If I had to guess, the explanation of the actual theory has been irretrievably butchered ("popularized", if we're being nice), which is why it doesn't make much sense as stated.
In general relativity, "time" plays several different roles, and you need to be more specific about which one you're talking about. You're usually talking about either proper time, which is the spacetime distance measured along a timelike curve (and also, up to a sign, the actual stopwatch reading you'd obtain by traveling that curve), or the coordinate time, the direction in spacetime that's the odd man out and has the "wrong" sign in the metric signature. This second definition (coordinate time) is wiggly, because there are infinitely many coordinate systems that you could pick to describe the same spacetime, each of which will use a different definition of coordinate time, and general relativity's main insight is that all of these coordinate systems are equally valid (actually, it says that the equations describing spacetime don't even change when you switch coordinate systems, perhaps one of the most profound discoveries in all of physics - if you add in the observation that curvature is caused by matter, you have almost enough in those two observations to construct the entire theory of general relativity from scratch).
Any physicist working in the field is intimately familiar with the subtleties here, and certainly knows that "clocks run slower" is a meaningless statement unless you're talking about speed relative to some other measure.
The gist of how time could run at a different speed is that if the time component of the spacetime metric was halved along your path, your stopwatch would tick off half as much time as you'd expect it to. But that's a very artificial scenario, because it presumes you have the original unaltered metric to compare to, which you don't. Locally everything would seem normal. Figuring out the global consequences of a decaying timelike component in a realistic metric is a decidedly nontrivial task, and from what I gather, that's what Senovilla is making a claim about, apparently involving string theory, as well.
Re: time starting to exist, the idea there is that if we follow a timelike geodesic (i.e. a spacetime path that matter can travel on) far enough back, we'll find that at some point the sign of "time" switches, and stopwatch readings would return negative numbers and other such nonsense. Time would "start" at the first point along that curve where a normal timelike component existed in the metric. So the more accurate statement would be that time in the spacetime metric started to exist at some point earlier along the backwards continuation of the line that we currently think of as time (though it measured no such thing before that point), which is a far more sensible thing.
Thanks for the explanation. What I gather from all of this is that I should probably either learn physics and the mathematics involved or stop listening to media blurbs about this subject or both.
It seems to me that what's happening is that physicists have created models that can be shown to work for certain parts of reality. That is, they can be applied with predictable outcomes in the real world.
The same models also have extreme states, where some variable switches sign or some function curve changes directions. And now they're asking, what would be the effects in the real world at these inflection points of the model?
It could well be that the model simply stops working at these points, like a variable representing the height of a person stops working once its value turns negative. It could also be that the model does work, but the semantics used for its popular description stop working.
Pretty much. Popularized descriptions already strain the edges of what could be considered correct under general relativity, and then when we throw string theory into the mix, things get even messier.
To give you a sense how bad it gets there, string theory results and arguments have to be "popularized" to an almost meaningless level just so that theoretical physicists that don't work in string theory can understand them, just because the whole field is so young and complex; filter that once more through a journalist, and you can end up with some pretty wacky claims, even if they're completely true.
I'd make no specific claims as to whether this research means anything or not, though; it's a famously speculative field, with only the barest of observable evidence to go on, and effects from pretty much every length and energy scale factor crucially into any cosmological evolution, making it all but impossible to say with any certainty that one proposed solution is better than another. This is where you start to get people arguing in terms of symmetry and beauty rather than observation, which brings physics awfully close for comfort to philosophy...
In general relativity, "time" plays several different roles, and you need to be more specific about which one you're talking about. You're usually talking about either proper time, which is the spacetime distance measured along a timelike curve (and also, up to a sign, the actual stopwatch reading you'd obtain by traveling that curve), or the coordinate time, the direction in spacetime that's the odd man out and has the "wrong" sign in the metric signature. This second definition (coordinate time) is wiggly, because there are infinitely many coordinate systems that you could pick to describe the same spacetime, each of which will use a different definition of coordinate time, and general relativity's main insight is that all of these coordinate systems are equally valid (actually, it says that the equations describing spacetime don't even change when you switch coordinate systems, perhaps one of the most profound discoveries in all of physics - if you add in the observation that curvature is caused by matter, you have almost enough in those two observations to construct the entire theory of general relativity from scratch).
Any physicist working in the field is intimately familiar with the subtleties here, and certainly knows that "clocks run slower" is a meaningless statement unless you're talking about speed relative to some other measure.
The gist of how time could run at a different speed is that if the time component of the spacetime metric was halved along your path, your stopwatch would tick off half as much time as you'd expect it to. But that's a very artificial scenario, because it presumes you have the original unaltered metric to compare to, which you don't. Locally everything would seem normal. Figuring out the global consequences of a decaying timelike component in a realistic metric is a decidedly nontrivial task, and from what I gather, that's what Senovilla is making a claim about, apparently involving string theory, as well.
Re: time starting to exist, the idea there is that if we follow a timelike geodesic (i.e. a spacetime path that matter can travel on) far enough back, we'll find that at some point the sign of "time" switches, and stopwatch readings would return negative numbers and other such nonsense. Time would "start" at the first point along that curve where a normal timelike component existed in the metric. So the more accurate statement would be that time in the spacetime metric started to exist at some point earlier along the backwards continuation of the line that we currently think of as time (though it measured no such thing before that point), which is a far more sensible thing.