A Brief Theory Of The Super-Universe
By Michael Spears
Copyright 2016 Michael Spears
Shakespir Edition, Licence Notes
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– Developing New Field Equations
– The Infinite Universe
A BRIEF THEORY OF THE SUPER-UNIVERSE
Part 1: Developing New Field Equations
Part 1A: The Hypothesis
According to Einstein’s theory of General Relativity
“in every gravitational field, a clock will go more quickly or less quickly, according to the position in which the clock is situated (at rest).”^1^
“a displacement towards the red ought to take place for spectral lines produced at the surface of stars as compared with the spectral lines of the same element produced at the surface of the earth.”^1^
In the words of Stephen Hawking
“Another prediction of general relativity is that time should appear to be slower near a massive body like the earth. This is because there is a relation between the energy of light and its frequency: the greater the energy, the higher the frequency. As light travels upward in the earth’s gravitational field, it loses energy, and so its frequency goes down.”^2^
Below I will examine the effects of these two confirmed proposals from the theory of General Relativity.
I propose that although Einstein was correct in his prediction, there is another explanation that would result in the exact same experimental results. An alternate explanation for these two experimental results becomes apparent from visualising the situation. One should consider the possibility that rather than moving at a constant velocity, light accelerates as it leaves a stronger gravitational field and enters a weaker gravitational field, proportional with an increase in the rate at which time advances.
I will now introduce a concept “the speed of time” (sot), where the sot is the ratio of the time at a certain location and/or velocity to the time as measured by someone in a fixed location and/or velocity. The simplest method is if the sot is measured in the S.I. units of seconds/earth seconds (s/sE), where an earth second could be a second as measured at a particular location on the earth. The sot on earth would therefore be equal to 1, while in regions where time is faster the sot is greater than 1 and where time is slower the sot is less than 1.
It is worthwhile to consider that if time is faster not only do clocks move faster, but everything moves faster, so is it not possible that light also moves faster? Any increase in the speed of light would be unnoticeable because the timing mechanism that is being used to measure the speed of light would also move faster. If the sot was greater, or “faster,” in a particular region, then a second (for example) would become shorter and therefore light would have to travel faster in that shorter second to cover the same distance as it would cover in a longer second (where the sot is less).
The speed of light in a vacuum could appear to remain constant when the speed of light in a vacuum may not actually be constant. However there would be one way that a change in the speed of light would be noticed, by the red/blue shift that would accompany this change in the speed of light. The hypothesis is that while frequency appears to change, this is only because our measure of time has changed. The frequency, and therefore the energy of light would remain constant, however the wavelength would have changed. By this proposal’s definition of time, if time is faster, then everything moves faster, including our clocks, and including light.
Part 1B: The Basic Equations
Let’s begin by introducing another new definition, “the speed of light as measured from the perspective of someone on earth,” and give it the value cE measured in the S.I. units of metres/earth second, or m/sE. The energy of light is given by the relation
(Where E = energy, h = Planck’s constant, υ~E~ = frequency from the perspective of an observer on earth.)
If we assume that energy is conserved, and if we also assume that frequency remains constant from the perspective of someone on earth, then we must first check that the units of measurement are balanced
If we study equation (2) we notice that the value for frequency ‘υ~E~’ must change if time changes, so let’s think about this carefully, the units for frequency aren’t really ‘1/sE’ but ‘waves/sE’ and if we take this into consideration while assuming that the number of waves per second does not change, then the equation makes more sense
Now we can consider the Planck constant to be a constant per wave, so it does not change with time but remains a constant independent of the sot. However it must be noticed that the units on the left hand side of equation (3) are not balanced, if ‘sE’ changes then the energy must also change, unless we introduce terms for either ‘kgE’ or ‘mE,’ which are kilograms as measured from the perspective of someone on earth, and metres as measured from the perspective of someone on earth respectively. Now we know that either mass or length must also change when time changes. Next let’s consider Einstein’s most famous equation but with the introduced term the speed of light as measured from the perspective of some on earth ‘cE’ while remembering the first law of thermodynamics
(Where cE = the speed of light from the perspective of an observer on earth, m = mass.)
