## The Space Production Model of Gravity

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### The Space Production Model of Gravity

￼Abstract

The Space Production Model of gravity is based on the premise that mass emits space and provides for an explanation for the expansion of the universe and Dark Energy. The SPM states that the mass of an object is proportional to the amount of space it emits per unit time.

The amount of space emitted by a given amount of mass can be calculated based on the Space Production Model of a black hole. According to the SPM, the singularity of a black hole emits more space per unit time than light can travel. The radius of the event horizon would therefore be represented by the distance from the singularity at which the rate of space production equals the speed of light.

Since light travels 1Planck length per Planck time a black hole emits a volume of space equal to 1 Planck length deep by the area of its event horizon per Planck time. Using this one can calculate the mass of the universe based on the Hubble constant.

Using 70 km/sec per mega parsec as the Hubble constant and assuming the radius of the universe is 46 billion light years the volume of the universe increases 1.26x10^20 m3/Planck time = 3x10124 Planck volume/Planck time= event horizon 3x10124 Planck area = 7.84x1054 m2 = a Schwarzschild radius of 7.9x1026 meters = a mass of 5.34x1053 kg. This is within the expected range for the mass of the universe.

If mass is the source of the newly created space associated with the expansion of the universe then the most massive gravitationally bound objects, galaxy groups and clusters, should produce more space per unit time and recede slightly ￼faster than a less massive lone galaxy at the same distance. Therefore, over the billions of years of expansion, the universe should become closer to the critical density rather than further from the critical density as is currently thought.

In essence, the universe is expanding at different rates in different regions depending on the local mass density. This phenomenon provides a further explanation for the "flatness" of the universe. This also provides a method of testing the model.

If the SPM is true, large galaxy clusters should recede slightly faster than lone galaxies at the same distance. A galaxy cluster with a mass of 1.988435×10^45 kilograms would have a Schwarzschild radius of 2.953×10^18 meters and an event horizon surface area of 1.1×10^38 square meters which would produce 3.298×10^46 cubic meters per second which at a distance of 3 mega parsecs would equate to a recession rate of approximately 0.3062 meters per second faster than predicted by the Hubble constant. Whether current technology is sophisticated enough to determine this small difference in recession rate is questionable.

However, if this were confirmed by observation, it would be extremely compelling evidence in support of the SPM. The attractive force due to the SPM is less intuitive than the repulsive force outlined above. According to the SPM, the attraction between objects is due to the pressure waves generated by their emission of space. These pressure waves travel through space away from their source at the speed of light. The waves from two objects create an interference pattern such that there is less energy emitted between the objects than in any other direction. This results in each object "pushing" itself towards the other. ￼

1. Introduction

The Space Production Model (SPM) of gravity reverts back to the idea of an ether. The SPM proposes that space is something tangible and that it is produced by matter. Some have suggested that Einstein's General Theory of Relativity did away with the idea of an ether and that the Michelson-Morley experiments proved there was no ether (Michelson, A. A. 1881).

The Michelson-Morley experiments, however, were designed to detect the presence of a stationary absolute ether. It was assumed that since the earth was traveling through this stationary ether that the ether was moving with respect to the earth. Therefore, it should take light longer to travel in one direction than another since light would have to travel through more ether in the direction of earth's movement. However, in their experiments the time it took light to travel a given distance was the same regardless of its direction of travel.

It is based partially on these experiments and many similar subsequent ones that the notion of an ether was discarded. However, even after the Michelson-Morley experiments had failed to detect the stationary ether and even after he published his paper on general relativity, Einstein still talked of the ether. He stated "the ether of the General Theory of Relativity is at every place determined by connections with the matter and state of the ether in neighboring places".

Interestingly, the first experiment to substantiate the Theory of General Relativity was similar to￼￼￼￼￼￼￼￼￼￼￼￼ ￼Michelson-Morley in that it also measured the time it took for light to travel a specific distance but on a much grander scale. This of course was the experiment by Arthur Eddington which showed that light from a distant star took longer to travel the same distance to earth if its path was in close approximation to a massive object, in this case the sun.

The Space Production Model of Gravity presented in this paper is consistent with the ether as Einstein described and states that space itself is the ether and that it is produced by matter. It contends that this is the mechanism by which mass curves space time. In essence, the curvature of space time represents the pressure waves generated by matter's emission of space. This model is therefore consistent with the general theory of relativity but is also able to provide answers to phenomenon not explained by the general theory of relativity.

2. Attractive Force of Gravity

The following concepts allow for a mechanistic understanding of the attractive force of gravity. The basic principle of the Space Production Model of gravity is that all matter is converted to and emits space. The mass of an object is proportionate to its rate of space production and objects are attracted to each other as a consequence of their emission of space. The SPM states that every time an object emits space it creates a pressure wave. Since an object's mass is proportional to the amount of space it produces per unit time, the energy contained in the￼￼￼￼￼￼￼￼￼￼￼￼ pressure wave created by the space emission is also proportional to the object's mass. This energy is distributed over the surface area of enlarging spherical pressure waves traveling away from the object at the speed of light. The surface area of a sphere is equivalent to 4pr2( Author 2000 ). As these spherical pressure waves travel away from their source and their radius increases, the energy in each wave is distributed over an area that is proportional to r2.

￼￼￼￼￼￼In essence, as the distance from the source increases the energy per unit surface area of the ￼spherical pressure wave decreases as a function of the inverse square. This is consistent with our current understanding of the force of gravity which also dissipates as a function of the inverse square of the distance from the center of an object.

￼Consider two space emitting objects in relatively close proximity to each other. Each object is producing pressure waves proportional to its mass that in the vector between the two objects are traveling in opposite directions. The Space Production Model proposes that these waves of pressure interfere with one another in such a way as to create an interference pattern such that there is more cancellation between the two objects than in any other direction.

Therefore part of the energy produced by object A in the direction of object B is cancelled and vice-versa. This creates a disequilibrium in each object's wave production pattern with more energy/pressure being emitted on the side opposite the other object. This results in each object "pushing" itself in the direction of the other.

This is demonstrated using a vibrating Styrofoam ball floating in a pool of water.

The vibrations send out pressure waves which when in close approximation to a wall are reflected back creating an interference pattern just as if the wall was￼ ￼another wave emitting ball. the ball is attracted to the wall, but when not vibrating there is no attraction.

In summary, the attractive force of gravity is a consequence of the pressure waves created by an object's emission of space. When the waves emitted by two objects interact with one another they produce an interference pattern such that more energy between the objects is cancelled than in any other direction. This then causes each object to push itself toward the other – in essence, an attractive force.

3. Repulsive Force of Gravity- Dark Energy

The expansion of the universe has been attributed to a heretofore unexplained force currently termed Dark Energy. With the Space Production Model ￼the repulsive force of gravity is more intuitive than the force of attraction. Consider the analogy of a waterfall. As the water falls into the pool below, it creates ripples/waves. As discussed in the first section, it is the waves that are responsible for the force of attraction. However, in addition to creating these waves, the incoming water adds to the volume of water in the pool. In the same way when an object with mass emits space it not only creates spherical pressure waves that travel through space, it also adds to the total amount of space present.

Therefore, while the attractive force is a consequence of the waves, the repulsive force is a consequence of the actual space produced or in the above analogy the added water. One obvious question becomes how much space does a given amount of mass emit per unit time?

The SPM's explanation of a black hole can be used to make this determination. According to general relativity a black hole is a singularity with infinite density and whose gravitational field is so strong its escape velocity exceeds the speed of light. The radius of the event horizon is the distance from the singularity at which the escape velocity equals the speed of light.

According to the SPM, the singularity of a black hole emits more space per unit time than light can travel. The radius of the event horizon would therefore be represented by the distance at which the rate of space production equals the speed of light. It is similar to a river that widens as it progresses toward the sea.
￼￼￼￼￼￼￼￼￼￼￼￼￼
￼￼In this analogy, the water is analogous to the space speeding away from the singularity. If the same amount of water is flowing downstream at each point along the river, the current slows as the river widens. Conversely the current increases as one moves upstream.

Consider a boat traveling upstream at the speed of light. The boat will always travel at the speed of light in relation to the water but as the river's current increases the boat slows in relation to the shore until it reaches a point where the speed of the current reaches the speed of light. At this point the boat is no longer moving in relation to the shore.

Getting back to the black hole this would mean that the event horizon is the point where space is flowing away from the singularity at the speed of light. Therefore, light traveling toward the black hole would get "stuck" at the event horizon. It would continue to travel towards the ￼singularity at the speed of light but it just can't get there because there is always more space coming towards it.

In this scenario the only thing on the inside of the event horizon is more space. With regards to black hole accretion the above scenario would mean that rather than nothing being able to get out of a black hole nothing would be able to get into a black hole. All matter being drawn toward the black hole, including light, would be "stuck" at or very close to the event horizon.

