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- Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories".
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Mathematics contains hypotheses, while physics contains theories. Mathematics statements have to be only logically true, while predictions of physics statements must match observed and experimental data. The distinction is clear-cut, but not always obvious. For example, mathematical physics is the
- Overview
- What is physics?
- What will I learn by studying physics on Khan Academy?
Let's think about what physics is and what topics are covered in an introductory physics course.
To be honest, it’s really difficult to define exactly what physics is. For one, physics keeps changing as we progress and make new discoveries. New theories don't just bring new answers. They also create new questions that might not have even made sense when viewed from within the previous theory of physics. This makes physics exciting and interesting, but it also forces attempts at defining physics into generalizations about what physics has been rather than what it might be at some point in the future.
That said, definitions are useful. So, if it’s a definition you want, it’s a definition you’ll get. For the most part, physicists are trying to do the following:
1.Precisely define the most fundamental measurable quantities in the universe (e.g., velocity, electric field, kinetic energy). The effort to find the most fundamental description of the universe is a quest that has historically always been a big part of physics, as can be seen in the comic image below.
[What does fundamental mean?]
2.Find relationships between those fundamental measured quantities (e.g., Newton’s Laws, conservation of energy, special relativity). These patterns and correlations are expressed using words, equations, graphs, charts, diagrams, models, and any other means that allow us to express a relationship in a way that we as humans can better understand and use.
[Math makes things simpler?!]
In physics, we want to explain why objects move around the way they do. However, it would be hard to explain motion if we didn't know how to describe motion. So first, in the topics One-dimensional motion and Two-dimensional motion, we'll learn how to precisely describe the motion of objects and predict their motion for some special cases.
With the ability to precisely describe motion under our belt, we'll learn in Forces and Newton's Laws how the concept of force allows us to explain why objects change their motion.
We'll continue mastering and expanding our ability to deal with motion by showing that conservation laws are an alternative way to explain the motion of an object. These conservation laws give constraints on how the motion of a system can change. Conservation of energy will be learned in Work and energy, and conservation of momentum will be learned in Impacts and linear momentum.
Up to that point we'll have mostly considered objects that are not changing their rotational motion, so in Moments, torque, and angular momentum we'll learn how to describe and explain rotational motion and pick up a new conservation law along the way—conservation of angular momentum.
After this point, we'll deploy what we learned about motion, forces, and conservation laws to analyze how to deal with a variety of new forces and phenomena. We'll learn how to deal with liquids and gases in Fluids and Thermal physics. Then in Electricity and Magnetism we'll learn about two new forces—the electric force and the magnetic force. In Circuits we'll see how electric forces cause current to flow. In Optics we'll investigate the ways in which electromagnetic waves (i.e., light) can bend and reflect. Once we learn about light, we get to learn Einstein's theory of Special relativity. And that's just to name a few.
By the end you should have a nice understanding of introductory physics and the mathematical tools physicists use to describe and explain the universe. But no summary can describe all the interesting and powerful aspects of physics. The best way to find out is to jump in and see for yourself.
May 6, 2024 · Physics can, at base, be defined as the science of matter, motion, and energy. Its laws are typically expressed with economy and precision in the language of mathematics.
Illustration of Hooke's law of elasticity of materials, showing the stretching of a spring in proportion to the applied force, from Robert Hooke's- Radio waves, infrared rays, visible light, ultraviolet rays, X-rays, and gamma rays are all types of electromagnetic radiation. Radio waves have the longest wavelength, and gamma rays have the shortest wavelength.
- Spectrum of white light by a diffraction grating. With a prism, the red end of the spectrum is more compressed than the violet end.
- Particle tracks from the collision of an accelerated nucleus of a niobium atom with another niobium nucleus. The single line on the left is the track of the incoming projectile nucleus, and the other tracks are fragments from the collision.
- Sequence of events in the fission of a uranium nucleus by a neutron.
Physics is not math. Despite the close relationship between math and physics, they are not synonyms. In mathematics objects can be defined exactly and logically related, but the object need have no relationship to experimental measurements.
Physics is the science aimed at describing the fundamental aspects of our universe. This includes what things are in it, what properties of those things are noticeable, and what processes those things or their properties undergo. In simpler terms, physics attempts to describe the basic mechanisms that make our universe behave the way it does.
Physics is a natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force. More broadly, it is the study of nature in an attempt to understand how the universe behaves.
Although related to theoretical physics, mathematical physics in this sense emphasizes the mathematical rigour of the similar type as found in mathematics. On the other hand, theoretical physics emphasizes the links to observations and experimental physics , which often requires theoretical physicists (and mathematical physicists in the more ...
