Oh my. So many answers here that misunderstand the nature of the Planck length.

First, the smallest measurable length given our present-day means is many orders of magnitude greater than the Planck length. But I presume the question is not about what’s measurable in practice but what’s measurable in principle.

So let us think about it for a moment. Are the Planck scale units really about limits? Hmmm… The Planck mass is about 21.7 micrograms. Is this the smallest measurable mass? Certainly not, since we can easily measure masses less than 21.7 micrograms with modest equipment. Is this the largest measurable mass, then? Well, my bathroom scale disagrees.

So if the Planck mass is not a limit either way, what makes us think that the Planck length is such a limit?

Obviously no one is going to produce a measuring stick shorter than about [math]1.6\times 10^{-35}[/math] meters but that’s not how we would measure such a short distance anyway.

But you know what… let me imagine a bit of interferometry with some futuristic equipment using 1 TeV (teraelectronvolt) gamma rays. Say, two such gamma rays differ in wavelength by half a Planck length. Well… if I am not mistaken, after a mere 10 centimeters or so, the two gamma rays would be at opposite phase, canceling each other out (apologies if I miscalculated, it’s easy to lose track of these exponents). A carefully arranged apparatus, then, could measure a difference in wavelength that is just half a Planck length, even in a tabletop scale (of course it’s hard to find a source of coherent 1 TeV gamma photons, but I did say futuristic, didn’t I.)

So then, if it is this “easy” to measure lengths shorter than the Planck scale, what’s the big deal you might wonder?

First of all, the Planck scale is not an inherent limit of anything. It is simply the set of “natural” units that characterize Nature. (In a rather weird way, it’s basically Newton’s constant of gravitation. The other constants in the calculation — the speed of light and the reduced Planck constant — are both dimensionless and set to 1 in natural units. Newton’s constant, however, has the dimensions of inverse energy squared.) The limit business arises from the fact that we have reason to believe that our best theory to date, quantum field theory (in the form of the Standard Model of particle physics) is only an “effective” theory that fails at the Planck energy scale. So the Planck scale is not a physical limit or a limit on what can be observed; rather, it’s a limitation of the theory that we use to describe the quantum world.

Long story short, the Planck length is probably not the smallest measurable length, but if it is, we don’t (yet) know why that it so.

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