Laws, rules, principles, effects, paradoxes, limits, constants, experiments, & thought-experiments in physics

The line integral of the magnetic flux around a closed curve is proportional to the algebraic sum of electric currents flowing through that closed curve.
This was later modified to add a second term when it was incorporated into Maxwell's equations.

Weak anthropic principle.
The conditions necessary for the development of intelligent life will be met only in certain regions that are limited in space and time. That is, the region of the Universe in which we live is not necessarily representative of a purely random set of initial conditions; only those favorable to intelligent life would actually develop creatures who wonder what the initial conditions of the Universe were.
Strong anthropic principle.
A more forceful argument that the weak principle: It states, rather straightforwardly, that if the laws of the Universe were not conducive to the development of intelligent creatures to ask about the initial conditions of the Universe, intelligent life would never have evolved to ask the question in the first place. In other words, the laws of the Universe are the way they are because if they weren't, you would not be able to ask such a question.

A bright spot that appears in the shadow of a uniform disc being backlit by monochromatic light emanating from a point source.

A body that is submerged in a fluid is buoyed up by a force equal in magnitude to the weight of the fluid that is displaced, and directed upward along a line through the center of gravity of the displaced fluid.

A weight-and-pulley system devised to measure the acceleration due to gravity at Earth's surface by measuring the net acceleration of a set of weights of known mass around a frictionless pulley.

The number of atoms or molecules in a sample of an idea gas which is at standard temperature and pressure. It is equal to about 6.022 52 x 10^23 mol^-1.

Equal volumes of all gases at the same temperature and pressure contain equal numbers of molecules. It is, in fact, only true for ideal gases.

An equation which describes the emission spectrum of hydrogen when an electron is jumping to the second orbital; four of the lines are in the visible spectrum, and the remainder are in the ultraviolet.

The theory, predicted by several grand-unified theories, that a class of subatomic particles called baryons (of which the nucleons -- protons and neutrons -- are members) are not ultimately stable but indeed decay. Present theory and experimentation demonstrate that if protons are indeed unstable, they decay with a halflife of at least 10^34 y.

An equation which states that an irrotational fluid flowing through a pipe flows at a rate which is inversely proportional to the cross-sectional area of the pipe. That is, if the pipe constricts, the fluid flows faster; if it widens, the fluid flows slower.

A theory put forth to explain both superconductivity and superfluidity. It suggests that in the superconducting (or superfluid) state electrons form Cooper pairs, where two electrons act as a single unit. It takes a nonzero amount of energy to break such pairs, and the imperfections in the superconducting solid (which would normally lead to resistance) are incapable of breaking the pairs, so no dissipation occurs and there is no resistance.

A law which describes the contributions to a magnetic field by an electric current. It is analogous to Coulomb's law for electrostatics.

The radiation -- the radiance at particular frequencies all across the spectrum -- produced by a blackbody -- that is, a perfect radiator (and absorber) of heat. Physicists had difficulty explaining it until Planck introduced his quantum of action.

A mathematical formula which generates, with a fair amount of accuracy, the semimajor axes of the planets in order out from the Sun. Write down the sequence 0, 3, 6, 12, 24, . . . and then add 4 to each term. Then divide each term by 10. This is intended to give you the positions of the planets measured in astronomical units.
Bode's law had no theoretical justification when it was first introduced; it did, however, agree with the soon-to-be-discovered planet Uranus' orbit (19.2 au actual; 19.7 au predicted). Similarly, it predicted a missing planet betwen Mars and Jupiter, and shortly thereafter the asteroids were found in very similar orbits (2.8 au actual for Ceres; 2.8 au predicted). However, the series seems to skip over Neptune's orbit.

The quantum of magnetic moment.

The distance corresponding the mean distance of an electron from the nucleus in the ground state.

A constant which describes the relationship between temperature and kinetic energy for molecules in an ideal gas. It is equal to 1.380 622 x 10^-23 J/K.

The product of the pressure and the volume of an ideal gas at constant temperature is a constant.

The series which describes the emission spectrum of hydrogen when the electron is jumping to the fourth orbital. All of the lines are in the infrared portion of the spectrum.

