# How far are we from reaching around $10^{16}~\rm GeV$ collisions experimentally?

I understand this is a highly speculative question, so I'm not expecting final words, but rather insights to deepen my notion on the issue. I know we reached about 209GeV at LEP in the end of 2000, and that the LHC is currently working at 13TeV. So what are the chances we'll see a collider testing our actual GU theories in the next few decades? What does it depend on?

• This will probably depend on the results the LHC experiment comes up with, because there will be little appetite to spend billions of dollars to confirm this theory to 5 sigmas. – Count Iblis Sep 16 '16 at 2:06
• I won't make an answer, but it should be noted that you aren't going to get to that energy scale just by turning a dial upward in Switzerland. That collider will need to be larger--probably big enough that the answer to your question is "not unless collider tech undergoes a massive advance" – zeldredge Sep 16 '16 at 2:46

After an initial period of exponential growth it looks like since the last half of the 20th century the trend has become decidedly subexponential. But let's ignore that at first. Given that we rose from $10^7$ to $10^{13}$ eV over 100 years, extrapolating that to $10^{25}$ eV would suggest we have somewhere in the neighborhood of 200 years to go.
The one thing that is safe to say is that we are terribly far away, with many completely unknown steps required. It is like if Charles Babbage were to write out a timeline to the smartphone, or the Wright brothers tried to predict interstellar exploration. On the bright side, perhaps we can hope to learn something about this regime before we can access it ourselves by observing rare high-energy astrophysical events, which can get at least up to $10^{20}$ eV.