Sorry, I've been run off my feet lately. The wife has a deadline, and we have a two-year old. Now where was I?

Good Elf wrote:In some ways quantum events and uncertainty at low energy reflect these general ideas we see with the analogy of a balloon. One other concept is an actual measurement disturbs what is being measured because the transfer of energy or momentum reacts on the instrument that is used to measure this event. To be able to measure tiny events the instrument must be responsive to accept the transfer of energy and momentum so it "kicks back" on the measurement system scattering the phenomenon. This results in a position and momentum (or energy) uncertainty...

And don't forget that instead of actually having a pin to burst that bubble, all you have is more of the same.

Good Elf wrote:"Superposition" is a valid concept since the fundamental "particles" we are speaking about are "fundamentally" waves. Any number of frequencies are required to "localize" a particle. If you think of a sine wave as the basic idea of a wave then it has an infinite extent because the mathematical function "extends" from +∞ to -∞.

You're talking my language. Love it. There's also an orthogonal extent, since the electromagnetic sine wave is representing a wave in space. Move away from it vertically, and you'd "feel" a weaker wave, but it's still there. IMHO ocean waves are a good way of understanding this. They extend deep into the water, where the circular motion diminishes:

Good Elf wrote:To reduce the "size or extent" of this infinitely long wave. We need to add in a number of truncation functions on of them. An example is the boxcar function and it is this... The left hand function is the boxcar which is in the time (or spatial) domain and is like a hammer blow striking a nail (an impulse or spatial particle) but the right hand function is the transform of this function in the frequency domain (or spatial frequency domain... like matter waves) and you can see it has a lot of internal frequencies to make the "clean" impulse on the right. Please note this is not symmetrical above and below the horizontal axis.

Noted. The wave conveys energy, the dimensionality of energy is pressure x volume, so if trough was an exact mirror of the crest around the horizontal axis, no energy would be being conveyed.

Good Elf wrote:Alternatively the right hand function can be considered as an "origin" as the time domain function (the inverse) this is often called a "packet"... a damped oscillation and the left hand diagram describes the frequency distribution of this function as the sum of a narrow band of frequencies around the origin. I may add or subtract frequencies to change the shape of the wavelet but what it is saying is that any shaped function is internally composed of a sum of internal frequencies which sum the final figure. The boxcar function is one dimensional function a three dimensional function that has the same response in three dimensions as a solid sphere... the ideal particle.

Now you're talking. I'll come back to this at a later date if you don't mind.

Good Elf wrote:This theory is called

Fourier Theory and applies everywhere even in quantum physics. Particle physics makes the global assumption that "particles" have wavelet compilations that make all particles behave like the

boxcar function while wave theory at low energy makes all particle behave like waves and look like wave packets composed of a

sinc function like on the right. In actual fact everything ultimately is composed of waves and "hardness" of a particle depends on the high frequency content of the wavelet... the higher the internal frequency the harder the particle. At low energy particles are 'softer"... if this word can be used and they interact like "wiggledly wobbley things".

Good stuff. It never ceases to surprise me that this isn't common knowledge.

Good Elf wrote:They then interfere with each other and with things ... like for instance "Young's double slit".... the distributed waves can pass through both slits at once whereas a "particle" is forced to pass through one slit at a time... the idea of particles is incompatible with waves in the low energy region. But still remember that the quantum is the minimum "packet" of energy that is able to be interchanged... while passing through a number of slits it either gives up all of its energy or none at all.

We should talk more about the quantum. Light waves can come in a smooth range of frequencies, thus a smooth range of energies, but when you look at a picture of the electromagnetic spectrum, the waveforms are drawn the same height. It was SP's paper on Vern's website that made me notice that, see

The Quantization of Electromagnetic Change.

Good Elf wrote:If you consider everything as waves then particles are one extreme of high energy interactions of wave packets. People like the idea of particles as little balls ... that is the real problem... this preference for regarding "matter" as being composed of stuff with ponderable and visible "mass"... actually that aspect of "reality" is more to do about electromagnetism than it is about mass.

Well said.