OverviewAccording to Relativity Theory, the presence of mass in a specific region in space causes a local spatial distortion in that region. This distortion is often termed a “gravity well”. First, time is dilated (dilated simply means expanded, or spread out) inside the region. To explain this, first assume we have two observers ‘A’ and ‘B’ who have negligible mass and so do not affect the spatial distortion. They first synchronise watches. ‘A’ - the remote observer - keeps well away from the mass, while ’B’ then spends 10 minutes at the mass in the distorted region of space. They get together again and compare watches. ’B’ finds his watch says 10 minutes were spent near the mass, but ’A’ finds that more than 10 minutes have elapsed. If the mass is small the difference may be a few nanoseconds, but near a huge mass like a black hole 10 minutes in the gravity well may be the same as millennia outside. So time is slowed down (=dilated) in the gravity well. Next, space is dilated. Suppose there is a satellite of negligible mass in orbit round the distortion. ‘A’ sees this as having an orbital radius ‘r’. While ‘B’ is at the center of the distortion in the vicinity of the original mass he sees the orbital radius as being greater than ‘r’.
Figure 1: Dilation of space In Figure 1, the remote observer ‘A’ sees the satellite at ‘p’, orbiting at a radius of ‘r’. ‘B’ is at the mass in the center of the gravity well and sees the satellite at ‘q’ orbiting at a greater radius. ‘B’’s space is dilated - his measurement of length is greater than ‘A’ ’s. In spite of the distortion the satellite still occupies the same solid angle of the sky, as shown by the lines in Figure 1. ‘B’ sees the same solid angle as ‘A’ would calculate he saw, so to ‘B’ the satellite is not only more distant, but larger too, in proportion to the dilated radius. So space is increased (=dilated) in the distortion. A very simple and graphical way of putting this is to say that the inside of such a distortion is larger than the outside, at least to a person who travels from the outside to the inside. If the outside measurement of ‘r’ is 100 meters then for a small distorting mass the inside measurement might be 100.000001 meters. For an immense distorting mass, approaching the black-hole limit, the inside might become light-years across. For black holes the inside becomes infinite. Nor is this all. The dilation of space means that to ‘A’ everything in the gravity well seems smaller. Everything that has the dimensions of space is smaller. Imagine a particle with an electric charge outside the distortion. ‘A’ measures a certain electric field strength at a radius ‘r’ from the electric charge, then sends it to the mass at the center of the distortion. What ‘A’ measures as a radius ‘r’ from the charge is now seen by the charge to be greater than ‘r’, so ‘A’’s perception is that the electric field has been reduced by the square of this change in ‘r’, and thinks that the charge has been reduced. The energy in the electric field is part of the rest mass/energy of the particle, and all forms of rest mass are affected by the dilation of space. Relativity is theoretically derived from the behaviour of electromagnetic waves, but measurements have shown that it applies to all forms of matter, not just electromagnetic matter as in the previous paragraph. So you can apply the same argument to mass in general. Take a test mass (i.e. one whose mass is trivial compared with the mass creating the distortion). ‘A’ will measure the test mass as having a certain gravitational field at a radius ‘r’. He then moves it to the mass at the center of the distortion. This remote observer ’A’ expects the gravitational field at ‘r’ to be the sum of the original mass’s gravitational field, plus what he measured for the test mass. However, from the point of view of the test mass the radius ‘r’ has been increased so its gravitational field at that radius is reduced and so ‘A’ finds that the actual measured gravitational field is less than expected. In summary, if we took two equal masses which the remote observer ‘A’ perceived to be the same, and moved them together, the resultant compound mass would appear to be less than the the sum of the two components. It is this last point that gives rise to gravitational forces. The natural behaviour of the universe is to reduce potential energy stored in matter, exchanging it for kinetic energy. So mass is reduced as it enters a gravitational well. From the point of view of an observer falling into the gravitational well there is no reduction in mass. Instead space opens up as he/she falls further into it. A descriptive way of putting it is that mass generates the space it needs to exist. If the universe had only a few kilograms in it, it would be tiny. The reason it is the size it is is the presence of its mass. The next stage is to look at the maths involved when matter falls into a gravitational well - gravitational attraction.