Now we understand that mass from the perspective of someone on earth must change in proportion to time from the perspective of someone on earth squared. In other words, when time becomes faster mass decreases. Let’s rewrite equation (4) now
Remember that energy is always conserved, according to this theory, the energy of light only appears to change due to changes in the measurement of time.
Now we must consider the equation for kinetic energy
(Where vE = velocity from the perspective of an observer on earth.)
According to the above hypothesis, if mass decreases in weaker gravitational fields (for example) velocity squared must increase proportionally, since energy is always conserved. Now we can understand mathematically the reason why when time is faster everything would move more easily through space. In weaker gravitational fields not only would light move faster, but so too would objects of mass. Objects of mass must move faster in weaker gravitational fields because their mass would decrease while their kinetic energy would remain constant, thus resulting in an increased velocity.
A similar effect would happen with gravitational potential energy, except that while velocity2 changes are inversely proportional to changes in earth mass, gravitational acceleration changes inversely proportionally to earth mass. Consider now the equation for gravitational acceleration
(Where GE = the universal gravitation constant from the perspective of an observer on earth, r = the distance from the centre of mass (or the radius), M = the mass of the object creating the gravity.)
Now we can see that GE must change inversely proportionally to earth mass in order for gE to change as a function of earth mass. Similarly to the speed of light in a vacuum, the universal gravitation constant would appear to be constant, but it would be time which has changed.
What we’ve learned is that mass may decrease in weaker gravitational fields, the combination of this decrease in mass and the conservation of energy would result in an increase in the velocity of matter and energy, and an increase in the gravitational acceleration of matter. What we’ve learned is that in weaker gravitational fields, when time is faster, it is entirely feasible that everything moves faster. While it may seem counter-intuitive that light would accelerate due to gravity, rather than decelerate, it is important to recall another of Einstein’s equations
(Where pE = momentum from the perspective of an observer on earth.)
According to this equation, if gravitational field strength decreases, time becomes faster and light accelerates, then the momentum of light must decrease proportionally to any increase in the speed of light. So while light may not slow due to gravity, and it may be the opposite that occurs, gravity would affect the momentum of light. It makes sense now that since gravity may change the momentum of light that the path of light could be bent by gravity, as predicted by Einstein.
Part 1C: Gravitational Time Dilation
According to my theory mass varies as a function of gravitational field strength, which creates a change in time due to conservation of kinetic energy and gravitational potential energy.
The scalar equation for gravitational field strength is
Now we wish to consider changes in the mass of an object in a particular gravitational field ‘mr’ with respect to mass as experienced on Earth ‘mE’. We also need to consider that mass will reach a minimum at a theoretical infinite distance from the gravitational field of which it is a part. However it becomes difficult because everything is a part of a different gravitational field. Earth is primarily a part of the gravitational field of the Sun, so at a theoretical infinite distance from the Earth the maximum speed of time and the minimum mass would be dependent on the gravitational field strength of our position orbiting the Sun. The Sun in turn is primarily a part of the gravitational field of the area of the Milky Way which we occupy, and the Milky Way is primarily a part of the local universe surrounding us.
When discussing changes in time it is important to remember that when time is faster a second becomes shorter, so the “length” or the “size” of an earth second decreases. This means that more seconds pass relative to an earth second, thus it is easier to think in terms of changes in time, how much time has passed for an object being observed in comparison to how much time has passed on earth. This way when time is faster the ratio Δtr/ΔtE is greater and vice versa when time is slower, this ratio is the inverse of tr/tE.
To determine the change in the mass of an object as a function of distance from the centre of mass of an object we could thus write the equation
Where ‘α’ is a constant. The term ‘m~∞~/mE’ is introduced because the formula calculates the deviation from the minimum possible mass at a theoretical infinite distance. Now integrating we have
Where ‘b’ is a constant, and since as r → ∞ the value for mr/mE → m~∞~/mE so therefore the constant ‘b’ must be m~∞~/mE and the equation for mass dilation due to gravity would be
Recall that mass dilation is proportional to the time dilation squared (from equations for the conservation of energy) or inversely proportional to the speed of time squared so
Compare to Einstein’s equation for time dilation due to gravity
(Where t0 = slower time, tf = faster time.)
