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**By R. J. Treharne**

**Published by R.J. Treharne at Shakespir**

**Copyright 2016 R.J. Treharne**

**ISBN:** **9781310437090**

**Shakespir Edition, License Notes**

This ebook is licensed for your personal enjoyment only. This ebook may not be re-sold to other people. If you would like to share this book with another person, please purchase an additional copy for each recipient. If you’re reading this book and did not purchase it, or it was purchased for your use only, then please return to Shakespir.com and purchase your own copy to help the author. Thank you for respecting the hard work of this author.

Some Basic Physics

For those of you who are cosmologically challenged or have physics phobia, this short book is written at a level that should be comfortable for most people. So before delving into demonstrating how the universe can be thought of as a large black hole some basic physics may help the background. Most of us know that atoms are comprised of electrons, protons and neutrons; three of the 12 known basic components of matter. The electron has a negative electrical charge, the proton a positive electrical charge, and the neutron, as it name suggests, is neutral or has no electrical charge; which is one of the reasons why the neutron was the last of the three to be discovered. Like charges repeal each other; for example, protons repeal other protons. Unlike charges attract. Neutrons, however, have neither mutual repulsion nor attraction. The specific number of the protons (and matching number of electrons) within in atom determine the element and its associated chemical properties. Hydrogen has one proton, Helium two protons, Lithium 3 protons and so forth up to Uranium which as 92 protons.

An atom is comprised of a small core or nucleus at its center usually comprised of both protons and neutrons (the exception being the lonely hydrogen atom which only has a single proton). The neutrons usually are equal to or close in number to the number of protons within the nucleus, and are what help overcome the proton’s repulsive forces, holding the protons together. Around this proton and neutron nucleus is a cloud of electrons (the number of electrons being equal to the number of protons). The term “cloud” is used because the electrons are not like small planets orbiting around a sun, but are more or less like statistical possibilities of an electron existing everywhere and nowhere at the same time. Yes, a very unsettling idea – welcome to world of quantum mechanics.

A neutron is essentially a proton (positive charge) combined with an electron (negative charge). The proton is about 1,836 times more massive than an electron; a neutron, about 1,837 times as massive. Consequently, the bulk of the mass of an atom is concentrated in the nucleus. Relative to the size of the nucleus, the cloud of electrons is massive; something like the Oort cloud of comets orbiting our own Sun. From the vantage point of the Oort cloud, at the far edge of our solar system, the Sun is but a dim point of light not much brighter than most other stars. There is a lot of empty space between the planets, asteroids and comets orbiting the Sun. Likewise in an atom there is a small volume of mass, the nucleus, surrounded by a very large volume of very little mass, the electrons. An atom is mostly nothing but empty space.

When a sun undergoes thermonuclear reaction it basically combine atoms with a few protons and neutrons into larger atoms containing the combined number of protons and neutrons into a single atom, a process called fusion. In the process a very small amount of the mass is converted into energy (E=mc^{2} stuff). The fusion occurs due to the enormous amount of pressure and temperature created by the relentless mutual gravitational attraction when a very large number of atoms (mass) are clumped together. It takes quantity of atoms greater than the mass of Jupiter, but less than our Sun, to achieve the critical mass threshold to cause the temperature and pressure needed to induce thermonuclear fusion. The larger the collection of atoms (mass), the stronger the gravity and thus the greater the temperature and pressure. The more massive the star the higher the atomic number (number of protons in an atom) it can fuse together to create new elements. Our Sun, for example, is only massive enough to fuse hydrogen into the next heavier element, helium. More massive stars can fuse together heavier elements up to iron (atomic number 26) which is relatively common in the universe (for a heavy element) and very stable. Beyond that, though, it takes a different process of stellar evolution, a stellar explosion of very massive stars (a supernova) to produce the heavier natural elements, up to Uranium (atomic number 92).

The structure of an atom is very strong, retaining its configuration even when two of them are forced together to fuse into a new heavier element. But if the temperatures and pressures get high enough, such as a result at the center of a supernova explosion, even the structure of the atom cannot hold itself together and the electrons are forced into the nucleus and bind with the protons, The result: nothing but neutrons are left – a neutron “star” is born. A neutron star could have the same mass of our Sun (which is about 1.4 million kilometers in diameter), yet only be a few kilometers across. Neutron stars are so dense that a teaspoon amount would weigh millions of kilograms; really dense stuff. A neutron star could be bright, but probably not as bright as the Sun, since it is only glowing because of its own heat and not because of nuclear fusion. If our Sun was replaced with an equivalent mass neutron star, the planets would still orbit as they do, held in orbit by its gravity.

