astro
03-03-2005, 12:22 PM
Rest Energy:
Where does an object’s rest energy come from? It comes from fact that the expanding time dimension is moving, giving a stationary object a velocity of c through space-time, even when the object appears at rest on a lab table. This massive velocity relative to time, when translated into the spatial dimensions via a Lorentz rotation of the velocity 4-vector, is manifested in energy. E=mc^2.
The Photon’s Null Vector:
How can we be comfortable that an entity of zero length moves at the speed of light? The only way for this to make sense is if the time dimension is moving relative to the spatial dimension. A null vector in space-time is defined by a photon, which moves at the velocity of light through space-time. So it is that to have zero length in space-time, an entity must translate through the three spatial dimensions at the velocity of light. This notion of maintaining zero interval by a velocity equal to c suggests that one of the coordinates, specifically the time coordinate, is moving at a velocity c relative to the three spatial coordinates.
The Notion of Standing Still in Space and Time:
The only way to remain stationary in space is to move through time with a velocity of c. The only way to remain stationary in time is to move through space with a velocity of c.
Thus the time and space dimensions must be moving relative to one another.
Einstein proclaimed that all objects travel through space-time at c. Even though we perceive a ruler along the x axis to be stationary, it is yet traveling through space-time at the fixed speed of c, implying that time is moving through it. Rotate it towards the y axis, and its projection upon the x axis shortens, yet it still appears to be stationary, and it is still traveling through space-time at the rate of c. Rotate it into the time dimension, and it's projection along the x axis still shortens (Lorentz contraction), but now it begins to move through the three spatial dimensions, while maintaining the fixed speed of c through space-time. Again, we see it move through the three spatial dimensions as it is rotated into the time dimension because the time dimension is moving relative to the three spatial dimensions.
As Brian Greene points out in the Appendix to Chapter 2 of The Elegant Universe, we note that from the space-time position 4-vector x=(ct,x1,x2,x3), we can create the velocity 4-vector u=dx/d(tau), where tau is the proper time defined by d(tau)^2=dt^2-c^-2(dx1^2+dx2^2+dx3^2). Then the "speed through space-time" is the magnitude of the 4-vector u, ((c^2dt^2-dx^2)/(dt^2-c^-2dx^2))^(1/2), which is identically the speed of light c. Now, we can rearrange the equation c^2(dt/d(tau))^2-(dx/d(tau))^2=c^2 to be c^2(d(tau)/dt))^2+(dx/d(tau))^2=c^2. This shows that an increase of an object's speed through space, (dx/d(tau))^2)^(1/2)= dx/d(tau) must be accompanied by a decrease in d(tau)/dt which is the object's speed through time, which also may be considered the rate at which time elapses on it's own clock d(tau) or the proper time, as compared with that on our stationary clock dt.
Conservation of Momemtum & Energy = Conservation of Momenergy
Red Shift
More Curvature = Slower Time:
Energy’s Mass:
Energy has mass because energy is mass rotated fully into the moving time dimension. Energy has zero rest mass, as mass represents the component of an object that exists in the spatial dimensions, through which time can expand.
Time Dilation:
Clocks slow down as they approach the speed of light, because they catch up with the expanding time dimension. All clocks measure time based on the emission of photons. The faster a clock travels, the less chance there is for it to emit a photon, as the photon will be reabsorbed.
Constancy of c in all frames:
The measurement of time is always measured with some mechanism that is based on the propagation of photons, whether it be photons in a clock spring or photons in a quartz crystal. Hence, when we measure the speed of light in a frame, we are always measuring it relative to a mechanism based on the speed of light in that frame. Hence the velocity of light is always viewed as a constant in all frames.
Length Contraction:
Picture four dimensions—three spatial dimensions and one time dimension. An object can be rotated so that its projection along any particular axis decreases. When an object is rotated into time, its projection along the x, y, and z directions decreases. This is known as relativistic length contraction. Relativistic length contraction is *always* accompanied by time dilation and an increase in the object's velocity. Because rotating an object along the time dimension always results in the object gaining a velocity relative to the spatial dimensions, one can conclude that the time dimension must be moving.
