Part 1d: Partial Derivation Of The Gravitational Deflection Of Light
Since momentum is inversely proportional to the speed of light (10)
Now
Since
And
Then
Since
Therefore
(15)
This value is analogous to acceleration, however since we know that light neither accelerates nor decelerates due to gravity but can only have its path bent, this value tells us how much the path of light is bent due to gravity. The value of this function is in the S.I. units of m-1 or (radians.m-1) with respect to r. Notice also that this equation is equivalent to
Now ‘r’ is the distance from the centre of mass ‘M’, ‘s’ is the distance along the light path, ‘d’ is the perpendicular distance from the centre of mass to the light path and ‘ϴ’ is the angle from the origin at M. We need to change equation (15) to be in terms of ‘s’ rather than ‘r’ and integrate over ‘s’ for the entire path length. The angle of deflection of the light path will be given the symbol ‘α’.
(16)
First let’s explore the scenario where (Δtr/Δt∞)2 is close to enough to 1 as to be insignificant. In this case, close to earth, the equation becomes
Which becomes
Which upon integration gives the solution
(17)
Which is identical to Einstein’s original equation from 1911 for the gravitational deflection of light9, however Einstein later updated this equation in 1915 after realising that this equation has assumed the value for ‘d’ to be constant. Einstein’s final equation had increased the value for the deflection angle by a factor of 2.
Just quickly, integrating the full equation yields the rather complex
(18)
Crunching the numbers for the two equations, using the deflection of a beam of light travelling around a point mass of one solar mass at a distance of one solar radius from the centre of mass gives, for equation (17) a value for the deflection angle of 0.875669arcseconds, while equation (18) gives a very slightly smaller value of 0.875666arcseconds. You might also notice that equation (18) collapses when the value for ‘d’ is inside the Schwarzschild radius, which should be expected since when a beam of light passes within the Schwarzschild radius it is believed to be sucked into the black hole, not merely have its angle deflected to a finite amount.
Although not a complete derivation, because I have assumed that the beam of light does not get any closer as a result of its gravitational deflection to the object of mass it is passing, the above should help to show that my theory should be able to account for everything that Einstein did if it is properly applied.
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Part 2: Visualising Gravity In Four Dimensions
Part 2a: The Curvature Of Space
Einstein proposed that spacetime is warped by mass to create gravity, I shall expand on this idea below, however rather than refer to “spacetime” I shall refer simply to “space”. Imagine the effect of an object of mass on a two-dimensional plane of space in one dimension, and let us draw a cross-section of said plane of space. Assume that space is repulsed by mass, or assume that mass repulses space, as first proposed by Einstein. [Figure 2a]
Of course, there wouldn’t be just one plane of space in all of space, there should theoretically be an infinite number of these planes, so let’s extend the idea. [Figure 2b]
Next we must take into consideration that space is not one dimensional but three dimensional, so let’s imagine space being repulsed by mass in every direction at once. [Figure 2c]
Therefore the net effect of space being repulsed by mass in every direction at once would be something like this. [Figure 2d]
According to the above diagrams, the net effect of space being repulsed by mass in every direction at once would create something of a “density of space”. In order for space to have a density there is no need to invent an æther to fill space, the curvature of space can create the effect of a density of space without the need for an æther to fill the voids.
Let’s now expand on this idea of an infinite number of planes of space being repulsed by mass.
Part 2b: Space And Mass
Next we’ll examine what would happen as an object of mass moves through space, let’s visualise the situation. Although these theoretical planes of space themselves would not move, the curvature of space would be pushed forwards as an object of mass moves through space and space would be pushing the object of mass from behind. Since every action force has an equal and opposite reaction force, while mass pushes on space, space also pushes on mass. [Figure 3]
Therefore, when an object of mass is in motion space would essentially move with it. While it would take energy to set an object of mass in motion, due to the need to move the space with it, once that object of mass is in motion it would continue to move through space. An object of mass must push space forward to move through it, but space pushing the object of mass from behind ensures that the object continues to move forward and the law of inertia can thus be visualised. If space offered no resistance to the forward motion of mass then mass must always move at its maximum velocity, which we know to be light speed, having to set space in motion would require a specific amount of energy, the amount of energy required would be determined by how much space needs to be moved.
