True Relativity A theory of three dimensional Spacetime Part I

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1 True Relativity A theory of three dimensional Spacetime Part I copyright 2007 Tony Stanton Abstract This theory is based on the constancy of speed of light in a vacuum no matter what inertial frame of reference it is viewed from and the generation of space and time in the presence of energy. The theory mathematically shows gravity to be localised and is also the first theory of gravity to give an explanation for the arrow of time. Overall this theory represents a paradigm shift in the way space and time is viewed yet it can match Newtonian gravity within the confines of the solar system where we know the effect of gravity to be accurate. If every object or body is generating a spacetime field around itself then every body or object will be truly relative to every other object or body, thus the name given to this theory is True Relativity. t99stanton@aol.com 1

2 The spacetime constant In Special Relativity Part III, [1] Einstein states: In the first place, we entirely shun the vague word space of which, we must honestly acknowledge we cannot form the slightest conception, and we replace it by motion relative to a practically rigid body at reference. Einstein s own words show that he never had a real understanding of space therefore it follows that he never truly understood the arrow of time. A complete understanding of space can only be realised if the arrow of time can be explained in physical terms which is what this three dimensional view of spacetime sets out to achieve. The intention of TR is to show that gravity can be modelled using only simple geometry and experimental data without the need to include Newton s gravitational constant G or the metric. Spacetime is three dimensional according to this theory and gravity becomes time dependant therefore it is not a force that operates over an infinite distance. I contend that from drop test data taken inside the Earth s gravity field (at the surface of the Earth), the gravity field of any object with mass can be calculated and modelled using simple geometry dismissing the need to use Newton s gravitational constant in this new theory of gravity. The varying density of material between the drop test tower and the Earth s centre of mass will also need to be taken into account to maintain accuracy. Figure 1 In figure 1 above an object will be displaced a given distance over one second purely due to the gravitational field. According to TR this distance is directly related to the volume of distortion caused by any large mass. The foundation of TR is that each object in this Universe generates its own spacetime field around itself at a constant flowing volume and it is this flow of volume that we experience as the flow of time, hence the flow of the volume of space generated by our own bodies is why we as human beings experience a flow of time. Whilst this view of spacetime is radical there is observational and experimental evidence in support of this concept. The displacement of an object due to the gravity field of a large mass such as the Earth tells us by how much spacetime is distorted at that point in the gravity field. If spacetime is distorted by volume then a simple calculation using geometry will enable me to find the total volume of the distortion of spacetime caused by mass. Therefore this missing volume of spacetime can be found using this simple geometric equation. 4 Vd ( R s ) 4 R (1) Where the volume of the distortion = Vd, R = Radius from the centre of mass and s = displacement of an object at that point due to the gravity field of the mass. This volume of distortion will have a direct relationship with mass and will enable the calculation of a spacetime constant STC, that allows TR to find the volume of spacetime distortion caused by any mass. STC = Vd/M (2) Where the spacetime constant = STC and M = mass. According to this concept of three dimensional spacetime, when an object experiences acceleration it becomes displaced from the centre of its own spacetime field causing its field to collapse. If the collapse of the spacetime field and the displacement from the fields centre for an object at any point on the surface of the Earth is exactly the same as the displacement of an object due to the gravitational field, then the value of the STC = x kg -1 m, however a much more accurate value of the STC can be determined by time dilation experiments using acceleration. This simple geometry provides us with a spacetime constant STC that directly links mass to the amount of spacetime distortion caused by any object with mass. Once the true value of the spacetime constant is found by experimentation Newton s universal gravitational constant can be accurately calculated because of the close relationship of STC/2G. The theory of True Relativity If TR is correct and all objects generate a spacetime field then there has to be a maximum of field generated over a given period of time which itself will be directly linked to the distance that light travels in that given period. The STC is calculated using the second as a time period so TR will use the second as its unit of time but a different time period could be used providing it is also used in the measurement of the displacement caused by the gravity field. 2

