The Pengembangan Perangkat Pembelajaran Materi Bangun Ruang Sisi Lengkung Berbasis Etnomatematika Berbantuan Aplikasi Google Form sebagai Penunjang Pembelajaran Daring

This research aims to know the process and the result of the development of Mathematics Learning Instruments for ethnomathematics based curved space chapter with the help of the Google Form aplication as a support for online learning. This research is development research. Learning instruments development model refers to four D models. The product of this research are teaching materials, student’s worksheet, and evaluation test. This research took place at IX A of junior high school 2 Puger, Jember with consist 36 students. The data collection methods used in this research are the interview, test, and questionnaire. Based on data analysis, this research has three result. First, the learning instrument developed have valid criteria. Secondly, the learning instrument developed have practical criteria based on interview and student’s responses. Third, the learning instrument developed have effective criteria based on student’s score and student’s positive responses.

Curvature Tensor of the Stationary Accelerated Frame in Gravity Field

We define an accelerated frame that moves along rˆ -axis in the general relativistic curved space-time. We then calculate the curvature tensor of this accelerated frame in the stationary gravity field. The curvature tensor is divided into two parts: the curvature tensor as observed by the observer and the curvature tensor of the observer’s own planet in the gravity field.

Tetrad in Curved Space-Time in Cosmological General Theory of Relativity

In the cosmological general theory of relativity, we define the tetrad that moves in r-axis in the curved space-time. We study an accelerated motion in curved space-time.

How can Einstein’s curved space apply to earthquakes?

Einstein believed that space is curved, but the influence of solar and lunar gravitational pulls on seismic activities is different at different times of the day or of the month. Accelerations and decelerations of a large or a small mass on the Earth can appear at different times.

Dirac–Kratzer problem with spin and pseudo-spin symmetries in curved space–time

In this work, the Dirac–Kratzer problem with spin and pseudo-spin symmetries in a deformed nucleus is analyzed. Thus, the Dirac equation in curved space–time was considered, with a line element given by [Formula: see text], where [Formula: see text] is a scalar potential, coupled to vector [Formula: see text] and tensor [Formula: see text] potentials. Defining the vector and scalar potentials of the Kratzer type and the tensor potential given by a term centrifugal-type term plus a term cubic singular at the origin, we obtain the Dirac spinor in a quasi-exact way and the eigenenergies numerically for the spin and pseudo-spin symmetries, so that these symmetries are removed due to the coupling of an Coulomb-type effective tensor potential coming from the curvature of space, however, when such potential is null the symmetries return. The probability densities were analyzed using graphs to compare the behavior of the system with and without spin and pseudo-spin symmetries.

Theory of Spinors in Curved Space-Time

By means of Clifford Algebra, a unified language and tool to describe the rules of nature, this paper systematically discusses the dynamics and properties of spinor fields in curved space-time, such as the decomposition of the spinor connection, the classical approximation of the Dirac equation, the energy-momentum tensor of spinors and so on. To split the spinor connection into the Keller connection Υμ∈Λ1 and the pseudo-vector potential Ωμ∈Λ3 not only makes the calculation simpler, but also highlights their different physical meanings. The representation of the new spinor connection is dependent only on the metric, but not on the Dirac matrix. Only in the new form of connection can we clearly define the classical concepts for the spinor field and then derive its complete classical dynamics, that is, Newton’s second law of particles. To study the interaction between space-time and fermion, we need an explicit form of the energy-momentum tensor of spinor fields; however, the energy-momentum tensor is closely related to the tetrad, and the tetrad cannot be uniquely determined by the metric. This uncertainty increases the difficulty of deriving rigorous expression. In this paper, through a specific representation of tetrad, we derive the concrete energy-momentum tensor and its classical approximation. In the derivation of energy-momentum tensor, we obtain a spinor coefficient table Sabμν, which plays an important role in the interaction between spinor and gravity. From this paper we find that Clifford algebra has irreplaceable advantages in the study of geometry and physics.

FREE CURVILINEAR SPACE WITH TORSION

Under the classical field theory, a variant unification of gravity and electromagnetism on the basis of four-dimensional curved space with torsion is proposed. The connection between electromagnetic field and torsion of space is discovered, a physical interpretation of the space scalar curvature as the density of matter mass is proposed. The solution for the eigenstate of a curved space with torsion, corresponding to the electron is obtained. The identification of the field equations as the Schrodinger equation for the hydrogen atom is shown. Cosmological solutions for the expanding Universe are found, the average mass density in the Universe is estimated, and the results corresponding to the data of astronomical observations are obtained.

The Fundamental Discussion between Newton, Maxwell, Bohr and Einstein

Isaac Newton, James Clerk Maxwell, Niels Bohr and Albert Einstein lived in fundamentally different time frames. Newton in the 16th century, Maxwell in the 18th century, Bohr in the 20th century and Einstein was physically living in the 20th century but he was his time far ahead and with his concept of a “curved space-time continuum” more connected to the 21st century. An interesting question would be: “Who would win the fundamental discussion about the interaction between “Gravity and Light” comparing the 4 fundamentally different time-frames? Newton, Maxwell, Bohr or Einstein? Newton with the fundamental “3rd law of equilibrium between the forces (force-densities)”. Maxwell who had built the “Mathematical Foundation for Electrodynamics”, Bohr (together with Heisenberg) who overruled Einstein during the 5th Solvay Conference in 1927 with the fundamental concept of “Quantum Mechanical Probability” or Einstein (his time-frame far ahead) who postulated a “Curved Space-Time Continuum” within a gravitational field. It is still the question who was right? Newton, Maxwell, Bohr or Einstein? This article will discuss the interaction between “Gravity and Light” based on a deductive discussion based on the fundamental arguments and way of thinking within that corresponding time-frame.