When a beam of x-rays strikes a crystal surface in which the layers of atoms or ions are regularly separated, the maximum intensity of the reflected ray occurs when the sine of the compliment of the angle of incidence is equal to an integer multiplied by the wavelength of x-rays divided by twice the distance between layers of atoms or ions.

The extent of the polarization of light reflected from a transparent surface is a maximum when the reflected ray is at right angles to the refracted ray.

The continuous random motion of solid microscopic particles when suspended in a fluid medium due to the consequence of continuous bombardment by atoms and molecules.

The theorem which states that no engine operating between two temperatures can be more efficient than a reversible engine.

A pseudoforce -- a fictitious force resulting from being in a non- inertial frame of reference -- that occurs when one is moving in uniform circular motion. One feels a "force" outward from the center of motion.

A limit which mandates that no white dwarf (a collapsed, degenerate star) can be more massive than about 1.2 solar masses. Anything more massive must inevitably collapse into a neutron star.

The volume of an ideal gas at constant pressure is proportional to the thermodynamic temperature of that gas.

Radiation emitted by a massive particle which is moving faster than light in the medium through which it is travelling. No particle can travel faster than light in vacuum, but the speed of light in other media, such as water, glass, etc., are considerably lower. Cherenkov radiation is the electromagnetic analogue of the sonic boom, though Cherenkov radiation is a shockwave set up in the electromagnetic field.

The principle that a given system cannot exhibit both wave-like behavior and particle-like behavior at the same time. That is, certain experiments will reveal the wave-like nature of a system, and certain experiments will reveal the particle-like nature of a system, but no experiment will reveal both simultaneously.

An effect that demonstrates that photons (the quantum of electromagnetic radiation) have momentum. A photon fired at a stationary particle, such as an electron, will impart momentum to the electron and, since its energy has been decreased, will experience a corresponding decrease in frequency.

A pseudoforce -- a fictitious force, like the centrifugal "force" -- which arises because the rotation of the Earth varies at different latitutdes (maximum at the equator, zero at the poles).

The principle that when a new, more specialized theory is put forth, it must reduce to the more general (and usually simpler) theory under normal circumstances. There are correspondence principles for general relativity to special relativity and special relativity to Newtonian mechanics, but the most widely known correspondence principle (and generally what is meant when one says "correspondence principle") is that of quantum mechanics to classical mechanics.

The background of radiation mostly in the frequency range 3 x 10^11 to 3 x 10^8 Hz discovered in space in 1965. It is believed to be the cosmologically redshifted radiation released by the Big Bang itself. Presently it has an energy density in empty space of about 4 x 10^-14 J/m^3.

An effect where light emitted from a distant source appears redshifted because of the expansion of space itself. Compare with the Doppler effect.

The primary law for electrostatics, analogous to Newton's law of universal gravitation. It states that the force between two point charges is proportional to the algebraic product of their respective charges as well as proportional to the inverse square of the distance between them.

A more general form of Curie's law, which states that the susceptibility of a paramagnetic substance is inversely proportional to the thermodynamic temperature of the substance less the Weiss constant, a characteristic of that substance.

The susceptibility of a paramagnetic substance is inversely proportional to the thermodynamic temperature of the substance. The constant of proportionality is called the Curie constant.

The total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of its components; that is, the sum of the pressures that each component would exert if it were present alone and occuped the same volume as the mixture.

An experiment that conclusively confirmed the wave nature of electrons; diffraction patterns were observed by an electron beam penetrating into a nickel target.

The prediction that particles also have wave characteristics, where the effective wavelength of a particle would be inversely proportional to its momentum, where the constant of proportionality is the Planck constant.

Waves emitted by a moving observer will be blueshifted (compressed) if approaching, redshifted (elongated) if receding. It occurs both in sound as well as electromagnetic phenomena, although it takes on different forms in each.

The molar heat capacity is approximately equal to the three times the gas constant.

