Saturday, October 17, 2015

Twere to consider too curiously, to consider so.

Could MI6 have an interest in my little story? Probably not, because I try not to live in the real world.

I spotted the following material online over a year ago, but as I'm currently short of time for blogging I thought I would tell this odd little tale in lieu of my otherwise absence from the blogosphere......

This paper on solid state physics written by Chinese authors  Xiang-Ying Ji and Xi-Qiao Feng is rather curious. Why so? .....because my book Gravity and Quantum Non-Linearity is referenced in it. Honours like this don't often come my way, so it's time to play it for all it's worth and bask in the glory.  Here's where in the paper's text the reference occurs:

The reference 14 attached to their biased diffusion equation (4) appears in their reference list as follows:

I wonder if these guys know who I am and what I'm about because there is a bit of "but" in all this! The equation in my book Gravity and Quantum Non-Linearity  that is nearest in form to equation (4) above is equation (3.13) below:
If you can read equations like this then you will understand that apart from a couple of differences my equation (3:13) is more or less of the same form as Xiang-Ying Ji and Xi-Qiao Feng's equation (4). Those differences are in the constants and also the appearance of the last term on the right hand side of (3.13).

But .. and here's that "but" I spoke of..... notice  I have "i" ( that is, root minus one) in front of the diffusion constant. When you add this complex factor to the diffusion term it changes an ordinary biased diffusion equation into a wave equation. The other thing to notice is the appearance of the last term on the right hand side - this is to compensate for the fact that in the kind of diffusion represented by (3.13) the diffusion is a process where in the underlying random walk the stepping agent bifurcates and steps both left and right at the same time. To prevent such a system violating conservation laws the third compensating term on the right hand side must be subtracted.  (This is not a point that appears in my book, but is something that has occurred to me more recently). It is this feature that gives my equation its relativistic character.

Xiang-Ying Ji and Xi-Qiao Fengstop stop short (wisely perhaps) of this "relativistic complexification" of biased diffusion - after all, their paper is really all about the ordinary diffusion of real particles in materials and not about a quantum equation or its extension into quantum gravity. It is perhaps a little strange that they should reference some weird and eccentric amateur theory of quantum gravity when the derivation of the non-imaginary form of their equation (4) is pretty standard fare! But I'm honoured that our esteemed Chinese friends have chosen to use this reference! I wonder if there are some security issues entailed here? I'll leave MI6 to decide on that one!