Does a physical theory need to be self-consistent?

[ikkyu]

self-consistent = contains no valid proposition that can prove true and prove false under the same theory

1. Does a physical theory need to be self-consistent? Why?

2. Is it possible to accept a theory that agree with all facts but contain inconsistencies?

3. Is a self-consistent theory better than inconsistent one?

The consistency condition which demands that new hypotheses agree with accepted theories is unreasonable because it preserves the older theory, and not the better theory.

- Paul Feyerabend (AKA: Enemy of science) -
Against Method

(I think that Feyerabend's arguments seem to contain a lot of fallacies. But I stuck on this one.)

It is possible to construct a mathematical theory that is inconsistent.
e.g. a theory that can talk about its own consistency.

What about Physics and Science?

This is not the same case to inconsistency between QM and GR. I'm talking about the inconsistency within the same theory.

 

[Doctordick]

1. Does a physical theory need to be self-consistent? Why?

Because a theory is an explanation of observations. A theory which is inconsistent with past observations is invalid a-priori. If it produces inconsistent predictions of observations, it does not serve a purpose. Now there are those who will hold that quantum mechanics is inconsistent because intermediate states involve superpositions of inconsistent states. This is false because what quantum mechanics does is to provide probability distributions and not specific events. So long as the probability distributions are internally consistent everything is fine.

2. Is it possible to accept a theory that agree with all facts but contain inconsistencies?

Sure, so long as you accept the fact that the theory is wrong: i.e., it is only applicable when those inconsistencies are not relevant (think of it as a useful rule of thumb for isolated cases). There is a lot of science which only models a very constrained situation. (Of course, I presume you don’t refer to the superposition issue above). I won’t even bother answering your third question. :yuck:

This is not the same case to inconsistency between QM and GR. I'm talking about the inconsistency within the same theory.

I don’t see why you are not bothered by that inconsistency. It certainly implies one of the two is WRONG!

Have fun -- Dick

 

[matt grime]

I don’t see why you are not bothered by that inconsistency. It certainly implies one of the two is WRONG!

No, it does not imply one or other is wrong, since they are not attempting to model or explain the same thing. As you admit yourself it is only intended to model a very small part of physics. Misapplying it to situations where it does not (or should not be used to) make any predictions is a disingenuous way of asserting something is 'wrong': find a better adjective.

 

[selfAdjoint]

Logical inconsistancy is a major test of proposed hypotheses. In the quantitative sciences most models which have irremovable inconsistancies are rejected. Physicists have accepted the idea that theories only account for some of experience, and even though two such theories (such as general relativity and quantum field theory) may not at present be unitable in a self-consistent way, they do describe different scales - QFT is valid where Planck's constant cannot be ignored and GR is valid where it can be ignored as to small to matter. Then so long as each of them is consistent within itself (which has been questioned but not disproved in both cases) all is well.

 

[Doctordick]

No, it does not imply one or other is wrong, since they are not attempting to model or explain the same thing. As you admit yourself it is only intended to model a very small part of physics. Misapplying it to situations where it does not (or should not be used to) make any predictions is a disingenuous way of asserting something is 'wrong': find a better adjective.

As I said to ikkyu, “Sure, so long as you accept the fact that the theory is wrong: i.e., it is only applicable when those inconsistencies are not relevant (think of it as a useful rule of thumb for isolated cases). Anyone competent in higher physics will admit that something is “WRONG” with their theories somewhere as evidenced by the incompatibility of quantum mechanics with general relativity. If you deny that, you simply do not understand the circumstances. :yuck:

Logical inconsistancy is a major test of proposed hypotheses. In the quantitative sciences most models which have irremovable inconsistancies are rejected.

The only occasion where they are not is when no one knows how to remove the troubling inconsistency. :rofl:

Then so long as each of them is consistent within itself (which has been questioned but not disproved in both cases) all is well.

I would agree with you entirely except for that final “all is well”. I am afraid that anyone competent in modern physics would recognize that the inability to unite QFT and GR is a major difficulty and should be seen as one. Something is wrong somewhere. :grumpy:

Have fun -- Dick

 

[matt grime]

Yes, something is wrong in some sense, and I believe it is with your attempts to imply that QM (either the model or the theory) is 'wrong' because it is incompatible with GR (or vice versa). Something is only 'wrong' within certain parameters, and yours appear to be attempting to apply them to situations they do not say anything about. They are certailny inadequate to be used as a unified theory of everything, but then no one is asserting that they are such.

