How Quantum Physics Explains Action Films

One of the key ideas used by cosmologists (yes, physics again, sorry) to explain away questions asked by annoying philosophical types is known as the anthropic principle. This has two forms (strong and weak) but the idea remains the same for both; that the reason for a situation being as it is is because, if it wasn’t, we wouldn’t be around to ask that question. For example, one might ask (as Stephen Hawking did in ‘A Brief History of Time’) why the universe is around 10 billion years old, a decidedly awkward question if ever there was one. The anthropic principle provides the simplest answer, stating that since organic life is such a complicated business and that the early universe was such a chaotic, unfriendly place, it is only after this vast amount of time that life forms capable of asking this question have been able to develop.

This answer of ‘because we’re here’ is a wonderfully useful one, albeit one that should be used with caution to avoid not answering valid question, and can be applied to problems that do not concern themselves directly with physics. One example concerns the origin of the human race, as we are all thought to stem from just a few hundred individuals who lived in East Africa’s Rift valley several million years ago. At that time our knowledge of weapons, fighting and general survival was relatively scant, and coming face to face with any large predator would have been a fairly assured death sentence; the prehistoric equivalent of a smart pride of lions, or even some particularly adverse weather one year, could have wiped out a significant proportion of the human race as it stood at that time in just a few months. Despite the advantages of adaptability and brainpower that we have shown since, the odds of natural selection were still stacked against us; why did we arise to become the dominant multicellular life form on this planet?

This question can be answered by listing all the natural advantages we possess as a species and how they enabled us to continue ‘evolving’ far beyond the mere natural order of things; but such an answer still can’t quite account for the large dose of luck that comes into the bargain. The anthropic principle can, however, account for this; the human race was able to overcome the odds because if we hadn’t, then we wouldn’t be around to ask the question. Isn’t logic wonderful?

In fact, one we start to think about our lives and questions of our existence in terms of the anthropic principle, we realise that our existence as individuals is dependent on an awful lot of historical events having happened the way they did. For example, if the Nazis had triumphed during WWII, then perhaps one or more of my grandparents could have been killed, separated from their spouse, or in some way prevented from raising the family that would include my parents. Even tinier events could have impacted the chance of me turning out as me; perhaps a stray photon bouncing off an atom in the atmosphere in a slightly different way could have struck a DNA molecule, causing it to deform the sperm that would otherwise have given me half my genes and meaning it never even made it to the egg that offered up the other half. This is chaos theory in action, but it illustrates a point; for the universe to have ended up the way it has depends on history having played out exactly as it has done.

The classic example of this in quantum physics is the famous ‘Schrodinger’s Cat’ experiment, in which a theoretical cat was put into a box with a special quantum device that had a 50/50 chance of either doing nothing or releasing a toxic gas that would kill the cat. Schrodinger’s point was that, when the cat is put into the box, two universes emerge; one in which the cat is dead, and one in which it is alive. Until we open the box, we cannot known which of these universes we are in, so the cat must be thought of as simultaneously alive and dead.

However, another thought experiment known as the ‘quantum suicide’ experiment takes the cat’s point of view; imagine that the cat is an experimenter, and that he is working alone. Imagine you are that experimenter, and that you had stayed in the box for five iterations of the 50/50 life/death random event. In 31 out of 32 possible futures, you would have been gassed, for at least once the device would have selected the ‘death’ option; but in just one of these 32 alternative futures, you would still be alive. Moreover, if you had since got out of the box and published your results, the existence of those results is solely dependent on you being that lucky one out of 32.

Or, to put it another way, consider a generic action hero, in the classic scene where he runs through the battlefield gunning down enemies whilst other, lesser soldiers fall about him from bullets and explosions. The enemy fire countless shots at him, but try as they might they can never kill him. They try, but he survives and the film reaches its triumphant conclusion.