Gravitational Attraction Let us take a simple closed system of two equal masses, initially separated by an immense distance, and look at what the remote (inertial) observer ‘A’ makes of them coming together under gravitational attraction. The rest mass of each is m0. The situation is entirely symmetrical so we need consider only one of the masses. The system is closed, so the application of the Conservation of Mass/Energy leads to the energy in the system always being m0.c2 for each mass. As they accelerate towards each other under gravitational attraction their rest mass/energy drops to m00 but since the system is closed and conserved the total energy associated with each mass is... E = m00.c2 / (1 - (v /c)2 )1/2 ...where ‘v’ is the velocity resulting from the acceleration, and ‘c’ is the speed of light. ‘E’ of course must be constant and equal to m0.c2 .... m0.c2 = m00.c2 / (1 - (v /c)2 )1/2 (m00 / m0)2 = 1 - (v/c)2 The loss in rest mass appears as the kinetic energy of the mass so mass/energy is conserved from ‘A’’s viewpoint. When our two masses finally collide they will have 2.m0.c2 mass/energy, but the rest mass will be just 2.m00. The excess energy is heat (molecular kinetic energy) which radiates away into space leaving only the rest mass. The above equation also appears in electrostatic fields, not because there is any similarity between electrostatics and gravity, but because the universe deals with potential energy in a standard way. As an example, consider a 1kg mass falling from infinity to the Earth’s surface. The mass of the Earth is 5.97E+24 kg, and gravitational constant ‘G’ is 6.673E-11. Then on the Earth’s surface (at a radius of 6.37E+6 meters from the center) the gravitational force is F = G.m1.m2 / r2 ...and the kinetic energy gained is... E = G.m1.m2 / r In other words from the point of view of the remote observer ‘A’ that 1kg mass loses 0.691 micrograms of mass and gains 62.2 MegaJoules of kinetic energy as it drops from infinity to the Earth’s surface. How about ‘B’, at the central distorting mass? - put him on the Earth’s surface for this example. Since he is in an inertial frame he should also see mass/energy conserved. His space is dilated so the test mass has further to fall. His time is dilated so there is less time for the test mass to fall. Just as well that he perceives the Earth’s mass, and therefore its gravitational field, to be greater than ‘A’ does, making it fall faster! For him the test mass starts out with a rest mass greater than 1kg and when it arrives this has fallen to exactly 1kg. Because of the greater distance he perceives, and because his perception of the Earth’s gravitational field is greater, he will also perceive a greater terminal velocity and kinetic energy than ‘A’. But all this says something even more important about the Earth. It lies in a gravity well (ignore the sun and the rest of the solar system for now) of its own making, causing a spatial distortion from flat space (at 1.0) of 0.999999691. In other words the Earth’s mass is reduced as seen by ‘A’. This is important in stars, for as massive suns collapse into a small volume their mass collapses with the increase in field strength and their remote gravitational fields fall accordingly. Also, the radius of the Earth as seen by ‘A’ is smaller than the radius of the Earth as seen by an observer standing on the surface of the planet. We therefore have two effects that are crucial in stellar gravitational collapse. Firstly, the mass and associated gravitational field that drives the collapse dissipates as matter is converted to kinetic energy by the increasing field strength. Secondly, an observer in the middle of the collapse site sees the space at the center of the collapse increase as the gravitational field rises during the collapse; as the collapse progresses he sees space being created by the rise in gravitational field strength. Both effects oppose the increase in field strength and may prevent the formation of a black hole; more of this in a later paper. Just a fun note:- It is interesting to note that as molecular structures realign there are minuscule changes in their mass. When fuel is burnt in oxygen the combustion gives off energy. The total weight of the combustion products is the sum of the weights of the oxygen and fuel used, less the mass associated with the energy given off, equal to E/c2. In a rocket lifting a satellite into orbit a part of this mass turns up as the increase in the satellite’s rest mass! Light behaves the same way. Light falling down onto the Earth’s surface is blue-shifted since it increases in energy. Light leaving the Earth’s surface is red-shifted. Gravity Waves There is an argument that goes...
