The Mathematics of the Electromagnetic Accelerator

Perhaps once you guys finish deriving this theory, I'll make a section in the FAQ compiling all the modern theories of FET (celestial gears, EA, DEF, etc) that are not in accordance to Earth:Not a Globe or the FAQ. This, I believe, may resolve some conflicts between various models. However, based on Joffenz's and Erasmus's work, the FAQ itself will still be a general overview of the FET.

Other suggestions are welcome.

I have an interesting find here.  The following picture shows the path of light rays in a medium with a uniform gradient in refractive index, increasing from left to right.

This produces the same kind of curves as required by FET.  The curves are catenaries, which are described by the hyperbolic cosine function.  This may provide a theoretical justification for bendy light.  I'll have to do the math later to see if it produces reasonable results.

Just out of curiosity, what do you suppose that the index of refraction would need to be in order to get the light to bend like that?

The index of refraction is 5 at the origin of the rays.  It is 0 at the vertex of the parabola.

The index of refraction is 5 at the origin of the rays.  It is 0 at the vertex of the parabola.

Wow!!    What medium could possibly have an index of refraction of 5?

Here is a graph of the light rays from the Sun.  The x axis is the horizontal distance from the sun to the observer.  The y axis is the height above the earth.  I have used a height of 4800 km for the sun and 10000 km for the equator-north pole distance.

Sorry to bother you and your fancy math but observation at sunset clearly shows that picture is such as below:


Below is shadow and above is sunlight. Your light bending doesn't fit in that picture.

I don't understand what your picture is trying to show.

I don't understand what your picture is trying to show.

 Really? What part of it you don't understand. It is so simple. Yellow is sunlight, gray is shadow. And situation is sunset.

Quote from: Euclid on April 02, 2009, 12:08:04 PM

I don't understand what your picture is trying to show.

 Really? What part of it you don't understand. It is so simple. Yellow is sunlight, gray is shadow. And situation is sunset.

YARLY.

It is so simple.

I agree.  So simple in fact, that no one knows what your point is.

Quote from: zork on April 02, 2009, 12:22:53 PM

Really? What part of it you don't understand. It is so simple. Yellow is sunlight, gray is shadow. And situation is sunset.

YARLY.

I agree.  So simple in fact, that no one knows what your point is.

What exactly you don't understand about sunset or how my simplified sketch fails to describe light at sunset? It is best observed at seashore. Ground is level. Sun sets. Behind you(some 100 meters) is some tall building, lets say 20 meters high. Upper half(10 meters) of it is lighted with yellow sunlight, lower half(10 meters) is in shadow. There is another building(also 20 meters high) behind you(some 1000 meters behind). Its upper part(9.5 meters) is lighted with yellow sun, lower part(10.5 meters) is in shadow. If you now draw imaginary line from one building to other you get line which is not parallel with ground but slanted. And that is a situation what my sketch shows. There is sunlit area and shadow area and between them is observable line which is slanted and is going down toward sun and up when you go away from sun.
 Just go and watch sunset at sea sometimes.

All easily explained by the fact that light bends upwards.

All easily explained by the fact that light bends upwards.

Yeah, easily. But you are unable to draw a picture about it. You can't visualize it. How does a light bend back in some place some 10 meters above ground and a little further  away it bends away at 10.5 meters height. And it kind of doesn't bend but it kind of folds suddenly back.  And how does it travel 3000 miles straight and then bend away 10 meters from earth. And how does the light not bend when I go to the roof of the building and show light down from there?

Look at the picture.


The ray farthest to the right, which corresponds to sunset, has a tail that bends upward after touching the ground.  This ray explains your observations.

Look at the picture.


The ray farthest to the right, which corresponds to sunset, has a tail that bends upward after touching the ground.  This ray explains your observations.

I like how that ray starts out bending upwards, is able to overcome the EA and bend downwards to the FE and then, just before it hits the ground, is overwhelmed by the EA to be bent upwards again.  Either that or there is something in the upper atmosphere with some really wild optical characteristics.  Steve is going to have a lot of fun working that into his theory.

BTW, how does a ray of light bend upwards after touching the ground? 

The fundamental reason cannot be due to refractive index as this effect would be highly chromatic. It would result in a bizarre, if not psychedelic, colour scheme to the atmosphere. Something im not against in principle as I find the blue has gotten rather old unfortunately nature is not in the business of modifying nature because we fancy a new colour scheme.

Quote from: Euclid on April 03, 2009, 12:47:46 PM

Look at the picture.


The ray farthest to the right, which corresponds to sunset, has a tail that bends upward after touching the ground.  This ray explains your observations.

I like how that ray starts out bending upwards, is able to overcome the EA and bend downwards to the FE and then, just before it hits the ground, is overwhelmed by the EA to be bent upwards again.  Either that or there is something in the upper atmosphere with some really wild optical characteristics.  Steve is going to have a lot of fun working that into his theory.

