Tag: wavefunction

All the science in ‘The Cloverfield Paradox’

I watched The Cloverfield Paradox last night, the horror film that Paramount pictures had dumped with Netflix and which was then released by Netflix on February 4. It’s a dumb production: unlike H.R. Giger’s existential, visceral horrors that I so admire, The Cloverfield Paradox is all about things going bump in the dark. But what sets these things off in the film is quite interesting: a particle accelerator. However, given how bad the film was, the screenwriter seems to have used this device simply as a plot device, nothing else.

The particle accelerator is called Shepard. We don’t know what particles it’s accelerating or up to what centre-of-mass collision energy. However, the film’s premise rests on the possibility that a particle accelerator can open up windows into other dimensions. The Cloverfield Paradox needs this because, according to its story, Earth has run out of energy sources in 2028 and countries are threatening ground invasions for the last of the oil, so scientists assemble a giant particle accelerator in space to tap into energy sources in other dimensions.

Considering 2028 is only a decade from now – when the Sun will still be shining bright as ever in the sky – and renewable sources of energy aren’t even being discussed, the movie segues from sci-fi into fantasy right there.

Anyway, the idea that a particle accelerator can open up ‘portals’ into other dimensions isn’t new nor entirely silly. Broadly, an accelerator’s purpose is founded on three concepts: the special theory of relativity (SR), particle decay and the wavefunction of quantum mechanics.

According to SR, mass and energy can transform into each other as well as that objects moving closer to the speed of light will become more massive, thus more energetic. Particle decay is what happens when a heavier subatomic particle decomposes into groups of lighter particles because it’s unstable. Put these two ideas together and you have a part of the answer: accelerators accelerate particles to extremely high velocities, the particles become more massive, ergo more energetic, and the excess energy condenses out at some point as other particles.

Next, in quantum mechanics, the wavefunction is a mathematical function: when you solve it based on what information you have available, the answer spit out by one kind of the function gives the probability that a particular particle exists at some point in the spacetime continuum. It’s called a wavefunction because the function describes a wave, and like all waves, this one also has a wavelength and an amplitude. However, the wavelength here describes the distance across which the particle will manifest. Because energy is directly proportional to frequency (E = h × ν; h is Planck’s constant) and frequency is inversely proportional to the wavelength, energy is inversely proportional to wavelength. So the more the energy a particle accelerator achieves, the smaller the part of spacetime the particles will have a chance of probing.

Spoilers ahead

SR, particle decay and the properties of the wavefunction together imply that if the Shepard is able to achieve a suitably high energy of acceleration, it will be able to touch upon an exceedingly small part of spacetime. But why, as it happens in The Cloverfield Paradox, would this open a window into another universe?

Spoilers end

Instead of directly offering a peek into alternate universes, a very-high-energy particle accelerator could offer a peek into higher dimensions. According to some theories of physics, there are many higher dimensions even though humankind may have access only to four (three of space and one of time). The reason they should even exist is to be able to solve some conundrums that have evaded explanation. For example, according to Kaluza-Klein theory (one of the precursors of string theory), the force of gravity is so much weaker than the other three fundamental forces (strong nuclear, weak nuclear and electromagnetic) because it exists in five dimensions. So when you experience it in just four dimensions, its effects are subdued.

Where are these dimensions? Per string theory, for example, they are extremely compactified, i.e. accessible only over incredibly short distances, because they are thought to be curled up on themselves. According to Oskar Klein (one half of ‘Kaluza-Klein’, the other half being Theodore Kaluza), this region of space could be a circle of radius 10-32 m. That’s 0.00000000000000000000000000000001 m – over five quadrillion times smaller than a proton. According to CERN, which hosts the Large Hadron Collider (LHC), a particle accelerated to 10 TeV can probe a distance of 10-19 m. That’s still one trillion times larger than where the Kaluza-Klein fifth dimension is supposed to be curled up. The LHC has been able to accelerate particles to 8 TeV.

The likelihood of a particle accelerator tossing us into an alternate universe entirely is a different kind of problem. For one, we have no clue where the connections between alternate universes are nor how they can be accessed. In Nolan’s Interstellar (2014), a wormhole is discovered by the protagonist to exist inside a blackhole – a hypothesis we currently don’t have any way of verifying. Moreover, though the LHC is supposed to be able to create microscopic blackholes, they have a 0% chance of growing to possess the size or potential of Interstellar‘s Gargantua.

