There is no acceleration the racer starts running before reaching the startline but both the racer and referee start their stopwatch at zero the exact moment the midpoint or center of the racers body crosses the startline and stop the stopwatch the moment the midpoint of the racers body crosses the finish line. The runner does not stop running when he crosses the finish line but maintains the same speed unless blocked by a wall eliminating the issue of acceleration from the calculations. The midpoint is measured in the direction the racer is running.
There shall be one more line called a "percentage line." The ( Y * 100 ) percent completion line marked whatever percent between the start line and the finish line one wants to know that fraction or percentage of the race has been complete. Where if Y = 0 the line would be at the start line, if Y = 0.5 the line would be half way between the start line and the finish line marking 50% completion when crossed and if Y = 1 the line will be at the finish line.
There is an observer who is stationary relative to the startline, finish line, racing track and wall who measures the following
all the following measurements are in one dimension going in the same direction and it's opposite
H is used to represent speed as a fraction times the speed of light
H and Y are unitless
0 < H < 1
0 <= Y <= 1
L, W and D are used to represent thr distances described below in units of the speed of light * time such as light years or light seconds
L, W and D have units of time
L > 0
W > 0
D > 0
If the racer stood still relative to the referee his body would have a length of 2D*c in the direction he is running, or the front of the runner's body is a distance D*c in front of his midpoint
The distance from the startline to the stopline is L*c
The distance from the finish to a wall is W*c
The racer is running at a velocity of H*c
The distance from the startline to the percentage line is Y*L*c
Is there any combination of these variables such that the runner will hit the wall at the exact moment in time when his midpoint touches the stopline from the point of view of the referee but not from the point of view of the runner or will hit the wall from the point of view of the runner but not from the point of view of the referee?
The distance L*c is not necessary to answer that question but prior to answering that question for the sake of practice the running time and running distance from start to finish from the point of view of both the runner and referee will be calculated and it will be confirmed that the speed of the wall moving toward the runner from the runners point of view is the same as the speed of the runner moving toward the wall from the referee's point of view
Even though both are observer's the referee shall be remembered by a lowercase o as in observer which can be a different symbol than the number 0 zero
The runner shall be remembered by j as in jogger because runner and referee both start with r even though running is usually considered faster than jogging
Tof= time to reach the finish line according to referee's stopwatch
Toy= time to reach the percentage line according to referee's stopwatch
Tjf= time to reach the finish line according to the runner's stopwatch
Tjy= time to reach the percentage line according to the runner's stopwatch
Sof = Distance from startline to finish line from referee's viewpoint, this is a proper or rest length
Soy = Distance from startline to percentage line from referee's viewpoint, this is a proper or rest length
Sjf = Distance from startline to start finish line from runner's viewpoint, this is not a proper nor rest length
Sjy = Distance from startline to percentage line from runner's viewpoint, this is not a proper nor rest length
Fow = Length from finish line to wall from referee's viewpoint, this is a proper or rest length
Fjw = Length from finish line to wall from runner's viewpoint, this is not a proper nor rest length
Do = Length from midpoint to front of runner's body from referee's viewpoint, this is not a proper nor rest length
Dj = Length from midpoint to front of runner's body from runner's viewpoint, this is a proper or rest length
From the point of view of the referee and according to the referee's stopwatch
The runners body would appear thinner being shorter in it's direction of movement because it is moving toward the referee
The running track would not have it's length distorted because it is stationary relative to the referee
Sof = L*c
Tof = Sof / ( H*c ) = L*c / ( H*c ) = L / H
Soy = Y*L*c
Toy = Soy / ( H*c ) = Y*L*c / (H*c) = Y * L / H
Dj = D * c
Do = Dj * (1 - [ ( H*c ) ^ 2 ] / c^2 ) ^ 0.5
Do = D * c * ( 1 - H ^ 2 ) ^ 0.5
Fow = W * c
From the point of view of the runner and according to the runners stopwatch
The runner would be stationary and the wall would be moving toward the runner and the running track, startline and finish line would be moving in the same direction as the wall
The runners body would not appear thinner because the runner is stationary relative to himself
The running track would appear shorter because it would be moving relative to the runner
Sjf = Sof * ( 1 - H ^ 2 ) ^ 0.5
Sjf = L*c * ( 1 - H ^ 2 ) ^ 0.5
Tjf = Sjf / H
Tjf = [ L*c * ( 1 - H ^ 2 ) ^ 0.5 ] / H
Sjy = Soy * ( 1 - H ^ 2 ) ^ 0.5
Sjy = Y*L*c * ( 1 - H ^ 2 ) ^ 0.5
Tjy = Sjy / H
Tjy = [ Y*L*c * ( 1 - H ^ 2 ) ^ 0.5 ] / H
Dj = W * c
Fjw = Fow * ( 1 - H ^ 2 ) ^ 0.5
Fjw = W * c * ( 1 - H ^ 2 ) ^ 0.5
Proof that special relativity can not change order of events when there is no acceleration
Percent of time complete = 100% * Tjy / TjF = 100% * Toy / Tof
Toy / Tof = ( Y * L / H ) / ( L / H )
Toy / Tof = Y
Tjy / Tjf = ( [ Y*L*c * ( 1 - H ^ 2 ) ^ 0.5 ] / H ) / ( [ L*c * ( 1 - H ^ 2 ) ^ 0.5 ] / H )
Tjy / Tjf = Y
The percentage of time completed is the same as the percentage of the distance completed on the race track from the point of view of both the referee and the runner.
