Question: Were people able to "lock" the Holodeck doors so that others couldn't just walk in on them? I don't recall an episode where the doors were locked that wasn't because of some malfunction. It seems like Lieutenant Barclay, for example, would either lock the doors during his "fantasies" or have some "fail-safe" that shuts the program off when being walked in on. Otherwise, it's just a really dumb thing to do (for him or anyone playing out a fantasy) knowing they could easily be caught.
Answer: Yes. The doors to the holodecks can be locked when in use by anyone aboard the Enterprise so they couldn't be disturbed. However, high ranking officers like Captain Picard could override the doors as it's seen that overrides are in use even for the crews quarters. Even Barclay, when he's indulging in one of his fantasies could have the doors to the holodeck unlocked by an override code.
Answer: Prior to the supernova, English script "three point eight billion kilometers", German script "3.8 Milliarden km" speed of light in vacuum c = 299,792,458 m/s 3.8 billion km = 3,800,000,000 km = 3,800,000,000,000 m (3,800 = 3.8 thousand, 3,800,000 = 3.8 million, 3,800,000,000 = 3.8 billion) in physics formula c represents speed aka. Velocity = v, s means distance (abbreviation not known to me), t = time v = s/t v * t = s t = s/v v = 299,792,458 m/s s = 3,800,000,000,000 m 3,800,000,000,000 m / 299,792,458 m/s = 12,675.435617529778 s = 3.5 hours The impression in the scene could be convincing of 1-5 minutes prior to seeing the supernova, and not 3.5 hours. I would argue in order to give them the benefit of the doubt they would have to be either less specific about the distance travelled or more respectful of c. The movement of the spaceship aka. Matter in this case being faster than c is implied to be part of the fictional part of sci-fi and not a logical oversight on my end. c is constant.
Sorry, this was meant as "mistake" under episode "Tin Man." Not familiar with the buttons here.