Insultingly Stupid Movie Physics

by Tom Rogers

  THE FIRST LAW OF THERMODYNAMICS—A SYNOPSIS

  Unlike Hollywood where nothing seems sacred, physics has a law that is as close to absolute truth as anything known to humanity. It’s called the conservation of energy, and is sometimes referred to as the first law of thermodynamics.

  The first law says that matter is essentially a form of energy, and that while energy can change its form, it cannot be destroyed or created. This law started out as two laws: the law of conservation of energy and the law of conservation of mass, but, when Einstein showed that mass could be converted into energy and vice versa, the two laws were combined into one. In this case, refining a law consisted of simplifying it. According to Nobel Prize–winning physicist Richard Feynman, “There is no known exception to this law—it is exact so far as we know.”2 If someone ever finds an exception it will shake science to its foundations.

  EINSTEIN SIMPLIFIES THE FIRST LAW

  At one time conservation of mass was considered separate from conservation of energy. Then Einstein demonstrated that mass could be converted to energy and vice versa, according to his famous equation:

  E = mc2

  Where:

  E = energy released when converting mass to energy, or energy

  required when converting in the opposite direction

  m = amount of mass converted to energy or amount of mass produced if converting in the opposite direction

  c = velocity of light in a vacuum

  Assume m = 1.0 kg

  E = 1.0 kg (3 × 108 m/s)2

  [] = 9.0 1016 J or 21.5 megatons of TNT

  Fortunately, it’s incredibly difficult to convert mass into energy, or even an innocuous object such as the phonebook could become a nuclear bomb. The conversion of energy into mass is likewise incredibly difficult.

  Movie violations of the first law should be unforgivable, and yet they’re common. In The Hulk [NR] (2003), a nerdy looking scientist transforms into a massive brute over two times taller, with no apparent intake of matter. The Hulk appears to grow larger as he absorbs the energy of various attempts to kill him. True, energy can be converted into matter, but the conversion is incredibly difficult and requires a massive amount of energy to produce a miniscule amount of mass. The energy output of roughly a 100-megaton nuclear bomb—the largest ever built—would create just 10 pounds (4.6 kg) of matter, assuming the conversion is 100 percent efficient. By contrast, any energy absorbed by the Hulk would be minor. Even if he could use it to increase his mass, the result would be imperceptible. For the Hulk, the only real possibility is to find a source of matter that can be easily scooped up, and air is about the only choice. Inconveniently, its density is at least a thousand times lower than the Hulk’s. Absorbing enough mass to make the hulk huge and maintain his density would create a whirlwind around him, not to mention inconvenient problems with chemistry. How are a few thousand pounds of oxygen and nitrogen atoms going to be transformed into Hulk-type material?

  In Spider-Man [NR] (2002), Peter Parker is bitten by a genetically modified spider, which imparts spider-like qualities to him. He finds he can shoot strands of spider web from his wrists. These web strands adhere instantly to objects like tall buildings, and enable Spider-Man to swing Tarzan-like while traveling great distances at fairly high speeds. Unfortunately, the web strands would also require a great deal of matter that seems to come from nowhere.

  A web strand would probably need to be at least 0.5 centimeters in diameter to support Spider-Man’s web-swinging antics. If such a strand were 100 meters long, it would have a volume of 0.002 cubic meters, compared to Spider-Man’s estimated volume of 0.07 cubic meters. Spider-Man would lose 2.9 percent of his volume every time he shoots a 100-meter-long web. Web swinging a mere mile (1.61 km) of horizontal distance would use up about 33 percent of his body volume (assuming his web makes a 45-degree angle with the vertical at the beginning and end of each swing, and each web is 100 m long). He would be skeletal by the time he arrived and would have to eat huge volumes of food to compensate.Yet, none of this happens in the movie.

  This analysis assumes that the volume of web-producing chemicals stored in Spidey equals the volume of web produced. However, even if the chemical volume were half the web volume, Spidey’s volume is still going to fluctuate wildly if he does much web swinging. Yes, he could grow a spider fluid tank that could fill and drain as needed. But, assuming he continues to require human internal organs to live, where is he going to inconspicuously put the tank? On the other hand, Spider-Man and The Hulk are obviously based on comic books, so . . . okay . . . they have to be begrudgingly forgiven.

  THE SECOND LAW OF THERMODYNAMICS—YET ANOTHER SYNOPSIS

  The second law of thermodynamics is much more difficult to state, not to mention grasp, but is considered about as immutable as the first law. It would be easy to write a book about the second law and still not totally explain it or explore all its aspects. Frank L. Lambert, Professor Emeritus, Occidental College3 summarizes the second law as follows:

  Energy spontaneously tends to flow only from being concentrated in one place to becoming diffused or dispersed and spread out.

  Mechanical energy and electrical energy can be considered concentrated forms, while heat or thermal energy would be considered dispersed. A concentrated form of energy is like water in a container on top of a hill. Tip the container over and the water flows downward, spreading out as it goes to a lower level. For all practical purposes it would never be possible to get all of the water back in the container. Likewise, concentrated forms of energy can easily be transformed into dispersed forms, but it’s difficult to do the reverse.

