“Τα πάντα ρει” says famous Greek philosopher Heraclitus; *everything flows. *With this expression, Heraclitus probably wanted to express the world view that, at the most basic level, everything is in constant motion. What is the most basic level of nature according to modern physics? Of course, the quanta! If Heraclitus’ view that everything flows is correct, then ..*quanta rei* as well; or, to take advantage of my Greek origins, ..*τα* *κβάντα* *ρει**, *right?

A few weeks ago, Gerardo, the Italian captain of our Quantum Correlations group in Nottingham, inaugurated our brand new Blog with a warm welcoming post, where he very illustratively explains why we chose the name “quanta rei”,

All entities move and nothing remains still. […] *This is remarkably true once one gets down to the smallest components of the fabric of the world, in the realm of quantum mechanics: even if something appears still to our macroscopic perception, the particles inside it never stop moving, fluctuating, exchanging energy and getting correlated with the others nearby, even when cooled down to the absolute zero temperature. From here comes the inspiration for the name of our blog, *

*“*

*κβάντα*

*ρει*

*”*

*(*

*“*

*quanta rei**“*

*).*

We certainly see many headlines reporting quanta fluctuating, even empty space itself,

**But is our claim, that quantum particles are in constant motion, really true?**

Well, according to the most advanced understanding of quantum theory the scientific community has up to this date… *we don’t know*! We don’t know if quantum particles move all the time, and most importantly we don’t know whether particles exist in the first place. To shock you even more, we don’t even know what quantum theory is about, what it actually describes, and how to interpret it. Quantum theory is the best physical theory we have at the moment, it describes (almost) everything with unparalleled precision. And yet, the ignorance of the scientific community about its actual interpretation is profound.

*But how is that possible**, *asks the interested yet puzzled reader. *You build quantum computers, you created the unbreakable quantum cryptography, your own research is about taking advantage of quantum effects to create new quantum technologies; how can you do all that, and yet have no idea what you are truly talking about? *

All these are great questions. An intuitive answer could be given by using a classical analogy. One may be able to drive a car, or use a computer, and do great things with it –like, win a car race, or make a 3D computer game – without necessarily knowing in detail the inner workings of the car or the computer respectively. The only thing one needs to know in this case is a set of rules on how to use the car/computer, e.g. how to use the gears in the car to make it move, or how to use programming languages to create computer games. It’s the same with quantum physicists (drivers) and nature (car). We have a set of rules, which we call *quantum theory*, about how nature works and behaves, and by using these rules in a smart way we can do amazing stuff like building new quantum devices and much more, without having a deeper knowledge of the inner workings (if such workings exist in the first place).

**What is quantum theory about? …16 possible interpretations**

We know a few things about how nature works at microscopic scales, which are summed up in the following set of rules that will allow us to *drive*:

- Every existing entity (and I intentionally avoid the word
*particle*), e.g. an electron, is described by a wavefunction Ψ(x,t) where (x,t) represent space and time accordingly. Therefore, every single entity in this universe – to the best of our knowledge – is described as a wave. - The wave Ψ(x,t) of a given entity evolves and interacts with waves of other entities according to a particular wave equation, Schrödinger’s equation.
- Any attempt to measure the position of this wave will interrupt it and eventually make it collapse randomly in a specific position x
_{0}with probability |Ψ(x_{0},t)|^{2}, where with |..| we denote the absolute value. This rule is well-known as Born’s rule.

These are the three rules that govern all physics in the non-relativistic regime of small energies that have puzzled physicists for more than a century about their actual meaning. The first two rules seem to give a quite straightforward interpretation: All entities are described like waves in space-time and they evolve via a wave equation, just like a water-wave! So, quantum entities must be waves right? Not quite according to Rule 3, the most puzzling one. Rule 3 says that if we try to measure the position of a wave Ψ(x,t), the wave will collapse to a single point with some probability determined by the wavefunction prior to measurement. Therefore, instead of seeing a wave we will actually see a dot, just as if we detected a single particle. In a few words, quantum entities behave like waves when you don’t interact with them and like particles when you do observe them. The moral of this story is that measurements, i.e. observations, of quantum systems unavoidably interrupt these fragile systems. To serve with an analogy, imagine as if you lived in the darkness and every time you shined your flashlight on an object to observe it, the object would absorb the momentum of the light you threw at it and disappear with high speed. If classical objects were so sensitive to light, we wouldn’t be able to *just observe* something without altering it. Of course, in the real world, classical objects are complex high-mass systems completely insensitive to the negligible energy of sun-light, therefore we never face such problems. But let’s keep this analogy in mind, of an ultra-sensitive classical world, to get a feeling on what is going on with the quantum.

