# The Mathematics of the Electromagnetic Accelerator

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#### Euclid

• 943
##### The Mathematics of the Electromagnetic Accelerator
« on: March 29, 2009, 10:22:24 PM »
Nevermind the cause of bending light, the purpose of this thread is to derive a set of equations that describes the trajectory of light from the Sun to the Earth.

Would anyone like to throw out a few basic assumptions to work with?
Quote from: Roundy the Truthinessist
Yes, thanks to the tireless efforts of Euclid and a few other mathematically-inclined members, electromagnetic acceleration is fast moving into the forefront of FE research.

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#### trig

• 2240
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #1 on: March 30, 2009, 12:04:50 AM »
• The length of the path that light travels from the Sun to any observer on Earth is approximately the same. Otherwise the brightness of celestial objects would change dramatically as they approach the horizon.
• There has to be a second effect that twists light horizontally. This cannot be produced by a one-dimensional acceleration effect.

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#### bowler

• 871
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #2 on: March 30, 2009, 02:28:49 AM »
1) cannot be chromatic, in any part of the EM spectrum (i.e., couples equally to photons of all momenta)
2) Only couples to the photon
3) Associated boson must be effectively massless.
4) Something to explain why it hasn't been observered over short but far more accurate laser experiments, not sure what.

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#### zork

• 3319
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #3 on: March 30, 2009, 07:30:48 AM »
Nevermind the cause of bending light, the purpose of this thread is to derive a set of equations that describes the trajectory of light from the Sun to the Earth.

Would anyone like to throw out a few basic assumptions to work with?
Before you throw some numbers into the play try to draw the path of light lines on my rough sketch.

It is evening and sun is already far away so that the building is lit up only to red point. The sun with red point is first position. Can you draw the light rays from sun with colored dot to the same color dot on building. There is a condition that the little man is always in the shadow.
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http://thulescientific.com/Lynch%20Curvature%202008.pdf - Visually discerning the curvature of the Earth
http://thulescientific.com/TurbulentShipWakes_Lynch_AO_2005.pdf - Turbulent ship wakes:further evidence that the Earth is round.

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#### bowler

• 871
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #4 on: March 30, 2009, 11:49:13 AM »
Its not like theres going to be any maths. Its not at all obvious to me how you do this without changing the apparent strength of the electromagnetic interaction.

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#### zork

• 3319
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #5 on: March 30, 2009, 01:28:43 PM »
Maybe if they can visualize the picture then maybe they can work out some crazy equations.
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http://thulescientific.com/Lynch%20Curvature%202008.pdf - Visually discerning the curvature of the Earth
http://thulescientific.com/TurbulentShipWakes_Lynch_AO_2005.pdf - Turbulent ship wakes:further evidence that the Earth is round.

#### Euclid

• 943
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #6 on: March 30, 2009, 02:08:09 PM »
Here are some more assumptions:

• The pole star must move a degree for every 111.12 km moved north or south.
• The sun and stars must trace circular arcs across the sky.
• The sun's apparent size must be constant

Quote
The length of the path that light travels from the Sun to any observer on Earth is approximately the same. Otherwise the brightness of celestial objects would change dramatically as they approach the horizon.

Not necessarily.  Only the divergence and convergence of rays determines apparent size and brightness.

Quote
There has to be a second effect that twists light horizontally. This cannot be produced by a one-dimensional acceleration effect.

I agree. There needs to be a tangential bending of light to preserve reasonable day-lengths in the Southern hemisphere.
« Last Edit: March 30, 2009, 02:22:58 PM by Euclid »
Quote from: Roundy the Truthinessist
Yes, thanks to the tireless efforts of Euclid and a few other mathematically-inclined members, electromagnetic acceleration is fast moving into the forefront of FE research.

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#### zork

• 3319
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #7 on: March 30, 2009, 02:58:04 PM »
I did another picture. In flat earth there must be point where shadow area starts. It means that starting from this point the light must start bending away from earth and that also means that this point moves constantly. So, the force that bends light must move around underneath earth.

There is two buildings. Other one is not behind the first but behind and on side as shown top of the picture. You can observe similar situation in any kind of city which resides beside sea. This is 100% observable that the line between light and shadow is higher on building that is behind first one. And below the line is always shadow. If you draw line from second to first and continue from there toward the direction of sun then you reach to the ground(or water) . I don't know if it is directly under the sun but I just draw it that way. Point is that it must be somewhere.
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http://thulescientific.com/Lynch%20Curvature%202008.pdf - Visually discerning the curvature of the Earth
http://thulescientific.com/TurbulentShipWakes_Lynch_AO_2005.pdf - Turbulent ship wakes:further evidence that the Earth is round.

#### Euclid

• 943
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #8 on: March 30, 2009, 04:22:36 PM »
Here are some more assumptions:

• The pole star must move a degree for every 111.12 km moved north or south.
• The sun's apparent size must be constant

Upon, further reflection, I have concluded that these properties are equivalent, at least moving from north to south.
Quote from: Roundy the Truthinessist
Yes, thanks to the tireless efforts of Euclid and a few other mathematically-inclined members, electromagnetic acceleration is fast moving into the forefront of FE research.

