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Quantum mechanics
In classical mechanics, variables like position and momentum are considered to have exact values at any given time. Although there will always be some error in their measurement, there is no lower bound on this error. In quantum mechanics there is a probability distribution for possible values of momentum. Heisenberg's uncertainty principle puts a fundamental lower bound on the uncertainties in position ($&Delta; x$) and momentum ($&Delta; p$):
 * $$\Delta p \Delta x \geq \frac{\hbar}{2}\,,$$

where ħ is the reduced Planck constant, defined as
 * $$\hbar \equiv \frac{h}{2\pi}\,$$

and $h$ is Planck's constant ($6.626 × 10^{−34} J s$). Position and momentum are conjugate variables.

There is a duality between waves and particles. In classical physics, Electromagnetic radiation (including visible light, ultraviolet light, and radio waves) is a wave phenomenon, but it is also carried by photons. Though photons have no mass, each particle carries a momentum that is proportional to the wavelength $&lambda;$:
 * $$p = \frac{h}{\lambda}\,,$$

where $h$ is Planck's constant ($6.626 × 10^{−34} J s$). Similarly, a particle such as an electron can also be considered a matter wave with wavelength given by the above formula.

Momentum is defined as an operator on the wave function.

For a single particle described in the position basis the momentum operator can be written as
 * $$\mathbf{p}={\hbar\over i}\nabla=-i\hbar\nabla\,,$$

where ∇ is the gradient operator, and i the imaginary unit. This is a commonly encountered form of the momentum operator, though the momentum operator in other bases can take other forms. For example, in the momentum basis the momentum operator is represented as
 * $$\mathbf{p}\psi(p) = p\psi(p)\,,$$

where the operator p acting on a wave function ψ(p) yields that wave function multiplied by the value p, in an analogous fashion to the way that the position operator acting on a wave function ψ(x) yields that wave function multiplied by the value x.

The momentum of photons can be utilized in applications such as the solar sail. The calculation of the momentum of light within dielectric media is somewhat controversial (see Abraham–Minkowski controversy).

Flagella
The rotational speed of flagella varies in response to the intensity of the proton motive force, thereby permitting certain forms of speed control, and also permitting some types of bacteria to attain speeds of up to 60 cell lengths per second. At such a speed it would take a bacterium about 245 days to cover a kilometre. The cheetah, with a top speed of 110 110 km/h, is far faster in absolute terms, but only achieves about 25 body lengths per second.

General terminology
In all the formulae for the day of the week, the day (a number) is represented by $d$, the month by $m$ and the year by $y$. The symbol $[ x ]$ is the nearest integer below $x$.

Gauss's formula
In a handwritten note in a collection of astronomical tables, Carl Friedrich Gauss described a method for calculating the day of the week for the first of January in any given year. He never published it. It was finally included in his collected works in 1927.

Gauss's method was applicable to the Gregorian calendar. He numbered the weekdays from 0 to 6 starting with Sunday. He defined the following operation: The weekday of the first of January in year number $A$ is
 * $$ 1 + R(5(A-1),4) + R(4(A-1),100) + R(6(A-1),400),$$

where $R(y,m)$ is the remainder after division of $y$ by $m$.

This formula was converted into a tabular method for calculating any day of the week by Kraitchik and then in a more mathematical form by Schwerdtfeger. In the version by Schwerdtfeger, the year is split into the century and the two digit year within the century. The approach depends on the month. For $m &ge; 3$,
 * $$ c = \left[y/100\right] \quad \text{and} \quad g = y - 100 c,$$

so $g$ is between 0 and 99. For $m = 1,2$,
 * $$ c = \left[(y-1)/100\right] \quad \text{and} \quad g = y - 1 - 100 c.$$

The formula for the day of the week is
 * $$ w = d + e + f + g + \left[g/4\right] \mod 7.$$

The value of $e$ is obtained from the following table:

Relevance to sports

 * Figure skater - starts with arms extended, then pulls the arms in to increase the rotation rate. Divers use a tuck to achieve the same effect.
 * Tightrope walker - the increased moment of inertia resists rotation, so when the acrobat starts to lose his balance, he has more time to respond. One way of responding is to push against the pole. If, for example, the acrobat is rotating clockwise, he pushes on the pole to make it rotate clockwise. The pole pushes back, counteracting the clockwise motion of the acrobat. This is similar to the more rapid arm swinging or flailing that people use to regain their balance. A large umbrella can also be used to increase the moment of inertia.

Other applications

 * Gyroscope!
 * Objects rolling down an inclined plane.
 * Flywheels - weight distributed as far from the axis as possible
 * Planets
 * Binary pulsars
 * Dark matter?
 * Flipping of icebergs?
 * inertial interchange true polar wander

Earth's magnetic field: rapid-decay and rapid reversals
NOTE: Rewrite using

This hypothesis was developed by Thomas G. Barnes, who was Creation Research Society president in the mid-1970s. Taking the assumption that the Earth's magnetic field decayed exponentially, and ignoring evidence of it fluctuating over time, he estimated that "the life of the earth's magnetic field should be reckoned in thousands, not millions or billions, of years." It has drawn harsh criticism from both scientists and some creationists.

