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Mueen Nawaz wrote:
> Invisible wrote:
>> "Real-world problems are simply degenerate cases of pure mathematical
>> problems."
>
> I recently attended a talk given by Arthur Jaffe, a (co)founder of
> the Clay institute and professor at Harvard (forgot if he's in the math
> or physics dept). His work is mathematical physics.
>
> I don't know his stance, but he knows many top physicists and
> perhaps mathematicians as well who'd disagree. Essentially, the (very
> boring) talk was about this very issue: Are mathematics and physics
> consistent with each other?
>
> A lot of the calculations in physics as currently performed are
> actually mathematically invalid. He gave this startling example. You see
> the g_s in the equation on this page?
>
> http://en.wikipedia.org/wiki/Magnetic_moment#Magnetic_moment_of_electrons
>
> It has now been measured to around 12 significant figures - perhaps
> the most precise measurement ever made. Those 12 figures agree with theory.
>
> And that theory is simply mathematically invalid (at least with the
> current state of mathematics).
I'm not sure that "mathematically invalid" means anything here. It
would be more precise to say that the model described by the mathematics
in question does not apply to the phenomena described.
Is .5c + .5c = 1c mathematically valid? Well, yes. If two observers,
moving at .5c relative to one observer, in opposing directions, observe
each other, do their observations of each others' motion equal 1.0c? We
now know that they will observe a lesser value (.75c, IIRC). .5c + .5c
=1.0c is still mathematically valid, but the math describes a model of
motion that does not apply to real-world motion (although the error is
important only at velocities that are significant fractions of c).
So it isn't a case of the math being wrong, it's a case of the math
being irrelevant, which is the reason for this famous physics quote by
Wolfgang Pauli: "This isn't right. This isn't even wrong."
Regards,
John
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