We also have considerable experience from accelerator physics that you still ignore for no reason:
1. Sophisticated detector systems (such as ATLAS and CMS at the LHC, ALEPH and DELPHI at LEP) are built around the locations in accelerators where collisions take place. When particles collide in accelerators, the collision produces many secondary particles which are then detected in these detection systems. By conservation of energy, the total energy of the products of the collision is the same as the total energy of the two particles that collided in the accelerator. This gives accelerator physicists a more-or-less direct measure of how powerful their accelerators are. The products of the collisions routinely have energies in the MeV and GeV ranges.
In proton-proton colliders like the LHC and proton-antiproton colliders like the Tevatron and the former SPS, it is individual quarks from the protons that collide, so the actual collision energy is typically much less than the "rated" energy of the accelerator. Electron-positron colliders such as LEP are much simpler to study in this regard. LEP was originally operated at a centre of mass (CM) energy of "91 GeV" by colliding "45 GeV" electron and positron beams. One of the simplest events observed was $$e^{+} e^{-} \,\rightarrow\, e^{+} e^{-}$$, where an electron and positron collided and an electron and positron were detected leaving the collision point in opposite directions. Often for these events, very near the full CM energy of 91 GeV was measured for the total energy of the detected $$e^{+} e^{-}$$ pair. Later, the CM energy was increased in several stages until it reached "209 GeV", and this was reflected in the total energy measured for the collision products. In particular, when LEP was operated at "161 GeV" in 1996, $$W^{+} W^{-}$$ events began to be observed, and in at least some cases the decay products were found to have a total energy approaching 160 GeV.
A gallery of some events observed by the DELPHI experiment is available
here. A gallery of some ALEPH events is available
here including a few
$$W^{+} W^{-}$$ candidate events.
2. At the LHC, the proton beams are circulated for approximately ten hours before being disposed of and replaced with fresh beams. Because of the high total energy of the beams, an arrangement for their safe disposal is necessary. The beams are disposed of by directing them into the
LHC beam dump, the target of which is a 7m long carbon cylinder. The beam is deliberately defocused while being disposed of in order to prevent it from boring straight through the beam dump.
3. In 2003 an
accidental beam loss at the Tevatron resulted in damage to the accelerator.
My point is, the people operating particle accelerators have ample evidence that their accelerators really are as powerful as they think they are.
