I've seen it.

Of course, there are some significant ways there are problems with measurement of extremely small distances. The Heisenberg Uncertainty Principle is going to mess with us if we try to push it to extremes.

I still don't think the Plank Length is significant for the reasons you've been putting forward in the past, unless I've dramatically misunderstood your point(s).

In the video what they're saying is that it's not so much the Planck Length that's significant as it is that the curvature of spacetime is more and more extreme in the vicinity of photons of ever-increasing energy.

One significant thing Matt was saying is that this distortion of spacetime means that the concept of distance loses meaning. Like, a black hole is an object whose diameter is larger than its circumference... so knowing the apparent outside diameter of the black hole doesn't tell you the diameter measured within the black hole. I.e. distance has lost its colloquial meaning.


What he did not say is that distances that small do not exist. What he did not say is that the universe has a "minimum step" distance that anything can move. What he did not say is that position is limited to points on a grid.

These are the things I've thought you were claiming about the Planck Length.


What he said was position-momentum uncertainty yields obscene levels of uncertainty in momentum when position is constrained to ever-decreasing sized volumes. So much that if you want to confine an electron to too tiny a volume (on the order of a Planck Length cube) that we can no longer be certain that there's exactly 1 electron in the volume.

Note that he repeatedly says phrases like, "when this volume is close to the Planck volume" the energy uncertainty approaches the energy of the particle in question - indicating that the exact volume is a function of each particle, I think. I mean that the energy uncertainty is a function of volume, but it takes different amounts of energy to create different particles, so the volume for each particle would be different.


Also note he does say it's just a trick of mathematics to get units of length out of other known constants.
Also note that he uses h_bar in his Planck Length, instead of h. This is an arbitrary choice and leaves us a factor of 2pi discrepancy between 2 possible choices for the value of the Planck Length. Which is more physical h or h_bar? It's an empty question, they differ by a factor of 2pi. We don't tend to consider constant factors to be more or less physical. It the relationship shown by the factor that matters, not the value of the number, as such. So... why choose h_bar over h? Why choose h over h_bar? There's a difference of a factor of over 6.25 between them. If we're going to tie physical meaning to the Planck Length, then we should have a solid argument for which of those (h or h_bar) is correct.

This was not done in the video. He didn't even mention that an arbitrary choice in there means we don't even know which value of the Planck Length is "the" value. All we are really saying is there's QM and GR weirdness when trying to discuss extremely tiny distances - distances on the order of a Planck Length. The Planck Length isn't really that significant, so much as there's a soft limit at the bottom where the universe simply refuses to define such small distances.