The universal gravitation reproduces the Kepler laws, that are based on observation.  The measures wasn't acurate enough to *reject* the theory, and a theory is deemed valid until it is falsified.   I don't know what Kuhn had in head, but he is misled, and thus the question rests on nothing.  The Higgs theory was consistent with experiment before the observation of the Higgs boson, there were no reason not to accept it, although it should still be tested.  That happend to all and every theory on the earth.  There is no other way to "decide the issue" than to reject a theory altogether, that's a very basic principle of the scientific method.

Akira, OK, we have understood, you mathematicians are the best, and anybody else is wrong in all concerns.  From other point of views, the lobby of the mathematicians is the more powerful and basta.  It claims the theory of relativity for Poincaré and it is only the beginning.  But after all, that's your and only your problem.  Think what you want, we don't care a fig.  For QM you are utterly wrong, you don't know what you are talking about, but never mind.

There are several such theories accepted on the basis of logical , mathematical, and physical structure.  Experimental evidences are yet to be found for their verification or falsification:

(1)Left-right symmetric gauge theory

(2)Pati-Salam gauge theory

(3)Supersymmetric gauge theories including MSSM

(4)Grand unified theories without or with supersymmetry

(5)N=1 Supergravity theory

(6)String theory 

(7) Flavor symmetric theories for fermion masses

(8)Theories of neutrino masses with seesaw mechanisms e.g. Type-I, Type-II, Type-II, Inverse seesaw, Radiative seesaw etc

and there could be several more.

Many physicists have pointed out that the axioms of quantum mechanics are inconsistent.  Many great spirits have searched for a better theory, and have failed.  The point of physics is to describe and predict the observations, not to haphazardly prove theorems that can be proven.  That's because a theory must be supplemented with an interpretation, that is, a correspondance between the mathematical beings and the outcomes of the experiments, and that's not mathematics.  Quantum mechanics is a heuristic theory, it works although we still don't know why.  But that's fine, it only shows that physics is not mathematics.

Claude,

your statement

will reinforce Akira's belief according to which physicists are illogical morons. Actually, if one would formulate the principles of non-relativistic quantum mechanics (as given for instance in Messiah's two-volume textbook) as axioms one would obtain a system for which it is easy to give models in the framework of rigorous functional analysis. So these axioms are at least relatively consistent with established mathematics (say, to ZFC to satisfy logic experts).

Of course they are inconsistent with relativity. They also are ad odds with many concepts that  people tend to take for granted on a common sense basis. The problems that Feynman bundled in the dictum 'Nobody understands quantum mechanics'  don't result from being unable to  understand and handle axioms but from having been unable so far to find rules that make Nature behave as She does and do so autonomously and requiring only a finite number of 'actions' in any finite 'interval' of space-time.

Thanks all for the enlightening feedback.

Mina Ketan Parida: What is the degree of credibility and acceptance of the theories you list? Can you give me a one-sentence summary of each of the theories you listed? Thanks,

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I share the frustration with the attitude of physicists toward math. Most physicists treat math as a way to extract quantitative predictions from theories to compare with measurements. They don't adequately recognize math as a way to validate theories.

I get feedback from very respected physicists has convinced me that very few physicists understand math deeply. Example: "You must base computations on exact symbolic solutions to be taken seriously." (This guy does not know that the preferred way in math to define solutions of PDEs is with weak solutions in Sobolev spaces, or that this is very practical stuff, as in finite elements and wavelets. He also seems not to know that most quantum field theory is based on series solutions.)

However, I believe that using terms like "moron" for physicists is dead wrong, and it detracts from the very valid criticisms of their attitude toward mathematics.

In defense of the physicists, their attitude toward math reflects the history of physics, which is dominated by the struggle against a priori reasoning that led to wrong conclusions, and to mathematical speculations that did not stand up to experimental tests. Their attitude grows from Francis Bacon's focus on empirical validation as the antidote to these problems.

I think the physics community has not yet absorbed the fact that mathematics in physics is now so sophisticated that it can be used, judiciously, to assign degrees of credibility to theories, and to promote theories from pure speculations to theories with a high degree of credibility that await empirical validation. I am referring to very restrictive nonlinear theories like general relativity and gauge theory based on differential geometry of connections in fiber bundles, not ad-hoc mathematical additions to equations.

String theory is the big exception, where theoretical physicists bought in big-time to the theory because of its mathematical structure and great results like removing divergences. However, physicists went overboard in thinking that pouring all their efforts into this theory for a few decades would yield a Theory of Everything, Physics has its own history of enforcing dogmas, such as the Copenhagen interpretation of quantum mechanics, which ruled out any ideas that something beyond the quantum wave field exists. The terror of the Copenhagen interpretation suppressed many lines of thinking for a long time, and that left theoretical physics ripe to overreact to the limited successes of string theory. 

