I. MOTION¶
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This is the first Volume of the series MODERN PHYSICS BY EXPLORING NOBEL PRIZES. It refers to movement and concerns the relationship between Mathematics, mostly Geometry, and Mechanics. We consider how mathematics has been useful in understanding and describing motion.
Mathematics refers to the formulation and application of properties of abstract objects such as numbers and their relationships, figures and their structures, quantities and theirs changes. The word is derived from ancient Greek μάθημα-máthēma: knowledge, study or learning. Geometry (from γεωμετία, from γῆ-earth and μετρέω-measure) is the study of properties related to spatial forms and to measurements associated with their properties. Geometry requires precise observations, experimental control, exact measurement, and appropriate mathematical treatment.
Mechanics (from μεχανικός derived from μεχανή-machine) is a branch of Physics that deals with concepts related to motion, like position, displacement, orientation, velocity, acceleration, mass, force, linear and angular momenta, work, energy, and other concepts related to motion. It looks for understanding, explaining, and applying knowledge to what moves in geometrical spaces and evolves in time.
Physical phenomena can be characterized by their states of motion: no motion means to be stationery and motion implies changes in time of positions, orientations or vibrational states. These motions are described by the paths or trajectories followed by the individual objects composing a system or the entire system. The purpose of classical mechanics is to calculate and interpret these trajectories.
In this Volume I we deal with the following aspects of motion: conceptualization of spaces in geographical, astronomical and quantum contexts, regions required to describe experiments about the motion of electrons, detection of motions in terms of signals in the eye and maps in the brain, and reconceptualization of space-time in non-Euclidean geometries.
The Chapters of this first Volume are the following:
1. Dictatorial and democratic conceptualizations of spaces.¶
1.1 Mathematics and science in ancient Greece.¶
1.2 Conceptualizations of spaces and quantum statistics.¶
1.3 Context learning for conceptualizing cognitive spaces.¶
Although motion usually refers to changes in time of certain properties of physical objects, it can also describe modifications of ideas or perspectives. These were the case with ancient Greek conceptualizations concerning dictatorial or democratic approaches for building circular spaces and with two Physics Nobel laureates (W. Pauli and M. Born) who classified elementary particles according to quantum statistics: fermions are elitists and bosons like to be together. Context learning consists in three steps: exploring problematic situations, analyzing leading questions and performing learning and evaluation activities.
2. Production and control of electronic motions.¶
2.1 Regions for doing experiments.¶
2.2 Physics Nobel Lectures by Thomson, Millikan, Franck, Hertz, and Compton.¶
2.3 Knowledge domains for understanding.¶
At the beginning of past century few critical experiments were dedicated to the observation and interpretation of electronic motions. Their purpose was to determine some of the properties of this elementary particle and their forms of interaction. The realization of such experiments were recognized with Physics Nobel Prizes to J.J. Thomson, R. A. Millikan , J. Franck, G. L. Hertz, and A.H. Compton. These experiments are described and analyzed in terms of three regions: Preparation, Transformation and Detection and Measurement. These regions are the scenarios where knowledge domains (Factual, Analytic, Conceptual and Operational) are applied for understanding how and when electrons move.
3. Detecting signals in the eye and creating maps in the brain.¶
3.1 Understanding the mechanisms of vision.¶
3.2 Existence of a mental Global Positioning System (GPS).¶
3.3 Cognitive procedures for creating scientific knowledge.¶
Detection of motion by humans is very complicated; however, in here we just refer to the detection of signals by the eye, which involves a mechanism of vision, and the production and use of maps in the brain, which implies the organization of a GPS created by a network of cerebral neuron cells. Different Nobel Prizes in Medicine were awarded to researchers in these fields: A. Gullstrand, R. Granit, K. Hartline, G. Wald, D. H. Hubel, T. N. Wiesel, J. O’Keefe, MB. Moser and E, Moser. The functions of such neural cells can be associated with the cognitive procedures required for creating scientific knowledge (Inquiring, Training, Comprehension, and Metacognition). These procedures serve to analyze the geometrical and physical explanations describing the movement of Mercury in its planetary orbit around the Sun.
4. Geometrization of the description of motion.¶
4.1 On Euclidean geometry and non-Euclidean geometries.¶
4.2 Einstein´s theories of relativity.¶
4.3 Factors and Aspects distinguishing scientific theories.¶
Any classic description of motion assumes that space and time are homogeneous and completely independent one of each other. Both coordinates have not privileged origins in their corresponding reference systems. However, descriptions of objects moving at speeds closer to the speed of light must be done according to a non-Euclidean geometry and following the approach of the theories of relativity. The theories explaining motion formulated by Kepler, Galileo, Newton, and Einstein are compared in terms of their different ways they satisfy the Aspects and Factors that distinguish a scientific theory. A. Einstein did not receive the Physics Nobel Prize for his works on relativity; they were considered pure speculations without the support of experimental evidence.
Created: 2023-03-12; Updated: 2024-04-15
Barojas-Weber, J., & Lizárraga-Celaya, C. (2023). Modern Physics by Exploring Nobel Prizes.
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