Einstein Mistake
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3.3
Einstein’s mistake
3. Relativity The following lines are part of
Logic in the universe
When I heard of the twin paradox for the first time, I thought: How can a relative movement raise an absolute time contraction? That was in 1957, I was 18. I forgot all about it until recently. I want to demonstrate that absolute time contraction is absurd. Relative movement can only produce relative time contraction. Since the idea of absolute time contraction is generally accepted by everyone, I am going to have a hard time demonstrating its’ absurdity. Let us start from the very beginning.
[email protected]
On page 11 of the English translation of his famous article “ON THE ELECTRODYNAMICS OF MOVING BODIES”, Einstein states: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at 2 2 rest the travelled clock on its arrival at A will be (1/2) tv /c seconds slow.
Paul Langevin, made more clear the idea with his known twin paradox. One of the twins travels at fast speed to a star. When he returns to Earth he will be younger that the one that stayed on our planet. We are going to go through the following small steps: 1. Every movement is relative 2. Details of absolute contraction 3. Contraction is not a property of the moving body 4. Contraction is relative 5. Where is the mathematical mistake? Let’s go.
1. Every movement is relative Newton’s words are the shortest and best way to enunciate Galileo’s relativity: There is no absolute movement, space doesn’t have any marks. Every movement is relative to another object that is taken as stationary.
2. Details of absolute contraction In Einstein’s version, he doesn’t speak of acceleration and deceleration. In fact, the high speed is only used to underline that contraction is visible. So we are going to forget completely about acceleration. Let’s say that when the traveling twin returns, after t seconds, he is younger than the earthly twin n seconds. He will stay younger n seconds for the rest of their lives, because contraction is absolute. Time contraction didn’t jump from nothing to n. It accumulated second by second, millisecond by millisecond. So, when t/2 seconds went through, the traveling twin was n/2 seconds younger. Given that the speed was constant, the contraction depends only on the time it lasted.
3. Contraction is not a property of the moving body.
Let’s continue with the paradox, but at t/2 seconds, a comet strikes Earth, and Earth disappears with the earthly twin and his clock. The traveling twin was moving inertial with constant speed, without using brakes or accelerator. He didn’t know about the crash. He just continues traveling as he was. Let’s answer the following questions: -
Will absolute contraction continue to grow at the same pace, but now relative to whom or what? Will absolute contraction vanish at the exact moment of the strike? Will absolute contraction stay as n/2 for the rest of his life?
There is not a good answer. This is because time contraction, absolute or not is not a property of the moving body.
4. Contraction is relative Let’s think about another experiment. Instead of twins, now we have quintuplets. They start moving at some place in space with different speed. We measure contraction of Quintuplet 1 relative to all the other four quintuplets. After t seconds, contraction relative to quintuplet 2 is n2, relative to quintuplet 3 is n3, relative to quintuplet 4 is n4 and relative to quintuplet 5 is n5. Quintuplet 1 could not have four different ages at the same time. It implies that contraction can only be relative.
5. Where is the mathematical mistake? No matter how convincing the logic I used can be, some people will need mathematical formulae as a demonstration. Einstein starts the second subsection “On the relativity of lengths and times” saying: The following reflections are based on the principle of relativity and on the principle of the constancy of the velocity of light.
Then he specifies that: velocity = light path / time interval
either when light is emitted by a moving or stationary body. This equation could be written as c=l/t or
t= l/c where c is the speed of light, l the length of the light path and t the time interval This linear relation between l and t, is the base of the constancy of light speed, the base of all the rest of the article. So if any transformation, conversion, simplification or interpretation breaks up this linear relation, nothing else makes any sense. Einstein’s line of thought is as follows: -
The length of a moving rod is shorter when measured from the stationary system. Light will travel a shorter path from one end to the other end of the rod. So time has to pass slower to maintain, the speed of light is constant,
In subsection 4. Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks, He states that the length of the moving rod will be v l 1− c
2
where l is the length of the static rod relative to the stationary observer when the relative speed is v. The contraction is the length of the stationary rod minus the length of the moving rod. Later he states, by using the conversion x = v t he comes to the equation v t 1− c
2
for the time elapsed in the moving clock measured from the stationary clock. Time contraction is the time elapsed in the stationary clock minus the time elapsed in the moving clock. But now Einstein says contraction is measured in seconds per second. Where did that change in unit of measurement come from? This is a violation of the linearity that states the constancy of the speed of light. This change has enormous implications. If the length contraction is given in meters per second instead of meters, length contraction would be permanent. If time contraction is given in seconds per second, time contraction would be permanent, but not if it is given in seconds. I cannot see how a transformation can change the units of measurement. I believe we have just found where Einstein inadvertently converts relative contraction to absolute contraction.
PD First we abbreviate as contraction factor as f(v) = sqrt(1 – v2 /c2) where c is the speed of light. When v = 0, f(v) = 1, it means no contraction. When v = c, f(v) = 0, which means contraction is 100%. As c is constant f(v) depends only on v. It doesn’t depend on t. The constancy of the speed of light means that c=l/t or t=l/c l is the length the light travels in t units of time. Let us consider a four dimensional system of coordinates. We name the coordinates h, w, l and t. We have that t is the time coordinate and l is the coordinate in the direction of the movement. For a unit sphere moving at the speed v relative to a stationary system h’ = h w’ = w l’ = l*f(v) t’ = l*f(v)/c = t*f(v) where the constancy of the speed of light is given by t’ = l’ / c. Of course time contraction is expressed in seconds, not in seconds per second.
