Can good theories be falsified?

See also
The Revolution That Didn't Happen (by Steven Weinberg)

Weinberg's essay explains the limitations of Kuhn's theory of
scientific revolutions in similar way as the present essay explains
the limitations of Popper's theory of conjectures and refutations.
.

The philosopher Karl Popper claimed that falsifiability is the
hallmark of scientific theories. But scientific practice speaks
against him.

A correct theory cannot be falsified, and in this sense is not
falsifiable, in spite of Popper. (Falsifiability can be asserted
only in a contrafactual sense, that there are _conceivable_ situations
that, according to the theory, are excluded. But for a correct theory,
these situation will never happen, hence are completely ficticious.)

What happens with good theories is, at worst, that their region of
validity or accuracy gets restricted as new data about more remote
instances come in.

In today's understanding, people are careful to indicate the
limits where a theory is claimed to be valid, and the accuracy
to which its answers are to be trusted.

For example, the Standard Model is claimed to be valid whenever
gravitation is negligible, accuracies conform to present possibilities,
and energies are well below a putative unification scale.
Failures outside this domain are not counted as falsifications.

While limits and accuracy claims are not necessarily part
of the theory proper, they are part of the theory as actually taught
and applied. Indeed, although people try to extrapolate, one can
never be sure whether a theory is correct outside the domain where
the data were collected.

But one can be reasonably sure within the domain where enough data
are available. Good scientific practice requires that a good theory
agrees with the data within the tolerances claimed.
Once this is the case, these theories can never be falsified.
Rather, if people find disagreement in experiments, the
theory falsifies the experimental arrangement or analysis.

All science students who ever did experiments in the lab know
very well that this is common practice.

The degree of caution and care at the highest
level of quality has been increasing through the centuries.
It is now too late to ask Newton whether he believed his theory was
valid without restrictions. (Or are there any hints in the Principia
Mathematica?) Certainly Newton's theory as taught today is valid as
taught (i.e., with the restriction that speeds are small compared
to c and at distances large compared to the radius of the largest atom).
But we nevertheless believe that it is the 'same' theory, and if
Newton would live today, I think he would agree with that.

And Newton's theory will never be falsified, unless God suddenly
decides to change the physics of the Universe.

(That the observed advance of Mercury's perihelion did not match
Newton's theory was known as a limitating condition already before
relativity was born.)

The meaning of ''Newton's theory'' is not invariant under time.
Newton might not even recognize ''Newton's theory'' as taught today
as his theory. The conceptual basis has shifted in the many years
since his time. Nobody knows whether Newton regarded his theory as
something universally valid for arbitrarily accurate observations.
It seems however likely to me that he never claimed this.

The point I made above is that to the extend a theory has been
found reliable at some point in time, it is reliable to the same
degree at all other times (unless the laws of Nature change),
irrespective of any falsification outside this core region.

Falsification of a theory correct in some domain in a previously
untested domain commonly leads to an extension of the theory, not to
its downfall. Otherwise Newton's theory would have had the fate of
Phlogiston, which died as a theory long ago as it was found to be a
truly misleading theory.

Real advances in theory - such as Newton's progress over Ptolemy and
Kepler, or Einstein's progress over Newton - usually lead to
simplification that unify many observations. This is one of the
hallmarks of theoretical progress.

But even Newton's simplifications leave the Navier-Stokes equations
(derived much under some assumptions from Newton's theory, extended to
the microscopic world) an unresolved mathematical region that needs
uncontrolled approximation heuristics to get high quality results.
Such heuristics allows checking (hence verification or falsification)
on a heuristic level only, as one never knows for sure (i.e., in a
mathematically rigorous way) how far off the true results are.

Quantum physics also has much mathematical simplicity, which makes it
an ideal tool to unify far more observations than Newton's or
Einstein's theory did.

However, the subarea of quantum physics called relativistic quantum
field theory (RQFT), treating the subatomic world of elementary
particles, is currently still in a state not so far from pre-Kepler
astronomy. The Feynman diagram expansion in RQFT are not very unlike
the epicycles of Ptolemy, to be replaces by better ''nonperturbative''
methods once they will be found. Surely, here some simplifying
progress can be expected, though the problem seems to be so hard that
there is no predictable road towards success.

Arnold Neumaier (Arnold.Neumaier@univie.ac.at) A theoretical physics FAQ