An official website of the United States government
We investigate the particle–antiparticle symmetry of the gravitationally coupled Dirac equation, both on the basis of the gravitational central-field problem and in general curved space–time backgrounds. First, we investigate the central-field problem with the help of a Foldy–Wouthuysen transformation. This disentangles the particle from the antiparticle solutions, and leads to a “matching relation” of the inertial and the gravitational mass, which is valid for both particles as well as antiparticles. Second, we supplement this derivation by a general investigation of the behavior of the gravitationally coupled Dirac equation under the discrete symmetry of charge conjugation, which is tantamount to a particle[Formula: see text]antiparticle transformation. Limitations of the Einstein equivalence principle due to quantum fluctuations are discussed. In quantum mechanics, the question of where and when in the Universe an experiment is being performed can only be answered up to the limitations implied by Heisenberg’s Uncertainty Principle, questioning an assumption made in the original formulation of the Einstein equivalence principle. Furthermore, at some level of accuracy, it becomes impossible to separate nongravitational from gravitational experiments, leading to further limitations.
more »
« less
Antimatter Gravity: Second Quantization and Lagrangian Formalism
The application of the CPT (charge-conjugation, parity, and time reversal) theorem to an apple falling on Earth leads to the description of an anti-apple falling on anti–Earth (not on Earth). On the microscopic level, the Dirac equation in curved space-time simultaneously describes spin-1/2 particles and their antiparticles coupled to the same curved space-time metric (e.g., the metric describing the gravitational field of the Earth). On the macroscopic level, the electromagnetically and gravitationally coupled Dirac equation therefore describes apples and anti-apples, falling on Earth, simultaneously. A particle-to-antiparticle transformation of the gravitationally coupled Dirac equation therefore yields information on the behavior of “anti-apples on Earth”. However, the problem is exacerbated by the fact that the operation of charge conjugation is much more complicated in curved, as opposed to flat, space-time. Our treatment is based on second-quantized field operators and uses the Lagrangian formalism. As an additional helpful result, prerequisite to our calculations, we establish the general form of the Dirac adjoint in curved space-time. On the basis of a theorem, we refute the existence of tiny, but potentially important, particle-antiparticle symmetry breaking terms in which possible existence has been investigated in the literature. Consequences for antimatter gravity experiments are discussed.
more »
« less
- Award ID(s):
- 1710856
- PAR ID:
- 10285350
- Date Published:
- Journal Name:
- Physics
- Volume:
- 2
- Issue:
- 3
- ISSN:
- 2624-8174
- Page Range / eLocation ID:
- 397 to 411
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract The semi-classical regime of static Dirac matter is derived from the Dirac equation in curved space-time. The leading- and next-to-leading-order contributions to the semi-classical approximation are evaluated. While the leading-order yields classical equations of motion with relativistic Lorentz and a geometric forces related to space curvature, the next-to-leading-order gives a transport-like equation with source terms. We apply the proposed strategy to the simulation of electron propagation on strained graphene surfaces, as well as to the dynamics of edge states in photonic graphene.more » « less
-
Abstract Lorentz space–time symmetry represents a unifying feature of the fundamental forces, typically manifest at sufficiently high energies, while in quantum materials it emerges in the deep low-energy regime. However, its fate in quantum materials coupled to an environment thus far remained unexplored. We here introduce a general framework of constructing symmetry-protected Lorentz-invariant non-Hermitian (NH) Dirac semimetals (DSMs), realized by invoking masslike anti-Hermitian Dirac operators to its Hermitian counterpart. Such NH DSMs feature purely real or imaginary isotropic linear band dispersion, yielding a vanishing density of states. Dynamic mass orderings in NH DSMs thus take place for strong Hubbard-like local interactions through a quantum phase transition, hosting a non-Fermi liquid, beyond which the system becomes an insulator. We show that depending on the internal Clifford algebra between the NH Dirac operator and candidate mass order-parameter, the resulting quantum-critical fluid either remains coupled with the environment or recovers full Hermiticity by decoupling from the bath, while always enjoying an emergent Yukawa-Lorentz symmetry in terms of a unique terminal velocity. We showcase the competition between such mass orderings, their hallmarks on quasi-particle spectra in the ordered phases, and the relevance of our findings for correlated designer NH Dirac materials.more » « less
-
Abstract Climate change poses growing risks to global agriculture including perennial tree fruit such as apples that hold important nutritional, cultural, and economic value. This study quantifies historical trends in climate metrics affecting apple growth, production, and quality, which remain understudied. Utilizing the high-resolution gridMET dataset, we analyzed trends (1979–2022) in several key metrics across the U.S.—cold degree days, chill portions, last day of spring frost, growing degree days (GDD), extreme heat days (daily maximum temperature >34 °C), and warm nights (daily minimum temperatures >15 °C). We found significant trends across large parts of the U.S. in all metrics, with the spatial patterns consistent with pronounced warming across the western states in summer and winter. Yakima County, WA, Kent County, MI, Wayne County, NY—leading apple-producers—showed significant decreasing trends in cold degree days and increasing trends in GDD and warm fall nights. Yakima county, with over 48 870 acres of apple orchards, showed significant changes in five of the six metrics—earlier last day of spring frost, fewer cold degree days, increasing GDD over the overall growth period, and more extreme heat days and warm nights. These trends could negatively affect apple production by reducing the dormancy period, altering bloom timing, increasing sunburn risk, and diminishing apple appearance and quality. Large parts of the U.S. experience detrimental trends in multiple metrics simultaneously that indicate the potential for compounding negative impacts on the production and quality of apples and other tree fruit, emphasizing the need for developing and adopting adaptation strategies.more » « less
-
We prove that the Novikov conjecture holds for any discrete group admitting an isometric and metrically proper action on an admissible Hilbert-Hadamard space. Admissible Hilbert-Hadamard spaces are a class of (possibly infinite-dimensional) non-positively curved metric spaces that contain dense sequences of closed convex subsets isometric to Riemannian manifolds. Examples of admissible Hilbert-Hadamard spaces include Hilbert spaces, certain simply connected and non-positively curved Riemannian-Hilbertian manifolds and infinite-dimensional symmetric spaces. Thus our main theorem can be considered as an infinite-dimensional analogue of Kasparov’s theorem on the Novikov conjecture for groups acting properly and isometrically on complete, simply connected and non-positively curved manifolds. As a consequence, we show that the Novikov conjecture holds for geometrically discrete subgroups of the group of volume preserving diffeomorphisms of a closed smooth manifold. This result is inspired by Connes’ theorem that the Novikov conjecture holds for higher signatures associated to the Gelfand-Fuchs classes of groups of diffeormorphisms.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/physics2030022
