In theory when an object falls into a black hole’s event horizon, an outside observer sees the last shred of time the object experience before falling in stretched to infinite duration (barring actual practical difficulties with redshift, etc.). BUT- quantum mechanics claims that we cannot ascribe any practical meaning to a duration less than the so-called Planck time, about 10^-43 seconds. So I have two questions: can anyone tell me how long it would take an outside observer to see the 10^-43 time mark; and does anyone have any idea what happens then?
To paraphrase Misner et al., photons near the black hole will be increasingly redshifted, so after a finite, relatively short amount of time you will receive no more photons from the object—it will disappear from view. Not sure what this has to do with the Planck time—just imagine someone shining a light towards you free-falling straight into a basic black hole.
@DPRK already has the answer, but for the record:
Quantum mechanics makes no such claim. In fact, quantum mechanics, by itself, doesn’t even say anything about the Planck time.
If you take the key physical constants associated with quantum mechanics and gravity, and combine them in the right way, you can get a quantity with dimensions of time. Combine them in a slightly different way, and you can get a distance, or a mass, or an energy, or a momentum, or any other sort of quantity from physics. These quantities are, collectively, known as the Planck units. And that’s all we actually know about them. All else is speculation.
Now, as for that speculation: Some of the Planck units have extreme values: The Planck distance and time, for instance, are both extremely low. On the other hand, the Planck temperature is extremely high, and the Planck speed is just the speed of light. Now, we do know that the speed of light is the maximum possible speed, which makes it tempting to think that the others are the maximum (or minimum) possible, but that’s certainly not always true: The Planck mass, for instance, is a typical mass for a bacterium, and the Planck momentum is about the momentum of a running housecat.
It is not currently known how to reconcile quantum mechanics with general relativity, but it’s widely suspected (but not known) that any such reconciliation would in some way involve quantization of spacetime. And if spacetime is quantized, then it might (but this is not known) be quantized in such a way that there exists some minimum possible length and time. And if there is a minimum possible length and time, then it might be (but this is not known) that the minimum possible length and time might be in the vicinity of the Planck length and time. And even if they’re in the vicinity, nobody would be particularly surprised if it ended up being half of the Planck length, or pi times it, or anything of the sort.
Or it might end up being billions of times larger or smaller, or there might not be a minimum possible length or time, or it might even be that spacetime isn’t quantized at all. Nobody knows.