- #1
kmarinas86
- 979
- 1
I have noticed something quite peculiar.
If you have equal numbers of e+ and e- charge, there will be more "force pairs" between opposite charges than there are between like charges.
Generally speaking, if X is the number of e+ charges and Y is the number of e- charges, then number of "force pairs" between opposite charges is X*Y, and the number of "force pairs" between like charges is X*(X-1)/2 + Y*(Y-1)/2
When X=Y, as X and Y both get larger, the % difference between both figures approaches 0. A difference of 0 can be obtained also from certain combinations of X and Y. The simplest case is where you have 3 e+ charges and 1 e- charge [i.e. (X,Y)=(3,1)], or conversely, 3 e- charges and 1 e- charge [i.e. (X,Y)=(1,3)].
If
X*Y > X*(X-1)/2 + Y*(Y-1)/2 [i.e. opposite charge "force pairs" > like charge "force pairs"]
2*X*Y > X*(X-1) + Y*(Y-1)
0 > X*(X-1)+ Y*(Y-1) - 2*X*Y
0 > X^2 - X + Y^2 - Y - 2*X*Y
X + Y > X^2 + Y^2 - 2*X*Y
(X+Y) > (X-Y)^2
If
X*Y = X*(X-1)/2 + Y*(Y-1)/2 [i.e. opposite charge "force pairs" = like charge "force pairs"]
(X+Y) = (X-Y)^2
Y=(2*X+1±sqrt(8*X+1))/2 [solution for solving Y in terms of X - quickmath.com]
All integer solutions for X and Y in this case are pairs of triangular numbers which are next to each other on the sequence "1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...", the sum of each results in a square, beginning with 1+3=4.
If
X*Y < X*(X-1)/2 + Y*(Y-1)/2 [i.e. opposite charge "force pairs" < like charge "force pairs"]
(X+Y) < (X-Y)^2
Knowing that opposite charges attract and like charges repel, it would appear that any electrical neutral system (i.e. consisting of equal positive and negative charge) may be "self-attracting" on the basis of electric forces, provided that the distances between charges is randomized. If an electrically-neutral system suddenly stops collapsing, then it would appear that the forces between like charges must have caught up with the forces between opposite charges. What causes this is probably a growing magnetic field component of the Lorentz force that begins to overtake the electrical component, where the like charges co-gyrate around an axis (corresponding to the magnetic attraction seen between two parallel e- currents) while opposite charges counter-gyrate.
Not only does the above indicate that it is quite possible from electrical forces alone to have some residual net attraction for electrically-neutral bodies, you could have situations where like charges could attract electrically so as long as they actually consisted of a certain number of both e- and e+ of charges satisfying one of the conditions provided above, which is:
(X+Y) > (X-Y)^2
Again, where:
X is the number of e+ charges
Y is the number of e- charges
With the added condition that X does not equal Y.
If we fix "X-Y" to a constant (i.e. constant=X-Y), by increasing X and Y by equal amounts, X-Y as a percentage of X+Y decreases, and the result is that the difference between X+Y and X-Y reaches a proportionality with non-signed sum of charges X+Y.
Of course, the formula requires sufficiently random charge distributions to have any direct connection with whether a given mass will either expand, contract, or remain at steady-state. Otherwise, one must obviously use more complicated calculations.
Whatever you might think of the above math, the fact that for equal numbers of opposite charges, more "force pairs" exist between opposite charges than between like charges, which suggests that supposedly charge-neutral objects will exert unusual "attractive" forces. Or perhaps this effect is so usual, that we call it by another name: Gravity?
Question: Has this apparent asymmetry ever been recognized in peer-reviewed physics research? Or am I just barking up a new tree?
If you have equal numbers of e+ and e- charge, there will be more "force pairs" between opposite charges than there are between like charges.
Generally speaking, if X is the number of e+ charges and Y is the number of e- charges, then number of "force pairs" between opposite charges is X*Y, and the number of "force pairs" between like charges is X*(X-1)/2 + Y*(Y-1)/2
When X=Y, as X and Y both get larger, the % difference between both figures approaches 0. A difference of 0 can be obtained also from certain combinations of X and Y. The simplest case is where you have 3 e+ charges and 1 e- charge [i.e. (X,Y)=(3,1)], or conversely, 3 e- charges and 1 e- charge [i.e. (X,Y)=(1,3)].
If
X*Y > X*(X-1)/2 + Y*(Y-1)/2 [i.e. opposite charge "force pairs" > like charge "force pairs"]
2*X*Y > X*(X-1) + Y*(Y-1)
0 > X*(X-1)+ Y*(Y-1) - 2*X*Y
0 > X^2 - X + Y^2 - Y - 2*X*Y
X + Y > X^2 + Y^2 - 2*X*Y
(X+Y) > (X-Y)^2
If
X*Y = X*(X-1)/2 + Y*(Y-1)/2 [i.e. opposite charge "force pairs" = like charge "force pairs"]
(X+Y) = (X-Y)^2
Y=(2*X+1±sqrt(8*X+1))/2 [solution for solving Y in terms of X - quickmath.com]
All integer solutions for X and Y in this case are pairs of triangular numbers which are next to each other on the sequence "1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...", the sum of each results in a square, beginning with 1+3=4.
If
X*Y < X*(X-1)/2 + Y*(Y-1)/2 [i.e. opposite charge "force pairs" < like charge "force pairs"]
(X+Y) < (X-Y)^2
Knowing that opposite charges attract and like charges repel, it would appear that any electrical neutral system (i.e. consisting of equal positive and negative charge) may be "self-attracting" on the basis of electric forces, provided that the distances between charges is randomized. If an electrically-neutral system suddenly stops collapsing, then it would appear that the forces between like charges must have caught up with the forces between opposite charges. What causes this is probably a growing magnetic field component of the Lorentz force that begins to overtake the electrical component, where the like charges co-gyrate around an axis (corresponding to the magnetic attraction seen between two parallel e- currents) while opposite charges counter-gyrate.
Not only does the above indicate that it is quite possible from electrical forces alone to have some residual net attraction for electrically-neutral bodies, you could have situations where like charges could attract electrically so as long as they actually consisted of a certain number of both e- and e+ of charges satisfying one of the conditions provided above, which is:
(X+Y) > (X-Y)^2
Again, where:
X is the number of e+ charges
Y is the number of e- charges
With the added condition that X does not equal Y.
If we fix "X-Y" to a constant (i.e. constant=X-Y), by increasing X and Y by equal amounts, X-Y as a percentage of X+Y decreases, and the result is that the difference between X+Y and X-Y reaches a proportionality with non-signed sum of charges X+Y.
Of course, the formula requires sufficiently random charge distributions to have any direct connection with whether a given mass will either expand, contract, or remain at steady-state. Otherwise, one must obviously use more complicated calculations.
Whatever you might think of the above math, the fact that for equal numbers of opposite charges, more "force pairs" exist between opposite charges than between like charges, which suggests that supposedly charge-neutral objects will exert unusual "attractive" forces. Or perhaps this effect is so usual, that we call it by another name: Gravity?
Question: Has this apparent asymmetry ever been recognized in peer-reviewed physics research? Or am I just barking up a new tree?