One of the things the article says is that space and time may not be fundamental properties of nature, but properties that emerge (i.e., are the result of) a more fundamental reality.
Warning: IANAP. But with some axioms, it is possible to reach the same conclusion.
Imagine a simple experiment with an electron source and a detector. An electron is emitted in the direction of a detector. The experiment is set up such that while travelling towards the detector, the electron does not interact. More precisely, in between the emitter and the detector, the electron does not exchange any energy. Then, the electron hits the detector and becomes detected (interaction two).
Has the electron physically travelled in the space between the electron source and the detector? May it be assumed that in between the interaction with the emitter and its subsequent interaction with the detector the electron is physically present?
Obviously, it is impossible to establish that the electron is present between the emitter and the detector without actually interacting with the electron. It is therefore herewith observed that any assumptions about physical presence of the electron in between the source and the detector can not be experimentally verified. More generally, it is observed that the assumption of physical presence of any elementary particle in between two interactions can not be falsified.
Equally impossible to falsify is the assumption that in between the emitter and the detector, the electron in the experiment was not physically present. This assumption implies that (in the reference frame of the observer) the electron disappeared at the emitter and reappeared at the detector, and did not take up any physical space at any time in between. In between interactions, the representation of the electron disappeared and became unobservable. For as far as an observer can tell, the electron disappeared from the universe completely in between interactions.
Since obviously, properties about the electron are preserved in between interactions, the electron must still somehow being represented – i.e., the representation of the electron has clearly not disappeared from the universe.
The notion “observable universe” is therefore being introduced to make the distinction between interactions which can be observed, and the herewith theorized part of the universe that is apparently capable of at least holding a representation of an elementary particle and which can not be observed.
Observable universe: The part of the universe in which an interaction manifests itself.
Let us formulate the following two axioms:
Axiom 1: An interaction is instantaneous, i.e., it lasts for an infinitely small amount of time.
Axiom 2: An elementary particle only exists in the observable universe at the moment of its interaction.
Notice that axiom 1 and 2 are unfalsifiable. Consider the reverse of axiom 2:
Reverse of Axiom 2: An elementary particle physically exists in the observable universe in the time that passes (in the reference frame of an observer) between two interactions.
This axiom is equally unfalsifiable, since physical presence of an elementary particle can only be proven by interacting with it. The reverse of axiom 1, which would postulate that an interaction lasts a non-zero amount of time, is equally unfalsifiable.
Elementary particles have no internal structure and are considered point particles. In other words, an elementary particle does not take up any physical space. If we assume that everything in the observable universe consists of elementary particles, then it follows that all particles that exist in the universe do not take up any space. The aggregate volume of all elementary particles is zero.
Combined, axioms 1 and 2 state that in between two interactions, an elementary particle is not present in the observable universe. A particle only manifests itself the instant moment it interacts, becoming part of the observable universe for an infinitely small amount of time, in an infinitely small amount of space.
Two more unfalsifiable axioms are now introduced:
Axiom 3: From the reference frame of an elementary particle, no time passes during an interaction.
Axiom 4: From the reference frame of an elementary particle, no time passes in between two subsequent interactions.
Combined, axioms 3 and 4 state that elementary particles do not experience any passing of time. Notice that again, axioms 3 and 4, as well as their reverses, are unfalsifiable.
For every elementary particle, these axioms say that a particle only exists in the observable universe for an infinite small amount of time and only when it interacts. It follows then, that the observable universe is a succession of momentary interactions that themselves do not take up any space or time.
From here, it can be concluded that it is not possible to disprove that space and time do not exist. From the axioms, each of them impossible to disprove, it follows that space and time are emergent properties of a more fundamental reality.
But, again, IANAP, perhaps it shows, but I just like to think about these things and would welcome any feedback, even if it demonstrates the above is complete nonsense.