3 Time cannot be extrapolated in three dimensional spacetime because time is the flow of space and only the time period used to gain accurate gravity data should be considered at this stage of TR s development. Photons of light are mass-less so according to this concept they would generate the largest volume of spacetime if they were considered at rest and as the constancy of light never changes this becomes the backbone of TR. The distance that light travels in one second is d = m so due to this fact, TR contends that the largest radius of the spacetime field that can be generated by any mass-less particle in a period of one second is r = m. As spacetime is measured by the flow of volume in TR we can calculate the volume of space generated by a mass-less particle considered at rest in a period of 1s. For this value I am going to use Phi (). = 4 / r () Where r = m. This equation is a fixed volume of space generated over a fixed period of one second so time has to be included in the equation to enable spacetime to flow. ST = (t (4) Here t = Universal seconds which in itself is just the multiple of because space and time are considered as exactly the same entity. Time and space have the same dimensions in TR. Equation (4) will give the volume of spacetime generated by a mass-less particle considered at rest over any period of time. The ST becomes the Universal clock from where all of time and space can be measured against. TR measures all spacetime fields generated by objects with mass against the spacetime field generated by a mass-less particle considered at rest which is why I will refer to the field generated by a mass-less particle as the Universal clock. The volume of the distortion of spacetime caused by any mass can now be found using the direct relationship of the spacetime constant. Vd = STC*M (5) Where Vd = volume of the distortion of spacetime caused by any mass and M = mass. TR contends that this volume of spacetime is missing and retards the time flow by a small amount so the volume of distortion needs to be converted to Universal time to calculate the time distortion. Td = (1/)* Vd Where Td = the distortion of time. (6) Every object has its own unique rate at which time runs due to its mass and we can begin to compare the radius of the field of any mass with that of a mass-less particle considered at rest once the time retardation is calculated using (7). tm = t - Td (7) Where tm = the amount of time retardation due to the mass. Objects with mass have their own beat of time and will run slightly differently from that of the Universal clock (4), this is given by STm = tm* (8) Where STm = the volume of spacetime generated by the mass over any period of time and from there the radius of the spacetime field of the mass can be calculated. RSTm = (*STm/4*) 1/ (9) Where RSTm = the radius the spacetime field of the object with mass has reached over any period of time and comparison field of the Universal clock will have a radius of spacetime RST = (*ST/4*) 1/ (10) Where RST = the radius the field of a mass-less particle considered at rest over time. The next equation will give the amount of displacement caused by the gravitational field of the mass at any point in space. s =RST - RSTm (11) This method will closely match Newtonian gravity within the confines of the solar system where we know the effect of gravity to be true therefore TR can match Newton s four dimensional view of spacetime. a = GM/R 2 s = ½at 2 (12) Where a = rate of acceleration in m s -2 at that point in the gravitational field, G = Newton s Universal Gravitational constant, M = Mass, R = radius from the centre of mass, s = the displacement caused to an object due to the gravitation field of the mass at that point in space and t = 1 s (four dimensional second). The value for the multiple of Phi t can be found from the radius of the spacetime field at any distance from the object with mass using equation (1).

4 t = 4R / (1) Where t = the time in Universal seconds that the Universal clock has to run for the spacetime field to reach a particular point in space. R = distance to that particular point in space from the objects centre of mass. Using the equations above, a single equation to find the displacement at any point in the gravitational field of an object with mass can be built. s R R MSTC (14) Equation (14) will calculate the amount of displacement due to the gravitational field at any point in that gravitational field. Because space and time are exactly the same dimensions in TR we can substitute 4R / with t and gravity becomes time dependant which means the maximum size of the gravitational field in TR depends on the age of the Universe. s R ( t M STC ) (15) Equations (14) and (15) will match Newtonian gravity within the confines of the solar system where we know the effect of gravity to be true without using Newton s universal gravitational constant. One major difference between TR and all other theories of gravity is TR does not introduce infinities when modelling gravity at the extremes of our Universe such as inside a black hole as shown by figure 1 below believed to be at the centre of the Milky Way galaxy. Dist ortion/f orce / m s E E E E E E E E E E E E E E x10 2 Distance / m 1 5.7x10 10 Schwartzschild radius 1 Sagittarius A* quantum gravitational field Newton s GM/r 2 True Relativity Figure 2 The graph above shows how gravity according to TR remains stable even inside a black hole. The pink line represents Newtonian gravity in m s -2 and the blue line is a representation of TR as twice the displacement i.e. 2s caused by the gravity field of the black hole. The red line is the Schwartzschild radius. A rearrangement of equation (1) shows the maximum radius a spacetime field can grow to is R = (*ST/4*) 1/ 1500AU if the Universe is 1.75 billion years old making the gravitational field of any object with mass localised because gravity is time dependant. According to TR every particle of gas, dust and larger objects generate their own spacetime field thus the inter-stellar medium (ISM) will behave like a thick soup of spacetime fields rotating around the centre of the Milky Way in an almost fixed manner without the need to include dark matter. Each object in this or any other galaxy is linked to each other object by their spacetime fields so what happens on one side of the galaxy will have an effect on the other side of the galaxy, albeit a small indirect effect. The stars within the galaxy will behave like a rotating collection of soap bubbles in the middle of a washing up bowl, almost rotating as one, each spacetime bubble only directly affecting the field next to it and these fields will overlap. Figure : This illustration shows that where the spacetime fields overlap another object, it will only experience the gravitational force of that object. Any object outside of that spacetime field has no direct effect. Object A and B are in the gravitational field of each other but object B is also in the gravitational field of object C but object A has no direct effect on object C. All these objects are linked to one another by their respective spacetime fields but in this illustration the Sun only has a direct gravitational effect on object D. Although figure shows only a few fields, there will be billions of fields present because of the dust, gas and larger objects present in the ISM. If this is true then any gas, dust and larger objects which are caught in the Sun s gravitational field will move in towards the Sun along with their spacetime fields and these fields will pass over the Earth on the journey towards the Sun for which there is experimental evidence. R.T. Cahill [2] from Flinders University in Australia reports that this turbulent inflow of space in towards the Sun has been directly detected by experiments which if true gives credence to the concept of three dimensional spacetime. 4

