A

t last, I've been able to resolve the accelerated expansion of the universe within the framework of my own "integer count" theory. After a year of mulling it over, I noticed something simple that I should have seen a year ago when the matter first came to my attention. So I have an explanation which is compelling because it is unforced (just needed a different perspective).

I owe it all to my long term observations of Honey Nut Cheerios.

The Initial 3-Dimensional Euclidean Grid

The context within which cosmology is played out is a standard three dimensional gridwork I will call the alpha field (). The bone of contention here is the "tension" of the constituent field lines. Surely they must have some, else light (a wave phenomenon) would not pass ... but are they in a relaxed state with zero tension (0), possessed of infinite tension (), or are they in a state of finite, unit tension (1)?

If infinite, the velocity of light would necessarily be infinite thereby running afoul of "finite logic" as previously stated. We cannot observe, as finite beings, infinite values else we should observe the infinitely small or espy an object at infinite distance. Similarly, infinite velocity is ruled out.

If zero, we should obtain a state similar to that of a "re-orderable field" wherein the constituent particles rearrange themselves without building up a "restoring" potential. Hence, it will not snap back causing a standard wave propagation. (I erred in another page when I ascribed to the initial zero tension and then allowed it to gain tension by applying any finite stretching. Such a stretching being finite would be damped by the infinite space of the field. Such a zero tension field would constitute an infinite tension sink for any finite stretching. A finite stretch would then not hold together to support wave propagation.

If finite, we have the necessary ingredient for wave propagation. There is a ready restoring force to push the wave form along. However, as in the zero tension case, any twang of these guitar strings will produce not only the music of the spheres but also some additional tension to add to the initial "unit tension". That is, any energy input into the unit field tension will raise that field tension above its original unit value arbitrarily assigned as "1".

The inclusion of the field (mass)

As explained at the beginning of these articles, the field is a spherical reference frame surrounding the "point" representatives of the integers (a positional field having two components - distance and direction). They are placed throughout the field randomly with an expectation of 1 per unit volume ... and are logically constrained to interact in some way with the field by the "principle of interaction" thus validating the existence of to and vice versa.

The form of their interaction is that they "bend" the field lines (as in the bending of the reference frame around a mass by gravity). Hence, potential energy has been added to the field's unit tension, i.e. it is stretched tighter that it would be without the inclusion of the fields. Since this is the fundamental initial setup, I might conjecture that the initial tension of the field, including the effects is increased to some simple number like "2" or even "2.71828...". In fact, I don't have a clue as to what it would be ... just more than "1", for certain.

Thus, by the general rules of transverse wave propagating materials, the speed of light in the field will be less than the speed of light in that same field with fields included. And this is the important point here ... greater tension = greater velocity ... and conversely ... lesser tension = lesser velocity.

[Let me here cut & paste the Cheerios paragraphs from the other web page ... pioneer.htm]

Cheerios to the rescue ...

Well, to do this experiment you will need a bowl, a spoon, some milk and some Cheerios (preferably Honey Nut Cheerios since you will be eating your experiment). Now, as the Cheerios disappear you will note that ... They tend to clump up ... and tend to stick to the sides of the bowl as they float in the soon to be consumed milk. Is this not so?

And the reason is that the milk tends to "wet" the Cheerios by climbing up the sides via Van DerWaals forces (capillary action) ... against the surface tension of the milk. So why do they clump?

They clump because when spread out, the milk has a larger surface area from all the bumps in it from wetting the O's. Hence, it's surface tension is greater. The measure of the extra energy contained in the surface tension when the Cheerios are spread out is the degree to which the milk is picked up higher than the general level of the milk. That is, the center of mass of the milk + Cheerios is ever so slightly higher when the Cheerios are spread out ... and lower when they clump (like you are when you stand on your tiptoes).

