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Just saw the new Total Recall and experienced a moment of "How could they do that?" The premise of the movie indicates the entire world has been laid to waste except for the UK/Europe region and the Australian continent called the Colony. People commute between the two environments.

Let's assume between the two regions there are 250,000,000 people between the two sites with a smattering of robotic help, (robots were used primarily for security/police services). The tube could not possible go directly through the core of the Earth, so if they went around, that would make the trip at least 10,000 miles long. With 80% of the world's population deceased:

  • How in the world could they build the amazing transport system that moves underground from Europe to Australia, in less than 30 minutes?
  • Where could they get the raw materials?
  • Or is this whole scenario part of the dream sequence and we as the viewers simply have to accept the nature of this technology as part of the dream?

Intra-planetary Rail System

One end of the Intra-planetary Rail System


Total Recall

  • Starring Kate Beckinsale, Colin Farrell, Bryan Cranston, Jessica Biel, Bill Nighy and Ethan Hawke
  • Total Recall is a Science Fiction/Action/Adventure film directed by Len Wiseman, and written by Philip K. Dick, Kurt Wimmer, Mark Bomback and James Vanderbilt.
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Nitpick: Philip K. Dick didn't write Total Recall. He wrote the short story We Can Remember It For You Wholesale, and without having seen the movie yet, I can guess they didn't really use the plot implications from the short story (not that the previous movie did, either). –  Andres F. Aug 15 '12 at 4:35
    
I actually knew that. I was just trying to keep it simple. They did not use the story any better than the first movie did either. –  Thaddeus Aug 15 '12 at 9:16
    
I really don't think the spoiler field is needed for the plot summary, considering it's all described in the first thirty seconds of the movie. Spoiler is more for things that are unexpected/mysterious (like the ending to Sixth Sense), not for the basic plot of the entire movie. –  John C Feb 8 '13 at 12:52
    
When I wrote this question, the movie had just come out. So to prevent being castigated or censured, I simply used the spoiler protection. If it is being requested, I will remove it now. –  Thaddeus Feb 8 '13 at 19:33
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3 Answers 3

up vote 7 down vote accepted

Alrighty, I'm breaking out the back of the envelope for this one.

  • Assuming based on eyeballing the maps on Earth's wikipedia page that the chord connecting Europe and Australia is roughly the Earth's mean radius (6371.0 km). This an extremely rough estimate, but is probably in the right order of magnitude.
  • Assuming that the train is designed for maximum comfort, it will accelerate and decelerate at a constant rate. Therefore, to travel the distance in 30 minutes, it has to travel, from a standing start, halfway in 15 minutes. x = .5at^2, so 3,183,500 m = .5a(15 min * 60 sec / min)^2, so the acceleration is 7.86 m/s^2. Factor in gravity and you're up to a little less than 12.57 m/s^2.

.... that's not implausible at all! I'm actually a little surprised. For reference, gravity is 9.8 m/s^2. Pulling a little more than a G would still be comfortable. While you wont go down anywhere near where you'd not feel Earth's gravity, you could quite plausibly go down far enough that the total acceleration vector is less than 1 G.

Note that since the train will be inside the planet, its experienced gravity will be reduced. There might even be a point where it's so reduced that the train's main acceleration switches to coming to the back or front of the train (depending on whether it's accelerating or decelerating), more like an elevator, as opposed to the main acceleration being vertical (like surface trains).

As for how they would build it, a direct, well-reinforced tunnel would do very well. At less than 10 m/s^2, any modern fuel source (internal motors with external wires, gasoline, or even external magnets could do the trick). We can already make most of those things. It would be monstrously expensive and time consuming (it's predominantly under land, which is good, but the sheer size is daunting). Imagine Boston's Big Dig. Look how long that took. Now scale that up ... 1000x or so.

