What "large size" unit of length could be considered at the opposite end of spectrum from Planck's length?

Is there a table of smallest and largest value for various physical quantities that can be defined from well-known constants?


I was teaching the exponential function and scientific notation to kids and I was looking for example of physical quantities that occur on vastly different scales. Length is the easiest and there are some demos as in The Scale of Universe. As the size of universe seems to be a function of time I wondered about other large lengths.

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    $\begingroup$ Do you mean units like "light years ..etc" ? $\endgroup$ – user29727 Oct 18 '13 at 20:54
  • $\begingroup$ Sorry, Maesumi, your first question doesn't make sense - it's like asking how big is infinite? Re your second question, sure there are tables about the constants, including revisions over time (normally due to increased precision). Here's a good jumping off point: en.wikipedia.org/wiki/Physical_constant $\endgroup$ – Howard Pautz Oct 18 '13 at 21:00
  • $\begingroup$ Planck's constant is necessary because it describes the quantum-ness of our world. Planck length is simply a length unit derived from that constant. However, quantum effects become insignificant on macroscopic scales, so there is no direct analog of a "large-scale" quantum constant. $\endgroup$ – Dmitry Brant Oct 18 '13 at 21:01
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    $\begingroup$ Planck's width? $\endgroup$ – Alfred Centauri Oct 18 '13 at 21:30
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    $\begingroup$ @Adobe Perhaps a proton-light year. The distance traveled by light during half life of a proton. But I was looking for something, if one exist, that is a meaningful unit of length. $\endgroup$ – Maesumi Oct 18 '13 at 22:35

The opposite of a universal minimum length scale would simply be a universal maximum length scale, which in principle would likely be set by the diameter of the Universe. It's currently unknown whether or not there exists a fundamental upper bound on lengths scales or not.

  • $\begingroup$ 13.7b lightyears? $\endgroup$ – user28737 Oct 19 '13 at 7:58
  • $\begingroup$ @WaqarAhmad No, the diameter of the observable universe is about 92b lightyears. 13.7b years is the time elapsed since the big bang, roughly, which is likely where you've heard that number before. $\endgroup$ – David H Oct 19 '13 at 8:16
  • $\begingroup$ ops, s=vt = 3*10^8 * 13.7b years? s=radius $\endgroup$ – user28737 Oct 19 '13 at 9:04
  • $\begingroup$ @WaqarAhmad First point: the speed of light is $c=1 \text{light-speed} = 1 \text{light-year per year}$, exactly. Not $3 \cdot 10^8$ or what have you. Units matter. $\endgroup$ – David H Oct 19 '13 at 9:21
  • $\begingroup$ @WaqarAhmad The speed of light is the fastest at which things can move with respect to space. But space itself can move as fast as it damn well pleases. So you cannot place such a simple upper bound on the radius to which the universe has expanded to since the time elapsed from the Big Bang like you were trying to do. $\endgroup$ – David H Oct 19 '13 at 9:26

Planck's constant is not at one end of a spectrum, so it has no "opposite" in this sense. In particular, it's not a minimum length. There is an argument for a minimum measurable length that is on the order of the Planck length, but that's different.

  • $\begingroup$ That said, if there is some minimum measurable length, then it is impossible to build a ruler scaled to a unit spacing finer than that minimum measurable length. Otherwise, you've just built a measuring instrument capable of measuring distances smaller than the minimum distance possible to measure! So I feel justified in calling the Planck length a minimum scale, but I want to delete my answer if there's something I'm just not getting here. Can I get you're take? $\endgroup$ – David H Oct 19 '13 at 6:07
  • $\begingroup$ @DavidH Calling it a "minimum scale" is misleading because it implies that smaller values of length just doesn't exist. There are some speculative theories that predict the existence of a minimum length in this sense, but they're not verified and thus outside the scope of the question. In current physics, the word "measurable" is very important. Saying "minimum measurable length" encapsulates the fact that you can't build a ruler (or equivalent) with finer spacing. Also, even if there is a true minimum length, it probably won't be exactly the Planck length, just something on that order. $\endgroup$ – David Z Oct 19 '13 at 16:59

Graham's number is the only practicable answer I can think of to answer your question.

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    $\begingroup$ That seems to be a mathematical number, I did not see a connection to physical quantities. $\endgroup$ – Maesumi Oct 29 '13 at 19:09

protected by Qmechanic Sep 2 '14 at 6:54

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