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Feb 11, 2024, 3:55:34 AMFeb 11

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One of the problems of science today is misconception of time,

presenting time as a sort of force that contracts lengths, curves space,

and distorts mathematics. Time is not a force. It is a measurement of

events. So let us consider time as shown by the Galilean transformation

equations.

x'=x-vt

y'=y

z'=z

t'=t

The problem scientists have with the Galilean transformation equations

is the last equation, t'=t, because they do not see it as providing for

the result of the Michelson-Morley experiment. The disagreement with

these equations can be shown by the example of a clock in a flying

airplane. Einstein says in his Special Theory that the time of that

clock would be slower than the time of a clock on the ground.

Scientists then experimented with clocks in airplanes and found that

they did indeed have slower rates than a clock on the ground. Then

Hafele and Keating experimented with cesium clocks flown on

transcontinental jet flights and said that their experiment had shown

that if an airplane flew around the earth one way, the clocks would be

slower, but if flown around the earth the other way, the clocks would be

faster. They attributed the slower clocks to the effects of Special

Relativity and the faster clocks to the effects of General Relativity.

Then GPS satellites were put in orbit, and a clock in a GPS satellite is

faster than a clock on earth, and scientists once again found a way to

determine the time of a GPS satellite clock by combining the perceived

effects of Special and General Relativity. But it would appear that

there is a simpler way to describe all of these times. Just because

Isaac Newton described time in his theory of gravitation as being

absolute does not mean he could not have worked the problem Einstein

claimed to have solved with the Lorentz equations. My own opinion is

that Newton was a good enough mathematician that he would have

considered the problem a different way and worked it with the

transformation equations he always used, the Galilean transformation

equations. There have always been faster and slower clocks. Scientists

of the times of Galileo and Newton did not have any problem representing

these times with the Galilean transformation equations. If a clock or

any other rate of time was faster or slower than the rate of a clock

that agreed with the rotation of the earth, which was considered the

standard of time when those scientists were alive, represented by the

equation t'=t, then those scientists would have just shown another set

of Galilean transformation equations with different variables for

velocity and time. So to represent the time of a clock in an airplane,

the inverse Galilean transformation equations would be

x = x' - (-vt/n')n'

y = y'

z = z'

n = n'

n' is the time of the faster or slower clock in the airplane, (-vt/n')

is the velocity of the ground relative to the airplane. and n=n' shows

that the time of the clock that shows n' is being used in both frames of

reference. So now we can show the results of the Michelson-Morley

experiment using the Galilean transformation equations. All we have to

do is to say that x=ct and x'=cn' instead of saying that x=ct and x'=ct'

the way Lorentz and Einstein did. Then according to the Galilean

transformation equations

x'=x-vt

cn' = ct-vt

n' = t-vt\c

This value for n' is actually the same as the numerator for Lorentz's equation for t'.

t-vt/c = t-vct/c^2 = t-vx/c^2

However, there is no need for the x in this expression in the Galilean

transformation equations because there is no length contraction. The

spatial coordinates are the same in both sets of equations. To show

this, we just cancel out the (n')'s in the inverse equations, and we

have our original Galilean transformation equations.

x = x' - (-vt/n')n'

x = x' + vt

t = t'

To show how this relates to gravitation, we consider the orbits of the

planets in our solar system. Mercury is the planet that is orbiting the

fastest, being the closest to the sun, its velocity being 30 miles per

second. A clock on Mercury would be slower than a clock on earth

because earth has a slower velocity in its orbit, 20 miles per second.

But what scientists do not seem to have realized is that if we compute

n' for the time on Mercury, we are not computing it from time on earth.

Earth is the third planet from the sun, and there would be an n' for

earth's clock derived from a clock that shows t that applies to all

planets, asteroids, etc., in the solar system. To imagine this common

clock, we go out through the planets, each having a faster clock than

the planets closer to the sun, until we run out of planets and other

things that are orbiting the sun. Then we are at a point, say halfway

to the nearest star, where the gravitation of the sun is of no effect,

and a clock at that point is faster than a clock on any planet in our

solar system. If we say that the time of that clock is t, then we can

calculate the time of a clock on any planet by the Galilean

transformation equations if the velocity of the planet is shown as v

according to the time of the clock halfway to the nearest star. So then

the speed of earth in its orbit would not be v, but (vt/n'), where v is

the velocity of earth's orbit computed from the outer space clock, t is

the time of the outer space clock, and n' is the time of a GPS clock on

earth. I hope this description of time can help scientists visualize

how time relates to motion and gravitation.

