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Is the "correct model" even well-defined or remotely falsifiable?

In my view, we're sailing awfully close to metaphysical waters with phrases like that.

It is currently known that to probe the Planck scale is practically impossible, or implausible depending on your level of optimism.

That scale is the point at which we might gain some level of confidence that we know what "really" is a particle (or its constitution), whether it is truly a point particle or if it is just convenient to assume that at the present time.

Not just practically impossible, it is theoretically impossible. Given Heisenberg's uncertainty principle, observing a position with a certainty of the planck length would require it to have so much energy that it forms a black hole. Since you cannot get information out of a black hole, this makes observations below this scale impossible.

Of course, the scales involved are far beyond anything we have been able to probe. And this arguement relies fundamentally on the interaction between gravity and quantum mechanics, even though those theories are famously not compatable. So the 'theoretically' in theoretically impossible is doing a lot of work.

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