Quantum physics

The German mathematician Gauss, one of the fathers of non-
Euclidean geometry, was involved in a land survey in Germany and
made many trigonometric measurements between 1818 and 1832. These included measuring the angles of a large triangle with vertices at the tops of three prominent hills near Gottingen in northern Germany. Within the accuracy of the measurements, the angles added up to the Euclidean value of 1800, giving no evidence of any curvature on the length scales that were accessible to him.
A modern measurement was made by the Planck satellite in 2015.
This set limits on any spatial curvature of our Universe over cosmological distances: if it is non-zero, it must involve length scales at least of order 1028m and possibly greater { some 100 times greater than the size of the observable Universe. The Planck results are compatible with zero spatial curvature.

As long as we restrict our considerations to regions of space over which a gravitational field does not vary appreciably in either magnitude or direction, we cannot tell the difference between a gravitational field and an acceleration this is known as the Equivalence Principle

what are pure state and mixed state in quantum mechanics?

Hubble-de Vaucouleurs tuning fork diagram, showing the
major morphological classification of galaxies into ellipticals (left) and
spirals (right), the latter consisting of standard and barred spiral galaxies.
(Source: The images of the galaxies were created from observations
taken by the Sloan Digital Sky Survey.)
Morphology
Themorphology of a galaxy gives us information about the distribution of
stars, gas and dust. Note that the appearance of a galaxy strongly depends
on the spectral window (see figure 1.1). Morphological studies normally
concern the stellar component as the main tracer of the gravitational potential
of the galaxy. Galaxies are split roughly into three main groups:
elliptical, spiral and irregular. The presence of a bar in spiral galaxies
motivates a branching in the classification scheme, illustrated by the
Hubble tuning fork diagram. Elliptical and lenticular galaxies
are combined into early-type galaxies and present a spheroidal distribution,
explained by a major merging event, or some collapse mechanism
by which the total angular momentum was kept low. The oblateness of
these systems cannot be fully explained by rotation , and
their spectral energy distribution corresponds to old and metal-rich stellar
populations, which reflect an early, intense and efficient process of
star formation and are corroborated by their chemical composition.
In contrast, spiral galaxies, more aptly described as disc (or latetype)
galaxies, are flatter systemswhere a large fraction of the total kinetic
energy is in the form of bulk rotation. For example, the (thin) disc of our
Milky Way galaxy has a vertical extent about one-tenth of the disc size.
The collapse of gas under gravity can develop such a rotating structure,
as for instance, during the formation of our solar system. Disc galaxies
have a more complex distribution of stellar populations than ellipticals,
featuring ongoing star formation as well as a substantial presence of old
stars. The central part of a disc galaxy usually hosts a spheroidal structure, a bulge, whose origin also constitutes an open problem, with some bulges
resembling an early-type galaxy (classic bulges) and others being the
product of secular dynamical evolution (pseudo-bulges). Spiral arms are
the most conspicuous features of disc galaxies. Their origin is based on
dynamical resonances, which will be briefly explored in chapter 5. Irregular
galaxies are more complex dynamical structures, often betraying the
presence of an ongoing merger or tidal interaction with a neighbour.

Hubble-de Vaucouleurs tuning fork diagram, showing the
major morphological classification of galaxies into ellipticals (left) and
spirals (right), the latter consisting of standard and barred spiral galaxies.
(Source: The images of the galaxies were created from observations
taken by the Sloan Digital Sky Survey.)
The morphology of a galaxy gives us information about the distribution of
stars, gas and dust. Note that the appearance of a galaxy strongly depends
on the spectral window (see figure 1.1). Morphological studies normally
concern the stellar component as the main tracer of the gravitational potential
of the galaxy. Galaxies are split roughly into three main groups:
elliptical, spiral and irregular. The presence of a bar in spiral galaxies
motivates a branching in the classification scheme, illustrated by the
Hubble tuning fork diagram . Elliptical and lenticular galaxies
are combined into early-type galaxies and present a spheroidal distribution,
explained by a major merging event, or some collapse mechanism
by which the total angular momentum was kept low. The oblateness of
these systems cannot be fully explained by rotation , and
their spectral energy distribution corresponds to old and metal-rich stellar
populations, which reflect an early, intense and efficient process of
star formation and are corroborated by their chemical composition.

The deeper scientists look into matter, the more it seems to vanish. Beneath the surface, everything we see atoms, molecules, even your body is made not of solid particles, but of pure energy vibrating in endless motion. In quantum field theory, particles like electrons and protons aren’t objects but ripples in vast invisible fields, constantly appearing and fading.

What feels solid is simply energy slowed and structured into patterns, like notes in a cosmic symphony. Quantum mechanics reveals that reality is not built from “things,” but from interactions waves of probability and motion that create the illusion of form. Every atom, every star, even our thoughts, are part of this universal rhythm, resonating through the quantum fabric of existence.

Source / Credit: Quantum Field Theory; Standard Model of Particle Physics; Quantum Electrodynamics (QED); Interpretations by Feynman, Higgs & Dirac.