Neutron stars, as inconceivably dense as they are, are still not the limits of possible compression of mass in a collapsed star. Even neutrons can only withstand so much pressure and temperature. Combine enough mass together and even the neutron structure will yield to the extreme pressure and temperature. When a neutron yields it identity, it collapses into God only knows – literally. Even physicists only speculate as to what really happens. All they really know is that all the mass is still there, and consequently so is all the gravity, but it exists in an even smaller volume of space. So much of the collapse of an neutron star is unknown that what happens next is simply referred to as a “black hole” – a point in space (and time) that yields ridiculous conditions where the laws of normal physics as we know them seem to break down. Gravity is so intense near the black hole’s surface and the gravity is so strong (that is the space is so warped) that nothing, not even a fleeting light particle the photon, can escape its gravitational pull. Which is one of the many reasons it is called a black hole, because if you could see it, there would be no light coming from it; hence it should be black. No one really knows for sure since no black hole has been seen directly. The point from the surface of a black hole where the light can no longer escape the pull of gravity is referred to as the “event horizon” which is even larger than the black hole itself. What is occurring at the event horizon or within the event horizon is the subject of many debates among cosmological physicists. Perhaps black holes themselves have different stages of development. For example, once the pressures break down the neutrons in a neutron star, the next collapse could be into a “quark star” – a stellar body comprised of nothing but the fundamental particles of neutrons themselves, quarks. And maybe, as the black hole’s mass continues to increase, even the internal structure of quarks themselves collapse into perhaps whatever the fundamental structure of quarks are, and then once again to nothing but pure compressed energy. No one really knows. We don’t even know if the inside of a black hole is even uniform, homogeneous or even black. What is inside a black hole is a big, big question.

Black holes with masses equivalent to millions and even billions times our Sun’s mass are now a well established phenomenon in the universe because of their influence on other heavenly bodies. Large black holes seem to populate the centers of every galaxy, and may be the reason why galaxies exist; or, vice a versa. No one knows for sure. There may be other black holes hovering around, either within or between galaxies. There may even be “mini” black holes, some as small as the size of an atom wondering around – again, no one is sure. Despite our ignorance, though, some interesting things have been figured out about black holes, most notably what size they would be relative to their mass. The relationship is known as the Schwarzschild radius, as defined through the formula:

2 G M Where: R_{Sch} = Schwarzchild radius

R_{Sch} = ---------- G = Gravitational Constant

c^{2} M = Mass of black hole

c = Speed of light

The Schwarzchild radius is the radius of the black hole. The gravitational constant (G) has been know since the days of Isaac Newton and basically defines the strength of force of attraction (actually the ability to curve space) between two objects on known mass and at a known distance as defined in the formula:

F = G (m_{1} m_{2}) / r^{2} m_{1} = mass of first object

m_{2} = mass of second object

r = distance between objects

G = Gravitational Constant

The value of “G” has a curious value and set of units equal to 6.67428 × 10^-11^ m^{3}/kg s^{2}, and is actually a relatively weak force. We often don’t think of gravity as being weak, but relative to the other known forces (electromagnetism, the strong and the weak nuclear forces) it appears strong because the other forces are almost always balanced or act at very small distances. Gravity alone is has no balancing force (no anti-gravity) and is able to act at extreme distances, so in our universe it seems to dominate.

From the Schwarzchild formula, as one would expect, as the mass of the black hole increases, the radius also increases, and it does so proportionally. Assuming black holes are like neutron stars and regular stars we can assume that they are spherical in shape. Then from basic geometry one could further deduce that as the radius increases the volume increases by a factor of the cube of the radius because the formula for a sphere is defined as:

4

V = --- r^{3}

3

Thus, a sphere with a radius of 2 units would have 8 times the volume of a sphere of only one unit. (2^{3} = 8). What is fascinating about the Schwarzchild formula is that as the mass and radius both increase, the density actually decreases! For example, let’s say we have a black hole with a mass 1 billion kilograms. The black hole, if it could exist at that size, would be very, very small.

2 G M 2 × (6.67428 × 10^-11^ m^{3}/kg s^{2}) (1.0 × 10^{9} kilograms)

R_{Sch} = ---------- = ---------------------------------------------------------------

c^{2} (299,792,456 m/s)^2^

R_{Sch} = 1.485 × 10^-18^ meters (smaller than the diameter of a proton)

Knowing that the volume of a sphere (again, assuming a black hole is a sphere) is V = 4/3 r^{3}; the volume of a 1 billion kilogram black hole would be:

V = 4/3 (1.485 × 10^-18^ m)^3^ = 1.37 × 10^-53^ m^{3}; again, a very, very small size.

Its density (mass divided by volume) would equal:

1.0 × 10^{9} kilograms / 1.37 × 10^-53^ m^{3} or roughly

7.29 × 10^{61} kg/m^{3}; incredibly dense; albeit very small.

Now double the mass of the black hole to 2 billion kilograms and its Schwarzschild radius doubles to 2.970 × 10^-18^ meters and its volume becomes 1.098 × 10^-52^ m^{3}; again very, very small but *four* times the size it was before, by volume. Is density becomes;

2.0 × 10^{9} kilograms / 1.098 × 10^-52^ m^{3}

= 1.82 × 10^{61} kg/m^{3}; again very dense, but only *one-quarter* the previous density.

Thus, as the mass of the black hole increases and so does it size, its density decreases. This may be a hard concept to understand, since it is not like a balloon filling up with air where the density of the air inside the balloon always stays the same no matter how big it gets. Instead, in the case of a black hole getting bigger, it keeps getting less and less dense. So then, what would be the density of a black hole which had the equivalent mass of say the entire universe?