It is a question of semantics, of when it is fair to use the phrase right or wrong and with what implications (and surely someone competent in physics would admit that an anonymous poster on an internet message board asserting that "GR is wrong" is not something to be encouraged), and not to do with understanding 'higher/modern physics".

 

[Doctordick]

Yes, something is wrong in some sense, and I believe it is with your attempts to imply that QM (either the model or the theory) is 'wrong' because it is incompatible with GR (or vice versa).

I’m sorry, I didn’t intend to imply it was wrong; I meant to say it was wrong: i.e., there is an error in the ideas upon which it is based. :rofl: :rofl:

They are certainly inadequate …

Any theory which is inadequate to be utilized in a conceivable circumstance is either wrong or the conceived circumstance is not logically achievable.

It is a question of semantics, of when it is fair to use the phrase right or wrong …

Einstein’s concept of a “space time continuum” is wrong in exactly the same sense as the concept of phlogiston was finally recognized as wrong. It is no more than a artificial construct convenient to certain specific calculations and not at all universally applicable. The common belief that it is beyond question the only way to view the structure of the universe is a block to rational analysis of the situation. To set any part of current belief above examination is to scuttle rational science. :yuck:

… and surely someone competent in physics would admit that an anonymous poster on an internet message board asserting that "GR is wrong" is not something to be encouraged …

Now doesn’t that strike you as quite similar to the Pope’s position five hundred years ago that someone asserting that the Earth goes around the sun should not be encouraged? :rofl: :rofl: :rofl:

And it has everything to do with understanding “higher/modern physics” as a science and not as a religion. :tongue2:

To insist that no one on this forum suggest that any current theory could be in error is disingenuous at best.

Have fun -- Dick

 

[ikkyu]

Because a theory is an explanation of observations. A theory which is inconsistent with past observations is invalid a-priori. If it produces inconsistent predictions of observations, it does not serve a purpose.

What you are talking is about the theory that failed to satisfy the fact, and has nothing to do with self-inconsistency.
Please carefully read the definition of "Self-Inconsistency" again.

Now there are those who will hold that quantum mechanics is inconsistent because intermediate states involve superpositions of inconsistent states. This is false because what quantum mechanics does is to provide probability distributions and not specific events. So long as the probability distributions are internally consistent everything is fine.

Right, that is not inconsistency in QM.

I don’t see why you are not bothered by that inconsistency. It certainly implies one of the two is WRONG!
Have fun -- Dick

I never said that I'm not bothered by that.
I'm talking about Self Inconsistency in the same theory. Not incompatibility between two theories.

If you have a reason why a self-inconsistent theory (That is well-satisfy the facts) must be reject. Please tell me.

Please not that I'm not think that we should accept a physical theory that is self-inconsistent. I just need a good reason to reject Paul Fereyabend's argument. :tongue2:

 

[selfAdjoint]

In your first post you quoted Feyerabend:

The consistency condition which demands that new hypotheses agree with accepted theories is unreasonable because it preserves the older theory, and not the better theory.

- Paul Feyerabend (AKA: Enemy of science) -
Against Method

This is not about internal consistency of A theory but about a consistent relation between a theory and its replacement. And I don't think in practice theorists do use rigid consistency; it would be foolish just as Feyerabensd says (he was not an enemy of science, in spite of popular opinions, only of bad philosophy of science). The criterion you hear from physicists, in this age of "effective" theories, is that the old theory should appear as a special case or limiting condition of the new one, quite like Hegel's Thesis (old theory), Antithesis (New concepts), Synthesis (new theory).

 

[vanesch]

self-consistent = contains no valid proposition that can prove true and prove false under the same theory

1. Does a physical theory need to be self-consistent? Why?

2. Is it possible to accept a theory that agree with all facts but contain inconsistencies?

3. Is a self-consistent theory better than inconsistent one?

1. Depends what you want to do with your physical theory. If you want to make *reliable* predictions with it, you better have a self-consistent theory. Indeed, by definition, in a non-self-consistent theory, the prediction and its contradiction can both be derived from the theory (by following different reasonings, both valid in the theory). So if your non-self-consistent theory tells you that the bridge will hold up, then that same theory will allow you also to derive that the bridge will fail.

2. In fact, a non-self-consistent theory is ALWAYS in agreement with ALL facts in some way, because all statements (and their opposite) can be derived from a non-self-consistent theory. As such, a non-self-consistent theory is always empirically superior :tongue:

3. A non-self-consistent theory is not only empirically "superior" because it is in agreement (and also of course in contradiction) with all empirical observations, but moreover, non-self-consistent theories allow for much more publications than self-consistent ones: indeed, you can write down what you want, and it will always have some meaning within a non-self-consistent theory.

