A relation between the size r

and the size R of the Hubble Universe

Deducing the Finite Size of Matter & Universe within an Infinite Space

So let us now explain, with a little basic mathematics, how we can now deduce the finite size of matter (which determines the size of our spherical universe) within an infinite Space.

Imagine a clear balloon, and you had a 'marker pen' that could make black dots on the surface of the balloon. If you were patient you could cover the balloon in black dots until the balloon was completely black and no light could get inside the balloon. Thus if we know the size of our dots, and how many dots we are allowed to use, then we could calculate the surface area and size of the balloon such that all the dots would just cover the balloon and block out the light.

This analogy is valid with our finite spherical universe within an infinite Space. The 'size of the balloon' is the size of our universe we wish to calculate. The size of our black dots is the size of the wave-centers ('particles'), the number of our black dots is the number of 'particles' in the universe. (We assume a 'particle radius **Re = 10 ^{-14}** and number of particles

Thus if we assumed that all matter in the universe was distributed on the
surface of a sphere, such that the wave-centers completely filled this surface,
then this means that the Out-waves of any more distant matter would not
directly contribute to our In-waves as they must flow through (and become
part of) one of these 'shielding' wave-centers, thus we have already counted
their wave contributions. (While the real universe obviously has some matter
closer and some farther out, this approximation is adequate for calculations.)
Our equations are; Area of wave-center = **pi Re ^{2}**;
area of

The Equation of the Cosmos: **4 R ^{2} = N Re^{2}**

Substituting in our values for N and Re we get a Radius of the universe **R = 10 ^{26}** m

Currently the classical calculation for the Hubble radius of the universe is

These simple calculations suggest that the redshift with distance is actually due to the decreased sharing of waves with distance (as we share less of a common spherical universe) and thus distant matter contributes less to our wave-amplitude and mass-energy density of space (the cause of our mass/energy) which we see as a redshift (energy decrease) with distance. This seems to be a most profound solution, for it explains and solves many of the current problems of Cosmology (as explained below) by finally solving the Problem of the Finite and the Infinite, how matter, with finite mass and spherical size, can perpetually exist in a finite spherical universe within an infinite Space.

Thus we see that logic from the Wave Structure of Matter, demonstrate a different cause of the redshift with distance, based on diminishing Huygens' wave combinations with distance. Further, it confirms Mach's Principle, that the Mass (energy density of space) is determined by all the other matter in our finite spherical universe, as only their Out-Waves directly contribute to our In-Waves.

Let us then briefly examine the classical assumptions of an expanding Universe. The calculation of the Hubble Radius is fairly simple. Edwin Hubble observed that spectral lines in the light from different stars shift towards longer wavelengths (towards the infra-red) in proportion to the distance of the star from us, the observers. If the cause is assumed to be a Doppler shift due to the receding motion of the stars, then a receding velocity **v** can be calculated. A 'Hubble constant' **H** is then obtained from **D = vH** where **D** is the measured distance of the star.

The constant can be written as a distance R such that the expansion velocity has reached **c**, the velocity of light. If light travels the distance **R**, it will require time **T**, where **R = cT**, thus **T** is often assumed to be the age of the universe, after the imagined 'Big Bang'. **R** is called the 'Hubble Radius', and represents the largest distance from which we can receive information by light transmission if our cosmological age is **T**. Thus **T = 1/H**. Using current values for** H** you get an age of the universe of about 10 billion years, and thus a radius of 10 billion light years = **10 ^{26} m.**

Most Cosmologists would now be painfully aware of the many problems associated with this assumption of an expanding universe. As Einstein explains, one of the fundamental problems for the Big Bang relates to this ‘apparent age’ of our Universe;

There does arise, however, a strange difficulty. The interpretation of the galactic line-shift discovered by Hubble as an expansion leads to an origin of this expansion which lies 'only' about a billion years ago, while physical astronomy makes it appear likely that the development of individual stars and systems of stars takes considerably longer. It is in no way known how this incongruity is to be overcome. (**Einstein**)

While modern cosmologists have been able to stretch this time from the Big Bang out to about 10-15 billion years (with the help of a dubious ‘inflation theory’), at the same time they now theorize that large super galaxy clusters likely take 80 billion years to form. A fundamental problem, as Lerner writes;

Present
evidence shows that the Big Bang, initially introduced to explain the Hubble
expansion, does not make predictions that correspond to observation. It
is clearly contradicted by Tully's observations of supercluster complexes
and by the more recent confirmations of large-scale structures. This returns
us to the problem: What caused the Hubble expansion? The cosmological debate
will not be resolved until this basic question is answered.

The question of the Hubble relation remains unanswered, and other fundamental
questions about the cosmos must also remain unanswered until an adequate
theory is found. Far more theoretical and observational work is needed.

(**Lerner**, 1991)

As we have explained though, the solution is quite simple - the Hubble Redshift is not caused by a Doppler shift due to the receding Motion of Matter in an expanding Universe, but rather, is due to this Huygens' sharing of waves, and thus a decreasing Wave Motion interaction with distance (there is less sharing of waves with distance as we share less of a common Spherical Universe) and thus distant matter contributes less to our Wave-Amplitude/Density (the cause of our mass and energy) which we see as a redshift (energy decrease) with distance.

