Quantum objects make up classical objects. But the two behave very differently. The collapse of the wave-function prevents classical objects from doing the weird things quantum objects do; like quantum entanglement or quantum tunneling. Is the universe as a whole a quantum object or a classical one? Artyom Yurov and Valerian Yurov argue the universe is a quantum object, interacting with other quantum universes, with surprising consequences for our theories about dark matter and dark energy.

1. The Quantum Wonderland 

If scientific theories were like human beings, the anthropomorphic quantum mechanics would be a miracle worker, a brilliant wizard of engineering, capable of fabricating almost anything, be it a laser or a complex integrated circuit. At the same token, this wizard of science would probably look and act crazier than a March Hair and Mad Hatter combined. The fact of the matter is, the principles of quantum mechanics are so bizarre and unintuitive, they seem to be utterly incompatible with our inherent common sense. For example, in the quantum realm, a particle does not journey from point A to point B along some predetermined path. Instead, it appears to traverse all possible trajectories between these points – every single one! In this strange realm the items might vanish right in front of an impenetrably high barrier – only to materialize on the other side (this is called quantum tunneling). In the quantum realm the two particles, separated by miles or even light years, somehow keep in touch via the link we call quantum entanglement. And, of course, we cannot talk about the quantum Wonderland without mentioning that a quantum object might (and usually does) exist at a few different places at the same time. For example, when we think about an electron in the hydrogen atom, we are tempted to imagine it as a small satellite swiftly rotating around a heavy atomic nucleus. But this image is all wrong! Instead, we have to try and imagine an electron simultaneously existing in infinitely many places all around the nucleus. This fascinating picture is called an electron cloud, and we know for a fact that it is a correct picture. We know this because the identical objects coexisting in a few different places produce a physical phenomenon known as interference, which is physically observable in a lab. The fact of these observations proves two things at once: first, that the physicists who study quantum mechanics have not gone completely mad (their relatives might disagree on this one), and secondly, that physical machinery of our universe defeats even the most unbridled human imagination.

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With all that in mind, it is quite natural to feel relief at the thought that no matter how strange the quantum laws are, they are safely confined to the realm of atoms and molecules, and simply cannot be encountered in normal everyday life. How precious it is to be able to lay on a sofa with no worries that it might suddenly dematerialize from underneath you at the most inopportune moment… Speaking of which, why doesn’t your sofa have any inclination to suddenly tunnel over the wall of your room? And what prevents a piece of apple pie from being entangled with the rest of the pie? We know that both the pie and the sofa are formed by lots and lots of atoms interacting with each other. So why do these atoms abide by one set of laws, while the pies and the sofas obey a very different legislation?

Truth be told, this is a very tough question. Niels Bohr, a Danish physicist and one of the founding fathers of quantum mechanics, spent quite a lot of time pondering it and eventually came to the following conclusion. According to Bohr, the difference between a pie and a particle is indicative of a more general divide. In fact, all the objects in our universe can be stacked into two distinct groups: the classical and the quantum. We as observers belong to the first group, and so do the instruments we use while measuring the properties of something that belong to a second group. This latter, quantum group is comprised of very small objects (such as atoms and particles), which can exist in many places at the same time – quite unlike the classical objects, which cannot. Furthermore, the properties of a quantum object are effectively stored in a very special mathematical object called a wave function. The wave functions are the solutions of one differential equation, derived by the famous Austrian physicist Erwin Schrödinger and henceforth named after him. The wave functions are very useful in understanding the weird properties of quantum objects. For example, when we say that an electron exists at two states at the same time, we mean that its wave function has two separate terms, one per possible state of that electron. Mathematicians call this property a superposition. Now, suppose we measure such an electron with a classical instrument. According to Bohr’s interpretation (usually referred to as “Copenhagen interpretation”), this very act destroys the superposition – one of the terms vanishes, leaving our electron in a unique classical state. This is called a collapse of the wave function and can be used, for instance, to explain why your oak cupboard grimly remains in its corner of the room instead of carelessly existing in every point therein – simply put, the wave function of the cupboard must have long collapsed to a classical state!

So, everything appears to be in order and explainable, right? Not exactly. We still have a small nagging problem – the collapse itself. It is supposed to be a physical process, but it cannot be derived from the Schrödinger equation. Worse still, it has so far resisted all attempts to explain and place it within the framework of quantum mechanics. It sat within the Bohr interpretation like a weirdly shaped metal piece in a box of plastic Lego parts, begging a natural question: does it actually belong in here?

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Consider once again an electron in a hydrogen atom. We have left it in a rather precarious state, being “smeared” all around the positively charged atomic nucleus, simultaneously coexisting everywhere all at once. Not in the de Broglie-Bohm theory!

