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<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>\n> Is it possible in nature to measure action values below hbar/2?\n\nTo make a long story, this is not possible. A new literature search\nshowed that Bohr told about the "indivisibility" of the quantum\nof action hbar for many years, in all his seminars\nthroughout the world.\n\nIt then was a shock, with the discovery of spin, that the\nindivisible value was hbar/2 and not hbar. But the\nresult remains. There is no action below hbar/2.\n\nAlready Bohr had told that all effects of quantum theory\nfollow from this indivisibility. His Como lecture is an example.\n\nAfter the spin/2 shock, these arguments somwehow were\nnot much used any more, out of fear that even smaller values would\nbe possible. However, hbar/2 really is the minimum value.\n\n> Arguments against:\n> - spin 0 particles do exist; spin and action has the same dimension,\n> thus action values below hbar/2 are possible.\n\nThe action W is defined as W= \\int L d phi, where L is the total\nangular momentum and\nphi the phase. The spin S enters in the total angular momentum\ntogether with orbital angular momentum.\n\nThere is no way to have W smaller than hbar/2 for a particle\nof spin 0 that is composed, because the finite extension\nof such a particle always leads to a finite orbital angular momentum,\nand thus W is never 0. Spin 0 could lead to a zero W only if\nthe particle is point-like, ie, elementary.\nHowever, no elementary particles of spin 0 are known.\nOne is predicted to exist: the Higgs particle. The statement that\nhbar/2 is the smallest action in nature thus implies that the\nHiggs is composed, not elementary. (We will see in 2008,\nwhen the LHC in Geneva is ready.)\n\n(Except if there might be another way out of the contradiction...)\n\n\n> I would be especially interested in getting more arguments *against*\n> the thesis.\nNo other attempts arrived yet.\n\n\nRegards\n\nChristoph Schiller\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>Is it possible in nature to measure action values below [itex]\hbar/2[/itex]?
To make a long story, this is not possible. A new literature search
showed that Bohr told about the "indivisibility" of the quantum
of action [itex]\hbar[/itex] for many years, in all his seminars
throughout the world.
It then was a shock, with the discovery of spin, that the
indivisible value was [itex]\hbar/2[/itex] and not [itex]\hbar[/itex]. But the
result remains. There is no action below [itex]\hbar/2[/itex].
Already Bohr had told that all effects of quantum theory
follow from this indivisibility. His Como lecture is an example.
After the [itex]spin/2[/itex] shock, these arguments somwehow were
not much used any more, out of fear that even smaller values would
be possible. However, [itex]\hbar/2[/itex] really is the minimum value.
> Arguments against:
> - spin particles do exist; spin and action has the same dimension,
> thus action values below [itex]\hbar/2[/itex] are possible.
The action W is defined as [itex]W= \int L d \phi,[/itex] where L is the total
angular momentum and
[itex]\phi[/itex] the phase. The spin S enters in the total angular momentum
together with orbital angular momentum.
There is no way to have W smaller than [itex]\hbar/2[/itex] for a particle
of spin that is composed, because the finite extension
of such a particle always leads to a finite orbital angular momentum,
and thus W is never . Spin could lead to a zero W only if
the particle is point-like, ie, elementary.
However, no elementary particles of spin are known.
One is predicted to exist: the Higgs particle. The statement that
[itex]\hbar/2[/itex] is the smallest action in nature thus implies that the
Higgs is composed, not elementary. (We will see in 2008,
when the LHC in Geneva is ready.)
(Except if there might be another way out of the contradiction...)
> I would be especially interested in getting more arguments *against*
> the thesis.
No other attempts arrived yet.
Regards
Christoph Schiller
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