Yeah, those breathless describers would do well to stop to breathe before they start describing. What we know about reality at the Planck scale is mostly just that we don’t know.
Professor Brian Cox thinks the Planck Length is a fundamental aspect of our universe.
Is he a “breathless describer” in your view?
(Posted 10 days ago, 20 minutes long)
FTR: That’s the same video I linked to when I resurrected this beast.
Sorry…I am used to the Board warning me a link was already posted. It didn’t do that for me this time.
Maybe because you embedded it and I just linked to it?
Back to the OP, then where di it becaome common thought that the Planck length is the smallest meaningful length in our uniiverse because it seems from the comments here it is an inportant length in physics such as "At the Planck length … " but if I’m reading the replies right we cannot say it is any sort of limiting length.
I think Cox explains this a bit in the video in the first few minutes. The Planck Length is not conjured up. It is derived by using exceptionally well established fundamentals in physics such as the speed of light.
Maybe there is something smaller but it is as inaccessible as flying your spaceship at FTL speeds.
As of today, we have no idea how to do any of that stuff so the Planck Length is, currently, a fundamental measurement (still waaaay beyond our ability to probe but it does seem a floor).
He’s no Michio Kaku, but he’s a little breathless. 40 milliKakus.
I think he’s wrong about the relationship between human units and the Planck length. Intelligent beings had to be approximately the size of humans (approximately: within several orders of magnitude). A single cell couldn’t ask these questions, and a being the size of a planet probably couldn’t evolve in the first place. If the Planck length really underlies all of physics, then everything stacked on top–quarks, nucleons, atoms, molecules, etc.–had to go up the same length scale. So it is natural that an intelligent creature would always discover that the Planck length is something like 10^-30 to 10^-40 the length of its body.
We’re very familiar with behavior at close to the speed of light, though. Time dilation and the works are exceptionally well-tested. You don’t need a whole spaceship to test these things.
IIRC I watched a Numberphile video where he was describing a number that was something like 10^10^10^10^3 (or something like that) and noted it need not matter if that were seconds or years. For numbers that big it kinda is all the same as far as we are concerned (I may be mis-remembering which video…it was a very big number).
This seems like that. It will not matter if you are measuring from human size or bacteria size. It’s about the same either way with such big numbers (or small in this case).
There are multiple levels to the way we ignore differences between large/small numbers. Sometimes you only care about getting the most significant digit right. Sometimes just the exponent. Sometimes just the first digit of the exponent. That’s about where it stops for actual physical stuff.
But then you get to crazy math stuff. Say you have 10^10^10^10^10 grains of sand. If you used it to fill the visible universe with sand, how many universes could you fill? It’s still 10^10^10^10^10.
And then there are numbers where anything you can write down with normal high school math symbols, even with all the mass of the universe converted to paper, basically rounds down to zero in comparison. And then numbers that make numbers like that round to zero, and so on.
This is, of course, just the not-at-all-a-coincidence relationship between the definitions of the Planck quantities, being that they are the only unit-ful building blocks in the story being told. If the only LEGO pieces you give yourself to make lengths and masses and times are G, \hbar, and c, you must find answers that are related to the Planck length, mass, and time.
It’s another case of the caution from above, namely: the Cox video is overall fine but does have that “40 milliKakus” of overreach where “Oh, isn’t that curious!” implies much more than it should.
I would bet that the Planck length is special, but it isn’t special because it shows up in calculations that take G, \hbar, and c as the inputs. That’s inevitable.
The “if” at the start doesn’t hold. The comparison requires fundamental quantities outside of the Planck items, such as aspects of the strong and electromagnetic forces and the Higgs sector. Those can be used to define other independent “magic” length scales, but the relation between those length scales and the Planck length is, with current understanding, completely arbitrary (so long as it doesn’t run afoul of anthropic considerations.)
Said another way: the size of a human might be fundamentally relatable to the Bohr radius, but the Bohr radius is not fundamentally relatable to the Planck length as far as we know.
(I haven’t gone back to the Cox video to see how this connects or not to any arguments made there.)
I don’t think that’s ignorable, though, since my original statement was anthropic in nature. Some of those things probably can’t be changed without altering the necessarily conditions for life.
Regardless, it could be true–even if just by coincidence–that the Planck length matches the underlying granularity of the universe, whatever that might be (if it’s even a sensible concept). If so, I’d suggest that the hierarchy of length scales we see is largely inevitable and means that the size of an intelligent being is (within several orders of magnitude) a constant multiple of that granularity (string length, Causal dynamical triangulation scale, etc.).
I agree that there are anthropic aspects, but there seemed to be a mixing of arguments present. My main amendment was that the Planck length doesn’t set the base of the length scale “stack” you outlined. You can stack up from elementary objects to the size of a mouse using physical and/or anthropic arguments while keeping the Planck length still immensely flexible. Making the additional leap to connect these length scales together requires additional and, it would seem to me, more subtle and potentially fragile anthropic arguments than I thought you were invoking.