From: George Murphy (gmurphy@raex.com)
Date: Wed Jul 09 2003 - 13:04:08 EDT
Gary Collins wrote:
>
> On Tue, 08 Jul 2003 06:46:42 -0400, George Murphy wrote:
>
> >Gary Collins wrote:
> >....................
> >> Q2) Is this not an assumption? I remember reading somewhere (don't ask
> >> me where now!!!) that space itself might be quantized; i.e. that there might
> >> be a minimum quantum length. Might this not also apply to angular measure?
> >> If so, again, it would alter the answer numerically but maybe not in principle.
> >> Same may possibly apply to your (2), (3) and (4) (which I have trimmed out)
> >> - or no?
> >
> > The uncertainty principle says that the accuracy of a clock is inversely
> >proportional to its energy, while general relativity says that the gravitational
> >effect of energy (aka mass) changes the rate at which clocks run. If these effects are
> >combined you find that for time intervals ~10^-43 sec the uncertainty in measurement is
> >of the order of the measurement itself, so intervals smaller than this - or the
> >corresponding length ~10^-33 cm - cant be measured. The classical concepts of space and
> >time lose their meaning below this "Planck length." But I don't see right offhand that
> >this would require a limit on angular measurements.
> >
> > Shalom,
> > George
> >
> Thanks for the info. I wasn't intending to suggest that any limit on angular measurement
> was required as a result of the limit on length (sloppy writing on my part) but rather
> inquiring as to whether there might be such a limit (for whatever reason). In any case,
> to assume that there definitely isn't seems to me to be an assumption.
> If the number of possible positions for a proton is limited, as seemed to be implied at
> least in previous posts) and presumably a similar restriction would apply to other types
> of particle as well (incidentally, is there a reason for the focus on the proton?) then it
> would seem to me that there would be a limit on the number of orientations possible
> for an object made of such particles. Or am I missing something?
> Wanting to understand this,
There is in one sense a limit on angles if we consider together the quantum
limit I noted earlier (~10^-33 cm) and the distance to the horizon (in cosmologies that
have one) ~10^28 cm. A triangle with the Planck length as base and the distance to the
horizon as height would have a vertex angle ~ 10^-61 radians.
Shalom,
George
George L. Murphy
gmurphy@raex.com
http://web.raex.com/~gmurphy/
This archive was generated by hypermail 2.1.4 : Wed Jul 09 2003 - 13:28:17 EDT