*A short answer of mine.*

First *whats potential*, before *whats gauge potential*.

A potential is the variable: **energy**. ( — Energy in its various forms eg *per* unit charge or unit mass, known as; electric potential vs gravitational potential ).

*All energy are integration of vector-field quantity*, so

*Force is the vector field quantity whose integration is energy*.

We say; *Force is the potential gradient of energy or potential*. ( — and this potential gradient which is a *derivative* of a higher variable, it could be both *negative* and *positive*)

Then we say also, in Physics, *Force per unit mass or unit charge*? Like we did that for energy. So this time you say electric field vector or gravitational field vector. Like Force was *positive* or *negative* gradient (of energy), Field (a force or vector per unit charge or mass) is *negative* or *positive* potential gradient.

Potential was, as said above, *energy per unit mass or charge*. So, we see that, in defining the higher quantity *energy* or *potential* (higher therefore closer to action, hence more fundamental or unified) we have to INTEGRATE the *lower variable*, here, Force, Field or (Any ) 3-vector. This entails therefore arbitrariness into the Physical solution when we solve for these quantities. These physical problems, as they involve differentials or integration, leads to a differential equation. Under further suitable physical conditions called eg laws of nature or physics, become whats called a wave-equation or for *particles*, *equation of motion*. We can say equation of motion for particles or equation of motion for waves if they are separate.

Now that we understand *what are potential, field, vector and gradient and integral in relation to each other,* comes requirements called as *symmetry* or laws of nature or laws of physics or in simple, boundary conditions *to these* differential equations known as, wave equation or equation of motion of particles OR waves. ( — which are separate so far )

These equations constrained by the conditions or restrictions which are *attributes of physical observation*, must therefore unite these variables (*potential, field*) into one entity which would *satisfy* the* wave or particle* equations of motion, the differential equations of motion in PARTICULAR ways only, known as Laws of Nature or Physics. So they become, from their **3**–*vector* or *scalar* attributes, **4**–*vectors* (or still higher, *Tensors*).

One word of concept, the *potential* is also a *field* but a *scalar*. So instead of (*potential*, *field*) we can write (*scalar*, **3**–*vector*) components of the **field**, that is, (**scalar** *potential*, **vector** *potential*) which as you can see in a 4-dimensional world; 1+3 = 4 components.

Then comes the *conditions* or inter-relations between these vector and scalar and their differential and integrals. ( — again known as a **theory** or *equation of motion*)

These *conditions* have an *arbitrariness* built into them,** puchho kyon? ***Munna bhai* says: *because there are integration*. How did Munna bhai figure that out?

He was in a bar dancing with a lady Physicist from Munich, who had come to Mumbai for a conference in Particle Physics.

The method-of-integration has a constant of integration, any one?

In going from *lower variables* such as **velocity** and **momentum** we gradually integrate them to find the higher, closer-to-action or fundamental variables, and incurr *arbitrariness* into our understanding.

But not all of these solutions are *physical* in nature, they are merely *invalid* mathematical solutions even if *not necessarily* trivial solutions. To remove these arbitrary ness is whats called **Gauge Condition**. That is, to chose the *right* scalar and vector *potential* among all solutions, only that, which would be Physically *correct*.

Therefore a *gauge* or *gauge* *potential* ( — or a *gauge field scalar* or *gauge field vector*) are what’s *more* fundamental and closer to a **theory**. *Theory* is a jargon among Theoretical Messiahs for the longer version “equation of motion“. When *two kinds* of equation of motion, one for the **wave** and one for the **particle** are united into one, a feat called as **unification **we obtain equations whose specific example is **Schrodinger Equation** also called a **wave equation of motion**, with the implicit understanding that, such are *conditions for particles and waves* both, rather than *just one, either of them*.

Categories: approach to understand Universe, author, basic physics, calculus of variation, Communication, Education, Ideas, manmohan dash, Mathematics, Methods, particles and their properties, Physics, quantum mechanics, Relativistic Quantum Mechanics, Relativity, Research, Research Article, Research Progress, string theory ideas, Teaching, Thoughts on Science

## Leave a Reply