Twins Paradox & Absolute Space
Created | Updated Sep 18, 2002
Quote, Gottfried Leibniz:
"Although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough, if, using reason well, we were never deceived by it."
The Twins Paradox:
The twins paradox has to do with the theory of special relativity and the realization that there is no preferred frame of reference. All motion is relative or so it would seem. Take the classic example of the travelling passenger train and the railway station. As the train is moving at a constant speed past the railway station, it can justifiably be said that the train is at rest and the railway station is moving. Because the same laws of physics hold for both systems.
The twins paradox has to do with the fact that one twin remains on the earth, while the other twin hops on a rocket for a space journey at a significant fraction of the speed of light. According to relativity, an object moving close to the speed of light undergoes what is called "time dilation" with respect to an object at rest. So the twin in the rocket's frame of reference does not age as quickly as the twin back on earth. When the first sibling returns to earth, he or she will find the earth bound sibling walking around with a cane.
Since relativity states that no preferred frame of reference exists, why can't we say that the twin in the rocket is the one who is "at rest" and the twin back on earth is the one who is "moving"? This is what is known as the "Twins Paradox".
A solution:
(r1)<-----(origin)----->(r2)
Imagine not just twins, but triplets.
One sibling (s1) travels velocity (v1) in rocket one...(r1).
Another sibling (s2) travels velocity (v2) in rocket two...(r2).
The third sibling (s3) remains at the origin.
The rockets travel at exactly the same speed even during the inevitable "acceleration phase".
(r1)<-----(origin)----->(r2)
--------------|-------------
--------------|-------------
--------------|-------------
--------------|-------------
--------------|-------------
--------------|-------------
--------------v-------------
Initially r1,r2, and the origin were "at rest with respect to each other, or it could be said that they were all within the same inertial reference frame. The downward pointing arrow represents the time axis and as you can clearly see, time is perpendicular to space. The rockets launch.
Since both rockets are moving at exactly the same speed but in opposite directions, the reference point at the origin effectively cannot be in relative motion with respect to both (r1) and (r2) simultaneously. Because if we say the the origin is moving to the left with respect to (r2), that would contradict with the origin's motion to the right with respect to (r1). In effect, the point of origin must be at rest with respect to both (r1) and (r2). So the point of origin can be explained as being "at rest" with respect to the two rockets. The origin cannot be in motion to the left or the right. When the two siblings return from their adventure. They will find their twin at the origin much older than themselves according to the relativistic time dilation formula...
t = (t')/[1-(v^2)/(c^2)]^(1/2)
Some theories postulate space as a "surface" or manifold. Tangent vectors are also on the surface of space(intrinsically speaking of course). With a little imagination these tangent vectors can be visualized as two putative "bugs" crawling on the surface of a 2D coordinate plane.
............(B1)<---(origin)--->(B2).....(1)
.........(B1)<------(origin)------>(B2)..(2)
.......(B1)<--------(origin)-------->(B2).(3)
....(B1)<-----------(origin)----------->(B2).(4)
The smallest measurement of time that has any meaning is a unit of "Planck time".
(hG/c^5)^(1/2) A quantum of time.
The time axis is perpandicular to the space axis.
The origin is at rest with respect to B1 and B2.
B1 and B2 are moving at exactly the same speed because they have "inertia measurement devices" to adjust their rates of velocity accordingly, i.e. a "constant acceleration".
There seems to be an aspect to space that is "absolute", otherwise, why should our reference frame be the prefered rest frame?
Space is a conductor, more specifically, space is a conductor of electricity and magnetism, with permittivity "epsilon" and permeability "mu". The velocity of electromagnetism through the vacuum of space is "c" , approximately 3 x 10^8 meters per second. Using the letters "e" for permittivity and "u" for permeability the speed of light in the vacuum is:
c = 1/(eu)^(1/2)
Let Dx be an interval of displacement along a spatial axis.
Let Dt be an interval of "time".
Dx/Dt = c = 1/(eu)^(1/2)
Dx/Dt = 1/(eu)^(1/2)
(Dx)*(eu)^(1/2) = Dt
Since c is a constant, i.e. 1/eu , then Dx and Dt change in tandem, depending on the relative velocity of the observer.