Spherical Symmetry of Photon Propagation:
Quantum mechanics teaches us that a photon propagates as a spherically-symmetric wavefront. This is because a photon is mass rotated into the time dimension, which is expanding as a spherically-symmetric wavefront.
Spherical Symmetry of Time Expansion through Three Dimensions:
The projection of a sphere in two dimensions is a circle. The projection of the fourth dimension in three dimensions is a sphere. And because this fourth dimension, time, is expanding, it appears as an expanding sphere. For a photon to stay stationary in time, it moves through space with a velocity of c. Think about that—the photon stays stationary in time, while moving at a velocity of c relative to the three spatial diemensions. It expands as a spherically symmetrical wavefront by staying stationary in time. Therefore, time must be expanding in a spherically symmetric manner throughout space.
Rest Mass Is Invariant
Rest mass represents an entity that exists fully in space. It is invariant.
Increase of System Mass:
As an object accelerates through space-time, the mass of the system increases as energy is added. The rest mass remains invariant, but it is pulled along through space-time by interacting with photons, which in turn no longer travel the speed of light. When photons interact with matter, matter accelerates, while photons slow down.
Entropy:
Because time is expanding as a spherically symmetric wavefront through the three spatial dimensions, photons, as well as all matter that interacts with photons, exhibits a probability to move in a spherically symmetric manner. Thus, if we have a clump of atoms in the middles of a room, a probability exists for the atoms to spread apart in a spherically symmetrical manner. at each point in space, they exhibit a probabilty of moving along any of the three spatial coordinates, carried along by the expanding time dimension.
The – c2t2 in the space-time metric
The four dimensions of space-time are divided into three spatial dimensions and one time dimension. In the space-time metric, where ds is an invariant expressed as\ ds^2=x^2+y^2+z^2-c^2t^2, the minus sign and c^2 distinguishes the t coordinate from the three spatial coordinates. Why the minus sign exists is most often glossed over—it is considered to just “be” there, because it is there.
That the time dimension is different somehow from the three spatial dimensions is obvious. This difference is a result of the time dimension moving relative to the spatial dimensions.
Planck’s constant
Fundamental Wave Nature
The fundamental wave nature of all matter is based upon the fundamental wave nature of space-time.
Wave-Particle Duality
Wave particle duality is a result of measurements of objects interacting upon a canvas of space and time dimensions that are moving relative to one another. Wave behavior, or interference, results when two photons interfere in the time dimension as it propagates through space. Particle behavior results when a photon interacts with an electron, when it is taken out of the moving time dimension and localized in the static spatial dimensions, being caught by the electron.
Philosophical and Physical Barriers to Moving Dimensions
Many trained physicists have a knee-jerk reaction that the time dimension cannot be moving because “dimensions cannot move.” First off, since the universe is expanding, space-time is also expanding, demonstrating that dimensions are moving and expanding. Secondly, general relativity demonstrates that massive objects warp space-time, meaning that as a massive object moves though space-time, it stretches space-time, showing again that space-time in one area can move, or deform, relative to space-time in another area. Thus there exist neither philosophical nor physical barriers to the concept of moving dimensions, but for artificial ones within lazy minds.
Rather than just accepting the minus sign in front of the c^2t^2 as being there because it “just is there,” this paper aims to look at the deeper reality which gives rise to the minus sign. A physicist’s job is not to accept things on blind faith, nor only ask questions that are allowed to be asked, but a physicist’s job is to wonder. And that wonder, which seems all but forgotten in the bureaucratization of modern physics, leads to the deeper beauty. “Imagination is more important than knowledge,” was how one physicist put it.
