The Ridgeway, nr Avebury, Wiltshire, UK. Reported 6th July.

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Updated Saturday 27th  July  2013

 

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Ridgeway of July 6, 2013 seems to show a “Schwarzschild wormhole” with the geometric shape of “Flamm's paraboloid”: messages in crops from an alternate universe?

“There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy”---Hamlet 1.5.166-7  

As noted previously on the Comments page for this crop picture (see www.cropcircleconnector.com/2013/ridgeway/comments.html), a new field image at Ridgeway seems to resemble what is known as a “Schwarzschild wormhole”, with its central “event horizon” and nine concentric outer rings. By this interpretation, a small central circle at Ridgeway could represent the “event horizon” of a black hole, having Schwarzschild radius Rs. Likewise its innermost ring could represent the smallest stable orbit of a Schwarzschild wormhole, typically with radius > 3 x Rs (see http://casa.colorado.edu/~ajsh/schwp.html or https://en.wikipedia.org/wiki/Wormhole). 

On the other side of that “wormhole”, there might exist another parallel universe which is mirror-plane symmetric to our own (see http://casa.colorado.edu/~ajsh/schwm.html). Could this be why certain crop pictures have shown astronomical events (for example the images of stars, planets or comets) as “mirror images” of how we see the same astronomical events here on Earth? Might we be receiving messages in crops from an alternate universe? Travel across a Schwarzschild wormhole by human beings is thought too dangerous to be possible (see http://arxiv.org/abs/0809.0927), but might it be possible to send small robotic probes?   

New measurements on the ground at Ridgeway by a local researcher (C.M.) have provided nine, well-measured radii for each of those nine concentric rings and its small central circle. Going out-to-in, their radii may be derived as 93.6, 79.9, 68.1, 57.95, 49.25, 41.0, 34.7, 28.95, 23.3 or 6.5 FT respectively.

 

How can we analyse these data in terms of a “Schwarzschild wormhole”? First we need to divide all of the numbers by a central “Schwarzschild radius” of Rs = 6.5 FT, to yield 14.40, 12.29, 10.48, 8.92, 7.58, 6.31, 5.34, 4.45, 3.58 or 1.00. For any Schwarzschild wormhole, one expects its innermost stable orbit to be > 3 x Rs = 3.0 (see www.astro.virginia.edu/~jh8h/Foundations/chapter9/chapter9.html). We find in crops a similar value of R1 = 3.6.

The spatial curvature of a Schwarzschild wormhole for R > Rs may be visualized in terms of “Flamm’s paraboloid”. Let us imagine that there is an extra dimension of space which is not part of our normal 4-D spacetime. Then we can replace a flat plane from our normal spacetime, with a curved surface which has been deformed into that extra dimension by a distance of w, where:

w = 2 x √ (Rs x (R - Rs))

This particular geometric shape is called “Flamm’s paraboloid” (see https://en.wikipedia.org/wiki/Schwarzschild_metric).

Since Rs = 1.00, then Rs x (R – Rs) = 13.40, 11.29, 9.48, 7.92, 6.58, 5.31, 4.34, 3.45, 2.58 or 0.00.     

Next √ (Rs x (R - Rs)) = 3.66, 3.36, 3.08, 2.81, 2.57, 2.30, 2.08, 1.86, 1.61 or 0.00. 

Finally w = 2 x √ (Rs x (R - Rs) = 7.32, 6.72, 6.16, 5.62, 5.14, 4.60, 4.16, 3.72, 3.22 or 0.00. 

The local change of distance w between concentric rings = 0.60, 0.56, 0.54, 0.48, 0.54, 0.44, 0.44, 0.50. These differences remain fairly constant as for “Flamm’s paraboloid”, given a slight random error in field measurements.  

We tried earlier to fit aerially-measured values of radius to exp (-nx) or to (1 – x)n. For the second expression, we found x = 0.154 and n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 16, going out-to-in. Still there was a systematic error where x = 0.146 for n = 1, but x = 0.159 for n = 8. Also our previous model did not explain a discontinuity in this series of crop rings near its centre, which is explained naturally by a Schwarzschild wormhole, in terms of an “event horizon” at Rs, then a “first stable orbit” at slightly more than 3 x Rs.  

Many previous crop pictures from the years 1994 to 2012 have suggested the existence of “extra dimensions” outside of our normal 4-D spacetime. Any readers who might wish to learn more about this important subject should study an article posted previously, titled “Extra-terrestrial physics as shown in crops” (see www.cropcircleconnector.com/anasazi/fringe2013b.html). Since our leading physicists on Earth today can only study wormholes theoretically, by writing equations on a sheet of paper, then we can hardly expect that they will know as much about the subject, as various extra-terrestrial races who can already use them in a practical sense.