The Universe is a Black Hole

When understanding the universe one has to realize that distance and time are interrelated; that is, the farther in distance you look into space, the father back into time you are looking as well. This phenomenon is courtesy of the unique behavior of the speed of light © which, although very fast, does have a finite speed of approximately 299,792,456 meters per second. It takes light time to travel a certain distance. At close distances, the time difference is negligible, but at larger distances it does become relevant. For example, our Sun is about 150,000,000 kilometers from the Earth – but it is also about 8.3 minutes away from us in time as well. Even at the speed of light, it still takes light about 8.3 minutes to traverse the 150,000,000 kilometers. The Sun we see now is actually how it was 8.3 minutes ago; it just took the sunlight that long to reach us. If the Sun were to instantly disappear, we would not know about it until 8.3 minutes later. In universe size distances, between galaxies, astronomers use the distance that light can travel in a year – known as a light-year – or approximately 9,460,730,472,580,800,000 meters or 9.46 × 10^{15} meters in scientific notation. So a distance of one light-year is both a distance in space and in effect a length of time.

Astronomers have probed the universe and seen galaxies as far away as 13.0 billion years and most “Big Bang” theories (a subject for later discussion) place the universe’s “birth” at roughly 13.82 billion years ago; so we are seeing very close to the beginning of time What happened in those first few hundred million years of universe evolution is still a subject of debate, since it cannot been seen. Nevertheless, assuming the “age” of the universe is estimated at roughly 13.82 billion years, or 4.36 × 10^{17} seconds; that would translate into a distance of roughly 1.307 × 10^{26} meters from Earth to the starting point of the Big Bang.

Now comes the confusing part. One has to put aside their normal notions of spatial thinking and pure geometry, such as the Cartesian coordinates of X, Y and Z or up, down, left, right, forwards and backwards. Because, one of stranger qualities of mass and its corresponding gravity, is that mass distorts or “curves” space. In fact, this curvature of space is what we interpret as gravity. The Sun warps or curves the space around it and the Earth. The Earth thinks it is moving in a straight line, but it is actually following a space that is curved by the mass of the Sun. It is like placing a bowling ball on your mattress then rolling a marble past it. Because of the deformed shape in the mattress, the marble rolls along a curved surface and is deflected from what would be normally a straight path. But to the marble, just like the Earth, it is following a straight line, but through curved space. Thus the Newton laws of motion are preserved.

Consequently, when we look across great depths of space, we have to realize that the path the light has traveled to us from some distant galaxy has been curved and bent possibly multiple times before reaching us. It is like a light beam passing through a fiber optic cable. The fiber optic cable may have been perfectly straight or it could have been winding through a maze of pipes going all different directions or even coiled around into a loop somewhere in its length. To an observer measuring the length of time it look a light beam pulse to go from one end to the other, all the observer could possibly determine is the length of the fiber optic cable; but not the true actual distance between the two ends of the cable. Similarly, light from galaxies seen as far away as 13 billion light-years, may in reality be considerably less distant than they appear or to use the term “as a crow would fly” distance away. Thus, the only way to know the true distance between us and some distant galaxy is to be able to observe that galaxy with no intervening mass (gravitational fields) between us and the galaxy which could alter its path. But for the purposes of this book, we shall assume that the difference is negligible.

Thus let’s assume then that the limit of the observable universe is roughly 13.82 billion light-years and hence agree that the distance to the “edge” of the universe is roughly 1.307 × 10^{26} meters. Now the question is: is this the diameter of the universe or is this the radius? Again, one has to throw out normal three-dimensional Cartesian coordinate thinking. On the one hand, no matter which direction we look from Earth, we see approximately 13.82 billion light-years – which would give you the impression that we are at the center of this humongous sphere, which has a radius of 13.82 billion light-years, therefore its total diameter would be twice that value. But, on the other hand, what we see at the end of that 13.82 billion light-year search is the same thing, in essence the same point in space. How can that be?

Perhaps a way to visualize this phenomenon is to imagine an observer in the middle of the South Pacific Ocean, exactly on the opposite side of the Earth from the famous landmark, the Eiffel Tower in Paris France. Now imagine the Eiffel Tower emitting a bright rotating light and that the light from Eiffel Tower was able to and in fact always followed the curvature of the Earth as it radiated away from the Eiffel Tower. Now the observer on a boat in the South Pacific has a very powerful telescope able to see that light. Looking through your telescope the observer could measure that distance to the Eiffel Tower and that distance would be, as one would expect, half way around the world, or about 20,000 kilometers. In fact, no matter what direction the observer looked from the observation point in the South Pacific, they would be able to see the rotating Eiffel Tower light and thus would always measure the same distance of 20,000 kilometers.

Now if observer did not know about the Eiffel Tower’s special light feature (that it was confined to follow the curvature of the Earth) and they did not know they were on a curved surface of the Earth (pre-Christopher Columbus thinking – the world is flat) and simply used that distance to compute what they thought was the total surface of the “flat” Earth, they would get an inflated size of the surface area of the Earth. By using the formula A = r^{2} for the area of a circle they would derive a value of approximately 2.5 billion square kilometers. In actuality the Earth’s true surface area is roughly 510 million square kilometers. The observer would be off by a factor of about 4.9. Had the observer, however, been able to see directly through the Earth, they would have realized that the “real” distance to the Eiffel Tower was only 2/ of about 63% of the 20,000 kilometer distance, or roughly 12,732 kilometers. But the observer, cannot see through the Earth, only around it. Likewise, we have similar limitations when looking into deep space.

