User:Marshallsumter/Radiation astronomy2/Transformations

Def. "the replacement of the variables in an algebraic expression by their values in terms of another set of variables; a mapping of one space onto another or onto itself; a function that changes the position or direction of the axes of a coordinate system" is called a transformation.

Chemical transformations
Def. a transformation that "describes only those changes that are involved in converting the structure of a substrate into that of a product, regardless of the reagent or the precise nature of the substrate, or (with some exceptions) the mechanism" is called a chemical transformation.

Def. "a process that leads to the chemical transformation of one set of chemical substances to another" is called a chemical reaction.

Phase transformations
Def. a "component in a material system that is distinguished by chemical composition and/or physical state (solid, liquid or gas) and/or crystal structure" is called a phase.

Def. a transformation from one phase to another is called a phase transformation.

Anatase to rutile transformations
"Titanium dioxide occurs as two important polymorphs, the stable rutile and metastable anatase. [...] Anatase transforms irreversibly to rutile at elevated temperatures."

Lorentz transformations
The Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity (v) relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity.

The most common form of the transformation, parametrized by the real constant $$v,$$ representing a velocity confined to the $x$-direction, is expressed as $$\begin{align} t' &= \gamma \left( t - \frac{vx}{c^2} \right)  \\ x' &= \gamma \left( x - v t \right)\\ y' &= y \\ z' &= z \end{align}$$ where $(t, x, y, z)$ and $(t′, x′, y′, z′)$ are the coordinates of an event in two frames with the origins coinciding at $t$=$t′$=0, where the primed frame is seen from the unprimed frame as moving with speed $v$ along the $x$-axis, where $c$ is the speed of light, and $ \gamma = \left ( \sqrt{1 - \frac{v^2}{c^2}}\right )^{-1}$ is the Lorentz factor. When speed $v$ is much smaller than $c$, the Lorentz factor is negligibly different from 1, but as $v$ approaches $c$, $$\gamma$$ grows without bound. The value of $v$ must be smaller than $c$ for the transformation to make sense.

Expressing the speed as $ \beta = \frac{v}{c},$ an equivalent form of the transformation is $$\begin{align} ct' &= \gamma \left( c t - \beta x \right) \\ x' &= \gamma \left( x - \beta ct \right) \\ y' &= y \\ z' &= z. \end{align}$$

Hypotheses

 * 1) Being repelled by the Earth is a lofting technology.