Re: How can the Planck length be claimed to be the smallest length?
- From: Igor Khavkine <igor.kh@xxxxxxxxx>
- Date: Tue, 6 May 2008 03:06:59 +0000 (UTC)
On May 5, 1:28 pm, JohnMS <john_m_stan...@xxxxxxxxxxx> wrote:
Many arxiv papers state that the Planck length
is the smallest measureable length.
Most of the time, this is merely a heuristic. The Planck length comes
up as the scale beyond which quantum gravitational effects become non-
negligible. This is shown using dimensional analysis, much in the same
way as the Bohr radius, beyond which the full quantum mechanical
description of the Hydrogen atom cannot be neglected. Note that the
Bohr radius was derived before a modern quantum mechanical treatment
of Hydrogen became available. A similar statement can be made about
the Planck length.
Current established theories neither require nor propose a minimal
length. However, tentative models proposed for quantum gravity
sometimes assume some kind of discreteness or granularity of space-
time at the Planck scale. Thus, the nature of the Plank length as the
smallest measurable one should be considered as one of the hypotheses
assumed by these models. While there are arguments for the validity of
this hypothesis, like all others, it must be subject to experimental
verification.
If you want a more detailed discussion of how to resolve your
"paradox", you'll have to specify which model of quantum gravity you
are assuming.
Hope this helps.
Igor
.
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