In fact, no matter which direction we look, we see the same thing, but from a different point of view. The light from that depth (referred to as “background radiation”) has curved through space so much that from our point of view it appears to be everywhere. We think of ourselves as being at the “center” of the universe somewhat like our pre-Christopher Columbus observer thought he was in the center of his flat “universe.” But our pre-Christopher Columbus observer was actually displaced from the true center of his universe, the center of the Earth, a three-dimensional distance in his two-dimensional world that he could not comprehend. Likewise, we are displaced from our true center of the universe, the center of time, a fourth-dimensional distance in our three-dimensional world. We think the universe is 13.82 billion light-years in size and thus 13.82 billion years old; but in reality we may only be a 2/ or some other fraction of that distance away from the “true” center of time in the universe; no way to know for certain, since we cannot “look through” the fourth dimension. Regardless of the true size, from a computational point of view we shall use the age of universe as a valid measurement, similar to our observer using the distance to the Eiffel Tower as a valid measurement, but when we compute the volume, just like our observer computing the area, we need to realize that the Cartesian spherical formula we are using may not necessarily apply because of the inherent curvature of space.

But for now, we shall assume that the universe follows close to the laws of a Cartesian sphere and the radius is equal to the observable radius, an estimated 1.307 × 10^{26} meters. If so, this yields a staggering volume for the known universe at around 9.343 × 10^{78} cubic meters; a very large, but still finite size. Now, if the average density of the universe is known, its total mass can be estimated. It is believe that the average density of the universe is on the order of 9.47 × 10^-27^ kg/m^{3} (only a few hydrogen atoms per cubic meter); mostly nothing – almost a perfect vacuum. If this true, the best guess of the total mass in the universe would be on the order of 8.85 × 10^{52} kilograms.

Now, if all that mass in the universe was compressed into a black hole, how large would it be?

Using Schwarzschild’s formula:

2 G M 2 × (6.67428 × 10^-11^ m^{3}/kg s^{2}) (8.85 × 10^{52} kg)

R_{Sch} = ------------ = -------------------------------------------------------------

c^{2} (299,792,456 m/s)^2^

R_{Sch} = 1.314 × 10^{26} meters or roughly 13.8 billion light years!

So a black hole having the mass of the universe would have a radius equal to the current best estimate of the radius of the universe and it would have an average density equal to the best density guess of the universe. Ergo, if it walks like a duck and quacks like a duck, maybe it is a duck.

Granted, there are a number of assumptions in demonstrating that the universe may be nothing more a giant black hole; but you have to admit the similarities are uncanny. So, the next time you wonder what may be inside a black hole, your best answer may be to simply look around you and witness your own universe. We often think of black holes as being incredibly dense with high temperatures and pressures – but when they get very massive, their insides have surprisingly low densities and consequently low temperature and pressure. The only thing peculiar about this particular universe-size black hole we live in is the non-uniformity of the mass inside of it, its clumping of the mass into stars and galaxies. Is this possibly a characteristic of other smaller black holes? Or does a black hole need to get to a certain mass before the incredible density drops (and its correspondent internal temperature and pressure drop) to a point where ordinary matter can again reestablish itself. At this threshold, where an incredibly dense ball of energy inside a black hole finally increases to size and drops to a density level and pressure and temperature level that pure energy could once again solidify into elementary particles, the black hole would transform itself back into an explosion of new particles; just like we currently believe started our own universe, called the “Big Bang.” So the life cycle of a black hole could go from a collapse of a star into a neutron star, which consumes even more mass to form a quark star, which consumes even more mass to form a ball of pure energy, which consumes even more mass to a point where its density finally drops to a point where a Big Bang like phenomenon forms, starting the process all over again.

Recent observations show that the universe is not only expanding, but accelerating in its expansion. This phenomenon would be exactly what someone would experience inside a universe-size black hole that was still growing and devouring mass from outside its boundaries. The expansion of the universe has been the subject of debate ever sense if was first observed by the famous astronomer, Edwin Hubble. No one really knows why the universe is expanding, especially expanding and at an accelerating rate; but they have been able to determines its rate of expansion with a surprising degree of accuracy from empirical observations. The most interesting thing about the expanding universe is that deeper you look into space, or the farther back into time, the faster the expansion rate. This ratio of expansion to the distance of the receding object is referred to as Hubble’s Constant. Depending upon your point of view, you can either think as the universe is expanding from you, because of the fleeing distant or galaxies; or you can think of the universe as a history of slowing down since are observing things which occurred in the past and the nearer they are to us in time, the slower the objects are moving. Welcome to the bewildering world of cosmology. Nevertheless, it is interesting to note that Hubble’s Constant is a measured value, that is empirically derived, and there is no mathematical basis for Hubble’s Constant, until now.