Consider the following quantum mechanical thought-experiment: Take a particle which is at rest and has spin zero. It spontaneously decays into two fermions (spin 1/2 particles), which stream away in opposite directions at high speed. Due to the law of conservation of spin, we know that one is a spin +1/2 and the other is spin -1/2. Which one is which? According to quantum mechanics, neither takes on a definite state until it is observed (the wavefunction is collapsed).
The EPR effect demonstrates that if one of the particles is detected, and its spin is then measured, then the other particle -- no matter where it is in the Universe -- instantaneously is forced to choose as well and take on the role of the other particle. This illustrates that certain kinds of quantum information travel instantaneously; not everything is limited by the speed of light.
However, it can be easily demonstrated that this effect does not make faster-than-light communication possible.

The basic postulate of A. Einstein's general theory of relativity, which posits that an acceleration is fundamentally indistinguishable from a gravitational field. In other words, if you are in an elevator which is utterly sealed and protected from the outside, so that you cannot "peek outside," then if you feel a force (weight), it is fundamentally impossible for you to say whether the elevator is present in a gravitational field, or whether the elevator has rockets attached to it and is accelerating "upward."
The equivalence principle predicts interesting general relativistic effects because not only are the two indistinguishable to human observers, but also to the Universe as well, in a way -- any effect that takes place when an observer is accelerating should also take place in a gravitational field, and vice versa.

The region around a rotating black hole, between the event horizon and the static limit, where rotational energy can be extracted from the black hole.

The radius of surrounding a black hole at which a particle would need an escape velocity of lightspeed to escape; that is, the point of no return for a black hole.

The electric charge carried by one mole of electrons (or singly- ionized ions). It is equal to the product of the Avogadro constant and the (absolute value of the) charge on an electron; it is 9.648 670 x 10^4 C/mol.

The line integral of the electric flux around a closed curve is proportional to the instantaneous time rate of change of the magnetic flux through a surface bounded by that closed curve.

1. The amount of chemical change during electrolysis is proportional to the charge passed.
2. The charge required to deposit or liberate a mass is proportional to the charge of the ion, the mass, and inversely proprtional to the relative ionic mass. The constant of proportionality is the Faraday constant.

1. An electromotive force is induced in a conductor when the magnetic field surrounding it changes.
2. The magnitude of the electromotive force is proportional to the rate of change of the field.
3. The sense of the induced electromotive force depends on the direction of the rate of the change of the field.

The principle, put forth by P. de Fermat, states that the path taken by a ray of light between any two points in a system is always the path that takes the least time.

E. Fermi's conjecture, simplified with the phrase, "Where are they?" questioning that if the Galaxy is filled with intelligent and technological civilizations, why haven't they come to us yet? There are several possible answers to this question, but since we only have the vaguest idea what the right conditions for life and intelligence in our Galaxy, it and Fermi's paradox are no more than speculation.

The electric flux through a closed surface is proportional to the algebraic sum of electric charges contained within that closed surface.

The magnetic flux through a closed surface is zero; no magnetic charges exist.

A paradox proposed to discount time travel and show why it violates causality. Say that your grandfather builds a time machine. In the present, you use his time machine to go back in time a few decades to a point before he married his wife (your grandmother). You meet him to talk about things, and an argument ensues (presumably he doesn't believe that you're his grandson/granddaughter), and you accidentally kill him.
If he died before he met your grandmother and never had children, then your parents could certainly never have met (one of them didn't exist!) and could never have given birth to you. In addition, if he didn't live to build his time machine, what are you doing here in the past alive and with a time machine, if you were never born and it was never built?

When charged particles flow through a tube which has both an electric field and a magnetic field (perpendicular to the electric field) present in it, only certain velocities of the charged particles are preferred, and will make it undeviated through the tube; the rest will be deflected into the sides. This effect is exploited in such devices as the mass spectrometer and in the Thompson experiment. This is called the Hall effect.

The theory that black holes emit radiation like any other hot body. Virtual particle-antiparticle pairs are constantly being created in supposedly empty space. Every once in a while, one will be created in the vicinity of a black hole's event horizon. One of these particles might be catpured by the black hole, forever trapped, while the other might escape the black hole's gravity. The trapped particle, which would have negative energy (by definition), would reduce the mass of the black hole, and the particle which escaped would have positive energy. Thus, from a distant, one would see the black hole's mass decrease and a particle escape the vicinity; it would appear as if the black hole were emitting radiation. The rate of emission has a negative relationship with the mass of the black hole; massive black holes emit radiation relatively slowly, while smaller black holes emit radiation -- and thus decrease their mass -- more rapidly.

