The twins
or clock paradox has been a subject of lively discussion and occasional disagreement
among both relativists and the public for over 100 years, and continues to attract
physicists who write papers giving new analyses or defending old ones, even though
many physicists now consider the matter only of educational interest. This paper
investigates the number of papers, which is increasing, and trends in explanations,
some of which are now targeted at professional physicists and other of which are
targeted at optical or radar visualization rather than problem solving. Observations
of students indicate that the latest techniques help but only somewhat. An analysis
is made of 21 previous treatments appearing in the education related American Journal
of Physics, Einstein’s discussions and several other pedagogical papers. A new memory
aid for simultaneity transformation is given that puts it on a par with “time dilation”
and “length contraction” for quick and easy problem visualization. The point of
view of a trailing twin is introduced to show how simultaneity changes account for
missing time in the turnaround. Length contraction is treated on equal footing with
time dilation, and Swann’s insight into clocks is extended to lengths. Treatments
using the conventionality of simultaneity are seen as equivalent to choice of co-moving
frames. Responses to difficult questions are suggested which avoid being dismissive,
and engage students’ critical thinking.

Abstract:
The aim of this work is to show that the currently widely accepted geometrical model of space and time based on the works of Einstein and Minkowski is not unique. The work presents an alternative geometrical model of space and time, a model which, unlike the current one, is based solely on Euclidean geometry. In the new model, the pseudo-Euclidean spacetime is replaced with a specific subset of four-dimensional Euclidean space. The work shows that four-dimensional Euclidean space allows explanation of known relativistic effects that are now explained in pseudo-Euclidean spacetime by Einstein’s Special Theory of Relativity (STR). It also shows simple geometric-kinematical nature of known relativistic phenomena and among others explains why we cannot travel backward in time. The new solution is named the Euclidean Model of Space and Time (EMST).

Abstract:
In Newton’s classical physics, space and time are treated as absolute quantities. Space and time are treated as independent quantities and can be discussed sepa-rately. With his theory of relativity, Einstein proved that space and time are de-pendent and must be treated inseparably. Minkowski adopted a four-dimensional space-time frame and indirectly revealed the dependency of space and time by adding a constraint for an event interval. Since space and time are inseparable, a three-dimensional space-time frame can be constructed by embedding time into space to directly show the interdependency of space and time. The formula for time dilation, length contraction, and the Lorenz transformation can be derived from graphs utilizing this new frame. The proposed three-dimensional space-time frame is an alternate frame that can be used to describe motions of objects, and it may improve teaching and learning Special Relativity and provide additional insights into space and time.

Abstract:
In classical physics, time and space are absolute and independent, so time and space can be treated separately. However, in modern physics, time and space are relative and dependent: time and space must be treated together. In 4-d s-t frames, we treat time and space independently, then add a constraint to link them together. In teaching, there is a big gap between classical and modern physics. We hope that we are able to find a frame connecting them to make learning simpler. 3-d s-t frame is the best candidate to serve this purpose: time and space are able to be treated dependently by defining the unit of time as T and the unit of space as λ in this frame. Furthermore, the ratio, λ/T, is the velocity, c, of the medium. This paper shows the equivalence between a 4-d s-t frame and a 3-d s-t frame by properly converting coordinates of two frames.

Abstract:
the principal consequences of the special relativity theory (srt) can be deduced considering the frequency measured by different observers (doppler effect) as well as the postulates of the srt, with no previous necessity of the lorentz transformation equations nor the space-time diagrams. if a source located in a system s' that is moving with uniform linear motion with respect to the other system s' emits pulses with frequency ν0 in its proper reference system (rs), the comparison between the frequencies measured by each observer o' (in s') and o (in s) permits to find the effects known as time dilatation and length contraction. then, by means of a simple algebraic procedure, the lorentz transformation equations are found.

Abstract:
This study reports the results of the derivation of the equation of the contraction of a rain drop in space as it moves in the gravitational field of a stationary homogeneous prolate spheroidal body. It highlights the issue of the universe being in dynamic equilibrium, unlike Einsteins viewpoint that adopts the Doppler effect for the explanation of cosmology.

Abstract:
Presenting a unified model of motion and gravity has proved difficult as current approaches to quantum and classical physics are incompatible. Using measurement quantization—a model that demonstrates the physical significance of Planck’s units of length, mass, and time—measure is expressed as counts of the fundamental units establishing a common framework for describing quantum and cosmological phenomena with expressions that are defined throughout the entire physical domain. Beginning with the Pythagorean Theorem, we demonstrate an understanding of measure with respect to static and moving references. The model is extended to include the measure of mass thus completing a single approach for describing the contraction and dilation of measure. With this new approach, relativistic effects are now described as properties of quantized finite units of measure. In support of the model, several descriptions of phenomena are resolved that match our most precise data such as the measure of dark energy, universal expansion, mass distribution, and the age of the Cosmic Microwave Background.

Abstract:
In this paper, a contraction-based backstepping nonlinear control technique was proposed. The proposed controller synthesis technique utilizes both the recursive nature of backstepping control and of contraction analysis. This approach results in a contracting closed-loop dynamics, with exponential stability. The use of the hierarchical contraction form in the control problem formulation also results in the exponential convergence of controlled variables and can be easily applied to non-autonomous systems. A flight path angle controller was synthesized and simulated using the proposed technique to demonstrate the exponential convergence achieved by the backstepping controller design.

The present
study was conducted in the laboratory to investigate the allelopathic effect of
Mexican poppy (Argemone mexicana L.)to the germination and growth
parameters of two native species Brachiaria dictyoneura Land Clitoria ternatea L.
Different concentrations of leaf and seed aqueous extracts from Argemone mexicana (0%, 25%, 50%, 75% and 100%) were evaluated.
Results showed that seed germination, root length, shoot length, seedling length,
fresh weight and dry weight of B. dictyoneura and C. ternatea seedlings were
significantly reduced by leaf and seed extracts compared with control
treatments. Roots were more affected than shoots; and leaf extract was more
suppressive than seed extracts. From
the results, it is concluded that leaf and seed extracts have some allelochemicals with inhibitory effect
on germination and growth of the tested plant

Abstract:
Time dilation and length contraction formulas are derived in Special Relativity. However, these phenomena cannot be visualized in four-dimensional space-time frames. From the time dilation formula, we can derive a relationship between space and time for a pair of inertial frames and, in turn, construct three-dimensional space-time frames based on this relationship. Furthermore, length contraction can be shown on these frames. Since space and time are inseparable, neither time dilation nor length contraction can be fully understood unless discussed together. We apply three-dimensional space-time frames to describe the motion of an object in the twin paradox. Using the concept of the center of mass of a pair of inertial frames, we are able to determine who is on the rest frame of a pair of inertial frames. This example demonstrates the advantage of three-dimensional space-time frames over four-dimensional space-time frames in describing relativistic motion.