Now, assuming that these enemies are not deliberately trying to miss him and can at least vaguely use their weapons, if our action hero tried to pull that ‘running through a hail of bullets’ stunt then 999 times out of a thousand he’d be killed. However, if he was killed then the film would not be able to reach its conclusion, since he would be unable to save the heroine/defeat the baddie/deliver a cliched one-liner, and as such the story would be incomplete.  And, with such a crappy story, there’s no way that a film would get made about it; therefore, the action hero must always be one of the lucky ones.

This idea of always triumphing over the odds, of surviving no matter what because, if you didn’t, you wouldn’t be around to tell the tale or even be conscious of the tale, is known as quantum immortality. And whilst it doesn’t mean you’re going to be safe jumping off buildings any time soon, it does at least give yo a way to bore the pants off the next person who claims that action movies are WAAYYYY too unrealistic.

Advertisement

Hitting the hay

OK, so it was history last time, so I’m feeling like a bit of science today. So, here is your random question for today; are the ‘leaps of faith’ in the Assassin’s Creed games survivable?

Between them, the characters of Altair, Ezio and Connor* jump off a wide variety of famous buildings and monuments across the five current games, but the jump that springs most readily to mind is Ezio’s leap from the Campanile di San Marco, in St Mark’s Square, Venice, at the end of Assassin’s Creed II. It’s not the highest jump made, but it is one of the most interesting and it occurs as part of the main story campaign, meaning everyone who’s played the game through will have made the jump and it has some significance attached to it. It’s also a well-known building with plenty of information on it.

[*Interesting fact; apparently, both Altair and Ezio translate as ‘Eagle’ in some form in English, as does Connor’s Mohawk name (Ratonhnhaké;ton, according to Wikipedia) and the name of his ship, the Aquila. Connor itself translates as ‘lover of wolves’ from the original Gaelic]

The Campanile as it stands today is not the same one as in Ezio’s day; in 1902 the original building collapsed and took ten years to rebuild. However, the new Campanile was made to be cosmetically (if not quite structurally) identical to the original, so current data should still be accurate. Wikipedia again tells me the brick shaft making up the bulk of the structure accounts for (apparently only) 50m of the tower’s 98.6m total height, with Ezio’s leap (made from the belfry just above) coming in at around 55m. With this information we can calculate Ezio’s total gravitational potential energy lost during his fall; GPE lost = mgΔh, and presuming a 70kg bloke this comes to GPE lost= 33730J (Δ is, by the way, the mathematical way of expressing a change in something- in this case, Δh represents a change in height). If his fall were made with no air resistance, then all this GPE would be converted to kinetic energy, where KE = mv²/2. Solving to make v (his velocity upon hitting the ground) the subject gives v = sqrt(2*KE/m), and replacing KE with our value of the GPE lost, we get v = 31.04m/s. This tells us two things; firstly that the fall should take Ezio at least three seconds, and secondly that, without air resistance, he’d be in rather a lot of trouble.

But, we must of course factor air resistance into our calculations, but to do so to begin with we must make another assumption; that Ezio reaches terminal velocity before reaching the ground. Whether this statement is valid or not we will find out later. The terminal velocity is just a rearranged form of the drag equation: Vt=sqrt(2mg/pACd), where m= Ezio’s mass (70kg, as presumed earlier), g= gravitational field strength (on Earth, 9.8m/s²), p= air density (on a warm Venetian evening at around 15 degrees Celcius, this comes out as 1.225kg/m³), A= the cross-sectional area of Ezio’s falling body (call it 0.85m², presuming he’s around the same size as me) and Cd= his body’s drag coefficient (a number evaluating how well the air flows around his body and clothing, for which I shall pick 1 at complete random). Plugging these numbers into the equation gives a terminal velocity of 36.30m/s, which is an annoying number; because it’s larger than our previous velocity value, calculated without air resistance, of 31.04m/s, this means that Ezio definitely won’t have reached terminal velocity by the time he reaches the bottom of the Campanile, so we’re going to have to look elsewhere for our numbers. Interestingly, the terminal velocity for a falling skydiver, without parachute, is apparently around 54m/s, suggesting that I’ve got numbers that are in roughly the correct ballpark but that could do with some improvement (this is probably thanks to my chosen Cd value; 1 is a very high value, selected to give Ezio the best possible chance of survival, but ho hum)

