# What is the Planck length?

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• edguy99
In summary, the Planck Length is the length-scale at which quantum gravity becomes relevant. It is roughly the distance things have to be before you start to consider “hmm I wonder if there’s a chance this whole system randomly forms a black hole.”.f

#### edguy99

Gold Member

http://www.symmetrymagazine.org/article/the-planck-scale

I believe I have read (but cannot find the reference now) the following explanation:

The energy of an electromagnetic wave is inversely proportional to its wave length. The Planck Length is so small that calculations show something vibrating within that length, would be so energetic it would become a black hole.

Does anyone know if this is true or false?

Have you tried simply Googling "what is Plank length"? It is well defined and
The Planck Length is so small that calculations show something vibrating within that length, would be so energetic it would become a black hole
sounds ridiculous to me.

https://en.wikipedia.org/wiki/Planck_length

This question comes up so often that it merits its own Insights article: https://www.physicsforums.com/threads/a-hand-wavy-discussion-of-the-planck-length-comments.831640/

I believe I have read (but cannot find the reference now) the following explanation:

The energy of an electromagnetic wave is inversely proportional to its wave length. The Planck Length is so small that calculations show something vibrating within that length, would be so energetic it would become a black hole.

"I believe I have read" doesn't even come close to meeting the minimum standards for citing a source here - and without more to go on, we have no way of knowing whether your source is wrong or you have misinterpreted or misremembered what you might or might not have read.

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• Greg Bernhardt
Perhaps I should rephrase the question "Since the energy of an electromagnetic wave is inversely proportional to its wave length, at what wavelength would a photon become so energetic that schwarzschild radius would match the wavelenght of the photon.?"

Is the answer to this question 1.616199(97)×10−35 meters?

@Nugatory Thank you for the reference. "Basically, the Planck length is the length-scale at which quantum gravity becomes relevant. It is roughly the distance things have to be before you start to consider “hmm I wonder if there’s a chance this whole system randomly forms a black hole.” I did not really understand this until I convinced myself with the following derivation, which was the main inspiration for this article."

Found it! http://math.ucr.edu/home/baez/lengths.html#planck_length - thanks @john baez

• Jilang
""The Planck Length is so small that calculations show something vibrating within that length, would be so energetic it would become a black hole ""

"sounds ridiculous to me."
On the contrary,
actually this (first quotation) is a slightly poetic version, but it is essentially true.

For every length, you can determine two energies, one for a photon (of that wavelength) and one for a black hole (of that Schwarzschild radius). At the Planck length, those two energies will be equal. At longer lengths, the black hole will be more energetic than the photon. At shorter lengths, the photon is more energetic than the black hole.

One can check it out using these three formulas:

E=Mc^2,

E=hc /lambda (photon energy)

R =2G M/c^2 (Schwarzschild radius for black hole)

Best,
Jim Graber

• Oh, well. I should know better by now than to think that just because something sounds ridiculous to me, that that has any bearing on whether it's true or not when it comes to quantum mechanics • 