In all, The Cloverfield Paradox is a waste of time. In the 2016 film Spectral – also released by Netflix – the science is overwrought, stretched beyond its possibilities, but still stays close to the basic principles. For example, the antagonists in Spectral are creatures made entirely as Bose-Einstein condensates. How this was even achieved boggles the mind, but the creatures have the same physical properties that the condensates do. In The Cloverfield Paradox, however, the accelerator is a convenient insertion into a bland story, an abuse of the opportunities that physics of this complexity offers. The writers might as well have said all the characters blinked and found themselves in a different universe.

The science in Netflix’s ‘Spectral’

I watched Spectral, the movie that released on Netflix on December 9, 2016, after Universal Studios got cold feet about releasing it on the big screen – the same place where a previous offering, Warcraft, had been gutted. Spectral is sci-fi and has a few great moments but mostly it’s bland and begging for some tabasco. The premise: an elite group of American soldiers deployed in Moldova come upon some belligerent ghost-like creatures in a city they’re fighting in. They’ve no clue how to stop them, so they fly in an engineer to consult from DARPA, the same guy who built the goggles that detected the creatures in the first place. Together, they do things. Now, I’d like to talk about the science in the film and not the plot itself, though the former feeds the latter.

SPOILERS AHEAD

A scene from the film 'Spectral' (2016). Source: Netflix
A scene from the film ‘Spectral’ (2016). Source: Netflix

Towards the middle of the movie, the engineer realises that the ghost-like creatures have the same limitations as – wait for it – a Bose-Einstein condensate (BEC). They can pass through walls but not ceramic or heavy metal (not the music), they rapidly freeze objects in their path, and conventional weapons, typically projectiles of some kind, can’t stop them. Frankly, it’s fabulous that Ian Fried, the film’s writer, thought to use creatures made of BECs as villains.

A BEC is an exotic state of matter in which a group of ultra-cold particles condense into a superfluid (i.e., it flows without viscosity). Once a BEC forms, a subsection of a BEC can’t be removed from it without breaking the whole BEC state down. You’d think this makes the BEC especially fragile – because it’s susceptible to so many ‘liabilities’ – but it’s the exact opposite. In a BEC, the energy required to ‘kick’ a single particle out of its special state is equal to the energy that’s required to ‘kick’ all the particles out, making BECs as a whole that much more durable.

This property is apparently beneficial for the creatures of Spectral, and that’s where the similarity ends because BECs have other properties that are inimical to the portrayal of the creatures. Two immediately came to mind: first, BECs are attainable only at ultra-cold temperatures; and second, the creatures can’t be seen by the naked eye but are revealed by UV light. There’s a third and relevant property but which we’ll come to later: that BECs have to be composed of bosons or bosonic particles.

It’s not clear why Spectral‘s creatures are visible only when exposed to light of a certain kind. Clyne, the DARPA engineer, says in a scene, “If I can turn it inside out, by reversing the polarity of some of the components, I might be able to turn it from a camera [that, he earlier says, is one that “projects the right wavelength of UV light”] into a searchlight. We’ll [then] be able to see them with our own eyes.” However, the documented ability of BECs to slow down light to a great extent (5.7-million times more than lead can, in certain conditions) should make them appear extremely opaque. More specifically, while a BEC can be created that is transparent to a very narrow range of frequencies of electromagnetic radiation, it will stonewall all frequencies outside of this range on the flipside. That the BECs in Spectral are opaque to a single frequency and transparent to all others is weird.

Obviating the need for special filters or torches to be able to see the creatures simplifies Spectral by removing one entire layer of complexity. However, it would remove the need for the DARPA engineer also, who comes up with the hyperspectral camera and, its inside-out version, the “right wavelength of UV” searchlight. Additionally, the complexity serves another purpose. Ahead of the climax, Clyne builds an energy-discharging gun whose plasma-bullets of heat can rip through the BECs (fair enough). This tech is also slightly futuristic. If the sci-fi/futurism of the rest of Spectral leading up to that moment (when he invents the gun) was absent, then the second-half of the movie would’ve become way more sci-fi than the first-half, effectively leaving Spectral split between two genres: sci-fi and wtf. Thus the need for the “right wavelength of UV” condition?

