_{1}

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This study shows that time dilation supposed by Einstein can be derived from absolute time supposed by Newton if Newtonian space is sloped where space of moving frames become sloped with respect to space of the stationary frame of reference. Slope of Newtonian space creates a new kind of energy that causes moving frames to experience slight resistance while moving to forward in Newtonian space; hence, moving frames rev
erse slightly backward in space. With respect to observers at rest, the sum of the distance that the light travels vertically during motion of the moving frame
S
' to forward (
x
_{v}
)
_{f}
and the distance that the light travels vertically during motion of the same frame to backward (
x
_{v}
)
_{b}
is equal to the distance (
x'
_{v}
) that the light travels vertically in frame S' from the perspective of the observers in the same frame
S'
. The motion of light through the reversed space dilates Newtonian time of the moving frames with respect to the stationary frame of reference, like a car that moves slowly because it is climbing a hill, the time of the moving bodies moves slowly because of the slope of Newtonian space. This work does not aim to prove slope or straightness of space, rather it aims to show that time dilation can be existed in nature as a result of a reaction between Newtonian time and slope of Newtonian space, therefore testing of slope’s property must be included in the interests of applied physicists in the next days.

In 1887, Michelson and Morley performed the well-known Michelson-Morley experiment to determine the speed of the earth relative to that of the luminiferous ether [

The null result of the Michelson-Morley experiment is considered strong evidence against the ether theory [

Following this, in 1905, Einstein posited the non-existence of the absolute medium and introduced the “special relativity” theory, which is based on two postulates: first, the laws of electrodynamics and optics are valid for all frames of reference; second, the speed of light is constant regardless of the motion of the light source [

The following postulate considered herein:

-Newtonian space is sloped, or in other words; the univere is sloped (

This study introduces the space-time continuum as an emerging phenomenon based on the absolute nature of space and time and the slope of space. To prevent confusion, this study provides a new analysis on the vertical motion of light in moving frames in case of slope of moving systems related to each other. A new theory on this concepts is also established without interfering with previous experimental work [

The theoretical analysis of emergence of time dilation from Newtonian time was performed in accordance with the constancy of the speed of light, regardless of the light source motion.

I find there are many results can be obtained based on slope of Newtonian space or slope of the universe.

The slope of Newtonian space or the universe makes the moving frames experience slope where space of the moving frame become sloped with respect to space of the stationary frame of reference that it exists at rest so it cannot experiences slope property of Newtonian space like moving frames (

This section describes the calculation of the difference, Δ x v , between the distances that light travels vertically in frames S ′ and S (frames in a uniform relative motion) according to the presence of a universal time between the two frames. In the next section, I will show and explain where light travels along this distance, Δ x v and explain the physical meaning or the physical name of Δ x v . Suppose that a vertical light beam is emitted in the x ′ direction in frame S ′ . Thus, x ′ v , which represents the distance that the light beam travels vertically in frame S ′ (

t a b = x ′ v c , (1)

x ′ v = c ⋅ t a b . (2)

The transformed distance, x v , which refers to the distance that light travels in frame S ′ , from the perspective of the observers in frame S will not be represented mathematically as a triangle’s string because according to the mentioned postulate, space of the moving frame S ′ is sloped with respect to the observers of the stationary frame S , therefore the transformed distance, x v , will be represented mathematically as a triangle’s rib while the distance, x ′ v , will be represented mathematically as a triangle’s string. Accordingly the transformed distance, x v , can be given as follows in the presence of a universal time (absolute duration):

( c ⋅ t a b ) 2 = ( x v ) 2 + ( v ⋅ t a b ) 2 , (3)

c 2 = ( x v t a b ) 2 + v 2 ,

c 2 − v 2 = x v t a b ,

t a b = x v c 2 − v 2 ,

t a b = x v c 2 ( 1 − v 2 c 2 ) ,

t a b = x v c 1 − v 2 c 2 ,

x v = c ⋅ t a b 1 − v 2 c 2 . (4)

The difference between the distances ( Δ x v ) that light travels vertically in frames S ′ and S is given as follows according to Equations (2)-(4):

Δ x v = x ′ v − x v , (5)

Δ x v = c ⋅ t a b − c ⋅ t a b ( 1 − v 2 c 2 ) ,

Δ x v = c ⋅ t a b ( 1 − 1 − v 2 c 2 ) . (6)