Einstein’s mistake
3. Relativity The following lines are part of
Logic in the universe
When I heard of the twin paradox for the first time, I thought: How can a relative movement raise an absolute time contraction? That was in 1957, I was 18. I forgot all about it until recently. I want to demonstrate that absolute time contraction is absurd. Relative movement can only produce relative time contraction. Since the idea of absolute time contraction is generally accepted by everyone, I am going to have a hard time demonstrating its’ absurdity. Let us start from the very beginning.
[email protected]
On page 11 of the English translation of his famous article “ON THE ELECTRODYNAMICS OF MOVING BODIES”, Einstein states: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at 2 2 rest the travelled clock on its arrival at A will be (1/2) tv /c seconds slow.
Paul Langevin, made more clear the idea with his known twin paradox. One of the twins travels at fast speed to a star. When he returns to Earth he will be younger that the one that stayed on our planet. We are going to go through the following small steps: 1. Every movement is relative 2. Details of absolute contraction 3. Contraction is not a property of the moving body 4. Contraction is relative 5. Where is the mathematical mistake? Let’s go.
1. Every movement is relative Newton’s words are the shortest and best way to enunciate Galileo’s relativity: There is no absolute movement, space doesn’t have any marks. Every movement is relative to another object that is taken as stationary.
2. Details of absolute contraction In Einstein’s version, he doesn’t speak of acceleration and deceleration. In fact, the high speed is only used to underline that contraction is visible. So we are going to forget completely about acceleration. Let’s say that when the traveling twin returns, after t seconds, he is younger than the earthly twin n seconds. He will stay younger n seconds for the rest of their lives, because contraction is absolute. Time contraction didn’t jump from nothing to n. It accumulated second by second, millisecond by millisecond. So, when t/2 seconds went through, the traveling twin was n/2 seconds younger. Given that the speed was constant, the contraction depends only on the time it lasted.
3. Contraction is not a property of the moving body.
Let’s continue with the paradox, but at t/2 seconds, a comet strikes Earth, and Earth disappears with the earthly twin and his clock. The traveling twin was moving inertial with constant speed, without using brakes or accelerator. He didn’t know about the crash. He just continues traveling as he was. Let’s answer the following questions: -
Will absolute contraction continue to grow at the same pace, but now relative to whom or what? Will absolute contraction vanish at the exact moment of the strike? Will absolute contraction stay as n/2 for the rest of his life?
There is not a good answer. This is because time contraction, absolute or not is not a property of the moving body.
4. Contraction is relative Let’s think about another experiment. Instead of twins, now we have quintuplets. They start moving at some place in space with different speed. We measure contraction of Quintuplet 1 relative to all the other four quintuplets. After t seconds, contraction relative to quintuplet 2 is n2, relative to quintuplet 3 is n3, relative to quintuplet 4 is n4 and relative to quintuplet 5 is n5. Quintuplet 1 could not have four different ages at the same time. It implies that contraction can only be relative.
5. Where is the mathematical mistake? No matter how convincing the logic I used can be, some people will need mathematical formulae as a demonstration. Einstein starts the second subsection “On the relativity of lengths and times” saying: The following reflections are based on the principle of relativity and on the principle of the constancy of the velocity of light.
Then he specifies that: velocity = light path / time interval
either when light is emitted by a moving or stationary body. This equation could be written as c=l/t or
t= l/c where c is the speed of light, l the length of the light path and t the time interval This linear relation between l and t, is the base of the constancy of light speed, the base of all the rest of the article. So if any transformation, conversion, simplification or interpretation breaks up this linear relation, nothing else makes any sense. Einstein’s line of thought is as follows: -
The length of a moving rod is shorter when measured from the stationary system. Light will travel a shorter path from one end to the other end of the rod. So time has to pass slower to maintain, the speed of light is constant,
In subsection 4. Physical Meaning of the Equations Obtained in Respect to Moving Rigid Bodies and Moving Clocks, He states that the length of the moving rod will be v l 1− c
2
where l is the length of the static rod relative to the stationary observer when the relative speed is v. The contraction is the length of the stationary rod minus the length of the moving rod. Later he states, by using the conversion x = v t he comes to the equation v t 1− c
2
for the time elapsed in the moving clock measured from the stationary clock. Time contraction is the time elapsed in the stationary clock minus the time elapsed in the moving clock. But now Einstein says contraction is measured in seconds per second. Where did that change in unit of measurement come from? This is a violation of the linearity that states the constancy of the speed of light. This change has enormous implications. If the length contraction is given in meters per second instead of meters, length contraction would be permanent. If time contraction is given in seconds per second, time contraction would be permanent, but not if it is given in seconds. I cannot see how a transformation can change the units of measurement. I believe we have just found where Einstein inadvertently converts relative contraction to absolute contraction.
PD First we abbreviate as contraction factor as f(v) = sqrt(1 – v2 /c2) where c is the speed of light. When v = 0, f(v) = 1, it means no contraction. When v = c, f(v) = 0, which means contraction is 100%. As c is constant f(v) depends only on v. It doesn’t depend on t. The constancy of the speed of light means that c=l/t or t=l/c l is the length the light travels in t units of time. Let us consider a four dimensional system of coordinates. We name the coordinates h, w, l and t. We have that t is the time coordinate and l is the coordinate in the direction of the movement. For a unit sphere moving at the speed v relative to a stationary system h’ = h w’ = w l’ = l*f(v) t’ = l*f(v)/c = t*f(v) where the constancy of the speed of light is given by t’ = l’ / c. Of course time contraction is expressed in seconds, not in seconds per second.
