Introduction

Dynamic Universe model is a singularity free tensor based math model. The tensors used are linear without using any differential or integral equations. Only one calculated output set of values exists.  Data means properties of each point mass like its three dimensional coordinates, velocities, accelerations and it’s mass. Newtonian two-body problem used differential equations. Einstein’s general relativity used tensors, which in turn unwrap into differential equations. Dynamic Universe Model uses tensors that give simple equations with interdependencies. Differential equations will not give unique solutions. Whereas Dynamic Universe Model gives a unique solution of positions, velocities and accelerations; for each point mass in the system for every instant of time. This new method of Mathematics in Dynamic Universe Model is different from all earlier methods of solving general N-body problem.

This universe exists now in the present state, it existed earlier, and it will continue to exist in future also in a similar way. All physical laws will work at any time and at any place. Evidences for the three dimensional rotations or the dynamism of the universe can be seen in the streaming motions of local group and local cluster. Here in this dynamic universe, both the red shifted and blue shifted Galaxies co-exist simultaneously.

In this paper, different sets of point masses were taken at different 3 dimensional positions at different distances. These masses were allowed to move according to the universal gravitation force (UGF) acting on each mass at that instant of time at its position. In other words each point mass is under the continuous and Dynamical influence of all the other masses. For any N-body problem calculations, the more accurate our input data the better will be the calculated results; one should take extreme care, while collecting the input data. One may think that ‘these are simulations of the Universe, taking 133 bodies is too less.’ But all these masses are not same, some are star masses, some are Galaxy masses some clusters of Galaxies situated at their appropriate distances. All these positions are for their gravitational centres. The results of these simulation calculations are taken here. 

 Here in Dynamic Universe Model simulations the universe is assumed to be heterogeneous and anisotropic. From the output data graphs and pictures are formed from this Model.   These pictures show from the random starting points to final stabilized orbits of the point masses involved.   Because of this dynamism built in the model, the universe does not collapse into a lump (due to Newtonian gravitational static forces). This Model depicts the three dimensional orbit formations of involved masses or celestial bodies like in our present universe. From the resulting graphs one can see the orbit formations of the point masses, which were positioned randomly at the start. An orbit formation means that some Galaxies are coming near (Blue shifted) and some are going away (Red shifted) relative to an observer’s viewpoint.
See further about Dynamic Universe Model here in the post below....

http://vaksdynamicuniversemodel.blogspot.in/2012/11/fundamental-questions-addressed-by.html

Fundamental questions addressed by Dynamic Universe Model

This Model is new Cosmological model fundamentally and mathematically different from Bigbang, Steady state model etc. I am giving below its Foundational points, Present Day unsolved problems, which can’t be solved by other prominent models, New Satellite Mass reduction technology and publications (Four Books published).

 Main foundational points of Dynamic Universe Model:

-No Isotropy

-No Homogeneity

-No Space-time continuum

-Non-uniform density of matter, universe is lumpy

-No singularities

-No collisions between bodies

-No blackholes

-No warm holes

-No Bigbang 

-No repulsion between distant Galaxies

-Non-empty Universe

-No imaginary or negative time axis

-No imaginary X, Y, Z axes

-No differential and Integral Equations mathematically

-No General Relativity and Model does not reduce to GR on any condition

-No Creation of matter like Bigbang or steady-state models

-No many mini Bigbangs

-No Missing Mass / Dark matter

-No Dark energy

-No Bigbang generated CMB detected

-No Multi-verses

Here:

-Accelerating Expanding universe with 33% Blue shifted Galaxies

-Newton’s Gravitation law works everywhere in the same way

-All bodies dynamically moving

-All bodies move in dynamic Equilibrium

-Closed universe model no light or bodies will go away from universe

-Single Universe no baby universes

-Time is linear as observed on earth, moving forward only

-Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

-UGF (Universal Gravitational Force) calculated on every point-mass

-Tensors (Linear) used for giving UNIQUE solutions for each time step

-Uses everyday physics as achievable by engineering

-21000 linear equations are used in an Excel sheet

-Computerized calculations uses 16 decimal digit accuracy

-Data mining and data warehousing techniques are used for data extraction from large amounts of data.

