Re: What is the Standard Model

From: Patrick Reany (reany_at_asu.edu)
Date: 06/19/04 

Date: 19 Jun 2004 12:32:36 -0700

glhansen@steel.ucs.indiana.edu (Gregory L. Hansen) wrote in message news:<cav3uk$f2v$1@hood.uits.indiana.edu>...
> In article <844a1b64.0406180609.638f4ae@posting.google.com>,
> Patrick Reany <reany@asu.edu> wrote:
> >glhansen@steel.ucs.indiana.edu (Gregory L. Hansen) wrote in message
> >news:<cati7i$uv6$1@hood.uits.indiana.edu>...
> >> In article <844a1b64.0406171317.7abcf2a9@posting.google.com>,
> >> Patrick Reany <reany@asu.edu> wrote:
> >> >glhansen@steel.ucs.indiana.edu (Gregory L. Hansen) wrote in message
> >> >news:<cas9hj$g1n$2@hood.uits.indiana.edu>...
> >> >> In article <844a1b64.0406162145.583ae9b0@posting.google.com>,
> >> >> Patrick Reany <reany@asu.edu> wrote:
> >> >> >glhansen@steel.ucs.indiana.edu (Gregory L. Hansen) wrote in message
> >> >> >news:<capp5n$ik7$1@hood.uits.indiana.edu>...
>
> >> >
> >> >I'd say that Newton's THEORY of gravitation REQUIRES the fixing of G
> >> >someway, somehow, in order for predictions to be made that are
> >> >empiricially testable.
> >>
> >> What makes it a theory? I'd have stayed with convention in calling it a
> >> law. That is, Newton's law of gravity wasn't derived from fundamental
> >> postulates, it's just what fits the data. That one *is* comparable to
> >> Boyle's law.
> >
> >OK, we can talk about Newton's Law of Gravity. I was not being
> >non-standard. When I said "Newton's THEORY of gravitation" I meant
> >Newton's mechanics plus his Law of Gravity. Either way, theory or law,
> >you need G to make predictions.
> >
> >It's interesting, now that I think of it, that Einstein called
> >Newton's mechanics without specified forces as no more than a
> >framework. Newton's theory then has to have some specific forces
> >included by hand, sotospeak. The nature of those forces is arbitrary
> >save for the constraints placed on them by Newton's first three laws.
> >(And pehaps a constraint about action-at-a-distance forces being
> >infinitely fast.)

I want to give the reference for this now:

     It was fortunate for the development of mechanics
     and hence also for the development of physics in
     general, that the lack of definiteness in the
     concept of objective time remained hidden from the
     earlier philosophers as regards its empirical
     interpretation. Full of confidence in the real meaning
     of the space-time construction, they developed the
     foundations of mechanics which we shall characterize,
     schematically, as follows:

     (a) Concept of a material point: a bodily object
     which---as regards its position and motion---can be
     described with sufficient accuracy as a point with
     coordinates X1, X2, X3. Description of its motion
     (in relation to the "space" B_0) by giving X1, X2,
     X3, as functions of the time.

     (b) Law of inertia: the disappearance of the components
     of acceleration for a material point which is sufficiently
     far away from all other points.

     (c) Law of motion (for the material point):
     Force = mass X acceleration.

     (d) Laws of force (interactions between material points).
     In this, (b) is merely an important special case of (c).
     A real theory exists only when the laws of force are
     given. The forces must in the first place only obey the
     law of equality of action and reaction in order that a
     system of points---permanently connected to each other
     by forces---may behave like one material point.
      --- Einstein, PHYSICS AND REALITY, Ideas and Opinions,
            p. 299-00.

So, although Einstein didn't use the term "framework" itself, he used
what I think is a synonym: something just shy of being a "real
theory."

>
> Let's dwell on this for a while. It's a simple theory with one adjustable
> parameter, and is analogous to more complicated theories.

Excellent post, Gregory. I want to explain my motives clearly for the
first time. I'm a pain in the neck on this NG because I had since
childhood until the last few years thought of physics as a field whose
basic temimology of science was clear and precise. I find out after
growing up that my naive youthful notions were wrong. This state of
affairs still flabbergasts me. What bothers me the most is that
apparently no physicist on this NG, with the possible exception of
yourself, seems to care that if he or she uses a BASIC term, such as
law, theory, model, or hypothesis, that he or she might be radically
misinterpreted because the terms have no well-defined and generally
accepted meanings. I don't know how you physicists can tolerate this
state of affairs or why you do tolerate it.

