Difference between deterministic and nondeterministic universal turing machine It is known that a nondeterministic universal turing machine (UTM) can simulate another nondeterministic TM with running time $t(n)$ in time $c t(n)$, where $c$ is a constant. It is also known that a deterministic UTM can simulate another deterministic TM with running time $t(n)$ in time $ t(n)\log(t(n))$. 

My question is: why is there a $\log(t(n))$ slowdown in the simulation of a deterministic TM by a UTM, as opposed to a constant factor slowdown in the nondeterministic case?
Please refer to the answer in the similar question, "Why is simulation by non deterministic Turing machine faster than a deterministic one?".

Basically, in the non-deterministic universal Turing machine we guess the contents of the tape and check if the guess is correct later on. This allows us to save time going to and fro in the work tape.