The above equations describe how mass and time dilate as a function of distance ‘r’ from an object of mass ‘M’ approaching a limit at a theoretical infinite distance from said object of mass. Due to the similarity to Einstein’s equation for time dilation due to gravity it is safe to assume that the value for the constant ‘α’ is equal to 2/c2.
Equation (12) becomes
Equation (13) becomes
Take note that ‘G’ and ‘c2’ are not constant as the sot changes, however these two variables change proportionally to each other and can therefore be treated as constants in this case.
Equations (15) and (16) bring to light Einstein’s oversight in developing his equation for time dilation due to gravity. Einstein failed to take into consideration that the limit for gravitational field strength depends on the greater gravitational field of which the object in question is a part. While Einstein’s equation for time dilation due to gravity would work well on Earth it would not work when studying galaxies, for example, because the time dilation within a galaxy would depend on the strength of the gravitational field of which that galaxy is a part. That’s the complicated reason that Einstein’s equation does not work, the simple reason is that Einstein’s function describing time dilation should be a continuous function, and as such his function cannot possibly be correct, since it is not continuous at t0=tf.
Notice that equations (15) and (16) do not collapse within the Schwarzschild radius, as radius ‘r’ approaches zero, mass (from the perspective of someone on earth) becomes infinite and time becomes infinitely slow. This idea has huge implications for “black holes” because it would mean that the laws of physics themselves do not collapse, but it is only Einstein’s equations which collapse.
Part 2: The Infinite Universe
Part 2A: Einstein and the Infinite Universe
In the theory of General Relativity, Einstein confronts the gravitational problems associated with an infinite universe and presents a solution. In his words
“If we ponder over the question as to how the universe, considered as a whole, is to be regarded, the first answer that suggests itself to us is surely this: As regards space (and time) the universe is infinite. There are stars everywhere, so that the density of matter, although very variable in detail, is nevertheless on the average everywhere the same.
This view is not in harmony with the theory of Newton. The latter theory rather requires that the universe should have a kind of centre in which the density of stars is a maximum, and that as we proceed outwards from the centre of this group-density of the stars should diminish, until finally, at great distances, it is succeeded by an infinite region of emptiness. The stellar universe ought to be a finite island in the infinite ocean of space.
This conception in itself is not very satisfactory. It is still less satisfactory because it leads to the result that the light emitted by the stars and also individual stars of the stellar system are perpetually passing out into infinite space, never to return, and without ever again coming into interaction with other objects of nature. Such a finite material universe would be destined to become gradually but systematically impoverished.”
Einstein argues the case well for an infinite universe, however he understands that matter could not exist in an infinite universe with an average density due to the problem of infinite gravity creating gravitational chaos. Einstein then proposes a solution to the problem while still keeping the idea of a universe without boundaries, Einstein proposes a “finite but unbounded universe.” Einstein invented the finite but unbounded universe, not based on scientific evidence, but based on his belief that there was no other way. There is another way.
Part 2B: The Big Bang
The first thing I would like to talk about is the very existence of singularities. According to my proposal, as gravitational field strength increases time becomes slower, and when time is slower everything moves slower. So what would happen to a star as it collapses to form a black hole? As the star collapses and as the centre becomes more and more dense, time would slow more and more. Although theoretically a singularity could become infinitely dense, in practise time would slow infinitely and it would literally take forever for a singularity to become infinitely dense and infinitely small.
Black holes are known sources of x-rays, according to my proposal in Part 1 there is no reason that those x-rays could not have been created within the Schwarzschild radius by the destruction of matter. As matter is destroyed upon entering a black hole mass would be converted to energy, and since from Part 1 light may not accelerate or decelerate due to gravity but only have its path bent, then any electromagnetic radiation leaving a black hole perpendicularly away from the centre of mass could theoretically escape the black hole. However, let us now consider what would happen if no electromagnetic radiation could escape from a black hole.
The internal energy of such a massive “singularity” would surely increase as more matter is destroyed upon approaching the “singularity” at the centre of the black hole. What happens when energy is added to a liquid? The internal energy of the liquid increases until a critical value is reached, the intermolecular forces binding the liquid together are overcome, and the liquid evaporates. Could the same thing have happened with the big bang? The early universe, in the time immediately following the big bang, was estimated to have a temperature in excess of 1030K. Could this extremely high temperature be an approximate “boiling point” of a universe sized black hole? Could some supernovae be smaller examples of just such an explosion?
