Wednesday, January 18, 2012

A Historical Look at Kaluza-Klein Particles?

In 1919, Kaluza sent Albert Einstein a preprint --- later published in 1921 --- that considered the extension of general relativity to five dimensions. He assumed that the 5-dimensional field equations were simply the higher-dimensional version of the vacuum Einstein equation, and that all the metric components were independent of the fifth coordinate. The later assumption came to be known as the cylinder condition. This resulted in something remarkable: the fifteen higher-dimension field equations naturally broke into a set of ten formulae governing a tensor field representing gravity, four describing a vector field representing electromagnetism, and one wave equation for a scalar field. Furthermore, if the scalar field was constant, the vector field equations were just Maxwell's equations in vacuo, and the tensor field equations were the 4-dimensional Einstein field equations sourced by an EM field. In one fell swoop, Kaluza had written down a single covariant field theory in five dimensions that yielded the four dimensional theories of general relativity and electromagnetism. Naturally, Einstein was very interested in this preprint (Link is now dead but what is said here is very important and may help with imagery needed?)


After having formulated general relativity Albert Einstein did not immediately focus on the unification of electromagnetism and gravity in a classical field theory - the issue that would characterize much of his later work. It was still an open question to him whether relativity and electrodynamics together would cast light on the problem of the structure of matter [?]. Rather, in a 1916 paper on gravitational waves he anticipated a different development: since the electron in its atomic orbit would radiate gravitationally, something that cannot occur in reality", he expected quantum theory would have to change not only the "Maxwellian electrodynamics, but also the new theory of gravitation" [?]2. Einstein's position, however, gradually changed. From about 1919 onwards, he took a strong interest in the unification programme3. In later years, after about 1926, he hoped that he would and a particular classical unified field theory that could undercut quantum theory. Such a theory would have to contain the material objects -sources and fields- and their dynamics. He would even expect the distinction between these concepts to fade: \a complete field theory knows only fields and not the concepts of particle and motion" [?]. We will study how he wanted to realize these principles in classical Kaluza-Klein theory, and try to see what his objectives and results were.See: Einstein and the Kaluza-Klein particle

moving on further in the article toward the end...

Bergmann, now in Syracuse, wrote Einstein and asked if they could have a discussion sometime:

As anyone can only be a crank about his own ideas, and as you are someone who combines steadfastness with the ability to acknowledge his hypothesis could go wrong (usually one can only and just one of these qualities, mostly the latter) I would appreciate very much talking to you and hearing your observations; whether we appreciate the same or not, what we want is sufficiently related that we could easily come to an understanding." [?] 2

Einstein replies:
You are looking for an independent and new way to solve the fundamental problems. With this endeavor no one can help you, least of all someone who has somewhat fixed ideas. For instance, you know that on the basis of certain considerations I am convinced that the probability concept should not be primarily included in the description of reality, whereas you seem to believe that one should first formulate a field theory and subsequently 'quantize' it. This is in keeping with the view of most contemporaries. Your effort to abstractly carry through a field theory without having at your disposal the formal nature of the field quantities in advance, does not seem favorable to me, for it is formally too poor and vague."17 [?] 2


Missing Energy Kicks New Physics Models Off The Board

The signature of large missing energy and jets is arguably one of the most important avenues for the study of potential new physics signatures at today's hadron colliders.

The above concept marks an interesting turn of events: the years of the glorification of charged leptons as the single most important tools for the discovery of rare production processes appears behind us. The W and Z discovery in 1983 by UA1 at CERN, or the top quark discovery by CDF and DZERO in 1995 at Fermilab, would have been impossible without the precise and clean detection of electrons and muons. However, with time we have understood that missing energy may be a more powerful tool for new discoveries.

Missing energy arises when a violent collision between the projectiles -protons against antiprotons at the Tevatron collider, or protons against protons at the world's most powerful accelerator, the LHC- produces an asymmetric flow of energetic bodies out of the collision point in the plane orthogonal to the beams: a transverse imbalance. This is a clear signal that something is leaving the detector unseen. And it turns out that there is a host of new physics signals which can do precisely that.

A large amount of missing transverse energy may be the result of the decay of a leptoquarks into jets and neutrinos, when the latter leave undetected; or from the silent escape of a supersymmetric neutral particle -the neutralino- produced in the chain of decays following the production of squarks and gluinos; or it may even be due to the escape of particles in a fourth dimension of space -an alternative dubbed "large extra dimensions".
(see more in linked title above)

I have been slowly moving through the explanations for the extra-dimensions that are being explained by Matt Strassler:

In this article and the next, we will learn why extra dimensions lead to “Kaluza-Klein (KK) partner” particles (described in the previous article in this series, which you should read before this one.)  If a known type of  particle of mass m can travel in a dimension of which we are unaware — an “extra” dimension — then we will eventually discover many other types of particles, similar to the known one but heavier, with masses M>m.
See: Kaluza-Klein Partners — Why? Step 1

No comments:

Post a Comment