Hubble’s Constant

As stated before, Hubble’s Constant is an empirically derived value (that is, one found only from observation) that relates the recessional velocities of fleeing galaxies to their distances away from the observer. The best measurement of Hubble’s Constant is about 70.1 ± 1.3 Km s-1 M pc-1 or 2.276 ± 0.042 × 10^-18^ m/s per m. That is for every meter of distance away from the observer, an object is seen to be moving away at a rate of 2.276 ± 0.042 × 10^-18^ m/s. A very slow rate indeed, but over very large distances it does add up. Furthermore, Hubble’s relationship appears to be a near linear function; that is, the farther away an object is, the faster its recessional velocity is proportionally. If there is an acceleration of deceleration, it is very, very slight. This recessional velocity, though, may actually not be because distant objects are literally moving from us but may because of another cause; the nature of the observation; a phenomenon caused by viewing something through space-time.

The basic idea is that distant galaxies appear to be moving away from us, (and also from each other for that matter), not as a result of some primordial “Big Bang” multi-dimensional explosion; but rather, because of the result of the nature (or should one say the “illusion”) of the observation. Distant galaxies may only have an “appearance” of recessional velocities (plus or minus there true independent three-dimensional “real” motions”) because they appear to be “falling” toward the “centers” of their own respective universes. A hard concept to understand, but every spot in the universe *is* the center of its own universe, and therefore follows the laws of physics within its respective universe. Any object at the center of its own universe would experience no motion, but from an observer some distance away from the object, it would look like it is trying to move to a point in space which is not the observer’s center of the universe; hence, the appearance of a recessional velocity from the observer.

As we all know, any object at the center of a gravity field experiences neither gravitational attraction nor any motion since all gravitational forces are in balance. The body is weightless and motionless. Likewise, all galaxies which are at the “centers” of their own respective universes, experience no gravitational force and thus no motion. However, relative to an observer at a considerable distance away from that galaxy (and its universe center) it would appear that that galaxy is “attracted” to and thus moving towards that particular point in space – the center of the universe, that is, *its* center of the universe. The distant object is following all the known laws of physics in *its* universe. However, it is not really moving at all, it just looks like it is moving. This is because the light emitted from that galaxy is (or was) adhering to the gravitational laws based upon that center of *its* universe center and not *our* center of the universe, the light waves lose energy (red shift) as they travel through time (and over distance) and they do so in a direct linear ratio (actually 1/x) to their distance (plus or minus any other Doppler shifts due to true relative motions of the light source and the observer).

A useful analogy to help understand this phenomenon could be made in our own common day experience with the laws of perspectives. We all observe that objects appear to be smaller when they are far away. Now, we all know that the objects do not actually get smaller, they only appear smaller because of the nature of the observation; that is, an observation over a distance. Similarly, all objects will also always appear to be moving away from us simply because they are being viewed at a distance (and through time) from the observer. It is this displacement in space-time which gives the illusion of motion. The “receding” velocity would be in direct proportion to the distance, just like a perspective. We just don’t seem to notice this for objects that are relatively close to us, that is distances closer than far away galaxies, because this “motion” is so insignificant that is unnoticeable or masked by other true “real” three-dimensional motions. The phenomenon is so slight that it takes tens of thousands of light years of distance (and time) before the effect starts to become even noticeable. Nevertheless, all objects will always appear to be receding from all observers at all times, even though these objects which are considered a “fixed” distance apart.

This observational phenomenon could be measured over time. For example, if a distant galaxy is truly moving away from us at some colossal speed like 1/3 the speed of light; then one would assume that after a number of years that the same galaxy should be even farther away and therefore should have even a greater recessional velocity; and that difference could be measurable. But as the theory suggests, astronomers would not find that to be the case. Instead, they would measure the exact same distance and the same recessional velocity as they did before! The receding galaxy never moved! (Unless it actually moved in three dimensional space relative to the observer). Besides, how could a receding galaxy gain speed when, with mutual gravitational attraction, it should actually be slowing down? It can’t do both. No matter what the appeared recessional velocity may be, and no matter what the time period, when one observes the same galaxy at two different times they should find that it never really moved and it never gained or lost speed (plus or minus any true three-dimensional motion) – it will always have the same observed recessional velocity.

So what is actually really occurring that causes this observable phenomenon? These galaxies are “falling” (not receding) toward the “center” of their respective universes! So how fast would a galaxy fall towards the center of its universe? To determine this, we must first compute the gravitational attraction of a body towards the center of *its* own universe, as if it was “falling” towards the center of *its* own universe. The gravitational force of attraction (and hence acceleration and instantaneous velocity) of any object falling towards the center of the entire universe can be determined by simply using Newton’s Law of Gravitational attraction:

F = G (M m) / r^{2} M = Mass of Universe

m = mass of any object

r = distance between objects

G = Gravitational Constant

Since “M,” the total mass of the universe is an unknown, we use instead the average density of the universe times an appreciably large volume, for example the known size of the universe. Assuming a sphere for the volume and substituting:

Volume of a sphere = V = 4/3 π r^{3}

Mass = Density x Volume = ρ V (where ρ = density)

F = G (M m) / r^{2} = G (ρ)( 4/3 π r^{3}) m / r^{2}

F = (4/3) π G ρ m r

Therefore, the force of attraction for single kilogram of matter to the entire universe would be:

F = 4/3 π G ρ r [m]

And the force of attraction for the entire universe to the single kilogram would also be:

F = 4/3 π G ρ r [m]

The combined force of attraction of the single kilogram and the entire universe would be:

F = 4/3 π G ρ r [m] + 4/3 π G ρ r [m] or

F = 8/3 π G ρ r [m]

We shall assume for the moment that the average density of the universe is equal to the best estimate of 9.47 × 10^-27^ kg/m3 and “r” is equal to the radius of the best estimate of the “size” of the universe 13.82 billion light-years, 4.36 × 10^{17} seconds or 1.307 × 10^{26} meters.