That physicists aren't logical like mathematicians and/or don't understand mathematics deeply doesn't matter since physics isn't mathematics.  Mathematics allows to avoid making contradicting predictions, however it happens that quantum mechanics does make contradicting predictions, according to whether the unitary evolution or the projection postulate is applied, even in the non relativistic case.  But for a physicist, adequate description of Nature is more important than logical consistency, and there isn't yet a theory of microscopic reality that fulfills both constraints.  Physics is an empirical science, mathematics is a pure mind game, there isn't necessarily an exact correspondance between them.  A mathematician will think everything is mathematics, like a plumber thinks everything is pipes.

Dear Richrd,

I know physicists, who correspond to your question: “Do you know of any case in which physicists accepted a basic theory based on a derivation from accepted theories, or its mathematical structure?” I am such a physicist. I am using a very simple idea, that the space-time geometry should be constructed by a deformation of the proper Euclidean geometry GE. The GE is constructed by Euclidean method, i.e. all geometrical relations are deduced from Euclidean axiomatics. Thereafter all relations of GE are expressed in terms of the world function \sigmaE=1/2\rhoE2, where \rho is the metric of GE. It is possible, and it means that GE is described completely by the world function. The  \sigmaE is replaced by the world function \sigma of the space-time geometry G. As a result one obtains all relations of G. Method of deformation is simpler, than the Euclidean method, where one needs to prove numerous theorems. Unfortunately, nobody believes in the method of deformation, because in the schools and in universities one teaches, that the geometry is a logical construction. Why? How is logic connected with geometry? Nobody knows. Nevertheless everybody does not accept a space-time geometry, which is not a logical construction in general.

Of course, the law of gravitation without taking into account the recoil, i.e. the third law, is inconsistent.  The second law is F = ma, bzw F = Ma.  The frames of each mass are not Galilean, Newton's laws aren't valid in them.

(Akira) "I think an average research student in pure mathematics are more intelligent than all geniuses of Physics combined."

That says it all.

Perhaps not in grammar, though.

Reductio ad absurdum is a fallacy since in the proof of a theorem, one of the hypothesis is that the theorem is false.  There are many reductio ad absurdum even in the most usual theorems, therefore mathematics as a whole is a fallacy.  It has been  a way that has been used by the Greeks to fight the domination of their barbarian neighboors.  They are the ones that have coined the term sophism, since mathematics is no less than a big sophism.  Socrate is neither a man nor mortal, he only has been sentenced to death because he wanted to expose the mystification.  If he wasn't dead, he would still be living.

reductio ad absurdum uses the theorem to prove the theorem, it is logically invalid.

Refuting a theory is identical to reductio ad absurdum.  The theory is taken as hypothesis, and is then disproven by an inconsistent experimental result.  The only remaining valid proposition is that the theory is false.  Or Russell is a moron, or you cited him incorrectly.

The big confusion that the mathematicians make, is that physics is not about truth, but about reality.  Mathematics is basically the calculation of the truth value of propositions. A theorem is composed of an hypothesis and a conclusion, thus it is a relative, or conditional, truth.  Physics only seaks to describe and predict real facts in an economical way, not to calculate the truth value of statements about Nature.  It can only be an empirical science.  A theory is accepted when it is validated with an acceptable accuracy in its own domain of application.  Without a comparision with experiment, a theory is merely useless.

Akira, all what you write is so off the mark and so surrealistic than we don't even know where to begin with to answer you. I already gave up for a long time. You have only read the books that reinforce your prejudices, and/or suitably misconstrued other ones. Your knowledge on the very matter, on the scientific community, on the methods, on the history must be very thin to utter such absurdities. Your motivation is only to put down the scholars, and not to seak the truth, so a discussion with you is pointless. You want to think that they are all mislead? All right, think so, it's your problem, not ours.

