Sunday, July 12, 2015

Creating A Wormhole - Mathematically

Two views of the wormhole I created using Mathcad 14. At each end are positioned M-branes.

How difficult is it to create an actual, physical wormhole? In fact, extremely difficult - if not impossible - if  you've  read the relevant pages (587-88) in Kip S. Thorne's 'Black Holes and Time Warps'.  You'd have learned why it would be wise - if you could create one - to keep it near Saturn and nowhere near Earth.

Thorne,. referring to his wormhole calculations, where the idealized entity is a sphere in 3 dimensions and "circular in cross section" with one dimension suppressed, also notes that the wormhole would be unstable and only an "infinitely advanced civilization" might be able to keep it open, e.g. by employing an "averaged negative density" - i.e. threading it using a light beam - with the light beam defocussed via negative energy. (A light beam can have positive energy from the light beam's reference frame and negative energy from the wormhole's reference frame.)

Just reading that ought to convince you that the barriers to such creation are formidable indeed. However, it's another thing to create a mathematical wormhole - which I did not long ago while using the Mathcad 14 software program, which has a 3D surfaces generating capability.

My first task then was to write out the Mathcad code which would allow the generation of a surface in 3 dimensions. This consumed about three minutes and I show the code below, copied after being converted to a jpeg from my module:

I then selected from the menu bar the options: Insert - Graph - Surface Plot and this produced the three dimensional frame (well, ok, to be technical a 3D perspective shown in 2 D). This was after filling in the function (X,Y,Z) in the place marker.

However, I noticed that no surface was being generated. After some googling I found that the reason was due to a bug so that one had to enter into 'Properties' by clicking on the frame, then go to 'General' and unmark 'Borders'.  Once this was done, Voila! The surface appeared.

The beauty of Mathcad 14 then is that you can apply your cursor and rotate the 3D perspective any way you want. Two such orientations are shown at the top. Clearly there is a "wormhole" evident going from one brane to one opposite.

We may not be able to create real wormholes, but at least we can generate the mathematical kind!