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Loading...to completely define the reality of our universe?
Einstein was able to define the relativistic properties of motion and the equivalence of gravitational and accelerated reference frames in terms of the geometry of space-time. However, as Lee Smolin mentions in Chapter Three (page 49) of his book "The Trouble with Physics" he was unable to physically connect them to electromagnetic energy.
Einstein himself acknowledges this when he said, "I have often tortured my mind in order to bridge the gap between gravitation and electromagnetism.”
One of the reasons may be because he and many other physicists defined electromagnetism in terms of a transverse wave while defining gravity in terms of a time component of a space-time dimension. However, time is observed to move only in one direction forward therefore it cannot support the bi-directional spatial properties of the transverse wave associated with electromagnetism. Therefore, it was not possible to define a physical connection between them because they were based on different aspects of the environment.
But as Lee Smolin also mentions (page 39) Gunnar Nordstrom discovered electromagnetism "pops out" of Einstein’s theory if one increases the dimensions of space by one. In other words, just by adding an extra dimension of space you get a unification of gravity with electromagnetism that was consistent with Einstein’s Special Theory of Relativity."
However, Einstein’s theories predicted that light would be bent by gravity while Nordstrom’s did not.
In 1919, Arthur Eddinngton observed that light was bent by gravity thereby verifying that Einstein’s theory was more consistent with observations and that gravity was not the result of an extra dimension as Nordstrom had postulated.
Since then there have been many attempts to unite gravity with electromagnetism simply by adding dimensions to Einstein’s space-time manifold.
The most promising of these is called string theory, which attempts to define all of the observed properties of our universe in terms of as many as ten dimensions.
However, as is pointed out on page 51 of "The Trouble with Physics" all attempts at unifying physics through extra dimensions suffer from the same problem. There are a few solutions that lead to the world we observe but there are many which do not. One has to set the initial conditions, which are found by observing our world to determine which solutions define what we observe. The use of the circular methodology means its validity is not based on its theoretical structure but on its flexibility.
But it may be possible to develop a theoretical connection between electromagnetism, gravity and its equivalence to accelerated reference frames if instead of adding a spatial dimension as Nordstrom did to Einstein’s space-time we replace its time component with a spatial one.
In the article "The Equivalence Principal: an alternative" July 15 2008 it was shown the observed properties of gravity and its equivalence to an accelerated reference frame can be derived in terms of a curvature in a "surface" of a three-dimensional space manifold with respect to a fourth *spatial* dimension as well as a curvature a space-time manifold as is suggested by Einstein’s theories.
Additionally the article "The "relativity" of four spatial dimensions" Dec 2007 showed one can derive a mechanism responsible for the relativistic properties of motion, space, and time in terms of the existence of four *spatial* dimensions that is consistent with Einstein’s Special Theory of Relativity.
While the article "The Photon: a matter wave?" Oct. 1 2007 showed one could derive the particle, wave and electromagnetic properties of light in terms of oscillations or spatial displacements in a "surface" of a three-dimensional space manifold with respect to fourth *spatial* dimension.
This suggests that assuming the universe is composed of four *spatial* dimensions instead of four dimensional space-time may allow one to theoretically "bridge the gap between gravitation and electromagnetism" because it may enable one to define a common mechanism responsible for their properties.
Additionally, if one can derive gravity in terms of a spatial curvature in a "surface" of a three-dimensional manifold with respect to a four *spatial* dimension and electromagnetism in terms of oscillations in that "surface" means it would be bent by gravity for the same reason it would be if it existed in Einstein’s space-time maniflod.
This means one may not have to increase number of spatial dimensions "in order to bridge the gap between gravity and electromagnetism" as Nordstrom did because it would be an integral part of the theoretical structure presented in The Imagineer’s Chronicles, whereas it would not be part of one based on Einstein’s space-time theories.
Therefore, the answer to the question as to "How many dimensions do we need to completely define the reality of our universe?" may be four.
Later Jeff
The "Shadows" of four spatial dimensions
Copyright Jeffrey O’Callaghan 2009
Good post! I am a college sophomore with a dual major in Physics and Mathematics @ University of Canterbury in Christchurch, New Zealand. I read about String Theory back in my high school. Enjoyed it!