This is a bad idea. First, causal sets are, to put it politely "not well-respected" in theoretical physics. These kinds of discrete structures tend to break a significant amount of the structure of the theories; enough that they typically can't reduce to anything that looks close to any existing theory in any limit.

In particular, they break Lorentz invariance pretty directly, which is tied up with energy and momentum conservation. The standard "hope" is that that this invariance is really "approximate" somehow, and becomes exact in some limit. But this can't really happen, because, in some sense the "errors" cannot average out, they can only add together.

In particular, you no longer have properties like $E = m$ in a particle's rest frame, because this formula is a consequence of local Lorentz invariance. So, what you end up with, is having to fine-tune because making this approximate means saying something like "$E=m+\delta$" for a particle. But what about when you have $10^{23}$ particles? Well, now, that $\delta$ term has to be fine-tuned by hand to be $10^{-23}$ to keep the microscopic deviations of order one (which is already way too big). Then you can ask what happens if you boost a collection of particles (e.g., a lead ion) to near the speed of light, etc....

There are many other problems with discreteness, too, but this is an immediate and fatal one.

Incidentally, due to the seriousness of making spacetime discrete, a lot of the people who try to do these things (causal sets, dynamical triangulations, LQG, etc) like to claim that their theories do not actually do this. But this is basically a lie; there's no politer way to put it. If you ever see someone claim they do not make spacetime discrete, but do sometime like that, walk away, because they're probably a crackpot.

Also, the idea that spacetime has to be "discrete" somehow is a huge (but, sadly, common) misunderstanding of what quantum mechanics means. There is nothing "inherently" discrete, or any need to introduce any discreteness into physics other than as a computational tool (e.g., lattice field theory) or as a physical system whose initial conditions make this a convenient approximation (e.g., a regular solid structure, crystals, etc).

The initial idea behind thinking about these kinds of things wasn't so bad, though. It comes from the thinking of, in GR, interpreting the abstract points on a spacetime manifold as corresponding to "events," and the geodesic structure as connecting events together (see, for example, the first few chapters of Misner, Thorne, and Wheeler's GR book). This lead to trying to think of, instead of the geometric structure, the structure of "events", not in the sense of the topological structure of the manifold, but as some other structure inherited by how one can connect things together with geodesics. This naturally partitions things into "all things that could have effected the point $x$" and "all things that the point $x$ can effect," with the hope that by studying the structure of these kinds of causal relations, one can reformulate GR in a new (but equivalent!) way that may fit together nicely with the "observables" formulation of quantum mechanics.

It turns out, this doesn't work so well. The structures that you get are so uncontrolled and pathological and unconstrained, that the only thing you can do to get anything sensible is by just doing GR. AFAIK, almost all physicists (and certainly all of the top people in GR) abandoned this approach by the '80s.

You can find some references for this kind of stuff if you look, but it does not really lead anywhere.

Unfortunately, in the past 10 or 15 years, a handful of people came along and misunderstood what these people were doing, and started building crazy discrete models analogous to these, sometimes in combination with taking "lattice GR" ideas way too seriously, and produced a bunch of nonsense.

And, really, the only thing stopping most physicists from calling these ideas outright crackpot nonsense, is the involvement of actual GR bigshots in the ancestors to these ideas decades ago! Although, there are certainly a few well known physicists out there who are famous for getting very angry when these ideas are brought up ;).

If you're really determined to discover in detail why these ideas are so wrong, other than working out stuff for yourself, or learning why things are the way they are in GR and QFT (which is tough!--but you should!) you may be in some trouble. Physicists aren't really in the habit of writing papers about theories that they think are obviously, fundamentally broken. We just tend to make fun of them when talking to our colleagues and otherwise ignore them! So you can't find much in the way of refutations of specifics in published literature. But if you search carefully you can find the occasionally angry rant published somewhere, and there are a few unpublished papers on the arxiv about why these theories are all broken. The only author I remember offhand doing this is Peeters about LQG's many problems, but there are others if you look.