# I Planck length confusion

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1. Feb 28, 2017

If I understand correctly, the Planck length, or maybe a tenth of it, is considered the point at which quantum effects mess up any attempt to apply our present physical laws, and so one could not even in theory make a dependable measurement of something smaller. However, I was wondering what would be wrong with the following simpler argument; it must be wrong somewhere because my answer is too big.

Suppose we had some slit of width d . To measure it would require a photon with a wavelength of d/2 or smaller, that is, an Energy of at least 2hc/d, the equivalent rest mass of 2h/(cd). If we try to get the photon into the slit of width d, d will have to be bigger than the Schwarzchild radius r = 2GM/c2 = 4Gh/(c3d) . That is, d>4Gh/(c3d), or d>2√(Gh/c3) , but that is a factor of 2√(2π) too big, as the Planck length is √(Għ/c3). What is wrong? Thanks.

2. Feb 28, 2017

Staff Emeritus
You're reading into terms of order one when you only have an order of magnitude estimate.

Last edited: Feb 28, 2017
3. Feb 28, 2017

Thanks for the reply, Vanadium 50. I ask forgiveness for my own density (hopefully less than that needed to collapse into a black hole), but I am afraid that I don't quite understand your comment. What are you saying that I am estimating?

4. Feb 28, 2017

### Staff: Mentor

Not "at which quantum effects mess up...." but "around which, give or take a factor of ten or thereabouts, quantum effects must mess up...."

The statement isn't precise enough to worry about a factor of $2\sqrt{\pi}$

5. Feb 28, 2017

Thanks, Nugatory. Ah. So the Planck length is a rather fuzzy border?

6. Feb 28, 2017