It has long been observed that Earth's magnetic field gradually changes over time (e.g., by Henry Gellibrand of Gresham College, in 1634). Much of this change is due to movement of the magnet poles, and changes in the Earth's non-dipole field. The Earth's magnetic field strength was measured by Carl Friedrich Gauss in 1835 and has been repeatedly measured since then, showing a relative decay of about 5% over the last 150 years.

One proposal is based on the assumption that Earth was created from pure water with all of the molecules' spins aligned creating a substantial magnetic field. However spin relaxation times, which measure the time nuclear magnetisations take to return to the equilibrium, are typically measured in the range of milliseconds or seconds.

Russell Humphreys accepts a core-current based magnetic field and archaeomagnetic measurements of the magnetic field (based on measurements of human artifacts), and concludes that several reversals of the magnetic field occurred during the biblical flood. The concept of rapid magnetic field reversals has been linked to the creationist theory that runaway plate subduction occurred during Noah's flood. Such rapid (month long) variation contradict measurements of the conductivity of the Earth's mantle.

Such ideas are inconsistent with the basic physics of magnetism. While short term variations have been shown to be due to a variety of factors, the long-term (million year) variation in field intensity (and even reversal in polarity) are modeled as due to changes in electric currents in the liquid outer core of the Earth.

Metascience critiques
Factors influencing probability of a research finding being true: prior probability, statistical power and statistical significance.

Discussions of Ioannidis:

Irrationalism and science
Kuhn, Popper, Feyerabend, Lakatos.

Acoustic transmissions and marine mammals
After the Heard Island Feasibility Test in 1991 established that acoustic transmissions could be detected around the globe, there was widespread concern among marine biologists and the public over the possible effects of acoustic transmissions on marine mammals (e.g., whales, porpoises, and sea lions). A lawsuit was filed in 1994 to stop the project, eventually leading to an out-of-court settlement where the scientists agreed to establish a Marine Mammal Research Program with an independent advisory board. The results of this research, published by the National Research Council in 2000, was inconclusive. It found no statistically significant effects, but left open the possibility that the data were inadequate. The permits were not renewed in 1999 and the scientists were required to remove their equipment from the seafloor. However, after a further environmental impact study, the Office of Naval Research issued a new authorization to resume the use of equipment off the coast of Kauai as part of the North Pacific Acoustic Laboratory (NPAL) project.

Some of the information that caused public concern was misleading, particularly the statement that the sources were transmitting at 195 decibels (dB). A sound level in decibels is the logarithm of a ratio of two pressures, the measured pressure and a reference pressure. The reference pressure in air is 20 micropascals (μPa) while that in water is 1 μPa. To convert a sound pressure level of 195 dB in water to the decibel equivalent in air, 26 dB must be subtracted, leaving 169 dB. However, the perceived loudness of a sound is related to its intensity, which is the power flowing through a unit area. This is reduced if the density or speed of sound in the medium are increased. Both are greater in water than air. To account for this difference, a further 35.5 dB must be subtracted from the sound pressure level, so 195 dB in water has the same intensity as 133.5 dB in air. A 195 dB source in water has an acoustic power of less than 260 watts, a factor of more than a million less than it would have in air. Finally, source levels are determined for a distance of one meter; if a source radiates isotropically, the pressure declines in inverse proportion to the distance.

The controversy over ATOC drew attention to the potential harm caused by a variety of human sources of noise, including airgun shots for geophysical surveys and Navy sonar. The actual threat depends on a variety of factors beyond noise levels, including sound frequency, frequency and duration of transmissions, the nature of the acoustic signal (e.g., a sudden pulse, or coded sequence), depth of the sound source, directionality of the sound source, water depth and local topography, and reverberation.

In the case of the ATOC, the source was mounted on the bottom about a half mile deep, hence marine mammals, which are bound to the surface, were generally further than a half mile from the source. This fact, combined with the modest source level, the infrequent 2% duty cycle (the sound is on only 2% of the day), and other such factors, made the sound transmissions benign in its effect on marine life.

Free-air anomaly
Rocks vary in density, and non-uniform density below the surface affects the gravitational acceleration above it. Small variations in gravity can be measured with a gravimeter. To extract meaning from the measurements, they must be corrected for various effects such as latitude and the motion of the survey instrument. Another is the altitude at which the measurement was made, since the force of gravity decreases as one moves away from Earth's center. This correction is known as the free-air correction because it ignores any matter between a reference level and the measurement point, as if the instrument were floating in the air.

The reference level is generally mean sea level or the geoid on land. This is approximately an ellipsoid because planetary bodies are flattened by their rotation, and the gravity on that surface computed using the International Gravity Formula. For limited surveys, the gravity measured at a point on a local datum is taken as a reference value.

For studies of subsurface structure, the Free-air anomaly is further adjusted by a correction for the mass below the measurement point and above the reference of mean sea level or a local datum. This defines the Bouguer anomaly.