# Quantum Backflow

In the most general sense, quantum theory and classical theory are the two concepts that define a point in space at a point in time. On the surface, the two may be compared as the micro and macro levels of observation respectively. But upon further scrutiny we ascertain the most fundamental difference between the two: while the classical theory results in a sole outcome to an action, the quantum theory predicts a range of outcomes for the same action. Safe to say, classical theory breaks down at the quantum level. Each outcome is then associated with a probability, and a singular outcome can never have a probability of 1, according to quantum theory. To simplify things a bit further: say a classical and a quantum object were sitting a test together (as unbelievable as that is, it is a reasonable example) comprising a single MCQ. Now while the classical object would choose one of the four options — say Option C — the quantum object would choose all the options simultaneously — namely Options A, B, C, and D.

The laws of Physics as we see and study them are no longer applicable at the quantum level. This happens everywhere around us! Indeed, this happens on the most micro level of observation. It is these quantum properties that are often dominant over classical properties, and consequently lead to the scientific digressions (but are they really?) we observe in the world around us, for example, wave-particle duality.

Before we discuss some properties that arise as a result of the quantum effect, let us first explore the origins of the term. Quantum comes from the Latin word Quantus — meaning how big. Stretching this idea a little bit, one can think to relate a quantum to the amount of physical entity — how big of an amount of some entity — involved in an interaction.

The idea of a quantum revolutionalized Physics when Max Planck first incorporated it in his theory of quantization. In this context, a quantum was used to describe a specific amount of matter, or electricity, or radiation. This meant that, on the quantum scale, various properties of an object (as energy and momentum to name a couple) were quantized — they exist in discrete amounts. For example, on the atomic scale, an electron will only absorb or emit a quantized amount of energy (through photons) in order to move from one orbit to another. Another property henceforth, is that matter behaves as both a particle and a wave at the quantum level — the phenomenon of wave-particle duality. And a third property is given by one of the most significant theories of the quantum regime — the Heisenberg Uncertainty Principle. According to this postulate, there is a constraint to the precision with which we can measure a particle’s (or a wave’s, you never know) properties, as its momentum and position for example. And while we shall not discuss this in much detail right away, what it basically entails is that one cannot measure exactly the momentum or the position of a particle (or any other supplementary pair of properties), without some degree of uncertainty. Rather, the more precisely one measured the position, the more the uncertainty in their measurement of the momentum. We can never measure either of the two properties with a 100% precision! Certainly, this postulate was in direct violation of the EPR papers that claimed we could determine without uncertainty the value of each physical property.

Before we proceed to the backflow effect itself, let us understand one final attribute associated with the Uncertainty Principle we have just discussed. One thing we need to wrap our head around is that quantum theory indicates that a particle will occupy a range of probabilities for its existence, to the point that a measurement is made on it. This measurement we make disturbs the system, and forces it to choose a singular value to collapse to. Similar behavior is reflected by a quantum system. A quantum system is a chunk of the world around us that obeys the laws of wave-particle duality. And because that means it is a wave as much as it is a particle, it has to have an associated wave function. This function is a mathematical probability description of the various states of existence of the system. It is important to know here that a wave function has a continuous probability distribution. And while a wave function is only reflective of the position, all other physical attributes of the quantum system are also associated with the same continuous probability distributions. Point of notice here is that while the properties collapse to a discrete value in the end, the likelihood of finding them having taken up that value is continuous. Empirically, this probability is of a continuous nature owing to the fact that we can never in reality know exactly the value of that property, and can only at best, determine a range of values it might occupy.

Okay now we can finally venture into backflow and see for ourselves why its quantum effect is of an alarming nature to scientists, at the very least. In layman’s terms, backflow is defined to be the movement of a fluid (liquid or gas) in the reverse direction, or towards the source it originated from. So imagine tap water flowing back into the tap (somehow defying gravity), despite your futile efforts to ramp up its rate of flow to try and get around the situation.

For the better of high school Physics, we have tried hard to understand the laws and consequences that govern the classical theory. We have studied that upon flowing out a pipe, water will fall towards the ground in a parabolic trajectory. What we may have never come across is the possibility of this flow of water actually reverting back into the pipe in spite of otherwise unchanged environmental conditions. While we are yet to stumble upon an observable consequence of the backflow effect at the macro level, we can rest assured it has experimentally been shown to be true on the quantum level.