We obtain the three following important equations based on the mathematics in this section:

If space is absolute in nature as Newton supposed, it should be determined why light travels vertically a shorter distance x v in frame S compared to that x ′ v in frame S ′ and where light travels along the distance Δ x v determined in the previous section. According to the mentioned postulate, which states that “Newtonian space is sloped,” the moving frame S ′ slightly slides backward with respect to the observers in the stationary frame S . This divides or classifies the distance that the light travels vertically in frame S ′ , from the perspective of the observers in frame S into two kinds with two different directions: the distance that the light travels or progresses to forward ( x v ) f and the distance that the light travels or regresses to backward ( x v ) b or Δ x v . The sum of the two distances that the light travels vertically to backward and forward in frame S ′ , from the perspective of the observers in frame S is equal to the distance x ′ v that the light travels vertically in frame S ′ from the perspective of the observers in the same frame S ′ (

By this explanation, the distance that the light travels vertically is the same for all the frames of reference regardless the motion:

x ′ v = x v , (8)

x ′ v = ( x v ) f + ( x v ) b . (9)

where,

( x v ) f = c ⋅ t a b ( 1 − 1 − v 2 c 2 ) , (10)

( x v ) f = x ′ v γ . (11)

while,

Δ x v = ( x v ) b , (12)

( x v ) b = c ⋅ t a b ( 1 − 1 − v 2 c 2 ) ,

( x v ) b = x ′ v ( 1 − 1 γ ) . (13)

where γ is the Lorentz factor. This phenomenon is named herein as “space reversal,” which refers to the reversal of the space of moving bodies with respect to a stationary frame of reference because of the slope of Newtonian space.

As mentioned in the previous section, the moving frame S ′ slightly slides backward because of the slope of space, thereby leading to the reversal of the time of frame S ′ with respect to the observers in frame S . The reversed time ( t b ) of frame S ′ as measured in frame S can be derived using the following equations if the backward distance that light reverses in frame S ′ as measured in frame S is ( x v ) b :

( c ⋅ t b ) 2 = ( x v ) 2 b + ( v ⋅ t b ) 2 , (14)

( c ⋅ t b ) 2 = ( c ⋅ t a b ( 1 − 1 − v 2 c 2 ) ) 2 + ( v ⋅ t b ) 2 ,

c 2 = ( c ⋅ t a b t b ( 1 − 1 − v 2 c 2 ) ) 2 + v 2 ,

c 2 − v 2 = ( c ⋅ t a b t b ) 2 ( 1 − 1 − v 2 c 2 ) 2 ,

c 2 − v 2 c 2 = ( t a b t b ) 2 ( 1 − 1 − v 2 c 2 ) 2 ,

1 − v 2 c 2 = ( t a b t b ) 2 ( 1 − 1 − v 2 c 2 ) 2 ,

1 − v 2 c 2 = t a b t b ⋅ ( 1 − 1 − v 2 c 2 ) ,

1 = t a b t b ⋅ ( 1 1 − v 2 c 2 − 1 ) ,

t b = t a b ⋅ ( 1 1 − v 2 c 2 − 1 ) ,

t b = t a b ⋅ ( γ − 1 ) . (15)

The reversed time of the moving frame S ′ with respect to the observers in frame S is determined using Equation (15). This phenomenon is named here as “time reversal” (

Like a car that moves slowly because it is climbing a hill, the time of the moving bodies moves slowly because of the slope of space. The total elapsed time ( t t o t a l ) in the moving frame with respect to the stationary frame of reference can be calculated as follows:

t t o t a l = t a b + t b , (16)

t t o t a l = t a b + [ t a b ( γ − 1 ) ] ,

t t o t a l = t a b + ( γ t a b − t a b ) ,

t t o t a l = t a b + γ t a b − t a b ,

t t o t a l = γ t a b . (17)

According to Equation (17), the clock in the moving frame moves slowly with with respect to the observers in the stationay frame S where the stationary clock exceeds the moving clock. This phenomenon is known as “time dilation” and it is the most important result of special relativity. This section shows how the result of “time dilation” can be obtained according to the “reversal of time” phenomenon. “Time in moving frames moves forward absolutely (as Newton suppose) and backward relatively, where the final result refers to the dilation of the elapsed time in the moving frames with respect to the stationary frame of reference depending on the velocities of the moving frames as measured in the stationary frame of reference (as Einstein suppose)”.

