Here is a quasi-Lorentz Contraction sketch, 9/5/16
Figure 1: Seven parallel lines define dilation and contraction variable v8
The FitzGerald-Lorentz length contraction factor formula
gamma = 1 / sqrt(1 - (v^2/c^2))
has been re-derived, without using the Pythagorean Theorem. Using Gravity Volume Theory and a geometric mean for the square root, the following formula is similar to the Lorentz gamma: Dilation means time gets smaller. Contraction means distance or time gets smaller.
v8 = distorted velocity = (c+v) / sqrt(1 - (v^2/c^2))
That is the "distorted velocity" used to find time dilation and length contraction. Time grows out of protons and neutrons. Space drains in. That is gravity. Those directions are used in the formulas that are in this derivation of the Lorentz factor without triangles..
Basics
A rocket passes Earth at the speed of 0.9c on the way to Proxima Centauri, 4 Light Years away. After 4 years have passed, the rocket is still in outer space, and measurements are taken and calculations made to find dilation or contraction. Two sets of velocity equations will be: first for Earth observers and second for astronaut observers on the rocket. Those two velocities are multiplied together for an energy equation, using a mass of 2kg. The mass magnitude does not influence the dilation or contraction. From the energy understanding, the potential, psi, is used and it has a square root taken to find the geometric mean of the two velocities. That is v8, the distorted velocity.
Details
Part 1 : relative to Earth. Time grows out of Earth at speed c, the speed of reality. Let t1=4 years. The rocket is passed by an amount of time from Earth t2 and a space from outer space of x3 going the opposite way from time.
t2 = t1 - t1(v/c)
x3 = x1 + x2
x3 = c t1 + v t1
v4 = x3 / t2 = (c + v) / (1 - (v/c))
Part 2 : See the sketch. This is relative to the rocket and outer space is used. For example, the position of a star is used in this calculation. The space that the rocket passes is the same as seen from Earth, x3, but a different time passes the rocket, relative to the rocket, t4.
t4 = t3 + t0 = t1 +t0
t4 = t1 + t1(c/v)
x3 = x1 + x2
x3 = c t1 + v t1
t3 is t1 grown from the rocket away from destination, t1(c/v) = t0 is passing the rocket from the direction of the destination. The velocity v6 is a second ratio like v4, but relative to the rocket.
v6 = x3 / t4 = (c + v) / (1 + (v/c))
To get an energy equation used E = 1/2 m v4*v6
E = 1kg v4 * v6 = 1kg(c+v)(c+v) / (1 - (v/c))(1 + (v/c))
The mass can be eliminated. Velocity squared is potential, (psi) like temperature or voltage. The square root of potential is velocity.
psi = v4*v6
The geometric mean of v4 and v6 is sqrt(v4*v6)=v7
v7 = sqrt((c+v)(c+v) / (1 - (v/c))(1 + (v/c)))
v7 = (c+v) / sqrt((1 - (v/c))(1 + (v/c)))
v7 = (c+v) / sqrt(1 - (v^2/c^2))
The final result:
v8 = (c+v) / sqrt(1 - (v^2/c^2))
v8 = gamma * (c+v)
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Definitions of variables
time grows at c, the speed of reality
space drains into objects at length rate of c. The volume rate is p= 7*10^-37 cubic meters per second for each baryon
t0 is the time from outer space that passed by the rocket from a position near Proxima Centauri called a "Goal Limit". That is how far light goes in t1. If no star is there, the same occurs. Time that left a distant place at time zero ( 4 years ago) has passed by the rocket by an amount t0. That is less then all the time sent. t0 < t1
t1 is the travel time for the rocket when measured from Earth. 4 years travel time means t1=4Y
t2 is how much time has passed by the rocket, sent from Earth. The faster the rocket goes, the less time can pass by the rocket, from Earth.
t3 is from the rocket's protons and neutrons. t3 grows out of the rocket and goes away from the destination. t3=t1
t4 is how much time from the direction of the destination has passed the rocket. t4 include two sources: the rocket grows time and time came from outer space and passed the rocket in the direction opposite from the rocket's motion.
