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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?

Mozibur Ullah
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    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! – Cosmas Zachos Dec 14 '17 at 15:54
  • @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. – Mozibur Ullah Dec 14 '17 at 16:05
  • related: https://physics.stackexchange.com/questions/280382/how-far-are-we-from-reaching-around-1016-rm-gev-collisions-experimentally/280390#280390 – Rococo Dec 15 '17 at 00:20

1 Answers1

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  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.

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!

J. Manuel
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coconut
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    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! – Mozibur Ullah Dec 14 '17 at 18:36
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    Don't forget Ultra High Energy Cosmic Rays, which have been observed above $60$ EeV, or $6 \times 10^7$ GeV. – JEB Dec 14 '17 at 20:28
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    @JEB I mention cosmic rays in the answer. I didn't know it is even one order of magnitude higher than what I said, though. – coconut Dec 14 '17 at 20:42
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    @MoziburUllah Keep in mind that while the Greeks (mainly Democritus) hypothesized the existence of atoms, they had no direct evidence of atoms. Indeed, atomic theory wasn't to gain traction for several centuries. – LastStar007 Dec 14 '17 at 20:50
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    @LastStar007: sure; but look at today, we have no direct evidence of strings but that hadn't stopped an Mende effort to theorise about them! – Mozibur Ullah Dec 14 '17 at 21:02
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    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. – Mike Scott Dec 14 '17 at 21:23
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    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. – Martin Argerami Dec 15 '17 at 13:03
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    @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 – coconut Dec 15 '17 at 13:06
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    @coconut: yes, and I could accurately say that since we can travel at close to 10^5km/h, we are 50% of the way from just walking (10^1km/h) to travelling to Pluto in one hour (10^10km/h). What would be the point of saying that? – Martin Argerami Dec 15 '17 at 13:19
  • @MartinArgerami Maybe not much... I guess it'd give an idea of how those three scales compare to each other, to someone not used to them? Do you think then that the last comment in the question is so misleading that it should be deleted? – coconut Dec 15 '17 at 13:28
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    @coconut: it's your answer, so it's up to you to decide. As I said, the comment sounds misleading to me. Many of those orders of magnitude were rather easy to achieve, but it has been harder and harder (and more and more expensive) to advance. – Martin Argerami Dec 15 '17 at 15:54
  • I'd agree with Martin Argerami in that we're much further away than half-way; that's why I said we're 9 orders further away than the Greeks were. Mike Scott made a good point that we plausibly might see Planck scale physics a few magnitudes above it. – Mozibur Ullah Dec 15 '17 at 20:11
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    @MoziburUllah We’re 9 orders of magnitude further than what the Greeks were to the atomic scale, but approximately the same orders of magnitude as the Greeks were to the current scale we have reached! That’s precisely the point of the last comment in the answer! – coconut Dec 15 '17 at 20:25
  • @coconut: ok, I think I probably misunderstood what you wrote; when we say we're a thousand times further away than the Greeks were it sounds almost reassuring...! – Mozibur Ullah Dec 15 '17 at 20:41
  • @MartinArgerami I think everybody is right here as we need to clarify halfway to what?. Plotting orders of achievement vs time in a graph we are halfway to Planck scale in the achievement axis. In fact, if knowledge improves exponentially than we are even closer than halfway in the time axis. Remember, it took $\approx 300.000$ years to improve $3$ orders of magnitude from homo-sapiens to optic microscope, but only $\approx 300$ years to improve the remaining $13$. However, the knowledge curve may be logistic and we won’t get there – J. Manuel Aug 18 '22 at 09:56