Quantum mechanics have been discovered independently by Schrödinger and Heisenberg, and in different forms.  But Schrödinger has proved that they are mathematically equivalent.  There was also an american physicist who discovered it even before De Broglie's thesis.  But his paper has not been accepted for publication for deemed to be too abstract. It has been destroyed, but Schrödinger saw it, and said that it was the same thing as his own work. This story is very little know, I can't find the references again. So, three identical and independent copies of the same theory, in different settings, there is certainly something in it.  Before the debate between Bohr and Einstein, and before the famous EPR paper, quantum mechanics was thought to be perfectly rational, even though not intuitive, not "anschaulich." It explained quite naturally the empirical rules of Bohr and Sommerfeld, without the irrational-magical tinge they carry.  In only two or three years after its official birth, quantum mechanics has been applied succesfully to a wealth of problems.  Since then, despite much efforts, and even despite the rationalist movement, no better theory could be found.  The only rôle we could ascribe to the "anti-rational hysteria," is that these invaluable papers could be published, contrary to with the stringent and arbitrary policy of the American Physical Society.  De Boglie who sparked this revolution was not in Germany.

Dear Dr. Petti,

Physicists are doing this all the time.  For example, most of them had accepted the standard model of particle physics (Glashow, Salam and Weinberg) before its basic tenets and predictions were tested out at CERN.  Sometimes theories are ahead of experiments; other times the opposite is true.  This is how advances in physics are made.  Incidentally, Higgs' mechanism is not exactly a 'theory'; it is a prediction made within the framework of a theory (namely, QFT).  Another example is Maxwell's great (theoretical) synthesis which was accepted admiringly by major physicists of the day; it came before Hertz's brilliant experimental confirmation.  And so on, and so forth.

In reply to Richard Petti I am inclined to support Humam Ghassib' statement "Physicists are doing this all the time." "Inclined" means it is still hypothesis to me, although I know some facts supporting it. I hope that with time I'll be able to provide a more definite answer.  I must warn you that I am working in classical physics, and it is up to you to decide whether   quantum physics develops in a in the same fashion or different.

Several qualifications are necessary to discuss the question. One is about the criteria of acceptance.  Accepted by whom?  What is important here: overall numbers, specific groups  or particular individuals? (I discussed this issue in "Discovery in Science").  The second one is about supporting evidence.  How much evidence is sufficient?  What is important here: numbers or names?  Until one makes assumptions about these issues, no answer to Richard is possible.  Note the word "assumptions": the implication is that they will not be same, even within a small group reading this post.  And don't try to look for "normative" criteria!

I am not trying to show that the question is meaningless.  On the contrary, I am looking for qualifications that make it meaningful.  The answer depends on the purpose of a responder. A small group of  researchers who work with the theory in question trying to expand its applications will be happy to use any new assumption which appears to them plausible even if it lacks empirical evidence.  Not so with the wide group of physicists who are not the specialist in the narrow filed but whose opinions matter, because they publicize new discoveries, distribute awards of different kinds, etc. They may not be in a rush to "accept" the new theory.  And if they do not, the third and the largest group of non-physicists may not even hear about the novelty.

Dear Nahum Kipnis,

I liked your well-balanced answer very much. It is my experience that theory and experiment/observation cannot do without each other, but that it is impossible to tell which of these should start. This probably is an unanswerable question, but we can learn a lot about it by looking at historical examples (even though we should be aware that history seldom does repeat). I think the structural approach discussed in Frederick Suppe ed., The structure of scientific theories : symposium, 1969, Urbana, Ill.:

outgrowth with a critical introduction and an afterword by Frederick Suppe,

University of Illinois Press, 1977, is a good candidate for a satisfactory methodology of physics, probably being closest to the one actually practised by physicists.

Willem de Muynck

Theories are not always accepted by everyone all at once, especially revolutionary ones.  There is often a time when experimental evidences are scarce, and at which different people have different opinions.  Often the death of the the most diehard champions of the classicism, especially if they have some influence, is necessary.  The situations are so diverse that I don't think an epistemolocal theory can be based on them.  Even when Newton's universal gravitation was accepted by the scholars, the geocentric system had still some favour among religious people, and even among some scientists.  It all depends on the importance the theory has on the society, the everyday life, and the philosophical ideas.

Claude, I am interested in motivations of scientists to accept a new theory. Can you give me an example where it is possible to distinguish between objective and subjective factors?

As to your statement  "Often the death of the the most diehard champions of the classissism, especially if they have some influence, is necessary", I suggest to replace "often" with "sometimes", unless you can provide at least 3 examples supporting your point.

The most known examples are as good as others, let's take Einstein's stance toward quantum mechanics.  There are subjective factor like the statement "God doesn't play dice" and many opinions Einstein had about how a theory must look like.  But on another hand, there are true objective factors like the EPR paradox, that didn't proved that quantum mechanics is incomplete, but revealed a spooky aspect of it.  On the side of its acceptation, there are the problems it allowed to solve, like the Zeeman effect, despite difficulties about its interpretation and its logical consistency.  But people really accepted it when they were convinced, rightly or wrongly, that it wasn't that mysterious.  It is now said that many aspects are counter-intuitive, but it is so.  Those subjective factors disappeared around the death of Einstein, and quantum mechanics is no longer challenged by the official scientific community.

