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Spinnor
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Should one be able to take the results of 5D Kaluza-Klein theory and turn it into a theory that works with two less space dimensions?
Thanks!
Thanks!
Orodruin said:It is unclear what you are asking. The entire point of KK theory is to have more than four space-time dimensions.
Orodruin said:You will have to be more precise. FWhat do you mean by "work"?
Well, it's not that GR is 'boring' in 2D, it is simply not defined because the Einstein eqns are identities. So what people try to do (at least, what I know of), is to describe gravity by a scalar field (dilatonic gravity). The reason is that if you fix your 2 diffeomorphisms in two dimensions, a metric has 1/2*2*(2+1) - 2= 1 degree of freedom. But if I were you, I would carry out the compactification explicitly and see what you get :) There are several interestic geometric identities in 2 and 3 dimensions, and I'm not sure how these mix up with compactification.Spinnor said:I guess GR is maybe boring with one space and one time dimension? Here I'm thinking we have one large space dimension and one compact space dimension in addition to time. I was hoping that KK theory could be simplified so that I might better understand the geometrical aspect of electrodynamics in lower dimensions.
Thanks!
Actually, that's an interesting question, because GR in D=3 doesn't have gravitational waves with the Einstein eqn's; the Riemann tensor is completely fixed by the Ricci tensor and the metric. So the question is how that translates itself into the electrodynamics.Spinnor said:It should reproduce classical electrodynamics of one space and one time dimension by proper interpretation of an additional compact dimension.
Kaluza-Klein Theory in 2D Space-Time is a mathematical model that attempts to unify the fundamental forces of nature by including an extra dimension of space. It was first proposed by Theodor Kaluza and Oskar Klein in the 1920s.
Kaluza-Klein Theory proposes that the extra dimension is a circular, compactified dimension that is too small for us to observe directly. It is only apparent at the subatomic level and plays a role in the unification of the fundamental forces.
The implications of Kaluza-Klein Theory are far-reaching and have led to advancements in our understanding of particle physics and cosmology. It suggests that the four known fundamental forces - gravity, electromagnetism, strong nuclear force, and weak nuclear force - are all different manifestations of a single unified force.
Kaluza-Klein Theory and string theory are both attempts at unifying the fundamental forces of nature. However, string theory goes a step further by proposing that the extra dimension is not just a mathematical construct, but an actual physical dimension made up of tiny strings.
While there is no direct evidence for Kaluza-Klein Theory, it has inspired many other theories and has played a significant role in the development of modern physics. Some of its predictions, such as the existence of extra dimensions, have been explored in experiments at the Large Hadron Collider. However, further research and experiments are needed to fully test and validate this theory.