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What everybody was waiting for ... Borcherd's new blog! And the first post is on the uselessness of Planck units. He's already on my blogroll.
posted by Kea | 2:46 PM
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5 Comments:
Glald that I have found your blog with good pics of APOD I so love. Good taste that's what one finds here and that's also what I hope and wish you'll find out in my PALAVROSSAVRVS REX!
It's an interesting post about the Planck units. Actually, the Planck units are very useful to befuddled lecturers who confuse fact with orthodoxy.
The Planck scale is purely the result of dimensional analysis, and Planck's claim that the Planck length was the smallest length of physical significance is vacuous because the black hole event horizon radius for the electron mass, R = 2GM/c^2 = 1.35*10^{-57} m, which is over 22 orders of magnitude smaller than the Planck length, R = square root (h bar * G/c^3) = 1.6*10^{-35} m.
Why, physically, should this Planck scale formula hold, other than the fact that it has the correct units (length)? Far more natural to use R = 2GM/c^2 for the ultimate small distance unit, where M is electron mass. If there is a natural ultimate 'grain size' to the vacuum to explain, as Wilson did in his studies of renormalization, in a simple way why there are no infinite momenta problems with pair-production/annihilation loops beyond the UV cutoff (i.e. smaller distances than the grain size of the 'Dirac sea'), it might make more physical sense to use the event horizon radius of a black hole of fundamental particle mass, than to use the Planck length.
All the Planck scale has to defend it is a century of obfuscating orthodoxy.
The "Planck units" can be very misleading, since they assume that h, c and G are all constant. Stating that h = c = 1 is a real absurdity. Too bad it is in so many books.
Hi Kea,
Thanks for this info.
When Borcherds posts an appropriate thread relating to VOA or the monster, I will have to ask him a question about something that I learned from A Rivero:
Golay Code(s) [error-correcting] appear to be related to some of the sporadic groups [Mathieu and Monster].
Binary [with link to ternary]
http://en.wikipedia.org/wiki/Binary_Golay_code
Does this raise the possibiity that Golay code(s) have some means of retaining an equilibrium?
If so, besides the game Mogul [24 coins] and other Conway contributions, is this another example of how sporadic groups like the Monster and VOA may be related to mathematical game theory?
Welcome, Joshua! Thanks Nigel and Louise. And Doug, yes it will be interesting to see what Borcherds thinks ...
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