Boundaries and Evidences

 

 

 

 

 

 

 

The Big Bang Theory implies that the space-time is not stretched indefinitely. The universe has boundaries.  It has a periphery that is marked by the outer boundary of the expanding universe. In the present model, we picture the universe as a sponge. Therefore, universe also has internal boundaries or interfaces with the medium entity. Hereafter, I will call the inside boundaries the Planck pores.  Furthermore I have assumed that consciousness is beyond the boundaries of space-time. 
Many physicists like James Hartle and Stephen hawking believe that the paradoxes in theoretical physics can only be solved by specifying the boundary conditions of the universe. Here we explore the boundaries and try to look for evidences according to the current knowledge. 
Before the brightness of day or the darkness of night we get the grays of dawn and dusk. Likewise the structure of the space-time pales whenever we get close to the interface between space-time and the proposed singularity namely the sub-atomic arena, mind and The Big Bang moment. In this chapter, I will show how the elements of space-time get pale as we approach the grays of dawn and set of our universe. That is when we get close to the boundaries.

Complex Numbers and my interpretation of them are explained in the first and the eight chapters (Complex Numbers and Wave Function chapters).
The diagram above shows how elements of space-time fade away as we approach the boundaries of universe and approximate the purely imaginary domain. This process is explored further in the lines below.

Matter 
By definition matter is an entity, which can occupy a definite location in space. If there is no space, matter looses its definition. Mass is also defined as being equal to inertia which is resistance to change in velocity. If there is no space, there is no velocity an therefore inertia looses its meaning. Underneath, we review matter in different arena to show how it gradually disappears when we get close to the boundaries of space.

 A) Microcosm
As we get down to particle physics the concept of matter gets more subtle and pale. The photon is mass-less and even its existence is under question. In 1969, Lamb and Scully showed that one could account for the photoelectric effect without using the concept of photon as a minimum packet of light energy. They were able to introduce an entirely different theory of the photo-electric effect, one that did not invoke the concept of light’s particle nature. They concluded that, photo-electric effect does not prove that photon exists. In addition, George Greenstein writes;

“[In 1956] The Hansbury-Brown and Twiss experiment failed to demonstrate the existence of photons and the indivisibility of weak light. It actually showed that light seemed to travel through space “bunched up”. One can divide the bunch in half, and the two half bunches arrive at the different photo detectors at the same time. These result startled the physics community and launched an entirely a new discipline, the explicit study of quantum nature of light.” ¹¹

 

Mach-Zehnder Interferometer

 

Later on, the same experiment was repeated by laser, which still did not support the particle nature of light. In 1986, in the Grangier, Roger, and Aspect experiment, the non-divisibility of a light unit was shown as evidence of the presence of photons. They used a well-collimated stream of calcium atoms. In their next experiment, they allowed the photon to pass through Mach-Zehnder interferometer. They obtained an interference pattern as a path length traveled by light in one arm of the interferometer was increased relative to the other. So, light divided and passed thorough both ways. Again, the result pales the concept of the photon. Greenstein and Zajong conclude: 

“It is ironic that Albert Einstein, arguably the greatest physicist since Newton, received the Nobel Prize for work that subsequently turned out to be flawed. And it is doubly ironic that this work, which was instrumental in placing before us the concept of wave particle duality, turned out to be correct even though flawed…The central lesson of the story we have recounted…Is that the concept of the photon is far more subtle that has been previously thought.” ¹¹

Wave particle duality also extends to the atom itself. Many experiments are performed passing one atom at a time through a double slit apparatus like the Mach-Zehnder interferometer shown above. Even one atom created an interference pattern. One expects to have two particles to create interference.  How can just one atom demonstrate the performance expected from two atoms? Here, the solidity of individual atoms goes under question.
Erwin Schrodinger goes even further to claim:
 

“One can think of particles as more or less temporary entities within the wave field whose form and general behavior are nevertheless so clearly and sharply determined by the laws of waves that many processes take place as if these temporary entities were substantial permanent beings.” ¹²  

