03-28-2016, 11:13 PM
Now let's look into why the speed of light is not the limit of how fast an object can travel. First, let's review why we currently believe that nothing can travel faster than the speed of light.
Special Theory of Relativity Re-examined -- Part 1
The speed of light, c, as the upper limit for the speed of travel arises from the Einstein's Special Theory of Relativity. The Special Theory of Relativity is essentially an interpretation (currently the most accepted one) of the Lorentz transformation of Maxwell's Field Equations. Maxwell's Field Equations (MFEs) are four equations that define the laws of electromagnetism. Since it is assumed that laws of physics remain the same whether a body is at rest or in motion -- this is called the Principle of Relativity -- people were surprised to find that Galilean transformation (https://en.wikipedia.org/wiki/Galilean_transformation), which had worked well with Newtonian mechanics and laws, cannot transform MFEs correctly. Instead, MFEs must be transformed with a type of transformation called the Lorentz transformation (https://en.wikipedia.org/wiki/Lorentz_transformation) for the Principle of Relativity to hold. The mathematical form of Lorentz transformation was know without the precisely defined coefficients before the Theory of Relativity.
Many physicists had tried to explain why MFEs need to be transformed by Lorentz transformation. Einstein approached it this way: he started with two simply assumptions: 1) that the Principle of Relativity must hold everywhere, and 2) that the speed of light is the same/invariant in all reference frames (i.e. the speed of light is measured to be the same regardless whether something is moving or stationary). The first assumption is a widely accepted principle, and the second assumption is an assertion, something that is assumed without proof or explanation as to why. With these two assumptions, Einstein was able to derive the Lorentz transformation with mathematically defined coefficients. It is then assumed that because Lorentz transformation is correctly derived, then the assertion (that the speed of light is invariant in all reference frames) and subsequent transformation formula must be correct. The interpretations/implications of Einstein's derivation of Lorentz transformation are collectively called the Special Theory of Relativity. Some of the implications include that not only space (e.g. spacial coordinates) but also time is changed in the transformation, resulting length contraction and time dilation when something is travelling at closer to speed of light; that time is inseparable from space in defining physical laws, thus the term spacetime.
The denominator of the scale factor in the Lorentz transformation derived by Einstein is sqrt(1-v^2/c^2), where c is the speed of light and v is the speed of travel of the moving object/reference frame. Since for the formulation to be meaningful, v cannot be equal to c for that would result in a zero in the denominator, and v cannot be greater than c for it would result in square root of a negative number, therefore, the conclusion is that v cannot be greater than c, thus the implication that nothing can travel faster than the speed of light. Another important implication of SR is the mass-energy equivalence equation E=mc^2. I consider it to be the only verifiable implication of SR, which unfortunately also brought in the terror of nuclear weapons to the mankind. Despite some difficult-to-acceptable implications, such as that time runs at a different rate when something is moving at a very high speed, and that there is no such thing as simultaneity, SR has become widely accepted. Questions about the theory, from its derivation to its implications have always existed, but were mostly ignored by the mainstream scientific community. Some of the problems with SR can be found here: http://www.physicsmyths.org.uk/#specrel
What I have come to understand is that while Einstein's assumptions, derivation and result are mathematically correct, their interpretations are not. This is largely because SR, unlike Newtonian physics laws, is not derived from physical observations, but purely from mathematical formulations. Secondly, at the time of development of SR, we have not made many observations into 4D phenomena to consider its existence. While we hold the math to be true, we have not fully understand its physical implications. Starting with Einstein's assertion regarding the speed of light, c, the error with this assumption is not that c is invariant but that c is the speed of light. My understanding is: c is not a speed, it defines the geometric property of light that corresponds to speed in certain cases. This will be examined in detail later.
My research has shown that the reason MFEs need to be transformed with Lorentz transformation is the result of the 4 dimensional nature of our space and the dynamics of our 3D environment within the 4D space.
Firstly, while SR concluded that time is also relative just like spacial coordinates, thus broke all our previous notion of simultaneity and such, we have failed to realize it simply means that the time we used in defining Lorentz transformation is not time as we believed it to be, but (another dimension of) space. There is no 4D spacetime, but 4D space and time.
When I say that we have misinterpreted space as time, I meant it this way: there is nothing wrong with our concept of time, the problem arises from how we measure it. Consider this hypothesis: we measure time through changes observed, and ultimately, we measure change of time by through our change in space. Specifically, these changes are related to the changes in position in the 4th dimension, the dimension that we do not experience with our senses. Everything on earth, regardless whether they are moving or staying at different 3D locations, share the same location in the 4th dimension, or that their relative location in the 4th dimension does not change. At the same time, everything on earth are also moving at a constant rate in the 4th D together, therefore everything experience the same consistent changes in the 4th D at the same rate. Therefore we had no problem measuring time this way: as we know, Newtonian physics works.
However, when we looking into thing that very large (cosmic scale) or very small (quantum scale), we start observing observing things that located at different 4D positions and changing at different rate in the 4D. MFEs which defines electromagnetism are laws arise from interactions of particles (electrons, etc.) at the atomic level that manifested on the Newtonian scale. They open the insight into interactions of objects that are located in different 4D positions where the rate of change in the 4th D will no longer be consistent for all. Therefore, understanding the Lorentz transformation of MFEs will help us further understand the 4 dimensional nature of space and our relationship to it.
p.s.
per my understanding stated above, I felt validation when I saw Ra's use of "/" in time/space, space/time. To me, Ra uses the "/" when stating something that's the same but viewed from different perspectives, such as love/light. For I already understood what we perceive as time is actually space, so what Ra refers as space/time, I understand it meaning the 3D space/reality that we perceive; and time/space refers to the space/reality beyond 3D that we currently understand as time.