Based on the premise that light travels 1 Planck length per Planck time, a black hole produces one Planck volume of space per Planck area of its event horizon per Planck time. In essence, a black hole emits a volume of space equal to one Planck length deep by the surface area of its event horizon every Planck time.

For example, a typical spiral galaxy with a mass of 105Msol would have an event horizon of 1.1×10^18 square meters equal to 4.211×10^87 Planck areas. If this is 1 Planck length deep it would equal 1.778×10^-17 cubic meters per Planck time or 3.298×10^26 cubic meters per second. It becomes clear that one of the implications of the SPM is that it provides a source for Dark Energy via its conversion of mass to space.

The amount of new space produced per unit time can be viewed as an enlarging sphere. While a sphere's surface area increases as a function of the square of its radius, a sphere's volume increases as a function of the cube of its radius. Therefore, while the attractive force diminishes as the inverse square of the distance the repulsive force, dark energy, dissipates as a function of the inverse￼￼￼￼￼￼￼￼￼￼￼￼ ￼cube of the distance.

This would mean that at "normal" distances the attractive force would dominate but at extremely small distances approaching the Planck length the repulsive force becomes a major factor. It also becomes a major factor at extremely large distances.
At first glance this would seem to be inconsistent with an accelerating expansion since it would result in a rate of expansion that decreases with increasing distance. However, the greater the distance between galaxies, the greater the number of intervening galaxies with each galaxy contributing additional space. Since galaxies are spread throughout the universe rather homogeneously the result is an expansion rate that is directly proportional to the distance.

Since matter is distributed throughout the universe rather evenly, the incoming "attractive" waves do not predominate from any particular direction. This results in no net attractive force. In essence, there is equal cancellation in all directions and the "attractive" force is no longer present. However, the production of space continues resulting in more space being created between each of the galaxies/clusters. One could argue that the galaxies are not "moving" apart in as much as they are just creating more space between one another.

To test whether the SPM is consistent with the current state of the universe one can calculate the amount of space emitted by all the mass in the universe for the life of the universe. If the SPM is true it should come close to the current size of the universe. The mass of the observable universe determined by its critical density is 1.53x10^53 kilograms.

The surface area of the event horizon of ￼black hole with that mass equals 6.488×10^53 square meters. Convert this to Planck area 2.484×10^123 and multiplying by the Planck length gives the volume of space emitted per Planck time equals 1.049×10^19 cubic meters per Planck time.

There are 5.85×10^50 Planck times per year multiplied by the age of the universe 13.75x10^9 equals 8.04375x10^60 Planck times. Multiply this by the 1.049×10^19 cubic meters per Planck time equals 7.36888x10^79 cubic meters which when converted to cubic light years equals 9.9646×10^31 cubic light years. This is reasonably close to the current estimation of 4.1 × 10^32 cubic light years.

Another way to test this is based on the Hubble constant. Using 70 km/sec per mega parsec and assuming the radius of the universe is 46 billion light years would represent an increase volume of 1.26x10^20 m3/Planck time = 3x10124 Planck volume/Planck time= event horizon 3x10124 Planck area = 7.84x1054 m2 = a Schwarzschild radius of 7.9x1026 meters = a mass of 5.34x1053 kg. This is within the expected range for the mass of the universe.

4. "Flatness of the Universe"

Current data from WMAP suggests that the universe is flat, meaning that the matter contained within the universe is distributed evenly very near the critical densit. According to Wikipedia, ￼“The flatness problem is a cosmological fine-tuning problem within the Big Bang model of the universe. Such problems arise from the observation that some of the initial conditions of the universe appear to be fine-tuned to very 'special' values, and that a small deviation from these values would have had massive effects on the nature of the universe at the current time.

In the case of the flatness problem, the parameter which appears fine-tuned is the distribution of matter and energy in the universe. This value affects the curvature of space-time, with a very specific critical value being required for a flat universe. The current density of the universe is observed to be very close to this critical value.

The early universe must have had a density even closer to the critical density, departing from it by one part in 10^62 or less. This leads cosmologists to question how the initial density came to be so closely fine-tuned to this 'special' value.”
While the SPM is consistent with the inflationary model that has been put forth in part to explain this phenomenon, it would seem to suggest that this fine tuning in the early universe was not necessary.

If mass is the source of newly created space then the most massive gravitationally bound objects, galaxy groups and clusters, should produce more space per unit time and recede slightly faster than a less massive lone galaxy at the same distance. Therefore, over the billions of years of expansion, the universe should become more isodense. In essence, the universe is expanding at different rates in different regions depending on the local mass density.

For example, a galaxy cluster with a mass of 1.988435×10^45 kilograms would have a Schwarzschild radius of 2.953×10^18 meters and an event horizon surface area of 1.1×10^38 square meters which would produce 3.298×10^46 cubic meters per second which at a distance of ￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼3 mega parsecs would equate to a recession rate of approximately 0.3062 meters per second.

A small lone galaxy could have a mass of as little as 3.97687×10^38 kilograms which has a Schwarzschild radius of 5.91×10^11 meters and an event horizon surface area of 4.38×10^24 square meters. It would produce 1.313×10^33 cubic meters per second which at a distance of 3 mega parsecs would equate to a recession rate of approximately 1.219×10^(-14) meters per second. Whether current technology is sophisticated enough to detect this small difference in recession rate is questionable. However, if this were confirmed by observation, it would be extremely compelling evidence in support of the SPM.

5. Motion

Currently there is a problem with the definition of motion since it is clear that galaxies in some parts of the universe are receding from other galaxies at greater than light speed. While it is understood that this is a consequence of the expansion of space, a more specific explanation is desirable. The Space Production Model provides such an explanation with its new definition of motion.

An object can be said to be in motion if it has a non-uniform space particle emission pattern and conversely an object can be said to be at rest if it has a uniform space particle emission pattern. In essence, an object can be said to be in motion if it is emitting more space in one direction than in another. In this case the object is moving in the direction of the least space particle production.

An object can be said to be at rest if its space ￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼￼particle production pattern is uniform.
In this case an object that is ￼receding from all surrounding objects such as a distant galaxy could be said to be at rest even though it would appear to be moving away from all other galaxies. Of course, the galaxy could also be "moving" i.e. non-uniform gravitation production pattern and still be receding from all other galaxies. In this case it would be receding from some galaxies faster than others.

A moving black hole would have a non-spherical event horizon. The distance from the singularity to the event horizon would be less in the direction of its movement. One way to envision SPM motion is to put Newton's first law of motion in terms of the Space Production Model.

First law: Every body remains in a state of constant velocity unless acted upon by an external unbalanced force. The space emission pattern of an object remains constant unless the object is acted upon by an external unbalanced force.

Imagine a pipe fitted with a T on one end. ￼￼￼￼￼￼￼￼￼￼￼￼￼￼The end with the T is submerged in a pool of standing water. Water is then pumped through the ￼pipe and out the T.

If everything is perfectly equal 50% of the water will exit the East end of the T and 50% will exit the West end of the T resulting in no net force in either direction.

However, it does create inertia in both the East and West directions. In this scenario the T pipe is at rest since it has a uniform space emission pattern.

Now instead of a pool of standing water let's submerge the T in a pool with a current running from East to West. In this case the T-pipe is attached to the side of the pool so that it is not moved by the force of the current. Here there would be more pressure on the East end of the T causing a disproportionate amount of water to exit the West end.￼￼￼￼￼ This will come to equilibrium so that the water exiting the West end of the
￼tube exerts a force that counteracts the force of the water current.

For example, 90% could exit out the west end and 10% out the east end. While the T-pipe is stationary in relation to the side of the pool, it is moving in relation to the water. One can say that the pipe is moving in the East ￼direction and the water is stationary or that the pipe is stationary and the water is moving past the pipe in the West direction.

The pipe is not able to tell if it is moving through the water or the water is moving past it. The pipe can then be released from its attachment to the side of the pool and it will remain stationary.

In this situation if the current in the pool is turned off the T-pipe would continue to move at the same rate in relation to the water but since there is no longer
a current, the T-pipe would also be moving with relation to the side of the pool.

￼￼￼￼￼￼￼If the pipe has in inexhaustible supply of water to emit and the pool was infinitely long the T pipe would continue to move at the same rate in East direction for an infinite time.

When an object is moving through space the pressure is constantly greatest in the direction of movement causing a constant space production pattern in the opposite direction. An object in motion continues in motion unless acted on by another force.
￼￼￼￼

￼6. SPM and Relativity A. Motion, Time, and Mass

The attractive force of SPM is consistent with Einstein's Theory of Relativity and merely provides a mechanism by which mass curves space-time. According to the SPM space is composed of particles or quanta. The mass of an object is determined by the number of space particles emitted per unit time and the resulting pressure waves represent the curvature of space- time.