Here, I could attempt to derive an equation for how velocity varies with distance travelled, but such things are complicated, time consuming and do not translate well into being typed out. Instead, I am going to take on blind faith a statement attached to my ‘falling skydiver’ number quoted above; that it takes about 3 seconds to achieve half the skydiver’s terminal velocity. We said that Ezio’s fall from the Campanile would take him at least three seconds (just trust me on that one), and in fact it would probably be closer to four, but no matter; let’s just presume he has jumped off some unidentified building such that it takes him precisely three seconds to hit the ground, at which point his velocity will be taken as 27m/s.

Except he won’t hit the ground; assuming he hits his target anyway. The Assassin’s Creed universe is literally littered with indiscriminate piles/carts of hay and flower petals that have been conveniently left around for no obvious reason, and when performing a leap of faith our protagonist’s always aim for them (the AC wiki tells me that these were in fact programmed into the memories that the games consist of in order to aid navigation, but this doesn’t matter). Let us presume that the hay is 1m deep where Ezio lands, and that the whole hay-and-cart structure is entirely successful in its task, in that it manages to reduce Ezio’s velocity from 27m/s to nought across this 1m distance, without any energy being lost through the hard floor (highly unlikely, but let’s be generous). At 27m/s, the 70kg Ezio has a momentum of 1890kgm/s, all of which must be dissipated through the hay across this 1m distance. This means an impulse of 1890Ns, and thus a force, will act upon him; Impulse=Force x ΔTime. This force will cause him to decelerate. If this deceleration is uniform (it wouldn’t be in real life, but modelling this is tricky business and it will do as an approximation), then his average velocity during his ‘slowing’ period will come to be 13.5m/s, and that this deceleration will take 0.074s. Given that we now know the impulse acting on Ezio and the time for which it acts, we can now work out the force upon him; 1890 / 0.074 = 1890 x 13.5 = 26460N. This corresponds to 364.5m/s² deceleration, or around 37g’s to put it in G-force terms. Given that 5g’s has been known to break bones in stunt aircraft, I think it’s safe to say that quite a lot more hay, Ezio’s not getting up any time soon. So remember; next time you’re thinking of jumping off a tall building, I would recommend a parachute over a haystack.

N.B.: The resulting deceleration calculated in the last bit seems a bit massive, suggesting I may have gone wrong somewhere, so if anyone has any better ideas of numbers/equations then feel free to leave them below. I feel here is also an appropriate place to mention a story I once heard concerning an air hostess whose plane blew up. She was thrown free, landed in a tree on the way down… and survived.

EDIT: Since writing this post, this has come into existence, more accurately calculating the drag and final velocity acting on the falling Assassin. They’re more advanced than me, but their conclusion is the same; I like being proved right :).

The End of The World

As everyone who understands the concept of buying a new calendar when the old one runs out should be aware, the world is emphatically due to not end on December 21st this year thanks to a Mayan ‘prophecy’ that basically amounts to one guy’s arm getting really tired and deciding ‘sod carving the next year in, it’s ages off anyway’. Most of you should also be aware of the kind of cosmology theories that talk about the end of the world/the sun’s expansion/the universe committing suicide that are always hastily suffixed with an ‘in 200 billion years or so’, making the point that there’s really no need to worry and that the world is probably going to be fine for the foreseeable future; or at least, that by the time anything serious does happen we’re probably not going to be in a position to complain.

However, when thinking about this, we come across a rather interesting, if slightly macabre, gap; an area nobody really wants to talk about thanks to a mixture of lack of certainty and simple fear. At some point in the future, we as a race and a culture will surely not be here. Currently, we are. Therefore, between those two points, the human race is going to die.