We describe the classification of the dimensions of the universe in this section.

a) First dimension “length”; absolute length, in its own nature, without regard to anything external, remains always similar. The absolute length ( x a b ) can be determined as follows:

x = x ′ = x a b . (18)

b) Second dimension “width”; width is relative with respect to stationary frame of reference as a result of slope of Newtonian space. The relative width ( y ) can be determined as follows:

y = y ′ γ . (19)

c) Third dimension “height”; height is relative with respect to stationary frame of reference as a result of slope of Newtonian space. The relative height ( z ) can be determined as follows:

z = z ′ γ . (20)

d) Time; Absolute, true and mathematical time, of itself, and from its own nature flows to forward equably without regard to anything external, so it can’t be considered as a dimension as it moves to forward regularly for everyone everywhere. The absolute time ( t a b ) can determined as follows:

t = t ′ = t a b . (21)

Thus, three dimensions of space are obtained while time can’t be considered as a dimension. The three dimensions of space are called “Newtonian Space” that is always sloped. The height with width form a new continuum called the “width-height continuum.”

As a result of slope of Newtonian space, the moving frame become sloped with respect to observers at rest and thus the space and time of moving frame S ′ become slightly reversed to backward with coordinates ( x b , y b , z b , t b ) from perspective of stationary frame of reference S , the reversed space-time can be determined as follows:

x b = x ′ ( 1 − 1 γ ) , y b = y ′ ( 1 − 1 γ ) , z b = z ′ ( 1 − 1 γ ) , t b = t ′ ( γ − 1 ) . (22)

where,

γ − 1 = 1 − 1 γ . (23)

Thus, three dimensions of the relative reversed space and one dimension of the relative reversed time are obtained. The four dimensions of space and time are called “reversed space-time.”

The final result of “Newtonian space” and “Reversed space-time” can be obtained as follows:

a) Regarding to the length, the total distance that light travels longitudinally ( x t o t a l ) through two dimensions; Newtonian length ( x ) and Reversed length ( x b ) in frame S is less than the distance that light travels longitudinally in frame S ′ that is ( x ′ ) :

x t o t a l = x − x b . (24)

And as

x = x ′ .

We find

x t o t a l = x ′ − [ x ′ ( 1 − 1 γ ) ] ,

x t o t a l = x ′ − ( x ′ − x ′ γ ) ,

x t o t a l = x ′ − x ′ + x ′ γ ,

x t o t a l = x ′ γ . (25)

b) Regarding to the width, the total distance that light travels transversely ( y t o t a l ) through two dimensions; Newtonian width ( y ) and Reversed width ( y b ) in frame S is equal to the distance that light travels transversely in frame S ′ that is ( y ′ ) :

y t o t a l = y + y b . (26)

By Equations ((19) and (22)), we can get,

y t o t a l = y ′ γ + [ y ′ ( 1 − 1 γ ) ] y t o t a l = y ′ [ 1 γ + ( 1 − 1 γ ) ] y t o t a l = y ′ [ 1 γ + 1 − 1 γ ] y t o t a l = y ′ [ 1 ] y t o t a l = y ′ . (27)

Thus the total distance ( y t o t a l ) that light travels transversely is the same for all the frames of reference.

c) Regarding to the height, the total distance that light travels vertically through two dimensions; Newtonian height ( z ) and Reversed height ( z b ) in frame S is equal to the distance that light travels vertically in frame S ′ that is ( z ′ ) :

z t o t a l = z + z b . (28)

By Equations ((20) and (22)), we can get,

z t o t a l = z ′ γ + [ z ′ ( 1 − 1 γ ) ] z t o t a l = z ′ [ 1 γ + ( 1 − 1 γ ) ] z t o t a l = z ′ [ 1 γ + 1 − 1 γ ] z t o t a l = z ′ [ 1 ] z t o t a l = z ′ . (29)

Thus the total distance ( z t o t a l ) that light travels vertically is the same for all the frames of reference.

d) Regarding to duration, the duration or the total time ( t t o t a l ) taken by light at the moving frame through two dimensions; Newtonian time ( t ) and Reversed time ( t b ) in frame S is more than the time taken by light in frame S ′ that is ( t ′ ) :

t t o t a l = t + t b . (30)

By Equations ((16) and (17)), we can get,

t t o t a l = γ t ′ . (31)

Thus the duration taken by light at the moving frames dilated with respect to the stationary frame of reference.