This is a most profound solution, for it solves the remaining major problems of Cosmology (as explained below) by finally solving the Problem of the Finite and the Infinite, how our Matter, with finite mass and spherical size can perpetually exist in our Finite Spherical Universe within an Infinite Space.

Let us now show how Dr Milo Wolff (Mathematical Physicist who first formalised the Wave Structure of Matter) comes to the same conclusion as to the Equation of the Cosmos, but using a method more suitable to Mathematical Physics.

From: http://quantummatter.com/articles_html/body_point.html

Note: Milo Wolf uses the term Space Resonance (SR) to describe the Spherical Standing Waves (SSW) that form matter.

The unknown origin of Newton's law of inertia, F=dp/dt, has attracted frequent attention. Ernst Mach in 1883 boldly suggested that inertia depends upon the existence of the distant stars. His concept arises from two fundamentally different methods of measuring the speed of rotation.

First, without looking at the sky, one can measure the centrifugal force on a mass m and use Newton's Law in the form, F=mv^{2 }/r, to find circumferential speed v. The second method compares the object's angular positions with the fixed (distant) stars.

Mysteriously, both methods give exactly the same result. Mach reasoned
that there must be a causal connection between the distant matter in the
universe and inertia. He asserted: *Every local inertial frame is determined
by the composite matter of the universe.*

The Solution to Mach's Principle is simple with the wave structure of matter. As explained above, our matter's in waves are formed from the out waves of all the other matter in our universe, thus this other matter determines the mass / energy density of our matter. Simple!

The following section explains this in more detail and provides mathematical calculations to show that it is correct.

The wave equation provided a structure which possesses some of the electron's characteristics but a means for the SRs to interact and exchange energy is also needed. Unfortunately, since waves in a homogeneous medium pass through each other, the medium has no means for interaction. To find the means of interaction, we recognize that space is not homogeneous everywhere. For example, it has been observed that a star will bend the path of light which goes near it. A similar behavior occurs at the center of a charged 'particle'.

To examine this requirement we first make a quantitative assumption, similar to Mach's Principle, which establishes the density of space (ether or vacuum). Then we will examine the density formula seeking a means of interaction.** The mass-energy density of space assumption is:**

**Assume that the mass (wave frequency) and propagation speed of an SR wave in space depends on the sum of all SR wave intensities in that space; a superposition of the intensities of waves from all particles inside the Hubble (H) Sphere of radius R = c/H, including the intensity of a particle's own waves.**

mc^{2}= hw= k' SUM OF:{(AMP_{n})^{2 }x (1/r_{n}^{2})} (4)

In other words, the frequency w or mass m of a particle depends on the sum of amplitudes squared of all waves **AMP _{n}**, from the N particles in the universe, whose intensities decrease inversely with range squared. That is, waves from all particles in the universe combine their intensities to form the total density of 'space'. This density determines the electron's wave frequency. This space corresponds to Einstein's 'aether' or quantum theory's 'vacuum.'

Now examine the homogeneity of the space. The universe contains so many particles that the density of space is nearly constant everywhere. But close to the center of an electron, the amplitude of an electron's own waves following the 1/r^{2} rule, is larger, producing a 'lump' in mass-energy density of space. This lump at the center of the electron causes wave interactions. It is the way energy is transferred and what we call 'charge'. Its correctness is tested below.

How does the charge mechanism operate? It is well-known that a-c signals flowing through a non-linear element in a circuit will mix. That is, if there is a two-signal input:

INPUT = Acos(w_{1}t ) + Bcos(w_{2}t)

then the output will be:

OUTPUT = AB[ cos(w_{1}t + w_{2}t) + cos(w_{1}t - w_{2} t ) ] /2 + other components

The non-linear element produces sum and difference frequencies of the original w_{1} and w_{2}.

Similarly in space, different waves passing through the dense, non-linear region at the particle center will mix. If an input frequency and a particle frequency are similar, resonance can occur. An example of this is a tuned radio receiver. An energy (frequency) exchange between resonances behaves like two coupled oscillators in a circuit, or like two pendulums joined with a spring.

If an electron's own waves can create a denser region near its center, then the intensity I of those waves at some radius of non-linearity r_{o}, must be comparable to the intensity of waves from all other N particles in the Universe. This requirement is written:

Intensity I = AMP_{o}^{2}/r_{o}^{2 }= SUM { AMP_{n}^{2}/r_{n}^{2} } = N/V x INTEGRAL OF:{ AMP_{o}/r_{o}}^{2} 4 pi r ^{2}dr

where V is the volume inside the Hubble Sphere and R its radius. The integral, from r = 0 to R = cT = c/H, extends over a sphere whose expanding radius R depends on the age T of the particle. Thus T is the maximum range of the particle's spherical waves. This reduces to

r_{o}^{2} = R ^{2}/3N (5)

Inserting values from astronomy measures, R = 10^{26} meters and N = 10^{80} particles, the critical radius r_{o} equals 6 x 10^{-15 }meter. If the assumption is right, this should approximate the classical radius r_{c} = e^{2} /mc^{2}of an electron, which is 2.8 x 10^{-15} meters. The two values almost match, so the prediction is verified. Apparently dense wave centers do exist, and

e^{2} / mc^{2} = R / SQUARE ROOT OF: {3N} (6)

Equation (5) is a relation between the size r_{o} of an electron and the size R of the Hubble Universe.

It is termed the** Equation of the Cosmos.**

A relation between the size r

and the size R of the Hubble Universe

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