astro
04-22-2008, 05:09 PM
MDT & the Unity of The Dualities
MDT unifies the dualities of mass and energy, space and time, and wave and particle. Each of these dualities resulted in a pivotal moment of unification in the physical realm; and each unification represented a milestone in physics, two formerly disparate entities where united by a simpler and more beautiful model. MDT’s simple postulate—the fourth dimension is expanding relative to the three spatial dimensions—unifies all these three pivotal dualities with its simple equation:
dx4/dt = ic
Mass and Energy Duality: By following the implications of the duality of space and time in relativity, Einstein happened upon the duality and equivalence of mass and energy, or E=mc2. MDT sees energy as mass that exists in the fourth expanding dimension. The more energy a massive object gains, the more mass it has in the fourth expanding dimension. Only objects which exist entirely in the fourth expanding dimension can move at the velocity of light. Hence only photons move at the velocity of light.
All motion automatically calculates the component of an object in the three spatial dimensions—its rest mass—and its component in the fourth expanding dimension—its energy. Because the fourth dimension is moving relative to the three spatial dimensions at the rate of c, the more of an object’s total mass which exists in the fourth expanding dimensions, the more energy it has, and the faster it moves.
Wave-Particle Duality: A photon appears as a symmetrically-expanding wavefront because it surfs the fourth expanding dimension, which expands as a spherically symmetric wavefront. The fourth dimension may be seen as a pilot wave as decribed by de Broglie et al, which guides the probabilistic propagation of the particulate photon. The photon is a particle, but because the fourth dimension is inherently nonlocal and continually expanding as it distributes locality in the fourth dimension throughout the three spatial dimensions, and because the photon’s particle exists entirely in the fourth dimension, there is equal probability of finding the photon anywhere upon the wavefront defined by the fourth expanding dimension.
Space-Time Duality: Space-time dualitywould be more properly described as the duality between the three spatial and the fourth expanding dimension. Time has oft been confused with the fourth dimension, but Einstein never stated that it is the fourth dimensions. Rather he and Minkowski stated x4 = ict, which directly leads to MDT, when one takes the derivative of both sides:
Time inherits properties of the fourth expanding dimension; and certainly the fourth expanding dimension is a dimension, and thus is capable of having objects rotated into it and out of it.
In his 1912 manuscript on Relativity, Einstein writes:
If we compare this with the considerations leading to the general Lorentz transformation, then we see that the transformation equations holding between x, y, z, u = ict and x’, y’, z’, u’ = ict’ of two justified space-time reference systems satisfy the same conditions and are constructed in the same way as in the just considered three-dimensional case. The only difference is that we now have four coordinates instead of three. We can formulate this in the following way: All of the “justified” time-space reference systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems with four axes that can be transformed into each other by mere rotation. One has to keep in mind that the fourth coordinate u is always purely imaginary.
Again, Einstein writes, “The only difference is that we now have four coordinates instead of three. We can formulate this in the following way: All of the “justified” time-space reference systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems with four axes that can be transformed into each other by mere rotation. One has to keep in mind that the fourth coordinate u is always purely imaginary.”
Nowhere does Einstein state that the fourth coordinate is time. He merely states, “One has to keep in mind that the fourth coordinate u (which Einstein sometimes writes as x4) is always purely imaginary.” It is imaginary because the expansion of the fourth dimension is orthogonal to the three spatial dimensions in every direction.
The only way to stay stationary in the three spatial dimensions is to travel at the velocity c through the fourth dimension. Ergo the fourth dimension is expanding relative to the three spatial dimensions.
The only way to stay stationary in the fourth dimension is to travel at the velocity c through the three spatial dimension. Ergo the fourth dimension is expanding relative to the three spatial dimensions.
A rotation (or boost) into the fourth dimension is always accompanied by an increased velocity in the three spatial dimensions. Ergo the fourth dimension is expanding relative to the three spatial dimensions.
All moving objects appear shortened in the direction they are traveling. This is because in order to propagate in the three spatial dimensions, an object must be partially rotated into the fourth dimension.
Picture a meter-stick at the end of a football field, parallel to the horizontal crossbar of the goalposts. If it rotates, it appears shorter and shorter to us, standing on the other end of the field.
Now if it were passing by us close to the velocity of light, it would also appear foreshortened, as it is rotated in the fourth expanding dimension. This rotation occurs at a microscopic quantum level--each atom or quantum is rotated more into the fourth dimension, resulting in an overall foreshortening of the yardstick in the three spatial dimension.
Velocity in the three spatial dimensions is always accompanied by foreshortening in the three spatial dimensions, as more of the object exists in the fourth expanding dimension.
Rotate an object out of the three spatial dimensions and into the fourth expanding dimension, and it will gain velocity.