*OK, *says the interested reader, *I understand that observation of the very-very small and fragile quantum systems unavoidably disturbs them. But let’s forget about observing these systems for a moment, and let’s think about what is really going on before any observation takes place!*

According to Rules 1 & 2, before any observation the peculiar quantum entities will behave like waves in space-time. There is a current big debate however about what this wave actually represents. Some physicists say that the wavefunction is *real*, in the sense that it’s all there is, nothing more nothing less. Others say that the wavefunction only represents our state of knowledge about the system, and that’s why we can only compute probabilities from it. Others believe in parallel universes where the particle occupies all possible positions in different universes simultaneously, while others say that there truly are point-particles and the wavefunction acts like a force-field that pushes the particles around, achieving even super-luminal speeds. All these are different views on the *inner workings* of nature, and actually constitute a small fraction of all possible interpretations of the wavefunction, and consequently of quantum theory. It is incredible how diverse two different interpretations of the same theory may seem to be, and yet, all of them lead to the same experimental predictions. In other words, there exists –at least for the moment– no experiment that can distinguish which interpretation is the *correct one.* In the figures below, borrowed from a recent paper of quantum physicist Adan Cabello**,** all known interpretations of quantum theory are listed; all **16** of them!

Believe it or not, we can design and build powerful quantum computers (well, we are working on that…) and other technologies even if we are completely ignorant about the interpretation of the three rules we listed above; i.e., the set of rules is enough *to drive the “car”*!

Now let’s get back to our original question.

**Τα κβάντα ρει**** or not?**

As the reader may suspect the answer to this question is ultimately interpretation dependent. Some interpretations of quantum theory would say ‘yes’ everything moves, some would say ‘no’, while others would consider the question ill-defined.

Let us consider an example, where a single quantum system is trapped inside a 2-dimensional empty box, and the system is forced to move on the x-y plane shown in the figure below, with 0 < x < 1 and 0 < y < 1. The system is assumed to interact with nothing else, being in the absolute zero T=0 K temperature. If it was a classical particle, absolute zero would imply total stillness, no motion. However, a quantum system in the absolute zero has a wavefunction distributed in the box as shown in the figure.

Let us investigate whether *quanta rei* in our example. As one can show by applying Schrödinger’s equation (Rule 2 for evolution of systems), the wavefunction Ψ(x) of the system stays still in time, does not evolve or “move”. Therefore, according to those interpretations of quantum theory that would consider the wavefunction to be *all there is –like the many worlds interpretation- *nothing moves ..Quanta *not* rei! Everything is *static.* On the other hand, another interpretation, known as Bohmian mechanics, would give the exact opposite answer. In this interpretation, there exists a point particle that moves around the box and the wavefunction plays the role of a force field that pushes the particle around. See the video below for an illustration of how point-particles move in random trajectories in the Bohmian interpretation.

(Note: The physical system in the video is different from the 2-dimensional box we considered here.)

Therefore, Bohmian mechanics would answer ‘yes’, everything moves around, even in the *absolute zero*. Finally, to complete the picture, according to the Copenhagen interpretation our question “quanta rei?” is ill-defined, since asking the question of what is really going on when we do not observe a quantum system is metaphysical, not subject to experimental test. Is the moon there when *no one* looks at it? According to the Copenhagen interpretation this is a metaphysical question.

What do we believe in our group? *Everything flows?* We are not really sure! Each one of us has their own taste and intuition on quantum theory, and it’s really difficult to choose a *favorite interpretation* when they all seem to be equivalent experimentally, at least up to this point.