WAVENATURE.COM/math.html

Some math and science links.

This page is not a comprehensive compilation of anything.
It just has a few things about waves and some mysteries of nature
that I personally find interesting and some are generally overlooked by the mainstream.


There are many unsolved mysteries of the Universe we live in.

Contrary to popular belief, we don't yet know what gravity really is.
Is Gravity a force as Newton assumed?
Or is it a result of space-time warping around all matter as Eintein calculated in General Relativity?
Or is it caused by an exchange of particles called gravitons as Quantum Theory assumes?
Or is gravity something completely different?
The math works quite well in each of these models, and a few others also, and yet we just don't know what gravity really is.
Maybe you can figure it out for us.

Electrons, which are the most stable and accessible particles known to exist, are very mysterious.
Are electrons particles or waves or are they some strange combination?
Are electrons infintely small point particles or do they have actual size?
Do all static electrons vibrate at a set frequency (named by Irwin Schroedinger in the 1920s "zitterbewegon")
Are electrons and other charged particles the source of the electromagnetic field or, as I see it, is the electromagnetic field the source for all particles?

Physicists are still trying to come up with an acceptable model for an electron.


A better understanding of the Wave Nature of the universe
can provide us an interesting perspective on how our universe works.
Way back in the 1920's theoretical physicists Irwin Schroedinger and Paul Dirac
took a mathematical look at the Wave Nature of the sub microscopic universe.
From their research we have Schoedinger's Wave Equation and Dirac's Wave Equation.
Both of these widely used equations of quantum physics show that musical harmony
of the electromagnetic field gives atoms and molecules their structure, stability and interactions.

Two similar but very different mathematical models for the Wave Nature of electrons (and therefore all particles) are:
1) Louis deBroglie's "Pilot Wave Model" from the 1920's
2) David Bohm's "Bohmian wave mechanics" from the 1950's


Pilot waves that exhibit some strange quantum effects can now be formed visibly in the lab using bouncing droplets. You tube video clip of bouncing droplets with pilot waves

Click here for a physicsworld.com article about the bouncing droplet lab experiment.

There was a conference in November 2011 to discuss the possible physics of the bouncing droplets.
Click here for a iopscience.iop.org conference EmerQuM 11: Emergent Quantum Mechanics 2011 (Heinz von Foerster Congress) 10–13 November 2011, Vienna, Austria

Here are 2 of the interesting papers published at the conference (there are lots more to check out if you have the time)

Y. Couder, E. Fort, Probabilities and trajectories in a classical wave-particle duality, Journal of Physics: Conference Series 361 (2012) 012001

H Schwabl, J Mesa Pascasio, S Fussy, G Grossing, Quantum features derived from the classical model of a bouncer-walker coupled to a zero-point field, Journal of Physics: Conference Series 361 (2012) 012021




We now have a field of mathematics that is very useful in unifying, clarifying and simplifying
the various mathematical systems of theoretical physics, quantum theory, relativity, applied physics, engineering, computer graphics and more.
This math system is called Geometric Algebra (GA) and Geometric Calculus (GC), a refined form of Clifford Algebra originally developed in 1878.

Arizona State University Physics Professor Emeritus David Hestenes Ph.D. web page about GA and GC

Many top Phyicists highly recommend that anyone interested in the mathematics of unlocking the mysteries of the Universe learn some GA.
Click on some of the links below for a good place to start learning GA.

Very good intro to GA

Maxwell's Equations in GA is much better
A simplified approach to electromagnetism using geometric algebra

Converting Einstein's warped space-time into easier non-warped Euclidian space-time using GA & GC helps clear some of the confusion about gravity:
Guage Theory of Gravity using Geometric Calculus that doesn't require all those exotic dimensions needed in String Theory

Search for more published papers on GA

Ian Bell's intro to Geometric Algebra

Cambridge University Geometric Algebra site





A better understanding of the
Wave Nature of electrons,
which is necessary for the electron microscope, clears up the confusion of the "wave-particle" duality

Check back for more information on this page when I have the time.

><> <><

Photons can now be manipulated to attract and repel on the nano scale.
Popular Version: Light's Repulsive Force Discovered

Techincal Version: Tunable bipolar optical interactions between guided lightwaves



Click here to go back to wavenature.com



If you ever wondered what really causes climate change on earth, check out information on solar weather.
After all the sun is the source of our Earth's weather.

See how different types of solar flares stack up in this SPACE.com infographic.
Source: SPACE.com: All about our solar system, outer space and exploration