Increasing Energy Increases Momentum
Conservation of Dimension
Gravity
Red Shift
The Increase of Mass With Velocity
Where does an object’s rest energy come from? It comes from fact that the expanding time dimension is moving, giving a stationary object a velocity of c through space-time, even when the object appears at rest on a lab table. This massive velocity relative to time, when translated into the spatial dimensions via a Lorentz rotation of the velocity 4-vector, is manifested in energy. E=mc^2.
The Photon’s Null Vector:
How can we be comfortable that an entity of zero length moves at the speed of light? The only way for this to make sense is if the time dimension is moving relative to the spatial dimension. A null vector in space-time is defined by a photon, which moves at the velocity of light through space-time. So it is that to have zero length in space-time, an entity must translate through the three spatial dimensions at the velocity of light. This notion of maintaining zero interval by a velocity equal to c suggests that one of the coordinates, specifically the time coordinate, is moving at a velocity c relative to the three spatial coordinates.
The Notion of Standing Still in Space and Time:
The only way to remain stationary in space is to move through time with a velocity of c. The only way to remain stationary in time is to move through space with a velocity of c.
Thus the time and space dimensions must be moving relative to one another.
Einstein proclaimed that all objects travel through space-time at c. Even though we perceive a ruler along the x axis to be stationary, it is yet traveling through space-time at the fixed speed of c, implying that time is moving through it. Rotate it towards the y axis, and its projection upon the x axis shortens, yet it still appears to be stationary, and it is still traveling through space-time at the rate of c. Rotate it into the time dimension, and it's projection along the x axis still shortens (Lorentz contraction), but now it begins to move through the three spatial dimensions, while maintaining the fixed speed of c through space-time. Again, we see it move through the three spatial dimensions as it is rotated into the time dimension because the time dimension is moving relative to the three spatial dimensions.
As Brian Greene points out in the Appendix to Chapter 2 of The Elegant Universe, we note that from the space-time position 4-vector x=(ct,x1,x2,x3), we can create the velocity 4-vector u=dx/d(tau), where tau is the proper time defined by d(tau)^2=dt^2-c^-2(dx1^2+dx2^2+dx3^2). Then the "speed through space-time" is the magnitude of the 4-vector u, ((c^2dt^2-dx^2)/(dt^2-c^-2dx^2))^(1/2), which is identically the speed of light c. Now, we can rearrange the equation c^2(dt/d(tau))^2-(dx/d(tau))^2=c^2 to be c^2(d(tau)/dt))^2+(dx/d(tau))^2=c^2. This shows that an increase of an object's speed through space, (dx/d(tau))^2)^(1/2)= dx/d(tau) must be accompanied by a decrease in d(tau)/dt which is the object's speed through time, which also may be considered the rate at which time elapses on it's own clock d(tau) or the proper time, as compared with that on our stationary clock dt.
Conservation of Momemtum & Energy = Conservation of Momenergy
Red Shift
More Curvature = Slower Time:
Energy’s Mass:
Energy has mass because energy is mass rotated fully into the moving time dimension. Energy has zero rest mass, as mass represents the component of an object that exists in the spatial dimensions, through which time can expand.
Time Dilation:
Clocks slow down as they approach the speed of light, because they catch up with the expanding time dimension. All clocks measure time based on the emission of photons. The faster a clock travels, the less chance there is for it to emit a photon, as the photon will be reabsorbed.
Constancy of c in all frames:
The measurement of time is always measured with some mechanism that is based on the propagation of photons, whether it be photons in a clock spring or photons in a quartz crystal. Hence, when we measure the speed of light in a frame, we are always measuring it relative to a mechanism based on the speed of light in that frame. Hence the velocity of light is always viewed as a constant in all frames.
Length Contraction:
Picture four dimensions—three spatial dimensions and one time dimension. An object can be rotated so that its projection along any particular axis decreases. When an object is rotated into time, its projection along the x, y, and z directions decreases. This is known as relativistic length contraction. Relativistic length contraction is *always* accompanied by time dilation and an increase in the object's velocity. Because rotating an object along the time dimension always results in the object gaining a velocity relative to the spatial dimensions, one can conclude that the time dimension must be moving.
