The Surprising Physics of the Star Wars Force
Only a Sith deals in absolutes. A physicist deals in probabilities.
In Star Wars Episode V: The Empire Strikes Back, Yoda dramatically demonstrates the power of “The Force” by lifting a spaceship out of a swamp and into the air without even touching it. This makes for a great science-fiction spectacle, but also seems to reinforce the sense that The Force is just magic that allows the user to violate the laws of physics.
One seemingly major objection is that it violates the conservation of energy – the principle that the energy needed to lift a spaceship cannot be created, it must have come from somewhere. Estimating the weight of the spaceship as ten tonnes, and the height Yoda lifts it as ten metres, we can calculate the energy this would take as 1000 kJ.1 This is actually surprisingly little! During a 15 km run, my fitness watch estimates I use over 5000 kJ of energy, so I should be tossing spaceships around for fun! Of course, while I can generate enough energy, the reason I cannot throw spaceships is that I cannot generate enough power. Power is the amount of energy used per second. While it takes me over an hour to run 15 km, Yoda lifts the spaceship in just 30 seconds. This would require Yoda to generate approximately 30 kW of power, which is about ten times the maximum power exerted by Usain Bolt during a sprint, and Bolt only maintained this for about a second.2 It seems implausible that old and frail Yoda could exert such superhuman power without even breaking a sweat, so perhaps magic is indeed afoot.
However, Yoda does not claim to be the source of the energy that lifts the ship. He explains of The Force that “its energy surrounds us”. Indeed, energy does surround us. What we experience as temperature is the energy of the air around us; the hotter the air is, the more energy it has. Even on a cool night, each cubic metre of air contains about 100 kJ of energy,3 which means that even in a region of air the size of a car, there is enough energy to lift the spaceship.4 Across the much vaster expanse of air around the swamp, there is so much energy that Yoda could easily access the 1000 kJ required without even having any noticeable effect on his surroundings. So conservation of energy is perhaps not the barrier it seemed!
How could Yoda harness this energy? The energy around us manifests as unceasing, random motion of air particles. We are constantly being pushed both left and right with immense force equivalent to the weight of a truck.5 The reason we don’t feel this is that each air particle is equally likely to push us one way as the other. Just as if we flip an immense number of coins, we get almost exactly the same number of heads and tails, with an immense number of air particles that are equally likely to travel left as right we end up with almost exactly as many particles pushing us left as pushing us right. This is why the huge quantity of energy in the air doesn’t do anything useful like lift spaceships; its effects all cancel each other out.
However, because the motion of air particles is random, there is always a chance that they don’t cancel out. If we flip a million coins, it is very unlikely that they will all land on heads, but it is not impossible. In the same way, it is not impossible for all the air particles around a spaceship to all push upwards at the same moment, just very unlikely. If this were to happen, we have seen that there is enough energy to lift the spaceship, so the spaceship really could rise out of the swamp and into the air! How likely is this to happen? As we have seen, there is enough energy in ten cubic metres of air. This volume of air contains about 10^26 (i.e., 100000000000000000000000000) air particles.6 So if these are all equally likely to push up as down, the chance that they all push upwards is one half to the power of 10^26. This number is so small that if I had begun writing it out in full when the universe started I would still be only a tiny fraction of the way there, but it is not zero.7 So the air spontaneously lifting a spaceship using its own energy is unspeakably unlikely, but not technically impossible!
Where does this leave The Force? First, Yoda’s feat of lifting the spaceship using the force does not contradict the conservation of energy, as there is more than enough energy for the task in the air around him. Second, there is some chance of this energy all being directed upwards on the ship at the same time to lift the ship into the air, but this chance is incredibly small so you would have to be incredibly lucky for it to happen.
So, perhaps The Force is a way for Jedi to create their own luck! In Harry Potter and the Half-Blood Prince, Harry Potter takes a “luck potion” in order to extract a secret. All the events that occur while he is affected by the potion are possible, but they just so happen to all conspire to lead Harry to an extremely convenient and otherwise unlikely scenario. Perhaps Jedi using the force achieve the same thing; they do not cause anything strictly impossible to occur, but they can make highly unlikely events occur to their benefit. The energy of the air lifting the spaceship is just a very extreme case of this. This explains Yoda’s admonition to Luke Skywalker that the fact that he could not believe that the ship being lifted was possible “is why you fail.” The Force user must see and believe in the possibility of what they wish to occur in order to make it happen.