The SPM also provides a quantum mechanism for the relationship between motion, time, and mass in accordance with the theory of general relativity. The passage of time requires change and change requires movement. One change we are familiar with, molecular electron transitions, is the basis for atomic clocks and is associated with atomic movement. In this regard, an electron orbits its nucleus x number of times per oscillation.

According to the SPM, in order for the electron to complete one revolution around the nucleus it must emit y number of space particles in the opposite direction of its movement. If the entire atom is at rest in relation to its surrounding space then the majority of the electron's space particle emissions are associated with its orbit around the nucleus.

For the sake of argument let's say at rest there are 1100 space particle emissions per revolution, 1000 of which are in the opposite direction of the electron's orbit and are responsible for its movement around the nucleus. The remaining 100 particle emissions are distributed evenly in all other directions.

However, when the entire the atom is moving close to the speed of light, the space particle emission pattern of the electron would be such that the majority of its particle emissions would be in the direction opposite the entire atom's movement.

This leaves only a small percentage of the electron's space particle emissions available for movement around the nucleus. Now, due to the movement of the entire atom, rather than 1100 particle emissions per revolution the electron may have to emit 1,000,000 space particles per revolution. It would still require1000 particle emissions in the opposite direction of orbit to complete one revolution but when the entire atom is moving it is also emitting 999,000 particles in the opposite direction of the entire atom's movement. This results in the electron having to emit more space particles per revolution around the nucleus than if the entire atom were at rest.

If the rate of molecular electronic transitions is a measurement of time and is proportionate to the number of electron revolutions, then when the entire atom is moving, there are more space particle emissions per electron revolution and therefore more particle emissions per unit time. According to the space production model, time is defined as change and the rate of time is defined as the number of space particle emissions per unit change.

Increasing the number of space particle emissions per unit change results in a decrease in the rate of time. According to the space production model, the mass of an object is defined as the number of space particle emissions per unit time (change). Therefore, decreasing the rate of time results in an increase in an object’s mass.

This would also apply to a strong gravitational field, such as if the atom were in close approximation to the event horizon of a black hole where space is moving toward the atom at close to the speed of light. Therefore, regarding time dilation there is no difference between an object moving through space at near light speed versus space emitted from a black hole moving toward the object at near light speed.

In both cases the space particle emission pattern of an electron orbiting the nucleus would be altered in such a way that the majority of its emission pattern would be in the direction opposite to the entire atoms direction of travel or in the case of a black hole, the direction opposite the event horizon. This would increase the number of total space particle emissions required for the electron to complete its orbit around the nucleus. Again, since mass is defined as the number of space particles emitted per unit time, and time is defined as change, there would be more particles emitted per unit change resulting in an increase in the objects mass.

In summary, if time is defined as a specific change such as molecular electronic transitions then the rate of time could be defined as the number of space particle emissions per unit change and the more particles emitted per unit change the slower the rate of time. So when moving close to ￼the speed of light or in close proximity to an event horizon more space particle emissions would be required per transition thereby slowing time and increasing mass.

7. Rotational Frame Dragging

Wikipedia describes frame dragging as follows:"Einstein's general theory of relativity predicts that non-static, stationary mass-energy distributions affect space-time in a peculiar way giving rise to a
phenomenon usually known as frame-dragging. The first frame-dragging effect was derived in 1918, in the framework of general relativity, by the Austrian physicists Josef Lense and Hans Thirring, and is also known as the Lense–Thirring effect. They predicted that the rotation of a massive object would distortspace-time metric, making the orbit of a nearby test particle precess. This does not happen in Newtonian mechanics for which the gravitational field of a body depends only on its mass, not on its rotation. The Lense-Thirring effect is very small—about one part in a few trillion."

According to the space production model an object can be said to be non-rotating if its space- particle emission pattern is perpendicular to its surface. ￼On the other hand, an object can be said to be rotating if its space particle emission pattern is tangential to its surface.

One analogy is a spinning sprinkler, where both the sprinkler and the water it emits are rotating. A person running by the sprinkler will get wetter if he passes by in the direction opposite the sprinkler's rotation than if he passes by in the same direction as the sprinkler's rotation.

Similarly, light takes longer to pass by a rapidly rotating object if it passes in the opposite direction of the objects rotation than if it passes the object moving in the same direction as the objects rotation. This is because light traveling against the direction of rotation has space traveling towards it whereas light traveling in the direction of rotation is being carried along by the space moving in the same direction.
It is similar to someone swimming against a current as opposed to someone swimming with a current.

￼8. Quantum space, String Theory, and Extra Dimensions

According to Wikipedia,
“string theory attempts to reconcile quantum mechanics and general relativity. String theory posits mainly that the electrons and quarks within an atom are not 0-dimensional objects, but rather 1-dimensional oscillating lines ("strings"). String theories also require the existence of several extra, unobservable dimensions to the universe, in addition to the four known space- time dimensions. string theory allows for the consistent combination of quantum field theory and general relativity, agrees with general insights in quantum gravity (such as the holographic principle and Black hole thermodynamics), and because it has passed many non- trivial checks of its internal consistency. However it is frequently criticized for not providing any quantitative experimental predictions.” (Wikipedia 2012)

One possibility that fits well with string theory is that all matter is composed of singularities that interact in specific ways to form the particles we are familiar with such as quarks, protons, electrons, neutrons, neutrinos, etc. Each singularity is composed of “compressed” space and emits particles of space. Based on the attractive mechanism already discussed, if two singularities come close enough to one another, they will capture each other and become an orbiting pair.

Orbiting pairs of singularities create space-particle emission patterns such that they are attracted to other pairs. This results in the formation of a string of orbiting pairs similar to a string of spinning doughnut It is possible that the opposite ends of the string could be attracted to each other forming a loop.

￼Each of these loops could of course create space particle emission patterns such that they line up with each other to form another string of bigger spinning doughnuts and on and on.

At some point these could reach the needed mass and arrange themselves into specificconformations to form electrons, protons and neutrons. For instance, an electron might be an open string of doughnuts, whereas neutrons and protons might have pairs of doughnuts stacked on each other like dumbbells to form much more compact closed (neutron) or open (proton) strings. The specific space emission patterns of each of these conformations would beresponsible for its behavior.

Whether this actually happens to form the particles we are familiar
with is highly speculative but it is one way to envision the multiple dimensions associated with string theory. String theory has been able to combine the weak force, electromagnetism, and the strong force. Therefore, if SPM is consistent with string theory, it too could possibly explain these forces.

9. Dark Matter

Wikipedia describes dark matter as follows:
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly seen with telescopes. Dark matter is believed to constitute 83% of the matter in the universe and 23% of the mass-energy.

Dark matter was postulated by Fritz Zwicky in 1934 to account for evidence of "missing mass" in the orbital velocities of galaxies in clusters. Subsequently, other observations have indicated the presence of dark matter in the universe; these observations include the rotational speeds of galaxies, gravitational lensing of background objects by galaxy clusters such as the Bullet Cluster, and the temperature distribution of hot gas in galaxies and clusters of galaxies.

The multiple dimensions discussed in the previous section provide a possible explanation of dark matter. While also highly speculative it would suggest that only matter in the final dimensional conformation is able to interact via electromagnetism. From what we know of Dark matter this would imply that the majority of matter exists in one of the other eight dimensions. It may be that only singularities within a narrow range of mass are able to consistently interact with one another in such a way as to form particles.

This would leave the majority of singularities in their one dimensional state unable to interact with "normal" matter except via gravity. The most extreme instance of this of course would be a black hole.

10. The speed of light

In quantum space the smallest unit of distance is the Planck length. If the space particle is the quantum of space then the distance from one space particle to an adjacent space particle defines the Planck length. Since there is no such thing as half a space particle the only distance something could move would be in increments of the Planck length, in essence there is no such ￼thing as an object moving half a Planck length.

Therefore at scales on the order of the Planck length something is either at space particle A or space particle B and there would only be one amount of time for something to go from A to B and that would be the Planck time. In this scenario all movement of matter occurs at the speed of light. In the Space Production Model of String Theory mentioned above it would be the singularities making up the hidden dimensions that would be moving at the speed of light and not the strings themselves. This is except for the strings that make up photons of course which are the only particles that consistently move in the same direction.

11. The Big Bang and the Fate of the Universe

Eventually the rate of expansion at galactic distances will exceed the speed of light. Once this occurs each of these gravitationally bound objects, galaxies and galaxy clusters, will be totally isolated from the rest of the universe and thereby become their own "universe".

