Electromagnetic Acceleration calculation
« on: July 05, 2020, 07:57:39 PM »
Hello, I'm new here so please forgive if I haven't got things straight. Been reading the Wiki as recommended and I'm intrigued by the Electromagnetic Acceleration equation.
This is a limit of a more complex (and not yet final) expression as x approaches infinity, so this will only work when y is much greater than x - that is to say, when the vertical distance traveled is much greater than the horizontal distance traveled. Put another way, its accuracy will improve the closer the light ray is to vertical. Therefore, while it is not valid for short-range experiments, it can give an idea of how much sunlight would bend on its way to the Earth, for instance.

Where (0,0) is understood to be the point at which the light ray is horizontal (that is, the derivative of this function is zero).

Definition of terms:

x, y - co-ordinates in the plane of the light ray, where y is increasing in the direction of fastest decreasing Dark Energy potential, and x is increasing in the direction of the component of propagation of the ray which is perpendicular to y.

c - the speed of light in a vacuum.

β - the Bishop constant, which defines the magnitude of the acceleration on a horizontal light ray due to Dark Energy. When the theory is complete, attempts will be made to measure this experimentally.

It is believed that the bending of light does not simulate the rate of globe earth curvature. Instead, the bending occurs more gradually over a greater distance.

I hope I'm understanding this correctly and have built an Excel spreadsheet to calculate values of vertical position of light from a starting position on the ground where the light starts horizontal, eg at sunset. The worksheet calculates vertical position up to 20,000 kilometres (horizontally) from the starting point for any value of β you care to input (the default value of β is 1). The worksheet displays results on a graph of y in metres and x in kilometres, although x is converted to metres for the calculation.

Hopefully people will find it useful!

NB I've checked the calculation by hand with repeated examples, but it's always possible I've missed something. The worksheet is locked so only the β value can be changed when first using it. However, should you want to edit anything, the lock is not password protected, so you can unlock it if you want.
The Scratchpad below the graph lets you input any two values of x you like and it will calculate y for the β value specified.

Electromagnetic Acceleration calculation examples
« Reply #1 on: July 05, 2020, 08:17:10 PM »
Here's three graphs of the result for β equal to 1, 20 and 0.2   disclaimer: I don't know the actual value of β

Re: Electromagnetic Acceleration calculation
« Reply #2 on: July 05, 2020, 08:19:22 PM »