Present day UNSOLVED problems, solved: 

 

      -Explains Formation of Astronomical Jets and their high Velocities at Galaxy centers.

      -Predicts Frequency shift in electro-magnetic radiation near huge gravitating masses 

-Galaxy Disk formation: Densemass Equations

-Explains gravity disturbances like Pioneer anomaly,

-Non-collapsing large scale mass structures

-Offers Singularity free solutions

-Solving Missing mass in Galaxies, and finds reason for Galaxy circular velocity curves….

-Blue shifted and red shifted Galaxies co-existence, in an Accelerating Expanding Universe…

-Explains the force behind expansion of universe

-Explains the large voids and non-uniform matter densities

-Predicts the trajectory of New Horizons satellite

-Withstands 10⁵ times the Normal Jeans swindle test

-Explains VLBI variations

-Explains Formation of Astronomical Jets and their high Velocities at Galaxy centers.

-Predicts Frequency shift in electro-magnetic radiation near huge gravitating masses  

DYNAMIC UNIVERSE MODEL: for Beginners

Introduction

A bit of History ------ 'Kepler-Newton-Poincare-Einstein'

One of the main problems faced by Newton in around 1650’s is Kepler’s third law. Then, at that time, Newton’s main task was to derive Kepler’s third law from Gravitation law. Finally Newton could solve this problem by using Two-body problem formulation. It was published in 1687 in Newton’s treatise ‘Principia'. 

Of course attempts to arrive at a solution to the 3-body problem started with Sir Isaac Newton in 1687 in Principia.

Later Many people tried to solve three body problem and in general N-body problem. Euler was the first to study the general n-body and in particular restricted 3-body problem, instead of planets in the solar system in the 1760s. He found it is difficult to solve the general 3-body problem as already said by Newton.  He tried to solve the restricted 3-body problem in which one body has negligible mass and it is assumed that the motion of the other two can be solved as a two-body problem, the body with negligible mass having no effect on the other two.  The problem is to determine the motion of the third body attracted to the other two bodies which orbit each other. Even this assumption does not seem to lead to an exact solution.  Very little is known about the n-body problem for n ≥ 3.  Many of the early attempts to understand the 3-body problem were quantitative in nature, aiming at finding explicit solutions for special situations. 

For example for the three body problem, in 1767, Euler found the collinear periodic orbits, in which three bodies of any mass move such that they oscillate along a rotation line.  In 1772, Lagrange discovered some periodic solutions which lie at the vertices of a rotating equilateral triangle that shrinks and expands periodically. This was a solution that  won the Academie des Sciences prize jointly by Lagrange and Euler in 1772 for work on the Moon’s orbit.  Lagrange submitted Essai sur le problème des trois corps in which he showed that Euler's restricted three body solution held for the general three body problem. 

Work had begun  later, on the general three-body problem during the 19th century to maintain two distinct lines.  One was the highly complicated method of approximating the motions of the bodies (celestial mechanics).  The other was to produce a sophisticated theory to transform and integrate the equations of motion (rational or analytic mechanics).  Both the theory of perturbations and the theory of variations of the arbitrary constants were of immense mathematical significance as well as they contributed greatly to the understanding of planetary orbits.

Bruns Poincaré proved in 1887 that there were a maximum of only 10 classical integrals, 6 for the centre of gravity, 3 for angular momentum and one for energy.  In 1889, Poincare proved that except for the Jacobian, no other integrals exist for the restricted three-body problem.  In 1890, Poincare proved his famous recurrence theorem which says that in any small region of phase, space trajectories exist and pass through the region often infinitely.  Poincare published 3 volumes of Les methods nouvelle de la mecanique celeste between 1892 and 1899.  He showed that convergence and uniform convergence of the series solutions discussed by earlier mathematicians was not uniformly convergent.  The stability proofs offered by Lagrange and Laplace became inconclusive after this result.  

Poincare discovered more topological methods in 1912 for the theory of stability of orbits in the three-body problem.  In fact, Poincare essentially invented topology in his attempt to answer stability questions in the three-body problem.  He thought that there were many periodic solutions to the restricted problem which was later proved by Birkhoff.  The stability of the orbits in the three-body problem was also investigated by Levi-Civita, Birkhoff and others.   