A principle, central to quantum mechanics, which states that the momentum (mass times velocity) and the position of a particle cannot both be known to infinite accuracy; the more you know about one, the lest you know about the other.
It can be illustrated in a fairly clear way as follows: To see something (let's say an electron), we have to fire photons at it, so they bounce off and come back to us, so we can "see" it. If you choose low-frequency photons, with a low energy, they do not impart much momentum to the electron, but they give you a very fuzzy picture, so you have a higher uncertainty in position so that you can have a higher certainty in momentum. On the other hand, if you were to fire very high-energy photons (x-rays or gammas) at the electron, they would give you a very clear picture of where the electron is (high certainty in position), but would impart a great deal of momentum to the electron (higher uncertainty in momentum).
In a more generalized sense, the uncertainty principle tells us that the act of observing changes the observed in fundamental way.

The stress applied to any solid is proportional to the strain it produces within the elastic limit for that solid. The constant of that proportionality is the Young modulus of elasticity for that substance.

The constant which determines the relationship between the distance to a galaxy and its velocity of recession due to the expansion of the Universe. It is not known to great accuracy, but is believed to lie between 49 and 95 km/s/Mpc.

A relationship discovered between distance and radial velocity. The further away a galaxy is away from is, the faster it is receding away from us. The constant of proportionality is Hubble's constant, H_0. The cause is interpreted as the expansion of space itself.

The mechanics propagation of a wave of light is equivalent to assuming that every point on the wavefront acts as point source of wave emission.

The constant that appears in the ideal gas equation. It is equal to 8.314 34 J/K/mol.

An equation which sums up the ideal gas laws in one simple equation. It states that the product of the pressure and the volume of a sample of ideal gas is equal to the product of the amount of gas present, the temperature of the sample, and the ideal gas constant.

Boyle's law.
The pressure of an ideal gas is inversely proportional to the volume of the gas at constant temperature.
Charles' law.
The volume of an ideal gas is directly proportional to the thermodynamic temperature at constant pressure.
The pressure law.
The pressure of an ideal gas is directly proportional to the thermodynamic temperature at constant volume.

The change in temperature that occurs when a gas expands into a region of lower pressure.

Joule's first law.
The heat produced when an electric current flows through a resistance for a specified time is equal to the square of the current multiplied by the resistivity multiplied by the time.
Joule's second law.
The internal energy of an ideal gas is independent of its volume and pressure, depending only on its temperature.

Electrical effects observed when two superconducting materials are separated by a thin layer of insulating material.

Kepler's first law.
A planet orbits the Sun in an ellipse with the Sun at one focus.
Kepler's second law.
A ray directed from the Sun to a planet sweeps out equal areas in equal times.
Kepler's third law.
The square of the period of a planet's orbit is proportional to the cube of that planet's semimajor axis; the constant of proportionality is the same for all planets.

The ability of certain substances to differently refract light waves whose vibrations are in different directions when the substance is placed in an electric field.

The emissivity of a body is equal to its absorptance at the same temperature.

The loop rule.
The sum of the potential differences encountered in a round trip around any closed loop in a circuit is zero.
The point rule.
The sum of the currents toward a branch point is equal to the sum of the currents away from the same branch point.

If a salt is dissolved in water, the conductivity of the solution is the sum of two values -- one depending on the positive ions and the other on the negative ions.

Lambert's first law.
The illuminance on a surface illuminated by light falling on it perpendicularly from a point source is proportional to the inverse square of the distance between the surface and the source.
Lambert's second law.
If the rays meet the surface at an angle, then the illuminance is also proportional to the cosine of the angle with the normal.
Lambert's third law.
The luminous intensity of light decreases exponentially with the distance that it travels through an absorbing medium.

A principle which states that it doesn't explicitly take energy to compute data, but rather it takes energy to _erase_ any data, since erasure is an important step in computation.

For steady-state heat conduction in one dimension, the temperature distribution is the solution to Laplace's equation, which states that the second derivative of temperature with respect to displacement is zero.

The pattern produced on a photographic film when high-frequency electromagnetic waves (such as x-rays) are fired at a crystalline solid.