What is mass? We know from Part 1 that mass is not constant but is dependent on the gravitational field strength that mass resides in, from Part 2a we know that the gravitational field strength is determined by the density of space, and from above we know that the energy required to set an object in motion is determined by how much space needs to be “pushed out of the way”. We could decide that mass is a measure of the effect an object has on the curvature of space. What is it about mass that causes space to warp? The traditional view is that space-time is repulsed by mass, but we also know that mass and energy are related, so perhaps we could take a new perspective and imagine that mass is the effect of an energy field that warps space. The greater the strength of this “mass energy” field, the greater the mass. In nuclear reactions “mass energy” could be converted to other forms of energy. The interchangeability of mass and energy was first proposed by Einstein with the equation E=mc2 but now we can understand for the first time why mass is not entirely separate from energy, mass is simply the effect of an energy field that warps space and is itself a measure of the energy required to move an object through space.
If mass is a measure of the energy required to move an object through space, and the greater the mass the greater the “mass energy” field surrounding that object, then objects with greater “mass energy” fields surrounding them would require more energy to set planes of space in motion.
Why could an object of mass move faster through denser regions of space? Perhaps in regions of denser space the time taken for one plane of space to push on the next plane of space is reduced because the planes of space are closer together. Perhaps the transfer of energy from one plane of space to the next is limited to the maximum value of light speed, these planes of space can push on each other no faster than light speed, with light speed being dependent on how close together these planes of space are.
Why is mass not conserved when moving through different densities of space? If mass is simply a measure of the energy required to move an object through space, and an object of mass moves into a region of space where motion through this space requires less energy, then naturally the mass would be less. In this situation mass may not be conserved, but the strength of the “mass energy” field being emitted by an object is conserved. Thus “mass energy” is conserved, however mass is not.
How does gravitational acceleration work? Let’s consider Figure 3 again and think about what would happen if there was more space on one side of an object of mass than the other. Every action force has an equal and opposite reaction force, so while mass pushes on space, space also pushes on mass. If space on either side of an object of mass was u
nbalanced, one could therefore expect that the side with more space would push the object of mass towards a region where there is less space. Thus objects of mass would be pushed by unbalanced space towards less dense regions of space, i.e. objects of mass would be pushed by the force known as “gravity” from weaker gravitational fields towards stronger gravitational fields. Gravity has long been considered a weak force, and it has also been shown that a large amount of energy is required to make a small amount of mass. The weakness of gravity can now be understood, consider the amount of energy that must be required to warp space, and consider also that gravity is the effect of unbalanced space on either side of an object of mass, then it is little wonder that so much energy is required to create the mass which is required to make so little gravitational force. In the context of my theory, gravity does not seem so weak after all, but is the effect of an energy field that warps the fabric of space itself!
Part 2c: Space And Electromagnetic Radiation
It has long been assumed that the constancy of light is explained by the Lorentz transforms, however this may not be the case. Let’s consider one of Einstein’s thought experiments, commonly found in textbooks, the thought experiment involving a light pulse on a train moving close to the speed of light. [Figure 4a]
The passenger (A) sees the light pulse travelling in a perfectly vertical direction. The observer (B) sees the light pulse follow a diagonal path. Since the observer (B) experiences a longer time interval than the passenger whilst observing the light pulse cover a greater distance than the passenger (A), light speed appears constant for both passenger (A) and observer (B).
For simplicity of numbers I shall use a train travelling at a velocity ‘u’ of 3/5 of the speed of light. Using the Lorentz transforms, the mathematics are as follows. [The subscript ‘A’ denotes time and distance as measured by the passenger, no subscript denotes time and distance as measured by the relatively stationary observer.]
The speed of light for the passenger is given by
A conversion of units yields
Adding vertical velocity of light to horizontal velocity of the train by Pythagoras yields
Therefore the light pulse appears to travel at a constant 3x108m/s for both the passenger (A) and the relatively stationary observer (B). While this thought experiment is very commonly found in textbooks, the mathematics does not work when the light pulse is travelling in any direction other than the vertical (from the perspective of the passenger (A)). [Figure 4b]
In the next example, as shown in the diagram above, both the passenger (A) and the relatively stationary observer (B) see the light pulse travel in the same direction as the train. For simplicity of numbers I shall again use a train travelling at a velocity ‘u’ of 3/5 of the speed of light. For this example length ‘l’ dilation also needs to be taken into consideration.