King Oscar II Prize & Poincaré

King Oscar II of Sweden announced a prize to a solution of N-body problem with advice given by Gösta Mittag-Leffler in 1887. He announced ‘Given a system of arbitrarily many mass points that attract each according to Newton's law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly.’ As in Wikipedia. [30]. The announced dead line that time was1st June 1888. And after that dead line , on 21st January 1889, Great mathematician Poincaré claimed that prize. The prize was finally awarded to Poincaré, even though he did not solve the original problem. (The first version of his contribution even contained a serious error; for details see the article by Diacu). The version finally printed contained many important ideas which led to the theory of chaos.

Later he himself sent a telegram to journal Acta Mathematica to stop printing the special issue after finding the error in his solution. Yet for such a man of science reputation is important than money [31]. He realized that he has been wrong in his general stability result!   However, until now nobody could solve that problem or claimed that prize. Later all solutions resulted in singularities and collisions of masses, given by many people…..

Now I can say that the Dynamic Universe Model solves this classical N-body problem where only Newtonian Gravitation law and classical Physics were used. The solution converges at all points. There are no multiple values, diverging solutions or divided by zero singularities. Collisions of masses depend on physical values of masses and their space distribution only. These collisions do not happen due to internal inherent problems of Dynamic universe Model. If the mass distribution is homogeneous and isotropic, the masses will colloid. If the mass distribution is heterogeneous and anisotropic, they do not colloid. This approach solves many problems which otherwise cannot be solved by General relativity, Steady state universe model etc…

The Big Bang

In the period 1906 to 1930s the Bigbang model came into existence. At that time it was understood that the Universe had a beginning, scientists began to ask “how did it come into existence, and what existed before it?”

Most scientists now believe that the answer to the first part of the question is that the Universe sprang into existence from a singularity -- a term physicists use to describe regions of space that defy the laws of physics. We know very little about singularities, but they believe that Black holes probably exist in the cores of Galaxies. Black holes are also another class of singularities, where light cannot escape from black hole is its definition.

The second part of the question, as to what existed before the Big Bang, has scientists baffled. By definition, nothing existed prior to the beginning, but that fact creates more questions than answers. For instance, if nothing existed prior to the Big Bang, what caused the singularity to be created in the first place?

Once the singularity was created (however it happened), it began to expand through a process called inflation. The Universe went from very small, very dense, and very hot to the cool expanse that we see today. This theory is now referred to as the Big Bang, a term first coined by Sir Fred Hoyle, who is working against Bigbang  by proposing Steady State Model, during a British Broadcasting Corporation (BBC) radio broadcast in 1950

Interestingly, there really wasn’t any sort of explosion (or bang) as the name suggests, but rather the rapid expansion of space and time. The expansion could be compared to the blowing up a balloon, where as you blow air in, the exterior of the balloon expands outward. There are many other analogies also. But none explain the force behind the expansion.

 

The Moments after the Big Bang

The early Universe was not bound by the laws of physics as we know them today. Consequently, we cannot predict with great accuracy as to what the Universe looked like during the first minutes of creation. In spite of this, scientists have been able to construct an approximate representation of how the Universe evolved.

Scientists believe that the Universe was initially so hot and dense, that even elementary particles like protons and neutrons could not exist. Instead, different types of matter (called matter and anti-matter) collided together, creating pure energy. But as the Universe began to cool during the first few minutes, protons and neutrons began to form. Then slowly over time these protons, neutrons and electrons came together to form Hydrogen and small amounts of Helium. During the billions of years that followed, stars, planets and galaxies formed to create the Universe as we see it today. But it can be seen that cores of stars and planets produce almost all the elements.

Evidences and Contradictions of the Bigbang...