Thus, F = 8/3 π (6.67428 × 10^-11^ m^{3}/kg s^{2})( 9.47 × 10^-27^ kg/m^{3})( 1.307 × 10^{26} m ) x 1 kg

F = 8.261 × 10^-11^ kg m/s^{2}

Hypothetically then, what would be the velocity of an object “falling” to the center of its universe, or as we commonly think of it, its recessional velocity “v_{r}” a known distance (“r”) away from this universe center?

Known:

F = m a (mass x acceleration) and a = v_{r}/t (velocity/time)

F = m v_{r}/t

v_{r} = (F t)/m = [(8/3 π G ρ r m) t] / m

H_{o} = 8/3 π G ρ t where “t” is the age of the universe

Note: This form of the equation has the same form as Hubble’s formula for recessional velocities.

Hubble’s formula: v_{r} = H_{o} r and substituting produces:

H_{o} = 8/3 π G ρ t when “t” is equal to the “age” of the universe (4.36 × 10^{17} sec)

H_{o} = 8/3 π (6.67428 × 10^-11^ m^{3}/kg s^{2})( 9.47 × 10^-27^ kg/m^{3}) (4.36 × 10^{17} s)

H_{o} = 2.309 × 10^-18^ m/s/m which is very close to the estimated empirical value for Hubble’s Constant of 2.276 ± 0.042 × 10^-18^ m/s per m; and within the tolerances of both the estimates of the average density and age of the universe.

Thus, using simple Newtonian physics, Hubble’s Constant can be now be mathematically derived.

It is interesting to note, using either the Hubble formula v_{r} = H_{o} r or the derived formula:

v_{r} = (8/3 π G ρ t) r

That when an object is the maximum distance (1.307 × 10^{26} m) or at its maximum time away (4.36 × 10^{17} sec) its recessional velocity (v_{r}) becomes:

v_{r} = 8/3 π (6.67428 × 10^-11^ m^{3}/kg s^{2})(9.47 × 10^-27^ kg/m^{3}) (4.36 × 10^{17} s) (1.307 × 10^{26} m)

v_{r} = 3.017 × 108 m/s or very close (<1%) to the value of “c”, the speed of light

And again within the tolerances of both estimates of the density and age of the universe.

Thus it is argued that since objects that are 13.8 billion light-years from an observer will have the appearance of a recessional velocity equal to the velocity of light, and since according to Einstein nothing can go faster than light; then this distance becomes in effect a “light barrier” beyond which nothing can be seen by an observer. The limiting speed of light also limits the distance one can see.

This strange concept is analogous to someone standing on the seashore and looking out at the horizon. At some point the curvature of the earth prohibits the observer from seeing any further. Obviously, the Earth extends past his viewing distance; but the observer just can’t see it because of the curvature of the Earth. Likewise, the “light barrier” is a maximum viewing distance within our universe, but it in no way limits the size the universe any more than the distance to a horizon limits the true size of the Earth. Therefore, the universe could be larger and older than the present estimated age of the universe; it just that one cannot see any farther. The appearance of the receding velocity when viewing objects over such a distance, near the “edge” of this observational limit, would give the appearance of something moving near the speed of light. Because of this illusion and adhering to the laws of relativity, these objects would appear to excrete tremendous amounts of energy and be very dense in would seem to shrink in their direction of motion. Which are phenomenon we currently see when we view the edge of the universe; but after it has been distorted due to the recessional velocity phenomenon.

But take a magical instantaneous trip to “edge” of the universe and one would probably find galaxies just like our own extend on another 13.8 billion light-years. Look back at our own Milky Way galaxy and it would be the one appearing to be moving near the velocity of light excreting enormous amounts of energy. As Einstein said, it is all relative.

Which introduces another paradox, what happens a billion years from now? Will the observer see a 14.8 billion year old universe or would he still only see back into time 13.8 billion years? Unless some laws of physics change, like the speed of light changing speed, the answer is the observer will still only see 13.8 billion light-years. And if this true, we will always be limited to a certain viewing distance. Furthermore, the notion than everything started from a primordial Big Bang 13.8 billion years ago is probably false. The universe and time itself could potentially go on forever.

Interestingly, when you set the recessional velocity (v_{r} ) equal to the speed of light ©:

H_{o} r = c (velocity of light) (observable limit)

Then, Hubble’s formula simply reduces to:

H_{o} = 1/t

Or, in short, Hubble’s constant is simply the inverse of time.