So an oscillating mass might generate a freely radiating gravitational distortion wave. If you like that idea, the first question is the speed of propagation. It can only exist if it carries energy, and this can only happen at a finite speed greater than zero and less than infinity. The preferred speed is the same as the speed of light but there is no proof. An infinite speed would coexist with a finite speed of light but would not be a wave as it would be unable to transport energy, although it would have an effect on space and time. Next, is it transverse (like light) or longitudinal (like sound)? The former would seem to be the case but requires a bipolar form (positive and negative distortion, equivalent to positive and negative gravitational fields - if you look at such a wave the other way up you see the opposite polarity). The problem with the negative form is that it is associated with negative mass and hence negative space - negative space is not just a hole, which is positive space with nothing in it, but a space in which something can be minus five meters long but not plus five meters long! There is also the question of whether a gravity wave j-component (like the magnetic component in electromagnetic propagation) is needed to maintain a constant energy density along the propagating wave. The longitudinal form needs nothing more than a disturbance in a reference background level, like sound in air. If you are interested, you may wish to search on “gravitational waves” or “gravity waves” via the internet. Although not everyone believes in their existence scientists are out there looking for them. Inertia At first it may seem odd to include inertia in a paper on gravity. But consider the equation for the total energy E of a moving body.. E = m0.c2 / ( 1 - (v/c)2 )1/2 If you compare that with the energy of the stationary body (m0.c2) you will see that it contains more energy. This energy has to come from somewhere, and it must be provided by the mechanism that accelerated the body from rest. Since the work done in accelerating the body is the integral of force over distance, it can be seen that the conservation of energy requires that an opposing force is required; this is simply the inertia of the body. It is crucially dependent on the speed of light and is an integral part of relativity. If light traveled at an infinite speed the term (v/c) would be zero and the total energy of a moving body would be the same at all velocities, so inertia would not exist. This mechanism is required because the speed of light is finite, and it is possible to put an arbitrarily large amount of energy into accelerating a body. It would soon be traveling faster than light but for the increase in mass/energy. It is the presence of matter that limits the speed of light through the medium of the gravitational field (an universe where the speed of light is infinite cannot support electromagnetic energy, whether as waves or as static fields). A high gravitational field reduces the speed of light and thus increases inertia as it dilates time and space, to the effect that physical experiments work the same in any gravitational field, provided the whole experiment is all in the same field strength. EquivalenceThe same effects that occur in a gravitational field can also be seen in a body under acceleration. Time and space are dilated in the direction of motion so that object traveling near light speed become flattened into a wave front. This appears flat to a stationary observer, but to the object itself in its own space it remains the same shape as always.. This common behaviour between for accelerating bodies and bodies in a gravity well is termed the Theory of Equivalence - there is no way for an instrument to discriminate between accelerative forces and gravitational forces. Notes on alternative viewpointsAn electric field strength has a specific energy density proportional to the square of that field strength, and this energy is (by E=m.c2) a part of the rest mass of the charged particle. Since electric fields are simply a form of mass/energy they are subject to the distortive effects of a gravity well, so some of the energy in the electric field is exchanged for kinetic energy as the particle falls into the well, just as with any other matter. However, there is a very popular school of thought that claims that electric charge is always conserved in the greater universe - i.e. from ‘A’s viewpoint - even though most agree that mass is reduced and space-time dilated in the gravity well. Imagine the observer ‘A’ at a radius of one light year from a massive sun, effectively outside the gravity well (mostly, anyway). He places one electron on the sun and another in free space also a light year away from him, but far outside any gravity well. The local field strength seen by ‘A’ is proportional to the electron charge divided by the square of the distance. For the electron in free space the distance is one light year, but for the one in the gravity well (on the sun) the distance only seems to be one light year to ‘A’, but because the electron lies in the dilated (expanded) space of the gravity well the electron’s field distance is longer and the local field strength is correspondingly weaker. Since the observer sees only the one-light-year distance from his non-dilated viewpoint, his measurements show that the charge on the electron is lower, and charge cannot be conserved on the larger universal scale. At least, this is what Relativity seems to tell us. If quantum terms, this is equivalent to saying that the probability distribution governing the position of a charged particle is unaffected by the space-time distortion. Hence as a charged particle falls into a gravity well and most matter shrinks (or space dilates), the interaction space of a charged particle will not. Hence to other matter in the gravity well the charged-particle diffraction pattern will appear to be associated with a larger distribution; there are corresponding changes to atomic structure. However, Relativity claims that all local viewpoints give the same results. This argument becomes important with black hole physics (which is covered in a later paper “Extreme gravity”). If charge is maintained in the greater universe there is always a part of the mass/energy of charged particles that will be outside the black hole to maintain that charge. This means that no charge fully enters the black hole, and in turn things that at least partly exist outside the black hole can still leave it entirely, so black holes (if they exist) can leak particles and so dissipate (Stephen Hawkins at Cambridge has put this argument forward). This argument is made complex by the fact that particles are not points as believed in the last century but very fuzzy objects, so different parts can be in different gravitational fields with differing space-time dilations, even to the extent of existing on both sides of an arbitrary event horizon. However, allowing for this, if charge is conserved from ‘A’s viewpoint then all the mass eventually leaks away from even the largest black hole; if it is not conserved but behaves like other matter then only a small proportion of the mass (negligible in large black holes) can leak away from just inside the event horizon. Since we cannot experiment on gravity in real life absolute proofs are virtually impossible to come by. |