The CMB signal detected by Penzias and Wilson, a discovery for which they later won a Nobel Prize, is often described as the “echo” of the Big Bang. Because if the Universe had an origin, it would leave behind a signature of the event, just like an echo heard in a canyon represents a “signature” of the original sound. The difference is that instead of an audible echo, the Big Bang left behind a heat signature throughout all of space. On the contrary the discovery of CMB by Penzias and Wilson was only for starlight and Galaxy light; which will amount to CMB radiation. No CMB generated by Big Bang has been measured till date by any instrument.

Edwin Hubble, in 1929, was able to correlate the distance to objects in the universe with their velocities -- a relation known as Hubble’s Law. Big Bang theorists later used this information to approximate the age of the Universe to be around 15 billion years old, which is consistent with other measurements for the age of the Universe. Again on the contrary, there are many prehistoric Galaxies found in the universe which have red shifts of 134 billion years. This means that there are such galaxies that are exist since 134 billion years. Thus the question remains as to how the official age would explain such observations. The better instruments and telescopes we make, the more older galaxies will be found. So how will the age calculations by Bigbang are ever explained?

Another prediction of the Big Bang theory is that the Universe should be receding from us. Specifically, any direction we look out into space, we should see objects moving away from us with a velocity proportional to their distance from us, a phenomenon known as the red shift. Again on the contrary, 75000 blue shifted Galaxies were found by the Hubble space telescope. If the whole universe is expanding how come so many Galaxies come near to us? How will an expanding universe model like Bigbang will explain such existence of 75000 blue shifted Galaxies...

Dynamic universe model is what I propose.

Alternatives to the Big Bang Theory

  

While the Big Bang theory is the most widely accepted theory about the origin of the Universe, and is supported by all the observational evidence, there are several other models that explain the evidence equally well.

Some of the theories argue that the Big Bang theory is based on a false premise -- that the Universe is built on an ever expanding space-time. Some, instead, prefer to build theories on a static Universe, which is what was originally predicted by Einstein’s theory of general relativity. Einstein’s theory was only later modified to accommodate the way the Universe appears to be expanding. Again on the contrary, static universe models were not stable.

Dynamic universe model is what I propose. In this model………

Dynamic Universe Model suggests that the universe is not a Newtonian type static universe. According to this model, there was no Big bang singularity, so the question “What happened before Big bang?” does not arise. It states that ours is neither an expanding nor contracting universe. It is not infinite but it is a closed finite universe. Our universe is neither isotropic nor homogeneous. It is LUMPY. But it is not empty. It may not hold an infinite sink at the infinity to hold all the energy that is escaped. This is closed universe and no energy will go out of it. Ours is not a steady state universe in the sense, it does not require matter generation through empty spaces. No starting point of time is required. Time and spatial coordinates can be chosen as required. No imaginary time, perpendicular to normal time axis, is required. No baby universes, black holes or wormholes were built in. This universe exists now in the present state, it existed earlier, and it will continue to exist in future also in a similar way. All physical laws will work at any time and at any place. Evidences for the three dimensional rotations or the dynamism of the universe can be seen in the streaming motions of local group and local cluster. Here in this dynamic universe, both the red shifted and blue shifted Galaxies co-exist simultaneously.

========================================

Present day UNSOLVED problems that can be solved by Dynamic Universe Model :

1. Galaxy Disk formation using Dynamic Universe Model (Densemass) Equations [See ref for chapter]

2. Solution to Missing mass in Galaxies:  It proves that there is no missing mass in Galaxy due to circular velocity curves [ref]

3. Explains gravity disturbances like Pioneer anomaly, etc [ref].

4. Non-collapsing Large scale mass structures formed when non-uniform density distributions of masses were used [ref]

5. Offers Singularity free solutions.

6. Non- collapsing Galaxy structures

7. Solving Missing mass in Galaxies, and it finds reason for Galaxy circular velocity curves….

8. Blue shifted and red shifted Galaxies co-existence…

9. Explains the force behind expansion of universe.

10. Explains the large voids and non-uniform matter densities.

11. Predicts the trajectory of New Horizons satellite.

12 Withstands 105 times the Normal Jeans swindle test

13. Explaining the Existence of large number of blue shifted Galaxies etc…..

Only differences used between the various simulations and Calculations are in the initial values & the time steps. The structure of masses is different. In the first 2 cases, I have used approximate values of masses and distances. In the third and fourth case, I have used real values of masses and distances for a close approximation.

