  The usual approach to Kaluza-Klein considers a spacetime of the form $M_4
\times K$ and identifies the isometry group of the internal vacuum metric,
$g_K^0$, with the gauge group in four dimensions. In these notes we discuss a
variant approach where part of the gauge group does not come from full
isometries of $g_K^0$, but instead comes from weaker internal symmetries that
only preserve the Einstein-Hilbert action on $K$. Then the weaker symmetries
are spontaneously broken by the choice of vacuum metric and generate massive
gauge bosons within the Kaluza-Klein framework, with no need to introduce ad
hoc Higgs fields. Using the language of Riemannian submersions, the classical
mass of a gauge boson is calculated in terms of the Lie derivatives of $g_K^0$.
These massive bosons can be arbitrarily light and seem able to evade the
standard no-go arguments against chiral fermionic interactions in Kaluza-Klein.
As a second main theme, we also question the traditional assumption of a
Kaluza-Klein vacuum represented by a product Einstein metric. This should not
be true when that metric is unstable. In fact, we argue that the unravelling of
the Einstein metric along certain instabilities is a desirable feature of the
model, since it generates inflation and allows some metric components to change
length scale. In the case of the Lie group $K = SU(3)$, the unravelling of the
bi-invariant metric along an unstable perturbation also breaks the isometry
group from $( SU(3) \times SU(3)) / Z_3$ down to $( SU(3) \times SU(2) \times
U(1) )/ Z_6$, the gauge group of the Standard Model. We briefly discuss
possible ways to stabilize the internal metric after that first symmetry
breaking and produce an electroweak symmetry breaking at a different mass
scale.
