The Mathematics of the Electromagnetic Accelerator

Quote from: zork on April 04, 2009, 11:11:49 AM

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?

Quote from: Euclid on March 31, 2009, 10:47:43 AM

The equation I have is purely empirical.

Exactly.  My equations are based on real-world observations.  You can see them in my assumptions.  There is ambiguity because observations do not uniquely determine a curve.  But, as is usually done when wanting an empirical estimate, one chooses a simple polynomial as a rough approximation to the curve.

Quote from: Euclid on March 31, 2009, 10:47:43 AM

The equation I have is purely empirical.

Exactly.  My equations are based on real-world observations.  You can see them in my assumptions.  There is ambiguity because observations do not uniquely determine a curve.  But, as is usually done when wanting an empirical estimate, one chooses a simple polynomial as a rough approximation to the curve.

As I said, you definitely don't have any real-world observational data. And experiments. And I ask you again and again. Why doesn't light bend when I direct it down at rooftop at same time when building is lighted halfway by sun? And why do you ignore totally all light properties in your equation? It is a light that bends, you can't ignore it's properties.

As I said, you definitely don't have any real-world observational data.

I rely on simple observations that have been used by navigators for thousands of years.  Assuming a flat earth, from that I get a simple rough equation.  FET lacks any serious scientific funding, hence the lack of experiments.

And I ask you again and again. Why doesn't light bend when I direct it down at rooftop at same time when building is lighted halfway by sun?

It's all easily explained by the fact that light bends upward.  Light comes down from the Sun.  It reaches a minimum then travels up again.  At sunset, this minimum is at the ground.  So after grazing the ground, sunlight moves up again.  This explains your observations.  You are just not thinking hard enough.

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As I said, you definitely don't have any real-world observational data.

I rely on simple observations that have been used by navigators for thousands of years.  Assuming a flat earth, from that I get a simple rough equation.  FET lacks any serious scientific funding, hence the lack of experiments.

You don't do equations from only simple observations by eye. You must have some measurements done on one, other and third places to get some numbers from what then you base your equation. If you don't have any data then you really just concocted your equation up.

And I ask you again and again. Why doesn't light bend when I direct it down at rooftop at same time when building is lighted halfway by sun?

It's all easily explained by the fact that light bends upward.  Light comes down from the Sun.  It reaches a minimum then travels up again.  At sunset, this minimum is at the ground.  So after grazing the ground, sunlight moves up again.  This explains your observations.  You are just not thinking hard enough.[/quote]
  First, you don't have any direct sunlight below straight line, the line which you can see on some building. So, it must bend at the line which is on air and moves constantly. Not at the ground.
 Second, I didn't ask about that. I did ask about why light that I shine down at rooftop at same time at the sunset doesn't bend. And why do you ignore totally all light properties in your equation?

I did ask about why light that I shine down at rooftop at same time at the sunset doesn't bend.

Light doesn't bend appreciably over very short distances.

And why do you ignore totally all light properties in your equation?

Because it is EMPIRICAL.  What properties do you speak of?  The catenary curves in a previous post provide a curve light may actually take and they have a theoretical basis.

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I did ask about why light that I shine down at rooftop at same time at the sunset doesn't bend.

Light doesn't bend appreciably over very short distances.

I wonder why is that so. Is light somewhat rigid when it comes out of from source and it must travel some way or through some specific material to get it soft so that it is able to bend?

And why do you ignore totally all light properties in your equation?

Because it is EMPIRICAL.  What properties do you speak of? 

Intensity, wavelength , polarization. Do you assume that any light bends in same way despite of different intensity or different wavelength? And does polarized light bends in same way as unpolarized?

 

a small thing i noticed (i might be wrong though): with a small height of the sun we saw that light would bend upwards after touching the ground. if you looked at such a ray you would see a virtual image of the sun on the surface of the earth / the earth's surface would seem to emit light. i never heared of such a phenomenom (no reflection ofc) so i think quite a huge distance to the sun is necessary.

btw nice work on that formula  

Quote from: Euclid on April 04, 2009, 01:31:36 PM

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I did ask about why light that I shine down at rooftop at same time at the sunset doesn't bend.

Light doesn't bend appreciably over very short distances.

I wonder why is that so. Is light somewhat rigid when it comes out of from source and it must travel some way or through some specific material to get it soft so that it is able to bend?

Local linearity. Look it up.
Something can bend over a vast distance and look straight at any part of that curved line by zooming in on it. Your observations with a flashlight are extremely small scale.

I have recently come to the realisation that for any function y = f(x) that models the curvature of light, its derivative function f'(x) must be an injective function. Otherwise, the action of Dark Energy on rays of light at a particular gradient will be ambiguous. Euclid's equation does not fit with this requirement, as its derivative function is a quadratic whose value therefore approaches positive infinity as x approaches either positive or negative infinity.