Thursday, September 1, 2011

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 = = 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 = = 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.


Nathalie said...

Ha, this kind of analysis is exactly what I've been looking for! This scene has bugged me ever since I've seen the movie as a kid. Thank you!

I hope if we ever get a visitor from Krypton he won't try something stupid like this ;)

The Engineer said...

Nathalie, I'm glad it helped to clarify the level of absurdity..

VEGA1145 said...

DUDE! He fly's faster than a speeding bullet, sees through solid objects, and lifts the entire continental shelf in a bed of lava over his shoulders. Give him the benefit of the doubt by letting him turn back time in an idiotic fashion. Guys, were talking about a super hero that does not exist and defies every law of physics. Please apply your problem solving skills to a more lucrative subject.

The Engineer said...

Vega, if one applies a large enough force, one can cause motion in a large enough body. Also, there is no reason why something cannot travel faster than a bullet... I would object to him travelling faster than light, but there is no evidence that this occurs.

I have no problem with superman having inexplicably incredible capabilities. The fact is that within the framework of this universe, if he used this capability to reverse the spin of the Earth, most people on Earth would die, buildings topple over, etc.

This website is intended as an informational resource for science and engineering, and as a teacher of physics, my motivation is not necessarily to study lucrative projects, but to examine thought-provoking ones, ie, to educate.

The average Joe watching this film leaves with the impression that one can go back in time, and that the mechanism for doing so is somehow linked to the rotation of our planet. I wanted to highlight the difference between extraordinary and just plain false.

The Engineer said...

I would prefer it be consistent with our universe, but fair enough, let us say Superman can go back in time. The rest of my argument still holds: he still reverses the direction of spin of the planet (for reasons unknown) and more absurdly, the time flows backwards as a result.

I am a big fan of superheroes, but tend to prefer those that play by some kind of rule book. I like fictional stories that exist within the framework of the governing laws of our universe. This actually immerses me, the viewer, much deeper into the content. If a story is to take place in a different universe, that's fine, but make it a much different one, that I could not mistake for my own.

Charlie Brown said...

I just watched this movie again on blu-ray along with superman II (richard donner cut) and superman returns to prepare myself for the upcoming man of steel adaptation since it made me believe men can fly when I was a child.

It did not however make me believe a superman can turn back time by reverse-rotating the world. I actually read the comics and I still thinks its the most ridiculous copout I ever saw in a superhero movie.

Thank you for the information on the possible consequences of his actions. To think he actually caused more damage trying to save the girl.

Anonymous said...

Since you state that there is no evidence that Superman travels faster than light, I thought I'd do a rough speed analysis.

As demonstrated in Superman: The Movie, there is a time index sample of roughly 4 seconds where you can get a good count of the number of orbital passes Superman makes around the Earth. Using a still image of the middle of this time span in Photoshop, I came up with this:

Diameter of Earth = 443.0px
Translates to: 7918.0 miles / 443.0 px = 17.9 miles/px

Measuring the average of all flight paths from end to end produces an average diameter of 726.5px for Superman's travel path.

Circumference of travel path = (726.5px x 17.9 miles) x π = 40794.1 miles

In the 4 second period, Superman makes 19 passes, giving a total distance of 775087.7 miles. That works out to 193771.9 miles per second...which is 7489.5 miles per second faster than the speed of light. Ta dah! Time Travel! (and a middle finger to Einstein)

The only problem with assuming Time Travel is that he uses the same mechanism to go back and forward. I don't believe you can use faster than light travel to go forward in the future.

The Engineer said...

Good kinematic analysis Brian... Let us say that Superman went faster than the speed of light... Then HE went back in time. This has no effect on the time passage on the surface of the Earth (where time was strangely reversed).

And you are right. Though time travel backwards does not seem permissible, time travel forwards is and has been done on a small scale... All one must do is approach the speed of light (it takes a lot of energy to do this, but it is within the realm of possibility).

Anonymous said...

I think the bigger issue of him accelerating to faster the speed of light is the fact his mass would become infinite and his length zero. He'd become a black hole travelling at the speed of light just above the Earth's surface. The tidal forces alone would rip the Earth apart!

The Engineer said...

Fair point anonymous... But the audience is not led to believe that Superman actually exceeds the speed of light. Of course, this would defy everything we know about mass-energy, not that the film-makers would be bothered by this.

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Rich Johnston said...

He is not turning the spin of the Earth backwards. He is travelling in time and taking the audience with him so that it appears as if the Earth is turning backwards. And everything else goes backwards as well. It's a point of view time travel. It's still nonsense, but that's clearly what's happening here. Come on now.

The Engineer said...

I disagree that anything about that scene is clear. The majority of audiences of that film were surely left with the impression that he reversed the spin of the earth and in so doing reversed the direction of time. Modern films would probably give some kind of explanation of such a phenomenon by foreshadowing it n an earlier scene. The original Superman offers no explanation, so the viewer has to work with what is given.

B-4 said...
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B-4 said...

First off you have misinterpreted what the movie is trying to show and also the director has misinterpreted what the writer has intended, superman flying around the earth at faster than light speed (theoretical impossible yes, but so is a man with super human abilities) so what he is doing is not turning the earth backwards by dragging the atmosphere, the earth spinning backwards represents time going backwards, now the part the director gets wrong (he must of been thinking along the same lines as you) is superman turning around in the opposite direction to make the earth spin normal again, there was no need for that part. so how did he turn back time? I will scale it down, OK imagine that you are standing outside a building on the corner, if you could run around the building at the speed of light you will see yourself leave, now go faster again and you will get there before you have even left, essentially you have gone back in time, just as superman did in the movie.
Try not to over think everything!

The Engineer said...

B-4, I really can only assess what is presented in the film. I have no way of knowing what the writer intended.

As for your advice regarding overthinking... This is fun for me. The kinds of readers that read posts such as these do it to flex their science muscles and geek out a little bit. If you don't enjoy thinking, then there are plenty of other blogs you will enjoy more than mine.