Cartesian Models |

particle | a | velocity | c | graph |

ground-state hydrogen atom | $(0, 0, 0)$ | |||

ground state proton | $(?, ?, 0)$ | |||

magnetically excited proton | $({\sf{v}}_{x}, ?, 0)$ | 1 | ||

ground-state electron | $(?, {\sf{v}}_{y}, 0)$ | 1 | ||

electromagnetically excited hydrogen atom | $({\sf{v}}_{x}, {\sf{v}}_{y}, 0)$ | |||

excited hydrogen atom | $({\sf{v}}_{x}, {\sf{v}}_{y}, {\sf{v}}_{z})$ |

## Unitary Gas Molecules

- note that even the fine-structure analysis of atomic hydrogen requires the use of just one type of stereochemical quark, i.e. so far shown as levo quarks
- so it is possible to model another type of hydrogen hydrogen by substituting dextro quarks for levo quarks, i.e. the two types are levo-rotary and dextro-rotary hydrogen
- to make a unitary model of molecular hydrogen gas, we need two distinct hydrogen atoms
- traditionally, we meet this requirement to be distinguishable by saying that different atoms are distinct from each other because they are in different places. But, by the premise of WikiMechanics, we cannot satisfy Pauli's exclusion principle by resorting to a spatial explanation.
- so instead we use stereo chemical quarks to distinguish the hydrogen atoms in hydrogen gas
- then we can satisfy Pauli's principle even for the form of hydrogen where spins are alligned
- small differences in the constants
*k*(levo) and*k*(dextro) can account for the energy differences between*ortho*and*para*forms of hydrogen gas. - Now $\begin{align} E_{\sf{\, chiral}} \equiv \frac{ \; s N^{\large{โ}} }{ \, {\mathrm{n}}^{6} } k_{\sf{chiral}} \end{align}$
- Change to?

$\begin{align} E_{\sf{\, chiral}} \equiv \frac{ \; s }{ \, {\mathrm{n}}^{6} } \left( N^{\large{โ}} k_{\sf{levo}} + N^{\large{โน}} k_{\sf{dextro}} \right) \end{align}$

- fix this

Nouns | Definition | |

Honey Constants | ${\sf{\text{Supplementary Fine Structure Constants}}} \\ k_{\sf{\, dextro}} \! = \; ? {\sf{ \; (neV) \; \; \; \; and}} \; \; \; \; k_{\sf{\, levo}} \! = \; ? {\sf{ \; (ยตeV) }}$ | 1-11 |

## Diatomic Hydrogen Molecules

- modeled as a two-body mechanical system in a three dimensional, isotropic, homogeneous space
- for spatial homogeneity, both bodies must have integer quantum numbers
- for spatial isotropy, both bodies must be at least a large as atoms
- for spatial isotropy, the description of chromatic sensation is glossed-over. Direct discussion about the categorical description of colour are overlaid by calibrated measurements
- measurements of displacement and elapsed time are what space time descriptions are made from

- knowledge about the direction of particle momentum is obtained by what can be measured: the velocity. But this vector is still constrained by quantization and conservation rules
- the direction of motion $\hat{p}$ is defined from $\mathsf{\overline{v}}$ in the Cartesian

$\begin{align} \hat{p} \equiv \begin{cases} (0, 0, 0) &\sf{\text{if}} \; {\large{\parallel}} \mathsf{\overline{v}} {\large{\parallel}} = 0 \\ { \mathsf{\overline{v}} } \; {\Large{/}} \, { {\large{\parallel}} \mathsf{\overline{v}} {\large{\parallel}} } &\sf{\text{if}} \; {\large{\parallel}} \mathsf{\overline{v}} {\large{\parallel}} \ne 0 \end{cases} \end{align}$

