Quantum Levitation: A Floating Columbia

“I had trapped the atom in mid-air. Colleagues called my Lutece Field quantum levitation, but in fact, it was nothing of the sort. Magicians levitate – my atom simply failed to fall. If an atom could be suspended indefinitely, well – why not an apple? If an apple, why not a city?

The city in the sky. Columbia, a fictional steampunk city-state found within the video game Bioshock Infinite, is a city that literally defies the law of gravity. Sitting at just over 15,000 feet high, Columbia sets the tone for the radical ideas that private detective Booker deWitt has to wrestle with throughout the rest of the perplexing story.

Columbia is undoubtedly an intriguing sight – but could it actually ever exist? Could these ‘Lutece fields’ be a real quantum phenomenon? Luckily for you, that is the question we are about to dive right into.

Rockets

The first and most obvious method in trying to ‘float’ a city would certainly involve the use of those large balloons we see attached to the bottom of each building. The most efficient way to go about building Columbia would to be by doing all the construction at ground level and then sending the buildings to the clouds. This brings us to our first calculations. Astronomer Phil Plait first carried out the calculations for the energy required to lift these giant buildings. In fact, the calculations are easily replicated, allowing us to determine how much energy it would take to lift a building the size of the Empire State Building up to the height which they are found in Columbia.

Considering that the Empire State Building weighs about 330 million kg [2], the gravitational potential energy required to lift this building by a height of 5 km (just over 15,000 feet) can be determined assuming the Galilean approximation:

fdgfd

That is 16.2 trillion Joules, a huge amount of energy. To let that sink in, a single bicep curl of a 2 kg weight uses about 10 Joules of energy [3] – meaning it would take the equivalent of 1,620,000,000,000 curls of energy to get that building into the atmosphere. As Kyle Hill over at Gizmodo puts it [1]: The Saturn V rocket is one of the largest rockets ever devised. At full burn, this monster can belch out enough fire and exhaust to produce 1.7 million pounds of thrust. [But] the math shows that we would need more than 420 Saturn V rockets to lift [the building]“. So can it be done using Helium filled blimps instead? The answer is yes, but we would vanquish all the Earth’s Helium in doing so (and keeping it up there).

420_Saturn_V

420 Saturn V Rockets – the amount required to lift the Empire State Building 15,000 feet into the atmosphere! Each rocket stands at around 111 metres tall – 65 times taller than the average person!

Balloons

Taking the density of air at sea level (which we shall approximate to be constant up to its destination) is 1.2 kilograms per cubic metre. The density of Helium on the other hand is only 0.2 kg/m^3. This lower density is what makes it ‘lighter’ than the surrounding air and is essentially why it rises. The difference between these densities is equivalent to how much mass can be lifted, which is conveniently 1 kg every cubic metre of Helium.

Since the mass of the Empire State Building is 330 million kg, this means that you would need an equivalent 330 million cubic metres of Helium. Using the volume of a sphere, we can calculate the radius of this balloon containing the Helium:

fgfgf

which is approximately the size of the building itself (meaning that the whole balloon’s diameter would be twice this). In terms of blimps, this would be equivalent to having 1650 Hindenburgs doing all the legwork [1]. Considering that this amount of Helium (to get this one skyscraper) up there is twice that of the total production worldwide, I think it is safe to say that Helium is not the way to go. But if our lightest gas is not viable, how else would we go about achieving this levitation?

Magnetic Levitation

What about those futuristic Maglev trains which use the phenomenon of magnetic levitation to float over guideways? By cooling superconducting magnets to sub-zero temperatures with the aid of liquid nitrogen, the phenomena known as the Meissner effect provides another opportunity for levitation using magnetic fields. The physics behind this phenomenon is simple – below a certain critical temperature in superconducting materials, the superconductor expels any magnetic field that pass through it by creating electrical currents near its surface [3]. These currents create their own magnetic fields which counters that of the external magnet – effectively shielding the materials from the external field. Here is a demonstration of the Meissner effect in action from my research lab:

However, to float a building using the Meissner effect is not feasible. Firstly, you would need to line the bottom of every building with some bloody big magnets, and even then, the magnetic field strengths coming from these magnets decay rapidly with distance (as an inverse cube law i.e. 1/R^3). The height at which these buildings could then levitate at would be severaly restricted. Secondly, above a certain magnetic field strength, superconductivity is abruptly destroyed. This effectively kills off the Meissner effect as the key to levitating a city!

Trapping an Atom

In the game, the Lutece twins talk about how they managed to suspend an atom mid-air, and follow this line of reasoning to levitating an entire city. Well, it turns out that trapping an atom is something scientists have managed to accomplish to a high fidelity using laser light [4] (see the 2018 Nobel Prize for Optical Tweezers).

Essentially, a source of atoms is generated by heating up a metal to sufficiently high temperatures which leads to the emission of an atomic vapour of the surface of the metal. A number of lasers can then be employed to slow these atoms down using the phenomena of laser cooling, by which changes in the momentum of the atoms can be achieved due to the Doppler effect [5]. This process is carried out in the centre of a spatially varying magnetic field which confines them to a specific region in space. Afterwards, a secondary laser beam accelerates this group of cool, slowed atoms towards another high powered trapping laser, which is able to trap a single atom from this group to a specific point in space using the same technique of laser cooling. These experiments are usually carried out under a vacuum to establish clear paths for the atoms to travel without bumping into other molecules in the atmosphere!

Check out this video animation from the MIT Lincoln Laboratory to see how trapping neutral atoms is achieved:

Ultimately, using lasers to suspend free atoms in a vacuum is one thing – levitating a city using light is another (which is prohibitive due to energy and momentum viewpoints)!

Will we ever be able to float a city using these techniques?

Probably not, no.

Will floating cities ever be a reality?

In Virtual Reality, yes!
In Reality Reality, maybe!

References

[1] Hill, K. (2013, April 5). Could You Actually Build BioShock Infinite’s Floating City in Real Life? Gizmodo. https://gizmodo.com/could-you-actually-build-bioshock-infinite-s-floating-c-470692206

[2] The Measure of Things – 331,000 tonnes. (n.d.). The Measure of Things. Retrieved June 20, 2021, from https://www.themeasureofthings.com/results.php?comp=weight&unit=tnsm&amt=331000&sort=pr&p=1

[3] The Editors of Encyclopaedia Britannica. (n.d.). Meissner effect | physics. Encyclopedia Britannica. Retrieved June 20, 2021, from https://www.britannica.com/science/Meissner-effect

[4] Optical tweezers achieve new feats of capturing atoms. (2019, April 3). ScienceDaily. https://www.sciencedaily.com/releases/2019/04/190403122432.htm

[5] Laser Cooling. (n.d.). Hyperphysics. Retrieved June 20, 2021, from http://hyperphysics.phy-astr.gsu.edu/hbase/optmod/lascool.html

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