So we can conclude that in micro-scale the solidity of matter gets pale. To solve the mysteries of nature, we must raise odd questions and move toward bold ideas. Here is another speculation:

 

B) Matter, Big Bang and Space-Time Singularities
According to the popular Big Bang Theory, matter gradually formed and appeared at the end of the initial rapid expansion.  The beginning of time is stated at 10^-43 sec. having  a temperature of 10¹⁹Gev.  After the cosmic inflation, vacuum energy transforms itself into an equal number of particles and anti-particles of matter. Prior to the electro-weak era, small excess of quarks and electrons appeared over anti-quarks and anti-electrons. At 10^-10sec, force and matter fields differentiated. At 10 ^-4sec. Quarks, joined and formed proton and neutron. At 100 sec. the nuclei of light elements began to form. It took 10,000 years before transition occurred from the domination of the radiation to that of matter.¹³
The followings are the fundamental forces of nature and their relative magnitudes:

Strong nuclear force            Strong_Nuclear_Force   ---------------10⁴⁰
Electromagnetic force             Electromagnetic Force -------------- 10³⁸
Weak nuclear force                Weak Nuclear Force-------------10¹⁵
Gravity                                 Gravity-------------------------- 10⁰

What is more, when the universe was 10^-39second old, strong, weak and electromagnetic forces were united. With the same token, while the above forces in larger scales differ greatly in magnitude (see the table above) as we examine them in distances about 10^-29 centimeter (ten thousand times larger than Planck distance) the three non-gravitational forces appear to become equal. It seems that in smaller scales the structural elements of space-time get simpler and melt away.
Therefore, we don’t have any trace of mass at the beginning; Matter only appeared as the universe developed.

C) Matter and Mind 
We have considered the mind function as an analogy for the nature and function of the proposed singularity.  Let us now use the same analogy to develop the concept further.
In the mind chapter, while talking about dreaming, we had seen that the dream house was an intangible mass-less image created within our consciousness domain. The actual matter is absent in the realm of the mind.
What did happen when we stopped dreaming and made the decision to go out and by the lottery ticket? An intention originated in our mind-domain initiated a series of incidences in space-time.  We had departed from our dream world and tried to materialize our dream. So with the postulation of mind as a being out of space-time universe, we see that matter fades away or flourish in interactions between mind and space-time universe.

Space  
Black Hole
By definition space and time get distorted and twist as it passes the event horizon of a black hole. They will be swallowed and disappear at the proximity of the singularity located at the center of each black hole.  The image below shows how space comes to an end inside a black hole. Here we witness the dusk of space as we leave the space-time.

Space and time swallowed by singularity

Andrew Hamilton from University of Colorado describes how space and time is swallowed by a black hole: 

“Free-fall coordinates reveal that the Schwarzschild geometry looks like ordinary flat space, with the distinctive feature that space itself is flowing radially inwards at the Newtonian escape velocity, V = (2 G M / r)^1/2. The in fall velocity V passes the speed of light c at the event horizon. Picture space as flowing like a river into the black hole. Imagine light rays, photons, as canoes paddling fiercely in the current. Outside the horizon, photon-canoes paddling upstream can make way against the flow. But inside the horizon, the space river is flowing inward so fast that it beats all canoes, carrying them inevitably towards their ultimate fate, the central singularity. Does the notion that space inside the horizon of a black hole falls faster than the speed of light violate Einstein's law that nothing can move faster than light? No. Einstein's law applies to the velocity of objects moving in space-time as measured with respect to locally inertial frames. Here it is space itself that is moving..”¹⁶

Space Phase Transition
The speculations about phase transition of space as it approaches infinite energy of proposed singularity are in line with Chapline presentation in Texas Conference on Relativisitc Astrophysics; Stanford, California, 12/12-17/04.
George Chapline from Lawrence Livermore, National Laboratory in California In his recent (Nature, March 2005) article “Black holes 'do not exist'”  mentioned that collapse of big stars creates a zone which differs from ordinary space-time and contains much larger vacuum energy. He calls this zone dark energy star that is different from condensed mass zero-point singularity of a black hole. The surface of such a dark energy star:

“Corresponds to a quantum critical surface for space-time. The behavior of matter approaching such a quantum critical surface can be surmised from the behavior in the laboratory of real materials near to a quantum critical point. One prediction is that nucleons will decay upon hitting the surface of massive compact objects.”³⁸

This strange behavior, he says, is the signature of a 'quantum phase transition' of space-time. However, even he confirms the phase transition of space and time in the proximity of the vacuum.