Physics is NOT just an activity done by one person. It is the mutual
activities of multiple people who have to intercommunicated amongst
each other what they have done and want to do, and also communicate to
potential physicists (students), congressional money brokers, and
laypeople as part of their general education in science. That
communication requires well-defined basic terms. So where the hell are
they?

Only recently did I hear from a philosopher friend of mine that
Wittgenstein held that the main duty of the philosopher is to seek the
logical clarification of thoughts. I can somewhat agree with that.
Now, I don't think of myself as a philosopher, or a renagade; I think
of myself as layperson pissed-off that the intellectual subject I
enjoy the most is so poorly founded in its own language. Why do you
physicists adopt this get-nothing-done, laissez-faire attitude about
the core terms in your field? If you find something broken in your
field, fix it -- and stop making excuses for it! Is the status quo
really worth maintaining or even defending?

There's one thing I've learned recently that I would never have
imagined even five years ago: That a typical physicist will tolerate
ambiguity of basic terms of his or her field that no self-respecting
philosopher would tolerate which corresponds to basic terms in his or
her own field.

>
> First, you don't need G to make predictions.

You're right. I misspoke. I meant to say, "you need G to make the full
range of predictions in Newton's theory of gravity."

> You need it to make some
> predictions, but whenever the situation allows, you should cancel out
> poorly known parameters. For instance,
>
> F1 / F2 = r2^2 / r1^2
>
> for the same masses with different separations. Or, for different masses
> with the same separation (perhaps weights on the surface of the Earth),
>
> F1 / F2 = m1 / m2
>
> Absolute measurements are hard, relative measurements are easy.
>
> I don't know what Einstein meant when he called Newton's mechanics
> a framework, but it seems sensible. Newton's mechanics don't say much
> about the world; it consists of Newton's laws (the dynamics) and Galilean
> transformations (the kinematics), and certain assumptions about the
> existence and nature of space and time, number of orthogonal spatial
> directions, and whatever other housecleaning you care to throw in.

Im going to describe the structure of a scientific theory at this
point because I can use Newton's theory of gravity as an example,
though the analysis also applies to the other theories you presented
below.

A scientific theory consists of three parts:

1) The Differentiating Part by which the theory is stated
   in its minimal form (i.e., as a framework). This is
   usually the basic laws, hypotheses, modeling constraints,
   and principles on which the theory is fleshed out with
   predictions. The name refers to what makes one theory
   distinct from others.

2) The Operational Definition Part by which measurements
   are assumed to be performed consistent with a) the
   Differentiating Part and convention or b) are specified
   by the theory itself (SR did that).

3) The Happenstance Part which treats the domain of
   interest as existing as a chance arrangement of "things"
   or attributes whose metric or otherwise relevant values
   can be ascertained by the definitions and procedures
   declared in the previous two parts.

Theory = DP + ODP + H

Now, the Differentiating Part of Newton's theory of gravity is his
modeling constraints that the fundamental model of matter is the point
mass particle model, and that the particles interact among themselves
by forces acting at a distance, and the three laws of mechanics and
the law of gravity. With that, I conclude, by the use of the above
model of a theory, that G is specified in Newton's theory implicitly
-- one need only "follow implicit instructions" on how to obtain it to
obtain it. The Differentiating Part tells us that we need to have its
unique value, and the Operational Definition Part tell us how to make
the measurments that will secure this value to within experimental
uncertainty. In this model, one can view the value of G as
happenstance, i.e., just happens to be the way the universe is.
Happenstance also contains all the information which is needed to
solve "real-world problems" which require initial, final, and/or
boundary conditions for differential equations specified or deduced on
the basis of the Differentiating Part of the theory.

So, if you accept this model of a theory as correct (at least in basic
outline), it's plain to see why normal presentations of Newton's
theory succeed only with their presenting a framework
imitation/abstraction of it (technically a misrepresentation of it),
since they only present the Differentiating Part of the theory.

Just because it's the habit of textbooks to present Newton's theory
this way does not justify me considering his theory to be a
"framework" only.