Now, from a purely biological perspective there is nothing especially surprising or worrying about this; species die out all the time (in fact we humans are getting so good at inadvertent mass slaughter that between 2 and 20 species are going extinct every day), and others evolve and adapt to slowly change the face of the earth. We humans and our few thousand years of existence, and especially our mere two or three thousand of organised mass society, are the merest blip in the earth’s long and varied history. But we are also unique in more ways than one; the first race to, to a very great extent, remove ourselves from the endless fight for survival and start taking control of events once so far beyond our imagination as to be put down to the work of gods. If the human race is to die, as it surely will one day, we are simply getting too smart and too good at thinking about these things for it to be the kind of gradual decline & changing of a delicate ecosystem that characterises most ‘natural’ extinctions. If we are to go down, it’s going to be big and it’s going to be VERY messy.

In short, with the world staying as it is and as it has for the past few millennia we’re not going to be dying out very soon. However, this is also not very biologically unusual, for when a species go extinct it is usually the result of either another species with which they are engaging in direct competition out-competing them and causing them to starve, or a change in environmental conditions meaning they are no longer well-adapted for the environment they find themselves in. But once again, human beings appear to be showing a semblance of being rather above this; having carved out what isn’t so much an ecological niche as a categorical redefining of the way the world works there is no other creature that could be considered our biological competitor, and the thing that has always set humans apart ecologically is our ability to adapt. From the ice ages where we hunted mammoth, to the African deserts where the San people still live in isolation, there are very few things the earth can throw at us that are beyond the wit of humanity to live through. Especially a human race that is beginning to look upon terraforming and cultured food as a pretty neat idea.

So, if our environment is going to change sufficiently for us to begin dying out, things are going to have to change not only in the extreme, but very quickly as well (well, quickly in geographical terms at least). This required pace of change limits the number of potential extinction options to a very small, select list. Most of these you could make a disaster film out of (and in most cases one has), but one that is slightly less dramatic (although they still did end up making a film about it) is global warming.

Some people are adamant that global warming is either a) a myth, b) not anything to do with human activity or c) both (which kind of seems a contradiction in terms, but hey). These people can be safely categorized under ‘don’t know what they’re *%^&ing talking about’, as any scientific explanation that covers all the available facts cannot fail to reach the conclusion that global warming not only exists, but that it’s our fault. Not only that, but it could very well genuinely screw up the world- we are used to the idea that, in the long run, somebody will sort it out, we’ll come up with a solution and it’ll all be OK, but one day we might have to come to terms with a state of affairs where the combined efforts of our entire race are simply not enough. It’s like the way cancer always happens to someone else, until one morning you find a lump. One day, we might fail to save ourselves.

The extent to which global warming looks set to screw around with our climate is currently unclear, but some potential scenarios are extreme to say the least. Nothing is ever quite going to match up to the picture portrayed in The Day After Tomorrow (for the record, the Gulf Stream will take around a decade to shut down if/when it does so), but some scenarios are pretty horrific. Some predict the flooding of vast swathes of the earth’s surface, including most of our biggest cities, whilst others predict mass desertification, a collapse of many of the ecosystems we rely on, or the polar regions swarming across Northern Europe. The prospect of the human population being decimated is a very real one.

But destroyed? Totally? After thousands of years of human society slowly getting the better of and dominating all that surrounds it? I don’t know about you, but I find that quite unlikely- at the very least, it at least seems to me like it’s going to take more than just one wave of climate change to finish us off completely. So, if climate change is unlikely to kill us, then what else is left?

Well, in rather a nice, circular fashion, cosmology may have the answer, even if we don’t some how manage to pull off a miracle and hang around long enough to let the sun’s expansion get us. We may one day be able to blast asteroids out of existence. We might be able to stop the super-volcano that is Yellowstone National Park blowing itself to smithereens when it erupts as it is due to in the not-too-distant future (we also might fail at both of those things, and let either wipe us out, but ho hum). But could we ever prevent the sun emitting a gamma ray burst at us, of a power sufficient to cause the third largest extinction in earth’s history last time it happened? Well, we’ll just have to wait and see…