Like a soap bubble which assumes the shape of a sphere to have the least surface area, the milk configures the Cheerios so as to put it in the least surface tension state. In the case of a soap bubble, if you were to blow up the bubble to a larger volume (and greater surface area), the surface tension would increase until the bubble popped. Same thing with a balloon ... the more you blow it up, the greater is the tension on the surface of the balloon because that surface has increased in area.

Cheerios are Beta ... Milk is Alpha

The tension in the field is greatest when the fields (matter) are spread out uniformly ... and least ... when matter is in clumps. Hence, there is a non-classical gravitational force at play which pushes matter together and is as yet undefined and unquantified.

End cut & paste ...

Now we come to the crux of the Accelerated Expansion

We measure the Hubble expansion rate from fairly nearby galaxies. Let us say that we measure 40 kilometers per second per megaparsec. Now, we divide 40 into 300,000 kilometers per second (light speed) ... and find the size of the universe ... in this case about 7500 megaparsecs. Then we measure the red shift of a distant galaxy and by its redshift we know its speed (from the straightforward Hubble linear increase in redshift with distance). Thus, if we see a galaxy speeding away from us at a redshift implied velocity of 200,000 kilometers per second, we deduce that it is about 2/3 of the way to the Hubble radius or, 5000 megaparsecs.

The trouble with this arrangement is that when Type 1A Supernovas are put to the test, they reveal a discrepancy. They are standard candles, known to emit a certain, predictable amount of energy. In fact, they are too dim for the distance implied by their redshift calculation. Their luminosity ... the total number of photons emitted ... their "flux" (photons per square meter) is too little implying a more distant object. They are measurably farther away than theory predicts them to be.

Now, if the expansion is accelerating ...i.e. if the Hubble rate of 40 kilometers per second per megaparsec used to be 30 kilometers per second per megaparsec, the universe used to be a bigger place ... because 300,000 divided by 30 is 10,000 megaparsecs ... which is more than the presently measured 7,500 megaparsecs.

Get it? Your use of the near galaxies to calculate the size of the universe distorts your estimate making it seem a smaller universe. If you could use (with any expectation of precision) galaxies far away to calibrate your calculation, you would generate a hypothetically larger universe.

I fully concur with this assessment if you are using the Standard Model. The implication is that the "visible" universe will become depopulated of galaxies as time progresses ... and ... my integer count theory is shot to hell. When the Hubble constant is 100,000 kilometers per second per megaparsec ... the universe will be exactly 300,000 divided by 100,000 = "3" ... count 'em ... one, two, three ... megaparsecs in diameter (or radius).

Now the simple revelation

... which required a full year's struggle to see ...

If we say that light speed (300,000 kps) was ... in the past ... 350,000 kps and keep the Hubble constant as a true constant instead of "accelerating" (getting bigger) ... we get exactly the same situation ... a smaller calculated size of the universe with the attendant Type 1A Supernovas which seem to be more distant (by luminosity) than they ought to be.

It's the same result. The difference is that, in the first case, we would then be using my integer count theory instead of the Standard Model as in the second case.

I say that the speed of light decreases ... from ... "1 + (plus whatever velocity would be added by spreading out matter and thereby increasing the field tension) ... to ... just "1", i.e. the speed of light approaches its initial "unit" velocity asymptotically as matter "clumps" up into stars and galaxies.

The same force that passes for "Dark Matter" is also "Dark Energy" or "Quintessence" ... < YUK! ... It is simply the surface tension analog found in field lines. Note that there are other, more important factors involved in the expansion of the universe. The main expansion, in my theory, is caused by the "shrinkage" of Compton wavelengths which is covered on other pages.

One other observation:
The potential energy which is stored in the field due to matter being spread out, must go "somewhere" when that tension weakens. I propose that this may be the source of "charge", i.e. charge does not exist in my theory initially ... only neutral particles. So, it may be that as the "clumping force" goes down, the electro-magnetic force rises but is cancelled out locally by opposite charges
(+ and ^_ ...=... neutral).

And, if you haven't read my piece about the relationship between the FSC and e/P mass ratio, I suggest you look there now.