>
> But what does it say about the world? Not a lot, until you add specific
> forces like F=-GMm/r^2. Or Hooke's law, and so on. Does Newton's
> mechanics require gravity to be F=-GMm/r^2? No. Any force at all can be
> plugged in there, even non-central forces or velocity-dependent forces.
> It just so happened that gravity seemed to follow the law that Newton gave
> for it. Gravity actually more closely follows something like Maxwell's
> equations with a finite propagation speed, and plugging that into
> non-relativistic Newtonian mechanics with the assumption of the principle
> of relativity would give you gravitational radiation and a gravitomagnetic
> force ("frame dragging") in a strictly non-relativistic context.
> Newtonian mechanics could have handled that perfectly well. Special
> relativity might have problems with Newton's action-at-a-distance, but it
> could handle the revised gravitational field theory. General relativity
> is the theory of the day, but many of the results are similar.
>
> Mati Meron has called special relativity a framework theory, and for much
> the same reason. It consists of the Lorentz transformations (the
> kinematics), and Newton's laws (the dynamics). That's right, the same
> Newton's laws that are in Newtonian mechanics are in special relativity.
> The only modification is that, say, the Newtonian F=ma is valid in a
> particle's instantaneous rest frame, and then the acceleration is
> transformed to an arbitrary frame to find the action of a force on a
> moving object. Accelerations transform trivially in Newton's mechanics,
> but they take more work in relativity. And even in the absence of forces
> that model specific interactions between particular things, the
> predictions are different from Newtonian. Clock rates and spatial
> distances depend on the observer, sequences of events are not absolute
> unless they're time-like (c^2t^2 > x^2), etc. It's a framework theory,
> but still testable versus Newton's framework theory.
>
> Then there's Lorentz's aether, which preserves the predictions of special
> relativity while using different words to describe it. That's the sort of
> difference that really makes no difference.
>
> You could call quantum mechanics another framework theory. It could be
> based on Galilean or relativistic kinematics. Newton's laws are still in
> there, although hidden. But quantum mechanics has a different definition
> of the state of a system; we go from a point in phase space to a point in
> a Hilbert space.
>
> I would just generically call each case a mechanics, but since a mechanics
> is the basic description of motion and forces, its the foundation for
> studies of anything at all that moves and interacts.
>
> The Standard Model concerns specific interactions between particular
> particles. Or rather, between fields. For instance, the U(1) part of it
> is electromagnetism. If you only insist on invariance under a U(1)
> gauge transformation, you get the Maxwell Lagrangian. Plug that into a
> classical mechanics and you get Maxwell's equations. Plug it into a
> quantum mechanics (it could be relativistic or non-relativistic) and you
> get quantizations of the electromagnetic field-- photons; quantum
> electrodynamics.
>
> SU(2) is the weak force part of the standard model. Transform your fields
> that way, find the terms needed to keep the Lagrangian invariant under
> that transformation, and you get your W and H particles. These are
> generically called gauge bosons, along with the photons and gluons. You
> can plug this one into a classical theory if you like, and derive
> classical fields relating to the electrons, neutrinos, and quarks, but it
> won't correspond to anything in the real world. Unlike photons,
> quantizations of these particles can't be ignored. But nothing stops you
> from developing the theory.
>
> >
> >>
> >> It has for a long time been agreed to provide the best theory with minimal
> >> surplus postulates. Contrast with, e.g., supersymmetry, or string
> >> theories, which make predictions that the Standard Model doesn't, but also
> >> predictions that can't currently be tested.
> >>
> >> It is set by convention in that they decided what to call the Lagrangian
> >> with U(1)xSU(2)xSU(3) gauge symmetry. It is not the best theory "at any
> >> moment", it is the theory with U(1)xSU(2)xSU(3) gauge symmetry.
> >
> >I understand your point concerning the U(1)xSU(2)xSU(3) gauge
> >symmetry, which is inviolate in the theory. But what about the
> >assignment of the particle masses? The general nature of this
> >arguement is what Lakatos talked about in his distinction between
> >"core hypotheses," of a theory, which are inviolate, and "protective
> >belt hypotheses," which are changable without a rename of the theory.
>
> I use cosmology as my canonical example of a theory and a physical model.
> Dark matter and dark energy were proposed to explain observations of the
> universe. But does that mean there's something wrong with general
> relativity, or does that mean we just didn't know what kind of stuff was
> Out There? General relativity has worked well under conditions that could
> be carefully controlled, like gravitational redshifting experiments on
> Earth, and the odds are very high that we don't have a complete
> understanding of the composition of the universe. So it's reasonable to
> adjust the physical model for now. Personally, I think something's
> wrong with general relativity, but a suspicion doesn't create a new theory
> and test it.
>
> The Standard Model is a model of which things physically exist, and how
> they interact. If we get some result like a finite triple correlation
> in beta decay, that will blow it apart. (The data has been taken, it will
> take about six more months to finish analyzing it.) In that case it will
> be the Standard Model, and not quantum mechanics, that gets a reworking.
> At least in the near term. Quantum mechanics is more directly tested by,
> e.g., the Aspect experiments.

