[2] **viXra:1109.0038 [pdf]**
*submitted on 18 Sep 2011*

**Authors:** Markos Georgallides

**Comments:** 9 pages

This article explains the correlation between Euclidean Geometry , Complex Numbers and Physics .
A Straight line AB is continuous in Points between A and B [ i.e. all points between AB are the elements which fill AB ] , which Points are also , Nothing , Everything , and maybe Anywhere , without any Dimension , and one has to
pass the infinite points between A and B . A point C is on line AB only when exists CA+ CB = AB , or the whole AB is equal to the parts CA , CB , and this
is an equation , which differentiates geometries .
Since points have not any dimension and since only AB has dimension ( the length AB and for ÃC the length AC ) and since on ÃB exist infinite AC → AB , which
have infinite Spaces , Anti-Spaces and Sub-Spaces , then
1. Straight line AB is continuous with points as filling ( Infinitively divisible ) .
2. Straight line AB is discontinuous (discrete) with dimensional Units , ds =AB
as filling ( that is made up of finite divisible or indivisible parts the Monads ds )
or ds → AB / n , where n = 1 , 2 , → ∞ ) , and for n = ∞ then ds = 0 .
3. Straight line AB is discontinuous (discrete) with dimensional Units ds , or
ds = quantum = AB / n [ where n = 1,2,3 → ∞ , = ( a + b.i ) / n , Infinitively
divisible and keeping always the conservation of properties at end points A , B ]
as filling , and continuous with points as filling ( for n = ∞ then ds = 0 i.e.
a point ) . This is the Vector relation of Monads , ds , ( or , as Complex
Numbers in their general form , ds = a + b. i ) , which is the Dual
Nature of lines AB , ( discrete and continuous ) . So travelling on Points
( ds = 0 ) between AB one never comes to B , on the contrary travelling
with ds > 0 one comes in finite time .
4 . Achilles has to pass every point of line AB which is then as passing from
the starting point A , ds =0 , where Velocity of Achilles is v(A) = ds/dt = 0 .
The same happens for Tortoise at point B where Velocity v(T) = ds/dt = 0 .
On the contrary , Achilles passing AB on dimensional Units , ds , then Achilles velocity v(A) = ds/dt(A) is greater than that of Tortoise v(T) = ds / dt(T) .
Since in PNS , v = ∞ , T = 0 , meaning infinite velocity and Time not existing , then
Arrow AB in [PNS] is constant because AB = ds = Constant = u . 0 = ∞ . 0 Straight line AB is discontinuous (discrete) with dimensional Units ds = AB / n
where n = 1 → ∞ and continuous with points [ n = ∞ ] . Continuously on AB happens also with all discrete ds , ( This is the Dual Nature of lines ( Geometry ), discrete and continuous ) .
Monads ds = 0 → ∞ are Simultaneously , actual infinite ( because for n = ∞ then ds = [ AB / n = ∞ ] = 0 i.e. a point ) , and potential infinite , ( because for
n = 0 then ds = [ AB / n=0 ] = ∞ i.e. the straight line through AB .

**Category:** Mathematical Physics

[1] **viXra:1109.0034 [pdf]**
*submitted on 16 Sep 2011*

**Authors:** Giuliano Bettini

**Comments:** 24 pages.

There is a lot of chattering on the Internet about Tesla waves, vacuum energy, scalar waves and so
on. Professor Meyl says he has a complete theory, experimental evidence and apparatus on these
waves. In a theoretical paper Van Vlaenderen introduced a generalization of classical
electrodynamics for the prediction of scalar field effects. It is said the Monstein has demonstrated
the physical existence of such scalar waves. NASA in a report seems to consider such waves as a
promising item to be studied. Some other papers appeared in arXiv.
I’ve already showed that such waves are a consequence of “generalized” Maxwell fields which
simply mean space time analytic functions not limited by the Lorenz gauge condition, but accepted
instead in a wide sense.
In this paper I remember my ideas on these waves, together with my doubts about their physical
existence. In fact, the deduction of the scalar waves equations, together with their physical
interpretation, in my opinion demonstrates nothing about the physical existence of scalar waves.
I discuss the experiment of Monstein, and suggest some other experiment.
Obviously I think that the lack of demonstration of the existence doesn’t mean the demonstration of
inexistence.

**Category:** Mathematical Physics