Ka-In Yen
Chungli city, Taiwan and
yenkain@yahoo.com.tw
Abstract: In 1828, Cauch first gave the idea
of elastic ether. After nearly one hundred years development, elastic ether was
abandoned in the early of 20th century. In this paper, a new model
of ether-string is suggested. Two components of magnetic force are derived from this ether-string model: one is
drag force, the other Bernoulli force. To derive them, negative potential mass , and vector of mass are is introduced.
Electric force and linear density of two point charges q1 and q2.
Electric force:
Potential energy
Potential mass
Linear mass density
I am very sorry for a mistake here. The potential energy and mass are not vector. The linear mass density is a vector. Please refer to my paper: "The proof of mass vector."(2005/11/15)
π=3.14159...
R is distance between q1 and q2.
ε0 : the electric permittivity
μ0 : the magnetic permeability
c : the speed of light
(1)
Equation (1) is deduced from
Weber’s equation
c=1/
and
Poincare’s equation E=mc2, it tells that lights are waves on strings. Charged particles are linked by
ether-strings. For n charge particles, n(n-1)/2 ether-strings are required to
link them. The mass of ether-string
is m=PE/c2, and the linear density is
L=m/R. The potential mass can be positive or negative.
In the above calculation, mass vector is
used. This is an important difference between ether dynamics and fluid
dynamics. In fluid dynamics, atoms are free particles; in ether dynamics, mass is restricted in its ether string.
Magnetic force between two steady currents i1 and i2.
/////////// surrounding //////////////////
////////////////////////////////////////////
(+q1,0)
(-q1,v1)=(-i1,ds1)
___________________@_________________ wire 1
(+q2,0)
(-q2,v2)=(-i2,ds2)
________@_____________________________ wire 2
////////////////////////////////////////////
/////////// surrounding //////////////////
Fig. 1
In the Fig. 1, wire 1 and wire 2 are two electric current lines. The whole electric wire is neutral; for every drifting electron(-), there is a resting ion(+). On a small section of wire 1, the (-q1,v1) is charges and velocity of drifting electrons, and the (+q1,0) is charges of resting ions. The (-q2,v2) and (+q2,0) on wire 2 have the same definition. The surroundings and the two wires are considered to be the rest frame. The distance between q1 and q2 is R. i1 and i2 are currents; ds1 and ds2 are delta length.
Magnetic field produced by current i1 (Biot-Savart Law):
("×"
is cross product, or vector product)
Magnetic force on i2 :
A × (B × C)= (A。C)B - (A。B)C, where "。" is dot product(or scalar product). Then,
(2)
The first term is drag force, and the second term is Bernoulli force. This situation is similar to two submarines cruising parallel under the surface of water. According to fluid dynamics, these two submarines produce drag force and Bernoulli force.
Derivation of drag force
An electron is a connecting node of enormous ether-strings. A drifting electron pushes the ether-strings, and the drag force is derived:
(dm is delta mass of ether-strings, dt is delta time)
(dp is delta
momentum upon ether-strings)
(Fd is the
drag force upon electron)
In the Fig. 1, currents i1 and i2 are steady, and the electron drifting velocity and linear density of ether-string are steady too. You may notice that the above equation of drag force is different to the drag force equation of fluid dynamics.
In the Fig. 1, the surroundings are assumed to be neutral, static, and far away from (+q1, -q1) and (+q2, -q2). In the neutral and static surroundings, all electrons bound to atoms. Between the atom and (+q1, -q1) (or (+q2, -q2)), positive potential mass and negative potential mass of ether-strings exist; they are with same magnitude due to the short distance of electrons and protons in the atom. The summation of linear densities between the surroundings and (+q1, -q1) (or (+q2, -q2)) is zero, and the velocity effects are zeros too(refer to below calculation); so the surroundings is neglected. Only three bunches of ether string are calculated.
a) drag force of (-q1,v1) and (-q2,v2)
pair
b) drag force of (-q1,v1) and (q2,0)
pair
c) drag force of (q1,0) and (-q2,v2)
pair
a + b + c =
(3)
The first term is a drag force upon -q2, and the second term is a drag force upon -q1.
Derivation of Bernoulli force
The Bernoulli's equation is:
P1 and P2 are pressures;
ρ1 and ρ2 are volume densities. Neglecting the
surroundings, only three pairs of potential mass are considered. Let y1=y2,
the static term (
) is cancelled due to zero effect of velocity. Multiplying the
cross area A of ether-string on both sides, and re-writing it:
(F is force, L linear density, and C constant.)
In the above equation, the force and the linear mass density are perpendicular to the cross area of ether string, and both of them are vector.(2005/10/17)
In the fluid, all pressures upon a point from different directions are same. P*A can be applied to any surface with area A.
When
, then
; we have
Between wire 1 and wire 2, a mass river of ether-strings flows. In ether dynamics, a vector of linear density is used. Three bunches of ether strings are calculated:
a) To (-q1,v1) and
(-q2,v2) pair, we have
b) To (-q1,v1) and (+q2,0) pair, we
have
c) To (+q1,0) and (-q2,v2) pair, we
have
(4)
Combining equation (3) and (4), we have:
Magnetic force upon -q1
Magnetic force upon -q2
Fm2 is same to equation (2).
Conclusion
Although Einstein’s special theory of relativity is very successful, but author believes that scientists must scrutinize all possibilities before making the final conclusion. In this paper, the two components of magnetic force, drag force and Bernoulli force, are successfully derived from ether dynamics. But there are a lot of questions waiting for answer in ether dynamics; for example, the relative mass, and slower atomic clock on airplane etc, are well explained in the special theory of relativity.
Acknowledgement:
This paper is posted to sci.physics, and thanks to those who help me -- Flaws wanted.