x1 is a length draining into the Earth at speed c for gravity volume theory, relative to Earth
x2 is the distance traveled by the rocket
x3 is the total length seen from Earth due to x1 plus x2 when viewing the rocket
v the rocket velocity, 0.9c
v4 = dx/dt = x3/t2 , this is the demi-velocity relative to Earth
v6 = dx/dt = x3/t4, this is the hemi-velocity relative to the rocket
v7 geometric mean of two quasi-velocities, sqrt(v6*v4)
v8 final result is the distorted velocity, ready to dilate time or mass
The gamma is similar to the formula derived here without needing any triangles. Only seven parallel lines are defining the geometry that provides the algebra for this factor:
sqrt(1 - (v^2/c^2))
Alan Folmsbee, September 5, 2016
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Begin section of September 9, 2016
Time Dilation according to Graviticspansion
The quasi-Lorentz dilation was described in a recent thread in sci.physics.relativity. The result was the next formula for a velocity.
v8 = ( c + v ) / sqrt( 1- (v^2 / c^2))
That is called the chasing velocity (v8) and it is used like gamma. This new essay completes the formulas for time dilation and length contraction. These were derived without using triangles. Only parallel motions in seven parallel lines were used, following the rules of graviticspansion. See Figure 1. New names are given to three values from the gravity volume theory. Instead of the Lorentz gamma, an alternative is given as The Chasing Velocity, v8. These names are describing a proposed law of how things really work. That is why these new formulas are valuable in ways beyond the Lorentz contraction gamma. They are using gravity and expansion to get the Lorentz formula for time dilation and length contraction.
v8 = ( c + v ) / sqrt( 1- (v^2 / c^2)) = chasing velocity
x3 = t1(c + v) = chase distance
c + v = flat velocity
where v is the rocket velocity, c is light speed, t1 is the travel time. The next two formulas give the dilated time t15 and the contracted length x15 of the rocket. The rocket had length x14 before launch. The formulas are made to show the simultaneous expansion and contraction of gravity. It is using counter flow momentum, so some directions are opposites. See Ref. 1. The dilated time is a distance divided by a velocity. The dilated time t15 is the chase distance divided by the chasing velocity.
t15 = t1 * (c + v) / v8 = x3 / v8
x15 = x14 * (c + v) / v8
The contracted length x15 of the rocket is: x14, the original length, times a ratio of velocities. The ratio is the flat velocity.divided by the chasing velocity. Dilation means the same as contraction: it gets smaller.
Conclusion
The rearrangement of the factors and terms was done to model reality as the way things really work. Gravity is real, but Lorentz did not include that in gamma. The new treatment does. September 11, 2016 acf.
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Begin September 11, 2016 section
Success! I have applied the gravity volume theory to derive the standard Lorentz contraction formula, gamma. This novel treatment means my theory is compatible with Einstein's theory of special relativity. Time dilation means time is getting smaller. Length contraction means length dilation. This new derivation has three articulated factors for gamma named:
chasing velocity = (c + v) / ( sqrt(1-(v^2/c^2)))
chase distance = t(c + v)
flat velocity = c + v
t' = t ( sqrt(1-(v^2/c^2))) = t / gamma
t' = chase distance / chasing velocity
t' = t(c + v) / ((c + v) / ( sqrt(1-(v^2/c^2))))
x' = x(c + v) / ((c + v) / ( sqrt(1-(v^2/c^2))))
Conclusion
The new formulas show the factors of gamma that are caused by The Gravity Volume Theory. This articulated version of gamma gives the same dilation as the Lorentz gamma, but it opens up new area of research. This is like force having two factors. Before Newton, force did not need factors. But by using mass and acceleration as factors allows many advances beyond brute force. Similarly, I expect that the new factorization of gamma will bear fruit in nuclear fusion research that leads to The Generator. Einstein's 1905 paper did not have c + v. That is about expansion of the universe from matter. This new derivation brings together expansion of the universe, gravity, and the Lorentz contraction formula.