Again, good post.

>From the following webpage:

http://www2.slac.stanford.edu/vvc/theory/modeltheory.html

we find this:

     Is the Standard Model a theory or a model?
     
     The words model, hypothesis, and theory are each
     used quite differently in science. Their use in
     science is also quite different that in everyday
     language.

     To scientists, the phrase "the theory of ..." signals
     a particularly well-tested idea. A hypothesis is an
     idea or suggestion that has been put forward to
     explain a set of observations. It may be expressed
     in terms of a mathematical model. The model makes a
     number of predictions that can be tested in experiments.
     After many tests have been made, if the model can be
     refined to correctly describe the outcome of all
     experiments, it begins to have a greater status than
     a mere suggestion.

     Scientist do not use the term "the theory of .."
     except for those ideas that have been so thoroughly
     tested and developed that we know there is indeed some
     range of phenomena for which they give correct
     predictions every time. (But, language being
     flexible, scientists may use "a theory" as a synonym
     for "a hypothesis", so listen carefully.)

     Today, any set of scientific ideas referred to as
     "the theory of ..." is a well-tested and well-established
     understanding of an underlying mechanism or process.
     Such a theory can never be proved to be complete and
     final -- that is why we no longer call it a "law."
     However, it is the same kind of well-tested set of
     rules, with an established area of applicability, as the
     older ideas called "laws".

This nonsense reveals the total chaos in the language of physics! It's
basically an apologetic for confusion and irrational definitions. SLAC
got one thing right: to answer the question, "Is the Standard Model a
theory or a model?" you have to know what a theory and a model are.

Below are the "definitions" I have tried to pull out of SLAC's
paragraphs above to accurately represent their viewpoint as faithfully
as I could. I refer to the four terms collectively as the "Big Four."

theory -- a particularly well-tested idea

model -- makes a number of predictions that can be tested
     in experiments. After many tests have been made, if
     the model can be refined to correctly describe the
     outcome of all experiments, it begins to have a
     greater status than a mere suggestion.

law -- well-tested rule

hypothesis -- an idea or suggestion that has been put forward
     to explain a set of observations

This is the typical nonsense that both laypeople and physicsts on this
NG have revealed over the years. Twenty years ago I would have had the
same misconceptions about these terms. You physicists have spent the
last twenty years of your lives studying physics and I respect you for
that, but over that same time I have spent my time studying the
logical structure of physics, and you could do me the courtesy just
once to hear me out completely with an open mind.

Let's get to cases. Before I criticize the SLAC definitions and its
apologetics, I want to give my criteria for how these terms ought to
be defined.

1) The definitions should be clear, simple (if possible),
    and mutually consistent.
2) The terms should be consistent with established usage,
   if possible.
3) The terms should not have useless verbiage in their
   defintions.
4) Taken as a set of terms, the Big Four should be defined
   to manifest their distinctions whenever practicable.

It is impossible to meet all these criteria at the same time for each
word, so choices have to be made. Most important is the dichotomy
between usage of these terms pre-WWII and post-WWII. Since the post
WWII usage has disintegrated to complete nonsense, I choose to conform
most to pre-WWII usage.

SLAC definition for "theory" -- a particularly well-tested idea

First, everything in theoretical physics is an idea, so the use of the
term adds nothing, in violation of my Rule 3. Second, a theory is not
necesarily "well-tested." Einstein's theory of general relativity was
published as a bona fide theory prior to any of its predictions being
tested in 1916. There can be good theories and bad theories. Bad
theories are still theories.

