Kaluza–Klein theory is theory which uses 5th dimension to unite Gravity with Electromagnetism.
does this theory have any short fall or is it perfect?
If someone can help me with original article it would be nice of them.
Regards,
Bhushan Poojary
http://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory
There is indeed a problem with Kaluza-Klein theory as it is formulated (i.e. 4D space cross a circle). When one dimensionally reduces the theory to 4D, one indeed obtains General Relativity + EM, although the 5D theory has an instability in that the radius of the extra dimension is unstable: small fluctuations will cause it to pinch off or expand outwards. This is typically true of any compact extra dimensions and in order to stabilize them you need to introduce various fluxes, which requires adding other matter fields to the theory. If the goal is to get matter exclusively from geometry, then adding matter in order to stabilize the geometry runs counter to that goal.
What's more is that we now know that EM is unified with the weak nuclear force, so why should we be interested in unifying gravity only with EM and not with the electroweak force? At the time of Kaluza and Klein, the weak nuclear force was not very well understood and it was certainly not known that it and EM are different manifestations of a single force. Nevertheless, the idea is intriguing that the particles we know and love can be obtained from dimensional reduction of a higher dimensional theory.
Thank you Dear Henk,
Will read it and get back to you.
Regards,
Bhushan Poojary
There is indeed a problem with Kaluza-Klein theory as it is formulated (i.e. 4D space cross a circle). When one dimensionally reduces the theory to 4D, one indeed obtains General Relativity + EM, although the 5D theory has an instability in that the radius of the extra dimension is unstable: small fluctuations will cause it to pinch off or expand outwards. This is typically true of any compact extra dimensions and in order to stabilize them you need to introduce various fluxes, which requires adding other matter fields to the theory. If the goal is to get matter exclusively from geometry, then adding matter in order to stabilize the geometry runs counter to that goal.
What's more is that we now know that EM is unified with the weak nuclear force, so why should we be interested in unifying gravity only with EM and not with the electroweak force? At the time of Kaluza and Klein, the weak nuclear force was not very well understood and it was certainly not known that it and EM are different manifestations of a single force. Nevertheless, the idea is intriguing that the particles we know and love can be obtained from dimensional reduction of a higher dimensional theory.
Dear Bhushan Bhoja Poojary,
I would suggest to take a look also at another article coauthored by P.S. Wesson:
http://de.arxiv.org/abs/gr-qc/9805018
It is somewhat older, but it compares and contrasts the 3 major approaches to the KK theory.
Kaluza and Klein's approach has the shortcoming that it is classical and can't define a quantum field theory, absent a cutoff-so all physical effects depend on the details of the cutoff. There's a book on the subject,
T.~Appelquist, A.~Chodos and P.~G.~O.~Freund,
``Modern Kaluza-klein Theories,''
READING, USA: ADDISON-WESLEY (1987) 619 P. (FRONTIERS IN PHYSICS, 65)
along with many reviews available through online searching.
Yes, The book suggested by Stam Nicolis is the best source book. Personally, I find KK theories as providing the best possible avenues for unification, esp. the five-dimensional one.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Particle Physics