Lately I have been thinking much about the problem of singularities ( both gravitational and cosmological ), and what the resolution to those could be; I'd just like to share some of my thoughts, perhaps in the hope that others members can contribute their own perspectives.

Let us start with a simple fact which, in my mind anyway, has tremendous implications - that one can associate entropy with the event horizon of a black hole, as described by Hawking and Bekenstein in some length and detail. All an event horizon is, is in effect the boundary of a region of space-time; entropy on the other hand is a measure of how many different ways one can arrange a thermodynamic system without affecting the overall dynamics, in other words, a measure of the number of microstates a system has. The surprising fact here is that the entropy of a black hole horizon is athis tells us that the region of space-time enclosed by the horizon has a finite, well defined number of degrees of freedom, i.e. afinite, well defined number;. If space-time were smooth and continuous ( or if it contained a physical singularity ), the entropy would be infinite - but it isn't.microstructure

Another important issue we have is the one of localisation, or rather the inherent impossibility of it - trying to localise a given event at higher and higher precisions implies probing space-time with higher and higher energies in smaller and smaller regions, eventually resulting in the event itself becoming hidden behind an event horizon, again enclosing a region with a finite number of degrees of freedom. This strongly hints at the existence of a minimum length scale, beyond which the very notion of space-time itself becomes meaningless.

Given these two issues, there is a strong argument to be made for the existence of a microstructure of certain degrees of freedom to space-time. The question then is of course - whatthose degrees of freedom, and how do they relate to the smooth space-time manifold we observe on macroscopic scales ? Surely, the fact that regions of space-time can have entropy and temperature are unlikely to be mere coincidences - I would thus like to continue my train of thought in the context of statistical mechanics, since this is the area in classical physics that gives rise to the notions of both entropy and temperature.are

Suppose now we had a "quantum liquid" of fundamental simplexes ( units ), which in themselves arespatio-temporal in nature, but merely fundamental units of "pre-geometry" of sorts. These could correspond to the spin-foam networks of LQG, or the simplexes of CDT, or something else entirely - there is no way to tell for the moment. The idea now is that these fundamental units can interact dynamically, but only in certain, well defined ways; in other words, these units have certain degrees of freedom, which, it must be said again, arenotof a nature that has anything to do with space or time. They are just generic degrees of freedom which allow these units to dynamically form certain states. This is all very similar to the idea of ordinary atoms - they are basic entities which can be described by given degrees of freedom, such as number of electrons, nucleons, orbitals etc etc. Now, the crucial bit is to realise that, given those degrees of freedom, atoms can dynamically interact and form larger, more complex structures, thus giving rise tonot.emergent properties

Consider for example hydrogen and oxygen atoms. One of the obvious ways for them to dynamically interact is to form H2O molecules, which, given suitable boundary conditions, will in turn interact to form ordinaryin one of its various phases. They could arrange themselves into ice crystals, or liquid water, or vapour. Each of these has completely different macroscopic properties; yet they are all just different phases of the same underlying substance. Through this simple example we can see the idea of emergence - ice emerges from isolated H2O molecules through a phase transition, and all its macroscopic properties emerge in the process. Water emerges from ice through a phase transition. Vapour emerges from water through a phase transition. All of these have very different properties, yet they all emerge from one common substance, being units of H2O.water

So what about if space-timeis just an emergent phenomena of some more fundamental state ? What if the underlying state if the universe is not spatio-temporal in nature, but some other dynamical system, from which space-time is merely an emergent property, like water is an emergent property of interacting H2O molecules ? We could, for example, take the fundamental ground state of the universe to be some form of "quantum liquid" of pre-geometric units of some form or another, which possess well defined degrees of freedom, and can dynamically interact in certain ways; space-time would then be an emergent property of this liquid through a phase transition, like ice emerges from water through a phase transition. The basic geometric law of space-time, the field equations of General Relativity, can then be understood asitselffor the fundamental units, whatever those are. I am not talking about a mere discretization of space-time here, but about space-time being an emergent property of an underlying system of fundamental units, which are in and of themselvesthermodynamic equations of statespatio-temporal in nature. With the field equations becoming equations of state, the fact that black holes have temperature and entropy is then no longer a surprise, but both expected and necessary.not

Immediately, there are two important consequences - the BB event now becomes a simple phase transition, where the underlying "quantum liquid" gives rise to space-time as an emergent property of the dynamic interactions of its fundamental units. This does not involve any time-like or space-like processes in the traditional sense, but more the realisation of one among many superimposed quantum states of the liquid.

Secondly, there will be no more singularities - the gravitational collapse during the formation of a black hole, as the density of energy-momentum increases, then once again becomes a phase transition - just as water "dissolves" into essentially unbound H2O molecules during excessive heating, space-time will quite literally "dissolve" back into its underlying constituents, being non-spatio-temporal units. What is hidden behind the event horizon is then not a singularity, but a phase transition where space-time as we know it quite simply ceases to exist and make sense.

Evidence ? I don't have any. These are just thoughts I have upon putting together several concepts and ideas I have been reading about recently, specifically Erik Verlinde's "Entropic Gravity", Wheeler's "Geometrogenesis", and of course CDT, though you will find that the above isn't quite like any of these.

Anyways, what do you guys think - am I totally off the bat, or would you consider this workable in any way, shape or form ? I have no maths to present yet, wouldn't even know where to begin with that, tbh. However, any criticisms or comments will be appreciated.