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?

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    $\begingroup$ Be quantitative in your question, by explicitly providing the distance and energy scales you are asking about, and reassuring the reader you are not really asking about what they are! $\endgroup$ – Cosmas Zachos Dec 14 '17 at 15:54
  • $\begingroup$ @Cosmos Zachos: I'm asking for quantitive estimates. I could have solved this question myself years ago when I knew quantitive estimates for such things as the relevant energy and length estimates. $\endgroup$ – Mozibur Ullah Dec 14 '17 at 16:05
  • $\begingroup$ related: physics.stackexchange.com/questions/280382/… $\endgroup$ – Rococo Dec 15 '17 at 0:20
  1. The highest energy reached so far by an accelerator is $13\,\text{TeV}$ in the LHC. The Planck scale is $\sim 10^{19}\,\text{GeV}$, 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 $\sim 0.1\,\text{mm}$ (according to wikipedia). The hydrogen atom is $0.1\,\text{nm}$ 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.

Notice also that the naked-eye scale corresponds to $10^{-12}\,\text{GeV}$ so we have improved this by $16$ orders of magnitude. This means that we’re halfway to the Planck scale!

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    $\begingroup$ So we're 9 orders further than the Greeks were when they conceptualised atoms...no wonder Planck scale physics is so problematic! And no wonder too, the dizzying levels of speculations associated with this too! $\endgroup$ – Mozibur Ullah Dec 14 '17 at 18:36
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    $\begingroup$ Don't forget Ultra High Energy Cosmic Rays, which have been observed above $60$ EeV, or $6 \times 10^7$ GeV. $\endgroup$ – JEB Dec 14 '17 at 20:28
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    $\begingroup$ Note that you can see clear evidence of atoms (Brownian motion) at several orders of magnitude larger than the atoms themselves. The same will likely turn out to be true of Planck-scale physics. $\endgroup$ – Mike Scott Dec 14 '17 at 21:23
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    $\begingroup$ The "half way" comment is misleading. First, because it's "half way" in orders of magnitude. And second, because there is absolutely no reason to assume that progress will be made, if at all, at a comparable rate. For an example of this, the faster a human could travel in 1900 was about 100km/h. One order of magnitude (1000km/h) was achieved with jet planes in the late 50s. Another one with space travel (say, 10000km/h) when going to the moon ten years later. That was fifty years ago, and there is no plan nor expectation to have humans travel faster in the foreseeable future. $\endgroup$ – Martin Argerami Dec 15 '17 at 13:03
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    $\begingroup$ @MartinArgerami But we’re halfway (in orders of magnitude)! I didn’t say and certainly didn’t want to imply that we’re going to improve at a constant rate $\endgroup$ – coconut Dec 15 '17 at 13:06

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