Everyone, me including, knows about Einstein.  I want to hear something not generally known, perhaps from your own field of research.  I need FACTS which upon a certain accumulation would allow a generalization.  The problem of acceptance of new theories is very little understood: which response is normal and which is abnormal, etc.  Philosophers of science think in terms of logic which  leads them to "must": if there is a supporting evidence, everyone must accept it.   But science is only partially logical, and scientists don't think like philosophers.

Nahum Kipnis,

For a generalization of quantum mechanics from the standard theory that can be found in most textbooks to a generalized theory in which observables correspond to positive operator-valued measures rather than Hermitian operators you might consult my Foundations of quantum mechanics, an empiricist approach, Kluwer, 2002, a pre-publication version of which can be downloaded as Publ. 52 here: http://www.phys.tue.nl/ktn/Wim/publications.htm#main

Willem de Muynck

Charles, you treat the modern nuclear-synthesis theory of stars as Perren's theory delayed in acceptance by half a century, right?  (The original question was about a delay in accepting a new theory.)  But are theories of Eddington, Bethe, Gamow, and Hoyle are the same and, even more so, the same as Perrin's?  But is it not true that the only thing they all have in common is Perrin's idea that the energy produced in a star is due to deficiency in mass, according to Einstein?  But an idea by itself does not make a theory which allows calculations comparable to experiment.

It is not uncommon to see a development of a theory where it retains some common elements but also acquires others, and those others are crucial in expanding the area of its application.  For instance, although all wave theories of light had one common element - propagation of light as a transfer of motion rather than of matter - it does not make sense to say that Euler's theory was a delayed reaction to Huygens, or that the theory of Young and Fresnel was that of Huygens and Euler offered again after a delay. 

When we speak of a delayed acceptance by comparing different theories, we must be sure they are essentially the same (independent discovery).  It is because of this confusion between an original theory gradually developed into something else and a delayed reaction to a single theory, that I asked for examples from your own fields of research.  In your own field you know the content of theories and their history and don't need to rely on their reinterpretation in secondary sources.

Charles,

Currently, I don't have access to articles by Perrin, Eddington, Gamow, and Bethe, and cannot say whether THEY treated their theories as the same theory.  If you have read these articles, you can enlighten me on this point.

It is easier in this respect with the wave theory.  You treat theories of Huygens, Euler, and Young and Fresnel as the same.  That is to say, you neglect their differences in the name of "integrated whole".  Usually, when one compares several theories in the same field, one focuses on their essential common element or important differences depending on the purpose of the discussion. For instance, when speaking of priority, the focus is on the common and the search is for the first one who pronounced it.  When one is trying to understand why one of the theories has a wider range of application, one turns to the differences. 

What shall we do in our case? What does it mean that an acceptance of a new theory was delayed?  The presupposition here that the theory deserved to be immediately accepted, because it was clearly stated, supported experimentally, etc. But how do we know that contemporaries treated it as "deserving"? Perhaps they treated its merits as insufficient compared to its drawbacks which each theory has?  Thus, in general, to talk about a delay of acceptance of ONE theory is unproductive.  When a similar theory offered again (an independent discovery), as it happens with Young's theory of diffraction, then we have some facts to compare and may suggest reasons for the delay of recognition of Young's theory until the publication of Fresnel's first  theory of diffraction (13 years).

However, Huygens' theory is VERY different from Euler's, because the two pursued different goals.  Young's goal was in part the same as Euler's but his means were very different.  Their theories were compared only at the stage of non-acceptance, when Young's theory came into favor no one accused him of stealing something from Euler.  You may have any hypothesis you wish, but you have to show its advantages (at least, some)  over the competing hypothesis.

I tried to understand your sentence: "it was not until Young that the evidence was available to call wave theory scientific, but that does not mean that the theory did not already exist."  My first question  is to the phrase "evidence was available".  Do you mean that the the phenomena Young brought forward to support his theory were unknown earlier?  If this is your meaning, it is erroneous, for most of them were known to Hooke and Newton.  The second question as about your definition of a "scientific" theory.  It appears that you consider the theories of light by Huygens and Euler non-scientific.  Again , you may conceive any definition, but would you care to show its advantages over other definitions?

Regards,

Nahum

Charles,

I see you are so happy with a history and philosophy of science of your own, that it does not make sense to try to convince you to read anything.