A law which states that, in a closed system, the total quantity of something will not increase or decrease, but remain exactly the same. For physical quantities, it states that something can neither be created nor destroyed.
The most commonly seen are the laws of conservation of mass- energy (formerly two conservation laws before A. Einstein), of electric charge, of linear momentum, and of angular momentum. There are several others that deal more with particle physics, such as conservation of baryon number, of strangeness, etc., which are conserved in some fundamental interactions but not others.

For a wavefront intersecting a reflecting surface, the angle of incidence is equal to the angle of reflection.

First law of black hole dynamics.
For interactions between black holes and normal matter, the conservation laws of total energy, total momentum, angular momentum, and electric charge, hold. Second law of black hole dynamics.
With black hole interactions, or interactions between black holes and normal matter, the sum of the surface areas of all black holes involved can never decrease.

First law of thermodynamics.
The change in internal energy of a system is the sum of the heat transferred to or from the system and the work done on or by the system.
Second law of thermodynamics.
The entropy -- a measure of the unavailability of a system's energy to do useful work -- of a closed system tends to increase with time.
Third law of thermodynamics.
For changes involving only perfect crystalline solids at absolute zero, the change of the total entropy is zero.
Zeroth law of thermodynamics.
If two bodies are each in thermal equilibrium with a third body, then all three bodies are in thermal equilibrium with each other.

A condition for the release of energy from a thermonuclear reactor. It is usually stated as the minimum value for the product of the density of the fuel particles and the containment time for energy breakeven. For a half-and-half mixture of deuterium and tritium at ignition temperature, n_G tau is between 10^14 and 10^15 s/cm^3.

If a system is in equilibrium, then any change imposed on the system tends to shift the equilibrium to reduce the effect of that applied change.

An induced electric current always flows in such a direction that it opposes the change producing it.

The number of particles per unit volume of an ideal gas at standard temperature and pressure. It has the value 2.687 19 x 10^25 m^-3.

A substance, which filled all the empty spaces between matter, which was used to explain what medium light was "waving" in. Now it has been discredited, as Maxwell's equations imply that electromagnetic radiation can propagate in a vacuum, since they are disturbances in the electromagnetic field rather than traditional waves in some substance, such as water waves.

The series which describes the emission spectrum of hydrogen when electrons are jumping to the ground state. All of the lines are in the ultraviolet.

The inertia of any particular particle or particles of matter is attributable to the interaction between that piece of matter and the rest of the Universe. Thus, a body in isolation would have no inertia.

A rotating cylinder in a moving fluid drags some of the fluid around with it, in its direction of rotation. This increases the speed in that region, and thus the pressure is lower. Consequently, there is a net force on the cylinder in that direction, perpendicular to the flow of the fluid. This is called the Magnus effect.

The light intensity travelling through a polarizer is proportional to the initial intensity of the light and the square of the cosine of the angle between the polarization of the light ray and the polarization axis of the polarizer.

A thought experiment illustrating the concepts of entropy. We have a container of gas which is partitioned into two equal sides; each side is in thermal equilibrium with the other. The walls (and the partition) of the container are a perfect insulator.
Now imagine there is a very small demon who is waiting at the partition next to a small trap door. He can open and close the door with negligible work. Let's say he opens the door to allow a fast-moving molecule to travel from the left side to the right, or for a slow-moving molecule to travel from the right side to the left, and keeps it closed for all other molecules. The net effect would be a flow of heat -- from the left side to the right -- even though the container was in thermal equilibrium. This is clearly a violation of the second law of thermodynamics.
So where did we go wrong? It turns out that information has to do with entropy as well. In order to sort out the molecules according to speeds, the demon would be having to keep a memory of them -- and it turns out that increase in entropy of the simple maintenance of this simple memory would more than make up for the decrease in entropy due to the heat flow.

