Re: SR and GR without math

From: Bill Hobba (bhobba_at_rubbish.net.au)
Date: 09/29/04 

Date: Wed, 29 Sep 2004 08:16:30 GMT

"Ilja Schmelzer" <q6867901@mailstore.fernuni-hagen.de> wrote in message
news:cjdkkn$3eb$1@beech.fernuni-hagen.de...
>
> "Bill Hobba" <bhobba@rubbish.net.au> schrieb
> > "Paul Bramscher" <brams006_nospam@tc.umn.edu> wrote
> > > I've got a question regarding relativity: is there any way to state
SR,
> > > GR, or QM fully without mathematics?
>
> > Well it depends what you mean by fully. Are the key ideas expressible
> > without mathematics? - then I would have to say yes. Is the detail
> > expressible without it? No. Physics is written in the language of
> > mathematics and why it is so is a bit of a mystery - see the following
> > classic essay by Wigner -
> > http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html. Also see
> > Feynman - The Character of Physical Law - page 35 Chapter 2 - The
Relation
> > of Mathematics to Physics.
>
> There is a nice joke from Popper about such "mysteries":
> "The universe may be described in English language, therefore
> the universe must be inherently British."
>
> The point is that math is simply a special human language, appropriate
> for exact, quantitative statements.

Of course. However I side with Wigner and think more is going on - as he
concludes:

'The miracle of the appropriateness of the language of mathematics for the
formulation of the laws of physics is a wonderful gift which we neither
understand nor deserve. We should be grateful for it and hope that it will
remain valid in future research and that it will extend, for better or for
worse, to our pleasure, even though perhaps also to our bafflement, to wide
branches of learning.'

>
> > You have hit upon a very interesting point. A number of supposed laws
of
> > physics such as Ohms law are in fact tautologies. Even Newton's first
law
> > is a tautology - ie a particle moves at constant velocity unless acted
on
> by
> > a force.
>
> Therefore theories have to be considered as a whole.

Sure. One must always be carefull to look below the surface to try and
undestand what is really happening - or as Feynman says what only becomes
apparent to 'eye of analysis' (Feynamn - Character of Physical Law - page
13).

> It is not a single
> statement from a theory which is falsifiable but the whole theory.
> (A more detailed consideration even shows that in every single
> experiment many theories are involved in the interpretation.
> In this sense only sets of theories are falsifiable. But this is
> not problematic from philosophical point of view - the only
> important thing is that the falsification should be considered
> as an open scientific problem - at least one of the involved
> theories requires modification.)
>

Yep.

> > > So is there a way to present SR, GR, and QM without math, or must they
> > > rely on (irrefutable) mathematics as a centerpiece to each theory?
>
> > The laws of SR, GR and QM are experimentally refutable.
>
> But, for example, GR alone, without any assumption about the matter,
> is irrefutable: You can simply take the Einstein equations as the
> definition of the dark matter part of the energy-momentum tensor of
> matter. Again, this decision is not problematic as long as the "dark
> matter" defined in this way is considered to be an open scientific
> problem.

Sure - some consequences of theories can not be refuted eg the existence of
the aether in LET is not subject to experimental investigation - we can not
even determine in that theory which frame the aether is at rest in. Or,
conversely, how to use SR to prove the aether does not exist (assuming you
believe the POR denies the existence of an aether - which is a point open to
debate). All that the scientific method really demands is that some
consequences are testable, not that the tests uniquely determine that a
particular theory is correct. For example I am not aware of any experiment
that can separate SR from LET.

Thanks
Bill

>
> Ilja
>
>

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