My understanding of science is that it is a process. Skepticism plays an important role, but the doubt should be reserved for the theories, without prejudice. What we are presenting is a block diagram of a theory of everything, and it is based on some previously unknown mathematics that we have stumbled across.
The problem is completely unlike anything else that exists in mathematics. Its solution is an identity that defines a family of functions. Because this single identity defines the behavior of each member of the family of functions, together with the behavior of the entire family, it is unique in mathematics (as far as we have been able to determine.) The identity only exists in three dimensions and it falls apart when all of the angles exist in a single plane. This is not unique, as there are other identities that are associated with spherical trigonometry that also require three dimensions.
Each member of the family of functions presents a representation of direction as a twodimensional curve. Since area is a scalar value, the area under the curve expresses direction as a quantity or a number, not as a ratio or vector as is the usual method.
3D identity (tridentity) in Euclidean 3space
Weâ€™ve prepared a proof of the equation, but it has not yet been peer reviewed. If there are any issues with the math, then that would definitely have an impact on our views about the block diagram. But until such time as the math has been proven to be correct or incorrect, we would like an opportunity to argue in support of some new interpretations of the significance of the underlying principles on which Euclidean geometry is based. Until now, direction has never been represented as a mathematical quantity. The ability to do this has some pretty significant implications. We refer to direction as a base quantity, or in other words a quantity from which other derived quantities are based. For example, time and direction can be combined to express frequency.
Due to relativity and the equivalence principle, there has to be some way to reconcile the universe in which direction is a quantity. One of the first things to acknowledge is the concept of scale. At the human scale, direction and distance have a relationship with one another that allows us to calculate the ballistic paths of objects and the orbits of planets. On the astronomical scale, this does not seem to be the case. Distances and directions no longer add up, as is indicated by the wagon wheel rotation of galaxies.
At the quantum scale, direction completely dominates distance. The radii become so tiny that they are almost insignificant, while at the same time, a turn is still a turn. There is no commensurate change of scale for direction. This fact only becomes significant because direction is also a quantity, in addition to being a ratio in orthogonal systems. When we look at direction as a ratio, it naturally changes scale when distance changes scale. This isnâ€™t the case with our observations. Our observations tell us that direction does not stay scaled with distance, or in other words, it is also a quantity in its own right. The math that we are presenting shows how direction can be represented as a quantity. It is only a quantity in three dimensions so there is no equivalent expression that can be made using plane geometry.
When we try to understand a photon under these circumstances, there is a package of directions or orientations that accompany that particle. It has its own system of direction, as does every other particle. These directions that accompany the photon theoretically extend indefinitely in all directions without regard to distance or Lorentz or c. When the photon passes through the doubleslit, some of its selfcontained direction passes through the alternate opening and reacts with the photon on the other side of the slit in order to create a wave pattern.
As for entanglement and superposition, these can also be explained in a similar manner. Since direction commutes (according to the mathematics), the entangled pair end up traveling in the same direction (according to their own system of directions) and they are also traveling at the same speed. In any other reference frame (any frame that does not include their own selfcontained system of direction), the two entangled particles appear to be in separate places in spacetime, but to the entangled pair, they are at one and the same place in timespace. Timespace, if it maintains its symmetry with spacetime, will have its own geometry and its own equations that will be based on direction instead of distance. In this alternative geometry, c will have no impact and time will only relate to periodic events.
Atomic wave function can be explained as several of these local selfcontained systems of direction in superposition with one another. There's plenty of observational data available to show whether or not this is the case. The only thing missing has been the hunk of math that will allow for the quantification of direction. This is what we have stumbled across.
One of the basic distinctions that should be made while considering this theory is between the mathematics that exist and the speculation for which there is no existing support. The way that this particular theory lays out, the mathematics are proven (as far as we can tell) and there should no longer be any doubt that direction is also a quantity (in addition to being the vector that we all know and love.) The speculation is all about how this fact would impact the math that underlies scientific observations.
