| From relativity to third order | ||
| Differentiate the t out | ||
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| Dear XXX, | ||
| You have asked me to explain how it can be plausible, starting from relativity, that it is necessary to calculate rotating gravitational ellipses in a Euclidean space. Rotating gravitational ellipses in a Euclidean are observed by Le Verrier (1811 - 1877) in 1859. | ||
| If we start with equation 1 we notice that if c1 is zero, we have the simple wave differential equation. We solve this equation by filling in a polynomial. But now there is an extra term (-C1 t) in the equation 1. The strengths of the string is get less over time. The string is aging. The t is time in seconds. The string is losing strength per second. This means that the frequency is get less over time. We could solve this equation by filling in the polynomial in equation 1 but we can also do this by filling in the polynomial in equation 3 or equation 4. | ||
| Note that equation 3 and 4 are created by differentiating by time, (That's dt). An extra t-term in the equations leads to a third order equation. | ||
| But now there is an issue. Equation 1 is action force is minus reaction force. Let's call this the second order principle. Equation 4 is third order interaction is minus third order reaction. Both equations (1 en 4) have the same mathematical outcome. So one cannot decide which principle (second or third order differential equation) is the better. They are equal. | ||
| If we look at equation 5 en 6, we have a gravitational ellipse and if Le Verrier stated these equations need to rotate, we use equation 7 en 8 to solve this problem mathematically. The extra 't' in equation 8 results in a third order differential equation, the same way as with the string. | ||
| Anything that has an aspect which is 'per second' leads to a higher differential equation when differentiating that equation by time. The electromagnetic circuits on satellites are losing nanoseconds per second. So that would mean t' = c0 + c1 t. Differentiating that t out, leads to a higher order differential equation. | ||
| All of this was started when Lorentz (1853 - 1928) stated x' = x + v t. Lorentz did not know that stating this, is attacking action force is minus reaction force. The equations 14 en 15 (see below) reveal that he stated a new principle, third order action is minus third order reaction. | ||
| The mathematical result of the third order equations is matching the observed facts. One cannot decide that using the third order equations is mathematical wrong, because it is equal. | ||
| Now there is one problem left and that is to show that certain problems cannot be solved using second order equations. Force is not the solution to everything. | ||
| Ir. Stefan Boersen - 25 september 2017 | ||
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| stefanboersen@hotmail.com |
