- #1
nomadreid
Gold Member
- 1,697
- 220
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.
(*) 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.