The speed of light for the passenger on the train is again given by
A conversion of units yields
Adding velocity of light to velocity of train gives
Which is > 3.0x108m/s and, skipping the calculations, if the pulse of light travels in the opposite direction to the train then the speed of the light pulse for the outside observer (B) is
Which is < 3.0x108m/s.
Put simply, the Lorentz transforms do not explain the constancy of light.
As explained earlier, when an object of mass is in motion, space would effectively move with that object of mass. Let’s consider the effect this moving space would have on electromagnetic radiation approaching an object of mass in motion. If the medium that electromagnetic radiation travels through is space and the space that the electromagnetic radiation is moving through is in motion, then surely light would change its velocity depending on the velocity of the space it is travelling through. This should explain how red/blue shifts work, the idea is simple, light waves are either “stretched” or “squashed” due to the motion of space. [Figure 5]
Red/Blue shifts are one situation in which traditional physics ignores the first law of thermodynamics, but by this model the first law of thermodynamics is always obeyed. Although the wavelength of light changes when red/blue shifts occur, the velocity of light also changes. If cE=λυE and the speed of light (cE) changes due to the motion of space, then the wavelength (λ) would change proportionally, leaving the frequency (υE) and therefore the energy of light constant.
Back to the problem of a light pulse on a train travelling close to the speed of light, according to my theory since light travels through moving space, there is no reason why light cannot travel faster or slower than 3x108m/s from the perspective of an outside observer. According to my theory space is not nothing, space consists of a theoretical infinite number of planes of what Einstein would call “space-time” through which all matter and energy must travel. The important thing is that while light may change velocity depending on the velocity of space it is travelling through, the outside observer could never know this. The outside observer could not actually see the light pulse inside the train, unless that light was transmitted out through the window of the train and into his eyes. Once the light left the train to be seen by the outside observer that light would then be travelling through the space surrounding the outside observer and no longer travelling through the space of the fast moving train. The speed of light appears constant to all observers in all inertial reference frames, but this does not necessarily mean that the speed of light is always constant, only that light speed appears constant.
Part 3a: Back to Three Dimensions
It was Einstein who proposed the idea of theoretical planes of space warping to create gravity, and I have extended upon this idea in the preceding section. However, are planes of space actually necessary? In all of my diagrams of the warping of space I have used simply lines, or “strings” if you prefer. Thus we find that rather than a theoretical infinite number of planes of space we can use a theoretical infinite number of strings instead for the same result. We have now stripped away an extra unnecessary dimension and we are left with a three dimensional picture of gravity, which is much more satisfactory.
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Part 3: Black Holes, The Big Bang And The Super-Universe
Part 3a: Black Holes
Recall from Part 1c that it is not the laws of physics which break down within the Schwarzschild radius, rather it is Einstein’s equations which collapse, the laws of physics remain the same. The first thing I would like to talk about is the very existence of singularities. According to my theory, as gravitational field strength increases time becomes slower, and when time is slower everything moves less easily through space. 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. I will therefore be calling the mass at the centre of a black hole a “black star” rather than a singularity.
Black holes are known sources of x-rays, in light of my theory there exists the possibility that these x-rays actually began as gamma-rays created by the destruction of matter upon entering a black hole. According to my theory light does not accelerate or decelerate due to gravity but the momentum of light can be changed causing the light path to change direction. Therefore if a gamma-ray was created somewhere within the Schwartschild radius of a black hole and that gamma-ray was travelling perpendicularly away from the centre of mass of the black star at the centre, there is no reason that gamma-ray could not escape with a greatly increased wavelength. However if a gamma-ray left at a large enough angle with respect to the centre of mass of the black star, that gamma-ray would have its path bent sufficiently for it to enter the black star, i.e. it would be unable to escape the black hole.
The final question with regards to black holes, is why would x-rays leave black holes concentrated in
jets at the poles? The very simple reason is that due to the conservation of angular momentum as a black star becomes smaller and smaller, the rotational velocity of the black star would be so great as to have its observed mass increase about the equator, since mass increases with velocity close to light speed by the Lorentz transforms. Therefore the margin of error for a gamma-ray to leave a black hole perpendicular to the centre of mass of a black star would be much smaller about the equator, it would be much easier for electromagnetic radiation to leave a black star at the poles, since the observed mass is much less at the poles.
Judgement Day Page 13
