I take the fact that you believe cash can't be double-spent in the past as strong evidence you don't own a working time machine.
That's why I said not enough, dah? 
Everything can be double-spent, but I'd prefer be double-spent on cash rather than on bitcoin. It'd ruin its purpose.
So this is another problem double-spend creates, which prevents us from time travelling. I think we should wait for a peer-to-peer time-travelling based e-cash that would prevent it.
(I personally don't mind if there's a third party or not)