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Some scientists have decided that the answer must be “no”. They aimed to show that it is possible to explain quantum mechanics without resorting to the ill-defined concept such as a collapse of a wave function. And they succeeded! In fact, now we know that there are two ways to do it. The first one, independently proposed by the physicists Louis de Broglie and David Bohm, reduces the quantum mechanical effects to a special “quantum force” which is simply added to the equations of classical mechanics. In the de Broglie-Bohm interpretation (often called the “pilot wave interpretation”), the “quantum force” is the one responsible for pulling the particles over the potential barrier (quantum tunneling) and for all the effects commonly associated with quantum interference. In reality, there are no superpositions and no electron clouds, argued de Broglie and Bohm; these are merely vague approximations invented out of desperation, simply because we did not think to look for an actual perpetrator of all the quantum tricks – namely, the quantum force. For instance, consider once again an electron in a hydrogen atom. We have left it in a rather precarious state, being “smeared” all around the positively charged atomic nucleus, simultaneously coexisting everywhere all at once. Not in the de Broglie-Bohm theory! Once we add a new quantum force into the mix, an electron immediately gets localized; in fact, it ends up being completely stationary, pinned at place by the competing forces of quantum repulsion and electromagnetic attraction to an atomic nucleus!

A second approach, proposed by the American physicist Hugh Everett III, is radically different. According to it, the superpositions are real, but the collapse is not. In other words, a measurement of a quantum object does not destroy terms in the wave function. If prior to a measurement an electron was in a superposition of two different states, both of those states must survive the measurement. What happens is that these two different states end up in two different parallel worlds, identical to each other in every respect except for one thing: the state of our hapless electron. Thus, according to the many-world interpretation, when we measure the spin of an electron (which can be either “up” or “down”), the universe splits into two: in one of them we observe the “up” spin, while our doppelganger in the parallel universe perceives the “down” spin.

At a first glance the Everett’s picture seems to be much more extravagant and significantly less plausible than the de Broglie-Bohm interpretation. But to an eye of a physicist, it is the latter that is much more suspect, as it fails to satisfactorily explain either a source or a physical nature of the proposed “quantum” forces. On the other hand, over the years the Everett’s many-world interpretation slowly but surely gained popularity among theoretical physicists. At first coldly received by the proponents of the Copenhagen interpretation, who found Everett’s lack of faith in the wave function’s collapse disturbing, new evidence began to sway the opinion of the public. One of the strongest pieces of evidence for it was the discovery, made independently by two prominent physicists Heinz-Dieter Zeh and Wojciech Zurek. They were trying to understand what happens when a quantum system interacts with its environment and found a curious effect called a decoherence. To explain what it is, imagine an electron in a closed room. Next, suppose that it exists in a superposition of being at two places at once – say, by the door at the east and near the western window. Naturally, any realistic room cannot be completely empty – even in a clean room we can find photons, a few dust particles, some residue molecules of oxygen and carbon dioxide, etc. For simplicity, let us restrict ourselves to photons. Zeh and Zurek have shown that when a single photon interacts with our electron, it utterly reduces the level of quantum interferences. To an imperfect eye of a classical observer, this looks as if a collapse of the wave function took place, and the electron became firmly localized (for example, near the window). But in reality, there was no collapse: the superposition remains, albeit in a significantly weakened form. This is what is called decoherence. One can show that under the normal condition (room temperature, pressure and moisture) any macroscopic object undergoes extremely rapid decoherence which all but renders its quantum abnormalities almost imperceptible.

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This was the generally accepted state of affairs in the field of quantum mechanics for the last few decades. However, an interesting discovery, made in 2014 by a group of theoretical physicists from Australia and US, has opened a new and very intriguing possibility: that the universe at large might actually behave like a quantum object! In order to explain why, we’ll have to take a little detour to contemporary cosmology – the science about the origins and the fate of the universe.

2. The Cosmological Phantom Menace

It is difficult to name another branch of physics that arose, developed and grew in popularity as fast as cosmology did in the course of the 20^th and 21^st centuries. We have truly learned a lot during this time. For example, we now know that the universe is about 13-14 billion years old. In its early infancy, the universe has undergone a mind-blowingly fast expansion, aptly named “the cosmological inflation” (the term borrowed from the economy). In a fraction of a second, a region of space the size of a pin head and weighing 1 milligram, had exploded in size, forming an entire observable universe. Such a rapid expansion has radically smoothed the distribution of matter in the region, making the universe extremely homogeneous and isotropic. Accidentally, this turned our universe into a relatively simple object of study, named an FLRW universe -- an acronym lovingly assembled out of family names of four mathematicians who first studied such universes: Alexander Friedman (USSR), Georges Lemaître (Belgium), Howard Robinson (USA) and Arthur Walker (UK).

One can surmise that a rapid expansion must have blown up any pre-existing imperfection. Think of a balloon with a little picture of a mouse – the mouse representing the imperfection. If we blow up the balloon, the picture would also grow in size, eventually rivalling in size not only real-world mice, but also a cat and even a medium-sized dog. In the early universe the role of such imperfections was played by the tiny, ever-present quantum fluctuations. Normally these fluctuations are too small and too faint to be noticed – but cosmological inflation is anything but “normal”. Under its strain the vacuum fluctuations grew up to become comparable in size with the contemporary galaxy nuclei – which, in fact, they eventually produced. Every galaxy can be traced to an embryonic vacuum fluctuation, caught and blown up by the cosmological expansion in the early universe. By extension, every star and every planet in our galaxy owes their existence to these quantum fluctuations. So, when you thank your “lucky stars”, don’t forget those tiny fellows as well!