#### Euclid

• 943
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #9 on: March 30, 2009, 05:35:22 PM »
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.

This is a cubic equation.  Further degrees of polynomials could be used up to an infinite Taylor series, but they would require more unknown parameters.  Perhaps a theory for cause of bendy light could provide values for these unknown parameters.  Quadratic and lower polynomials are unable to satisfy the assumptions.
Quote from: Roundy the Truthinessist
Yes, thanks to the tireless efforts of Euclid and a few other mathematically-inclined members, electromagnetic acceleration is fast moving into the forefront of FE research.

#### Euclid

• 943
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #10 on: March 30, 2009, 05:51:07 PM »
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.

Quote from: Roundy the Truthinessist
Yes, thanks to the tireless efforts of Euclid and a few other mathematically-inclined members, electromagnetic acceleration is fast moving into the forefront of FE research.

#### Euclid

• 943
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #11 on: March 30, 2009, 09:27:32 PM »
Upon more thinking, the height of the sun is a free parameter in my equation.  It is possible that the sun may be many hundreds of thousands of kilometers above the surface.  This graph illustrates a height of 25000 km.

Quote from: Roundy the Truthinessist
Yes, thanks to the tireless efforts of Euclid and a few other mathematically-inclined members, electromagnetic acceleration is fast moving into the forefront of FE research.

#### Ski

• Planar Moderator
• 8730
• Homines, dum docent, dispenguin.
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #12 on: March 30, 2009, 10:00:43 PM »
Though I'm not a proponent of "bendy light", I'm chiming in to compliment you on the time you put into this.
"Never think you can turn over any old falsehood without a terrible squirming of the horrid little population that dwells under it." -O.W. Holmes "Truth forever on the scaffold, Wrong forever on the throne.."

#### Euclid

• 943
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #13 on: March 30, 2009, 10:05:04 PM »
Thanks.  It really wasn't much time for me.  However, I insist bending light is necessary for FET to work.
Quote from: Roundy the Truthinessist
Yes, thanks to the tireless efforts of Euclid and a few other mathematically-inclined members, electromagnetic acceleration is fast moving into the forefront of FE research.

#### Ski

• Planar Moderator
• 8730
• Homines, dum docent, dispenguin.
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #14 on: March 30, 2009, 10:13:24 PM »
Well, I don't deny that light bends. I think that celestial light bends before it reaches the atmosphere, or as it reaches the atmosphere. I'm not at all convinced that "bendy light" or any such nonsense accounts for horizons, etc.
"Never think you can turn over any old falsehood without a terrible squirming of the horrid little population that dwells under it." -O.W. Holmes "Truth forever on the scaffold, Wrong forever on the throne.."

#### Euclid

• 943
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #15 on: March 30, 2009, 10:23:30 PM »
Well, I devised these equations to explain the motion of Polaris as one moves from north to south, but as a side effect they do explain why things disappear over the horizon.  Depending on the parameters I insert, this can be smaller or larger than what is predicted by RET.
Quote from: Roundy the Truthinessist
Yes, thanks to the tireless efforts of Euclid and a few other mathematically-inclined members, electromagnetic acceleration is fast moving into the forefront of FE research.

#### Parsifal

• Official Member
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• Bendy Light specialist
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #16 on: March 30, 2009, 11:14:31 PM »
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.

This is a cubic equation.  Further degrees of polynomials could be used up to an infinite Taylor series, but they would require more unknown parameters.  Perhaps a theory for cause of bendy light could provide values for these unknown parameters.  Quadratic and lower polynomials are unable to satisfy the assumptions.

Interesting. I will give this some thought when I have time. In my (as yet incomplete) calculations, I was assuming a parabolic path with only one unknown (corresponding to the parabola's concavity), for lack of any reasons to choose a more complex shape, but yours may turn out to be a better hypothesis.
I'm going to side with the white supremacists.

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#### bowler

• 871
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #17 on: March 31, 2009, 02:01:59 AM »
What causes it? Kudos on the derivation.

#### Euclid

• 943
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #18 on: March 31, 2009, 10:47:43 AM »
What causes it? Kudos on the derivation.

That's up for debate now.  The equation I have is purely empirical.  There are 4 constraints such an equation must have.

• The light must leave from the height of the Sun
• The light must strike the earth at a given distance
• The light must strike the earth at an angle proportional to distance from the edge of the spotlight
• The size of the sun must remain constant

The simplest equation that can satisfy these constraints is a cubic equation since it has 4 coefficients.  Of course, there are infinitely many curves the light could take and still satisfy the constraints.  But these curves would require more parameters.  Perhaps a theory could decide the exact form of the equation.  I just chose the cubic because it was simple and did not require anymore unknown parameters.
« Last Edit: March 31, 2009, 10:55:12 AM by Euclid »
Quote from: Roundy the Truthinessist
Yes, thanks to the tireless efforts of Euclid and a few other mathematically-inclined members, electromagnetic acceleration is fast moving into the forefront of FE research.

?