The probability current is described as the rate of flow of probability per unit time per unit area. It is analogous to the rate of the flow of mass, for example, out of a system — even something as common as squeezing the juice out of a lemon. It basically follows the rate of flow of probability. For the sake of scientific terminology, a quantum system is said to be undergoing the backflow effect if it has a negative probability current, in spite of having a positive momentum (any property with a probability distribution). In routine, we have seen that we cannot correlate a property to a negative probability. But we have now seen how that is indeed the case if that particular property is said to be undergoing backflow. So imagine giving a frog a small push into a pond, but something happened that somehow the frog leaped backwards towards you instead.

For the time being, the quantum backflow effect has only been observed to occur in one dimension, so for a particle travelling front-to-back or side-to-side. Second, this negative probability current has only been linked to the property of momentum on the quantum scale as yet. What’s an astonishing and exciting find for scientists, is the fact that a particle would continue to experience backflow in spite of being acted upon by an external force. So in other words, backflow cannot be stopped through imparting a disturbance along its trajectory. Does that mean that it is then unstoppable?! Does it also mean that the quantum backflow effect has the potential to pose an exception to Newton’s 1st Law — whereby a particle at rest/constant velocity has no option but to deviate along/from its existing route in the case that an external force acts on it? These are all big words to put out there, and have not yet been proven to be true. For now, scientists are deeming quantum backflow as yet another one of nature’s oddities!

One thing though, that has been observed alongside all experimental instances of quantum backflow, is the occurrence of superposition. Quantum Superposition is the phenomenon whereby a quantum system occupies multiple quantum states at the same time — there exists an overlap of quantum states at any given time. The consequential quantum state is a combination of all its constituent states, and may lead to either constructive or destructive results. Under constructive superposition, wave crests/troughs coincide to produce a quantum system with an amplitude equal to the sum of the constituent amplitudes. Under destructive superposition, however, a crest meets a trough, and the amplitude cancels out to 0 in the resulting quantum state. So any amount of quantum states can combine to produce a new and overlapping quantum state that the quantum system then occupies.

A second similarity between all quantum systems that depict backflow is the fact that they all exhibit Gaussian behavior. in their wave functions (a function of their position). What this means is that their graph of wave function against x (an arbitrary coordinate) is a Gaussian — bell curved — distribution. So at any one value of x, the wave function peaks (like a mountain) with a steep exponential decrease on either side of the peak. This Gaussian behavior is contingent upon the peak x value, its corresponding wave function, and the overall standard deviation of the whole distribution.

We have to acknowledge that this last bit of discussion may have been a forced narrative of sorts. It might seem to you as if two disjointed pieces of the puzzle may have been forced to come together in an effort to reach the end. But that’s just it with the nature of the quantum backflow effect. As of the present, it has only been experimentally observed a handful of times, and because any periodic repetitions point at a pattern and then a new theory, the backflow effect has become something of an enigma. So to conclude our discussion, we are going to discuss the most recent instance of experimental observation of quantum backflow.

This was the very recent discovery of the optical backflow of light by graduate students at Tel Aviv University, earlier this year. They commented that the whole process was of an incredibly delicate nature, and each wavelength and spectrum had to be set up with incredible scrutiny and focus to observe fluctuations at the most micro levels. They began by recreating a laser beam using constructive superposition of its spectrum of colors. They then introduced a movable slit in the path of the laser beam. They then manoeuvred the slit up and down orthogonally to gauge the position of the light beam at different locations on the emergent side. It was then that they observed, albeit a small minority of the cases, that the light seemed to have traversed along a negative angle upon emerging on the other side of the slit. For the remaining cases, the beams had, as expected, traversed a positive angle. This negative angle pointed at the possibility of the optical beam having reverted backwards in its previously forwards track. It was concluded that this observation very vehemently opposed what was expected of matter on the macro scale (to travel along the direction it was pushed and not reverse), and yet, it fell within the ambit of possibility delineated by nature — namely quantum mechanics.

With that, we shall conclude our discussion that has hopefully left you thinking a tad bit more on the absolute marvel that is the quantum theory of physics. And while it is not as commonly acknowledged as its classical counterpart, its repercussions on the everyday phenomena around us are just as implicating.

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