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 Originally Posted by mojo
I feel like in the latter parts of this post, you've conflated the Planck constant and the Planck length as the same thing.
I can see how I'm giving this impression but it's because I'm lazy with my language. The Planck constant is a constant of nature, the Planck length is a unit that emerges from it. But what seems clear is that something happens at this exact scale (either h or h-bar, idk) in the same way something happens at the event horizon of a black hole... physics "changes" in the sense we do not have a working model to describe and predict behaviour, it's a barrier when the laws of physics as we know them are no longer valid.
Now if we look at it from that pov, do you think the event horizon is just a mathematical trick? Or is this region of gravitational curvature really that curved such that moving away from the gravity source requires a velocity exceeding c? All our observations suggest the latter. We can talk about what someone sees if from their FoR if they drift across the event horizon, but the tidal forces felt by anything larger than a singularity makes this concept utterly absurd in its own right.
The math appears to be telling us that something important happens at the Planck scale, there's an abrupt change from classical to quantum.
If angular momentum is quantised then surely so too is spacetime. How can an object rotate perfectly smoothly through spacetime if the energy value changes in integers? That motion from one minimum quanta to the next is rather like the second hand on a clock ticking, only the space between the ticks doesn't exist. If that space does exist, if the ticker moves through smooth space at a consistent rate, then angular momentum is smooth, and therefore not quantum. That's my interpretation anyway. The motion from one quanta to the next is instant, if it isn't there's an intermediary period between the quanta, that is, fractions of integers, ie not quantum.
Here, I'm starting to question if you have the Planck constant and the Planck length mixed up.
Is spacetime is quantised, there's a minimum distance and time. These are constants, right?
Whether the larger or smaller Planck Length is considered fundamental, it's a constant of nature either way.
Yes but only one can be "fundamental". This is kinda like saying that both one and two electrons are constant so there's nothing special about one electron.
My assumption is that spacetime is quantised and the implications of this is that there is a minimum distance, both in space and in time. Given our models break down at the Planck length (h or h-bnar, idk), then the Planck length seems the leading candidate for the length of space quanta, and the Planck second the length of the time quanta.
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