As time goes by all matter will be drawn to the event horizons of the black holes at the center of these galaxies. However, according to the Space Production Model, while this matter is associated with the black hole it does not cross the event horizon. It is just "stuck" near the event horizon traveling at or close to the speed of light toward the singularity. Over billions of years almost all of the mass of the singularity will be converted into space to the point where the singularity's mass drops below the Planck mass. When this occurs the singularity no longer produces space faster than light can travel, therefore there is no longer an event horizon￼￼￼￼￼￼￼￼￼￼￼￼￼ ￼and the black hole evaporates into a naked singularity.

At this point all of the light and other matter that was traveling toward the singularity is "released" in a Big Bang. The Space Production Model of gravity proposes that this is likely the mechanism by which our current universe began. Of course this scenario could repeat itself over and over. Each time the original matter is divided into fewer or smaller galaxies that eventually become isolated and condense into the event horizon of their black hole until its singularity evaporates resulting in a smaller "Big Bang”.

This process would then continue until all of the matter in the universe is converted to space. As mentioned earlier, at “normal” distances the attractive force associated with the spherical pressure waves generated by the emission of space predominates. However, at very short distances the repulsive force due to the generation of the space itself becomes a major factor. This would be the case at the instant of the Big Bang and would explain the faster than light expansion of the universe at that time.

12. Conclusion

The Space Production Model of gravity is based on the premise that mass emits space and proposes that this is the mechanism by which mass curves space-time. It states that the pressure waves created by the production of space are responsible for the attractive force of gravity and should be consistent with Einstein's field equations. It proposes a new mechanism of attraction based on wave interference. It provides a source for dark energy that is consistent with ￼the size and mass of the universe and provides an answer to the flatness problem of the universe.

It is testable in that recession rates of galaxies should correlate to their mass. It proposes a radically different model of a black hole that allows one to determine the amount of space emitted by a specific amount of mass per unit time.

It puts forth a new definition of motion that is able to differentiate between motion and recession. It incorporates time into the definition of mass and provides a quantum explanation for time dilation, relativistic mass, and rotational frame dragging. Ultimately, it allows for a new understanding of the Big Bang and provides insight into the final fate of the universe.

DEFINITIONS:
Space-particle- the quantum of space, volume equal to 4/3pi(.5Planck length)3 It is likely a spent singularity.

Singularity- the quantum of matter composed of compressed space

Matter- made up of singularities that emit space in the form of space particle

Dark Matter- matter that is not in the final dimensional conformation of the matter that makes up the particles with which we are familiar. Or it may be composed of singularities that do not have the specific mass required to assimilate into the particles with which we are familiar. The majority of these would be naked singularities but black holes are also included.

Mass- matter that emits space in all directions

Inertia- a consequence of an objects emission of space consistent with Newton's 3rd Law of Motion. Any force acting on an object with mass would be countered by the force of the objects space emission in the opposite direction.

EMR- matter that does not emit space in the direction of its travel, i.e. it has no inertia in the direction of its movement

Density- number of space particles emitted per unit time per unit surface area of an object with mass.

￼Motion- an object can be said to be in motion if it has a non-uniform space particle emission pattern and conversely an object can be said to be at rest if it has a uniform space particle emission pattern. In essence, an object can be said to be in motion if it is emitting more space in one direction than in another. In this case the object is moving in the direction of the least space particle production. An object can be said to be at rest if its space particle Production pattern is uniform. In this case an object that is receding from all surrounding objects such as a distant galaxy, could be said to be at rest even though it would appear to be moving away from all other galaxies. Of course, the galaxy could be "moving" i.e. non-uniform gravitation production pattern and still be receding from all other galaxies. In this case it would be receding from some galaxies faster than others. A moving black hole would have a non-spherical event horizon. The distance from its singularity to the event horizon would be shorter in the direction of its movement and longer in the direction opposite its movement.

Acceleration- change in an objects space particle emission pattern.

Rotation- an object can be said to be rotating if its space particle are emitted tangentially to its surface. In this event light traveling towards a rotating object has to travel further if it approaches the object from the opposite direction as rotation than if it approaches from the same direction of rotation.

Dark Energy- the "energy" responsible for the expansion of the universe and is derived from the conversion of mass to space.

￼Recession- an effect of Dark Energy. An object can be at rest but still be getting further away from other objects. In essence, the object is not "moving away from other objects because it has a uniform space particle emission pattern, it is just creating more space between itself and other objects.

Time- unit of change.

Rate of time- is a function of the number of space particles emitted per unit change. An increase in the number of emitted space particles per unit change results in a slower rate of time. Maximum rate of time occurs when an object has a uniform emission pattern i.e. is at rest. The more asymmetrical an objects' space particle emission pattern the slower its rate of time. An objects space particle emission pattern becomes more asymmetric the faster it is moving. This also occurs when an object is in a gravitational field. Time would stop if an object were able to reach the speed of light or was able to reach the event horizon of a black hole.
rlloydbowen
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### Re: The Space Production Model of Gravity

Thank you for a most fascinating article. Although I'm not very good at maths and generally the type of equations you present give me an enormous headache the overall theory is exciting.
It also seems to add to my own thinking that gravity consists of the gases produced by the planet through volcanic action and water evaporation. In respect of my thinking I've also come to an understanding that these gases are released into space on a regular basis usually on the opposite side to the star the planet orbits.
Controversially in regards to light emission and travel my thinking is that light doesn't travel. Light is stationary to the object that is lit. My belief is that there are sub-atomic particles released that collide with other particles in their path creating an illusion of light travelling. Otherwise we are saying that these particles are able to penetrate and pass through all other particles in space.
JohnD
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### Re: The Space Production Model of Gravity

Welcome rlloydbowen,

The biggest problem (among many) is that this doesn't match the observed Universe, where Expansion is greatest when furthest from Galaxies and Expansion is most minimal near or inside Galaxies.

Does this apply (and in what form) to the Galaxy Rotation Problem where stars near the edge of a Galaxy are moving too fast to be explained by conventional Gravity? Stars are too far apart and present to small a profile to be being pushed together by each other. So what keeps them bound to the Galaxy?

Why does light bend as it does around a Star if new space is being created by the Star. Seems that would bend light the wrong way.

Neat idea though..

Best wishes,
Dave :^)

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### Re: The Space Production Model of Gravity

Is it that matter particles are spigots of fields and that these fields ARE space?

DragonFly
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### Re: The Space Production Model of Gravity

Rlloydbowen, I am not going to criticize your 'SPM', but rather show where you are missing (or misrepresenting) something in the standard cosmological model. It is wise to understand the thing that you want to compete with...

rlloydbowen wrote:Interestingly, the first experiment to substantiate the Theory of General Relativity was similar to Michelson-Morley in that it also measured the time it took for light to travel a specific distance but on a much grander scale. This of course was the experiment by Arthur Eddington which showed that light from a distant star took longer to travel the same distance to earth if its path was in close approximation to a massive object, in this case the sun.

No, Eddington measured the bending of the starlight around the Sun. The effect you are talking about is the "Shapiro time delay" of light, which has a different explanation.

The expansion of the universe has been attributed to a heretofore unexplained force currently termed Dark Energy. With the Space Production Model ￼the repulsive force of gravity is more intuitive than the force of attraction.

No, the expansion of the universe does not depend on "dark energy". The only thing dark energy contributes is a very tiny acceleration in the overall expansion rate at present. What we observe is that galaxies/clusters were moving away from each other much faster in the distant past, but slowed down to mutual gravity of the radiation and matter energy density of the universe.

Getting back to the black hole this would mean that the event horizon is the point where space is flowing away from the singularity at the speed of light. Therefore, light traveling toward the black hole would get "stuck" at the event horizon. It would continue to travel towards the ￼singularity at the speed of light but it just can't get there because there is always more space coming towards it.

General relativistic views (and mathematics) say the opposite. Space can be thought to fall into a black hole. (BH). Only hypothetical "white holes" can theoretically "eject space". We observe thing falling into BHs, not flowing away from them.

Current data from WMAP suggests that the universe is flat, meaning that the matter contained within the universe is distributed evenly very near the critical density.

Not quite. The total of ordinary plus dark matter count is around 30% of what is required for spatial flatness, with ordinary matter less than 5%. The other 70% is 'dark energy', which is currently thought to be nothing more than a intrinsic curvature of spacetime, a.k.a Einstein's cosmological constant.

Currently there is a problem with the definition of motion since it is clear that galaxies in some parts of the universe are receding from other galaxies at greater than light speed.

"At rest" in a cosmological sense means that you observe the CMB radiation to be isotropic, i.e. having the same average temperature in all directions. Every galaxy that is farther from us than the Hubble Radius (RH) has a recession rate of larger than c - not just certain regions. One can rephrase that to say that any two galaxies that is separated by a distance larger than RH recede from each other at a rate larger than c.

A moving black hole would have a non-spherical event horizon. The distance from the singularity to the event horizon would be less in the direction of its movement.

Ouch!! Not according to GR. Non-spherical (elliptical) event horizons only happen in rotating BHs.