Now, to the third property. Not all particles can be used to make BECs. Its two predictors, Satyendra Nath Bose and Albert Einstein, were working (on paper) with kinds of particles since called bosons. In nature, bosons are force-carriers, acting against matter-maker particles called fermions. A more technical distinction between them is that the behaviour of bosons is explained using Bose-Einstein statistics while the behaviour of fermions is explained using Fermi-Dirac statistics. And only Bose-Einstein statistics predicts the existence of states of matter called condensates, not Femi-Dirac statistics.

(Aside: Clyne, when explaining what BECs are in Spectral, says its predictors are “Nath Bose and Albert Einstein”. Both ‘Nath’ and ‘Bose’ are surnames in India, so “Nath Bose” is both anyone and no one at all. Ugh. Another thing is I’ve never heard anyone refer to S.N. Bose as “Nath Bose”, only ‘Satyendranath Bose’ or, simply, ‘Satyen Bose’. Why do Clyne/Fried stick to “Nath Bose”? Was “Satyendra” too hard to pronounce?)

All particles constitute a certain amount of energy, which under some circumstances can increase or decrease. However, the increments of energy in which this happens are well-defined and fixed (hence the ‘quantum’ of quantum mechanics). So, for an oversimplified example, a particle can be said to occupy energy levels constituting 2, 4 or 6 units but never of 1, 2.5 or 3 units. Now, when a very-low-density collection of bosons is cooled to an ultra-cold temperature (a few hundredths of kelvins or cooler), the bosons increasingly prefer occupying fewer and fewer energy levels. At one point, they will all occupy a single and common level – flouting a fundamental rule that there’s a maximum limit for the number of particles that can be in the same level at once. (In technical parlance, the wavefunctions of all the bosons will merge.)

When this condition is achieved, a BEC will have been formed. And in this condition, even if a new boson is added to the condensate, it will be forced into occupying the same level as every other boson in the condensate. This condition is also out of limits for all fermions – except in very special circumstances, and circumstances whose exceptionalism perhaps makes way for Spectral‘s more fantastic condensate-creatures. We known one such as superconductivity.

In a superconducting material, electrons flow without any resistance whatsoever at very low temperatures. The most widely applied theory of superconductivity interprets this flow as being that of a superfluid, and the ‘sea’ of electrons flowing as such to be a BEC. However, electrons are fermions. To overcome this barrier, Leon Cooper proposed in 1956 that the electrons didn’t form a condensate straight away but that there was an intervening state called a Cooper pair. A Cooper pair is a pair of electrons that had become bound, overcoming their like-charges repulsion because of the vibration of atoms of the superconducting metal surrounding them. The electrons in a Cooper pair also can’t easily quit their embrace because, once they become bound, the total energy they constitute as a pair is lower than the energy that would be destabilising in any other circumstances.

Could Spectral‘s creatures have represented such superconducting states of matter? It’s definitely science fiction because it’s not too far beyond the bounds of what we know about BEC today (at least in terms of a concept). And in being science fiction, Spectral assumes the liberty to make certain leaps of reasoning – one being, for example, how a BEC-creature is able to ram against an M1 Abrams and still not dissipate. Or how a BEC-creature is able to sit on an electric transformer without blowing up. I get that these in fact are the sort of liberties a sci-fi script is indeed allowed to take, so there’s little point harping on them. However, that Clyne figured the creatures ought to be BECs prompted way more disbelief than anything else because BECs are in the here and the now – and they haven’t been known to behave anything like the creatures in Spectral do.

For some, this information might even help decide if a movie is sci-fi or fantasy. To me, it’s sci-fi.

SPOILERS END

On the more imaginative side of things, Spectral also dwells for a bit on how these creatures might have been created in the first place and how they’re conscious. Any answers to these questions, I’m pretty sure, would be closer to fantasy than to sci-fi. For example, I wonder how the computing capabilities of a very large neural network seen at the end of the movie (not a spoiler, trust me) were available to the creatures wirelessly, or where the power source was that the soldiers were actually after. Spectral does try to skip the whys and hows by having Clyne declare, “I guess science doesn’t have the answer to everything” – but you’re just going “No shit, Sherlock.”

His character is, as this Verge review puts it, exemplarily shallow while the movie never suggests before the climax that science might indeed have all the answers. In fact, the movie as such, throughout its 108 minutes, wasn’t that great for me; it doesn’t ever live up to its billing as a “supernatural Black Hawk Down“. You think about BHD and you remember it being so emotional – Spectral has none of that. It was just obviously more fun to think about the implications of its antagonists being modelled after a phenomenon I’ve often read/written about but never thought about that way.