SLAC definition for

 "model" -- makes a number of predictions that can be tested
     in experiments. After many tests have been made, if
     the model can be refined to correctly describe the
     outcome of all experiments, it begins to have a
     greater status than a mere suggestion.

Models are not suggestions. Models may or may not make predictions.
They do not graduate to become laws or theories. Confidence in them is
irrelevant from the logical point of view. Models can be effective or
ineffective. You can model knowledge. You can model physical things as
faithful speculations (in the sense of scientific realism) or as
theoretical "speculations" made arbitrarily. You can model formal
points of view, research programs, or general approaches (frameworks).

There seems to be a profound misconception in physics among physicists
and laypeople that somehow a linear progression of "reliablity" has
been constructed on the Big Four. At the bottom of this progression is
the hypothesis, then the model, then the theory, then the law. SLAC
seem to think that at least a part of this construction needs to be
deconstructed. They're right about that. If physicists really think
that this misconception exists, and it seems to exist among a lot of
people, then they should deconstruct it right away. But the
deconstructions offered by SLAC above do not go far enough; in fact,
their "corrections" merely promote the same kind of misconceptions.
There is only one progression that can be made: hypotheses of
empirical nature, rather than of ontolgic nature, can be "graduated"
to the more reliable state of being, called a "law." By repeated
testing, 1) models do not become hypotheses, laws, or theories; 2)
theories do not become hypotheses, laws, or models; and 3) hypotheses
do not become theories or models.

SLAC definition for "law" -- well-tested rule

I don't have much to criticize this on, except that the nature of rule
could be made explicit, and I will do this when I give my definitions
of the Big Four below.

SLAC definition for
 "hypothesis" -- an idea or suggestion that has been put forward
     to explain a set of observations

The main object in science that has responsible for explaining is the
theory. Hypotheses are also used for explaining, so what distinguishes
them?

My general definitions of the Big Four:

theory -- an explanation in the form of a deductive system

model -- representation of a thing, concept, or relationship

law -- invariable relationship on values and/or events

hypothesis -- a logically simple speculation

To tailor the above for specific use in science requires only a little
effort. For example, a physical law -- invariable relationship on
physical values and/or physical events.

----------------------------------------------

A deductive system uses hypotheses and/or principles as postulates to
deduce theorems. A theory can be a model because it can represent what
we know about a phenomena of interest. A hypothesis is usually used 1)
as an explanation for a single attribute of a phenomena of interest,
or 2) to account for (explain away) a discrepancy between measurement
and prediction of a theory (the ad hoc hypothesis).

SLAC says this about the scientific theory:

     Today, any set of scientific ideas referred to as
     "the theory of ..." is a well-tested and well-established
     understanding of an underlying mechanism or process.

That's not the older meaning to theory. A theory can be brand new and
still be a theory. Einstein's GR was theory right out of the box.

     Such a theory can never be proved to be complete and
     final -- that is why we no longer call it a "law."

Only in the morass of confusion of the last couple decades could a
physicist or layperson ever confuse a law as a "proved theory." Even
in the days before the positivist philosophers debunked the notion
that a theory can be proved, no one ever thought of a "proved" theory
as a "law."

SLAC offers the apologetic:

     But, language being flexible, scientists may use
     "a theory" as a synonym for "a hypothesis", so
     listen carefully.

It's just about as ludicrous to allow physicists to use the terms
"rainbow," "zener diode," "rigid rod," and "black hole" as synonyms --
all in the name of "flexibility." All it is, is after-the-fact
justification of bad habits.

I have no doubt that some scientists use the terms in the Big Four
interchangeably and they should stop doing that! It is not the point
of language that the terms in it should be so over-loaded with
conflicting definitions that one is never sure what the terms mean
when one encounters them in the writing of others, especially in
scientific writing. To accept this state of affairs is a damn copout.

---------------------------------

So, how do I answer the question "Is the Standard Model a theory or a
model?" using my own definitons? Simple, whether you regard the SM as
a theory (because it makes predictions from a set of postulates) or
you think of it as a mere framework, it represents the framework or
the theory. So it is a model. The only remaining question to me about
the SM is just how big of a theory it is. If it containts the accepted
assignments of all particle masses was well as the obligatory
U(1)xSU(2)xSU(3) gauge symmetry then it is a "bigger" theory than if
it does not.

Patrick

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