The attractive force of SPM is consistent with Einstein's Theory of Relativity and merely provides a mechanism by which mass curves space-time.

I do not get the impression that you understand the 'attractive force" of Einstein's ToR well enough to make such a claim for SPM. It is possible to convert Einstein's spacetime curvature to an equivalent "pseudo force", but that's not a simple task.

It is testable in that recession rates of galaxies should correlate to their mass.

Nothing like this has ever been observed.

I have not dealt with your theory itself, because IMO, the things that I've pointed out above put it on a very flimsy footing. It was an entertaining read though. ;)

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Jorrie

BurtJordaan
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### Re: The Space Production Model of Gravity

First let me say to everyone thank you for taking the time to read and comment on the post. I will try to reply to each point made.

BurtJordaan wrote:Rlloydbowen, I am not going to criticize your 'SPM', but rather show where you are missing (or misrepresenting) something in the standard cosmological model. It is wise to understand the thing that you want to compete with...

Agreed

rlloydbowen wrote:Interestingly, the first experiment to substantiate the Theory of General Relativity was similar to Michelson-Morley in that it also measured the time it took for light to travel a specific distance but on a much grander scale. This of course was the experiment by Arthur Eddington which showed that light from a distant star took longer to travel the same distance to earth if its path was in close approximation to a massive object, in this case the sun.

BurtJordaan wrote:, Eddington measured the bending of the starlight around the Sun. The effect you are talking about is the "Shapiro time delay" of light, which has a different explanation.

What I was thinking Eddington measured was that stars appeared to be in a different place when their light passed closely to the sun. And that this is due to the fact that the path light travels when passing a massive object such as the sun is "curved" due to the effect of mass on space-time. It is my understanding that the path taken by the light when passing by the sun is longer. Therefore, it takes light longer to reach us and the star appears in a different location. You are correct that the effect MM were trying to measure was much different but the result is that when light travels a curved path it takes more time for for it to reach us. All I am saying is that in both MM and Eddington there is a measurement of the time it takes to travel a certain distance. And that the current interpretation of GR is that with Eddington the distance was increased. The same would have been true if MM had shown a difference... the light would have had to travel longer due to traveling through more aether. I am not familiar with the "Shapiro time delay". How is it different from what the Eddington experiment showed?

rlloydbowen wrote: expansion of the universe has been attributed to a heretofore unexplained force currently termed Dark Energy. With the Space Production Model ￼the repulsive force of gravity is more intuitive than the force of attraction.

BurtJordaan wrote:No, the expansion of the universe does not depend on "dark energy". The only thing dark energy contributes is a very tiny acceleration in the overall expansion rate at present. What we observe is that galaxies/clusters were moving away from each other much faster in the distant past, but slowed down to mutual gravity of the radiation and matter energy density of the universe.

You are correct, thanks for pointing this out.

rlloydbowen wrote:Getting back to the black hole this would mean that the event horizon is the point where space is flowing away from the singularity at the speed of light. Therefore, light traveling toward the black hole would get "stuck" at the event horizon. It would continue to travel towards the ￼singularity at the speed of light but it just can't get there because there is always more space coming towards it.

BurtJordaan wrote:General relativistic views (and mathematics) say the opposite. Space can be thought to fall into a black hole. (BH). Only hypothetical "white holes" can theoretically "eject space". We observe thing falling into BHs, not flowing away from them.

if an outside observer was to witness an astronaut falling into a black hole, relativity dictates that we would see him approach the black hole slower and slower until he ultimately "freezes" in our relative time due to time dilation. Since the escape velocity exceeds the speed of light we can't know if the astronaut actually crosses the event horizon. Couldn't he just as easily really be "stuck" at the event horizon. If so there would still be accretion since the astronaut would be permanently associated with the black hole.

I am definitely interested in any mathematics and their resulting physical consequences that would negate this model.

rlloydbowen wrote:Current data from WMAP suggests that the universe is flat, meaning that the matter contained within the universe is distributed evenly very near the critical density.

BurtJordaan wrote:Not quite. The total of ordinary plus dark matter count is around 30% of what is required for spatial flatness, with ordinary matter less than 5%. The other 70% is 'dark energy', which is currently thought to be nothing more than a intrinsic curvature of spacetime, a.k.a Einstein's cosmological constant.

From most of the reading I have done there does not appear to be any consensus on "dark energy." What SPM proposes is that matter's emission of space is the source of the intrinsic curvature.

rlloydbowen wrote:Currently there is a problem with the definition of motion since it is clear that galaxies in some parts of the universe are receding from other galaxies at greater than light speed.

BurtJordaan wrote:"At rest" in a cosmological sense means that you observe the CMB radiation to be isotropic, i.e. having the same average temperature in all directions. Every galaxy that is farther from us than the Hubble Radius (RH) has a recession rate of larger than c - not just certain regions. One can rephrase that to say that any two galaxies that is separated by a distance larger than RH recede from each other at a rate larger than c.

I agree with "at rest" in the cosmological sense and this is in agreement with SPM. Interestingly, SPM can predict the Hubble Radius based on mass density. See my posts in the forum "Change in Hubble Radius over time." Basically, the mass density of the universe is such that the mass contained within a sphere with a radius equal to the Hubble Radius has the same mass as a black hole with that event horizon radius.

Even though it is not a black hole the mass is equivalent and in this case one does see things flowing away from the "event horizon" (not a true event horizon).

rlloydbowen wrote: A moving black hole would have a non-spherical event horizon. The distance from the singularity to the event horizon would be less in the direction of its movement.

BurtJordaan wrote:Ouch!! Not according to GR. Non-spherical (elliptical) event horizons only happen in rotating BHs.

This is great!
So GR would dictate that if the singularity of a black hole were moving at close to light speed it would still generate a spherical event horizon? For example, are non-rotating binary black holes thought to have spherical event horizons? Is there a way to observe this and if so has it been done?

rlloydbowen wrote:The attractive force of SPM is consistent with Einstein's Theory of Relativity and merely provides a mechanism by which mass curves space-time.

BurtJordaan wrote:I do not get the impression that you understand the 'attractive force" of Einstein's ToR well enough to make such a claim for SPM.

You are probably correct about my understanding of Einstein's ToR. I do understand that it is a function of curved space time and that objects are merely "falling" through this curved space. What I am trying to say is that Einstein's field equations should correspond to the field generated by the spherical energy waves created by matter's emission of space. In a quantum perspective, each of these waves are separated by 1 planck length. If one were able to "freeze" time and look at the change in energy density of these waves I would predict that they would correspond to the curvature of space-time in GR.

rlloydbowen wrote: It is testable in that recession rates of galaxies should correlate to their mass.

BurtJordaan wrote:Nothing like this has ever been observed.

I have not dealt with your theory itself, because IMO, the things that I've pointed out above put it on a very flimsy footing. It was an entertaining read though. ;)

You are correct this has never been observed but according to the calculations presented, the differences in recession rates are below the sensitivity of current technology. I only put this in to show that the model is testable even though current technology does not permit.
rlloydbowen
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### Re: The Space Production Model of Gravity

I obviously did something wrong in my reply since everything ended up in the white box.
rlloydbowen
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### Re: The Space Production Model of Gravity

Hi rlloydbowen,

This looks like a rewrite of the hypothesis that Gravity Pushes, which has been shot down many times. The idea being that a body close to another body, shields each other from this pushing force, thus they seem to attract each other. The biggest fault, like in yours, is the profile of remote stars is too small to create an effect that will hold a Galaxy together.

The Curvature of Space is actually another way to express a Gravitational Gradient Field. Light follows this Gradient when passing a Star. And again, you haven't addressed the issue that Cosmological Expansion is most active furthest from Masses. If Matter was Generating new space, then Galaxies should be expanding too, which they are not.

My personal take on Gravity is that it compresses Space-Time, by stealing it from elsewhere. Compressed Space-Time reconfigures Matter to take on the Geometry one would find in Matter with Kinetic Energy, where the direction of that Kinetic Geometry is towards Greater Space-Time Density.

Regards,
Dave :^)

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### Re: The Space Production Model of Gravity

rlloydbowen wrote:I obviously did something wrong in my reply since everything ended up in the white box.

It all looks good, Lloyd. Maybe you or somebody else edited, after you posted at 10:36,and made changes you wanted. Or I'm missing something. If you ever want help modifying something or learning to use the setup, let us know.

Marshall
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### Re: The Space Production Model of Gravity

Marshall,
Right after I posted that it changed to the correct format. Maybe I didn't give it enough time to post fully. Thanks for the offer for help. I will likely take you up on it.

This looks like a rewrite of the hypothesis that Gravity Pushes, which has been shot down many times. The idea being that a body close to another body, shields each other from this pushing force, thus they seem to attract each other. The biggest fault, like in yours, is the profile of remote stars is too small to create an effect that will hold a Galaxy together.