Spherical Symmetry of Photon Propagation:
Quantum mechanics teaches us that a photon propagates as a spherically-symmetric wavefront. This is because a photon is mass rotated into the time dimension, which is expanding as a spherically-symmetric wavefront.
Spherical Symmetry of Time Expansion through Three Dimensions:
The projection of a sphere in two dimensions is a circle. The projection of the fourth dimension in three dimensions is a sphere. And because this fourth dimension, time, is expanding, it appears as an expanding sphere. For a photon to stay stationary in time, it moves through space with a velocity of c. Think about that—the photon stays stationary in time, while moving at a velocity of c relative to the three spatial diemensions. It expands as a spherically symmetrical wavefront by staying stationary in time. Therefore, time must be expanding in a spherically symmetric manner throughout space.
Rest Mass Is Invariant
Rest mass represents an entity that exists fully in space. It is invariant.
Increase of System Mass:
As an object accelerates through space-time, the mass of the system increases as energy is added. The rest mass remains invariant, but it is pulled along through space-time by interacting with photons, which in turn no longer travel the speed of light. When photons interact with matter, matter accelerates, while photons slow down.
Entropy:
Because time is expanding as a spherically symmetric wavefront through the three spatial dimensions, photons, as well as all matter that interacts with photons, exhibits a probability to move in a spherically symmetric manner. Thus, if we have a clump of atoms in the middles of a room, a probability exists for the atoms to spread apart in a spherically symmetrical manner. at each point in space, they exhibit a probabilty of moving along any of the three spatial coordinates, carried along by the expanding time dimension.
The – c2t2 in the space-time metric
The four dimensions of space-time are divided into three spatial dimensions and one time dimension. In the space-time metric, where ds is an invariant expressed as\ ds^2=x^2+y^2+z^2-c^2t^2, the minus sign and c^2 distinguishes the t coordinate from the three spatial coordinates. Why the minus sign exists is most often glossed over—it is considered to just “be” there, because it is there.
That the time dimension is different somehow from the three spatial dimensions is obvious. This difference is a result of the time dimension moving relative to the spatial dimensions.
Planck’s constant
Fundamental Wave Nature
The fundamental wave nature of all matter is based upon the fundamental wave nature of space-time.
Wave-Particle Duality
Wave particle duality is a result of measurements of objects interacting upon a canvas of space and time dimensions that are moving relative to one another. Wave behavior, or interference, results when two photons interfere in the time dimension as it propagates through space. Particle behavior results when a photon interacts with an electron, when it is taken out of the moving time dimension and localized in the static spatial dimensions, being caught by the electron.
Philosophical and Physical Barriers to Moving Dimensions
Many trained physicists have a knee-jerk reaction that the time dimension cannot be moving because “dimensions cannot move.” First off, since the universe is expanding, space-time is also expanding, demonstrating that dimensions are moving and expanding. Secondly, general relativity demonstrates that massive objects warp space-time, meaning that as a massive object moves though space-time, it stretches space-time, showing again that space-time in one area can move, or deform, relative to space-time in another area. Thus there exist neither philosophical nor physical barriers to the concept of moving dimensions, but for artificial ones within lazy minds.
Rather than just accepting the minus sign in front of the c^2t^2 as being there because it “just is there,” this paper aims to look at the deeper reality which gives rise to the minus sign. A physicist’s job is not to accept things on blind faith, nor only ask questions that are allowed to be asked, but a physicist’s job is to wonder. And that wonder, which seems all but forgotten in the bureaucratization of modern physics, leads to the deeper beauty. “Imagination is more important than knowledge,” was how one physicist put it.
Increasing Energy Increases Momentum
Conservation of Dimension
Gravity
Red Shift
The Increase of Mass With Velocity