Robert B. Winn

presenting time as a sort of force that contracts lengths, curves space,

and distorts mathematics. Time is not a force. It is a measurement of

events. So let us consider time as shown by the Galilean transformation

equations.

x'=x-vt

y'=y

z'=z

t'=t

The problem scientists have with the Galilean transformation equations

is the last equation, t'=t, because they do not see it as providing for

the result of the Michelson-Morley experiment. The disagreement with

these equations can be shown by the example of a clock in a flying

airplane. Einstein says in his Special Theory that the time of that

clock would be slower than the time of a clock on the ground.

Scientists then experimented with clocks in airplanes and found that

they did indeed have slower rates than a clock on the ground. Then

Hafele and Keating experimented with cesium clocks flown on

transcontinental jet flights and said that their experiment had shown

that if an airplane flew around the earth one way, the clocks would be

slower, but if flown around the earth the other way, the clocks would be

faster. They attributed the slower clocks to the effects of Special

Relativity and the faster clocks to the effects of General Relativity.

Then GPS satellites were put in orbit, and a clock in a GPS satellite is

faster than a clock on earth, and scientists once again found a way to

determine the time of a GPS satellite clock by combining the perceived

effects of Special and General Relativity. But it would appear that

there is a simpler way to describe all of these times. Just because

Isaac Newton described time in his theory of gravitation as being

absolute does not mean he could not have worked the problem Einstein

claimed to have solved with the Lorentz equations. My own opinion is

that Newton was a good enough mathematician that he would have

considered the problem a different way and worked it with the

transformation equations he always used, the Galilean transformation

equations. There have always been faster and slower clocks. Scientists

of the times of Galileo and Newton did not have any problem representing

these times with the Galilean transformation equations. If a clock or

any other rate of time was faster or slower than the rate of a clock

that agreed with the rotation of the earth, which was considered the

standard of time when those scientists were alive, represented by the

equation t'=t, then those scientists would have just shown another set

of Galilean transformation equations with different variables for

velocity and time. So to represent the time of a clock in an airplane,

the inverse Galilean transformation equations would be

x = x' - (-vt/n')n'

y = y'

z = z'

n = n'

n' is the time of the faster or slower clock in the airplane, (-vt/n')

is the velocity of the ground relative to the airplane. and n=n' shows

that the time of the clock that shows n' is being used in both frames of

reference. So now we can show the results of the Michelson-Morley

experiment using the Galilean transformation equations. All we have to

do is to say that x=ct and x'=cn' instead of saying that x=ct and x'=ct'

the way Lorentz and Einstein did. Then according to the Galilean

transformation equations

x'=x-vt

cn' = ct-vt

n' = t-vt\c

This value for n' is actually the same as the numerator for Lorentz's equation for t'.

t-vt/c = t-vct/c^2 = t-vx/c^2

However, there is no need for the x in this expression in the Galilean

transformation equations because there is no length contraction. The

spatial coordinates are the same in both sets of equations. To show

this, we just cancel out the (n')'s in the inverse equations, and we

have our original Galilean transformation equations.

x = x' - (-vt/n')n'

x = x' + vt

t = t'

To show how this relates to gravitation, we consider the orbits of the

planets in our solar system. Mercury is the planet that is orbiting the

fastest, being the closest to the sun, its velocity being 30 miles per

second. A clock on Mercury would be slower than a clock on earth

because earth has a slower velocity in its orbit, 20 miles per second.

But what scientists do not seem to have realized is that if we compute

n' for the time on Mercury, we are not computing it from time on earth.

Earth is the third planet from the sun, and there would be an n' for

earth's clock derived from a clock that shows t that applies to all

planets, asteroids, etc., in the solar system. To imagine this common

clock, we go out through the planets, each having a faster clock than

the planets closer to the sun, until we run out of planets and other

things that are orbiting the sun. Then we are at a point, say halfway

to the nearest star, where the gravitation of the sun is of no effect,

and a clock at that point is faster than a clock on any planet in our

solar system. If we say that the time of that clock is t, then we can

calculate the time of a clock on any planet by the Galilean

transformation equations if the velocity of the planet is shown as v

according to the time of the clock halfway to the nearest star. So then

the speed of earth in its orbit would not be v, but (vt/n'), where v is

the velocity of earth's orbit computed from the outer space clock, t is

the time of the outer space clock, and n' is the time of a GPS clock on

earth. I hope this description of time can help scientists visualize

how time relates to motion and gravitation.

Robert B. Winn

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