Doug S., I believe according to quantum mechanics the smallest unit of length is Planck length and all distances must be finite multiples of it.
Not in standard quantum mechanics. Certain of the many theories unsupported hypotheses of quantum gravity (such as Loop Quantum Gravity) might say something similar to this, but that doesn’t abolish every infinite set in the framework. The total number of “places where infinity can happen” in modern models has tended to increase, rather than decrease, over the centuries, as models have gotten more complex. One can never prove that nature isn’t “allergic to infinities” (the skeptic can always claim, “wait, but if we looked even closer or farther, maybe we would see a heretofore unobserved brick wall”), but this allergy is not something that has been empirically observed.
Doug S., I believe according to quantum mechanics the smallest unit of length is Planck length and all distances must be finite multiples of it.
Not in standard quantum mechanics. Certain of the many
theoriesunsupported hypotheses of quantum gravity (such as Loop Quantum Gravity) might say something similar to this, but that doesn’t abolish every infinite set in the framework. The total number of “places where infinity can happen” in modern models has tended to increase, rather than decrease, over the centuries, as models have gotten more complex. One can never prove that nature isn’t “allergic to infinities” (the skeptic can always claim, “wait, but if we looked even closer or farther, maybe we would see a heretofore unobserved brick wall”), but this allergy is not something that has been empirically observed.