> To the best of my knowledge, mainstream quantum mechanics assumes continuous spacetime, so the argument that the primary reason it can't be reconciled with general relativity is continuity seems pretty specious to me.
Your criticism is right and that is a bad argument. The real reasons they are hard to reconcile are technical (see for example [1]), and not mentioned in the source I referred to.
The article only says that a discrete theory of spacetime "might be essential" for the reconciliation; the arguments for this are philosophical - it would be beautiful and historically completing. Read the article if you're interested in the arguments, which aren't included in my comments.
> And it's possible to come up with a model where the universe is infinite but the visible universe is finite. In fact, I believe FLRW is one such a model, and is supported with high accuracy by the latest experimental observations.
I agree with you that the universe could be infinite, but that doesn't contradict my previous comment. I explained that I was talking about local (causally connected to us) space-time, only. I admit this is a bit of a trick, but the parent comment used the term "real space" which I interpreted in such a way to favour an argument for finite space.
> So again, your argument doesn't seem that compelling to me.
I've given reasons but I think it might be helpful to restate what I am actually claiming. I admit I don't know that space and time are discrete. The source I gave is a poetic and philosophical argument that it might be. I think it's established fact that energy and matter are, and that time is finite in the past, so the visible universe is finite. I think it's possible that the future is finite too.
> I think it's established fact that energy and matter are, and that time is finite in the past, so the visible universe is finite.
None of that is established, actually:
Metric expansion of space comes with a cosmic event horizon where redshift goes to infinity. While the energy contained within that region is finite, there's no reason to assume that the universe outside the horizon looks any different than inside the horizon, and it might very well be spatially infinite.
As to time being finite in the past, it is possible to generalize Einstein's equations so that they can be extended past the big bang singularity, and what you get is a mirror universe on the other side. The issue here is that as we approach Planck scale, quantum gravity becomes relevant, and we have no predictive theory of that.
Your criticism is right and that is a bad argument. The real reasons they are hard to reconcile are technical (see for example [1]), and not mentioned in the source I referred to.
The article only says that a discrete theory of spacetime "might be essential" for the reconciliation; the arguments for this are philosophical - it would be beautiful and historically completing. Read the article if you're interested in the arguments, which aren't included in my comments.
> And it's possible to come up with a model where the universe is infinite but the visible universe is finite. In fact, I believe FLRW is one such a model, and is supported with high accuracy by the latest experimental observations.
I agree with you that the universe could be infinite, but that doesn't contradict my previous comment. I explained that I was talking about local (causally connected to us) space-time, only. I admit this is a bit of a trick, but the parent comment used the term "real space" which I interpreted in such a way to favour an argument for finite space.
> So again, your argument doesn't seem that compelling to me.
I've given reasons but I think it might be helpful to restate what I am actually claiming. I admit I don't know that space and time are discrete. The source I gave is a poetic and philosophical argument that it might be. I think it's established fact that energy and matter are, and that time is finite in the past, so the visible universe is finite. I think it's possible that the future is finite too.
I don't know what FLRW is. My best guess is https://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–W...
[1] http://www.theory.caltech.edu/people/jhs/strings/str115.html