, an ongoing scientific debate has been resolved. Instead, certain configurations were shown to implement a quantum version of the special-relativistic twin paradox, for which an experiment has been proposed. Finally, requirements on atomic sources and atom optics for scenarios of gravitational wave detection on ground and in space have been investigated.
Quantum Tests of the Universality of Free FallIn the process of formulating a "theory of everything" that aims to provide a self-contained model of modern physics by unifying all four fundamental interactions, two theoretical frameworks have yielded important contributions: quantum mechanics, which can explain the nature of physics at the most microscopic length scales such as the origin of spectra of electrons bound in atomic systems, and Einstein's general relativity, that conveys our understanding of gravity over the largest distances across the universe.Although no theory of "quantum gravity", that is consistent over all energy scales, exists to date, certain modifications may enable a reconciliation of quantum mechanics and general relativity.These approaches allow for violations of the universality of free fall (UFF), that among Lorentz invariance and local position invariance constitute Einstein's equivalence principle.The UFF states that all bodies, located at the same space-time point, experience the same acceleration in a gravitational field independently of their composition.Because of its central role in modern physics the UFF has been tested extensively in many experiments, most of which utilized classical test masses.Quantum mechanical tests of the UFF differ from classical ones in various aspects such as the coherence length and spin polarization of the test masses.In this thesis, the first inertial-sensitive matter wave interferometer comparing the free fall of two different elements, 87 Rb and 39 K, was realized.This quantum test of the UFF yielded an Eötvös ratio 𝜂 Rb,K = (0.3 ± 5.4) × 10 -7 , and was limited by statistical uncertainty.In this work, an existing apparatus for rubidium interferometry was extended to the use of potassium and the first inertial-sensitive potassium matter wave interferometer with a resolution to gravitational acceleration of 𝜎 K = 3 × 10 -6 m/s 2 after 4096 s integration has been demonstrated.A description of the experiment including the technical realization and the techniques used is provided.Specifically, the challenges imposed by the use of potassium, which in comparison to rubidium has a smaller mass and lower hyperfine energy splitting, are examined.The thesis furthermore discusses an assessment of the systematic effects influencing the dual species measurement and presents future strategies to further improve the performance of the apparatus.As a preliminary result, it was possible to improve the potassium short-term sensitivity to gravitational acceleration to 𝜎 K = 2.1 × 10 -5 m/s 2 / √ Hz.The results of this thesis pave the way for exciting future experiments to be performed in large-scale apparatuses and in space.
“Despite almost a century’s worth of study, it is still unclear how general relativity (GR) and quantum theory (QT) should be unified into a consistent theory. The conventional approach is to retain the foundational principles of QT, such as the superposition principle, and modify GR. This is referred to as ‘quantizing gravity’, resulting in a theory of ‘quantum gravity’. The opposite approach is ‘gravitizing QT’ where we attempt to keep the principles of GR, such as the equivalence principle, and consider how this leads to modifications of QT. What we are most lacking in understanding which route to take, if either, is experimental guidance. Here we consider using the Dirac–Pauli representation of free Dirac equation to search for the clues. In particular, we study how the double-slit diffraction experiment, when only one Dirac particle (‘say’ electron) at a time is in the apparatus, could test a gravitizing QT proposal in which the wavefunction collapse emerges on the detector screen from the Dirac–Pauli representation, as an objective process, resolving the measurement problem of QT.” [1] We found that the Dirac–Pauli representation is inherently a unified theory embodying a gravitizing QT proposal that Dirac–Pauli representation as wave nature is manifestation of inertial mass and the Foldy-Wouthuysen representation as particle nature is manifestation of gravitational mass such that the fact, that same physics is involved in these two representations, is simply the validity and exhibition of the principle of equivalence, of GR, in QT. [1] Richard Howl et al 2019 New J. Phys. 21 043047 DOI 10.1088/1367-2630/ab104a