Figure 1: Seven parallel lines define dilation and contraction variable v8
The FitzGerald-Lorentz length contraction factor formula
gamma = 1 / sqrt(1 - (v^2/c^2))
has been re-derived, without using the Pythagorean Theorem. Using Gravity Volume Theory and a geometric mean for the square root, the following formula is similar to the Lorentz gamma: Dilation means time gets smaller. Contraction means distance or time gets smaller.
v8 = distorted velocity = (c+v) / sqrt(1 - (v^2/c^2))
That is the "distorted velocity" used to find time dilation and length contraction. Time grows out of protons and neutrons. Space drains in. That is gravity. Those directions are used in the formulas that are in this derivation of the Lorentz factor without triangles..
Basics
A rocket passes Earth at the speed of 0.9c on the way to Proxima Centauri, 4 Light Years away. After 4 years have passed, the rocket is still in outer space, and measurements are taken and calculations made to find dilation or contraction. Two sets of velocity equations will be: first for Earth observers and second for astronaut observers on the rocket. Those two velocities are multiplied together for an energy equation, using a mass of 2kg. The mass magnitude does not influence the dilation or contraction. From the energy understanding, the potential, psi, is used and it has a square root taken to find the geometric mean of the two velocities. That is v8, the distorted velocity.
Details
Part 1 : relative to Earth. Time grows out of Earth at speed c, the speed of reality. Let t1=4 years. The rocket is passed by an amount of time from Earth t2 and a space from outer space of x3 going the opposite way from time.
t2 = t1 - t1(v/c)
x3 = x1 + x2
x3 = c t1 + v t1
v4 = x3 / t2 = (c + v) / (1 - (v/c))
Part 2 : See the sketch. This is relative to the rocket and outer space is used. For example, the position of a star is used in this calculation. The space that the rocket passes is the same as seen from Earth, x3, but a different time passes the rocket, relative to the rocket, t4.
t4 = t3 + t0 = t1 +t0
t4 = t1 + t1(c/v)
x3 = x1 + x2
x3 = c t1 + v t1
t3 is t1 grown from the rocket away from destination, t1(c/v) = t0 is passing the rocket from the direction of the destination. The velocity v6 is a second ratio like v4, but relative to the rocket.
v6 = x3 / t4 = (c + v) / (1 + (v/c))
To get an energy equation used E = 1/2 m v4*v6
E = 1kg v4 * v6 = 1kg(c+v)(c+v) / (1 - (v/c))(1 + (v/c))
The mass can be eliminated. Velocity squared is potential, (psi) like temperature or voltage. The square root of potential is velocity.
psi = v4*v6
The geometric mean of v4 and v6 is sqrt(v4*v6)=v7
v7 = sqrt((c+v)(c+v) / (1 - (v/c))(1 + (v/c)))
v7 = (c+v) / sqrt((1 - (v/c))(1 + (v/c)))
v7 = (c+v) / sqrt(1 - (v^2/c^2))
The final result:
v8 = (c+v) / sqrt(1 - (v^2/c^2))
v8 = gamma * (c+v)
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Definitions of variables
time grows at c, the speed of reality
space drains into objects at length rate of c. The volume rate is p= 7*10^-37 cubic meters per second for each baryon
t0 is the time from outer space that passed by the rocket from a position near Proxima Centauri called a "Goal Limit". That is how far light goes in t1. If no star is there, the same occurs. Time that left a distant place at time zero ( 4 years ago) has passed by the rocket by an amount t0. That is less then all the time sent. t0 < t1
t1 is the travel time for the rocket when measured from Earth. 4 years travel time means t1=4Y
t2 is how much time has passed by the rocket, sent from Earth. The faster the rocket goes, the less time can pass by the rocket, from Earth.
t3 is from the rocket's protons and neutrons. t3 grows out of the rocket and goes away from the destination. t3=t1
t4 is how much time from the direction of the destination has passed the rocket. t4 include two sources: the rocket grows time and time came from outer space and passed the rocket in the direction opposite from the rocket's motion.
