S.Sesselmann (27/07/2015) Absolute potential

[Steven Sesselmann]

We start with the following statement;

Relative velocity is limited to the speed of light,
the only cause of relative velocity is relative potential,
therefore relative potential is limited.

Relative velocity is limited to the speed of light
The first part of my statement is well known from special relativity and has been tested multiple times by experiment and found to be verifyable and true.

the only cause of relative velocity is relative potential,
The second part states that potential is the only cause of a bodies motion, this is true weather an object is dropped, pushed or pulled, these actions which cause relative motion are directly or indirectly rooted in potential.

therefore relative potential is limited.
The final part of this statement says that when the first and second axiom is true, then there must be a universal limit to potential.

Potential
It is important not to confuse the term potential with potential energy, potential energy is the stored energy of a body by way of elevation in a potential field, while potential is the currently unrealized ability. Potential is usually denoted as \(\Delta V \) or \( \Delta U \), while potential energy is usually written as \( U_p \).

Proof that potential is limited;

Potential energy, corrected for gravitational redshift is;

\[ U_p = - \frac{GMm}{r\sqrt{1-\frac{2GM}{rc^2}}} \]

divide by mass (m) to get the raw potential

\[ \Delta U = - \frac{GM}{r\sqrt{1-\frac{2GM}{rc^2}}} \]

break it up (take out gamma)

\[ \Delta U = - \frac{GM}{r} * \frac{1}{\sqrt{1-\frac{2GM}{rc^2}}} \]

we understand that the Schwartschild radius is approached when escape velocity is equal to c

\[ \sqrt{\frac{2GM}{r}} - c = 0 \]

it follows that a potential limit is reached when

\[ \frac{2GM}{r} = c^2 \]

As the speed of light (c) is a constant, any increase in mass (M) implies an increase in radius (r)

Therefore the unrealised potential \(\Delta U \)between any Schwartzchild radius and infinity is absolute and constant with respect to all observers.

What does it mean?
Put simply it means that the difference in potential between the radius of a black hole and radius at infinity is presisely so large that the escape velocity is equal to the speed of light. As the saying goes "what goes up must come down".

Absolute potential implies that the observers own potential must lie somewhere on the absolute scale, so there must be a way to define it precisely.

Groundpotential theory sets out to explore the relationship between potential and velocity to the fullest.

[Steven Sesselmann]

To further back up my argument for an absolute and limited potential. let us do the dimensional analysis for gravitational potential.

We know from classical Newtonian physics that gravitational potential energy is:

\[ U_p = - \frac{GMm}{r} \]

we also know how to correct this Newtonian term with gamma to make it relativistic;

\[ U_p = - \frac{GMm}{r} * \frac{1}{\sqrt{1 - \frac{2GM}{rc^2}}} \]

the second term \( \gamma \) is a dimensionless factor, so it can be ignored for the purpose of dimensional analysis.

to convert potential energy to potential we divide by mass, in this case the lower case m.

\[ \Delta U = - \frac{GM}{r} \]

this gives us the dimensions as follows;

\[ \Delta U = - \frac{meter^3 * kilogram}{meter * kilogram * second^2} = - \frac{m^2}{s^2} = - \frac{m}{s} \]

So as the dimensional units for gravitational potential is speed, it seems self evident that gravitational potential like speed should be absolute and limited, else a theory would be inconsistent.

By definition the lowest gravitational potential value is at the Schwartzchild Radius and the highest gravitational potential is at infinity where it by definition goes to zero.

The argument here is that the size of any black hole (SR Radius) or the major radius (Size of Universe) is irrelevant, the standing potential between the SR radius and infinity is and must be constant.

So when described as a velocity \( \Delta U \) simply reduces to c.

Observer Domain

domain.png (33.78 KiB) Viewed 10934 times

It is now going to be relatively easy to prove that the dimension we call gravitational potential and measure in m/s is the exact same dimension we call electrical potential and measure in Volts.