Space is orthogonal to time.
"Although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough, if, using reason well, we were never deceived by it."
The Twins Paradox:
The twins paradox has to do with the theory of special relativity and the realization that there is no preferred frame of reference. All motion is relative or so it would seem. Take the classic example of the travelling passenger train and the railway station. As the train is moving at a constant speed past the railway station, it can justifiably be said that the train is at rest and the railway station is moving. Because the same laws of physics hold for both systems.
The twins paradox has to do with the fact that one twin remains on the earth, while the other twin hops on a rocket for a space journey at a significant fraction of the speed of light. According to relativity, an object moving close to the speed of light undergoes what is called "time dilation" with respect to an object at rest. So the twin in the rocket's frame of reference does not age as quickly as the twin back on earth. When the first sibling returns to earth, he or she will find the earth bound sibling walking around with a cane.
Since relativity states that no preferred frame of reference exists, why can't we say that the twin in the rocket is the one who is "at rest" and the twin back on earth is the one who is "moving"? This is what is known as the "Twins Paradox".
A solution:
(r1)<-----(origin)----->(r2)
Imagine not just twins, but triplets.
One sibling (s1) travels velocity (v1) in rocket one...(r1).
Another sibling (s2) travels velocity (v2) in rocket two...(r2).
The third sibling (s3) remains at the origin.
The rockets travel at exactly the same speed even during the inevitable "acceleration phase".
(r1)<-----(origin)----->(r2)
--------------|-------------
--------------|-------------
--------------|-------------
--------------|-------------
--------------|-------------
--------------|-------------
--------------v-------------
Initially r1,r2, and the origin were "at rest with respect to each other, or it could be said that they were all within the same inertial reference frame. The downward pointing arrow represents the time axis and as you can clearly see, time is perpendicular to space. The rockets launch.
Since both rockets are moving at exactly the same speed but in opposite directions, the reference point at the origin effectively cannot be in relative motion with respect to both (r1) and (r2) simultaneously. Because if we say the the origin is moving to the left with respect to (r2), that would contradict with the origin's motion to the right with respect to (r1). In effect, the point of origin must be at rest with respect to both (r1) and (r2). So the point of origin can be explained as being "at rest" with respect to the two rockets. The origin cannot be in motion to the left or the right. When the two siblings return from their adventure. They will find their twin at the origin much older than themselves according to the relativistic time dilation formula...
t = (t')/[1-(v^2)/(c^2)]^(1/2)
Some theories postulate space as a "surface" or manifold. Tangent vectors are also on the surface of space(intrinsically speaking of course). With a little imagination these tangent vectors can be visualized as two putative "bugs" crawling on the surface of a 2D coordinate plane.
............(B1)<---(origin)--->(B2).....(1)
.........(B1)<------(origin)------>(B2)..(2)
.......(B1)<--------(origin)-------->(B2).(3)
....(B1)<-----------(origin)----------->(B2).(4)
The smallest measurement of time that has any meaning is a unit of "Planck time".
(hG/c^5)^(1/2) A quantum of time.
The time axis is perpandicular to the space axis.
The origin is at rest with respect to B1 and B2.
B1 and B2 are moving at exactly the same speed because they have "inertia measurement devices" to adjust their rates of velocity accordingly, i.e. a "constant acceleration".
There seems to be an aspect to space that is "absolute", otherwise, why should our reference frame be the prefered rest frame?
Space is a conductor, more specifically, space is a conductor of electricity and magnetism, with permittivity "epsilon" and permeability "mu". The velocity of electromagnetism through the vacuum of space is "c" , approximately 3 x 10^8 meters per second. Using the letters "e" for permittivity and "u" for permeability the speed of light in the vacuum is:
c = 1/(eu)^(1/2)
Let Dx be an interval of displacement along a spatial axis.
Let Dt be an interval of "time".
Dx/Dt = c = 1/(eu)^(1/2)
Dx/Dt = 1/(eu)^(1/2)
(Dx)*(eu)^(1/2) = Dt
Since c is a constant, i.e. 1/eu , then Dx and Dt change in tandem, depending on the relative velocity of the observer.
Space is orthogonal to time.
