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## A Ground-State Proton

This article shows a few different ways of making spacetime descriptions of protons. It extends an earlier discussion that presents the proton as a bundle of quarks like this

Spacetime descriptions require a frame of reference which is noted by The frame is characterized by its helicity which is marked using a subscript like or The frame’s helicity is used to determine a phase for each quark. And for a ground state model of the proton, quarks in the front and back rows are required to be out of phase with each other. Then the proton has perfect phase symmetry. There are no anti-symmetric quark-pairs, so the proton can be represented by a pair of phase components written as

where

and

The two phase-components are shown separated from each other, and a rod connecting them represents the polar axis. Thus a ground-state proton is illustrated in a one-dimensional quark space.

For an isotropic Cartesian spacetime description of the proton, this clump of quarks is presumably whirling around the polar axis such that colors and shapes become indistinct. So we make a heuristic picture of a proton in spacetime as a greyish spheroid with a protruding arrow to represent the axis of rotation.

There are four down-quarks, and no up-quarks in the ground-state model. So in this configuration, the proton’s helicity is and we call it a spin down particle. The total angular momentum quantum number of the proton is

And its principal quantum number is

Recall that the spatial extent of any particle is characterized by its orbital radius which in-turn depends on the mechanical energy. This energy is observed to be (MeV). So the orbital radius of the proton is

(m).

This dimension is comparable to observations of the proton’s charge radius at (m). And both values are about a million times smaller than the Bohr radius of a hydrogen atom.

## A Proton in 1-Dimensional Space

We mark the polar-axis of a proton using the algebraic notation This axis is used to define the direction of the angular momentum vector. So in a particle-centered Cartesian frame, Following the usual graphic conventions, we draw this axis vertically, with the positive direction pointed towards the top of a page. By definition, the -component of the angular momentum is

This quantity is negative because the helicity of a ground-state proton is And so

The spatial character of the proton is described by its inner radius which is defined by

And its outer radius which is

For the unadorned proton and so But the wavevector of any particle is defined by

So for the proton, The wavenumber is defined by the norm of a wavevector. It is written without an overline as . Thus Moreover, the wavelength of any particle is given by

So for the proton too. We use this wavelength to describe the proton’s motion. If the frame F is inertial, then And for any particle P, the momentum is defined by

So the ground-state proton has no momentum. It is stationary, and in any inertial frame of reference.

### History of a 1D Proton

EthnoPhysics describes the history of a proton using an ordered chain of events noted by Events are repetitive so that the chain may be written as

where each repeated cycle is a bundle of quarks generically noted by

Any displacement of the proton during this history is defined by

But as shown above, the wavelength of a ground-state proton is zero. So too. The Cartesian coordinate of the event is given by

So for any And the position of the proton on the polar-axis does not change.

The history of a proton may be represented using a Cartesian plane where different bundles are illustrated in different locations along the temporal axis. Here is a diagram showing the event.

The period of any particle is defined by

A ground-state proton is stationary in any inertial frame, Dp

(s)

The time of occurrence for any specific event is given by a sum of periods.

So gives the elapsed time between consecutive events.

This is the finest possible resolution along the temporal axis because spacetime is quantized. Any measurements of must be at least this big.

## An Excited Proton

Next we wrap a naked proton with a field additional quarks. The extra stereochemical quarks give the proton a left-handed twist. Some down anti-quarks are included to flatten And the muonic quarks give the proton some spatial presence that is transverse to the polar axis. These extra quarks are all paired with each other in simple field quanta. Taken together, they comprise an electromagnetic field that is written as

This specific field is also used to model a hydrogen atom in its spin-down ground-state which is conventionally written as So the field is noted by

The additional muonic quarks bring red and green chromatic sensations into the description. So in quark-space, the model becomes two-dimensional. A grey rod is used to illustrate this new magnetic axis. Here is a short movie (jump) that gives a quick look around the model.

The quark coefficients of the excited proton give and all equal to zero. So the enthalpy of the chemical quarks in P is nil, and .

The inner radius of the excited proton is also zero because But so the excited proton’s outer radius is given by

For the excited proton discussed above, So we say that the proton is rotating. And while so the rotation has a left-handed character.

## A Proton in 2-Dimensional Space

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## A Proton in 2-Dimensional SpaceTime

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