================================================

 Need for Dynamic Universe model

The failure to arrive at a singularity free solution for a general N-body problem for nearly 300 years has led people to treat this case of N-body simulations as being very turbulent.  But I would like to reiterate and say that there is no reason for chaos here in Dynamic Universe Model.  I am able to say this confidently after having worked on this Model for the last 18 years and creating 100,000 simulations using this SITA algorithm.  

The trick here is to follow the law of Newtonian Gravitation fully without any deviation to calculate the Universal Gravitational force (UGF) on each mass.  Other N-body simulations either deviated from this law or did not calculate UGF.

Apprehensions abound in any new field. As pointed earlier, my work in the last 18 years has given me enough confidence and I can say that the solution proposed hereunder will work almost in any physical situation and explain all the anomalies which arose due to the earlier theories.  I can prove the working of the algorithm to any technical team. 

Many people asked me the reason for selecting 133 masses. There are many reasons for this ‘why133 masses?’ question.

It was in the beginning of the 1990’s that the Dynamic Universal Model project began.  The common man had minimal access to computers during this period in India.  Processor 8088 prevailed.  PC with two floppy drives was becoming redundant and was being slowly replaced by the hard drive.  This resulted in limitations to data handling capacity.  Computers used to take a few hours to calculate something like 50 iterations.  Today, these iterations can be done in 8 to 10 minutes with a five – year old laptop. 

The Milkyway, our Galaxy has 10¹¹ Stars approximately with number of planets being an additional 10 times.  Estimated number of dwarf planets would be 1000 times the number of planets, say about to 10¹⁵.  Chunks of planets and asteroids may be a million times the number of planets, say about 10¹⁸.  All these figures are on the lower side.  Hence, about 10¹⁹ masses and their positional data is required to simulate a Galaxy.  The total number of masses required to simulate would be about 10²⁵ to 10²⁸. Is there any Super computer on Earth, which can handle such huge amount of data, today? Do we have all such data to feed the computer?

May be 133 masses are too less a number to begin a simulation.  However, even 3 body problem is not simple to solve directly with the usual differential equations method.  Even if we create a simulation with a million or 10 million masses, it will approximately be 10²⁰ less than what is required for simulating the universe.  My resources being limited and having no access to higher computers, the best I can do is testing this SITA algorithm of Dynamic Universe model  for the various situations within the available resources and time.  I have carried out this work out of my own interest and have not sought any Government or University funding for the same. 

I came up with the Dynamic Universe Model after 18 years after much effort and hard work. The Model uses Newtonian Gravitation for calculating the resultant Universal Gravitational force on every mass.  No special assumptions have been made for arriving at the Model. In those days I did not think of lower side at all like N=2,3 4..etc. What I was aiming is to accommodate as many numbers of masses as possible. I did not take it in the way of mathematical induction process, i.e., if it is true for n=2, and n=3, then test for n and n+1. I have no way of testing that approach.

People asked me why I worked with only 133 masses.  The SITA simulations can be done with higher number of masses on any Supercomputer provided funds and resources are available.  I have successfully tested the SITA solution for 2, 3, 4, 133, 25000 point masses.  I am sure we can arrive at the same results when tried with higher masses also. 

Now I can say, this Dynamic Universe model is no more a fantasy, but it is reality …………..

A note about this Blog:

1. This is a general Physics blog. A small portion of the copyrighted material exists on this blog for the review purposes…

 2. You can search the blog using the Google search on top of the Right Column…

3. The left column show the photo and data of the Author of Dynamic Universe Model : SNP. Gupta

4. These are two more tabs on the top in addition to Home tab,  CV and Books published

5. The Tab CV is of the author SNP. Gupta

6. The Tab Books Published lists the books written by the author of the Dynamic Universe Model

7. There are various posts in this blog that are given in the Blog Archive on the Right Column…

8. You can go through the posts in any order, but the first timer may like to see starting from Need for Dynamic Universe model  ( this post) and in that order starting with post What is Dynamic Universe Model &SITA?  that are given in the Blog Archive on the Right Column…

========================================