Approximate formula for EA theory (NOT complete documentation yet)

Since there has been such a long wait for a conclusive equation describing EA theory, here is an approximate formula for large-scale bending. To find this, I took the limit of a much longer and nastier 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 travelled is much greater than the horizontal distance travelled. Put another way, its accuracy will improve the closer the light ray is to vertical. Therefore, it is not valid for short-range experiments such as the one proposed by Sentient Pizza, but it can give an idea of how much sunlight would bend on its way to the Earth, for instance.

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, named in honour of the great Flat Earth zetetic Mr. Tom Bishop, 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.

The equation itself is:



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).

and what is the value of beta?

and what is the value of beta?

At this point, it is unknown. See:

When the theory is complete, attempts will be made to measure this experimentally.

**applauds**

Excellent! I truly think that the development of EAT is real asset to to FET.

What is the lower limit where the equation can be applied? A difference of 1 in 2? 1:5? 1:10? 1:100? 1:1000?

The equation is as x approaches infinity. It is for large values of EA.

so its inapplicable to anything terrestrial?

What is the lower limit where the equation can be applied? A difference of 1 in 2? 1:5? 1:10? 1:100? 1:1000?

It can be applied anywhere, but the lower the absolute value of dy/dx at that particular location, the higher the error will be. For |dy/dx| > 10, it should give results within 30% of the full equation (which will be published in about a week's time, when I have organised the material) based on a quick error estimate. This makes the approximate equation most useful for things like considering the path of sunlight around the middle of the day, but not so good for things like sunsets and the sinking ship experiment, where the light would sweep much further down towards the surface of the Earth much sooner than this equation would suggest.

Again, this equation is intended only as an approximation for what happens on large scales, and the full equation (which has many more terms, cube roots and such that cancel when you limit x to infinity) will be available very soon.

Edit: Note that the 30% error mentioned is the vertical difference between the predictions; the difference perpendicular to the light ray will be much smaller, around 3% of the vertical distance of the ray above its horizontal point.

so its inapplicable to anything terrestrial?

Yes. As I stated in my previous post, the full equation will be available when I publish the documentation on the matter.

Good work this will take FET to new heights.

this will be a very large leap in FET in that it proves that FE and RE can share the same properties in a much contested topic. If bendy light works why not everything else? 

β - the Bishop constant, named in honour of the great Flat Earth zetetic Mr. Tom Bishop, 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.

this made me laugh since bishop uses the perspective argument

Umm. I don't think that's what is required from a bendy light equation at all. What's needed is something to explain when the horizontal distance travelled is much larger than the vertical. As in: I can see 5 kilometres to the horizon at shore level. Then I can see 11 kilometres from 10 metres up.

Can you make it answer that?

Yes, I can. Can you read?

Quote

β - the Bishop constant, named in honour of the great Flat Earth zetetic Mr. Tom Bishop, 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.

this made me laugh since bishop uses the perspective argument

I have seen him make reference to EA theory in the past, although as far as I am aware he does indeed use the perspective argument these days.

Edit:

Sorry, this post mixes up "EA" with the "Star Sphere Universe Model".

I'll leave it up, though, as the latter does need the former.

----------------------------------------------------

Edit 2: This post is OK as it is replying to "if bendy light works why not everything else".

----------------------------------------------------

this will be a very large leap in FET in that it proves that FE and RE can share the same properties in a much contested topic. If bendy light works why not everything else?  

Because The South Geographical Pole - 90 degrees south - is a single, unique point in space, not a circle or tropic?

Quote from: 3 Tesla on July 15, 2009, 12:49:46 PM

Whilst there is no real South "Pole", there will be a "Southern Circle/Tropic" on which you would always measure your position as 90 degrees south (by star or Sun) so that could be where Scott and Amundsen went (etc.).

A slight problem with this is that Scott and Amundsen set out from different points on the Antarctic coastline:

http://en.wikipedia.org/wiki/File:TerraNova2.png

So if they both headed off due south towards a point on your "Southern Circle/Tropic" they would have arrived at widely different locations.

But we know that Scott arrived at exactly the same point as Amundsen because he (disheateningly) discovered a Norwegian flag waiting for him.

This evidence would suggest that The South Geographical Pole is a real, unique point and not a "Southern Circle/Tropic" that your model predicts.

The equation itself is:

Key question:

Do all frequencies of electromagnetic radiation bend to the same degree?

Or does the "blue bends best" rule still apply?

This will feed back into the "Star Sphere Universe Model" thread again, you see:

Quote from: trig on July 16, 2009, 07:05:08 AM

the hypothesis needs light to bend in such dramatic ways in all three dimensions, and in exactly the same proportion for all detectable colors from infrared to ultraviolet, without any visible distortion.

Chromatic abberation?

Problem number three!

Key question:

Do all frequencies of electromagnetic radiation bend to the same degree?

Or does the "blue bends best" rule still apply?

