Aether Dynamics

Magnetic force: Combining drag force and Bernoulli force of ether dynamics

2009-04-25T17:32:00.043+08:00

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 20^th 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.

If you find any flaws of the the theory, please kindly advise me; it's grateful

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.

IQ test for PHYSICISTS

How to correctly measure an unknown length with a clock

2009-04-25T09:23:00.002+08:00

by Ka-In Yen,
Chungli city, Taiwan
yenkain@yahoo.com.tw

Example 1: Tom sits in a train which moves at a constant velocity. Tom need to measure the distance from city A to city B. Obviously, He can not use a ruler to do this. Fortunately, Tom has a clock, and he cleverly figures out a method which allows him to measure the distance with a clock. Tom has no idea about the speed of the train, but he knows that a railroad bridge's length is L. When the train passes the bridge, Tom records the time difference, t0, of two ends of the bridge; Next, he records the time difference, t1, between city A and city B. Finally, Tom does his calculation.
```
      distance AB = L * t1 / t0.

Surprisingly, Tom finds the negative of the length contraction.

  |     Tom, clock
  |     Train 
  |     -->
  |         ----         --------------------
  |         bridge(L)    city A             city B
  +----------------------------------------
  Frame S(ground)   
               Fig. 1
```
Discussion: The most primitive way to measure a length is a ruler. But in many situation, a ruler is fail to measure; for example, a tall tree, or a long distance. A lot of alternate methods are invented for measuring length, and most of them need a known length as reference. In example 1, a measuring method is proposed: a clock can be used to correctly measure an unknown length without contraction.
Conclusion: Example 1 shows: to an intelligent life form, the length contraction is a result of wrong measuring method.

P.S. This paper was posted to sci.physics

The proof of mass vector

2009-04-25T08:51:00.002+08:00

Ka-In Yen
yenkain@yahoo.com.tw


Introduction:
In this paper, we will prove that linear mass density and
surface mass density are vector, and the application of mass
vector is presented.

1. The unit of vector.

In physics, The unit of three-dimensional cartesian coordinate
systems is meter. In this paper, a point of 3-D coordinate
system is written as

    (p1,p2,p3) m, or (p:3) m

and a vector is written as

    <a,b,c> m, or <a:3> m

or

    l m<i,j,k> = <a,b,c> m

where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
and <i,j,k> is a unit vector which gives the direction of
the vector.

For three reasons, a magnitude of a vector can not add to a
scalar:
    i) The magnitude belongs to the set of vector; it's a
portion of a vector. Scalar belongs to a field.
   ii) The magnitude is real non-negative number, but scalar
is real number.
  iii) The unit of magnitude is meter, but scalar has no unit.
This is a major difference between physics and mathematics.
5m+3 is meaningless.


2. Linear mass density is a vector.

The mass of a string is M kg, and the length of the string
is l m<i:3>. Where l m is the magnitude of the length, and
<i:3> is a 3-D unit vector which gives the direction of the
string. Then the linear mass density of the string is:

    M/(l<i:3>)=(M/l) (kg/m)<i:3>

The direction, <i:3>, is not changed by "division", so we
can move <i:3> from denominator to numerator. A direction
is changed by -1 only. A proof is found in Clifford algebras:

[Proof]
    k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2]
             =(k/l) <i,j,k>
    where l is the magnitude of <a,b,c>, and <i,j,k> is the
unit vector of <a,b,c>.
[Proof]


3. Surface mass density is a vector.

A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3>
and <j:3> are unit vectors. The area vector of the parallelogram
is the cross product of these two vectors.

    l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3>
                       = lh abs(sin(theta)) (m^2)<k:3>

Where theta is the angle between <i:3> and <j:3>. <k:3> is
a unit vector which is perpendicular to <i:3> and <j:3>.
For AXB=-BXA, an area has two directions.

We can divide the area vector by the length vector.

    lh*abs(sin(theta))<k:3>/[l<i:3>]
   =h<i:3>X<j:3>/<i:3>
   =h(<i:3>X<j:3>)X<i:3>
     (The direction, <i:3>, is not changed by "division", and
      the division is replaced by a cross product.)
   =-h<i:3>X(<i:3>X<j:3>)
   =-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)]
      (where o is dot product.)
   =-h(cos(theta)<i:3>-<j:3>)
   =h(<j:3>-cos(theta)<i:3>) m

The result is a rectangle, not the original parallelogram. We
can test the result.

    h(<j:3>-cos(theta)<i:3>)Xl<i:3>=lh m^2<j:3>X<i:3>

The magnitude of the area vector is conserved, but the direction
is opposite.

The mass of a round plate is M kg, and the area vector is
A m^2<i:3>; then the surface mass density is

     M kg/(A m^2<i:3>)=M/A (kg/m^2)<i:3>


4. Mass vector in physics.

Mass vector has been found in two equations: 1) the velocity
equation of string. 2) Bernoulli's equation.

i) For waves on a string, we have the velocity equation:

   v=sqrt(tau/mu).  v is velocity of wave, tau is tension
   applying to string, and mu is linear mass density of
   string. We can rewrite the equation:

   mu=tau/v^2.