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There's no way I'm going to do the math any better than you, but note that the train would feel a net pull of gravity downward as long as it was still "near-ish" the surface, it would just be less than the pull at the surface. The acceleration due to gravity is >0, but decreasing, everywhere except the exact center of mass. –  Michael Edenfield Aug 15 '12 at 14:10
    
... did I write that? Goodness. You're absolutely right. It's a manifestly simple shape integral. :\ Thanks for keeping me honest, I'll go fix that. –  rsegal Aug 15 '12 at 17:10
    
Great thought about the calculation for travelling through the core of the earth. I liked the numbers, it gives me a clue for understanding better how fast physics work. ;-) So keep up the good posts! Cheers, pir8danou. –  user1601949 Aug 16 '12 at 0:56
    
As a back of the envelope assumption, using the chord connecting Australia and Europe is fine, and if you replace it with a curved path more or less following the surface of the Earth, you'll find that the acceleration is still quite reasonable (still on the order of 1/3 g). However, it's important to note that you would be approximately following the surface of the Earth, as our deepest digging project so far only takes us less than 7.7 miles below the surface. See en.wikipedia.org/wiki/Kola_Superdeep_Borehole –  Ben Hocking Aug 16 '12 at 1:48
    
Ah, but if you go straight through, gravity actually helps both your acceleration and deceleration, as opposed to merely holding you to a track. It may not be as cost-efficient on the digging step, but it's significantly cheaper on manufacturing and operating ends of it, which would probably make up it. Plus, we're talking about a society with the technology to put memories in a machine. Maybe the more-ideal solution is implausible for us - but it's not impossible. –  rsegal Aug 16 '12 at 3:43
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Whilst working at Eton College, I had the pleasure of attending many society debates concentrating on alternative energy. one posited idea was to drill a tunnel through the moon, line it with copper wire, and drop a giant magnet down one end. The magnet would fall through the tunnel, initially accelerating towards terminal velocity, and with its inertia carrying it through the core where it is effectively weightless. As the magnet approached the other side, it would slow down due to gravity pulling it from behind.

if the tunnel is a complete vacuum with no air resistance, the magnet should emerge on the other side, completing the journey with the exact amount of inertia it began with. allowing this magnet to fall back into the hole would start it all again and if left undisturbed, would continue to journey though the hole back and forth, creating a current through the copper wire and hey presto, we have power.

I'm not supposing that this hypothetic could actually ever be accomplished, but as a thought experiment it was entertaining.

The moon is a dead celestial body. the Earth on the other hand is very much alive. Unless the tunnel is dug through the earth at True celestial north, the axial rotation of the planet could make it difficult. that's of course after you've figured out a way to dig through the crust, through thousands of km of molten rock (churning away at thousands of Kelvin with thousands of atmospheres of pressure) through an outer core of liquid iron and nickel, and finally a superdense inner core composed of crystaline Iron which is rotating and oscillating. Then theres the issue of tectonic shift....

HOWEVER. They managed it in that film 'The core' with nothing but a giant LED torch so you never know....

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Slightly aside from the main question, but the field generated in the fall through the wire coils would provide resistance on the magnet, preventing it from oscillating long enough to generate much power. If you take the power generated and compare it to the power used getting the magnet back to the surface to do it again, you should have a net loss... –  Izkata Dec 5 '12 at 0:07
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Assuming you can dig a hole through or nearly through the center of the earth (as it appears in the film) and re-enforce the sides, while ignoring the affects of tectonic plates moving around amongst other things as mentioned in other answers, dropping something through this hole (I.E. the drop train in the film) would take about 37 minutes to reach the other side if there was no air resistance, meaning that it would be reasonably easy to accelerate for the first half and decelerate on the way out a little faster to make the journey in 30 minutes. However as the train would be accelerating at somewhere in the region of 9.8 m/s^2 the people inside would independently be accelerating at the same speed (or slightly slower if we want to make the journey in 30 minutes) they would thus, feel weightless (or be pushed against to roof of the train) for the entire journey, as everything around them would be falling at the same speed as they would independently. however in the film they are depicted as only being weightless when passing the earth's core. thus even assuming man had the ability to build the tunnel and train it would not work as shown in the film.

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