Viewing The Force as causing the occurrence of possible but lucky outcomes fits with its other uses. In Episode IV: A New Hope, Obi-Wan Kenobi convinces guards not to investigate him on entering a city. To Luke, this appears to be an incredible bit of luck, until Obi-Wan explains that he used The Force. Similarly, in Episode I: The Phantom Menace, Anakin Skywalker’s freedom is contingent on the outcome of a dice roll after his enslaver decides to “let fate decide”. Qui-Gon Jinn appears to use The Force to “get lucky” in the game, and ensure that he wins. On the other hand, the ability of Jedi to see visions of the future could be interpreted as them seeing possibilities and then subsequently subconsciously using The Force to cause the events they expect to occur. This deepens the tragedy of Anakin Skywalker who foresees the death of his mother (in Episode II: Attack of the Clones) and his wife (in Episode III: Revenge of the Sith) and believes that these events will happen unless he can prevent them, with his failure to do this triggering his transition to Darth Vader. It seems that Anakin unintentionally uses The Force to create his own bad luck. This explains Yoda’s warning that “fear of loss is a path to the dark side”; via The Force, fear of bad outcomes can become a self-fulfilling prophecy that leads to darkness.
Star Wars aside, we can learn a valuable lesson about modern physics from this analysis. Traditional physics - the kind we are usually taught in school - depends on the physicist knowing everything about the system they study so that they can determine what will happen with certainty. This is usually impossible for real systems, so physicists make approximations, such as ignoring air resistance when considering what happens to a falling object. However, an alternative approach is to deal with systems as they really are and to accept and account for our incomplete knowledge of them. This is the approach pioneered by statistical mechanics, which is the branch of physics we have used for our analysis here. Statistical Mechanics studies the behaviour of systems that are far too complex for us to understand completely, such as the billions of billions of billions of particles that make up the air. It is continued by quantum mechanics, which confronts systems where perfect knowledge is theoretically impossible, as uncertainty transpires to be intrinsic to even a single particle.
Both statistical mechanics and quantum mechanics teach us humility. They do not allow us to say with certainty what will occur, only to calculate probabilities and say what is likely and what is (very) unlikely. Of course, the Star Wars Force is not scientific – we cannot manipulate uncertainty to create our own luck, we are forced to accept whatever fortune deals us. It does remind us, however, that modern physics does not deal with absolute certainties and we should not be too hasty in dismissing the “impossible”. Remember: Only a Sith deals in absolutes. A physicist deals in probabilities.
Assuming the planet Dagobah has the same gravitational pull as Earth (approximately 10 N/kg), the gravitational force of the 10000 kg spaceship is approximately 10000 kg × 10 N/kg = 100000 N so the total energy Yoda must exert to lift it 10 m is 100000 N × 10 m = 1000000 J = 1000 kJ.
See “The force, power and energy of the 100 meter sprint” by O. Helene and M. T. Yamashita at https://arxiv.org/abs/0911.1952.
The thermal energy of air is about nkT, where n is the number of air particles, k is Boltzmann’s constant and T is the temperature. By the ideal gas law, pV=nKT where p is pressure and V is volume. So, in V = 1 m^3 of air with a typical pressure of p = 100 kPa (one atmosphere), the thermal energy is approximately E=nkT=pV=100 kPa × 1 m^3 = 100 kJ.
A car small car is approximately ten cubic metres (see here for example). So, the energy in this region of air is approximately 100 kJ/m^3 × 10 m^3 = 1000 kJ.
Atmospheric pressure is about 100 kN/m^2 and the surface area of a person is about 1.6 m^2, so the total force the air exerts is about 100 kN/m^2 × 1.6 m^2 = 160 kN, which is approximately the gravitational force of two eight-tonne trucks. For comparison, this is what would happen if the force was all applied in the same direction.
Using the ideal gas law with pressure p = 100000 Pa, V = 10 m^3, k = 1.4×10^-23 J/K and T = 300 K, the number of particles is approximately n = (pV)/(kT) = 10^26.
2^(10^26) is a bit more than 10^(10^25) which has 10^25 digits. Writing three digits per second, this would take about one hundred quadrillion years to write, which is several million times the age of the universe.