MDT unifies the dualities of mass and energy, space and time, and wave and particle. Each of these dualities resulted in a pivotal moment of unification in the physical realm; and each unification represented a milestone in physics, two formerly disparate entities where united by a simpler and more beautiful model. MDT’s simple postulate—the fourth dimension is expanding relative to the three spatial dimensions—unifies all these three pivotal dualities with its simple equation:
dx4/dt = ic
Mass and Energy Duality: By following the implications of the duality of space and time in relativity, Einstein happened upon the duality and equivalence of mass and energy, or E=mc2. MDT sees energy as mass that exists in the fourth expanding dimension. The more energy a massive object gains, the more mass it has in the fourth expanding dimension. Only objects which exist entirely in the fourth expanding dimension can move at the velocity of light. Hence only photons move at the velocity of light.
All motion automatically calculates the component of an object in the three spatial dimensions—its rest mass—and its component in the fourth expanding dimension—its energy. Because the fourth dimension is moving relative to the three spatial dimensions at the rate of c, the more of an object’s total mass which exists in the fourth expanding dimensions, the more energy it has, and the faster it moves.
Wave-Particle Duality: A photon appears as a symmetrically-expanding wavefront because it surfs the fourth expanding dimension, which expands as a spherically symmetric wavefront. The fourth dimension may be seen as a pilot wave as decribed by de Broglie et al, which guides the probabilistic propagation of the particulate photon. The photon is a particle, but because the fourth dimension is inherently nonlocal and continually expanding as it distributes locality in the fourth dimension throughout the three spatial dimensions, and because the photon’s particle exists entirely in the fourth dimension, there is equal probability of finding the photon anywhere upon the wavefront defined by the fourth expanding dimension.
Space-Time Duality: Space-time dualitywould be more properly described as the duality between the three spatial and the fourth expanding dimension. Time has oft been confused with the fourth dimension, but Einstein never stated that it is the fourth dimensions. Rather he and Minkowski stated x4 = ict, which directly leads to MDT, when one takes the derivative of both sides:
Time inherits properties of the fourth expanding dimension; and certainly the fourth expanding dimension is a dimension, and thus is capable of having objects rotated into it and out of it.
In his 1912 manuscript on Relativity, Einstein writes:
If we compare this with the considerations leading to the general Lorentz transformation, then we see that the transformation equations holding between x, y, z, u = ict and x’, y’, z’, u’ = ict’ of two justified space-time reference systems satisfy the same conditions and are constructed in the same way as in the just considered three-dimensional case. The only difference is that we now have four coordinates instead of three. We can formulate this in the following way: All of the “justified” time-space reference systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems with four axes that can be transformed into each other by mere rotation. One has to keep in mind that the fourth coordinate u is always purely imaginary.
Again, Einstein writes, “The only difference is that we now have four coordinates instead of three. We can formulate this in the following way: All of the “justified” time-space reference systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems to which the four-dimensional manifold of events is referred are orthogonal coordinate systems with four axes that can be transformed into each other by mere rotation. One has to keep in mind that the fourth coordinate u is always purely imaginary.”
Nowhere does Einstein state that the fourth coordinate is time. He merely states, “One has to keep in mind that the fourth coordinate u (which Einstein sometimes writes as x4) is always purely imaginary.” It is imaginary because the expansion of the fourth dimension is orthogonal to the three spatial dimensions in every direction.
The only way to stay stationary in the three spatial dimensions is to travel at the velocity c through the fourth dimension. Ergo the fourth dimension is expanding relative to the three spatial dimensions.
The only way to stay stationary in the fourth dimension is to travel at the velocity c through the three spatial dimension. Ergo the fourth dimension is expanding relative to the three spatial dimensions.
A rotation (or boost) into the fourth dimension is always accompanied by an increased velocity in the three spatial dimensions. Ergo the fourth dimension is expanding relative to the three spatial dimensions.
All moving objects appear shortened in the direction they are traveling. This is because in order to propagate in the three spatial dimensions, an object must be partially rotated into the fourth dimension.
Picture a meter-stick at the end of a football field, parallel to the horizontal crossbar of the goalposts. If it rotates, it appears shorter and shorter to us, standing on the other end of the field.
Now if it were passing by us close to the velocity of light, it would also appear foreshortened, as it is rotated in the fourth expanding dimension. This rotation occurs at a microscopic quantum level--each atom or quantum is rotated more into the fourth dimension, resulting in an overall foreshortening of the yardstick in the three spatial dimension.
Velocity in the three spatial dimensions is always accompanied by foreshortening in the three spatial dimensions, as more of the object exists in the fourth expanding dimension.
Rotate an object out of the three spatial dimensions and into the fourth expanding dimension, and it will gain velocity.