Thus, finally there is an equation which can interrelate the values of “G”, “c” with both the age and density of the universe. Furthermore, if the theory of recessional velocities as a function of distance is true, then there must be some distance “z” where two objects can be placed so that there velocity due to mutual gravitational attraction is equal and opposite to their respective recessional velocities due to their separation. This distance “z” can be determined by setting the formula for gravitational attraction equal to recessional expansion. The value of “z” is equal to:

z = ( G / H_{o} ) ^{-1/3}

If this is true, two 1 kilogram objects placed a distance of 308.78 meters apart, where one of the 1 kilogram objects is fixed and the other is free to move, the kilogram object which is free to move should have a recessional velocity of 7.00 × 10^-16^ m/s while at the same time, after one second, should have an instantaneous velocity due to its attraction to the fixed 1 kilogram object also equal to 7.00 × 10^-16^ m/s. The two opposing velocities should equal each other out so that 1 kilogram object would instead of moving toward the fixed 1 kilogram object according to Newton’s Law of Gravitational would remain motionless because of its respective recessional velocity due to Hubble’s Law of recessional velocity. Thus, there is always some distance between any two bodies of any mass where the velocity from their acceleration due to their gravitational attraction is insufficient to overcome their recessional velocity due to their distance of separation. In effect, the “reach” of gravity does have its limit, beyond which recessional velocity due to distance becomes the overcoming motion.

For example, our Sun which has a mass of approximately 1.989 × 10^{30} kg has a “reach” to a 1-kilogram object of approximately 3.9 × 10^{12} meters. At that distance, the recessional velocity becomes equal to its velocity from the acceleration due to gravitational attraction. Not surprisingly, this is about the distance to the edge of the Oort cloud, considered the outer edge of the Sun’s orb of physical orbiting bodies.

Another example, the Moon’s recessional velocity relative to the Earth would only be about 8.7 × 10^-10^ m/s, virtually impossible to measure. Nevertheless, the recessional motion is still there. In a year’s time, though would cause a recessional movement of a little over 2.7 centimeters. Currently, the Moon is moving away from the Earth at a rate of about 3.8 centimeters per year – or is it?

The relationship between Mass and Time

Another derivation of the H_{o} = 8/3 π G ρ t formula when H_{o} r = c is:

M = (c^{2} / 2 G) r , (a variation of the Schwarzchild formula)

Thus, if you know the radius of the universe, you can compute its total mass.

For r = 1.307 × 10^{26} meters

The total mass of the universe is calculated to be:

M = c^{2} r / 2 G = (299,792,456 m/s)^2^ (1.307 × 10^{26} m )/ 2 (6.67428 × 10^-11^ m^{3}/kg s^{2})

M = 8.8 × 10^{52} kg ±

Since there is a relationship between distance and time, that is c = r / t, then the formula can also be rewritten to express the mass of the universe as a function of its age:

M = (c^{2} (c/ t) / 2 G) = (c^{3} / 2 G) t, substituting

M = c^{3} / 2 G = ((299,792,456 m/s)^3^ / 2 (6.67428 × 10^-11^ m^{3}/kg s^{2}) ) (4.36 × 10^{17} s)

M = 8.8 × 10^{52} kg ±

Just as there is a relationship between distance (space) and time through the relationship r = ct; that is distance equals the speed of light times time and there is a relationship between energy and mass in the equation E=mc^{2} ;there is also a relationship between mass and time in the formula:

c^{3}

m = ------- t

2 G

Where m = mass

c^{3} = speed of light cubed

G = Gravitational Constant

t = time

This formula suggests the reason why the universe appears to be 13.82 billion years old is because it has a specific mass! Thus, mass and time are interrelated. Just like space-time; there must be also be space-mass-time. And with the relationship of energy to mass, in reality there is a space-mass-energy-time relationship. There is a fundamental relationship between mass and time.

For example, 1 second is equivalent to 2.02 × 10^{35} kg! As hard as it is to imagine, a small amount of time is equivalent to a tremendous amount of mass. It is easy to get lost when dealing with such larger values but remember, the age of the universe, 4.36 × 10^{17} seconds, equals 8.80 × 10^{52} kg. On the other hand, 1 kilogram only equals to about 4.95 × 10^-36^ seconds.

Rewriting the formula in terms of time “t”:

2 G

t = ------- m

c^{3}

2 G 2 (6.67428 × 10^-11^ m^{3}/kg s^{2})

t = ------- m = ------------------------------------- (1 kg)

c^{3} (299,792,456 m/s) ^{3}

1 kg = 4.95 × 10^-36^ seconds

Thus, if you have mass, you must also have time, and vice a versa. You cannot have one without the other. It may be easier to imagine what value energy has to time with the sister formula:

c^{5} (299,792,456 m/s)^5^

E = ------- t = ---------------------------------- (1 sec)

2 G 2 (6.67428 × 10^-11^ m^{3}/kg s^{2})

Thus, 1 second equals 1.814 x^{52} Joules; or, 1 Joule = 5.51 × 10^-53^ seconds. One second of time is equivalent to a tremendous amount of energy. But can you convert one into the other?

