A microscopic application of logarithmic spirals in theoretical physics?

[Quartile]

As the topic says I was wondering if there are any microscopic applications of logarithmic spirals in theoretical physics, or any attempts to incorporate them, or any data to support them? I was thinking that since quantum phenomena only has real significance at the quantum scale and yet is still applicable at the macro scale it might be possible that the prevalence of logarithmic spirals in nature might not be so coincidental that they would be confined to only living, macro scale objects/phenomena? To clarify: we obviously don't understand the reason for the existence of logarithmic spirals in nature, but could there be physical significance inherent to some underlying process that could be extrapolated to all matter?

 

Also, as an aside, I think discussion of the golden spiral has been left with a whimsical connotation on accident. A lot of time it seems like people consider those who talk about it "more of those damn newbies ranting about fractals."

[Schrödinger's hat]

Things like logarithmic spirals and exponentials or trig functions (which are also secretly exponentials) come up a lot whenever you have something that changes based on a function of itself, such as size of a new shell segment being proportional to the size of the total shell.

 

 

This ties back to differential equations and self-organising structures. It's one of many complicated looking structures that come from very simple rules.

The exponential function comes up as a solution to almost all of the equations in physics, so in a way I guess you could say that quantum physics is similar.

I guess if one were to use polar coordinates rather than Cartesian to display things then many of our graphs would be logarithmic spirals.

 

Let's take -- as a random example -- nuclear decay

The rate of decay depends on how much material you have so:

[maths]A'=kA[/maths]

The solution of which looks like this:

 

 

Or in polars

 

 

They also come up a lot in something called a phase portrait, if you plot an oscillating decaying function against its rate of change you will usually get a logarithmic spiral, or something very similar. These tend to be useful for analysing chaotic systems among other things

Edited March 8, 2011 by Schrödinger's hat

[Humblemun]

As the topic says I was wondering if there are any microscopic applications of logarithmic spirals in theoretical physics, or any attempts to incorporate them, or any data to support them? I was thinking that since quantum phenomena only has real significance at the quantum scale and yet is still applicable at the macro scale it might be possible that the prevalence of logarithmic spirals in nature might not be so coincidental that they would be confined to only living, macro scale objects/phenomena? To clarify: we obviously don't understand the reason for the existence of logarithmic spirals in nature, but could there be physical significance inherent to some underlying process that could be extrapolated to all matter?

 

Also, as an aside, I think discussion of the golden spiral has been left with a whimsical connotation on accident. A lot of time it seems like people consider those who talk about it "more of those damn newbies ranting about fractals."

 

Hi Quartile,

 

It's a good question you ask. There's a physics contest where I put forward the idea of an Archimedes screw as a model for the graviton. If the screw turns the opposite way it becomes a force of repulsion i.e. an anti-graviton. Why did Newton miss this obvious explanation for the spooky action-at-a-distance? Who knows. Anyway, I just discovered that Descartes had been toying with the very same ideas in 1644, and was one of the very first to draw the field lines of a magnet using this methodology.

 

 

It implies that the atomic nucleus emits both gravitons and anti-gravitons and that all modern physics based on Newton's equation are simple incorrect, despite Einstein's attempt to rectify the situation (he just made it worse in fact, oh dear(!)).