How far away are we from probing Planck scale physics directly?

Question

There are three related questions here:

1. Given the current limits of technology how far away are we from probing Planck scale physics directly?

2. It's well known, at least in some circles, that atoms were thought of in Antiquity; given the limits of their technology how far were they away from probing atomic phenomena directly. I'm taking atom here to be atoms in the usual sense, ie an atom of hydrogen or of Iron, and not in the philosophical sense of being uncuttable or decomposable.

3. Are we as far away from Planck scale physics, as they in Antiquity were from probing atoms? Or are we further away?

Answer 1

1. The highest energy reached so far by an accelerator is $13\,\text{TeV}$ in the LHC. The Planck scale is $\sim 10^{16}\,\text{TeV}$, so we are $15$ orders of magnitude away. (Cosmic rays with a center-of-mass energy of about an order of magnitude above the scale of the LHC have been observed).

2. If by Antiquity we mean a period of history in which there were no measurement instruments for small distance scales, they would have to use the naked eye. Then the smallest distance they could resolve is $\sim 10^{-1}\,\text{mm}$ (according to wikipedia). The hydrogen atom is $10^{-7}\,\text{mm}$ in size, so they were $6$ orders of magnitude away.

3. They were much closer to the atomic scale than we are now to the Planck scale.

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Notice also that the naked-eye scale corresponds to $10^{-15}\,\text{TeV}$ so we have improved this by $16$ orders of magnitude. This means that we’re halfway to the Planck scale!