Dave,
Good comment. You are correct there are some similarities but the major difference is that with SPM the "pushing" is due to the object's intrinsic emission of space. It is not the emission of space that causes two objects to move closer to one another it is the cancellation of the waves emitted due to the emission of space.

One way to think of it is if you had a floating disc with water cannons spraying water away from its center equally in all directions. The cancellation I am talking about would be similar to stopping the flow of water from one of the cannons. The result would be that the disc would move in the direction the non-functional cannon was pointing.

My personal take on Gravity is that it compresses Space-Time, by stealing it from elsewhere. Compressed Space-Time reconfigures Matter to take on the Geometry one would find in Matter with Kinetic Energy, where the direction of that Kinetic Geometry is towards Greater Space-Time Density.

I'll have to noodle on that for a while.
Last edited by rlloydbowen on August 17th, 2013, 3:50 pm, edited 1 time in total.
rlloydbowen
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### Re: The Space Production Model of Gravity

DragonFly wrote:Is it that matter particles are spigots of fields and that these fields ARE space?

The way I see it matter particles are actually spigots producing two fields. One field is due to the space itself and this field diminishes as a function of the inverse cube of the distance. The other field is due to the waves traveling through this space and this field diminishes as a function of the inverse square of the distance.
rlloydbowen
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### Re: The Space Production Model of Gravity

rlloydbowen wrote: It is my understanding that the path taken by the light when passing by the sun is longer. Therefore, it takes light longer to reach us and the star appears in a different location.

It takes the light a little longer, but it does not take a "longer path" through spacetime. Actually, it takes the path of least action, which could be translated to "the shortest possible path". It is more like it is going through denser spacetime, which delays it a little and bends the light, similarly to any denser medium that would delay and bend light. GR explains this perfectly and gives precisely the observed values for both the delay and the bending. Other theories of gravity are hard-pressed to match this precision.

Since the escape velocity exceeds the speed of light we can't know if the astronaut actually crosses the event horizon.

No, this is just due to an arbitrary choice of coordinates that do not work at the event horizon. There are other choices of coordinates which work all the way past the event horizon, right up to the center, where all current theories break down (the mathematical singularity).

From most of the reading I have done there does not appear to be any consensus on "dark energy."

Yep, but as far as I can see, there is not much hope for consensus on SPM either... ;)

Basically, the mass density of the universe is such that the mass contained within a sphere with a radius equal to the Hubble Radius has the same mass as a black hole with that event horizon radius.

This is an invalid statement. Do you have a reference for it? The present Hubble radius of the universe is about 14.4 billion light years and it depends on a lot more than the matter density (which is only about 30% of the critical density, remember?)

So GR would dictate that if the singularity of a black hole were moving at close to light speed it would still generate a spherical event horizon?

Moving at near the speed of light relative to what frame? In the frame where the non-rotating BH is at rest, the event horizon will be spherical. If you pick any frame where the BH is in relative movement, the event horizon will theoretically be Lorentz contracted in the direction of relative movement, but you cannot attach a physical meaning to that (other than that is what the reference frame observe). AFAIK, no such contraction has been observed, simply because we do not directly observe BH event horizons. We only see the effect on the matter around them.

I am not yet convinced that your model is worth investing time in, but other readers may think differently. IMO, you will have to give a mathematically consistent treatment that covers everything GR covers and then some more. Do you thinks this is realistic?

--
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Jorrie

BurtJordaan
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### Re: The Space Production Model of Gravity

rlloydbowen wrote:Basically, the mass density of the universe is such that the mass contained within a sphere with a radius equal to the Hubble Radius has the same mass as a black hole with that event horizon radius.

This is an invalid statement. Do you have a reference for it? The present Hubble radius of the universe is about 14.4 billion light years and it depends on a lot more than the matter density (which is only about 30% of the critical density, remember?)

I have inserted below some recent posts from the forum "How the Hubble Length has changed over time" that covers this.

Marshall wrote:Just now by chance I happened to see an old table made with Jorrie's calculator that gives the Hubble radius over time. RHub = c/H

so they are basically reciprocals and plotting the growth of R(t) is equivalent to showing the decline of H(t).

Let me see if I can print the table here:

You can see that in year 67.4 million the Hubble radius was about 0.1 billion ly. That is equivalent to distances growing about 1% per million years. One whole percent per million years, really fast growth.

${\small\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline T (Gy)&R (Gly) \\ \hline 0.0674&0.1021\\ \hline 0.0956&0.1445\\ \hline 0.1354&0.2044\\ \hline 0.1917&0.2890\\ \hline 0.2713&0.4086\\ \hline 0.3839&0.5775\\ \hline 0.5430&0.8160\\ \hline 0.7676&1.1522\\ \hline 1.0847&1.6251\\ \hline 1.5315&2.2869\\ \hline 2.1589&3.2044\\ \hline 3.0346&4.4534\\ \hline 4.2427&6.0957\\ \hline 5.8756&8.1265\\ \hline 8.0089&10.3976\\ \hline 10.6648&12.5991\\ \hline 13.7872&14.3999\\ \hline 17.2617&15.6499\\ \hline 20.0000&16.2548\\ \hline 22.8231&16.6519\\ \hline 25.7011&16.9035\\ \hline 28.6133&17.0597\\ \hline \end{array}}$
And it shows that in year 13.8 billion (the present day) the Hubble distance R = 14.4 billion ly.
And that in the distant future R will approach 17.3 billion ly.
T.

Marshall wrote:We can find the corresponding densities for times in the past or in the future easily enough.

But maybe you prefer to divide those energies by speed-of-light-squared and get tiny fractions of a kilogram. Insanely tiny amounts of mass.

A joule I kind of know what it is, like lifting a 1 kilogram physics textbook about 10 centimeters and letting it drop with a thud. But in MASS terms it is insanely small. However you decide what units. Metric I hope.

BTW if you do a little algebra with metric units you find that 1 joule/m^3 = 1 Newton/m^2 = 1 Pascal
spatial energy density and pressure (force per area) actually basically the same metric unit.
So nanojoule per m^3 is the same as nanoPascal.

Try putting this into google and pressing return:
3 c^4/(8 pi G)/(14.4e9 light years)^2

Do you see where the Hubble radius of 14.4 billion lightyears is in this expression? You can change that to any other Hubble radius in the table I printed out earlier and get the corresponding densities.

Footnote: instead of 0.8 and 0.2, if you want more accuracy (and to use the latest Planck figures) then
0.78 and 0.24

rlloydbowen wrote:Using a Hubble radius of .816 billion ly a black hole with that event horizon radius has a mass of 2.079×10^52 kilograms. Divide this by the volume inside its event horizon 1.9272×10^75 cubic meters equals 1.079×10^-23 kilograms per cubic meter which equals 9.698×10^-7 joules per cubic meter which equals 9.698×10^-7 pascals. Multiply this by .286 (the percent of energy density attributed to matter) equals 2.774×10^-7 pascals.

This is very close to the energy density of 2.42424948 × 10^-7 pascals which I get by putting 3 c^4/(8 pi G)/(.816e9 light years)^2 into google calculator.

Using the current estimate of the Hubble Radius of 14.4 billion ly we get

3 c^4/(8 pi G)/(14.4e9 light years)^2 = 7.78453443 × 10^-10 pascals

A black hole with an event horizon radius of 14.4 billion ly has a mass of 3.67×10^53 kilograms

divide that by the volume of a sphere with radius 14.4 billion ly

3.67×10^53 kilograms/1.25077×10^31 cubic light years =3.465×10^-26 kilograms per cubic meter = 3.114×10^-9 joules per cubic meter = 3.114×10^-9 pascals multiply times .28 (energy density due to matter)

= 8.719×10^-10

Again very close to the 7.78x10^-10 pascals
rlloydbowen
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### Re: The Space Production Model of Gravity

rlloydbowen wrote:Basically, the mass density of the universe is such that the mass contained within a sphere with a radius equal to the Hubble Radius has the same mass as a black hole with that event horizon radius.

This is an invalid statement. Do you have a reference for it? The present Hubble radius of the universe is about 14.4 billion light years and it depends on a lot more than the matter density (which is only about 30% of the critical density, remember?)

Hi Jorrie, hi Lloyd,
As I understand it the usual BH radius formula cannot be applied in expanding space. It is good only as an approximation if you apply it at scales where the rate distances expand is small and can be neglected. So it does not make sense to talk about the Hubble sphere as a black holeeven though the matter density might be same order of magnitude as a Schw. black hole would have in a nonexpanding asymptotically flat geometry.

