If you have good eyes, the smallest objects you can make out are about a tenth of a millimeter: roughly the width of a human hair. Add technology, and the smallest structures we have measured so far are approximately 10^-19 m, that’s the wavelength of the protons collided at the LHC. It has taken us about 400 years from the invention of the most primitive microscope to the construction of the LHC – an improvement of 15 orders of magnitude in four centuries.
Quantum effects of gravity are estimated to become relevant on distance scales of approximately 10^-35 m, known as the Planck length. That’s another 16 orders of magnitude to go, or another factor of 10^16 in terms of collider energy. It makes you wonder whether it’s possible at all, or whether all the effort to find a quantum theory of gravity will forever languish as idle speculation.
I am optimistic. The history of science is full with people who thought things to be impossible that have meanwhile been done: measuring the light deflection on the sun, heavier-than-air flying machines, detecting gravitational waves. Hence, I don’t think it’s impossible to experimentally test quantum gravity. Maybe it will take decades, or maybe it will take a number of centuries – but if only we keep pushing, one day we will measure quantum gravitational effects. Not by directly crossing those next 16 orders of magnitude, I believe, but instead by indirect detections at lower energies.
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