If this is the case, and my proposal in Part 1 is correct, then the universe would have initially expanded at a much slower rate due to the massive gravitational field surrounding it, and as time became faster the universe would have accelerated in its expansion. This is similar to the inflationary early universe model, or the effect we know as “dark energy”. Although the universe would accelerate as it expands and gravitational field strength within the universe decreases, velocity squared increases proportionally to gravitational acceleration back toward the centre of the universe. Therefore as observed mass approaches zero, gravitational acceleration would increase at a much greater rate than velocity, meaning that the universe may end in a big crunch.
The logical conclusion is that if the universe collapses at the end of its life it would again form a universe sized “singularity”. This universe sized “singularity” would again destroy atoms as they approached, the internal energy of the “singularity” would continue to increase, until boiling point was reached again, and the universe would begin anew.
Part 2C: The Infinite Universe
If space was infinite but the universe was finite, then surely there would be more of these “big bang universes” outside of our own. No matter how massive something is, when compared to the infinite, it is as nothing.
Imagine if our big bang universe is not all that there is, imagine if our universe was nothing more than the equivalent of a star in a bigger universe, let’s call it “super-universe (I)”. This super-universe (I) would be an unfathomably massive universe containing not merely galaxies and stars and planets, but containing entire systems of big bang universes and universe sized “singularities”. Now imagine that super-universe (I) also undergoes a similar cycle of boiling, expanding, cooling, contracting and boiling again, just like our own big bang universe may. No matter how massive this super-universe (I) would be, it is still as nothing when compared to the infinite. Now imagine that this super-universe (I) was nothing more than the equivalent of a star in a bigger universe, let’s call it “super-universe (II)”. This super-universe (II) contains not merely systems of galaxies, and stars and planets, nor does it merely contain systems of big bang universes and universe sized “singularities,” but this super-universe (II) contains entire systems of super-universe (I)’s. This super-universe (II) also undergoes cycles of boiling, expanding, cooling, contracting and boiling again.
I needn’t think I should continue explaining this hypothesis further, imagine that the infinite universe is essentially an infinite, cyclical, regenerative universe with no beginning and no end. Imagine that infinite space consists of an infinite series of these super-universes within super-universes. Imagine that the infinite universe has always existed and will continue to exist forever in some form or another. Now infinite space can finally be filled with an infinite universe.
Recall Einstein’s quote in Part 2A, in order to prevent gravitational chaos in an infinite universe the density of matter must decrease the further away from the centre of the universe you travel. This model of the infinite universe is the one feasible model of the infinite which obeys this requirement. While our universe may have an average density of matter, once you leave our universe the density of matter would drop tremendously. Super-universe (I) may have an average density of matter, but once you leave super-universe (I) the density of matter would again drop tremendously. Thus if we were to consider the centre of our big bang universe to be the centre of the infinite universe, then the further from the centre of the infinite universe you travel the less the average density of matter becomes. Einstein’s justification for the finite but unbounded universe is invalid, because there is a model of the infinite universe that works.
1) ‘Relativity: The Special and General Theory,’ by Albert Einstein, translated by Robert W. Lawson (Authorised translation), Meuthen & Co Ltd, 1916, revised 1924, World Publications Group Inc, 2007.
2) ‘The Illustrated A Brief History Of Time: Updated And Expanded Edition,’ by Stephen Hawking, Bantam Books, 1996.
Contact: [email protected]
Einstein stated that the universe could not be infinite unless matter became less dense the further you travelled from the centre of the universe, otherwise the gravity from all of the stars would accumulate and create infinite gravity. Einstein therefore believed that it was not possible for the universe to be infinite, but there is one way. In this article I am proposing a working model of the infinite universe, I call it “the super-universe”. In Part 1 I propose new field equations for gravitational time dilation that work inside black holes, but still yield the same experimental results as Einstein’s equations. In Part 2 I propose my working model of the infinite universe, that what we presently call “the universe” is nothing more than the equivalent of a star in a bigger “super-universe”, and this super-universe is nothing more than the equivalent of a star in a bigger “super-universe”, and so on and so on, unto infinity.