Smallest Observable Angle? [Archive]

Chris Pollett

Dec8-04, 06:53 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hi,\n\nI was wondering if anyone has considered the angle from say someone\non Earth observing an object one Planck length in size at some point\nshortly after the Big Bang? This seems to me like a reasonable\ncandidate for a smallest possible angle. One would have to worry\nabout inflation and other kinks in space but I am ignoring this. Does\nanyone have an argument why all observable angles must be bigger (maybe\nfrom quantum mechanics?) Or can smaller ones be allowed?\n\nAny pointers into the relevant literature would be welcome.\nChris\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hi,

I was wondering if anyone has considered the angle from say someone
on Earth observing an object one Planck length in size at some point
shortly after the Big Bang? This seems to me like a reasonable
candidate for a smallest possible angle. One would have to worry
about inflation and other kinks in space but I am ignoring this. Does
anyone have an argument why all observable angles must be bigger (maybe
from quantum mechanics?) Or can smaller ones be allowed?

Any pointers into the relevant literature would be welcome.
Chris

Uncle Al

Dec9-04, 02:02 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Chris Pollett wrote:\n>\n> Hi,\n>\n> I was wondering if anyone has considered the angle from say someone\n> on Earth observing an object one Planck length in size at some point\n> shortly after the Big Bang? This seems to me like a reasonable\n> candidate for a smallest possible angle. One would have to worry\n> about inflation and other kinks in space but I am ignoring this. Does\n> anyone have an argument why all observable angles must be bigger (maybe\n> from quantum mechanics?) Or can smaller ones be allowed?\n>\n> Any pointers into the relevant literature would be welcome.\n> Chris\n\nWhat angle does a Planck length subtend at 14 billion lightyears\'\nradius assuming Minkowski space? How would that angle be\ndistinguishable from zero even in principle?\n\n--\nUncle Al\nhttp://www.mazepath.com/uncleal/\n(Toxic URL! Unsafe for children and most mammals)\nhttp://www.mazepath.com/uncleal/qz.pdf\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Chris Pollett wrote:
>
> Hi,
>
> I was wondering if anyone has considered the angle from say someone
> on Earth observing an object one Planck length in size at some point
> shortly after the Big Bang? This seems to me like a reasonable
> candidate for a smallest possible angle. One would have to worry
> about inflation and other kinks in space but I am ignoring this. Does
> anyone have an argument why all observable angles must be bigger (maybe
> from quantum mechanics?) Or can smaller ones be allowed?
>
> Any pointers into the relevant literature would be welcome.
> Chris

What angle does a Planck length subtend at 14 billion lightyears'
radius assuming Minkowski space? How would that angle be
distinguishable from zero even in principle?

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

antimatter33@yahoo.com

Dec10-04, 10:18 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nWhatever it is,\n\nsin (P/R) ~ P/R\n\n-drl\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Whatever it is,

sin (P/R) ~ P/R-drl

me@privacy.net

Dec13-04, 10:33 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>of the entire system.\nIn other words, by revolutionaries, not reformers.\n\n112. People anxious to rescue freedom without sacrificing the supposed\nbenefits of technology will suggest naive schemes for some new form of\nsociety that would reconcile freedom with technology. Apart from the\nfact that people who make suggestions seldom propose any practical\nmeans by which the new form of society could be set up in the first\nplace, it follows from the fourth principle that even if the new form\nof society could be once established, it either would collapse or\nwould give results very different from those expected.\n\n113. So even on very general grounds it seems highly improbably that\nany way of changing society could be found that would reconcile\nfreedom with modern technology. In the next few sections we will give\nmore specific reasons for concluding that freedom and technological\nprogress are incompatible.\n\n\n\nRESTRICTION OF FREEDOM IS UNAVOIDABLE IN INDUSTRIAL SOCIETY\n\n\n\n114. As explained in paragraph 65-67, 70-73, modern man is strapped\ndown by a network of rules and regulations, and his fate depends on\nthe actions of persons remote from him whose decisions he cannot\ninfluence. This is not accidental or a result of the arbitrariness of\narrogant bureaucrats. It is necessary and inevitable in any\ntechnologically advanced society. The system HAS TO regulate human\nbehavior closely in order to function. At work, people have to do what\nthey are told to do, otherwise production would be thrown into chaos.\nBureaucracies HAVE TO be run according to rigid rules. To allow any\nsubstantial personal discretion to lower-level bureaucrats would\ndisrupt the system and lead to charges of unfairness due to\ndifferences in the way individual bureaucrats exercised t\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>of the entire system.
In other words, by revolutionaries, not reformers.

112. People anxious to rescue freedom without sacrificing the supposed
benefits of technology will suggest naive schemes for some new form of
society that would reconcile freedom with technology. Apart from the
fact that people who make suggestions seldom propose any practical
means by which the new form of society could be set up in the first
place, it follows from the fourth principle that even if the new form
of society could be once established, it either would collapse or
would give results very different from those expected.

113. So even on very general grounds it seems highly improbably that
any way of changing society could be found that would reconcile
freedom with modern technology. In the next few sections we will give
more specific reasons for concluding that freedom and technological
progress are incompatible.

RESTRICTION OF FREEDOM IS UNAVOIDABLE IN INDUSTRIAL SOCIETY

114. As explained in paragraph 65-67, 70-73, modern man is strapped
down by a network of rules and regulations, and his fate depends on
the actions of persons remote from him whose decisions he cannot
influence. This is not accidental or a result of the arbitrariness of
arrogant bureaucrats. It is necessary and inevitable in any
technologically advanced society. The system HAS TO regulate human
behavior closely in order to function. At work, people have to do what
they are told to do, otherwise production would be thrown into chaos.
Bureaucracies HAVE TO be run according to rigid rules. To allow any
substantial personal discretion to lower-level bureaucrats would
disrupt the system and lead to charges of unfairness due to
differences in the way individual bureaucrats exercised t