- in the new space, $\hat{p}$ has no manifest relationship with $\overline{\rho}$. But the norm of the momentum, $p$ is the same in both quark-space and Euclidean-space. So in the glossy descriptions we write $\overline{p} = p \hat{p}$. Then, in the Euclidean/Cartesian system, rules about the conservation of momentum are expressed by vector sums of this quantity.
- so the smallest two-body system that is fully three-dimensional is diatomic hydrogen, $\mathbf{H_{2}}$
- photons?
- subatomics?
- for ortho/para freedom or choice in view of Pauli's principle, let $\mathbf{H_{2}}$ contain one each of a levo-rotary and dextro-rotary hydrogen atom
- Let one of the hydrogen atoms, $\mathbf{H_{o}}$ or? $\mathbf{H}_{\sf{F}}$, provide a reference frame for describing the other hydrogen atom, $\mathbf{H}$. The position of this atom is called the
*spatial origin*. - the handedness of the coordinate system depends in the chiral character of the hydrogen atom selected a the spatial origin. E.g., if $\mathbf{H}_{\sf{F}}$ is dextro-rotary, then it is called a right-handed coordinate system.
- The polar axis of the reference frame is noted by $\hat{z} \equiv (0, 0, 1)$. The abscissa is written as $\hat{x} = (1, 0, 0)$, and the ordinate is $\hat{y} = (0, 1, 0)$. We generally assume that the space has a Euclidean metric and that $\hat{x}$, $\hat{y}$ and $\hat{z}$ are all orthogonal to each other.
- The total angular momentum vector of $\mathbf{H_{o}}$ is noted by ${\rm{\overline{J}}}$. We say that ${\rm{\overline{J}}}$ and $\hat{z}$ are aligned or
**parallel**to each other. By our premise, we prefer to avoid mysteriously received knowledge about length and lines. So to be as explicit as possible, for WikiMechanics this means that ${\large{\parallel}} \, {\rm{\overline{J}}} \, {\large{\parallel}} = {\rm{J}}_{z} = \frac{h}{\rm{2} \pi} \sqrt{ \, ๐ \, \left( ๐ + \rm{ 1} \right) \; \vphantom{1^{2}} }$ where $๐$ is the total angular momentum quantum number. - The separation vector, $\overline{r}$, notes the position of $\mathbf{H}$.
- The velocity of $\mathbf{H}$, in a frame provided by $\mathbf{H_{o}}$, is noted by the vector $\mathsf{\overline{v}}$. And the net displacement over one atomic cycle, of any atom, is always along its own polar axis. So if ${\mathsf{\overline{v}}} \ne ( 0, 0, 0 )$, then it also indicates the direction of the total angular momentum vector of $\mathbf{H}$. In general, it is not aligned with the polar axis of the reference frame.
- In principle, $\overline{r}$ and $\mathsf{\overline{v}}$ are established by measurements of sensation, and nothing else. Space itself is defined as an elaborate way of organizing and storing experimental data. And empty space is not defined.
- the force binding hydrogen atoms together into the ground-state of $\mathbf{H_{2}}$ is accurately represented by a chemical bond composed of five chemical quarks and two electrons

$\large{\mathbb{B}}\small{ \sf{( 1) }} \equiv \, \,${ {e^{โ}, , } , {e^{โ}, , }, }

## Ground-state Model of Atomic Hydrogen

- three spatial dimensions
- both atoms in ground-state, so no temporal dimension required because there is no net atomic motion, $\mathbf{H}$ is static
- $\mathsf{\overline{v}} = ( 0, 0, 0 )$
- both atoms just do subatomic vibrations back and forth along the axes of their angular momenta
- in general, the separation vector can take on any values for Cartesian coordinates; $\overline{r} = ( x, y, z )$

## Hydrogen Excited by Electromagnetic Field

- two spatial dimensions plus time coordinate in lieu of polar axis
- $\overline{r} = ( x, y, 0 )$
- $\mathbf{H}$ has uniform linear motion along the axis of the momentum of $\mathscr{F}$ which is limited to the xy plane by electromagnetic requirement. So no strange quanta or weak forces in this model.
- $\mathsf{\overline{v}} = ( \mathsf{v}_{x}, \mathsf{v}_{y}, 0 )$

## A Two-dimensional Model of Hydrogen Excited by Electromagnetic Field

## Experimental

- no radiative transitions between homonuclear ortho and para forms (p.2 Habart)
- electronic transitions, rotational spectra, vibrational spectra, Raman

Related WikiMechanics articles.