   In the above equation, the mu is parallel to tau, and both
   of them are vector.

ii) Bernoulli's equation is:

   P + k*v^2/2=C  (P is pressure, k is volume density, and v is
   velocity. Here we neglect the gravitational term.)

   Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's
   equation(where <i:3> is a unit vector),

   P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3>
   F<i:3> + L<i:3>*v^2/2=C*A<i:3>
     (where F is the magnitude of force, and L is the magnitude
      of linear mass density.)

These two equations are well used in the theory "Magnetic force:
Combining Drag force and Bernoulli force of ether dynamics."

This paper was posted to sci.physics.

The similarity between light and wave on string

2009-04-25T08:25:00.005+08:00

by Ka-In Yen,
Chungli city, Taiwan
yenkain@yahoo.com.tw

Abstract: Time dilation and length contraction are introduced to explain the null result of Michelson-Morley experiment. In this paper, light and wave on string are compared to find their similarity, and a model of the propagation of light, without time dilation and length contraction, is suggested.
Wave on string:
Example 1: Two equal strings are put on a round table. A shematic diagram is shown as figure 1(a).
```
             |                                |
             |                                |
             |                                |
             |                                |
             +---------              ---------+
                 (a)                   (b)
                         Figure 1
```
The length of string is L. The tension on string is tau. The mass of string is m, and linear density is mu=m/L. Then, the speed of wave on string is v=sqrt(tau/mu).
Two pulses of wave are simultaneously produced on the connective node of two strings; One pulse travels along east string, and the other pulse travels along north string. These two pulses will hit the end of string and reflect back to the connective node in the same time, t=2L/v. Then, the round table is turned 90 degrees as Figure 1(b), the above experiment is repeated, and we will get the same result, t=2L/v.
In this simple example, time dilation and length contraction are not required to interpret the result. Comparing example 1 to Michelson- Morley experiment, the similarity are extracted. Based on their similarity, a model of the propagation of light, without time dilation and length contraction, is suggested.
The silk of force(distance force): There are four forces in physic world: gravitational force, electromagnetic force, strong force, and weak force. Silk is a abstract description to the distance force between particles. A silk of force has three components: two elementary particles on each end of the silk, and the silk itself. A schematic diagram is shown as figure 2.
```
       (particle 1) *-----------------------* (particle 2)
                          silk of force

                         Figure 2.
```
If there are n electrons, then the electromagnetic force between electrons can be abstractly described by n(n-1)/2 silks.
Two electrons are separated by a distance R. The repulsive force of these two electrons is tau=K*e^2/R^2; where K is a constant, and e is the charge of electron. The potential energy is PE=K*e^2/R, and the linear density is mu=PE/c^2/R; where c is the speed of light. We can get the propagation speed of wave on silk is
```
     v=sqrt(tau/mu)=c.                (1)
```
Light wave is a wave on the silk of force. A light wave has frequency f. The photon energy is E=hf; where h is Plank's constant. The tension (average force of light wave) is tau=E/landa. The average linear density of photon is mu=E/c^2/landa. Then, the speed of photon is v=sqrt(tau/mu)=c. It is same to equation (1).
Conclusion: Based on example 1, a model of the propagation of light is suggested in this paper. Photon is a wave on silk of force. The propagation speed of wave on silk is c. Based on this model, time dilation and length contraction are not required to interpret the null result of Michelson- Morley experiment.

P.S. This paper originally was posted on internet: sci.physics.relativity

Vector by vector division

2009-04-25T08:21:00.001+08:00

>> jose said：
>> Quaternions are an extension of complex number, 
>> as you know and, any way we can divide them, we are 
>> dividing quaternions and not vectors. The result of 
>> dividing two quaternions is a quaternion too.  If 
>> we divide two quaternions Q1/Q2 the result is a 
>> quaternion Q, as you know but not for all case we 
>> have that Q1 = Q*Q2. 


Dear Jose, 
I am very glad to hear from you again, and thank 
you for your comment. Perhaps we should call them: 
dot division and cross division; just like dot product 
and cross product. 

1) dot division /.
A /. B =  (A dot B) / B^2      or
A /. B = A^2 / (A dot B)
where A and B are two vectors.

MATLAB, a famous software, had implemented dot division. 

2) cross division /x
A /x B =  (A x B) / B^2      or
A /x B = A^2 / (A x B) 

Physicists have been doing  vector-by-vector-division 
for a hundred years. The equation of magnetic force 
is "vector division by vector".

F=iLXB   (X is corss product).
L is a length vector; assuming L=l < i > m, < i > is a 3D 
  unit vector.
B is magnetic flux density. Its unit is tesla, or Wb/m^2. 
Wb, Weber, is the unit of  magnetic flux. Assuming
   B= b < j > (Wb/m^2),   < j > is a 3D unit vector.
Since B is a vector of surface density, we can rewrite it:
   B= (b/< j >) (Wb/m^2),   < j > is moved to denominator.

   LXB= l < i > X b < j >  m(Wb/m^2)
         = (lb < i > / < j >)  (Wb /m) 

It's VDV.

test

2009-04-25T07:28:00.006+08:00