Even Superman Can’t Turn Back Time

I, like many men that are 30 going on 13, have always had an affinity for superheroes, and in particular, superhero movies.  There are so many reasons why this genre of movie appeals to me, but what I enjoy first and foremost is the notion of fantasy set in reality.  Among my favourites are The Watchmen, Batman (the original and the Dark Knight), and X-Men.

I must admit, there is a certain inherent fallacy to the notion of fantasy set in the real world.  Some stories, like that of Star Wars, avoid any real world association, as they are set far from the world we know in both time and space.  Fantasy set in reality presents an internal conflict for the viewer: “Do I just go with the fantasy and ignore reality, or do I go with the reality and question the fantasy?”

    

While the first option allows one to achieve the escapism that such films offer, my mind has trouble turning off completely, and I tend to walk a line somewhere between both options.  A premise such as that of The Matrix avoids this issue, as it offers a compelling reason for why the rules of the universe, the laws of physics, need not apply.

While nearly any sci-fi movie, if analyzed carefully enough, can be criticized for taking liberties with science, the award for “Most ridiculous violation of the laws of science in one scene” must go to the climactic finale of the first Superman film.  [As an aside, the award for “Most consistently false science throughout” may be shared by Armageddon and Independence Day.]

Don’t get me wrong – I have nothing against Superman.  The mild-mannered reporter, Clark Kent, is perhaps the most iconic alter ego of any Superhero, as he is the exact opposite.  Also, as the origins of Superman exist somewhere else in the universe, I am more forgiving as to why this being can fly, be indestructible, have super strength, cool things with his breath and heat them with his eyes.

The original Superman film is excellent as a whole, with Gene Hackman’s Lex Luthor as a worthy adversary for the Man of Steel.  And, for a film made in the late seventies, the special effects are exceptional.  It is a shame then, that the climax of the film is so unbelievably ridiculous.  Yes, even when compared to the central notion of an alien sent to Earth, where he develops superhuman qualities due to his proximity to our particular star, the final scene of the film is preposterous.

If you have not seen the film yet (what are you waiting for?), allow me to summarize the ending... Lois Lane dies as her car is crushed with her inside it, and Superman gets angry.  To undo her death, Superman causes the Earth to spin in the opposite direction.  He does this by flying around the Earth at super speeds in the opposite direction to that which it spins.  Once the Earth has rotated “backwards” for a while, he gets it rotating in its original direction by flying against the grain once more.  As a result of these actions, Superman manages to press rewind on the timescale of the Earth, and then set it back in motion at precisely one spin per twenty-four hours.  He then rescues Lois from the impending accident before it occurs. 

Perhaps the logic on the part of the writers was, “If the viewer can accept the notion of Superman, they will accept anything.”  This is not the case.  I can blissfully overlook the fantasy component, but I think it is essential that the rest be realistic.  If not, the film becomes pure fantasy, and is in many ways diminished as a result.

Let us first analyze the magnitude of force that Superman must exert on the Earth by dragging the air around it in a shear sense.  First, what is the rotational inertia of the Earth?  The Earth’s resistance to angular acceleration is equal to 0.4MR², where M is its mass, and R is its radius.  Inputting the Earth’s mass of 5.97*10²⁴ kg, and radius of 6,378,000 m, we see that the Earth has a rotational inertia of 9.7*10³⁷ kgm².

Superman seems to get the Earth to change its direction of spin in a matter of seconds.  The Earth’s 24-hour period translates to an angular velocity of 7.27*10^-5 rad/s.  If Superman can bring the Earth to rest in a rotational sense in 5 seconds, he must cause an angular acceleration of 1.45*10^-5 rad/s².  Due to the unimaginably large inertia of the Earth that we calculated a moment ago, the torque or moment that Superman must exert on the Earth is T = Iα= 1.4*10³³ Nm.  For a comparison point, when a person opens a heavy door, they exert a torque of about 10 Nm about the door’s pivot axis.

The force that it would take Superman to generate this torque about the spin axis of the Earth is F = T/R = 2.2*10²⁶ N, because the load is placed along the equator of the Earth, perpendicular to the Earth’s radial arm.  Being generous to Superman’s abilities, let us assume that this aerodynamic shear force is distributed evenly around the entire length of the equator at all times, and has a width of ten kilometres.  This corresponds to a surface area of 4*10¹¹ m².  In this case, the pressure gradient of the air as it drags against the surface of application must be on the order of P = F/A= 5.5*10¹⁴ Pa, or 550,000 GPa.  This air pressure, which exceeds the standard atmospheric value by a factor of over five billion, would kill all life in the vicinity of the surface area of application. 

But, that’s OK, because Lois was in the United States, which is far enough from the equator, where Superman exerted this massive aerodynamic shear drag force.  Still, the local acceleration of the land anywhere but at the poles would be significant due to the large angular acceleration experienced by the Earth.  Indeed, the transverse acceleration at the surface anywhere near the equator would be a = Rα = 92.5 m/s², or nearly 10-g’s!  This would cause pretty well every human being on Earth to puke simultaneously and be rendered unconscious, and that includes Lois.  Also, every structure on Earth would collapse, and tsunamis would occur along every coast.

OK, so clearly the effects of Superman’s actions to manipulate the motion of planet Earth would, in reality, have had many unintended repercussions on it.  But even if we agree to ignore these, can we be led to believe that Superman’s actions would have the intended consequence of turning back time?  Of course not!

The notion that time’s arrow is somehow linked to the direction in which the Earth spins is absurd.  Time flows in one direction; it is a corollary of the second law of thermodynamics.   Although the passage of time is relative (faster or slower for objects moving at different speeds), its direction is unshakable.  If the plot of the story really did require time to turn back, then the writers ought to have come up with a more plausible way to have it occur, like by way of a flux capacitor, for example. 

It is fun to dream about going back in time.  If I could do that, I might consider paying a visit to the writers of the first Superman film, and encouraging them to let Lois die.  In addition to this ending being more believable, the change in the screenplay would likely cause the future disasters known as Superman III and IV to be averted.