While Dyneema is in use for cordelettes for quite some time manufacturers started bringing long ropes made of dyneema on the market. The benefits are obvious: Less weight, less volume and no water absorption. The big difference: The rope is static so it does not stretch and take up energy in case of a fall. This makes it unsuitable for climbing. So I am thinking glacier tours and ski touring.

How does the dyneema rope being static influence the ability to stop a fall into a crevasse? 

If as a consequence the same procedure as for dynamic ropes cannot be applied: Is there a method so that static ropes are save to use in this scenario?

Are there any other factors to consider when using dyneema ropes on glaciers?

Clarification on the material:  

Dyneema is a Ultra-high-molecular-weight polyethylene (UHMWPE, UHMW), also known as high-modulus polyethylene (HMPE), or high-performance polyethylene (HPPE). Spectra is the same material. From my web search it looks like dyneema is more commonly used in Europe and spectra in the US.