As the title implies, this post is about gravity. It is not so much about the force of gravity, but gravity as an acceleration field having a constant parameter referred to as the gravitational constant, denoted G, which is otherwise known as Newton’s gravitational constant. This constant appears in Newton’s gravitational law and in Einstein’s theory of general relativity. Though it features in both Newtonian & Einsteinian definitions of gravity, its physical significance remains ambiguous.
In this post, I shall reveal its physical significance in simple language and very little mathematics, but in accordance with the definition of the atom, which I covered in my post Anatomy of Atoms and which is based on the UP hypothesis.
In Newtonian physics gravity is defined as radial acceleration produces by an object towards its centre of mass. Therefore, any object that has mass has a gravitational field. Based on this definition, any material object entering the gravitational field of another is immediately attracted to it and attracts it. The question of what constitutes a physical field and causes matter to accelerate has never been answered satisfactorily and therefor the nature of gravity has remained ambiguous!
Though the attraction is mutual between objects, if one thinks of a particle entering the gravitational field of the sun, one realises that it must immediately be encapsulated by that field. On the other hand, the particle’s own field would not have even registered at the mass of the sun, despite the theoretical assumption that gravitational fields are infinite in space. Therefore, gravity is essentially a form of interaction of quantum fields. In fact, the UP hypothesis, on which this post is based defines gravity as the outcome of interaction of the magnetic fields of objects. More on that latter.
From a Newtonian perspective, gravity is encapsulated in Newton’s equation [F = G.m1.m2/R²], which expresses the attraction force F between two objects in terms of their masses m1 and m2, the square of the radial distance between them R², and the gravitational constant G— the subject of this post.
Clearly, in the absence of one of the masses, let us say in this case m2, the equation does not hold true for the force F, as [m2 = 0 –> F = 0], though it holds for acceleration. This is easily verified by substituting [F = m2. g] in Newton’s equation, where g is the acceleration due to gravity. Thus, m2 cancels on both sides of the equation and we are left with [g = Gm1/R²], which confirms the existence of gravity as an acceleration field in the absence of a second mass. However, as I shall explain in due course regarding the photon as a massless particle, whilst it does not experience acceleration towards the mass, it is affected by gravity. In fact, photons are diverted away from the mass! Therefore, although the gravitational field exists in the absence of a second mass, it only induces force in objects having mass.
In contrast to Newtonian gravity, Einsteinian gravity not only considers the magnitudes of force and acceleration between two object, it also defines the geometry of the surrounding space due to the presence of mass. Consequently, it caters for the interaction of gravitational fields of different object based upon the geometry and dynamics of those fields. Thus, it establishes a framework linking gravity to the geometry and dynamics of the fabric of space, which helps explain the behaviour of the fabric of space in the presence of different objects with different masses in different locations. And it does not stop there. It also defines the effect of events in space-time beyond the bounds of their localities to cover the effect on the global space-time— i.e., on the universe, by incorporating the cosmological constant.
To that extent, general relativity is much more rigorous and complex than the force-mass-distance relationship of the Newtonian gravity. In fact, general relativity is the best candidate for a theory of everything, but only if it proves possible to reformulate with reference to the background vacuum containing the fabric of space. In fact, the main obstacle in the way of unifying quantum theory and general relativity is the different perspectives from which each of them has been developed. Whereas quantum objects interact in a smooth background vacuum, which makes the fabric of space appears as a granular field, in general relativity objects are defined with respect to the fabric of space as a smooth background, the geometry of which is shaped by the distribution of matter. Clearly, the two theories cannot be reconciled, unless this anomaly is resolved and the effect of the background vacuum is incorporated explicitly and correctly.
Quantum field theories, whilst appearing to neglect the fabric of space and the effect of the background vacuum, they incorporate them in numerous mathematical models, by defining different types of spaces, manifolds and groups, each of which caters for a specific condition or a phenomenon. Quantum fields are essentially the fabric of space modelled to facilitate understanding of the behaviour of quantum objects and their surroundings under different conditions and from different perspectives. There are various theoretical spaces, manifold and groups with varying properties, dimensions and behaviour that are used to model different phenomena. General relativity itself can be formulated using Minkowski or De Sitter spaces as modified versions of Euclidian space-time, which confirms that all fields are one, but are considered mathematically from different perspectives.
Returning to the task in hand, I see no need to discuss Einstein’s field equations in any detail, because our main concern is the gravitational constant G and its physical significance. However, it is worth touching on the reason that makes light affected by gravity, as another piece of evidence in support of the notion that the fabric of space is physical and is as described in the UP hypothesis.
As I have already mentioned, the force of gravity exists only between objects having mass and as such, a photon does not experience the force of gravity. Although Newton’s equation says nothing about the behaviour of photons in a gravitational field, Einstein’s field equations do. Ignoring the cosmological constant, Einstein’s field equations equate the parameters which define space in terms of curvature and metric tensors on one side and stress and energy tensor, which defines the resulting forces, on the other side. Since light as electromagnetic waves is a form of dynamics of space-time and since gravitational fields are another form of the dynamics of the same space-time, it follows that general relativity must incorporate both sets of behaviour of space-time, if it is modelling space-time geometry and dynamics correctly, and it has been proven to do so.
Therefore, in the case of light, the force of gravity does not apply and the effect is mere change of the direction of light, resulting from the angular motion of the elements of the fabric of space (UPs) forming the gravitational field. In fact, gravity affects even the direction of light radiating from the source-object of the gravitational field. The limit of that effect is reached when the surface of an object reach rotational speed that causes it to break continuity with the surrounding fabric of space. That occur when UPs in its immediate surroundings acquire purely tangential speed, isolating the object from the fabric of space and terminating the propagation of light to and from it, which marks the development of an event horizon of a black hole. Light’s speed can never change, unless the properties of the medium change, but the direction of light can be changed by changing the direction of the fabric of space through which it is propagating.