  Heat can, figuratively speaking, be pumped uphill from its dispersed state into a concentrated form, but it can’t be done with 100 percent efficiency. For example, less than 40 percent of the heat used to generate electricity in a typical coal-fired power plant actually ends up as electrical energy. The other 60 percent remains as heat and is dumped out of the power plant into the environment. In essence this is the cost for producing the electrical energy.

  CARNOT EFFICIENCY—THE ULTIMATE LIMIT

  Heat engines are the devices used to convert thermal energy (heat) into useful power. These include steam engines, gas turbines, and the various forms of internal combustion engines used in cars. The second law places strict limits on the maximum possible efficiency of heat engines. This maximum efficiency is called Carnot (pronounced car-no) efficiency and is calculated as follows:

  e = (1 – TC/TH) • 100.

  Where:

  e = efficiency in %

  TC = cold temperature at which heat is expelled into the surrounding environment

  TH = hot or elevated temperature produced within the heat engine by combustion, solar energy, geothermal energy, nuclear energy, or some other source

  Actual efficiencies are a fraction of the Carnot efficiencies. The Carnot calculation does not account for real-world losses due to problems such as heat loss out the walls of the engine or any form of friction. In the case of automobiles, heat has to be removed from the walls of the engine’s cylinders to keep them from welding themselves to the moving pistons inside. Yet even in a perfect world with no friction, the Carnot efficiency says that 100 percent of the energy contained in gasoline or any other fuel could never be converted into useful work by a car’s engine.

  Generally, lowering the temperature of the heat source rapidly lowers the efficiency of converting it to electrical energy. Current power plants, even nuclear ones, typically get efficiencies less than 40 percent.The 60 percent or more of unusable heat dumped into the environment after exiting the power plant is now at a much lower temperature.

  It seems that this exiting heat could be run through yet another power plant to convert more of it to electrical energy, but the temperature is now too low. The heat ends up being wasted because the efficiency would be too low to reasonably attempt converting it to electrical energy.

  When energy from a concentrated form, such as mechanic
al energy, is converted by friction to a dispersed form such as heat, it essentially can never be converted back. Hence, the second law says that there can never be a perpetual motion machine, except possibly in a frictionless environment. Unfortunately, friction is ubiquitous. The first law says that if a perpetual motion machine did exist, it could do no useful work on outside objects because that would drain energy out of it and eventually cause it to stop.

  BATHTUBS AND BATTERIES

  The Matrix [RP] (1999) was rising as a cinematic masterwork until about midway through, when it plummeted into the pit of first law violations. During the masterful first part, its main character, Neo (Keanu Reeves)—unknowingly trapped inside a vast computer simulation—begins to question his existence. He is approached by Trinity (Carrie-Anne Moss) and later Morpheus (Laurence Fishburne) who offer him the chance to find answers.

  When Neo accepts, he discovers that he, along with most of humanity, actually exists in clear slime-filled bathtubs with all sorts of tubes and cables connecting him to a gigantic computerized machine system. The tubs are housed in a cavernous room tended by gargantuan mechanical tarantulas and are illuminated in part by frequent lightning-like, high-voltage discharges.

  After freeing Neo and giving him lengthy rehabilitation treatments, Morpheus reveals the truth. The machines were given artificial intelligence (AI), which apparently turned them into control freaks. One might think that possessing intelligence—artificial or otherwise—would have led to understanding, but no, it led to war.

  The machines were running on solar energy, so humans attempted to pull the plug by blotting out the Sun. This was very clever since humans are powered by food, which also depends on an abundant supply of solar energy. Evidently, humans stocked up on canned goods before blotting out the Sun. The machines turned the tables by enslaving humans and plugging into them as a power source.

  Morpheus tells us that a human has the bioelectrical energy of a 120-volt battery; but is it a camera battery, a car battery, or something else? Volts are a measure of electrical potential energy per unit of charge, not just a measure of energy. A small 120-volt battery could provide a tiny flow of charge and, hence, a tiny amount of energy; a large 120-volt battery, a huge amount. Besides, 120-volt batteries are hard to find. Certainly, Wal-Mart doesn’t carry them, so what Morpheus means when he refers to one is hard to discern.

  We’re also told that humans put out 25,000 British thermal units of body heat. If this happens continuously each second, it’s an impressive rate of 26.4 megawatts. If the heat could magically be converted to electricity, it could power a small city. If the body heat were given off over a year, it would be a paltry rate of 0.84 watts. Even if it were magically converted to electricity, 0.84 watts would not be enough to power most light bulbs.

  Unfortunately, the second law casts doubt on whether any significant part of body heat could be converted to electrical energy. Body heat is a very dispersed form of energy, while electrical energy is a very concentrated form. Body temperature is so low that converting the body’s heat to electrical energy would have a miniscule efficiency. How human body heat would be useful to a vast electronic computer system is a mystery. Generally, electronics have to be cooled.

