High energy photons collapsing into small black holes?

1. Dec 1, 2009

One of the arguments for the existence of a minimum distance, the Planck distance, is
(*) that in order to probe a smaller distance, you need a probe, e.g. a photon, of wavelength smaller than that distance, that is, of very high energy, and indeed such high energy that when it is localized it would collapse into a black hole, hiding any information about that particle and hence of the distance it was meant to probe. A bit simplified, but that seems to be the gist.
Now, my questions:
(1) A rejoinder to this would seem to be, at first glance, that the miniature black hole would immediately deteriorate by giving off Hawking radiation. In fact, it would happen so fast that it would be a question whether one could measure it except as a theoretical intermediate process to account for the effects. So, in order for the argument (*) to hold up, there must be a difference between these effects from a scenario where the photon was absorbed and then given off by the object the size of which is under question. Where, precisely, are these differences?
(2) one would be tempted to say that the radiation given off from the deteriorating black hole could be collected and analyzed to find out information about the radiation that had collapsed to make the black hole in the first place. If the above argument (*) is to hold up, this argument must have serious holes. Off the top of my head, I would suspect that one problem would be the uncertainty of the vacuum energy that triggered the deterioration, but I am not sure if this is a fruitful idea to pursue.
Any indications to one or both of these questions would be welcome.

2. Dec 1, 2009

bcrowell

Staff Emeritus
I think the part of the argument you're missing is that the black hole has a certain size (the size of its event horizon), and it can't be used to probe structure on scales smaller than this size. A photon with the Planck energy becomes a black hole with its size equal to the Planck length. If you try to put in more energy in an effort to shorten the photon's wavelength and probe shorter distance scales, you actually make a black hole that has a *bigger* size.

Re the Hawking radiation, I think the idea is that the Hawking radiation with the minimum wavelength is made by the black hole that forms when the photon has an energy equal to the Planck energy -- and this wavelength equals the Planck length. So you still can't probe less than the Planck length.

I don't know whether it's inevitable that the black hole decays before you can use it to probe anything. I would assume that in its own rest frame, a one-Planck-mass black hole has a lifetime equal to the Planck time. However, it seems to me that you could have the black hole moving at close to c relative to your lab, so conceivably its lifetime could be long enough to reach the thing you're trying to probe.

3. Dec 1, 2009