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Weird Physics

Section 7 – Overlapping Wave Functions – Mass and its Basis Set

Now that we’ve disposed of the ether question for light waves, we have to face the same question as regards the waves that make up matter.  To do that right you’re going to have to dig deeper into modern physics than I’m comfortable with, and maybe the answers involve quarks and maybe they don’t.  I’m going to have to adopt the age-old stand of chemists when talking to physicists – I just see what works.  I will proceed on an operational level.

We talked before about how any space can be carved up any number of ways, limited only by your mathematical imagination.  The digital pixel or the analog sine-wave collections are equally valid basis sets – orthogonal and complete as they would say in linear algebra.  It is an array of “vectors” that describe space.  On a flat map there are just two, latitude and longitude but in infinite space there is an infinite array of vectors, whether you use a set of points along a ruler or a set of waves of tunable frequency.

Let’s talk about the wave-nature of protons or neutrons.  They’re like points in space, but not perfect, in that they have some size to them.  Let’s simplify by talking in 2 dimensions and say that whatever their shape, we can approximate them as a bell-curve shape with certain parameters TBD.  Or maybe it’s triangle shaped or box shaped – doesn’t matter, you can still build up whatever shape wave pattern you want using whatever valid basis coordinate vector set you want.  The thing I want to talk about is what happens when there are two or more of them in the same universe.

So, when drawing the picture of a neutron mass using sine waves, how do you proceed?  First you throw out all waves that don’t have the right symmetry, so you throw out all the sine waves that cross the axis at zero and keep the cosines that make humps at zero.  Then you take a little bit of every wave with different frequencies.  If you’re stuck inside a space with boundary conditions, those wave choices are quantized.  In an infinite space, the choice of frequency (wiggles per unit length) is continuous.  But still, you build up the picture by taking a certain amount of each wave and adding them together.  But that other neighboring particle must also be drawn up, and it is using the same basis set as the first particle.  What do you have to do?  Throw out a bunch of the low-frequency/long-wavelength waves that don’t line up with the right spacing and use more of the high-frequency waves to fill in a picture that includes both bumps.  In other words, the presence of that second bump puts constraints on which of the basis vectors you can use to “paint” the first bump.

Whatever the underlying mechanism, this seems to be a road to understanding inertia.  To change the position or momentum of a wave packet, you don’t just have to change it alone, you must deal with every other wave packet that is built from the same basis set.  Now, if the wave packets are truly non-interacting and independent (“orthogonal” as they say in linear algebra) then you could move one without affecting the others.  If the wave packets are interacting, like coupled harmonic oscillators are prone to do, then changing one involves changing all the others.

I would suggest that the resistance to change seen in particles, called inertia, is the result of  interactions with other particles.  The more their wave functions are coupled, the harder it is to get that particle to move.  Understand this, and you’re on the road to understanding mass and inertia.  We just have to figure out how protons and neutrons are coupled to each other.  And that puts us on the road to understanding gravity and making a universal field theory.

[© Copyright 2016 by Gerald Keep.  All Rights Reserved.]


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