Looper: Questions about Time, Energy, and Power

Last weekend, Looper came out in theaters, bringing time travel back to the big screen. But there are lot of questions that can be asked about the science of the world it portrays. We will visit some minor spoilers along the way, so you may want to wait to read this post until you see the movie. In addition to time travel, Looper depicts widespread solar power and almost ubiquitous telekinesis. What can Wolfram|Alpha tell us about this and other aspects of the film?

Let’s start with time travel. Bruce Willis, who plays the older version of the main character, Joe, is no stranger to science fiction (especially time travel, as the film 12 Monkeys attests). Wolfram|Alpha can give us details on much of time-travel fiction, from the novel The Time Machine to the film Primer, whose director was involved in the design of the effects of Looper. It can also tell us about real (forward) time travel in the form of time dilation, which involves moving at speeds close to the speed of light.

We have seen many different versions of time travel in popular culture, from vehicles such as the TARDIS to mental transfer, as in Quantum Leap. The method used in Looper is straightforward teleportation, where someone from the future just suddenly appears in the middle of a cornfield. In this regard, it is similar to the Terminator series (complete with a would-be assassin from the future)… except with clothing as an option. But what does it mean for an object the size of a person to suddenly appear?

Well, first, that mass needs to come from somewhere. Physics tells us that energy must be conserved. Since mass is made up of energy, we might conclude this is something like the Star Trek universe’s teleporter, where a person is broken up into energy and then reconstituted elsewhere (or in this case, elsewhen). So, how much energy is in a person?

Wolfram|Alpha tells us the mean human mass is 70 kg. The relativistic total energy of 70 kg is 6.291 x 10^18 joules. This is equivalent to 1,500 megatons of TNT or 47% of the total yearly electrical energy production of the United States (as of 2001). By way of comparison, Tsar Bomba, the largest nuclear device ever detonated, was a mere 58 megatons of TNT. Obviously we want Joe to arrive as matter and not the world’s largest nuclear explosion. Even a 20-megaton nuclear explosion blast radius will kill everything in a 4.6 mile radius and devastate structures within 12 miles:

Of course, he doesn’t have to become pure energy. What if his atoms just flew apart? Well, the number of atoms in a human is about 7 x 10^27, or 11,624 moles. Assuming the binding energy is on the order of the carbon hydrogen bond strength, or 411 kilojoules per mole, we find if that energy was released at once, it would be 4.777 gigajoules, or the energy of 1.142 tons of TNT. So only the cornfield is destroyed.

In comparison, Back to the Future‘s flux capacitor power requirements are relatively modest: 1.21 gigawatts, or 1/10 of the energy needed to launch the Space Shuttle.

Moving away from science fiction, we might ask how the older and younger versions of the main character of Joe compare. We can compare the actors playing them—Joseph Gordon-Levitt versus Bruce Willis—to see how closely they resemble each other and the characters. From this we can see that Bruce Willis is, in fact, about 26 years older than Joseph Gordon-Levitt, which resembles the 30-year gap shown in the film. Of course, Bruce Willis, playing older Joe, is also about five cm, or about two inches, taller, which is something the film works to hide:

One thing that struck me was the widespread usage of solar power in the film. It seems like every home and car in 2044 is covered in solar panels. But how much energy can be extracted from sunlight? Well, the mean solar irradiance is 340.2 W/m^2. The surface area of a car can vary greatly, but let’s presume we can get at least 5 feet by 12 feet of coverage on average. 340.2 W/m^2 times 5 ft by 12 ft is 1896.3 watts, or about 2.543 hp. Obviously solar power is not about to replace gasoline at the moment.

Another interesting feature of the movie, introduced early on in the film, is the idea of widespread telekinesis. It is established that 10% of the population has a minor level of telekinesis, sufficient to lift a quarter and move it about at a modest speed.

So, how much power does that take, and if 10% of humanity is able to do this, how much energy can they generate? In the film, it appears that (most) telekinetics can only lift a small object a few inches. Again, the main example we have is a quarter moving in a small circle above a person’s hand.

Now, power is work divided by time. In this case, we can calculate it based on the time it takes to lift an object a given height combined with the weight of the object. The mass of a quarter is 5.7 grams. Weight is mass times gravity. The weight of 6.7 grams is 0.0559 newtons. In the film it looks like most telekinetics can only lift objects to a maximum height of about two inches or so. The time it takes isn’t clearly shown, but given the speed the object moves while hovering and the general trend of objects in the film (with more powerful telekinesis) to move equally fast when rising or floating, I estimate it might take a second.

0.0559 newtons times 2 inches divided by 1 second gives a power of 2.84 milliwatts. Not very much. But 10% of the population has this power. Now, the population of 2044 is unclear, but current projections suggest that the world population will increase during the next century to 10 billion. So I think we can safely guess there are at least 700 million telekinetics. That yields a total power of 1.988 megawatts, enough to power 331 to 663 US households:

This is pretty weak. In comparison, if you were chopping wood, you would use 2.9 dietary calories per pound hour. So chopping 1 pound of wood would be 2.9 dietary calories per hour or 3.37 watts—or a thousand times more energy.

Now for bigger spoilers.

There are more powerful telekinetics out there. One is able to move a lighter (the kind that typically weighs 2.4 ounces) with much faster speed and accuracy—let’s estimate 3 times as fast. 2.4 ounces x Earth gravity x 2 inches/0.3333 seconds is 0.102 watts. Substantially better, but not enough to change the world.

Of course, that is how things are in the world of Looper. As Joe explains, they thought they would get superheroes, but instead they got just this. But a movie like Looper doesn’t introduce psychic powers without a reason. There is a much more powerful telekinetic who shows up: the Rainmaker.

Now, the Rainmaker does quite a few impressive telekinetic feats in the movie, such as flipping a pickup truck and lifting a room full of furniture. In the case of the pickup, it is lifted clear into the air with the front bumper just above the ground. The pickup itself is loaded with supplies and 2 passengers. We can estimate the mass of the truck as at least 2.5 tons. The flip happens fairly quickly, within 2 seconds. Assuming the truck is about 20 feet long, that means we need to raise it 10 feet. 2.5 tons x Earth gravity x 10 feet / 2 seconds yields 34 kW. That’s enough to power up to 11 homes. If 10% of the population had this level of power, we’d easily solve any energy problems.

In the film, it is not clear if the Rainmaker can sustain this level of power. However, earlier in the film he lifts a room full of furniture (include several small tables, a few chairs, a sofa, and an unfortunate occupant). I’ll estimate the contents of the room at perhaps 1,000 lbs. They lifted a meter in about a second and then held there for several seconds before their destruction. 1000 lbs x Earth gravity x 1 meter / 1 seconds yields 4.448 kW. Still enough to power a house, but not enough to to make it practical to power the planet.

So the viability of telekinesis as a power source comes down to how well the Rainmaker can sustain that power level and whether we would want a world of potential telekinetic psychopaths as a utility company.