Re: Incorrect mathematical integration

On Fri, 19 Jul 2024 19:51:32 +0000, Richard Hachel wrote:

>
I once explained to a speaker that additions of relativistic speeds were
not done in a common way, and that for example 0.5c+0.5c did not make c.
>
This Internet user refused to believe me.
>
For what? Because it is very difficult to give water to a donkey who is
not thirsty, and who categorically refuses to understand or discuss.
>
I think that this makes most of the speakers smile, because they know A
LITTLE realtivity, and if they do not necessarily know the general
formula
for adding relativistic speeds, they at least know the longitudinal
formula that is w=(v +u)/(1+v.u/c²) or here w=0.8c.
>
But we must go further. Physicists don't make this kind of mistake, but
they do make others. I told Paul B. Andersen that his magnificent
integration formula
>
<http://news2.nemoweb.net/jntp?EKV4LWfwyF4mvRIpW8X1iiirzQk@jntp/Data.Media:1>
>
was incorrect PHYSICALLY even though mathematically it was obviously
perfect.
>
Paul doesn't want to believe me. This confuses him.
>
However he is wrong and I pointed out to him that if we could integrate
all the proper times, to obtain the sum of the total proper time, we
could
not do it with improper times, the sum of which segment by segment was
greater than the total evolution.
>
A bit like realtivist speed additions where the sum is not equal to the
common, mathematical sum.

That's not a valid comparison, Dr. H.

Paul doesn't want to believe me, because he wasn't taught that way, and
he complains about me.
>
Why doesn't he complain about those who taught him incorrectly?
>
R.H.

It seems to me that he complained properly.  You have made an accusation
without a justification.  If one can't use "improper" times to integrate
a proper time, what does one use?  And if using "improper" times is
wrong in this case, that throws all of calculus in doubt.
Frankly, I found that physicists get into more trouble when they ignore
mathematical rules.  The case where they didn't get in trouble was when
Heaviside developed operational calculus for use in transmission line
analysis.  Heaviside's work was panned by mathematicians because it
wasn't mathematically rigorous (but it worked just fine).
So please, pray tell what works just fine but fails mathematical rigor?
And how do you know it works just fine?