On the airplane home from Spitzer Science Center and LIGO I made the mistake of watching the new Total Recall (2012 remake
). (I also made the good decision to watch Men in Black 3 but that is not relevant to this post.) Central to the story is a tunnel through the Earth through which a train called The Fall
goes from Britain to Australia in 17 minutes. Important to the plot is a gravity reversal
on the journey in the core of the Earth, where the riders on The Fall are briefly weightless, and their chairs rotate from one orientation to the opposite so they are reoriented for arrival.
As everyone in first-year physics (well, for Physics Majors anyway) ought to calculate, the no-air-resistance, free-fall time for this journey (indeed on any straight chord through the Earth) is about 45 minutes (yes, identical to the time to go half-way around the Earth ballistically). That means that if riders were weightless for the entire journey the crossing would take 45 minutes.
The fact that The Fall does the journey faster than that would mean not one gravity reversal but three gravity reversals, because you would have to start the journey accelerating faster than gravity, and end the same. So the whole thing, which was obviously so highly thought out and worked out for the story, was just straight-up wrong.
I think if we ever do dig a chord-like tunnel through the Earth (the Chunnel is getting close to the relevant scale), we probably should run the trips at 45 minutes, because I think for pretty deep reasons this will be very close to minimum-effort travel times. In thinking about this, I have also thought about the relevant engineering gains and safety losses incurred if the Chunnel were operated evacuated of air or at low pressure. There were also idiotic things in the movie related to the implied air pressure, temperature, and air flow in the tunnel outside The Fall but these are more subtle. I digress.
Actually, the excellent MIB3 was even more physically unrealistic than Total Recall (bad time travel and so on), but the tone of the movie made it absolutely clear that you were expected to cut them physics slack.
