MODIFIED HUBBLE DYNAMICS (MOHD)
In all my other publications, I consistently demanded that the universe consists of an additional extremely large but finite bounded fourth spatial dimension. Each of the formulations in those articles depended on such. Again, this article will try to convince the readers for such a need.
With that in mind, this article shows how easy it is to solve the problem of the cosmic red shift controversies and in particular, solve the problem of quantized red shifts. This article is going to create some problems on how the universe got into this situation in the first place, like having a big bang origin ///////////////////// taking place at the same time! I would like to call this the Big Bang ////////. The solutions and the numbers to follow will speak for itself.
Hubble’s research gave us the now famous formula:
v = H r…………………………………………………….1.
Where ‘v’ is currently interpreted by all cosmologists as the cosmic expansion recessional velocity at a distance ‘r’ and ‘H’ is the Hubble constant, which is an inverse period of time, associated with the age of the universe. This is the reason that prompted the popular Big Bang Theory, as interpreted by cosmologists. The Hubble formula 1 is a purely observational fact and will remain so, but the interpretation of the cause by the main stream cosmology, is controversial, because it is incomplete.
Then came TIFFT, his observations of quantized red-shifts, upset the works of the cosmic expansion red shift model, from which there is no escape. I guess all cosmologists tried to ignore this now established fact. Then there is ARP, amongst some others, who, argued that the red shift is composed of a cosmic expansion part and an additional part working together. Finally, the latest Supernova observations of an accelerated expansion of space left every body dumfounded. I say they are correct, as will be shown below.
To this day, there is not a viable explanation of all these observed anomalies of the
Cosmic red-shift behavior. There are many hypothesis formulated and based on many
assumptions to explain the observed anomalies, they create more questions than simple solutions.
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Hubble gave us equation 1. This kind of simple linear relation of velocity and distance is observed to be isotropic and therefore the only conclusion is that the universe is expanding every where every which way we look. We simply cannot claim that we are at the center of anything, therefore this observation must apply from any vantage point from anywhere in space. This brings on a unique possibility that the universe may have another unseen dimension in space. As you may imagine, moving into another large dimension in space would have the effect of virtually extending into our space in all directions at the same time. We cannot perform the feat of moving into an additional dimension since we are stuck in our 3D world, but the additional dimension can co-move our co-ordinate system without us feeling anything. Except light, light has this unique constancy of relative speed, it appears that light can traverse an additional dimension and therefore appear to have a constant relative velocity in any direction.
LARGE 4D SPACE-MATTER DYNAMICS
One singular assumption of an additional very large fourth spatial dimension with a large cylindrical topology, in addition to our existing and familiar three dimensional vast space, is capable of simply explaining all the mysteries of Physics of the whole universe.
I have thought very deep into the 4D Large bounded cylindrical nature of space for a very long time, and was able to over the years to formulate all the mechanics of the very small and the very large space-matter dynamics using simple mechanical mathematics.
The more I dwell into this hypothesis, the more I was able to dream out possible solutions to existing physical problems that have no clear answers at present. In addition, for each qualitative solution I dreamed of, I was surprised to be able to quantify mathematical numbers that almost fell into place so as to justify every solution.
I will begin the analysis and discussion starting from the equations I derived in my other article "EXTENDED NEWTONIAN DYNAMICS(END)", there, I showed how Newton’s inverse square distance force law was modified effectively to an inverse distance law beyond a long range distance "R". I argued that this long range distance "R" cutoff point was none other than half the circumference distance of a fourth large cylindrical dimension, which therefore naturally solved the problem of Dark Matter. Now I will show that the consequence of the 4th large cylindrical dimension and the extended force law equation is far more reaching than expected.
Below the cut off distance, Newton’s law F(r) = -GM/r^2 applies.
After the cutoff distance the extended force law F(r) = - (GM/2)/r^2 - (GM/2)/Rr applies.
Where "2R" is the constant circumference of the 4th cylindrical dimension, and "G" is Newton’s gravitational constant, "M" is the central Mass.
