Harmonics Theory - The Physics and Maths
This pagediscusses the fundamentals of physics in layman's terms, showing how presenttheory must inevitably lead to all waves losing energy and forming harmonicallyrelated waves, the end result is a very specific detailed structure thatmatches the observed universe and explains many previously mysteriousobservations.
| Universal Waves |
Maxwelldeveloped his famous equations for electromagnetism around 1870 and showed thatnot only electricity and magnetism behaved according to wave equations, butthat interactions of the two also behaved as waves that travelled at the speedof light and produced the phenomena known as light, later found to includewaves from long radio waves down to very short gamma ray waves. Since then,major discoveries in fundamental physics have been dominated by the wave natureof all things, as shown by Einstein, Schroedinger, de Broglie and many others.
Althoughthe diverse phenomena modelled by the various physics equations have not yetbeen brought into the sphere of a single model, there are enough clues to saythat such a model ought to be possible. It is natural that such a model wouldinclude a wave equation, and the universe is essentially a wave phenomenon.
Oftenwhen people think about waves they only think about travelling waves, the typethat happen when you drop a stone into a calm pond, a series of concentric wavestravelling out from a central disturbance, all the time getting weaker throughspreading over a larger circumference. There is another type of wave also,called a standing wave, an example of which is a vibrating guitar string or abeaten drum. In these types of waves the energy is mostly constrained fromleaving a limited region and so wrap back on themselves producing a wave thatoscillates in place.
Thequestion of whether the universe is finite or not is generally considered tostill be open. When cosmologists mention the "size of the universe"they are generally referring to a parameter related to the distance to ahorizon beyond which we cannot see. However in present models of the universethere is nothing to prevent the actual size being much greater. If the universehas a finite size then it can support standing waves which fit evenly into thatsize in much the same way that a guitar can. Even if it is not finite, theremay be characteristic wave sizes that form as a result of the prevailing conditions,much as waves form in the wide ocean.
Thereare many reports of regular spacing in "things", ranging fromnucleons and atoms through to planets, galaxies and even galactic clusters.This regularity is evidence for waves underlying things. The reason for"things" being in quotes is that once the wave nature of all thingsis properly understood it is found that there are in fact no such things asthings. There are only waves and processes. When we watch the surf, we seewaves come travelling in and hitting the shore to fall away and die. Howeverthe wave is not a thing, it is a trick of mind following the eye, seeing aprocess of adjacent regions rising and falling as a moving thing when in factno thing actually does that motion that we see as a wave.
Similarlywhen we watch TV we see images of people moving about on the screen, butactually they do not move, they are constantly reconstructed by electron*****ting the screen. Even my explanation in terms of this thing called theelectron is equally wrong because the moving electron is also an illusion ofenergy arriving at adjacent locations in a stream that makes the appearance ofa thing. This is the essential nature of matter that wave energy arrives waveafter wave at a central location which may even be moving, and after passingthrough the centre travels out again as the other half of the standing wavethat makes it seem like a thing wobbling in place.
| Waves of Matter |
Themathematician and physicist, William Clifford, suggested that matter was anelectromagnetic standing wave form very soon after Maxwell produced hisequations, and de Broglie showed the essential wave nature of matter followedfrom Einstein's and Schroedinger's equations, making predictions that werecorrect. Eventually whole atoms were passed through a version of Youngs twoslit experiment and showed the characteristic interference pattern of waves.There is no doubt that matter has a wave nature, although sometimes it isdescribed as also having a particle nature. We shall see that particle natureis really the fact that the standing wave has a definite centre.
Next,Wheeler and Feynman came very close to realizing that the electron wasn't justsomething that manifested waves, but was nothing other than this wave. Theyarrived at an understanding of the incoming and outgoing waves and the standingwave formed by these. However they could not fully accept the mysteriousincoming wave - how did it know where to arrive and to produce this tightcentre that we know as an electron? The mystery entirely vanishes when it isfully understood that the electron is the wave and nothing else. The wave doesnot need to know where the electron is, as wherever the wave converges that"is" the electron. The forces of nature are to be understood as thoseevents that cause the place of convergence to move in various ways.
Althoughphysicists accept the wave nature of matter, some still seem to hang on toideas that there is something other than waves while others seem quite contentin the wave nature. Perhaps the confusion for some is caused by the peskyparticle nature and this duality that is often mentioned. In essence, a"particle" is a standing wave that has a definite centre where theconcentration of the energy is greatest and which may move about andinteract with other such "particles". Each different type of particlehas its own characteristic wavelength and energy.
Thatwasn't so difficult to digest, but when it comes to light, the"particle" behavior is more difficult to fathom. In essence, whenlight is emitted by an atom due to a rearrangement in the structure of anelectron relative to the nucleus, the change in energy of the atom is quitediscrete. Therefore the light has a particular wavelength related to thatenergy. A similar thing is observed if different sized stones are dropped inthe pond, or a single stone from different heights.
Thelight wave created by this atomic event then spreads out over the universe justlike the ripples in the pond, eventually getting all but lost in the backgroundripples that exist everywhere in the electromagnetic field. However at someother place, this ripple may combine with a fortuitous combination ofbackground energy to cause an exact reverse of the atomic event that startedthe ripple. This absorption is of about the same amount of energy as theearlier emission event and is causally related to it through the ripple.However it would be a wrong description to say that a "photon" oflight travelled between one atom and another. The electromagnetic field iscontinuous not discrete. The discreteness only exists in the possible energylevels of atomic and nuclear configurations.
| Non-linearity of Waves |
WhenMaxwell produced his equations they were what is called linear equations. Thismeans that when one wave and another meet they can travel right through eachother without any interaction, just as if the other wave was not there. This isa necessary condition for light because if we look at the Moon, we are notobstructed in seeing it by the light of the Sun travelling across the path thatwe look through. So the linearity of light's behavior is acceptable for thisreason.
Howeverlight does some other things that are quite different. Firstly, we can see it.That proves that it didn't just pass through our eye without interacting, itquite clearly did interact. In fact we know that most solid things obstructlight completely, or at the very least refract it. We can add to this behaviorthat Einstein correctly predicted from General Relativity that light is bent bygravity, and twice as much as is expected by Newton's theory.
Einstein'sresult gives us a big clue, because it shows that gravitation, a very weakforce compared to the charge forces that hold matter together, can affect lightif there is a big enough concentration of matter, even totally trapping lightin the extreme limit of a black hole.
Althoughphysicists refer to Einstein's equations as bending space, they do not do thesame thing with respect to the refraction of light by matter such as glass. Itis unreasonable to refer to light that is refracted in different substances asbeing a change in velocity while referring to the bending of light by massiveobjects as a change in the metric of space. These two behaviors should be seenas different aspects of the same thing. Different to be sure, because the onecase is due to gravity and the other due to charge forces.
Theseinteractions show quite clearly that in the presence of matter light isbehaving as if it is non-linear. Perhaps it is the case that light is alwaysreally non-linear, but that under common circumstances the non-linearity is soslight as to go unnoticed. In fact, experiments with powerful lasers confirmthat very concentrated light can interact with itself without the presence ofmatter.
Thisis a very important conclusion, because it is only possible for light andmatter to be united in being made of the same stuff if that stuff allows boththe interactions and the apparent non-interactions that we observe. Light, andMaxwell's electromagnetic equations are non-linear. This is true even thoughsome physicists have been taught otherwise. It is true in general relativity,because the equations show that energy, be it matter or light, affects themetric or warping of space. This accepted conclusion that Maxwell's equationsunder general relativity form a non-linear system is very important forunderstanding the behavior of the universe.
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