But we could still do the calculation just for fun!!!
I tend to agree with Jorrie on matters of fact like this but we could check. I recall using the two Hubble radii we got from Planck data, 14.4 and 17.3 Gly, and finding that critical density (including the cosmo const. equivalent "dark energy" of 0.54 nanopascal) was 0.78 nanopascal. Sorry I'm being sloppy-lazy, instead of pascal I should really say "joule per cubic meter".
So assuming spatial flatness the MATTER density (energy equivalent) is 0.24 nanopascal.

I never checked to see if that was the density of a black hole with radius 14.4 Gly in non-expanding space. But we could do that.

R = 2GM/c^2 = 2 GMc^2/c^4 = 2 GE/c^4 = 2G Vrho/c^4 where V = (4/3)pi R^3

1 = 2G(4/3) pi R^2 rho/c^4

So the BH density is given by
rho = (3 c^4/(8 pi G))/R^2

I think if you put R = 14.4 Gly into that, then the rho you get is NOT the matter density 0.24 nanojoule per cubic meter.
I think what you get is the conventional critical density including the "dark energy" equivalent, which totals 0.78 nanojoule per cubic meter.

So I guess that confirms what Jorrie said.

The conventional critical density "depends on a lot more than the matter density". As far as we can estimate, the matter density is only around 0.24
whereas IF WE LIVED IN A NON-EXPANDING SPACE SO THAT IT MADE SENSE TO TALK ABOUT SCHWARZSCHILD BLACK HOLES AND USE THAT RADIUS FORMULA then 0.24 would not be enough. You would need matter density 0.78.

Anyway, that's my take on it. I'm no great expert, could have made a mistake. Jorrie or anyone, if you see something wrong here, please let me know.
Have to go help with some domestic stuff.

As a general remark, I like having some discussion that involves quantitative calculation like this! Thanks to both.

Marshall
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### Re: The Space Production Model of Gravity

Marshall wrote:As a general remark, I like having some discussion that involves quantitative calculation like this! Thanks to both.

Another way is to view it graphically. Below are the two most important 'horizons' used in cosmology: the Hubble radius (R) where the recession rate reaches 'c' and the communication horizon (D_Hor), which is the largest proper distance that light can traverse at the time. Scale factor a=1 represents the present time.

Cosmic Horizons (Click for clearer view and then Browser 'back')

The curves are from LightCone 7, preview option.

As you have stated, the normal Schwarzschild event horizon for matter embedded in flat space is not applicable. The fact that both change drastically over time and tend to a constant value in the future, tells us that they are not determined by matter density alone, but by a rather technical combination of all the energies around. For those interested, the equations behind the curves are here.

The near-correspondence between critical density and the present Hubble radius is likely a coincidence, just like the fact that the Hubble radius is close to the distance that light could have traveled in flat, non-expanding space since the BB is a coincidence. One can easily see that it was not like that in the past in it would not be like that in the future.

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Jorrie

BurtJordaan
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### Re: The Space Production Model of Gravity

BurtJordaan wrote:As you have stated, the normal Schwarzschild event horizon for matter embedded in flat space is not applicable.

I am not sure I understand what you are saying. Are you saying that there the correlation between matter density and Hubble Radius I referred to is coincidental?
rlloydbowen
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### Re: The Space Production Model of Gravity

rlloydbowen wrote:I am not sure I understand what you are saying. Are you saying that there the correlation between matter density and Hubble Radius I referred to is coincidental?

Firstly, the baryonic energy matter density only makes up around 5% of the critical energy density of the cosmos. The latter is of the same order of magnitude as the simplistic calculation of the average density of a Schwarzschild BH with radius equal to the Hubble radius. This is coincidental, because there is no physical correspondence between them. The radius of a Schwarzschild BH is determined by the matter inside it; the Hubble radius is determined by the dynamics of expansion.

Secondly, the Hubble radius is not an event horizon - matter, information, etc. can and do move outwards across it. The total matter inside it is presently decreasing, while the Hubble radius is still increasing. This is not the behavior of a black hole...

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### Re: The Space Production Model of Gravity

Hi Lloyd, there is a famous coincidence that I've heard referred to a lot, but I'm not sure if it is what you referred to. I'll mention it anyway, in case it might interest you.
One way to say it is to point out that 0.24 nJ per m3 is the same order of magnitude as two other energy densities---the "dark energy" equivalent of the cosmological constant, namely 0.54, and the sum of the two, namely 0.78.

Isn't it strange (some suggest) that we live at a moment in the history of the cosmos when the MATTER DENSITY IS SO CLOSE to the other, associated with the cosmological constant. They differ by hardly more than a factor of 2---compare 0.24 and 0.54. According to our standard theory they might just as well differ by a factor of 100 or 1000. So (some ask) could they actually be related??? Could there be some mechanism linking them that we don't know about???

According to standard cosmic model, the cosmo constant does not change, and the observations so far seem to confirm this. It really has been acting as a constant---that gives the best fit to the data that has been accumulating.

So maybe it is just a coincidence. We just happen to live at a time when matter density 0.24 (which is constantly declining) happens to be in same ballpark as that constant 0.54.
================

I wouldn't say it was a coincidence that the Schw. black hole radius formula is the same as the Friedmann equation critical density formula with cosmological constant equal to zero. They are mathematically the same formula!
But this does not mean that the Hubble sphere surrounding our galaxy is a black hole!

Most of the universe which we can observe e.g. with Hubble telescope is outside the Hubble sphere, BTW. and the Schw. BH model is only valid in non-expanding space. Plus you couldn't make a black hole using the "antigravitational" dark energy---it doesn't clump, and it may very well be a fiction. As far as we know, not an actual energy field but simply a constant vacuum curvature appearing in Einstein GR equation.

I'm supposed to be doing some real life stuff, this may be a bit incoherent. Hope Jorrie clarifies. I'll check in later.

Marshall
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### Re: The Space Production Model of Gravity

OOPS I had to take a break while I was writing this, during which I see Jorrie already responded :^D. Had to take time out for some domestic stuff. So what I wrote is largely superfluous.

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### Re: The Space Production Model of Gravity

Marshall wrote:this does not mean that the Hubble sphere surrounding our galaxy is a black hole!

I did not mean to say that the Hubble sphere surrounding our galaxy is a black hole. I fully understand that is not the case. What I am saying is that the SPM model predicts that the amount of energy contained in the Hubble sphere surrounding us is equivalent to the energy/mass contained within a black hole with the same radius. According to SPM this is because the amount of space produced by the matter contained in a sphere with a radius equal to the distance between us and a co-moving object 14.4 billion ly away is 6.991×10^61 cubic meters per second. Increasing the volume of the sphere at that rate results in the radius increasing at a rate = c.

BurtJordaan wrote:Secondly, the Hubble radius is not an event horizon - matter, information, etc. can and do move outwards across it.

I know it is not a black hole event horizon but it is a horizon in that light emitted now from beyond that distance can never reach us.

BurtJordaan wrote:The total matter inside it is presently decreasing, while the Hubble radius is still increasing. This is not the behavior of a black hole...

Did you mean the matter density is decreasing or the absolute amount of matter. Because according to SPM the absolute amount of matter/energy should increase at a rate of 2 planck mass/planck length of increase in the Hubble radius. If this is the case the total amount of matter will be increasing yet the matter density will be decreasing.

BurtJordaan wrote:This is coincidental, because there is no physical correspondence between them. The radius of a Schwarzschild BH is determined by the matter inside it; the Hubble radius is determined by the dynamics of expansion.

What SPM proposes is that the dynamics of expansion of the universe are determined by the matter contained within it.
rlloydbowen
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### Re: The Space Production Model of Gravity

BurtJordaan wrote:I am not yet convinced that your model is worth investing time in, but other readers may think differently. IMO, you will have to give a mathematically consistent treatment that covers everything GR covers and then some more. Do you thinks this is realistic?

Yes I do believe it is realistic. General relativity is correct it is just not complete. All that may need to be done is to incorporate the "repulsive force" or "reverse curvature of space-time" into the current field equations. Unfortunately, my math skills are not up to the task but I am hoping to collaborate with someone who possesses the needed expertise.
rlloydbowen
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### Re: The Space Production Model of Gravity

rlloydbowen wrote:I know it is not a black hole event horizon but it is a horizon in that light emitted now from beyond that distance can never reach us.

Look at the graphs that I posted earlier - as long as the Hubble radius (R) is smaller than the distance of the Cosmic Horizon (RH), light transmitted can reach us.

Did you mean the matter density is decreasing or the absolute amount of matter.

The absolute amount of matter inside the Hubble radius is presently decreasing. More and more galactic clusters will cross the Hubble radius and the Cosmic Horizon (which will eventually be the same), to be cut off from our view.

What SPM proposes is that the dynamics of expansion of the universe are determined by the matter contained within it.

Only partially so. The cosmological constant has the dominant effect.

