Confirmation of the theory under discussion Wave - Particle Duality as Kinetic Energy Against and In Direction of Motion in discussion group Theoretical Physics !!!! Eureka !!!! Light Captures as Both Particle and Wave Sergey V. Efremov @Sergey V., Thank you, thank you, thank you, thank you very much .... In a Physics First, Light is Captured as Both Particle and Wave Physicists have theorized for over a century that light acts as both a particle and a wave, depending on the conditions, but they've never been able to capture it being both at once — until a team in Switzerland did just that in a recent experiment. Scientists at the Ecole Polytechnique Federale de Lausanne managed to take a snapshot of light in all its elusive wave-particle duality, a form first proposed by Einstein in 1905. It was no easy task: You need light in order to take pictures of things, but how do you take a picture of light itself? The EPFL team, led by Fabrizio Carbone, started by exposing a tiny metallic nanowire to a pulse of laser light. The light travels up and down this wire and interferes with itself, forming stationary and illustrating that portion of light's dual nature. At the same time, though, those waves are made of innumerable photons. This was shown by barraging the standing waves with electrons — some of which would speed up, and some slow down, depending on how they strike photons in the stream. The simple fact that these quanta of exchanged energy exist proves that there are particles there, not just a simple waveform of radiation (like a magnetic field). The result is the image above, which shows light exhibiting wavelike and particle-like properties at the same time. This research, published in the journal Nature Communications, significantly advances our understanding of how light works on the smallest detectable scales, and may be highly valuable in the field of quantum computing. It is fully in line with Wave - Particle Duality as Kinetic Energy Against and In Direction of Motion. Kinetic energy of a charge moving at the velocity of v has two different values: Kinetic energy against direction of motion as wave in transmission medium (as the energy of the electromagnetic field) Tkin ad = mc2[ln |1+v/c|- (v/c)/(1+v/c)] Kinetic energy in direction of motion as particle (as its own kinetic energy of particle ) Tkin id = mc2[ln |1-v/c|+ (v/c)/(1-v/c)]
Quantum simulators are attracting great interest because they promise insight into the behavior of quantum many-body systems that are prohibitive for classical simulations. The generic output of quantum simulators are snapshots, obtained by means of projective measurements. These provide new information, such as full distribution functions, that goes beyond the more commonly evaluated expectation values of observables while adding shot-noise uncertainty to the latter. Hence, a central goal of theoretical efforts must be to predict these exact same quantities that can be measured in experiments. Here, we report on a snapshot-based study of particle currents in quantum lattice models with a conserved number of particles. It is shown how the full probability distribution of locally resolved particle currents can be obtained from suitable snapshot data. Moreover, we investigate the Hall response of interacting bosonic flux ladders, exploiting snapshots drawn from matrix-product states. Flux ladders are minimal lattice models, which enable microscopic studies of the Hall response in correlated quantum phases, and they are successfully realized in current quantum-gas experiments. Using a specific pattern of unitary two-site transformations, it is shown that the Hall polarization and the Hall voltage can be faithfully computed from a realistic number of snapshots obtained in experimentally feasible quench and finite-bias simulations.
Quantum computers and simulators offer unparalleled capabilities of probing quantum many-body states, by obtaining snapshots of the many-body wave function via collective projective measurements. The probability distribution obtained by such snapshots (which are fundamentally limited to a negligible fraction of the Hilbert space) is of fundamental importance to determine the power of quantum computations. However, its relation to many-body collective properties is poorly understood. Here, we develop a theoretical framework to link quantum phases of matter to their snapshots, based on a combination of data complexity and network theory analyses. The first step in our scheme consists of applying Occam's razor principle to quantum sampling: given snapshots of a wave function, we identify a minimal-complexity measurement basis by analyzing the information compressibility of snapshots over different measurement bases. The second step consists of analyzing arbitrary correlations using network theory, building a wave-function network from the minimal-complexity basis data. This approach allows us to stochastically classify the output of quantum computers and simulations, with no assumptions on the underlying dynamics, and in a fully interpretable manner. We apply this method to quantum states of matter in one-dimensional translational invariant systems, where such classification is exhaustive, and where it reveals an interesting interplay between algorithmic and computational complexity for many-body states. Our framework is of immediate experimental relevance, and can be further extended both in terms of more advanced network mathematics, including discrete homology, as well as in terms of applications to physical phenomena, such as time-dependent dynamics and gauge theories.
A classical wave (string, sound, water etc) which satisfies the classical wave equation is described by a “snapshot” profile cos(-Et+px) at an instant in time. By changing t and x such that -E dt + p dx = 0 one follows this translating profile through time and space, but physically a sound, string or water wave is not simply translating like this.The medium fills the “trough” where the wave once passed, but the medium is not part of the wave and so need not be included in its solution. There is a wave profile, but at the same time changes to the profile which are excluded. In this note we speculate that the form exp(-iEt+ipx) used to describe a free quantum particle (and associated with a kind of dynamic probability like the classical wave’s cos(-Et+px)) is two dimensional because it describes both a profile in space due to a kind of momentum-energy wave acting on a single particle, but also as a second dimension the magnitude of the change in this wave sin(px) unlike the classical wave approach. In other words, for a single particle which is the medium of the energy-momentum wave, it cannot be removed or excluded (hence a particle-wave duality). We suggest there should be a physical mechanism associated with this - in other words the motion of a quantum particle is not a simple translation.