Re: [Vo]:Three Words That Could Overthrow Physics

[Stephen A. Lawrence]

Harry Veeder wrote:
On 4/6/2008 10:53 PM, Stephen A. Lawrence wrote:


Harry Veeder wrote:
I am calling your bluff. ;-)
Not a bluff, though it involves some fuzzy reasoning.  The difference
between a "proof" and an "explanation" has bugged me since junior high,
when I found out that most mathematical facts are "proven" without ever
being "explained".

As I said before, a "model" may predict what's going to happen but will
never tell you why.  Using a model is a tacit admission that we don't
know what the "reasons behind" things are, or even if there are any such
reasons.

I would think the _construction_ of a model depends on some a-priori
explanations (or stories?) of the world.


Not necessarily, though some certainly seem to be.

Aether theory is predicated on the notion that there is some kind of 
aether which carries some kind of vibrations; as such that's a sort of 
fuzzy explanation (though the details are pretty wild if you stop and 
think about what sort of material aether must be, keeping in mind the 
obvious fact that planets and stars plow through the aether with no 
impediment to their motion, along with the fact that vibrations 
traveling in any known medium go faster as the medium becomes stiffer 
and slower as the medium becomes floppier -- and vibrations in the 
aether travel really wicked fast, so it must be really wicked stiff, 
which makes those planets cruising through the middle of it all the 
harder to understand).

But to take a contrary example, special relativity postulates no 
mechanism at all for anything; it's just a proposal that the geometry of 
space is just like what you get if you assume the distance between any 
two events is fixed for all observers *if* you measure distance as x^2 - 
t^2.  The justification for it is that it works, with no reference to 
whether or not it "makes sense" or "explains" anything.

Another contrary example is Ptolemaic cosmology, which as far as I can 
see explains nothing, and is really just a mathematical construct.



What is the difference between an explanation and a model?
You have said something substantive about models, but nothing substantive
about explanations, except to say that explanation is not a model.
Or is it just an issue of semantics?
Maybe it's just semantics, but I actually think it's more a matter of
gut feel, and "satisfaction level".  If you look at the link Terry gave,
the author's objection is that physics doesn't say "why" magnets
attract.  Well, what would it mean to say why they attract?

This is the heart of the issue -- just exactly what is an explanation?
In physics it's hard to say, for me, at least, because I don't know of
any explanations.  As far as I know modern physics has none.

It does and it is called "mechanics",


I can't really agree.  We tend to think "mechanics" explains something 
because it so neatly matches our experience with stuff, but really it is 
nothing more than a *description* of what Newton thought things did.

A centerpiece of Newtonian mechanics is the law of gravity, which is 
simply a bald statement that two bodies attract with a force equal to

  G m_1 m_2 / r^2

with no hint of an explanation -- and what's more, that's a description 
of action at a distance, with information as to where each body is 
located being transmitted to the other body in *zero* time, with, again, 
no proposed mechanism for this information transfer.  Newton, as I 
recall, had misgivings about that (and he was right, of course).

More basically, Newton's second law (I think it's the second law -- it's 
hot has heck here today and my head's full of fuzz as a result) says that

  sum (dx_i/dt * m_i)

must be constant.  No reason is given; no mechanism is provided; it is 
merely a mathematical statement, chosen to match Newton's observation.

Of course it turns out that there can be no simple (and correct) 
mechanism given for either Newtonian gravitation nor the conservation of 
Newtonian momentum, because both laws turn out to be untrue at the 
"edges" -- over very large distances, at very high velocities, they 
don't work perfectly.  So their "mechanism", if it were stated, would 
necessarily be something which doesn't quite apply in all situations. 
That would tend to make it less than satisfactory as an "explanation", I 
would think.


and to ensure mechanical
explanations remain dominant and universally applicable they have been
revamped by the quantum hypothesis.


But again, they're not "explanations", at least not as I understand the 
term.

Tell me *why* momentum is conserved -- that would be an "explanation". 
But Newton didn't tell us *why*, he merely told us that it *is* 
conserved.  It's like the following little convsersation:

"Go to bed NOW!"

"Why?"

"Because I told you to!"




In math it's easier to see the difference.  For example, we can find pi
by integrating the arctan function, or by integrating sqrt(1-x^2), both
of which are stunningly opaque approaches.  We can prove that the area
of a circle is pi*r^2 using calculus, which is, again, an amazingly
opaque approach.  Alternatively, we can find the circumference and area
of a circle using Pythagoras's theorem and some simple drawings, and we
can extract a value for pi that way.  I would call the latter approach
an "explanation", because, to me, it "explains why" the circumference
and area of the circle are what they are.

But something this is pointing up is that the word "explanation" is
rather slippery.  I could struggle with it a bit more, and perhaps say
that an explanation works from simple things which we "know" to be true
to show that other more complex things follow inevitably from those
simple things -- but the phrase "know to be true" is already flirting
with vagueness.  So I'll just let it go at saying that an explanation
leaves one feeling satisfied; a model may not...

I guess the question becomes how do we learn a particular sense of
satisfaction, and are there other senses of satisfaction that should be
allowed in physics other than those rooted in mechanics and probability
theory.


Yes, I agree; that sounds right.


 
By the way, the derivation of pi from Pythagoras's theorem to which I
referred, and the derivation of the area of a circle and volume of a
sphere using geometric arguments, are here:

http://physicsinsights.org/pi_from_pythagoras-1.html

http://physicsinsights.org/sphere-volume-1.html

You may not feel these pages actually "explain" anything, of course!
:-)  That was, however, part of the reason for putting them together,
and perhaps these pages will give you an idea of what I think an
explanation is.  Or maybe not...


Aristotle's explanation of why some things fall (gravity) and why other
things rise is that each element seeks its natural place of rest. Bodies
made of the element "earth" tend to fall, while bodies made of the element
"air" tend to rise.

This may not be satisfying from a modern sensibility, but it was satisfying
to many people in the past. Likewise, the sensibilities of future
generations might regard today's physics as unsatisfying. In fact many
people do right now. ;-)


Yes indeed -- and learning more of it doesn't necessarily make one feel 
more "satisfied" with it...



Harry