5 Research into absolute motion and a review of existing data from experiments using interferometers as performed by Michelson- Morley [4], Miller [], DeWitte [5] and the Torr-Kolen [6] experiment in 1981 have revealed an in-flow of space towards the Sun. Not all experiments using interferometers have given the expected results. R.T. Cahill [2] reports that the Shamir-Fox experiment used a Solid-State Michelson Interferometer and unknowingly Flinders University repeated the experiment using a He-Ne laser light source and single-mode optical fibres with a refractive index of n1.5, both came up with a null result. However the non solid-state experiments like that performed by the Michelson-Morley [4] experiment revealed a fringe shift as reported in [2] and is shown below. The data can be explained without using the inflow of space as a reference point and the assumption that the fluctuations or turbulence are a form of gravitational waves are, I believe incorrect. Gravity probe B [8] may be the biggest test yet of General Relativity and is a fantastic technical achievement for all those involved. The effect predicted by General Relativity should give the geodetic precession due to the Earth s rotation at 6.6 arcsec/yr north, and the motional precession due frame-dragging at about arcsec/yr east. I believe the motional procession will give a higher value because True Relativity predicts that local spacetime is rotating with the Earth and not being dragged around by the Earth as shown in Figure 26. Figure 4: The sample of results shown above, reproduced from [2] are from the Miller experiment []. What the sample shows are the projected Michelson speed M in km/s and azimuth angle in degrees plotted against the sidereal time in hours. Miller computed the running time average and this is shown as the smoother line in the graphs where the data points have been joined together to make it easier to see the data. Figure 5: Example of the Michelson-Morley fringe-shift micrometer readings. Plot of micrometer readings for July hr (7:00 ST) showing the motion of spacetime induced fringe shifts. This fringe shift was discounted and put down to interference from the experimental equipment and it appears that Michelson-Morley came to the incorrect conclusion and gave a null result supporting Einstein s assumption that there is no such thing as absolute motion. This is where, even with the new data, I disagree with R.T. Cahill [2] in that I believe Einstein is correct. Figure 6: (a) Diagram showing how according to True Relativity the local spacetime field rotates with the Earth. Shown in (b) according to General Relativity Space-Time is being dragged around by the Earth. I cannot emphasise the importance of this experiment enough. The fact sheet from the Gravity probe B website [8] states; Any geodetic and frame-dragging effects are being measured to exceptional precision by GP-B s gyroscopes. These measurements will help shape our understanding of Einstein s theory. If GP-B gives results consistent with general relativity, it will help solidify our understanding of topics like black holes and the evolution of the universe. If, however, the results of the GP-B experiment are inconsistent with Einstein s theory, it will significantly change our perception of the universe. I eagerly await the release of the data and conclude that the results will give the motional precession above arcsec/year, possibly nearer to arcsec/year. The gravity probe B [8] experiment is due to release its findings in April 2007 and if TR holds merit the rate for frame dragging will be higher than expected by General Relativity because according to True Relativity local space near the Earth will be rotating around with the Earth and is not being dragged around by the Earth. Unfortunately it is not within my present mathematical ability to be able to calculate the predicted frame dragging according to True Relativity at this present time. 5

