Is time an entanglement emergent phenomenon?

It is very common to see articles in divulgation journals, blogs and general media with too optimistic claims, transforming hypothesis in facts, probing too impressing stuffs and this king of things. It is very typical with results that regards extra dimensions or multiverses (both hypothesis), cosmology, the holographic principle and so on. Recently, quantum optics and quantum information has also joined that club. In my opinion, there are many articles titles with thing like: "Scientist probe that we are living in a hologram", or "Information travels to past".

I understand that journalist look for impressive titles, and something like: "Scientist calculate Helium spectrum with 17 decimals accuracy", or "Scientist probe that a quantum walks is faster than a classical one", are less impressive and too technical. Furthermore, scientist have ego too, and many of them like to appear in the media. On the other hand, we should be careful. It is not appropriate to have sensationalist news, or directly communicate things that are not true. If we do we follow a dangerous path, this leads us to the loose of our credibility.

Because of that, I want to talk about a recent article called: Quantum experiment shows how time 'emerges' from entanglement.

Time

But let start from the beginning. Time is a complicated concept. The most important genius of humankind, Isaac Newton, defined it as an absolute concept. He wrote in his master piece,  Philosophiæ naturalis principia mathematica

Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time ...

This idea changed with Einstein Relativity, where time and space are related by Lorentz transformation.  That broke with the idea of an absolute external time, and it was transformed into a new dimension, similar to space.

Lorentz transformation in one dimension

That was a breakthrough. Time was neither external or absolute, and it was mixed with space. Different observers measure different intervals between two events.

On the other hand, the main question remained, what is time and where comes it from? Thats still an open question, and it is close to both philosophy and science. Recently, if we believe this article,  Quantum experiment shows how time 'emerges' from entanglement, the question has been answer, time emerges from entanglement, a scientist have probed it!

Nice, the question is solved, an essential philosophical problem it is not a problem anymore, let prepare the Nobel Prize. Maybe, if we have a look on the technical paper, here, we should lower our claims a little, just a little bit.

Explanation of the paper

The draft, that is still unpublished, is titled "Time from quantum entanglement: an experimental illustration". The claim is much modest than the previous one. Illustrating is not showing, much less is probing. Illustrating can be to show an example, related with the topic, but essentially different to the real problem. Probing is much more difficult. Unluckily, the draft goes more in the "illustrating" path and less in the "probing" one. 

But let start from the beginning, as everything is easier in this way. The idea of an emerging time is not new. It was first proposed in 1983 by Page and Wooters, in a paper in Physical Review D. This paper was a response to certain solutions of Einstein equations that lead to a static universe, without temporal evolution. Basically, it is proposed that an external observer to the universe could see it static, but the interaction with different parts, inside the universe, leads to observe an evolution. This is not an universally accepted principle, and there are many critics to it as we will see at the end. In any case, this hypothesis is what is illustrated by the experiment.

By "illustrating" we mean to show in a very small and different to the universe case. More concretely, in the experiment two entangled photons were used. It is clear that two photons are not the universe, just a very small piece of it.

This two photons are, initially, in a Bell state $\Psi=\frac{1}{\sqrt{2}} \left(\left| H\right> \left| V\right>-\left| V\right> \left| H\right>\right)$. Where H and V mean that each photon is polarized in a horizontal or vertical state (details are not important, just we need to understand that there are two possible states for each photon). This state is entangled, as both photons are in both states at the same time, and by measuring one of the the second one will collapse to the opposite state.

Thats the initial state of the system but, how will it evolve? Thats depends on external factor, of course. The evolution of a quantum system is given by Schrödinger equation

$$\frac{d}{dt}\left| \Psi\right>=H |\Psi>$$

Thats means that by multiplying the Hamiltonian to the system we obtain the evolution. There are som special cases, called eigenstates or eigenvectors, that do not evolve. This states, when are multiplied by the Hamiltonian give the same value, and they are frozen. To simulate this kind of no evolution, the authors used the following Hamiltonians

$$H_c=H_r= i\hbar \omega \left(\left| H\right> \left<V \right|-\left| V\right> \left<H \right|  \right)$$

Where c and r represents both photons. Then, the evolution of both photons is the same, and they are switching between the two possible states in a continuous way. As they are anticorrelated that global state does not change. It is different is you observe one of the photons, then the system collapse, both photons are uncorrelated and the second one evolves. By doing this you can measure a time dependence.

Experimental setup

Basically thats what they did in this experiment. To prepare two entangled photons, make them to have the same evolution and them to measure them globally. Technical details are very important, but we don't need them for this discussion. It is enough to know that the external observer can not see any evolution, but if you measure (internally) one of the photons you will see the time dependence by measuring the second one. This can be realized in the following plot.

Evolución del segundo fotón

A very interesting experiment, with very interesting conclusions.

Critics to Medium's article

As I have already said, it is norma to see in general media too strong conclusions. This one is a very interesting experiment, but is far from probing that time is an emergent phenomenon. Wooters and Page theory has been longly criticized, and it is far from accepted.

Personally, I found criticizable

1. Wooters and Page assumed that quantum physics can de used in order to describe Universe as a whole. It is clear that it describes a two photon system, as the one from the experiment, but the theory limits are not clear. It is not clear that it can be used to describe normal macroscopical things, as a car, so extrapolating it to universe is going quite far. 
2. The experiment is based in a concrete system with a concrete evolution. Only if the state of the system is an eigenstate of the Hamiltonian it does note evolve. Even if quantum physics can describe Universe, who says that the Hamiltonian and the states are like that? It is enough to have a different state in order to see the time evolution.
3. The problem of quantum mechanics and time is old and difficult. It is simple to understand it, Quantum evolution is always reversible, but in our normal lives we observe many non reversible phenomena. That implies that the macroscopical to microscopical transition is far from trivial. 

In my opinion, Medium´s article should state, from the first beginning, that the experiment has been performed in a very concrete system, and that the results cannot be extrapolated to other systems, as the Universe.