Red Collie (Dr. Horace R. Drew, Caltech 1976-81, MRC LMB Cambridge 1982-86, CSIRO Australia 1987-2010) 

P.S. We would like to thank the local researcher (C.M.) who made these new field measurements, as well as the producers and actors of “Fringe”, who recently popularized an “alternate universe” idea.

P.S.S. In their Crabwood picture of 2002, the crop artists said that they were sending messages to us through a “conduit”, which is just another name for “spacetime wormhole” (see time2007n  or time2007o)


 

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Circles as a Result of Solving Laplace's Equation in a Cylindrical Coordinate System 

We believe the crop formation reported on 6th July 2013 resembles a solution to Laplace's equation in a cylindrical coordinate system. The Laplace's equation describes many physical phenomena, for example, an electric field, heat field or gravitational field. The Laplace's equation is a partial differential equation written as 

 

On the left side of the equation we can see the Laplace operator (delta) applied to a scalar function (phi). The Laplace operator in a cylindrical coordinate system is given by 

 

The crop formation represents a special solution dependent on the coordinate r only. Therefore, to get the solution, only the first part of this equation is applied. We obtain an equation 

 

An analytical solution to this equation is 

 

The constants A and B are determined by Dirichlet boundary conditions, i.e. by the known values of a scalar function on the boundaries of the solved area. 

The following example shows the distribution of the electric potential inside a cylindrical capacitor (Fig. 1). The inner electrode of the cylindrical capacitor has the electric potential 8 volts and the outer electrode is grounded, i.e. the electric potential is zero volts. The radius of the inner and outer electrode is set to be equal to the crop formation. The information about how to set the ratio of these radii can be found in the centre of the crop formation (see Fig. 2). The distribution of the electric potential is solved by Laplace's equation. 

Fig. 1: The cross-section of a cylindrical capacitor 

Fig. 2: The information about how to set the ratio of the radii 

Fig. 3 and Fig. 4 show the distribution of the electric potential in a cross-section of the cylindrical capacitor in two versions: surface and contour. Contours separate the values ​​of the electric potential by 1 volt. The computations were done by COMSOL Multiphysics. 

Fig. 3: The electric potential in a cross-section of the cylindrical capacitor 

Fig. 4: The electric potential in a cross-section of the cylindrical capacitor – in contours 

Fig. 5: The comparison of the crop formation with the obtained results 

As you can see in Fig. 5, the distances between the individual circles of the crop formation are the same as in the solution to Laplace's equation in a cylindrical coordinate system depicted in Fig. 4. As the aerial shot was not taken perpendicularly to the crop formation, the circles of the crop formation do not correspond to the circles of the solution to Laplace's equation in the upper and lower part of Fig. 5. 

It seems that the creators of this crop formation try to remind us of the beauty of mathematics again. They have already done so through pictograms about Ludolph's number, golden ratio and fractals. 

Jitka & Roman Hamar, The Czech Republic, 20/07/2013



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A precise mathematical description of the nine outer rings at Ridgeway, in terms of a linear geometric series and “collapsed space” 

There has been considerable discussion as to what the Ridgeway crop picture might signify. Some workers have suggested “music” from a diatonic scale, others have suggested the “electrical potential of a cylinder” (see below), while others have suggested a “spacetime wormhole”. If we study this problem in a quantitative sense, we can see right away that the Ridgeway crop picture does not represent “music”, because the numbers for that theory do not match the actual numbers seen in crops: 

Still we have not provided a precise mathematical description of those nine outer rings at Ridgeway, by which to test any possible theory. In their direct unaltered form, those radii do not even fit well to a linear geometric series, as noted in the slide above!  

It turns out that we can fit those nine rings to a linear geometric series, if we “expand” the centre of the crop picture by 3 x Rc, where Rc is the radius of its small central circle. Now the measured numbers fit well to a geometric series, which keeps the same base value of 1.13 when going in to out:  

How might we interpret this result in visual terms? If Rc = Rs for the radius of a Schwarzschild wormhole, then 3 x Rs would be the radius of its smallest stable orbit. Hence space seems to have “collapsed inward” at the centre of Ridgeway by that amount, just like “falling down into a wormhole”. Such space needs to be “expanded outward” again, in order for its outer region of nine rings to return to normal. This was the mathematical basis for a very clever visual illusion, designed somewhere by unknown crop artists. Many thanks to L.H. and C.M. for help.  

Red Collie (Dr. Horace R. Drew)



 



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