Special Theory of Relativity Re-examined -- Part 1
The speed of light, c, as the upper limit for the speed of travel arises from the Einstein's Special Theory of Relativity. The Special Theory of Relativity is essentially an interpretation (currently the most accepted one) of the Lorentz transformation of Maxwell's Field Equations. Maxwell's Field Equations (MFEs) are four equations that define the laws of electromagnetism. Since it is assumed that laws of physics remain the same whether a body is at rest or in motion -- this is called the Principle of Relativity -- people were surprised to find that Galilean transformation (https://en.wikipedia.org/wiki/Galilean_transformation), which had worked well with Newtonian mechanics and laws, cannot transform MFEs correctly. Instead, MFEs must be transformed with a type of transformation called the Lorentz transformation (https://en.wikipedia.org/wiki/Lorentz_transformation) for the Principle of Relativity to hold. The mathematical form of Lorentz transformation was know without the precisely defined coefficients before the Theory of Relativity.
Many physicists had tried to explain why MFEs need to be transformed by Lorentz transformation. Einstein approached it this way: he started with two simply assumptions: 1) that the Principle of Relativity must hold everywhere, and 2) that the speed of light is the same/invariant in all reference frames (i.e. the speed of light is measured to be the same regardless whether something is moving or stationary). The first assumption is a widely accepted principle, and the second assumption is an assertion, something that is assumed without proof or explanation as to why. With these two assumptions, Einstein was able to derive the Lorentz transformation with mathematically defined coefficients. It is then assumed that because Lorentz transformation is correctly derived, then the assertion (that the speed of light is invariant in all reference frames) and subsequent transformation formula must be correct. The interpretations/implications of Einstein's derivation of Lorentz transformation are collectively called the Special Theory of Relativity. Some of the implications include that not only space (e.g. spacial coordinates) but also time is changed in the transformation, resulting length contraction and time dilation when something is travelling at closer to speed of light; that time is inseparable from space in defining physical laws, thus the term spacetime.
The denominator of the scale factor in the Lorentz transformation derived by Einstein is sqrt(1-v^2/c^2), where c is the speed of light and v is the speed of travel of the moving object/reference frame. Since for the formulation to be meaningful, v cannot be equal to c for that would result in a zero in the denominator, and v cannot be greater than c for it would result in square root of a negative number, therefore, the conclusion is that v cannot be greater than c, thus the implication that nothing can travel faster than the speed of light. Another important implication of SR is the mass-energy equivalence equation E=mc^2. I consider it to be the only verifiable implication of SR, which unfortunately also brought in the terror of nuclear weapons to the mankind. Despite some difficult-to-acceptable implications, such as that time runs at a different rate when something is moving at a very high speed, and that there is no such thing as simultaneity, SR has become widely accepted. Questions about the theory, from its derivation to its implications have always existed, but were mostly ignored by the mainstream scientific community. Some of the problems with SR can be found here: http://www.physicsmyths.org.uk/#specrel
What I have come to understand is that while Einstein's assumptions, derivation and result are mathematically correct, their interpretations are not. This is largely because SR, unlike Newtonian physics laws, is not derived from physical observations, but purely from mathematical formulations. Secondly, at the time of development of SR, we have not made many observations into 4D phenomena to consider its existence. While we hold the math to be true, we have not fully understand its physical implications. Starting with Einstein's assertion regarding the speed of light, c, the error with this assumption is not that c is invariant but that c is the speed of light. My understanding is: c is not a speed, it defines the geometric property of light that corresponds to speed in certain cases. This will be examined in detail later.
My research has shown that the reason MFEs need to be transformed with Lorentz transformation is the result of the 4 dimensional nature of our space and the dynamics of our 3D environment within the 4D space.
Firstly, while SR concluded that time is also relative just like spacial coordinates, thus broke all our previous notion of simultaneity and such, we have failed to realize it simply means that the time we used in defining Lorentz transformation is not time as we believed it to be, but (another dimension of) space. There is no 4D spacetime, but 4D space and time.
When I say that we have misinterpreted space as time, I meant it this way: there is nothing wrong with our concept of time, the problem arises from how we measure it. Consider this hypothesis: we measure time through changes observed, and ultimately, we measure change of time by through our change in space. Specifically, these changes are related to the changes in position in the 4th dimension, the dimension that we do not experience with our senses. Everything on earth, regardless whether they are moving or staying at different 3D locations, share the same location in the 4th dimension, or that their relative location in the 4th dimension does not change. At the same time, everything on earth are also moving at a constant rate in the 4th D together, therefore everything experience the same consistent changes in the 4th D at the same rate. Therefore we had no problem measuring time this way: as we know, Newtonian physics works.
However, when we looking into thing that very large (cosmic scale) or very small (quantum scale), we start observing observing things that located at different 4D positions and changing at different rate in the 4D. MFEs which defines electromagnetism are laws arise from interactions of particles (electrons, etc.) at the atomic level that manifested on the Newtonian scale. They open the insight into interactions of objects that are located in different 4D positions where the rate of change in the 4th D will no longer be consistent for all. Therefore, understanding the Lorentz transformation of MFEs will help us further understand the 4 dimensional nature of space and our relationship to it.
p.s.
per my understanding stated above, I felt validation when I saw Ra's use of "/" in time/space, space/time. To me, Ra uses the "/" when stating something that's the same but viewed from different perspectives, such as love/light. For I already understood what we perceive as time is actually space, so what Ra refers as space/time, I understand it meaning the 3D space/reality that we perceive; and time/space refers to the space/reality beyond 3D that we currently understand as time.
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