Maybe I’m just too steeped in pragmatism to notice, but it seems your question has already been answered. For example:
Does a limit on the precision of time at this level imply that these are actual indivisible and discontinuous units?
No, a limit on precision tells you that it’s not meaningful to ask whether or not there are actual indivisible and discontinuous units. There’s no experiment that could tell the difference.
I think pragmatism is a fine approach here, but could you clarify for me what your think the answer to my question is exactly? If it’s not meaningful to ask whether or not there are indivisible and discontinuous units, then is the answer to my question “Does QM’s claims about Planck time imply that time is discontinuous?” simply “No” because QM says nothing meaningful about the question one way or the other?
In ‘pure’ QM (without gravity), the Planck length has no special significance, and spacetime is assumed to be continuous. But we know that QM as we know it must be an approximation because it disagrees with GR (and/or vice versa), and the ‘correct’ theory of quantum gravity might predict weird things at the Planck scale. So far, most proposed theories of quantum gravity have little more predictive power than “The woman down the street is a witch; she did it”, though some do predict stuff such as the dispersion of gamma rays I’ve mentioned elsewhere.
is the answer to my question “Does QM’s claims about Planck time imply that time is discontinuous?” simply “No” because QM says nothing meaningful about the question one way or the other?
We’re trying to dissolve the question by pointing out that there exists a third option besides “continuous” or “discontinuous”. So the answer to “Does QM’s claims about Planck time imply that time is discontinuous?” would be “No, but neither is it continuous, but a third thing that tends to confuse people.”
Edit: retracted because I don’t think this is helpful.
Maybe I’m just too steeped in pragmatism to notice, but it seems your question has already been answered. For example:
No, a limit on precision tells you that it’s not meaningful to ask whether or not there are actual indivisible and discontinuous units. There’s no experiment that could tell the difference.
I think pragmatism is a fine approach here, but could you clarify for me what your think the answer to my question is exactly? If it’s not meaningful to ask whether or not there are indivisible and discontinuous units, then is the answer to my question “Does QM’s claims about Planck time imply that time is discontinuous?” simply “No” because QM says nothing meaningful about the question one way or the other?
In ‘pure’ QM (without gravity), the Planck length has no special significance, and spacetime is assumed to be continuous. But we know that QM as we know it must be an approximation because it disagrees with GR (and/or vice versa), and the ‘correct’ theory of quantum gravity might predict weird things at the Planck scale. So far, most proposed theories of quantum gravity have little more predictive power than “The woman down the street is a witch; she did it”, though some do predict stuff such as the dispersion of gamma rays I’ve mentioned elsewhere.
We’re trying to dissolve the question by pointing out that there exists a third option besides “continuous” or “discontinuous”. So the answer to “Does QM’s claims about Planck time imply that time is discontinuous?” would be “No, but neither is it continuous, but a third thing that tends to confuse people.”
Edit: retracted because I don’t think this is helpful.