6 There are other aspects of three dimensional spacetime which are testable. These include the collapse of the spacetime field when under acceleration, time dilation due to acceleration and the manipulation of spacetime fields emanating from a suitable material. Although this view of spacetime is radical, it is a testable theory by a number of experiments. The first of these is the time dilation experiment using a centrifuge and two atomic clocks. TR can give quantitative predictions for time dilation from a Universal second in free space when under acceleration, using equation td 1 4 r 2 (16) Where td = the time dilation per second, r = m, = the rate of acceleration in the frame of the atomic clock. Equation (16) will give the time dilation between a frame under acceleration and a clock in free space. Time dilation between different frames inside a gravity field will be discussed in more detail in a later paper. The second of these is an observational experiment using a vacuum chamber, two test masses and a projectile. According to TR when an object is accelerated its own spacetime field collapses by the amount of displacement from the fields true centre so if this is true then the experiment shown in figure 7 will reveal a movement of the two test masses when a projectile is accelerated between them. Figure 7 In (a) above are two non-metallic test masses are attached to the ceiling of the vacuum chamber with a projectile held in place by a magnetic field. In (b) the projectile is accelerated by the magnetic field causing its own spacetime field to collapse and the two test masses will move in towards each other. (c) is a side view of the experiment. The third experiment is to see if it is possible to manipulate the spacetime field of a particular type of material and involves the use of a piece of super conducting material sat on top of a magnetic field inside a smoke chamber as shown below in figure 8 Figure 8 The piece of super conducting (suitably cooled and shown in blue) is placed on a magnetic field inside a smoke chamber. If TR holds merit the piece of super conductor will rotate and the smoke will rise in a column just above it. Any slight difference in the thickness of the superconductor will cause it to rotate. The smoke will rise above it because the superconductors is generating a positive spacetime field on one side and the smoke will be pushed along with this positive spacetime field. These three simple experiments will prove TR has merit and I believe the results from these experiments cannot be explained by General Relativity. Thus what the concept of True Relativity is trying to convey, is a concept of three dimensional spacetime where all matter/mass, therefore energy, generate spacetime fields around themselves. The volume of these fields is dependent on their mass and any field distortions (gravity) in the inertial frame of any object under consideration. None of the equations used are against any known science, they are built from basic geometry and TR is based on the constancy of the speed of light in a vacuum. The ability to track Newtonian gravity within the confines of the solar system where we know the effects of gravity to be true, without using Newton s universal gravitational constant and using only simple geometry has never yet been achieved by any professional or institution. TR s simplicity is a sign that this concept may well hold merit, at least according to Occum s razor. If this concept turns out to hold merit, then there are a number of consequences to three dimensional spacetime that should be stressed and they will be discussed in further papers, these are; 6

7 1) The possibility of faster then light space travel. 2) The exclusion of gravitational radiation. ) The exclusion of dark matter. 4) The exclusion of dark energy. 5) The explanation for mass. 6) The exclusion of the Higgs field. 7) The exclusion of the Higgs boson. 8) The possibility of manipulating and controlling spacetime fields (anti-gravity). 9) The calculation of time dilation between frames to within at least 10-9 s. 10) The modelling of spacetime inside black holes. 11) The modelling of events before and after the big bang. 12) A possible explanation for the Pioneer anomaly. 1) A possible macro explanation for the phenomenon of quantum entanglement. The Principles Principle I A body or object A can move within the spacetime field of any other body or object 'B' but its relative velocity is governed by the volume of the spacetime field that body or object A has generated.. (PI) Principle II A body or object A in motion as viewed from an observers inertial frame of reference B cannot have a velocity faster than the radius of the spacetime field that body or object A generates. (PII) Principle III When a body or object A is under acceleration as viewed from an observer s inertial frame of reference B, the volume of the space field that body or object A generates, diminishes, according to the rate of acceleration the body or object A experiences due to its displacement within its own spacetime field. (PIII) Principle IV The rate at which a space-time field is generated from every body or object at rest is dependant on the mass of that object or body. (PIV) Principle V Only the force of acceleration can affect the spacetime field, velocity plays no part in time dilation. (PV) Principle V1 All true measurements of space and time must be made using the Universal clock (PV1) References [1] A. Einstein Space and time in classical mechanics. (available at ) [2] R. T. Cahill Absolute Motion and Gravitational Effects, physics/ (available at ) [] D. C. Miller, The Ether-Drift Experiment and the Determination of the Absolute Motion of the Earth, Rev. Mod. Phys. 5, (19), (available at ) [4] A. A Michelson and E.W. Morley, Philos. Mag. S.5, 24, No. 151, (1887), (available at ) [5] R. DeWitte, [6] D.G. Torr and P. Kolen,Precision Measurements and Fundamental Constants, B. N. Taylor and W. D. Phillips, Eds. Natl. Bur. Stand. (U.S.), Spec. Publ. 617, 675 (1984). [8] The Gravity Probe B Experiment (available at ) 7