It is worthwhile to consider that if time is faster not only do clocks move faster, but chemical reactions happen faster, flora and fauna age faster, our brains work faster, so is it not possible that light also moves faster? According to the aforementioned, any increase in the speed of light in a vacuum would be unnoticeable because the timing mechanism that is 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).
Thus by this definition of time the speed of light in a vacuum can appear to remain constant when the speed of light in a vacuum is not actually constant at all. However there is one way that a change in the speed of light is noticed, by the red/blue shift that accompanies 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 remains constant, however the wavelength has changed. By this theory’s definition of time, if time is faster then everything moves faster, including our clocks and including light.
In the course of this paper, and my theory as a whole, I will examine some of the implications of this new interpretation of some old experimental results and develop a new theory of time and gravity from first principles.
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
(1)
(Where E = energy, h = Planck’s constant, υE = frequency from the perspective of an observer on earth.)
If we assume by the first law of thermodynamics 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, so we will now consider the S.I. units of measurement with regards to this equation.
(2)
If we study equation (2) we notice that the value for frequency ‘υE’ 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. We could talk about the number of “earth waves” and consider them to change in proportion to earth seconds, however a wave is a wave regardless of what your measure of time, an “earth wave” is no different to simply a “wave”.
(3)
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 distance 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 keeping the units in mind and remembering the first law of thermodynamics, the law of the conservation of energy
(4)
(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, from the perspective of someone on earth of course. Let’s rewrite equation (4) now
(5)
Ignoring the units now equation (1) is simply the same
(1)
While rewriting equation (5) without the units is simply
(6)
It must be kept in mind that energy is always conserved, that energy remains constant no matter what the change in the sot, according to this theory energy only ever appears to change due to changes in the measurement of time.
Now we must consider the equation for kinetic energy
(7)
(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. Now we can understand mathematically the reason why when time is faster everything moves more easily through space. In weaker gravitational fields not only does light move faster, but so too do objects of mass. Objects of mass must move faster in weaker gravitational fields because their mass decreases while their kinetic energy remains constant thus resulting in an increased velocity, from the perspective of someone on earth of course.
The next equation to consider is the simplified equation for gravitational potential energy
(8)
(Where gE = gravitational acceleration from the perspective of an observer on earth.)
According to this equation, if mass ‘mE’ decreases then gravitational acceleration ‘gE’ must increase proportionally. Now let’s consider the proper equation for gravitational acceleration, recall that if mass decreases the sot increases and gravitational acceleration increases
(9)
(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 in question.)
Now we must conclude that if the mass of an object subject to gravitational acceleration decreases the value for the gravitational constant ‘GE’ must increase proportionally. Consider next the S.I. units
We can see that the value for the gravitational constant changes depending on the strength of the gravitational field an object subject to gravity is in, or if you prefer, the value of the gravitational coefficient changes depending on the sot in that location in space. I propose changing the name of the gravitational constant to the ‘gravitational coefficient’.
Let’s stop for a moment and think about the equations we have been discussing and their full implications. I have now developed a series of equations from the reinterpretation of one single experiment. What we’ve learned is that mass decreases in weaker gravitational fields, the combination of this decrease in mass and the conservation of energy results 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, 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
(10)
(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 is actually the opposite that occurs, gravity affects the momentum of light. It makes sense now that since gravity changes the momentum of light that the path of light can be bent by gravity, as predicted by Einstein.
Consider now what the implications of assuming light speed to be constant might be, for example, we use electromagnetic radiation (emr) to measure distances within the solar system. If this hypothesis is correct our measurements of the solar system must be very slightly incorrect, as emr moves away from the sun time must become faster, emr must accelerate, and the outer planets must be further away and moving faster than what is presently believed. If this hypothesis is correct, the size of the
solar system could be an optical illusion. Of course, were you to send a spacecraft to a planet on the outskirts of the solar system as time becomes faster that spacecraft would also accelerate, just the same way that light would. We could never know that our measurements are an illusion unless we could observe gravitational motion in its entirety, from outside a gravitational field, not from within it. The true extent of this effect within our solar system is difficult to calculate, for reasons which will become clearer shortly, but I am certain that it can be calculated.