Four elegant equations which describe classical electromagnetism in all its splendor. They are:
Gauss' law.
The electric flux through a closed surface is proportional to the algebraic sum of electric charges contained within that closed surface.
Gauss' law for magnetic fields.
The magnetic flux through a closed surface is zero; no magnetic charges exist.
Faraday's law.
The line integral of the electric flux around a closed curve is proportional to the instantaneous time rate of change of the magnetic flux through a surface bounded by that closed curve.
Ampere's law, modified form.
The line integral of the magnetic flux around a closed curve is proportional to the sum of two terms: first, the algebraic sum of electric currents flowing through that closed curve; and second, the instantaneous time rate of change of the electric flux through a surface bounded by that closed curve.
In addition to describing electromagnetism, his equations also predict that waves can propagate through the electromagnetic field, and would always propagate at the same speed -- these are electromagnetic waves.

The decrease of the magnetic flux within a superconducting metal when it is cooled below the critical temperature. That is, superconducting materials reflect magnetic fields.

Possibly the most famous null-experiment of all time, designed to verify the existence of the proposed "lumeniferous aether" through which light waves were thought to propagate. Since the Earth moves through this aether, a lightbeam fired in the Earth's direction of motion would lag behind one fired sideways, where no aether effect would be present. This difference could be detected with the use of an interferometer.
The experiment showed absolutely no aether shift whatsoever, where one should have been quite detectable. Thus the aether concept was discredited as was the constancy of the speed of light.

A famous experiment designed to measure the electronic charge. Drops of oil were carried past a uniform electric field between charged plates. After charging the drop with x-rays, he adjusted the electric field between the plates so that the oil drop was exactly balanced against the force of gravity. Then the charge on the drop would be known. Millikan did this repeatedly and found that all the charges he measured came in integer multiples only of a certain smallest value, which is the charge on the electron.

Two bodies attract each other with equal and opposite forces; the magnitude of this force is proportional to the product of the two masses and is also proportional to the inverse square of the distance between the centers of mass of the two bodies.

Newton's first law of motion.
A body continues in its state of rest or of uniform motion unless it is acted upon by an external force.
Newton's second law of motion.
For an unbalanced force acting on a body, the acceleration produces is proportional to the force impressed; the constant of proportionality is the inertial mass of the body.
Newton's third law of motion.
In a system where no external forces are present, every action is always opposed by an equal and opposite reaction.

The ratio of the potential difference between the ends of a conductor to the current flowing through it is constant; the constant of proportionality is called the resistance, and is different for different materials.

If the Universe is infinite, uniform, and unchanging then the entire sky at night would be bright -- about as bright as the Sun. The further you looked out into space, the more stars there would be, and thus in any direction in which you looked your line-of- sight would eventually impinge upon a star. The paradox is resolved by the Big Bang theory, which puts forth that the Universe is not infinite, non-uniform, and changing.

Pressure applied to an enclosed imcompressible static fluid is transmitted undiminished to all parts of the fluid.

The series which describes the emission spectrum of hydrogen when the electron is jumping to the third orbital. All of the lines are in the infrared portion of the spectrum.

No two identical fermions in a system, such as electrons in an atom, can have an identical set of quantum numbers.

The change in temperature produced at a junction between two dissimilar metals or semiconductors when an electric current passes through the junction.

The ratio of the magnetic flux density in a substance to the external field strength for vacuum. It is equal to 4 pi x 10^-7 H/m.

The ratio of the electric displacement to the intensity of the electric field producing it in vacuum. It is equal to 8.854 x 10^-12 F/m.

The series which describes the emission spectrum of hydrogen when the electron is jumping to the fifth orbital. All of the lines are in the infrared portion of the spectrum.

An effect explained by A. Einstein that demonstrate that light seems to be made up of particles, or photons. Light can excite electrons (called photoelectrons) to be ejected from a metal. Light with a frequency below a certain threshold, at any intensity, will not cause any photoelectrons to be emitted from the metal. Above that frequency, photoelectrons are emitted in proportion to the intensity of incident light.
The reason is that a photon has energy in proportion to its wavelength, and the constant of proportionality is Planck's constant. Below a certain frequency -- and thus below a certain energy -- the incident photons do not have enough energy to knock the photoelectrons out of the metal. Above that threshold energy, called the workfunction, photons will knock the photoelectrons out of the metal, in proportion to the number of photons (the intensity of the light). At higher frequencies and energies, the photoelectrons ejected obtain a kinetic energy corresponding to the difference between the photon's energy and the workfunction.