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I also derived the potential energy of the Extended Newtonian system as:
It is clear that the Field Energy in the Extended Newton’s law term is opposite to that of standard Newton’s law. Therefore at very large distances from masses, i.e. distances much greater than the circumference of the 4th cylindrical dimension, space field has negative energy compared to at close range and therefore space tends to expand. Whereas, at less than the distance of the cylindrical circumference, the space field has positive energy, therefore space tends to contract or bind. Note that this effect is entirely a natural consequence of the cylindrical 4D spatial topology. This therefore gives an explanation as to why there is no local expansion of space surrounding matter, but only a cosmic scale of expansion, beyond "R". Note at present locally, R = 3.0 Kpc (See my other article: "EXTENDED NEWTONIAN DYNAMICS(END)".
From the extended part of equation 2 we obtain:
This formula shows that the extended field energy is negative and grows exponentially, therefore it would be natural that the expansion of space is accelerating. I therefore conclude that the space expansion comes in exponential form at long distances and is only linear at relatively small distances as observed by Hubble. But the overall growth of the 4 dimensional space volume can still remain fixed as explained below.
MODIFIED HUBBLE DYNAMICS(MOHD)
Let us therefore assume that the space expansion take an exponential form as follows:
As I mentioned in the introduction, the crucial point is the existence of the four dimensional cylindrical large spatial extent coupled with time, i.e. the new topology of
time-space. As I showed in my other article "EXTENDED NEWTONIAN DYNAMICS(END)" I will again analyze the 4 dimensional space from the point of
view of time-Space where ‘2R’ the circumference of the cylindrical 4th dimension that matters.
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V(4) = KR*r^3………………………………………………………5
Equation 7 shows that the fractional expansion of 4 space volume is equal to 3 times the ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
Dividing equation 9 by 4:
This is the new cosmic 3D space expansion red shift law, i.e. the modified Hubble Law.
It agrees with Hubble’s law for small "r" compared to "c/H".
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THE 4D REDSHIFT COMPONENT
I now hypothesize that the observed Red shift consists of two components.
Let me analyze the properties of equation 13.
Hence the observed red shift is:
THE NEW REDSHIFT PLOT
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The above figure shows the graph of equation 14. First, we note that the maximum extent ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
The upward sloping dashed line is the linear distance red-shift relation, and the plot agrees pretty well with Hubble’s Law up to a Red-shift of 2. Beyond red-shift 2 and half way from the Big Bang ///////////, the red-shift takes on the natural exponential expansion, continuing towards infinity around /////// at the beginning of the Big Bang ////////. This agrees with the accelerated expansion discovered in recent times that is associated with a so called dark energy. Dark energy is therefore nothing but a natural manifestation of the 4 dimensional bounded cylindrical large space nature of the universe.
The second point to note is that the curve appears to decelerate till a red-shift of 1.4 compared to what is expected and thereafter go back to normal, till the red-shift of 2.
TIFFT AT LARGE
look back time.
So every star will have two red shifts, one due to direct travel and another due to ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
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15*10^9 / 2^(12) = 3.66 MLY
Using a Hubble Constant of 65 Km/Sec/Mpc we obtain a recession velocity of :
These are the same order of the principal red shift periodicity observed by Tifft.
Now, we can use the small "r" tripling condition and obtain the basic period to order.
Dividing 73 by 2 we obtain 36.5Km/Sec. Dividing by 3 we get 24.3 Km/Sec. Dividing again by 3 we get 8.1 Km/Sec. Dividing by 3 again then comes to the last basic observed quantization of 2.7 Km/Sec.
With one simple, but far-reaching assumption of the existence of a 4th large cosmic dimension(which I believe is coupled with the time dimension), I have provided a convincing argument for the resolution of all existing cosmological problems such as the red shift periodicity derived above and the anomalous galactic rotation curves explained in another article. I have no idea how the universe got into this situation of the ///////////////////, but it appears to work. It is no longer necessary to think of the universe to have come into existence out of nothing, because the universe did exist as a single compact dimension of finite volume. 60 billion years ago, the big bang occurred, ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
I have no new predictions to announce at this time, except that Hubble’s law is basically valid upto a red-shift of 2 and thereafter Hubble’s law needs to be modified according to equation 14. The red-shift appears to show an apparent slow down of the expansion till up to a red-shift of 1.4 and then stabilizes till red-shift 2, after which an accelerated expansion takes over forever. I hope this hypothesis is crazy enough to be true and wish the experts would research to prove me right or wrong.