Emergence of Friedmann Equation of Cosmology of a Flat Universe from the Time-Energy Uncertainty Principle

Friedmann equation of cosmology is based on the field equations of general relativity. Its derivation is straight-forward once the Einstein’s field equations are given and the derivation is independent of quantum mechanics. In this paper, it is shown that the Friedmann equation pertinent to a homogeneous, isotropic and flat universe can also be obtained as a consequence of the energy balance in the expanding universe between the positive energy associated with vacuum and matter, and the negative gravitational energy. The results obtained here is a clear consequence of the fact that the surface area of the Hubble sphere is proportional to the total amount of information contained within it.

Time-energy analysis of the photoionization process in a double-XUV pulse combined with a few-cycle IR field

We calculate the time-energy distribution(TED)and ionization time distribution(ITD)of photoelectrons emitted by a doubleextreme-ultraviolet(XUV)pulse and a two-color XUV-IR pulse using the Wigner distribution-like function based on the strong field approximation.For a double-XUV pulse,besides two identical broad distributions generated by two XUV pulses,many interference fringes resulting from the interference between electrons generated,respectively,by two pulses appear in the TED.After adding an IR field,the TED intuitively exhibits the effect of the IR field on the electron dynamics.The ITDs during two XUV pulses are no longer the same and show the different changes for the different two-color fields,the origin of which is attributed to the change of the electric field induced by the IR field.Our analysis shows that the emission time of electrons ionized during two XUV pulses mainly depends on the electric field of the combined XUV pulse and IR pulse.

A Universal Condition Satisfied by the Action of Electromagnetic Radiation Fields

The action (the product of radiated energy and the time of emission) of the radiation fields generated by four types of radiators, namely, short electric dipole, small magnetic dipole, travelling wave antenna and bi-conical antenna is investigated with special reference to the charge associated with the current waveform which is responsible for the radiation. The results obtained can be summarized by the order of magnitude inequality where A is the action (product of the radiated energy and the time of emission), h is the Planck constant, q is the charge associated with the current that gave rise to the radiation and e is the electronic charge. The condition is obtained when the length of the antenna and its radius are pushed to its extreme natural limits. Based on the results obtained here and elsewhere, it is suggested that this inequality is valid in general for electromagnetic radiation fields as predicted by classical electrodynamics.

Realization of a source-device-independent quantum random number generator secured by nonlocal dispersion cancellation

Quantum random number generators(QRNGs)can provide genuine randomness by exploiting the intrinsic probabilistic nature of quantum mechanics,which play important roles in many applications.However,the true randomness acquisition could be subjected to attacks from untrusted devices involved or their deviations from the theoretical modeling in real-life implementation.We propose and experimentally demonstrate a source-device-independent QRNG,which enables one to access true random bits with an untrusted source device.The random bits are generated by measuring the arrival time of either photon of the time–energy entangled photon pairs produced from spontaneous parametric downconversion,where the entanglement is testified through the observation of nonlocal dispersion cancellation.In experiment,we extract a generation rate of 4 Mbps by a modified entropic uncertainty relation,which can be improved to gigabits per second by using advanced single-photon detectors.Our approach provides a promising candidate for QRNGs with no characterization or error-prone source devices in practice.