Unless it is specifically mentioned in the series somewhere, I would say it could go at least to the 27:37 timestamp on the video (~200 trillion trillion trillion trillion trillion trillion trillion trillion and one years). There would be nothing different about space/time that should prevent a time machine from going there.
There just wouldn’t be anything to do once he got there.
The biggest and practical limitation is, how many digits does the date counter hold in the TARDIS controls?
eta now I have a story idea: the Doctor goes to the end of time and meets an immortal being, who is really really really really really really really really bored. He tries to steal the TARDIS so he can go back to Year Zero and do it all again.
Yes, but that’s a trivial statement. The way that we know that anything beyond the Higgs requires more energy is, itself, the fact that the LHC didn’t find them. Before the full-power LHC runs, it wasn’t known if there was anything else within its reach, and there was considerable hope that it would find something else interesting (precisely what interesting thing, who knew, and it might well have been something completely unanticipated, but we got unlucky and it was nothing).
Right, the fact that the LHC didn’t find much of anything after the Higgs is a retroactive observation. No one could have predicted what it might (or might not) find. The fact that it didn’t find anything new or special is information in itself, though not especially exciting information.
Arguments are now being made for new particle accelerators with enormously higher energies, but it’s not clear that there’s much support for them. What if you built a new collider with many orders of magnitude of energy greater than the LHC, and still nothing new turned up? It’s a difficult question to answer, and a difficult scenario to justify at a cost of many tens of billions of dollars.
A rather big problem in the Standard Model can be fixed if there is new physics hiding at energy scales not too far above the electroweak scale (which is to say not too far above the highest-mass particles we know about), and another problem can be fixed in parallel if that happens. So, there was some excitement about looking for this new physics at the LHC. No new physics appeared, and this is the reason minimal supersymmetry is bent (though not broken) by the data.
But the problems in the SM are still present all the same.
He would either validate or refute our current theories of what will happen. The linked videos above are nice to watch sound so sure, but what if it ain’t so? That would make many a scientist happy and give them data to think about, debate and get new insights.
And if there is indeed nothing left and everything has decayed as foreseen in the current model the TARDIS experiment would show that the current model is quite right. Or as Chronos writes:
There are different potential paths, with different strategies. There is also often inconsistency in how costs are reported.
Getting to enormously higher energies in accelerators is not practical. There are discussions about what the next leap in energy would look like and what science it can provide, but it would be less than an order of magnitude increase in center-of-mass collision energy. However, that’s not the most compelling next collider at the high-energy frontier. One can look for evidence of new physics by better measuring the properties of the newest member of the crew – the Higgs boson. Due to its special role in the Standard Model, it’s very hard to have new physics at somewhat higher energy scales not show up as perturbations in precision measurements of the Higgs’ properties. And most of the Higgs’ basic properties are very poorly measured right now (like +/-100% error in some cases.)
The design of such a machine (a “Higgs factory”) is based not on an increase in energy but an increase in luminosity – the collision rate, more or less – at the energy of interest, along with a corresponding increase in the sophistication of the detectors to match the machine’s capabilities.
Quoted costs are usually integrated over decades, multiple countries, etc, so the annual expenditures don’t seem nearly as scary when placed alongside other things in an apples-to-apples way. This also holds when viewing the costs as a fraction of the total expenditures in just the subfield(s) of particle and nuclear physics.
Last I knew, high luminosity was also the approach being taken by Fermilab. They decided that it wasn’t economical to try to compete directly against CERN on energy, but higher luminosity makes Fermilab much better than CERN for studying neutrinos (about which we also have a lot left to learn).
Just a pet peeve of mine when it comes to this “hypothesis”-it is FAR more likely that the random gunk in question will assemble by happenstance a computer and not a biological brain or the equivalent. The former would also have much higher (tho still meager) odds of persisting long enough to actually have more than a few passing and fragmentary thoughts before the surrounding chaos inevitably tears it apart.
In general tho it’s a pretty silly thought experiment, as the chaotic and malfunctioning ones (be they organic or not) will tremendously outnumber the rational more organized ones, and that is assuming that said prospect is even remotely possible anyway, no matter how many digits you tack onto the denominator.
Just because the Universe will exist for an infinite amount of time doesn’t mean that it’s inevitable that it’ll eventually create Boltzmann brains. It doesn’t even mean it’s necessarily very likely. The problem is that not all times are equal. There’s some probability of a Boltzmann brain forming now. As the Universe expands, and matter gets sparser, and entropy increases, that probability gets smaller, very rapidly. The expected number of Boltzmann brains in the observable Universe can be found from an infinite series, but that series almost certainly converges, and it almost certainly converges to a number much, much less than one.
Dark energy doesn’t get sparser, though. The volume of the universe and thus the energy goes up exponentially over time, even if there’s almost no matter.