The point to note here is that as a soliton or a wave-packet propagating though a gravitational field, a photon must be affected by the global motion of that field, provided the gravitational field is sufficiently strong— i.e., its UPs have the density and speed which make the effect observable. Since gravitational field intensity is a function of mass, it follows that the greater the mass the greater the observed effect, hence the phenomenon of gravitational lensing produced by massive objects.
Returning to Newton’s gravitational constant G and its significance in the mathematical models for gravity, we can begin by considering its dimensions— i.e., its units of measurement. The units of G are [m³ kg-¹ s-²], which reflect a constant radial acceleration (m.s-²) across a unit area (m²). But what of the mass (kg-¹)? This requires some explanation and therefore, I shall state what G is, then I will explain the reason behind my statement.
G is the constant acceleration of a unit area of the fabric of space (UPs) induced by a unit of mass.
This definition leads us to an obvious question: if G is the acceleration of UPs towards the centre of mass, where do they end up? The answer lies in the workings of subatomic particles, as I shall explain, but let us first analyse G.
Based on this definition of G, its units could be expressed as [(m².kg-¹) (m.s-²)] and therefore, G can be expressed in terms of the acceleration g, mass m, and the area of the fabric of space A enclosing the mass, which in Newton’s equation appears as R². Thus, G can be expressed as [G = g A/m].
Since G is a universal constant and g is a constant at a given radial distance, it follows that at a given radial distance from the centre of mass, the greater the mass the greater the surface area enclosing it. This, on the face of it, seems like a trivial result. However, it is also saying that increasing the mass m, at constant surface area increases the acceleration g. Therefore, the denser the object the greater the gravity it produces at a given location from the mass. Consequently, lighter objects experience greater acceleration towards heavier objects. Note that (A/m) is the inverse of density per unit length.
In terms of UPs, this interpretation relates the negative pressure produced by mas m, to their acceleration g towards that mass. However, there is another component to gravity, which relates to the interaction between UPs forming the magnetic fields of the objects. For any given distance between two objects of different masses, UPs forming the magnetic field of the more massive object have greater angular speed. Consequently, UPs of the magnetic field of the less massive object progressively acquire greater angular speed as they near the larger mass. That increasing angular speed translates to linear acceleration of the object towards the heavier object. I now return to answer the question of where UPs end up as a result of being accelerated towards the centre of mass and confirm the above physical definition of G.
The divergence theorem expresses the flow of a vector field through a surface in terms of the behaviour of the field within that surface. In effect, the theory models the reverse of gravity, whereby the vector field is attracted towards the centre of mass instead of radiating away from it. This of course calls for an explanation of how the mass absorbs a physical field. In other words, what is the sink through which the victor field vanishes?
In view of my definition of the atom in my post Anatomy of Atoms, which is based on the UP hypothesis, the answer can be found in the action of the string element of subatomic particles and the effect that has on UPs in the surrounding, which I have ignored previously. I now stress that all string based particles must produce a flow of UPs at the poles through the mass. That flow is the dipolar magnetic field associated with some forms of molecular matter, though it is so weak at the scale of individual particles that it is undetectable. It nonetheless exists. In fact, it is the weakness of that field, which lies behind the small magnitude of G and stops gravity from featuring in the standard model.
The sketch in Fig. 1 is 2-D representation of the hydrogen atom showing the mass and pressure direction on the surrounding UPs. It is possible to envisage the mechanics involved as UPs accelerate towards the mass before being expelled by the rotating string within the charge. Fig. 2 shows the electric charge and string element of the proton and illustrates the effect of that mechanism as a net flow of UPs through the poles of the proton. UPs and the mass are not shown in Fig 2 for clarity. Inspecting the two sketches reveals the effect of the proton in the surroundings.
As the string rotates within the charge, it expels UPs attracted into the mass cavity due to the negative pressure. Since the electric charge encloses the perimeter of the mass, UPs collapsing into it are expelled in orthogonal direction to the plane of rotation. This creates a circular flow of UPs through the mass, with UPs accelerating as they fall into it at the rate they are expelled from it, because the flow must balance as the mass is constant. This generates a very weak acceleration in the surrounding UPs towards the mass, which is a function of the volume of the mass. This weak acceleration is the source of the gravitational constant G.
The accumulation of atoms, in view of their geometric configuration— see my post Anatomy of Atoms, may produce net unidirectional flows of UPs that results in a strong dipolar magnetic field or they may cancel out within the molecular structure. The outcome depends upon the geometry of the atoms and the molecular structure they form. However, the radial acceleration they produce as gravity, like the magnetic field produced by the charge, can only increase with increased number of particles. This is due to the fixed orientation of matter particles in space, as I explained in my post Quantum Gyroscopes.
On this basis, the atom is perhaps best modelled as a special type of vortex in which the angular speed of UPs forming the magnetic field is inversely proportional to the radial distance from the mass. Mass being the eye of the vortex, inducing negative pressure and accelerating UPs towards it at a constant rate. The combination of radial acceleration of UPs towards the mass and their rotational speed around it force object to attract one another, hence the force of gravity. Since G is a function of the rate of flow of UPs though the mass due to the negative pressure, it follows that the greater the mass the greater the pressure and therefore the greater the radial acceleration.