We need help with proving/disproving this theory. Weâ€™re not quite sure how to go about it. The underlying math seems very solid. Any help or criticism will be greatly appreciated.
The problem is completely unlike anything else that exists in mathematics. Its solution is an identity that defines a family of functions. Because this single identity defines the behavior of each member of the family of functions, together with the behavior of the entire family, it is unique in mathematics (as far as we have been able to determine.) The identity only exists in three dimensions and it falls apart when all of the angles exist in a single plane. This is not unique, as there are other identities that are associated with spherical trigonometry that also require three dimensions.
Each member of the family of functions presents a representation of direction as a twodimensional curve. Since area is a scalar value, the area under the curve expresses direction as a quantity or a number, not as a ratio or vector as is the usual method.
3D identity (tridentity) in Euclidean 3space
Weâ€™ve prepared a proof of the equation, but it has not yet been peer reviewed. If there are any issues with the math, then that would definitely have an impact on our views about the block diagram. But until such time as the math has been proven to be correct or incorrect, we would like an opportunity to argue in support of some new interpretations of the significance of the underlying principles on which Euclidean geometry is based. Until now, direction has never been represented as a mathematical quantity. The ability to do this has some pretty significant implications. We refer to direction as a base quantity, or in other words a quantity from which other derived quantities are based. For example, time and direction can be combined to express frequency.
Due to relativity and the equivalence principle, there has to be some way to reconcile the universe in which direction is a quantity. One of the first things to acknowledge is the concept of scale. At the human scale, direction and distance have a relationship with one another that allows us to calculate the ballistic paths of objects and the orbits of planets. On the astronomical scale, this does not seem to be the case. Distances and directions no longer add up, as is indicated by the wagon wheel rotation of galaxies.
At the quantum scale, direction completely dominates distance. The radii become so tiny that they are almost insignificant, while at the same time, a turn is still a turn. There is no commensurate change of scale for direction. This fact only becomes significant because direction is also a quantity, in addition to being a ratio in orthogonal systems. When we look at direction as a ratio, it naturally changes scale when distance changes scale. This isnâ€™t the case with our observations. Our observations tell us that direction does not stay scaled with distance, or in other words, it is also a quantity in its own right. The math that we are presenting shows how direction can be represented as a quantity. It is only a quantity in three dimensions so there is no equivalent expression that can be made using plane geometry.
When we try to understand a photon under these circumstances, there is a package of directions or orientations that accompany that particle. It has its own system of direction, as does every other particle. These directions that accompany the photon theoretically extend indefinitely in all directions without regard to distance or Lorentz or c. When the photon passes through the doubleslit, some of its selfcontained direction passes through the alternate opening and reacts with the photon on the other side of the slit in order to create a wave pattern.
As for entanglement and superposition, these can also be explained in a similar manner. Since direction commutes (according to the mathematics), the entangled pair end up traveling in the same direction (according to their own system of directions) and they are also traveling at the same speed. In any other reference frame (any frame that does not include their own selfcontained system of direction), the two entangled particles appear to be in separate places in spacetime, but to the entangled pair, they are at one and the same place in timespace. Timespace, if it maintains its symmetry with spacetime, will have its own geometry and its own equations that will be based on direction instead of distance. In this alternative geometry, c will have no impact and time will only relate to periodic events.
Atomic wave function can be explained as several of these local selfcontained systems of direction in superposition with one another. There's plenty of observational data available to show whether or not this is the case. The only thing missing has been the hunk of math that will allow for the quantification of direction. This is what we have stumbled across.
One of the basic distinctions that should be made while considering this theory is between the mathematics that exist and the speculation for which there is no existing support. The way that this particular theory lays out, the mathematics are proven (as far as we can tell) and there should no longer be any doubt that direction is also a quantity (in addition to being the vector that we all know and love.) The speculation is all about how this fact would impact the math that underlies scientific observations.
We need help with proving/disproving this theory. Weâ€™re not quite sure how to go about it. The underlying math seems very solid. Any help or criticism will be greatly appreciated.
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