Re: Explaining Schroedinger's equation

You wrote:
The fact of the matter is that the laws of quantum theory do
exhibit laws of language. Hence, if we wish to understand quantum theory
we must distinguish properties of the language from properties of
physics. Also, we must understand the language (which is a mathematical
language) if we are to understand statements made in that language about
reality.

And you explined:
I identify the wave function f(t,x),
with the sentence "if we were to do a measurement of position at time,
then we would find the particle at position x". Sentences of this sort
are given values by means of the inner product in Hilbert space, and we
also have a rule which enables us to calculate the probability that we
actually do find the particle at x if we do the experiment. The
Schrodinger equation acts on such sentences, telling us the value of the
sentence for different x and t from a given initial condition, and hence
enables us to calculate probabilities for results of measurements. I
show in the paper that the probability interpretation (not underlying
physical structure) imposes a first order Schrodinger equation.

Hermitian operators correspond to physical measurement processes such
that the result has a definite value - the eigenvalue. Then the
sentences say that in another measurement of the same quantity, the same
eigenvalue will be found.

I've tried, but I couldn't make sense, neither of your original statements,
nor of their explanations. Here are a few examples:

The Schrodinger equation acts on such sentences...

It is beyond my understanding how an eqation can act on a sentence.

I identify the wave function f(t,x),
with the sentence "if we were to do a measurement of position at time t,
then we would find the particle at position x".

I do not know what it means - or what *you* mean - by "*identifying* a
function with a sentence". Further, the word "identify" suggests some sort
of bijectivity; however, from the values/probabilities of all x at all
times t you cannot hope to reconstruct the wave function itself, but at
most its module. The wave function itself describes much more than the
statistics of x: it describes the statistics/distribution of *all* physical
properties of the corresponding system: momentum, energy, etc. So that your
"identification" is highly questionable.

Besides, your sentence suggests a subjectivist and operationalist
philosophical premises. For example, if *nobody* were to do a measurement
of position, where would it be? And would it exist at all :-)

If you still insist in identifying the wave function with a sentence, this
sentence should be: "what are the statistics for all physical properties of
the system at time t".

You then continue:

Sentences of this sort
are given values by means of the inner product in Hilbert space, and we
also have a rule which enables us to calculate the probability that we
actually do find the particle at x if we do the experiment.

"To give value to a sentence" .... you don't explain what it does mean! I
can only guess, but then it is not you the explainer :-) , but it is me!!

And, again, you do not explain what happens if we do *not* do the
experiment ;-)

Hermitian operators correspond to physical measurement processes such
that the result has a definite value - the eigenvalue.

In normal language this should mean, I guess, that to a physical property
there corresponds a Hermitian operator, and the values that property can
take are the corresponding eigenvalues.

Then the
sentences say that in another measurement of the same quantity, the same
eigenvalue will be found.

What will be found in the second measurement - and in the first, for that
matter - is anyone's guess, if we are talking about *real* measurements,
the only ones that exist. The result of a real measurement depends on the
apparatus's construction, on its precision, on the whole experimental
environment, on the experimenter's skill, and what not.

Quantum mechanics is *not* about experiments and their results, including
the non-existent "ideal" experiments, It is also not about observers.

To summarize. Your attempt to explanations is raising further serious
questions - about your view of physics and also about the clarity of your
writing.

All in all, your explanations did not advance my understanding of your
original statements

... the laws of quantum theory do exhibit laws of language.
Hence, if we wish to understand quantum theory
we must distinguish properties of the language from properties of
physics.

BTW, Quantum logic is not alien to me: years ago I discussed at length this
approach with a colleague of mine who was a big fan of it and who even
published a number of papers in a prestigious journal - Helvetica Physica
Acta. Despite being less then enthusiastic about QL, I must note that his
writing was, in comparison, a model of clarity.

Alex

.

Relevant Pages

  • Re: Explaining Schroedingers equation
    ... ements/clauses about measurement results. ... exhibit laws of language. ... also Physics studies phrases? ... Mathematics is based in logic, ...
    (sci.physics.research)
  • Re: Re: entangled states
    ... >> which either measurement occurs first. ... > is not the physics described by quantum theory. ... the correlation between the outcome of measurements is ... Hopefully not in any physics departments. ...
    (sci.physics.research)
  • Re: Explaining Schroedingers equation
    ... ements/clauses about measurement results. ... The fact of the matter is that the laws of quantum theory do ... exhibit laws of language. ...
    (sci.physics.research)
  • Re: Hooray: the Church of Scotland shows the way
    ... the measurement processes. ... phenomena - the classical mechanics of Newton for particles and the wave ... Unlike the other great pillar of modern physics, General Relativity, quantum ... needed is an understanding that includes the human observer as part of the ...
    (uk.religion.christian)
  • The idea that something is measureable is a human invention
    ... made up concept as is EVERY other physical concept used in physics. ... >> How is the measurement of time with a clock different than the ... > Show me the theory which tells us that time is more than an illusion. ...
    (sci.physics.relativity)