Quantum Gravity 221.0: Schrodinger-Riccati Relationships and Causation

From Osher Doctorow

From the various works of Haret Rosu of Mexico (I keep forgetting the
name of the University - look it up on the internet), we know that the
one-dimensional Schrodinger equation and the Riccati Differential
Equation are inter-convertable under the conditions of the former.

That the two-dimensional Stationary Schrodinger Equation is
convertable to a complex Riccati Differential Equation is proven by K.
V. Khmelnytskaya and V. V. Kravchenko of CINVESTAV del IPN Mexico in
"On a complex differential Riccati equation," arXiv: 0705.1744 v1
[math.AP] 12 Jun 2007, 14 pages.

One of the more educated trolls/graffiti artists recently claimed that
not only is the Riccati Differential Equation "antiquated", but that
so is the whole notion of Causation/Causality. Presumably he/she/it
had a course in 1st year Philosophy in which David Hume is usually
paraphased as saying that no matter how hard we try, we can't find
anything in Causation other than Correlation or "contiguity".

Hume is not generally considered today as the "last word" on Causation
in philosophy, although he did help found the field of Experimental
Psychology indirectly. What he was referring to, however, is what we
today call Non-Spurious Correlation, which is to say Correlation not
due to accidents, coincidences, etc. If two events or variables are
Non-Spuriously or Non-Accidentally Correlated, then it is usually
considered that they Cause each other, and in such cases of
"simultaneous Causation" it is indeed difficult to measure any
passsage of time between one variable and the other. In such cases,
we can equally say that they are Correlated or mutually Causal, and
the former expression is more common in sciences or problems
concerning with simultaneous variation since they are "isomorphic".

This does NOT apply to cases where event A clearly precedes event B in
time. Hume happened to forget to consider such cases more than
fleetingly, which is not surprising since Causation was such a little
understood thing before him and during his lifetime. For an example
that might even appeal to trolls and graffiti artists with a little
education, if somebody were to go back in time and kill his
grandmother with a gun, then pulling the trigger of the gun certain
preceded the death of his grandmother. If you can't find millions of
other examples where one event or variable or process preceded (the
action of) another in time, then I'd be surprised. You can start with
the Big Bang versus the present-day Universe if you want to, or your
birth versus your current situation.

Hume did know that there is such a thing as time, but he couldn't find
anything theoretical to distinguish Causes and Effects in Non-
Accidental Causation, and when he rarely looked at a Cause which did
precede its Effect in time, he considered that because he couldn't
see, hear, touch, or otherwise perceptually detect how the Cause was
transmitted to the Effect, then it must not have any substantive or
theoretical basis.

Today, sciences and engineering and even criminal investigation study
Causes and Effects quite often, usually as qualitative problems and
guides rather than quantitative ones except (1) that in Special
Relativity the light cone is supposed to give an upper boundary on
Causation/Causality because the Cause couldn't supposedly be
transmitted to the Effect outside the light cone (it would have to
exceed light speed); and (2) in Probable Causation/Influence (PI), a
Causal Set (A-->B) is defined which is the set theory and probability
space analog of logical implication or the logical conditional, and a
probability is defined on such sets.

So you have to know more about sciences than you learn in Philosophy 1
or Chemistry 1 in order to usually know about Causation/Causality. I
should also mention Path Analysis in Statistics which is usually
considered to be "Causal" in a partly related sense.

The "final topper" or "clincher" to this story is that we now know, as
Hume apparently did not or forgot, that even in Correlation, an
equation with real variables of form x = y or x = ay + b or a
nonlinear equation or ANY real-variable equation is really composed of
two parts: x < = y and x > = y in the first case (simultaneously
satisfied by x = y), each of which in the space or time domains does
involve the notion of "preceding" or "precedence" which in the time
domain is precisely the "before-and-or-during" vs "after-and-or-
during" concepts.

If you don't know that an apple falling from a tree started falling
before it hit you on the head, then you need to have your head
examined.

Osher Doctorow
.

Relevant Pages

  • Re: Some quotes for RH
    ... What you mean is that *you* only use a correlation when it ... "From Association to Causation: ... History of Statistics", Statistical Science, vol 14, no.3, pp 243-258, ... As Hume pointed out causation cannot be demonstrated. ...
    (uk.sport.cricket)
  • Re: Information-Knowledge Holographic Principle
    ... their real quarrel is not with me but with Causation. ... Having heard that non-spurious correlation is Causation, ... But they tend to get thrown for a loop when asked what is physics ... Everybody, I think, would agree that physics and mathematics intuition ...
    (sci.physics)
  • Re: Clamping babys cord - is baby still breathing through it?
    ... Correlation between 2 phenomena is all that can EVER be shown. ... feel a pain at the moment of impact and a bruise comes up at that site ... accurately-predictive theories that describe the mechanical reactions ... impossible to prove that such a thing as causation even EXISTS! ...
    (sci.med)
  • Re: Research hounds needed
    ... >That's true, Kurt, but it's a question of definition, isn't it? ... >instance, aspartame, that it's only carcinogenic in very large doses ... that correlation is not causation. ...
    (misc.writing)