#### niceguybut

• 184
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #19 on: March 31, 2009, 11:39:26 AM »
Any chance of a horizontal scale on that graph?  As far as a representation goes it looks plausible, now all we need is a reason for light to behave that way without us either scrapping or adding some major caveats to Snell's law...
"The Zetetic Astronomy has come into my hands ... if it be childish, it is clever; if it be mannish, it is unusually foolish."

A Budget of Paradoxes - A. de Morgan (pp 306-310)

#### EnigmaZV

• 3471
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #20 on: March 31, 2009, 12:02:08 PM »
I must say I am impressed with your work.  I don't like the cubic equation though simply because it complicates the explanation of a source for the bendy light.  What I mean by this is that at some point, the mechanism that bends light will have to change the direction of the bend from concave up, to concave down.
I don't know what you're implying, but you're probably wrong.

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#### bowler

• 871
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #21 on: March 31, 2009, 01:16:59 PM »
We still haven't addressed mechanism. I posted a handful of requirements. After Euclid's efforts on the geometry I could try and some up with something but i'm not sure I know howt o go about doing something as major as adding a new coupling to the photon without changing the EM force, at second order at least.

#### Parsifal

• Official Member
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• Bendy Light specialist
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #22 on: March 31, 2009, 03:28:11 PM »
That's up for debate now.  The equation I have is purely empirical.  There are 4 constraints such an equation must have.

• The light must leave from the height of the Sun
• The light must strike the earth at a given distance
• The light must strike the earth at an angle proportional to distance from the edge of the spotlight
• The size of the sun must remain constant

The simplest equation that can satisfy these constraints is a cubic equation since it has 4 coefficients.  Of course, there are infinitely many curves the light could take and still satisfy the constraints.  But these curves would require more parameters.  Perhaps a theory could decide the exact form of the equation.  I just chose the cubic because it was simple and did not require anymore unknown parameters.

Good work with the derivation, although the idea is that the light continues bending up away from the surface of the Earth. I'm inclined to think that, if not expressable in quadratic form, the path of the light must be given by a quartic or higher order polynomial.
I'm going to side with the white supremacists.

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#### bowler

• 871
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #23 on: March 31, 2009, 03:30:42 PM »
Well yeah, if you add enough degrees of freedom you can fit any arbitrary function with a polynomial of high enough order.

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#### BuStErBuNkEr

• 44
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #24 on: April 01, 2009, 02:08:44 AM »
Light doesn't bend.

#### Lord Wilmore

• Vice President
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##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #25 on: April 01, 2009, 03:53:52 AM »
I think Euclid is doing invaluable work here. I think that if all the FES members of a scientific/mathematic bent were to work together on this, it could become a prestige project. I have always had faith in the concept of the EA.
"I want truth for truth's sake, not for the applaud or approval of men. I would not reject truth because it is unpopular, nor accept error because it is popular. I should rather be right and stand alone than run with the multitude and be wrong." - C.S. DeFord

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##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #26 on: April 01, 2009, 11:44:48 AM »
Take a circle and use its equation.  This dictates the equations close to earth.  Like Newton however, this is an estimate.  The real question is the factor or factors that change it as we move further and further away from earth.  This will look like the eddification formula, only merged with that (roughly) of a circle.

That is what I've been investigating the last few months.
Quantum Ab Hoc

1 + 1 = 2
"The above proposition is occasionally useful." - Bertrand Russell

#### Euclid

• 943
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #27 on: April 01, 2009, 12:36:00 PM »
Why a circle?
Quote from: Roundy the Truthinessist
Yes, thanks to the tireless efforts of Euclid and a few other mathematically-inclined members, electromagnetic acceleration is fast moving into the forefront of FE research.

?

#### trig

• 2240
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #28 on: April 01, 2009, 03:10:04 PM »

Quote
The length of the path that light travels from the Sun to any observer on Earth is approximately the same. Otherwise the brightness of celestial objects would change dramatically as they approach the horizon.

Not necessarily.  Only the divergence and convergence of rays determines apparent size and brightness.

This point requires some additional explanation:

The same amount of energy (for example, a one degree arc of the Sun in each of two dimensions) covers an area of the flat Earth that is several times larger at mid-afternoon than it is at noon.

Because of this, something has to give: either the brightness of the sun is much lower at mid-afternoon (and I do not mean 20% lower) or the apparent size of the Sun is dramatically reduced, or the speed of light is less than half on the vertical direction compared with the horizontal direction, or all of the above.

Now, if you think for a second that the Sun might produce more light through the borders than through the center, you can explain how the exact same sunspots can be seen from every place on Earth at the same time.

#### Euclid

• 943
##### Re: The Mathematics of the Electromagnetic Accelerator
« Reply #29 on: April 01, 2009, 03:36:04 PM »
The conclusion I came upon is that light bends in such a way that the two line segments you have drawn on the ground corresponding to one degree arcs coming from the sun are the same length.  This characteristic guarantees that the sun is both constant in size and brightness.
Quote from: Roundy the Truthinessist
Yes, thanks to the tireless efforts of Euclid and a few other mathematically-inclined members, electromagnetic acceleration is fast moving into the forefront of FE research.