Even Superman Can’t Turn Back Time

I, like many men that are 30 going on 13, have always had anaffinity for superheroes, and in particular, superhero movies.  There are so many reasons why this genre ofmovie appeals to me, but what I enjoy first and foremost is the notion offantasy set in reality.  Among myfavourites are The Watchmen, Batman (the original and the DarkKnight), and X-Men.

I must admit, there is a certain inherent fallacy to thenotion of fantasy set in the real world. Some stories, like that of StarWars, avoid any real world association, as they are set far from the worldwe know in both time and space.  Fantasyset in reality presents an internal conflict for the viewer: “Do I just go withthe fantasy and ignore reality, or do I go with the reality and question thefantasy?”
While the first option allows one to achieve the escapismthat such films offer, my mind has trouble turning off completely, and I tendto walk a line somewhere between both options. A premise such as that of TheMatrix avoids this issue, as it offers a compelling reason for why therules 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 “Mostridiculous violation of the laws of science in one scene” must go to theclimactic finale of the first Supermanfilm.  [As an aside, the award for “Mostconsistently false science throughout” may be shared by Armageddon and IndependenceDay.]

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

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

If you have not seen the film yet (what are you waitingfor?), allow me to summarize the ending... Lois Lane dies as her car is crushedwith 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 atsuper speeds in the opposite direction to that which it spins.  Once the Earth has rotated “backwards” for awhile, he gets it rotating in its original direction by flying against thegrain once more.  As a result of theseactions, Superman manages to press rewind on the timescale of the Earth, andthen set it back in motion at precisely one spin per twenty-four hours.  He then rescues Lois from the impendingaccident before it occurs. 

Perhaps the logic on the part of the writers was, “If theviewer 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 isin many ways diminished as a result.

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

Superman seems to get the Earth to change its direction ofspin in a matter of seconds.  The Earth’s24-hour period translates to an angular velocity of 7.27*10-5rad/s.  If Superman can bring the Earthto rest in a rotational sense in 5 seconds, he must cause an angularacceleration of 1.45*10-5 rad/s2.  Due to the unimaginably large inertia of theEarth that we calculated a moment ago, the torque or moment that Superman mustexert on the Earth is T = = 1.4*1033 Nm.  For a comparison point, when a person opens aheavy door, they exert a torque of about 10 Nm about the door’s pivot axis.

The force that it would take Superman to generate thistorque 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 theEarth’s radial arm.  Being generous toSuperman’s abilities, let us assume that this aerodynamic shear force isdistributed evenly around the entire length of the equator at all times, andhas a width of ten kilometres.  Thiscorresponds to a surface area of 4*1011 m2.  In this case, the pressure gradient of theair as it drags against the surface of application must be on the order of P = F/A= 5.5*1014 Pa, or 550,000GPa.  This air pressure, which exceedsthe standard atmospheric value by a factor of over five billion, would kill alllife in the vicinity of the surface area of application. 

But, that’s OK, because Lois was in the United States, whichis far enough from the equator, where Superman exerted this massive aerodynamicshear drag force.  Still, the localacceleration of the land anywhere but at the poles would be significant due tothe large angular acceleration experienced by the Earth.  Indeed, the transverse acceleration at thesurface anywhere near the equator would be a= = 92.5 m/s2, ornearly 10-g’s!  This would cause prettywell every human being on Earth to puke simultaneously and be renderedunconscious, and that includes Lois. Also, every structure on Earth would collapse, and tsunamis would occuralong every coast.

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

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

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


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