Think now about stars on the outskirts of galaxies, stars on the outskirts of galaxies have been found to be moving faster than predicted by the theories of Newton and Einstein, the most popular explanation for observed galactic rotation curves is that there must be a large amount of unseen matter in galaxies, it is known as the theoretical dark matter. However if my theory is correct it may be that dark matter is unnecessary and that galaxy rotation curves can be explained by a new understanding of exactly how gravity works.
Part 1c: Gravitational Time Dilation and Dark Matter
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 it is a part of. However it becomes difficult because everything is a part of a different gravitational field. Although the speed of time on Earth would be equal to 1, Earth is primarily a part of the gravitational field of the Sun, so at a theoretical infinite distance from the Earth m∞/mE < 1 or t∞/tE < 1 or Δt∞/ΔtE > 1 and is dependent on the gravitational field strength of the Sun. The Sun in turn is primarily a part of the gravitational field of the Milky Way, and the Milky Way a part of the local universe around it.
When discussing changes in time it is important to remember that when time is faster a second becomes shorter, so the “length” or “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 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 t∞/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 can 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 and then the constant must be m∞/mE and therefore the equation for mass dilation due to gravity is
Or
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
Or
Compare to Einstein’s equation for time dilation due to gravity
(11)
(Where t0 = slower time, tf = faster time, other values as before.)
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 thus my equations are complete.
(12)
(13)
It is important to test different scenarios with regards to equations (12) and (13) to ensure their success.
When r → ∞ (12) becomes
When r → ∞ (13) becomes
When r → 0 (12) becomes
When r → 0 (13) becomes
Equations (12) and (13) 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 for time dilation due to gravity does not work, the simple reason is that Einstein’s function describing time dilation should have the range 0 < Δt0/Δtf < ∞ and as such his function cannot possibly be correct, since it is not continuous. Please note that while my theory says that neither ‘c2’ nor ‘G’ are constant in different gravitational fields, ‘c2’ varies proportionally to ‘G’ so for simplicity in this situation they may be assumed to be constant.
Notice that equations (12) and (13) 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 means that the laws of physics do not collapse but it is only Einstein’s equations which collapse. However I will talk more about black holes in Part 3.
Modified Newtonian dynamics (MOND) has attempted to explain dark matter by tweaking Newton’s equations for gravity on the outskirts of galaxies. The creator of MOND, Mordehai Milgrom, proposes that gravity behaves differently when gravitational acceleration becomes very small. He has found that when studying galaxies, if centripetal gravitational acceleration varied as a function of radius ‘r’ rather than the square of the radius ‘r2’ then the velocities of stars on the outskirts of galaxies could be explained without the need for the theoretical dark matter.8 Let’s now examine how my equations would behave when studying gravitational acceleration within a galaxy.
Recall
And equation (12)
Now we have
As r becomes relatively small, as compared to a very large mass, the equation becomes
Although without the changes in the gravitational constant balancing the changes in the speed of light, gravitational acceleration would change with the change in the speed of light, so really we should rewrite this as
(14)
As all other terms are constant as r becomes relatively small centripetal gravitational acceleration varies as a function of radius ‘r’ rather than radius squared ‘r2’ at a relatively small distance from the centre of a very large mass, just as explained in the empirically based MOND theory.
Let’s do a plot of rotational velocities around a point mass, with mE/m∞ given a value of 10.
The above plot is very interesting with regards to the search for dark matter. We can see that for large mass, by my theory, we have essentially a linear relationship between distance ‘r’ and the rotational velocity. My theory could be the explanation that we have been searching for. The position where the lines intersect is the location where the sot in my equation is the same as it is on earth, i.e. Δtr/ΔtE = 1. Although the trends shown on the above plot are very interesting, further investigation on the subject of dark matter is required.
My hypothesis, in addition to the possible explanation for dark matter, would also logically explain the observed acceleration of the universe as it expands. According to my theory, as the universe expands the gravitational field strength within the universe would decrease and therefore time would become faster. As the universe expands and time becomes faster within the universe, not only would the expansion of the universe accelerate, but the wavelength of light travelling from distant galaxies would shift further towards the red as the sot increases while this lig
ht is in transit. The mysterious expanding force acting on the universe, which has become known as “dark energy,” could be easily explained by gravitational time dilation. I will discuss the expansion of the universe further in Part 3.
Judgement Day Page 12