A% will never be completed before B% for both the referee and the runner when A is less than B
B% will never be completed before A% for both the referee and the runner when B is less than A
This proves that the order of events never changes in special relativity without acceleration, the time that the same event occurs would sometimes be different for both the referee and the runner but the order that events occur in does not change. The order of events is the same for both the referee and the runner.
Example to help understand the proof
For both the referee and the runner these 11 events happen in the same order
First 0% completion Y = 0
Toy = 0
Tjy = 0
Second 10% completion Y = 0.1
Toy = 0.1 * L / H
Tjy = [ 0.1 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H
Third 20% completion Y = 0.2
Toy = 0.2 * L / H
Tjy = [ 0.2 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H
Fourth 30% completion Y = 0.3
Toy = 0.3 * L / H
Tjy = [ 0.3 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H
Fifth 40% completion Y = 0.4
Toy = 0.4 * L / H
Tjy = [ 0.4 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H
Sixth 50% completion Y = 0.5
Toy = 0.5 * L / H
Tjy = [ 0.5 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H
Seventh 60% completion Y = 0.6
Toy = 0.6 * L / H
Tjy = [ 0.6 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H
Eighth 70% completion Y = 0.7
Toy = 0.7 * L / H
Tjy = [ 0.7 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H
Ninth 80% completion Y = 0.8
Toy = 0.8 * L / H
Tjy = [ 0.8 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H
Tenth 90% completion Y = 0.9
Toy = 0.9 * L / H
Tjy = [ 0.9 * L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H
Eleventh 100% completion Y = 1
Toy = L / H
Tjy = [ L * c * ( 1 - H ^ 2 ) ^ 0.5 ] / H
Disproof of special relativity
Proof of contradiction with reality inherant in special relativity
If someone can hit the wall when their midpoint crosses the finish line from the point of view of one observer but not hit the wall when the midpoint crosses the finish line from the point of view of the other observer then special relativity can not be a true representation of reality and no excuses about diffetent orders of events from different reference frames can justify the theory of special relativity because it has already been proven above that the order of events is the same in all reference frames in cases such as this one where no acceleration is occuring
If Dj = Fjw but Do does not equal Fow for at least one positive combination of values for the variables in which travel occurs slower than the speed of light then special relativity is in contradiction with physical reality
or
If Do = Fow but Dj does not equal Fjw for at least one positive combination of values for the variables in which travel occurs slower than the speed of light then special relativity is in contradiction with physical reality
or
If Do < Fow and simultaneously Dj > Fjw for at least one positive combination of values for the variables in which travel occurs slower than the speed of light then special relativity is in contradiction with physical reality
or
If Do > Fow and simultaneously Dj < Fjw for at least one positive combination of values for the variables in which travel occurs slower than the speed of light then special relativity is in contradiction with physical reality
Example of disproof
In the case where the proper distance between the front of the runner's body and the center of the runner's body when the runner is at rest is equal to the proper distance from the finish line to the wall when the wall is at rest
If Dj = Fow
then
Do = Dj * ( 1 - H ^ 2 ) ^ 0.5
Do = Fow * ( 1 - H ^ 2 ) ^ 0.5 < Fow
Do < Fow
meaning collision with wall does not occur from referee's viewpoint
Fjw = Fow * ( 1 - H ^ 2 ) ^ 0.5
Dj = Fow > Fow * ( 1 - H ^ 2 ) ^ 0.5 = Fjw
Dj > Fjw
meaning collision with wall does occur from runner's viewpoint
Copyright Carl Janssen 2022
https://wikimedia.org/api/rest_v1/media/math/render/svg/37ae2718b3d30ba8c8f9019bedde2e289f1f3b28
http://web.archive.org/web/20220312022749/https://wikimedia.org/api/rest_v1/media/math/render/svg/37ae2718b3d30ba8c8f9019bedde2e289f1f3b28
https://en.m.wikipedia.org/wiki/Length_contraction
http://web.archive.org/web/20211130084048/https://en.m.wikipedia.org/wiki/Length_contraction
The proper length[1] or rest length[2] of an object is the length of the object measured by an observer which is at rest relative to it, by applying standard measuring rods on the object.
https://en.m.wikipedia.org/wiki/Proper_length
http://web.archive.org/web/20211126104939/https://en.m.wikipedia.org/wiki/Proper_length
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