Minimum Viable Size for a Black Hole?

[Saintheart]

It's a common misconception that "the Planck Length is the smallest possible length". There are multiple layers of ignorance between us and any sort of statement like that.

First, it's possible that spacetime is quantized. I think most physicists would say that it's plausible or even likely, but we don't actually know it is, and certainly we don't know the details.

Then, if spacetime is quantized, it's possible that it's quantized in such a way that there's a minimum possible length... but not everything that's quantized has a minimum possible value, so it's also possible that there isn't such a minimum length.

If there is a minimum possible length, then we don't know what it would be. We know that it must be smaller than what we've probed, but we don't know how much smaller. Something in the vicinity of the Planck length is certainly plausible, since it is indeed much smaller than what we've probed, and it bears a natural relation to constants of the Universe that we do know about... but that's just our best guess; it could be something completely different.

And even if there is a minimum possible length and it's in the vicinity of the Planck length, that doesn't mean it's the Planck length exactly. Nobody would be in the least surprised if it turned out that the minimum possible length were half the Planck length, or pi times it, or whatever.

Now, one situation where we do know that the Planck scales have relevance is in the final stages of the evaporation of a black hole. If what we know about black holes extrapolates smoothly down to those scales (and that's a VERY big if), then a black hole with a mass comparable to the Planck mass would be radiating particles with an energy comparable to the Planck energy, which would indeed seem to set a limit of the Planck mass as the smallest possible size for a black hole. Actually, it'd mean a smallest possible size of many times that, as such a hole would be radiating a very great many particles. Of course, it's also quite possible, likely even, that what we know of black holes doesn't extrapolate that far, and that there's some new physics that we don't know that becomes relevant before then, but then the Planck scale is still relevant, as it provides a scale to let us know when we must be approaching that new physics.

I have nothing to add here other than to post my delight that a titan named Chronos is in here posting about time and space.

[Chronos]

Well, it's not entirely coincidental. I chose the name I did because I'm fascinated with spacetime, and pursued that fascination through grad school. The fact that my forum title, at the moment, happens to be "titan", though, is a coincidence.

[halfeye]

The fact that my forum title, at the moment, happens to be "titan", though, is a coincidence.

Or Peelee got at it, he admits he thinks he's funny.

[Bohandas]

It's a common misconception that "the Planck Length is the smallest possible length". There are multiple layers of ignorance between us and any sort of statement like that.

First, it's possible that spacetime is quantized. I think most physicists would say that it's plausible or even likely, but we don't actually know it is, and certainly we don't know the details.

Then, if spacetime is quantized, it's possible that it's quantized in such a way that there's a minimum possible length... but not everything that's quantized has a minimum possible value, so it's also possible that there isn't such a minimum length.

If there is a minimum possible length, then we don't know what it would be. We know that it must be smaller than what we've probed, but we don't know how much smaller. Something in the vicinity of the Planck length is certainly plausible, since it is indeed much smaller than what we've probed, and it bears a natural relation to constants of the Universe that we do know about... but that's just our best guess; it could be something completely different.

IIRC the planck length is calculated to be the minimum possible margin of error under the uncertainty principle for position/length/spatial measurement, and so even if it isn't the minimum possible length, it is the mimimum meaningful length, and so even if something could be smaller it would always in practice be about a planck length. IIRC.

EDIT:
I can't seem to find verification for this in the relevant wikipedia article. Although looking at the article's history page there appears to have been an edit war, so I may have indeed seen it there at some point. Will have to check elsewhere.

EDIT:

Found it on Fermilab's website:
https://www.fnal.gov/pub/today/archi...lReadMore.html

Although they do stress that this may turn out to be inaccurate due to gaps in our knowledge of how gravity works on a subatomic scale. (So I guess we're both right. Based on known physics it's the smallest meaningful length, but there are known unknowns in that area that may change that)

"...So why is the Planck length thought to be the smallest possible length? The simple summary of Mead's answer is that it is impossible, using the known laws of quantum mechanics and the known behavior of gravity, to determine a position to a precision smaller than the Planck length. Pay attention to that repeated word "known."...our understanding of subatomic gravity is incomplete"

[Peelee]

Or Peelee got at it, he admits he thinks he's funny.

Yeah, but that's an admin power.

[halfeye]

Yeah, but that's an admin power.

Oops, so who? or really a coincidence? Funny anyway

[Peelee]

Oops, so who? or really a coincidence? Funny anyway

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