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The remaining 96% of visible matter, hidden by the darkness of our ignorance, consists of two components: 27% of it is called dark matter (DM) and 68% is so-called dark energy (DE). The former behaves like an ordinary atomic matter, except that it is non-luminous. The latter, however, is something else

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Another interesting thing that we have learned about the universe is how little we matter – literally. It appears that all the visible matter (such as photons, protons, neutrinos, etc) constitutes a paltry 5% of total ledger. The remaining 96%, hidden by the darkness of our ignorance, consists of two components: 27% of it is called dark matter (DM) and 68% is so-called dark energy (DE). The former behaves like an ordinary atomic matter, except that it is non-luminous. The latter, however, is something else. The DE behaves like an ideal fluid with a negative pressure, which fills an entire universe and causes it to expand –with acceleration. There are different hypotheses regarding the nature of this strange fluid. Many scientists claim that it is a manifestation of a vacuum energy. The others insist that it may be a product of a hypothetical quintessence field, varying in space and time. Some hypothesize that it might be a very special type of quintessence field, called the phantom energy, in which case the universe will expand so fast it will risk literally tearing itself apart in a cosmological event morbidly called the Big Rip singularity.

Then again, there might be one other explanation. But in order to understand it, we’ll have to travel back in time, to the year 2014.

3. The Many Interacting Universes

In 2014 three physicists, Michael Hall, Dirk-André Deckert and Howard Wiseman made a fascinating discovery: they have managed to unite together the de Broglie-Bohm and the Everett interpretations, constructing a brand new model, called the Many Interacting Worlds interpretations (MIW). They proposed that our universe is indeed one of many other universes, just like in the many-world interpretation of Everett. But this time there was a little twist: while Everett treated the different universes as distinct and independent from each other, Hall et al. have assumed that the universes might actually influence one another. And how exactly do they do that? Why, via the “quantum” forces, proposed by de Broglie and Bohm, of course! Here is how it works: for any object (say, an aforementioned electron in a hydrogen atom) there exists a number of its doppelgangers, “doubles” from the parallel universes (different versions of our electrons). We cannot see those doppelgangers, because they interact only with each other. What we can see is the result of that interaction, which manifests itself as an additional repulsive force. In fact, according to MIW, all quantum effects that affect an object are produced by the forces of interaction with the object’s doubles from other universes. Interestingly, the strength of this force is determined by how similar the doubles are to each other. When they are not very similar (have different energies, are located in different places etc) the quantum force is diminished. If the “quantum” force becomes so small that it gets downright negligible compared to the normal classical forces, our object ceases to be quantum and becomes purely classical. This is what happens when an object in question consists of many particles with a lot of degrees of freedom. For example, consider a… soccer ball. As a macroscopic object it consists of about  atoms; if we want it to behave “quantum-mechanically” – for instance, tunnel right through the enemy team’s goalkeeper, – most of those atoms must be extremely similar to all their doubles in the parallel universes. Which is, of course, a statistical impossibility, and is therefore not recommended as a viable method of scoring goals.

So, MIW is a good sport when explaining why we see no discernible quantum effects on the macroscopic scale. But what about… the universe itself? We have already discussed how the cosmological inflation in an early universe has produced a very smooth, homogeneous and isotropic FLRW universe. It is in fact so uniform, that its history is essentially an evolution of a single, time-dependent parameter called a scale factor. In a strange way, our universe as a whole is fundamentally much simpler than a soccer ball – or any other macroscopic object! But we have already learned that the simpler the object, the stronger the quantum forces – even if the object itself is as large as a universe! All we have to do is to consider a multiverse consisting of many different FLRW universes with various scale factors and add an interactive repulsive force. Following this idea, we have derived the cosmological equations for a universe interacting with its nearby “neighbours” via the quantum force. To say that what we’ve got has exceeded our expectations would be an understatement. The preliminary results have predicted that the “quantum” forces might act like a dark energy of a special sort! And not only that: the parallel universes closest to ours might also manifest themselves as a dark matter. Imagine our astonishment!

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Naturally, this is just a beginning of a story. Our model requires further adjustments and verifications. At this juncture, we cannot claim that the mysteries of dark matter and dark energy are resolved at last. We have merely pointed out a new promising avenue of research. And yet we cannot shake the feeling of awe when we think that our world, so familiar and clearly comprehensible, the world of sofas and soccer balls, is but a tiny classical sliver sandwiched between the two frighteningly strange quantum realms of atoms and universes. Ancient Greek philosophers believed that the same laws must govern the very large and the infinitely small. Maybe they were not too far from truth, after all?