You can still log the hours...
errrm.....
How so? If, in a single pilot aircraft (which I am guessing this is what we're talking about) there is either crew or non-crew (i.e. Passengers!). The clue is in the title,
SINGLE pilot. The only time there is legally two 'crew' in a single pilot aircraft is when the person manipulating the controls is under instruction from an instructor. The instructor logs P1 the 'student' logs U/T. If you're a passenger then you could put the flight in a logbook to the record, but non of the totals/flight time would be eligible for inclusion in flight time totals.
There is discussion about AOC operators declaring multi-crew ops on SPA, but that is a whole different ball game.
As GTE says, any flight, legal or not has to have a commander - someone who will be responsible at all times (and carry the can) for the safe operation of the flight.