  Morpheus concludes his energy discussion by lofting a copper-topped D-cell flashlight battery (ironically rated at 1.5 volts), implying that this represents the puny power output of a human. It’s meant as a highly dramatic gesture, but the numbers make it look like a parody.

  A bed-ridden, six-foot-tall, 160-pound, twenty-five-yearold male requires about 2,000 kilocalories worth of food energy per day just to stay alive. Note, that one food calorie equals 1,000 calories. In other words the calories reported for foods are really kilocalories. (Why they’re not called kilocalories instead of capitalizing the “c” is anyone’s guess.) This works out to a power rate of 96.6 watts, or about as much as a typical incandescent light bulb.

  In a day’s time a tub-bound human uses 2.3 kilowatt-hours of energy to stay alive. A copper-topped D-cell flashlight battery holds about 0.023 kilowatt-hours of energy. In other words, it would take about one hundred D-cells worth of food energy every day to keep a human going.

  The first law clearly says that humans cannot produce more energy than they consume. Hence, humans cannot be considered an energy source. At best, they are devices that can convert food energy (a type of chemical energy) into electrical energy. If they produce the output of a D-cell, they have a best-case food conversion efficiency of less than 1 percent. However, the energy required to collect and distribute the food as well as maintain the slime tubs would be more than the human electrical output. Why would the machines bother to keep them?

  Feeding liquefied dead humans (as done in the movie) back to the living ones doesn’t help. Meeting human energy needs with this system would make it a giant perpetual motion machine—clearly impossible according to the second law of thermodynamics.

  A 160-pound human probably contains about as many food calories as (please forgive the comparison) 160 pounds of hamburger meat. At about 1,200 kilocalories per pound this works out to 19,200 kilocalories of possible food energy. Just to stay alive for fifty years this human would have to consume over 36 million kilocalories—equivalent to ingesting 190 recycled humans, or about 3.8 dead humans a year. Where are all these people supposed to come from?

  Matrix apologists have proposed that humans are not a primary power source but a backup source like the battery in a car. Here’s a thought: why don’t the machines just use car batteries? Had the machines been thinking, they would have raided their local Wal-Mart for automotive batteries before starting the war.

  Surely the machines have some nonhuman form of energy storage in their hordes of sentinels—the octopus-like robots that float around in subterranean tunnels seeking to kill humans who’ve escaped their bathtubs. Sentinels would have to carry a large amount of stored energy to keep going.

  To cover itself, the movie throws in a quick mention that the human energy source powering the machines is combined with a source of fusion. This is like getting on a jet airliner and having the captain explain in great detail that the plane is rubber band powered, then adding that it also has four jet engines. Guess which power source gets it off the ground? Duh.

  MYTHICAL ROBOTS

  A.I.: Artificial Intelligence [XP] (2001) couldn’t even make it past the opening without slamming into the first and second laws. The movie opens with a scene of churning surf. The narrator proclaims that greenhouse gasses have warmed Earth, causing the ice caps to melt and flood major cities in coastal areas. As a result, populations have been displaced and “hundreds of millions” in poor nations have starved. So far it’s science fiction, but not for long.

  The narrator continues by announcing that prosperous nations have sustained their prosperity to a large extent by creating the perfect low-cost labor force: robots. According to the narrator, these robots require no resources beyond those used to create them. In other words, we’re asked to believe that the robots never need to be recharged, refueled, or rebuilt. They are essentially perpetual motion machines, which break the first and second laws.

  As mentioned in the first chapter, sometimes there are good artistic reasons to defy a law of physics. Great artists have often been defiant. Edouard Manet and René Magritte are both famous for creating paintings that look realistic but use impossible physics.

  Manet defied physics to provoke the French Academy. His painting Le Bar aux Folies-Bergère (The Bar at the Folies-Bergère) deliberately shows an impossible reflection of a young woman in a mirror. The viewer is standing directly in front of the young lady. Her reflection in the mirror on the wall behind her should be directly behind her and almost impossible to see. Instead, Manet painted it to the far right side (see Figure 6). This no doubt horrified official art critics of the time, much to the delight of Manet.

  Magritte broke the laws of physics as a type of visual joke or riddle. His painting L’Empire des Lumie
res (The Domain of Lights) shows a night scene occurring during the day. The sky is noticeably in daylight while the house below is obviously illuminated as it would be at night.

  There’s a big difference between insightful or clever rule breaking and the clumsiness of an amateur who can’t get perspective, proportions, and the overall physics of vision right. Unfortunately, the statements concerning robots in A.I. don’t seem to be particularly clever or insightful.

  The tendency to view machines as superior to their biological counterparts has been widespread. Biomedical engineering literature of the early 1970s proclaimed that science would produce a viable mechanical heart replacement for humans in about twenty years. By now, individuals with artificial tickers should be commonplace—a heart was, after all, merely a pump. How hard could it be to replace it? But even today, replacing a human heart with a mechanical device is still in the experimental phase. Yes, considerable progress has been made, but the truth is, biologically produced hearts are still vastly superior to mechanical ones.