x1 is a length draining into the Earth at speed c for gravity volume theory, relative to Earth
x2 is the distance traveled by the rocket
x3 is the total length seen from Earth due to x1 plus x2 when viewing the rocket
v the rocket velocity, 0.9c
v4 = dx/dt = x3/t2 , this is the demi-velocity relative to Earth
v6 = dx/dt = x3/t4, this is the hemi-velocity relative to the rocket
v7 geometric mean of two quasi-velocities, sqrt(v6*v4)
v8 final result is the distorted velocity, ready to dilate time or mass
The gamma is similar to the formula derived here without needing any triangles. Only seven parallel lines are defining the geometry that provides the algebra for this factor:
sqrt(1 - (v^2/c^2))
Alan Folmsbee, September 5, 2016
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Begin section of September 9, 2016
Time Dilation according to Graviticspansion
The quasi-Lorentz dilation was described in a recent thread in sci.physics.relativity. The result was the next formula for a velocity.
v8 = ( c + v ) / sqrt( 1- (v^2 / c^2))
That is called the chasing velocity (v8) and it is used like gamma. This new essay completes the formulas for time dilation and length contraction. These were derived without using triangles. Only parallel motions in seven parallel lines were used, following the rules of graviticspansion. See Figure 1. New names are given to three values from the gravity volume theory. Instead of the Lorentz gamma, an alternative is given as The Chasing Velocity, v8. These names are describing a proposed law of how things really work. That is why these new formulas are valuable in ways beyond the Lorentz contraction gamma. They are using gravity and expansion to get the Lorentz formula for time dilation and length contraction.
v8 = ( c + v ) / sqrt( 1- (v^2 / c^2)) = chasing velocity
x3 = t1(c + v) = chase distance
c + v = flat velocity
where v is the rocket velocity, c is light speed, t1 is the travel time. The next two formulas give the dilated time t15 and the contracted length x15 of the rocket. The rocket had length x14 before launch. The formulas are made to show the simultaneous expansion and contraction of gravity. It is using counter flow momentum, so some directions are opposites. See Ref. 1. The dilated time is a distance divided by a velocity. The dilated time t15 is the chase distance divided by the chasing velocity.
t15 = t1 * (c + v) / v8 = x3 / v8
x15 = x14 * (c + v) / v8
The contracted length x15 of the rocket is: x14, the original length, times a ratio of velocities. The ratio is the flat velocity.divided by the chasing velocity. Dilation means the same as contraction: it gets smaller.
Conclusion
The rearrangement of the factors and terms was done to model reality as the way things really work. Gravity is real, but Lorentz did not include that in gamma. The new treatment does. September 11, 2016 acf.
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
Begin September 11, 2016 section
Success! I have applied the gravity volume theory to derive the standard Lorentz contraction formula, gamma. This novel treatment means my theory is compatible with Einstein's theory of special relativity. Time dilation means time is getting smaller. Length contraction means length dilation. This new derivation has three articulated factors for gamma named:
chasing velocity = (c + v) / ( sqrt(1-(v^2/c^2)))
chase distance = t(c + v)
flat velocity = c + v
t' = t ( sqrt(1-(v^2/c^2))) = t / gamma
t' = chase distance / chasing velocity
t' = t(c + v) / ((c + v) / ( sqrt(1-(v^2/c^2))))
x' = x(c + v) / ((c + v) / ( sqrt(1-(v^2/c^2))))
Conclusion
The new formulas show the factors of gamma that are caused by The Gravity Volume Theory. This articulated version of gamma gives the same dilation as the Lorentz gamma, but it opens up new area of research. This is like force having two factors. Before Newton, force did not need factors. But by using mass and acceleration as factors allows many advances beyond brute force. Similarly, I expect that the new factorization of gamma will bear fruit in nuclear fusion research that leads to The Generator. Einstein's 1905 paper did not have c + v. That is about expansion of the universe from matter. This new derivation brings together expansion of the universe, gravity, and the Lorentz contraction formula.
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