The answer to that question depends on what theory you adopt for *time*. In the particular case of the Cordus theory, time is caused by matter, i.e. time is an emergent property of matter, especially discoherent matter.
This is a very different proposition to practically every other theory of time. The main other theory is to link SPACE and TIME together in the SPACE-TIME concept. This also means that such theories are locked into a concept where time is a continuous variable, and is a dimension. Therein lie a lot of deep problems: first that a continuous or ratio variable is not easy to break into discrete units, and hence the difficulty of reconciling the *time* concepts in general & special relativity with quantum mechanics; second that a dimension implies something that can go backward or forward, and it is not at all apparent that time actually does that, and no one really knows why.
The Cordus theory is different in that it proposes that *time* is the interaction of cause and effect between two pieces of discoherent matter. It provides a natural explanation for the tick of time, rooted in what might generally be considered the de Broglie frequency of matter, and for the one-way direction or arrow of time. The Cordus theory also predicts that time does not work this way for coherent assemblies of matter, which may be falsifiable. (Coherent matter is a very specialised state of matter that includes superfluids and Bose-Einstein condensates, and is not something that is typically encountered at the macroscopic level of our daily existence).
With that in mind, what does the Cordus theory say about the end of time? Well, with time being a property of matter, it implies that time emerges with matter at genesis, and shares the same fate. Therefore time as we know it will cease when the universe does.
Just how the universe will end is another question altogether. One option is that it will continue to expand, and eventually just wimp out (heat death), in which case Cordus theory predicts time would just slow down to a crawl too. The other option is that the universe collapses in on itself, in which case Cordus theory suggests time would speed up and then suddenly stop altogether. There is a third option, which no-one believes, which is that the universe is static. That seems ruled out by the red-shift.
Those outcomes are unimaginably far into the future, and there are more proximal existential threats to worry about. More interesting to us in the present epoch of the universe, is another curious prediction of the Cordus time theory. This is that there is no time (as we know it) outside the universe, i.e. beyond the cosmological boundary (DOI: http://vixra.org/abs/1303.0017.). This means that there is no time in the void into which the universe is expanding. Likewise for a being outside the universe (God) there need be no time either (atemporal). There are some interesting philosophical implications of this. We will leave that discussion for another day.
Read more about the Cordus theory here:
Pons, D.J. (2013) What really is time? A multiple-level ontological theory for time as a property of matter. vixra, 1-40 DOI: http://vixra.org/abs/1301.0074.
Pons, D.J. and A.D. Pons (2013) Outer boundary of the expanding cosmos: Discrete fields and implications for the holographic principle vixra (1303.0017), p. 1-26, DOI: http://vixra.org/abs/1303.0017. Available from: http://vixra.org/pdf/1303.0017v1.pdf.
- Which perspective of time is correct: the absolute clock of quantum mechanics or the spacetime of general relativity? (cordus.wordpress.com)
- Reality and apparent simultaneity (cordus.wordpress.com)
- Holographic principle (cordus.wordpress.com)
- It’s All Relative (stevespen.wordpress.com)