Chromatic aberration has not been observed in situations such as the Sinking Ship experiment, and therefore there is no reason to assume that it occurs as part of the bend due to Dark Energy. EA theory postulates that all frequencies bend in exactly the same way, so that equation is valid (as an approximation) for all frequencies.

What's the dimension of that constant?

What's the dimension of that constant?

It has units of acceleration, its magnitude being equal to the magnitude of the acceleration on a horizontal light ray due to Dark Energy.

Quote from: Maxus on July 19, 2009, 04:16:39 AM

What's the dimension of that constant?

It has units of acceleration,

I.e. L(ength) / T(ime) / T(ime) in "fundamental units".

I.e. L(ength) / T(ime) / T(ime) in "fundamental units".

Yes.

Quote from: 3 Tesla on July 19, 2009, 02:24:02 AM

Key question:

Do all frequencies of electromagnetic radiation bend to the same degree?

Or does the "blue bends best" rule still apply?

Chromatic aberration has not been observed in situations such as the Sinking Ship experiment, and therefore there is no reason to assume that it occurs as part of the bend due to Dark Energy. EA theory postulates that all frequencies bend in exactly the same way, so that equation is valid (as an approximation) for all frequencies.

So this mechanism has nothing to do with refraction, then?

http://en.wikipedia.org/wiki/Prism_(optics)

The equation itself is:

In other words, y=rx^4/3, where the constant r (for Robosteve's) is unknown.

Unfortunately, this is a lot less than an approximate formula. It just says that the bending is softer than y=rx² but stronger than y=rx.

The real equation, if it even can be expressed analytically, is humungously  more complex, bending the light in all three dimensions, and in a different way depending on the latitude and longitude of the observer.

Edit: I had written x=ry^4/3 instead of y=rx^4/3. All the comments I made stand.

So this mechanism has nothing to do with refraction, then?

No. Euclid's bendy light model is based on the idea of refraction; EA theory is based on the idea that Dark Energy affects electromagnetic radiation as well as ordinary matter, but in a different way, and that radiation is not shielded from its effect by the Earth as ordinary matter is.

In other words, x=ry^4/3, where the constant r (for Robosteve's) is unknown.

Except that my β has direct physical meaning where your r does not. I did not simply pull this equation out of nowhere; I began with the idea that the magnitude of the acceleration on a light ray is given by the product of the Bishop constant and the cosine of the acute angle between the light ray and the horizontal and derived this equation using calculus and trigonometry. Also, your equation is invalid.

Unfortunately, this is a lot less than an approximate formula. It just says that the bending is softer than x=ry² but stronger than x=ry.

On the contrary, it tells us that the extent of the bend is dependent only on two physical constants. It also tells us how those physical constants affect the general shape of the bend (and the longer formula which contains four cube root terms, each itself containing several more terms gives more precise information on this). But most importantly, it tells us what sort of shape we can expect given the simplest possible relationship between the slope of the light ray and the magnitude of the acceleration on it.

The real equation, if it even can be expressed analytically, is humungously  more complex, bending the light in all three dimensions, and in a different way depending on the latitude and longitude of the observer.

No. EA theory only covers the bending of light in a single plane which is perpendicular to an equipotential line in the Dark Energy field; in other words, up/down bending of light. Three-dimensional bending may be required to explain astronomical observations, but that is beyond the scope of this hypothesis.

Quote from: 3 Tesla on July 19, 2009, 02:24:02 AM

Key question:

Do all frequencies of electromagnetic radiation bend to the same degree?

Or does the "blue bends best" rule still apply?

Chromatic aberration has not been observed in situations such as the Sinking Ship experiment,

That experiment might not be evidence for lack of chromatic aberration in "bendy light" ...

Because the results can also be explained by the ship disappearing over "The Horizon" on a Round Earth.

That experiment might not be evidence for lack of chromatic aberration in "bendy light" ...

Because the results can also be explained by the ship disappearing over "The Horizon" on a Round Earth.

I never said it was evidence for lack of chromatic aberration in bendy light, I said that there is no reason to believe that it does occur. If, in attempting to measure the Bishop constant, we discover otherwise, then the theory will need to be adjusted to accommodate new evidence.

(Massive editing)
Can you post the way you derived that equation?

Quote from: 3 Tesla on July 19, 2009, 05:21:33 AM

So this mechanism has nothing to do with refraction, then?

No. Euclid's bendy light model is based on the idea of refraction; EA theory is based on the idea that Dark Energy affects electromagnetic radiation as well as ordinary matter, but in a different way, and that radiation is not shielded from its effect by the Earth as ordinary matter is.

I like this idea for its unifying property.  It is another step in the direction of a FETOE.

FYI, there will be at least a two week delay in any further updates to the EA theory due to the author being temporarily banned. 

FYI, there will be at least a two week delay in any further updates to the EA theory due to the author being temporarily banned. 

Yes, it's a terrible shame he had to go and get himself banned while working on this theory.  It would be nice if he was serious more and trolled less, huh?

Well I'm glad I live on a spherical Earth, facts don't need just equations to be proven.