Accordingly length of moving frames is decreased and time move slowly with respect to stationary frame of reference while width and height of moving frames are the same for everyone everywhere (

t t o t a l = γ ( t ′ + v x c 2 ) , x t o t a l = γ ( x ′ + v t ) , y t o t a l = y ′ , z t o t a l = z ′ . (32)

From perspective of observer at rest | t t o t a l | x t o t a l | y t o t a l | z t o t a l |
---|---|---|---|---|

The moving frame to forward | t ′ | x ′ | y ′ γ | z ′ γ |

The moving frame to backward | t ′ ( γ − 1 ) | x ′ ( γ − 1 ) | y ′ ( γ − 1 ) | z ′ ( γ − 1 ) |

The final result | t ′ ( γ ) | x ′ γ | y ′ | z ′ |

From perspective of observer at rest | t t o t a l | x t o t a l | y t o t a l | z t o t a l |
---|---|---|---|---|

The moving frame to forward | Absolute | Absolute | Width-height continuum | Width-height continuum |

The moving frame to backward | Relative Reverse time | Relative Reverse length | Relative Reverse width | Relative Reverse height |

The final result | Space-time continuum | Space-time continuum | Absolute | Absolute |

In this section, we aimed to calculate the value of slope of Newtonian space of the moving frame with respect to space of the stationary frame of reference (

θ = sin − 1 ( ( x v ) f x ′ v ) , (33)

θ = sin − 1 ( x ′ v γ x ′ v ) ,

θ = sin − 1 ( 1 γ ) . (34)

θ = cos − 1 ( v ⋅ t a b x ′ v ) , (35)

θ = cos − 1 ( v ⋅ t a b c ⋅ t a b ) ,

θ = cos − 1 ( v c ) . (36)

θ = tan − 1 ( ( x v ) f v ⋅ t a b ) , (37)

θ = tan − 1 ( x ′ v v ⋅ t a b ⋅ γ ) ,

θ = tan − 1 ( c ⋅ t a b v ⋅ t a b ⋅ γ ) ,

θ = tan − 1 ( c v ⋅ γ ) , (38)

slope angle = 90 − θ . (39)

By Equations ((34), (36), (38) and (39)), we can get the angle of slope of the moving frame ( S angle ) as,

S angle = 90 − θ = 90 − ( sin − 1 ( 1 γ ) ) . S angle = 90 − θ = 90 − ( cos − 1 ( v c ) ) . S angle = 90 − θ = 90 − ( tan − 1 ( c v ⋅ γ ) ) . (40)

From Equation (40) the slope of space of a moving frame with respect to space of an observer who exists at rest is given by,

m = tan ( S angle ) . (41)

According to the previous equation, we find that space of moving frames is sloped positively with respect to space of the stationary frame of reference.

I find there is a simple method that by it space-time continuum can be emerged from absolute space and time that is denied after special relativity. If absolute space is sloped, time dilation and its implications (length contraction) will be the result. The study explains time dilation as follows: the moving frames experiences resistance while progressing to forward; thus, light slides slightly backward during its forward motion, leading to a delay in moving clocks with respect to stationary clocks, where the second in a stationary frame of reference precedes the second in the moving frames. Referring to this phenomenon as time dilation is not accurate because time runs regularly everywhere. Therefore, it is better to refer to it as time delay where time in moving frames moves forward absolutely (as Newton suppose) and backward relatively.

The previous sections show that Newtonian space is sloped and the value of

slope is relative and changed depending on velocity of the moving frame with respect to the observer at rest, so I conclude that Newtonian space (the universe) is in motion where its horizontal axis is changed from time to time; in other words, Newtonian space is movable towards axis of Newtonian time where slope of Newtonian space that the moving frame experience. It depends on velocity of the moving frame and speed of axis of Newtonian space itself toward axis of Newtonian time, that speed equals speed of light (

I would like to thank Editage (https://www.editage.com/) for the English language editing and publication support.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Husseiny, M.A. (2017) Time Dilation Can Be Emerged from Newtonian Time in One Case. Open Access Library Journal, 4: e3908. https://doi.org/10.4236/oalib.1103908