String theories seem to required many additional dimensions.
How can this possibly relate to our 4-d reality.
T. Kaluza and by O. Klein (1920's) introduced the idea that our universe might have more than the three familiar spatial dimensions
Introduced more than half a century before the advent of string theory .
The basic premise of such Kaluza-Klein theories is that a dimension can be either large and directly observable or small and essentially invisible.
An analogy with a garden hose can be helpful
two extended dimensions and two compactified dimensions
T. Kaluza and by O. Klein (1920's) introduced the idea that our universe might have more than the three familiar spatial dimensions
Introduced more than half a century before the advent of string theory .
The basic premise of such Kaluza-Klein theories is that a dimension can be either large and directly observable or small and essentially invisible.
An analogy with a garden hose can be helpful
two extended dimensions and two compactified dimensionsFor string thoery the familiar 3 -spatial dimensions are
revealed when six of the dimensions are compactified on a particular manifold
The manifold is called a Calabi--Yau manifold
and Now
The manifold is called a Calabi--Yau manifold