So I'd say that in all cases of scientific endeveour where the reliability of the result is not an issue, but only the publications and experimental success, non-self-consistent theories are preferable.
However, if your life depends on the accuracy of its predictions, then I'd rather go ... eh.. for a nice self-consistent one :rofl: :rofl:

 

[Doctordick]

Well, hi everybody. I hadn't looked at this thread for quite a while because I had the impression no one understood my earlier post. At the moment, it appears that perhaps a few of you do have an inkling of what I was talking about.

This is not about internal consistency of A theory but about a consistent relation between a theory and its replacement. And I don't think in practice theorists do use rigid consistency; it would be foolish just as Feyerabensd says (he was not an enemy of science, in spite of popular opinions, only of bad philosophy of science). The criterion you hear from physicists, in this age of "effective" theories, is that the old theory should appear as a special case or limiting condition of the new one, quite like Hegel's Thesis (old theory), Antithesis (New concepts), Synthesis (new theory).

I agree with this comment entirely; however, it appears to me that, in practice, current physicists (this age of "effective"theories) simply presume that no new concepts exist. Over thirty years ago, I tried to publish a way of looking at things which was one hundred percent consistent with the experimental results of QM and general relativity and was rejected by the physics community journals with the comment that I was trying to publish in the wrong area as I was discussing philosophy not physics. The philosophy guru's held that I was discussing mathematics, not philosophy and the mathematicians held I was discussing physics and not mathematics.

Since that time I have distilled the essence of my thoughts down to roughly three pages and, as of yet, found no one sufficiently interested to even take examination of that paper seriously. I deduce a rather simple equation from an exact definition of "an explanation". Every professional who has ever seen http://home.jam.rr.com/dicksfiles/Explain/Explain.htm has chosen to ridicule it rather than point out any error in my deductions. What I am looking for is someone capable of comprehending the validity of the equation I have deduced: i.e., validity of the deduction itself. If I ever do find such a person, I will explain to them how to work out the solutions. As it turns out, all of the predictive equations of standard QM, standard electrodynamics, standard relativistic QM and Newtonian physics can be shown to be approximations to that equation. The general relativistic consequences of that equation are almost exactly the same as Einstein's GR, differing only by a very small radial term which is pretty well outside our current range of experimental accuracy. In my opinion, this certainly passes the test described by selfAdjoint and justifies a serious examination.

If anyone on this forum actually wishes to think about the question, "Can physics explain everything?" they need to understand my deduction. To ignore it is to support ignorance on the subject.

Have fun -- Dick

 

[ikkyu]

This is not about internal consistency of A theory but about a consistent relation between a theory and its replacement.

Hi selfAdjoint,
I don't claim that Fereyabend's argument is about self-consistency.
And adding "new hypothesis" does not necessary mean finding a new theory.

But *my question* here is about self-consistency. Talking about other thing, such as consistency between theories or whether the theory can satisfy the facts, will not resolve my doubt.
If you read some book about *first order logic* or *mathematical model*, you will see that it is possible to construct a theory that lack of self-inconsistency. I'm asking about self-consistency in physics, which is built on mathematical models.

 

[selfAdjoint]

Hi selfAdjoint,
I don't claim that Fereyabend's argument is about self-consistency.

Your original post certainly gave that impression.

And adding "new hypothesis" does not necessary mean finding a new theory.

Oh, agreed. Irrelevant though.

But *my question* here is about self-consistency. Talking about other thing, such as consistency between theories or whether the theory can satisfy the facts, will not resolve my doubt.
If you read some book about *first order logic* or *mathematical model*, you will see that it is possible to construct a theory that lack of self-inconsistency. I'm asking about self-consistency in physics, which is built on mathematical models.

I have taken courses in logic and I understand the difference. But the acceptance of a theory by the scientifiic community is a sociological process, and can't be handled by first order logic. A theory can be, and has been accepted and regarded as valuable even though it is widely believed to be self-inconsistent. The theory is Quantum Electrodynamics, "the most accurate theory ever developed". Only a few years after it was unified (by Dyson, from the proposals by Tomonaga, Schwinger and Feynmann), Dyson and Landau gave separate arguments why it might be not consistent when processing high energies. But since it has never been required to process high enough energies to trigger the problem, it remains in productive use.

Just to forestall unecessary posting, the replacement of QED by the electroweak theory has not fixed the problem, and the modern renormalization group view of effective theories in general only requires that theories be mathematically consistent within specified energy ranges.