Here I'll talk only about the Planck length and not the Planck time, though these ideas apply to it just as much.
The Common Interpretation
Here is what Wikipedia currently says about the physical interpretation of the Planck length: |
| Snapshot of Wikipedia taken November 2nd |
The smallest possible length? How does that make any sense? It baffled me when I was younger. How could a length define when the notion of length no longer worked? When you measured something just larger than the Planck length, your measurements would work, but try and measure something smaller than that and it would no longer work? This doesn't make much sense as a hard-and-fast line. Supposing it was a blurry effect didn't help: how could the effect be blurry, but the number be so well-defined? Couldn't we measure the "blurriness", and wouldn't that be the most interesting part? Was length "pixelated"?
Something like this train of thought bothered me, and I think it highlights just what is so absurd about the typical physical interpretation of this concept. How could one define the point at which a particular concept no longer made sense to use, when the definition of that point used that concept? It's as if someone temporarily decreed that no one was allowed to use calendar measures of time anymore. When asked when the decree would no longer be in effect, they would look silly if they said "two weeks from now".
What I think
So that's why the common interpretation is rubbish. Utterly unhelpful. The better interpretation of the Planck length is that it refers to when many of our physical theories begin to break down. This is very different. We can, and do, continue to use the concept of length well beyond the limit of the Planck length. The notion of space and dividing that space into points, lines, and distances are the mathematical basis for our physical theories. But while they are fundamental to the physical theory, they are not exactly "part of it" since they can be used meaningfully in the exact same way in many other contexts.
And that's exactly what we do. We use these concepts in quantum mechanics for different purposes, but they are nonetheless the same concepts. The concept of distance is unaltered at that scale, it's our classical theories that no longer work. And part of our classical theory is the notion that physical matter is made up of particles and those particles have locations. At the Planck scale, it doesn't really make sense anymore to ask where a particle is, since that is the scale at which their location begins to be indeterminate.
And that indeterminacy is definitely part of physics. When it's said that a particle has an indeterminate location, it doesn't mean that we simply cannot determine it's location. It means that that location is not determinate. It's location is blurry. This is what is significant about the Planck scale; the concept of length is still just as meaningful, it's just that physical particles no longer have well-defined locations. That indeterminacy is well-defined, actually. It's worth pointing out that physical quantum waves are not indeterminate at that scale; they are perfectly well defined at that scale.