The fundamental constant equal to the ratio of the energy of a quantum of energy to its frequency. It is the quantum of action. It has the value 6.626 196 x 10^-34 J s.

A law which more accurately described blackbody radiation because it assumed that electromagnetic radiation is quantized.

See Arago spot. Poisson predicted the existence of such a spot, and actually used it to demonstrate that the wave theory of light must be in error.

The principle that cause must always preceed effect. More formally, if an event A ("the cause") somehow influences an event B ("the effect") which occurs later in time, then event B cannot in turn have an influence on event A.
The principle is best illustrated with an example. Say that event A constitutes a murderer making the decision to kill his victim, and that event B is the murderer actually committing the act. The principle of causality puts forth that the act of murder cannot have an influence on the murderer's decision to commit it. If the murderer were to somehow see himself committing the act and change his mind, then a murder would have been committed in the future without a prior cause (he changed his mind). This represents a causality violation. Both time travel and faster-than-light travel both imply violations of causality, which is why most physicists think they are impossible, or at least impossible in the general sense.

The principle that if one knows the state to an infinite accuracy of a system at one point in time, one would be able to predict the state of that system with infinite accuracy at any other time, past or future. For example, if one were to know all of the positions and velocities of all the particles in a closed system, then determinism would imply that one could then predict the positions and velocities of those particles at any other time. This principle has been disfavored due to the advent of quantum mechanics, where probabilities take an important part in the actions of the subatomic world, and the Heisenberg uncertainty principle implies that one cannot know both the position and velocity of a particle to arbitrary precision.

A criterion for the how finely a set of optics may be able to distinguish. It begins with the assumption that central ring of one image should fall on the first dark ring of the other. relativity principle; principle of relativity

A formula which describes all of the characteristics of hydrogen's spectrum, including the Balmer, Lyman, Paschen, Brackett, and Pfund series.

A thought experiment designed to illustrate the counterintuitive and strange notions of reality that come along with quantum mechanics.
A cat is sealed inside a closed box; the cat has ample air, food, and water to survive an extended period. This box is designed so that no information (i.e., sight, sound, etc.) can pass into or out of the box -- the cat is totally cut off from your observations. Also inside the box with the poor kitty (apparently Schroedinger was not too fond of felines) is a phial of a gaseous poison, and an automatic hammer to break it, flooding the box and killing the cat. The hammer is hooked up to a Geiger counter; this counter is monitoring a radioactive sample and is designed to trigger the hammer -- killing the cat -- should a radioactive decay be detected. The sample is chosen so that after, say, one hour, there stands a fifty-fifty chance of a decay occurring.
The question is, what is the state of the cat after that one hour has elapsed? The intuitive answer is that the cat is either alive or dead, but you don't know which until you look. But it _is_ one of them. Quantum mechanics, on the other hands, says that the wavefunction describing the cat is in a superposition of states: the cat is, in fact, fifty per cent alive and fifty per cent dead; it is both. Not until one looks and "collapses the wavefunction" is the Universe forced to choose either a live cat or a dead cat and not something in between.
This indicates that observation also seems to be an important part of the scientific process -- quite a departure from the absolutely objective, deterministic way things used to be with Newton.

The radius that a spherical mass must be compressed to in order to transform it into a black hole; that is, the radius of compression where the escape velocity at the surface would reach lightspeed.

A relation which relates the change in incidence angle of a wavefront due to refraction between two different media.

One of the postulates of A. Einstein's special theory of relativity, which puts forth that the speed of light in vacuum -- often written c, and which has the value 299 792 458 m/s -- is measured as the same speed to all observers, regardless of their relative motion. That is, if I'm travelling at 0.9 c away from you, and fire a beam of light in that direction, both you and I will independently measure the speed of that beam as c.
One of the results of this postulate (one of the predictions of special relativity is that no massive particle can be accelerated to (or beyond) lightspeed, and thus the speed of light also represents the ultimate cosmic speed limit. Only massless particles (photons, gravitons, and possibly neutrinos, should they indeed prove to be massless) travel at lightspeed, and all other particles must travel at slower speeds.

An effect that causes atomic energy levels to be split because electrons have intrinsic angular momentum (spin) in addition to their extrinsic orbital angular momentum.