We often think of energy and matter as interchangeable, illustrated in the famous equation E=mc^{2}. You either have one or the other. If you destroy one, you automatically create the other. Energy/Matter cannot be created or destroyed, only transformed from one state into another.

But as seen from above, we have time because we have mass. And since we are gaining time, that is, the universe is getting older since our clocks seem to be moving forward, there must be a corresponding increase in mass in the universe to account for the increase in time. The conversion of energy into mass would not account for this additional mass since they are basically two sides of the same coin. Instead, mass (or an equivalent amount of energy) must be added to the universe from outside the universe in order for its total mass to increase. This would jive with the earlier notion that the universe is a large black hole which is still devouring mass from an even larger universe. It is either that, or the fact that since time is moving forward, mass is somehow being created out of nothing. But why would or how would time create mass? The more likely scenario is that mass is being continually added to the universe from outside the universe and, surprisingly, that is adding time to the universe. If the addition of mass to the universe stops, then it is conceivable that time could stop as well.

The Five Dimensions

It is common to hear of the three “dimensions” of space and a fourth dimension of time. Actually, there is a better way to think about dimensions. There are at least five dimensions, of which space is but just one not three of this dimensions; but one that one has three directions.

The first “dimension” is time. Time is like a line, it has only length, but no width or thickness nor any other property. Time can be forward or positive or it can be backwards or negative, or it can be zero. The notion of time itself is meaningless unless there something to measure its presence.

The second dimension is Energy. The second dimension is like a plane, it can have length and width but no thickness. Energy is always confined to a plane. It can be a curved plane, like a surface of a sphere, but still only having only two directions. Electromagnet energy propagates along these planes being at all places (on the surface) at the same instance until it encounters something that changes its state; at which point the wave front collapses instantaneously. Electromagnetic energy wave forms are really minor fluctuations of time, positive and negative time. Their net average is always zero or no time and Energy is immune to time; energy waves are timeless. Together, an energy plane moving along a time line (Energy-Time) creates the volume of a third dimension.

The third dimension is Space. Space has the three directions, like a volume, just like classical Cartesian coordinates portray. Interestingly, space can only be visualized if there are at least two objects in space in which to measure between. And that measurement can only be accomplished with the aid of energy. If there are no objects (mass) or energy in the space, there is no means to measure the space; but it nevertheless can still exist. Space (distance) relates to time by the relationship of d=c t; or distance is the speed of light times time. When Energy-Time moves through Space, this is what creates the fourth dimension.

The fourth dimension is actually Matter. Matter is created when Energy-Time moves through Space, not in two-directional way, but rather in a three-directional way in either a rotational or revolutionary manner. Energy spinning on its axis creates a particle. Energy revolving around a point, such as in the electrons orbiting an atom, also creates a particle. Destroy that rotation or revolution of an Energy wave, and you will destroy the particle and thus will release the Space-Time embodied within it. We often think of Einstein’s famous equation, E=mc^{2}, as a small amount of mass equals a tremendous amount of Energy. Actually what the formula really states is that mass is equal to energy and Space-Time. The “c” in the formula is the speed of light which is measured in meters per second (space-time). This is why the value of “c” is in the relationship between E and m in the formula E=mc^{2}. When Energy moves in either of these types of motion, in addition to creating mass, it also causes an equivalent distortion or warping of space. This phenomenon we call gravity.

The fifth dimension occurs when Mass is moving through either Space or through Time, and only relative to something else. When matter (embodied energy) itself is moving such as revolving, it still possesses its gravity phenomenon, but also causes a distortion or warping of energy. We call this angular momentum. When matter is moving through space (relative) to something else it also distorts energy. We call this phenomenon momentum. As you would imagine, Mass at rests does not like to change its relative position in space, because if it does it induces the distortion of energy. We call this phenomenon inertia. The greater the mass, the greater the distortion of the space and the greater its inertia.

Summary

This book describes the logic behind why the universe is more than likely simply a very large black hole; a universe-size black hole in an even larger universe. It also shows how that the unique size and age of the universe is directly linked to the amount of mass within it. And that the notion of an expanding universe or a universe with a specific size and age is really more of an observational phenomenon due to the limiting speed of light rather than actual behavior of the universe itself. The Big Bang is an illusion, not a primordial event of creation.

If you have read through this entire manuscript to this point, I congratulate you for your perseverance and having at least an open mind. It is very probable that one or more of the ideas presented in this book may not agree with your understanding of the cosmos. If so, I challenge you to contact me and feel free to either point out the flaws in my logic or present an alternative solution. My telephone number is 321-698-5739 and my email is [email protected]. I claim no mystical knowledge or divine inspiration – but rather from experience, observation and pure thought believe that the cosmological ideas presented are a truer understanding of our universe.

The END.

This book describes the logic behind why the universe is more than likely simply a very large black hole; a universe-size black hole in an even larger universe. It also shows how that the unique size and age of the universe is directly linked to the amount of mass within it. And that the notion of an expanding universe or a universe with a specific size and age is really more of an observational phenomenon due to the limiting speed of light rather than actual behavior of the universe itself. The Big Bang is an illusion, not a primordial event of creation.

- ISBN: 9781310437090
- Author: R. J. Treharne
- Published: 2016-03-16 06:50:08
- Words: 8637