Periphery of the Universe
We do not have much evidence coming from outer peripheries of the universe, for we do not have access to it. But if we believe that our universe is an expanding system, then one expects to see the signs of the outside entity at the outer boundaries of the premature space. The outside layer of the space that is under construction.

Space and Microcosm
Space gets pale in smaller scales. The Heisenberg Uncertainty Principle also suggests that the uncertainty of the particle’s location in ultra small distances is fundamental and does not happen because we do not have sensitive enough instruments or because of errors in measurement, but because in subatomic scale particles do not possess locality. In these ultra small scales, location and mass pales.
Tonomura's Double Slit experiment (which is described in Quantum Mechanics Chapter) tells us that in ultra small scale, particles do not even have a specific trajectory. The experiment puts the presence of space and location in smaller scales under question. 

In addition, inside the smallest spatial distance ( Planck distance) space cease to exist.

Time  
Microcosm
Time-energy uncertainty is an extension of the Heisenberg Uncertainty Principle. The uncertainty principle governs at smaller scale, therefore,

DE (energy) * DT(time) ≥ h(Planck Constant)/ 2pi

The above principle is also fundamental. The problem is not because our measurement apparatus is not sensitive enough. It happens because in smaller scales the notion of time becomes scrambled and it is interchangeable with energy. In smaller scales even long before we come to Planck Time, the notion of time gets blurry and vague.

Compton Scattering²³

Feynman Diagrams

Compton Scattering refers to the way that a photon strikes and scatters from an electron. The diagrams above shows two of many different Feynman Diagrams representing possible scenarios for meeting a photon and an electron. According to Richard Feynman all of these scenarios are simultaneously happening in the event.
In th second diagram, we will see the distortion of time at the infinitesimal instant of the collision. In this diagram, time reverses; this means that the particles scatter from each other before they even collide. The diagrams show how the sequence of events in a microcosm gets mixed up.
What is the time scale for Compton Scattering? If the energy of the incoming photon were 100 keV, then the intermediate state lasts for 6.6X 10^-21s.¹¹
This is still many times longer than the Planck time of 10^-43s. In comparison to Planck time, it is a very long dusk, like a fall sunset in the North Pole. In fact, Feynman Diagrams of Compton scattering suggests infinite expressions representing infinite ways that an electron and a photon can interact. All of these possible ways are happening in a very short time. These different possibilities cannot simultaneously happen in our space-time. Different reasons such as the Conservation of Energy Law inside space-time, will not allow this to happen. We need a domain with an infinite amount of energy, which at the same time is not time bounded for these infinite possibilities to take place.

In addition, within the smallest fraction of time ( Planck Time) time ceases to exist.

Time and Macrocosm
In the large scale, we are looking at the light cone, which initiates at the Big Bang and extends to this moment. So we may claim that the outer boundary of time is now, approximately 14 billion years away from the Big Bang moment. Beyond this instant, time has not reached yet. What we can foresee beyond this moment are potentials. The possibilities are purely determined by the existing data and available energy, the two elements that we have assumed for the singularity. Can we conclude that in the outer limit of time we face singularity in the large scale?
In addition, according to Einstein’s Special Theory of Relativity, as an object accelerate from lower speeds to relativistic speeds (speeds approaching the speed of light) time slows down. Once in proximity of this speed, time will dilate and eventually disappear. Brian Greene writes:

“The maximum speed through space occurs if all of an object's motion through time is diverted to motion through space...but having used up all of its motion through time, this is the fastest speed through space that one object - any object - can possibly achieve.”¹

 

 

Therefore, if we are traveling with full speed (speed of light) in space, we are not traveling in the time dimension at all. So, we may conclude that in outer space boundaries (borderline with singularity) there is no time.
 
