On 1/22/2026 3:46 AM, John Clark wrote:
On Wed, Jan 21, 2026 at 9:35 PM Brent Meeker <[email protected]>
wrote:
//
/> OK, I see my mistake. I was looking at whether the swapping
was order independent.
But your post, "and because they are Non-Abelian, swapping M1 and
M2 and then M2 and M3, gives a different result than swapping M2
and M3, and then M1 and M2." is unnecessarily complicated.
Swapping M1 and M2 gives a different results if they are non-Abelian./
*I used that as an examplebecause not only does it demonstrate how
exotic non-Abelianparticles can encode information in ways that
regular everyday Abelianparticles cannot, *
Yes, M1*M2 is a different bit than M2*M1.
Brent
*it also shows how that information can be used to perform
calculations that Abelianparticles cannot. *
*John K Clark See what's on my new list at Extropolis
<https://groups.google.com/g/extropolis>*
*
*
6hu*
*
eh7
Brent
On 1/21/2026 5:16 AM, John Clark wrote:
On Tue, Jan 20, 2026 at 4:02 PM Brent Meeker
<[email protected]> wrote:
//
/> Doesn't that give different results whether they are
Abelian or not.
m1, m2, m3 -> m2,m1,m3 -> m3,m1,m2
m1, m2, m3 -> m1,m3,m2 -> m2,m3,m1/
*If the interactions with the following particles _are
__Abelian_then the final result of*
*
*
*{ [(M1*M2)*M3]*(M2*M1)*M3*] }*(M3*M1)*M2*
*
*
*would be _identical_ to the final result ofthe following reactions
*
*
*
*{ [(M1*M2)*M3]*(M1*M3)*M2*] }*(M2*M3)*M1 *
*
*
*But if you do the same thing with particles that _areNOT
Abelian_then those two results would NOT be the same. *
*
*
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