The distance from a rotating black hole where no observer can possibly remain at rest (with respect to the distant stars) because of inertial frame dragging.

The constant of proportionality present in the Stefan-Boltzmann law. It is equal to 5.6697 x 10^-8 W/m^2/K^4.

The radiated power (rate of emission of electromagnetic energy) of a hot body is proportional to the emissivity, an efficiency rating, the radiating surface area, and the fourth power of the thermodynamic temperature. The constant of proportionality is the Stefan-Boltzmann constant.

An experiment that demonstrates the features of spin (intrinsic angular momentum) as a distinct entity apart from orbital angular momentum.

The phenomena by which, at sufficiently low temperatures, a conductor can conduct charge with zero resistance.

The phenomena by which, at sufficiently low temperatures, a fluid can flow with zero viscosity.

The net force on a body is equal to the sum of the forces impressed upon it.

The resultant quantum mechnical wavefunction due to two or more individual wavefunctions is the sum of the individual wavefunctions.

The resultant wave function due to two or more individual wave functions is the sum of the individual wave functions.

When an electric current flows through a conductor whose ends are maintained at different temperatures, heat is released at a rate approximately proportional to the product of the current and the temperature gradient.

One of the most famous "paradoxes" in history, predicted by A. Einstein's special theory of relativity. Take two twins, born on the same date on Earth. One, Albert, leaves home for a trip around the Universe at very high speeds (very close to that of light), while the other, Henrik, stays at home at rests. Special relativity predicts that when Albert returns, he will find himself much younger than Henrik.
That is actually not the paradox. The paradox stems from attempting to naively analyze the situation to figure out why. From Henrik's point of view (and from everyone else on Earth), Albert seems to speed off for a long time, linger around, and then return. Thus he should be the younger one, which is what we see. But from Albert's point of view, it's Henrik (and the whole of the Earth) that are travelling, not he. According to special relativity, if Henrik is moving relative to Albert, then Albert should measure his clock as ticking slower -- and thus Henrik is the one who should be younger. But this is not what happens.
So what's wrong with our analysis? The key point here is that the symmetry was broken. Albert did something that Henrik did not -- Albert accelerated in turning around. Henrik did no accelerating, as he and all the other people on the Earth can attest to (neglecting gravity). So Albert broke the symmetry, and when he returns, _he_ is the younger one.

A shortcoming of the Rayleigh-Jeans formula, which attempted to describe the radiancy of a blackbody at various frequencies of the electromagnetic spectrum. It was clearly wrong because as the frequency increased, the radiancy increased without bound; something quite not observed; this was dubbed the "ultraviolet catastrophe." It was later reconciled and explained by the introduction of Planck's radiation law.

The constant of proportionality in Newton's law of universal gravitation and which plays an analogous role in A. Einstein's general relativity. It is equal to 6.664 x 10^-11 N m^2/kg^2.

Forces responsible for the non-ideal behavior of gases, and for the lattice energy of molecular crystals. There are three causes: dipole-dipole interaction; dipole-induced dipole moments; and dispersion forces arising because of small instantaneous dipoles in atoms.

The principle of quantum mechanics which implies that light (and, indeed, all other subatomic particles) sometimes act like a wave, and sometime act like a particle, depending on the experiment you are performing. For instance, low frequency electromagnetic radiation tends to act more like a wave than a particle; high frequency electromagnetic radiation tends to act more like a particle than a wave.

The ratio of the thermal conductivity of any pure metal to its electrical conductivity is approximately constant for any given temperature. This law holds fairly well except at low temperatures.

For a blackbody, the product of the wavelength corresponding to the maximum radiancy and the thermodynamic temperature is a constant. As a result, as the temperature rises, the maximum of the radiant energy shifts toward the shorter wavelength (higher frequency and energy) end of the spectrum.

Rules governing the formation of products during certain types of organic reactions.

A famous experiment which shows the wave nature of light (and indeed of other particles). Light is passed from a small source onto an opaque screen with two thin slits. The light is refracted through these slits and develops an interference pattern on the other side of the screen.

The splitting of the lines in a spectrum when the source is exposed to a magnetic field.