Re: [Phys-l] The "why" questions

[Stefan Jeglinski <jeglin@4pi.com>]

>  > I am not sure that I could argue persuasively because I never
> >  believed I quite got it back in the day, but what about this:
>  > http://en.wikipedia.org/wiki/Kramers-Kronig_relation
>
> That's quite an open-ended question, but let me guess that
> the intent was to ask whether the K-K relation is asymmetric
> with respect to time.

I'm not sure :-)

I have 3 different competing notions going on in my head and I can't 
find a way to make them come together (or remain separate if need be).

My original intent with the KK comment was to at least refute the 
notion that physics "never deals explicitly and directly with these 
ideas" [regarding causality].

1. Hand in hand, discussions of KK always are connected to causality. 
I haven't in a while tried going thru the detailed explanations of 
this and haven't here either, so I'm a bit at a disadvantage, but the 
discussions seem restricted to E&M (or at least most appropriate 
there). I don't know if that is an artificial restriction or not. Why 
is there not some KK-like relationship in Lagrangian/Hamiltonian 
mechanics, for example?

2. Like some others, I am squarely in the camp of F(t) = ma(t), where 
t is t. To me, any non-philosophical discussion of causality would 
require consideration of integral formulations of F(t) ~ ma(t-t') or 
a(t) ~ (1/m)F(t-t').

3. But speaking of which, I previously posed a question about 
convolution. It was pointed out that convolution merely expresses the 
idea that an output is a
superposition of impulse responses. Considering linear systems alone, 
it was also pointed out that some relationships are of the form

	(a) f(t) ~ y(t)

while others are more generally of the form

	(b) f(t) ~ Integral[h(t')y(t-t')dt']

These are the same only to the extent that h can be expressed as a 
delta function. JD gave the example of Ohm's Law being in camp (a) 
whereas anything with a capacitor in it requires camp (b). The 
obvious difference between these 2 entities (resistor/capacitor) is a 
phase difference between voltage and current. And interestingly, we 
are again led to a similar painful discussion! To wit, does voltage 
"cause" current or is it the movement of charge that "causes" a 
potential difference to be created? I =want= to identify this with 
the F(t) = ma(t) discussion but I'm not so sure it's as clear.

Somehow I feel there is a more formal connection between these 3 
items. My intuition tells me that dispersion is at least in part the 
key.


Stefan Jeglinski