Speed of Light and the Principle of Relativity - Special and General Relativity - The Physics of the Universe Main Topics > Special and General Relativity > Galileo used the example of a ship traveling at constant speed, without rocking, on a smooth sea, and he noted that any observer doing experiments in a dark room below deck would not be able to tell whether the ship was moving or stationary. As a slightly updated example, a ball thrown in an airplane flying at 800 kilometers per hour 12,000 meters above the Earth follows the same path, and is indistinguishable from, one thrown in the airplane at rest on the ground. Mathematical constant A mathematical constant is a special number, usually a real number, that is "significantly interesting in some way".[1] Constants arise in many different areas of mathematics, with constants such as e and π occurring in such diverse contexts as geometry, number theory and calculus. What it means for a constant to arise "naturally", and what makes a constant "interesting", is ultimately a matter of taste, and some mathematical constants are notable more for historical reasons than for their intrinsic mathematical interest. The more popular constants have been studied throughout the ages and computed to many decimal places. All mathematical constants are definable numbers and usually are also computable numbers (Chaitin's constant being a significant exception). Common mathematical constants[edit] These are constants which one is likely to encounter during pre-college education in many countries. Archimedes' constant π[edit] The circumference of a circle with diameter 1 is π. Besides
Inertial frame of reference Fundamental concept of classical mechanics In classical physics and special relativity, an inertial frame of reference (also called inertial space, or Galilean reference frame) is a frame of reference not undergoing any acceleration. It is a frame in which an isolated physical object—an object with zero net force acting on it—is perceived to move with a constant velocity or, equivalently, it is a frame of reference in which Newton's first law of motion holds.[1] All inertial frames are in a state of constant, rectilinear motion (straight line motion) with respect to one another; in other words, an accelerometer moving with any of them would detect zero acceleration. In classical mechanics, for example, a ball dropped towards the ground does not move exactly straight down because the Earth is rotating. This means the frame of reference of an observer on Earth is not inertial. Introduction[edit] Newton's inertial frame of reference[edit] Absolute space[edit] Newtonian mechanics[edit] where .
Physical constant There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, Planck's constant h, the electric constant ε0, and the elementary charge e. Physical constants can take many dimensional forms: the speed of light signifies a maximum speed limit of the Universe and is expressed dimensionally as length divided by time; while the fine-structure constant α, which characterizes the strength of the electromagnetic interaction, is dimensionless. Dimensional and dimensionless physical constants[edit] Whereas the physical quantity indicated by any physical constant does not depend on the unit system used to express the quantity, the numerical values of dimensional physical constants do depend on the unit used. However, the term fundamental physical constant is also used in other ways. The fine-structure constant α is probably the best known dimensionless fundamental physical constant. Anthropic principle[edit]
Laws of thermodynamics The three laws of thermodynamics define physical quantities (temperature, energy, and entropy) that characterize thermodynamic systems at thermal equilibrium. The laws describe how these quantities behave under various circumstances, and preclude the possibility of certain phenomena (such as perpetual motion). The three laws of thermodynamics are:[1][2][3][4][5] In addition, there is conventionally added a "zeroth law", which defines thermal equilibrium: Zeroth law of thermodynamics: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. There have been suggestions of additional laws, but none of them achieve the generality of the four accepted laws, and they are not mentioned in standard textbooks.[1][2][3][4][6][7] The laws of thermodynamics are important fundamental laws in physics and they are applicable in other natural sciences. Zeroth law[edit] The zeroth law of thermodynamics may be stated in the following form:
Corpuscular theory of light In optics, the corpuscular theory of light, arguably set forward by Descartes (1637) states that light is made up of small discrete particles called "corpuscles" (little particles) which travel in a straight line with a finite velocity and possess impetus. This was based on an alternate description of atomism of the time period. This theory cannot explain refraction, diffraction, interference and polarization. Mechanical philosophy[edit] Pierre Gassendi's atomist matter theory[edit] The core of Gassendi's philosophy is his atomist matter theory. God existsGod created a finite number of indivisible and moving atomsGod has a continuing divine relationship to creation (of matter)Free willA human soul exists.[1] He thought that atoms move in an empty space, classically known as the void, which contradicts the Aristotelian view that the universe is fully made of matter. Corpuscularian theories[edit] Corpuscularian theory to describe light[edit] Sir Isaac Newton[edit] See also[edit]
Relativistic mechanics Theory of motion and forces for objects close to the speed of light In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non-quantum mechanical description of a system of particles, or of a fluid, in cases where the velocities of moving objects are comparable to the speed of light c. As a result, classical mechanics is extended correctly to particles traveling at high velocities and energies, and provides a consistent inclusion of electromagnetism with the mechanics of particles. This was not possible in Galilean relativity, where it would be permitted for particles and light to travel at any speed, including faster than light. The foundations of relativistic mechanics are the postulates of special relativity and general relativity. Relativistic kinematics[edit] The relativistic four-velocity, that is the four-vector representing velocity in relativity, is defined as follows: In the above, where .
Kinetic energy Energy of a moving physical body In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a speed v is . In relativistic mechanics, this is a good approximation only when v is much less than the speed of light. The standard unit of kinetic energy is the joule, while the English unit of kinetic energy is the foot-pound. History and etymology The adjective kinetic has its roots in the Greek word κίνησις kinesis, meaning "motion". The principle in classical mechanics that E ∝ mv2 was first developed by Gottfried Leibniz and Johann Bernoulli, who described kinetic energy as the living force, vis viva. Overview Energy occurs in many forms, including chemical energy, thermal energy, electromagnetic radiation, gravitational energy, electric energy, elastic energy, nuclear energy, and rest energy. The kinetic energy in the moving cyclist and the bicycle can be converted to other forms. Kinetic energy can be passed from one object to another. Newtonian kinetic energy
Brownian motion Random motion of particles suspended in a fluid 2-dimensional random walk of a silver adatom on an Ag(111) surface[1] This is a simulation of the Brownian motion of 5 particles (yellow) that collide with a large set of 800 particles. The yellow particles leave 5 blue trails of (pseudo) random motion and one of them has a red velocity vector. This is a simulation of the Brownian motion of a big particle (dust particle) that collides with a large set of smaller particles (molecules of a gas) which move with different velocities in different random directions. Brownian motion, or pedesis (from Ancient Greek: πήδησις /pɛ̌ːdɛːsis/ "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas).[2] This pattern of motion typically consists of random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. History[edit] The first person to describe the mathematics behind Brownian motion was Thorvald N. (i.e to ). . where