Energy
According to our original assumption, energy increases as we approach the boundaries of the universe.
Energy and Big Bang
Donal Goldsmith writes:

“Particle physics proposes that during inflationary era, the universe acquired an enormous cosmological constant, which faded to zero as the universe became 10^-30 second old.”²⁹  

This is the De sitter model which claims that a tremendous amount of energy set off the initial inflation of the universe.  Therefore, in De sitter model we just have energy, prior to the appearance of other elements in space-time. The familiar particles start to appear after that big moment. 

Energy and Microcosm
In small scale, we can write the Heisenberg Uncertainty relation again as:

DE * DT = h(Planck Constant)/2p
DE = h/2pDT
As the changes of time gets smaller changes in energy and therefore the energy itself increases. When DT approaches 0 then DE approaches infinity. ⁴⁰
So at smaller time intervals, as we get closer to boundaries of space-time and Planck Sea the energy can increase up to infinity. As mentioned before zero point energy is believed to be a huge source of energy, which is extractable.
 
A) Energy and Quantum Mechanics
c² = E/m
In the Einstein' equation as mass decreases, energy increases. The amounts of energy for molecules are 10 to 10^-3ev. The energy of electrons bonds in atoms is 10ev. Inside the nuclei the energy goes up to 10⁸ev. When particles are at rest the energy level is up to 10¹¹ev. And at the exit (Planck scale) the energy increases to an enormous amount of 10²⁸ev.¹³
  
B) Energy and Space-Time Singularities  
When we pass the event horizon of black holes, as space and time shrink again, gravity crushes all in-falling masses. Later on supposedly, matter will be decayed and will liberate energy, which will dissipate as radiation back to space-time. By definition, this is the way black holes disappear.
The above concept is in line with the wave-particle model that will be described in the next chapter. In my model, matter converts to energy upon exiting space-time and inside the black holes.
What if black holes are the big gates for energy exchange? Small gates being, Planck distances which are much smaller but infinitely more frequent holes. 

Information
Information also has to increase as we get close to boundaries. The second law of thermo-dynamics indicates that in a closed system entropy increases while organization decreases with the passage of time. In an organized system, information is limited to the structural data of the system. On the contrary, in a structureless and chaotic system, information is invariant and maximal. As a matter of fact, information and organization have a complementarity relationship with each other. Pure information is found in the quantum vacuum ( the proposed singularity in this model) and as we pass through the border and enter the space-time we enter the era of more specification and structural organization and the amount of information decreases.

Information and Big Bang
If we bring the above principle to the time of The Big Bang when structure in the early universe was minimal, the information potentials should have been maximal. As the universe becomes more structured the information is reduced and gets limited to the data of the existing structure of the space-time.

Please note that , energy is not the only factor needed to form the universe. Laws of physics were also essential. Information should have been abundant at the initial moments. Inside of the differentiated universe information is reduced.

Information and Microcosm
The information at the proximity of internal borders of space-time increases rapidly. This can be observed in the ultra small (quantum mechanical) scale. In Compton Scattering, as Feynman's diagrams indicates, the probability of different modes of scattering are endless. It means that there are infinite data available for infinite possible variation of events.

 

 

 

 

 

 

 

To conclude it could be said that, as we move farther from the Planck arena and draw into space-time, the information diminishes. Conversely, in the smaller scales superposition of states requires maximum data. Therefore, at the inner boundaries of the universe we should face with abundant information.

Summary
In this chapter, I have demonstrated how gray zones appear at the inner and outer boundaries of the universe and how upon approaching these boundaries, the three elements of space-time go pale and information and energy gradually prevail. More evidences can be derived and presented to show how the intermingling of elements between the proposed singularity and space-time appears gradually around the boundaries.

The arguments presented are open for debate. The reader is encouraged to email his/her inputs to correct, modify or develop the contents. Please send your emails to; zpfields@yahoo.ca

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