According to SPM this is because the amount of space produced by the matter contained in a sphere with a radius equal to the distance between us and a co-moving object 14.4 billion ly away is 6.991×10^61 cubic meters per second. Increasing the volume of the sphere at that rate results in the radius increasing at a rate = c.

What we observe does not bear this out. The Hubble radius is not increasing "at a rate = c." There was only one era (when the time since the BB was about half the present time) when this happened. The matter energy density and the cosmological constant's equivalent energy density were then equal. Over the last 7 billion years, the matter energy density has dropped to about half that of the cosmological constant and the growth rate of the Hubble radius also dropped proportionally.

Your proposal seems to have some characteristics of "Self-Creation-Cosmologies". AFAIK, all have been discredited due to lack of strong observational support.

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A little more on the Hubble radius (where the rate of increase of cosmological distances equals the speed of light).

BurtJordaan wrote:The Hubble radius is not increasing "at a rate = c." There was only one era (when the time since the BB was about half the present time) when this happened. The matter energy density and the cosmological constant's equivalent energy density were then equal. Over the last 7 billion years, the matter energy density has dropped to about half that of the cosmological constant and the growth rate of the Hubble radius also dropped proportionally.

If we hypothesize an all-matter universe at critical density (the Einstein-de Sitter model), it is interesting to note that the Hubble radius itself increases at a constant rate of 1.5c (line 1,0 in the graph).[1] Since the proper distance of co-moving objects at the Hubble radius grows at exactly c, a constant stream of co-moving objects would seem to "fall into the Hubble sphere".

A hypothetical energy-less flat spacetime universe would have a Hubble radius growing at exactly c (line 0,0 in the graph). In a realistic universe with cosmological constant, the Hubble radius initially starts growing at 1.5c and the growth rate gradually drops to zero in the very distant future (curve 0.3,0.7 in the graph).

Hubble Radius growth against Cosmic Time

In the realist case (0.3,0.7, LCDM model), the growth rate of the Hubble radius drops to below c at around 7.5 Gy. Before this time some co-moving galaxies moved from the outside through the Hubble radius; thereafter some galaxies started to move from the inside to the outside of the Hubble sphere.

The reason for posting it under this thread is that one needs such understanding in order to evaluate other theories.

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Edit: [1] Actually, right near the beginning, virtually at the origin of the graph, the Hubble radius increased at 2c, driven by the dominance of radiation energy[2]. This dominance came to an end at around 50,000 years, due to the radiation being redshifted by the expansion, which meant that its energy density dropped faster than matter density.

Edit: [2] Calling it "driven by the dominance of radiation energy" may be a confusing here - although true that the Hubble radius (in units of proper distance) increased at 2c during the radiation dominance, the actual expansion rate was slowing down rapidly during that phase. The Hubble radius is not the physical distance to any one galaxy, but a relative distance which (then) increased faster than the distance to the galaxies in its vicinity.
Last edited by BurtJordaan on August 21st, 2013, 9:50 am, edited 2 times in total.

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### Re: The Space Production Model of Gravity

BurtJordaan wrote:Over the last 7 billion years, the matter energy density has dropped to about half that of the cosmological constant and the growth rate of the Hubble radius also dropped proportionally.

When you say the "Hubble radius also dropped proportionally" proportionate to what?

Currently the matter density, including dark matter, is estimated to be 28.4% of the energy density of the universe. Marshall provided a formula to determine the energy density based on the Hubble radius. Is there a way to determine what percent of this was/is composed of matter and what part was/is composed of "Dark Energy" in the past and in the future?
rlloydbowen
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### Re: The Space Production Model of Gravity

rlloydbowen wrote:"When you say the "Hubble radius also dropped proportionally" proportionate to what?

Note, not the Hubble radius itself - I wrote: "matter energy density has dropped to about half that of the cosmological constant and the growth rate of the Hubble radius also dropped proportionally", meaning that the growth rate dropped to about half the speed of light. If you look at the graph and estimate the slope of the blue curve at about 14 Gy, you will find it to be about 0.5 (~1 Gly growth over about 2 Gy time, roughly).

Currently the matter density, including dark matter, is estimated to be 28.4% of the energy density of the universe. Marshall provided a formula to determine the energy density based on the Hubble radius. Is there a way to determine what percent of this was/is composed of matter and what part was/is composed of "Dark Energy" in the past and in the future?

It is easy to express this in terms of the stretch factor S, but not easy to do in terms of time, so we use the Lightcone calculator to find S for the time you are interested in. Say you want to know the density values when the cosmic time was 10.0 Gy. Playing around with the S-ranges of the calculator, I got S=1.329.

If we assume a spatially flat universe and neglect radiation energy density, $\Omega = \Omega_\Lambda + S^3 \Omega_m = 1$.* Hence at S=1.329, the matter density was (1.329)3 = 2.35 times what it is today. It is then easy to get the 'then' ratios or percentages. Let us know if you have difficulties with it, but it may be worth your while to give it a shot by yourself.

Marshall is the best guy I know to make these things crystal clear, so maybe he will also help out.

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Jorrie

* $\Omega$ is the total energy density parameter, expressed as a fraction of the critical energy density (needed to make the cosmos spatially flat).
* $\Omega_\Lambda$ is the "energy density" parameter equivalent to the cosmological constant, which can be thought of as the constant energy density of the vacuum. It does not get thinned out by cosmic expansion.
* $\Omega_m$ is the matter energy density parameter, which reduces as the volume of a large scale piece of vacuum expands (proportional to the cube of the radius). It includes large scale normal and dark matter density.
* S is the "stretch factor", the same as redshift + 1. It tells us by how much distances have increased since some point in the past. E.g. S=10 means that distances (and wavelengths) have stretched by a factor 10 since the light that we receive now has been emitted.

All the density parameters are expressed as (decimal) fractions of the critical energy density.

-J
Last edited by BurtJordaan on August 22nd, 2013, 4:54 am, edited 3 times in total.
Reason: some explanatory footnotes

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### Re: The Space Production Model of Gravity

Marshall wrote:I wouldn't say it was a coincidence that the Schw. black hole radius formula is the same as the Friedmann equation critical density formula with cosmological constant equal to zero. They are mathematically the same formula!

By using the SPM I was able to develop the exact same formula as the Friedmann equation with which I was unfamiliar. Wouldn't this seem to support the SPM.
rlloydbowen
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### Re: The Space Production Model of Gravity

rlloydbowen wrote:By using the SPM I was able to develop the exact same formula as the Friedmann equation with which I was unfamiliar. Wouldn't this seem to support the SPM.

Yes, but what you got is just a special case of the Friedman equation, based on Newtonian dynamics. This is easy to obtain by simply considering masses flying away from a center, each at its escape velocity $V_e = 2GM/r$, with $r$ the radial distance from the center. This gives the special case as:

$da/dt = \sqrt{8\pi G \rho /3}$, where $a$ is the scale factor, so that $da/dt$ represents a rate of expansion.

It can also be written in terms of the Hubble constant $H_0$ and density expressed as a fraction of the critical density, $\Omega$:

$da/dt = aH_0\sqrt{\Omega/a^3}$

We know that this equation does not agree with observations - we need general relativistic dynamics. The special case is only applicable in a perfectly flat space with matter-only content at critical density ($\Omega=1$).

Observations favor the full Friedman equation, including about 70% cosmological constant and 30% (normal plus dark) matter. The full Friedman equation is general relativistic and also includes the effects of radiation and caters for non-flat geometries.

For comparison, here is the full (1st) Friedmann equation, written in terms of all the Omegas.

$da/dt = aH_0\sqrt{\Omega_{\Lambda}+ (1-\Omega)/a^2 + \Omega_m/a^3 + \Omega_r/a^4}$

There is also a 2nd Friedmann equation, dealing with the deceleration/acceleration of expansion.

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Last edited by BurtJordaan on August 24th, 2013, 2:56 am, edited 3 times in total.
Reason: semantics improved

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### Re: The Space Production Model of Gravity

Jorrie,
Thanks for the comment. I agree that this is a simplistic view the phenomenon. And I am not saying that this in any way "proves" the SPM to be correct.
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### Re: The Space Production Model of Gravity

Hey guys, I was wondering if the only information available is the density of an object, is it possible to calculate its schwarschild radius?
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### Re: The Space Production Model of Gravity

rlloydbowen » 23 Aug 2014, 14:15 wrote:Hey guys, I was wondering if the only information available is the density of an object, is it possible to calculate its schwarschild radius?

Yes, more or less so. If something exceeds a certain critical density ($\rho_{crit}$), it becomes a black hole with Schwarzschild radius

$R_S = \sqrt{\frac{3c^2}{8 \pi G \rho_{crit}}}$

This radius remains constant once the critical density is reached, irrespective of how small the actual object collapses into. When the density is below the critical density, you would need the density and the radius (or the mass) in order to determine R_S.

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