This is why I suspect the Sun is much higher than 3000 miles.  This eliminates the problem of light bending downward then upward.  See my other diagram.

BTW, how does a ray of light bend upwards after touching the ground? 

It grazes the ground at a tangent.

The fundamental reason cannot be due to refractive index as this effect would be highly chromatic. It would result in a bizarre, if not psychedelic, colour scheme to the atmosphere. Something im not against in principle as I find the blue has gotten rather old unfortunately nature is not in the business of modifying nature because we fancy a new colour scheme.

This depends on the composition of the medium.  Perhaps the refractive index is essentially constant over visible and other commonly used frequencies.

that would be a pretty awesome material. Simplify lens making incredibly.

that would be a pretty awesome material. Simplify lens making incredibly.

Not really, since this "dark matter" is so diffuse and apparently has little or no interaction with ordinary matter.

Look at the picture.


The ray farthest to the right, which corresponds to sunset, has a tail that bends upward after touching the ground.  This ray explains your observations.

  It quite doesn't. Because simplified picture of day, morning and evening is going to be in flat earth as following.


 And it doesn't explain why light doesn't bend when I go on the roof of building which is lit to halfway and show light straight to ground. The light which I shine directly toward ground reaches to the ground but suns light doesn't. Why is that so?

Think harder.  Also, I still don't know what your picture is trying to show.

 And I don't get what part of reality your graphic is trying to show. My picture describes exactly the situation of day, morning and evening on flat earth. How your graphic fits there? And you still ignore the question why light which is directed down at building roof reaches to the ground when sunlight doesn't.

My graphic shows the path of light rays from the Sun to the Earth.  I still don't know what your pictures are trying to show.  Your questions and descriptions are hard to understand.

Why a circle?

Because that seems to be a rough estimate of what we obvserve.  Obviously it is an estimate.  But it works well enough on the small scale( sinking ships etc)

My graphic shows the path of light rays from the Sun to the Earth.  I still don't know what your pictures are trying to show.  Your questions and descriptions are hard to understand.

And I still don't know what observable part of real world your graphics describe. I don't have any 3D software but flat earth morning-day-evening areas must be like on picture if you look at side. I quite fail to understand how you can't grasp so simple description.

 Or you can do itself some picture which visualizes the area which is lighted by sun. Evening and morning ares must have areas which are in shadow because they are in shadows if you observe sunset/sunrise and there is observable sunlight above your head at some N meters height.

Quote from: Euclid on April 04, 2009, 01:34:16 AM

My graphic shows the path of light rays from the Sun to the Earth.  I still don't know what your pictures are trying to show.  Your questions and descriptions are hard to understand.

And I still don't know what observable part of real world your graphics describe. I don't have any 3D software but flat earth morning-day-evening areas must be like on picture if you look at side. I quite fail to understand how you can't grasp so simple description.
Or you can do itself some picture which visualizes the area which is lighted by sun. Evening and morning ares must have areas which are in shadow because they are in shadows if you observe sunset/sunrise and there is observable sunlight above your head at some N meters height.

There's how it all works, just like magic eh?

There's how it all works, just like magic eh?

Your other part is curved too but we get staright line at sunset. And it still doesn't answer the question why that light which I show with flashlight or something similar goes straight to the ground and doesn't bend anywhere. I can go to the roof of the building and show light down in any angle(straight down or 45 degrees or 60 degrees or whatever) and it doesn't bend anywhere.

Success!  I have derived an equation for the path of light from the north star in the north south direction that exhibits the above assumptions.
y(x) = h - x Cot[r/h] - (x^2 (3 h - 2 r Cot[r/h] - r Tan[Pi/2 (1 - r/R)]))/r^2 - (x^3 (-2 h + r Cot[r/h] + r Tan[Pi/2 (1 - r/R)]))/r^3
y is the height of the light beam as a function of x, the distance from the north pole.  h is the height of the Sun.  r is distance of a ground observer of the light beam from the north pole.  R is the distance from the equator to the north pole.

I guess that there is no reason to ask any meanings for these divisions, x^2, x^3, tangenses and cotangenses, another things and any real world observational data/measurements which backs up your concocted equation. I bet you just fitted different possibilities together until you got your desired curved line. But one thing interests me because light has several properties(intensity, frequency for example). Why do you ignore them when you deal with bending of light?

I guess that there is no reason to ask any meanings for these divisions, x^2, x^3, tangenses and cotangenses, another things and any real world observational data/measurements which backs up your concocted equation. I bet you just fitted different possibilities together until you got your desired curved line. But one thing interests me because light has several properties(intensity, frequency for example). Why do you ignore them when you deal with bending of light?

You do understand what "empirical" means, don't you?

The equation I have is purely empirical.