The Fundamental Difference in Interpretations of Quantum Mechanics - Comments

[bhobba]

So the inconsistency that I worry about is not in the mathematical formalism, but in applying the mathematical formalism to a real measurement. Is the description of the measurement process as a complex quantum interaction among a macroscopic number of particles consistent with the abstraction described in that paper?

Its a textbook by mathematicians for mathematicians.

Now in applying it you have to map the formalism to things you want to apply the theory to. In principle you should be able to do it, but using the methods in that book I haven't seen it, but using normal methods at least a partial solution is known in decoherence models. Its like Hilbert's Euclidean Geometry axioms and Euclid's. Everybody in practice uses Euclid - but in principle you could use Hilbert's.

Thanks
Bill

 

[stevendaryl]

Now in applying it you have to map the formalism to things you want to apply the theory to. In principle you should be able to do it, but using the methods in that book I haven't seen it, but using normal methods at least a partial solution is known in decoherence models.

I don't think that decoherence changes anything in principle. In practice, decoherence makes it impossible to see macroscopic superpositions. So we're free to assume that once decoherence has occurred, that the miracle of collapse has already happened. We're free to assume that in the practical sense that observations are not likely to prove us wrong.

 

[A. Neumaier]

the MEANING of to measure/observe. That however is a minefield if you want to pin it down exactly - but almost trivial in use.

This is the root of the problem in clarifying the precise meaning of quantum mechanics, and hence the source of the many interpretations.

 

[bhobba]

This is the root of the problem in clarifying the precise meaning of quantum mechanics, and hence the source of the many interpretations.

Yes .

But then again it likely applies to a number of areas in applied math if you think about it hard enough eg normal probability theory - John Baez certainly thinks so:
http://math.ucr.edu/home/baez/bayes.html

Thanks
Bill

 

[bhobba]

I don't think that decoherence changes anything in principle. In practice, decoherence makes it impossible to see macroscopic superpositions. So we're free to assume that once decoherence has occurred, that the miracle of collapse has already happened. We're free to assume that in the practical sense that observations are not likely to prove us wrong.

Correct - other assumptions are required without detailing them eg you assume an observation has occurred once decoherence happens.

Thanks
Bill

 

[Fra]

This is the root of the problem in clarifying the precise meaning of quantum mechanics, and hence the source of the many interpretations.

Another distinguishing factor that reflects the selection principle for our interpretations is wether it is rational to enter the minefield in order to progress fundamental physics or not?

This is another factor that divides us.

/Fredrik

 

[A. Neumaier]

Yes .

But then again it likely applies to a number of areas in applied math if you think about it hard enough eg normal probability theory - John Baez certainly thinks so:
http://math.ucr.edu/home/baez/bayes.html

Yes, see https://www.physicsforums.com/posts/5918976/ for a reference that discusses this in some depth.
But in classical mechanics this is no fundamental issue since probability enters only through the approximation process.

 

[A. Neumaier]

whether it is rational to enter the minefield in order to progress fundamental physics

This is not primarily a matter of ratio but of personal preferences and risk profiles.

I find it worth my time to ponder about the measurement problem at its root.

 

[Fra]

So the inconsistency that I worry about is not in the mathematical formalism, but in applying the mathematical formalism to a real measurement.

Indeed. And this is exactly where the physics part lies.

A mathematician can easily enter the mine field as he can walk without feet.

I think of the mathematical theory of QM as incoherent from the point of a general inference perspective. Sometimes i think of this as inconsistent reasoning. But this reasoning is not deductive in nature its more abductive but even such may have consistency requirements.

/Fredrik

 

[AlexCaledin]

... mathematical theory of QM as incoherent ...

But how it can be coherent? What happens in every local measurement is choice between variants of the whole universe, while QM is telling about a limited experimental system.

 

[bhobba]

I think of the mathematical theory of QM as incoherent from the point of a general inference perspective. Sometimes i think of this as inconsistent reasoning. But this reasoning is not deductive in nature its more abductive but even such may have consistency requirements.

Gee - I wonder why it has never been falsified.

The mathematics is not incoherent - what is incoherent is thinking the obvious mapping you use to apply is somehow at fault - it isn't. Its like saying the obvious mapping you use in applying Euclidean Geometry to points and lines is incoherent. Its a very difficult philosophical question when looked at deeply enough - but even 10 year olds have no trouble doing it. The same in QM - if you look at it very deeply its a morass (just one obvious thing - since observations occur here in the macro world how does a theory that assumes such in the first place explain it - a lot of progress has been made - I think the answers we now know are just fine - others disagree) - if not its rather obvious. Its a matter of taste if you think such questions are worthwhile. I happen to think going too deep into it isn't that worthwhile - but not everyone agrees.

Thanks
Bill

 

[bhobba]

But how it can be coherent?

The same way arithmetic is coherent.

Thanks
Bill

 

[Greg Bernhardt]

Great job Peter!

 

[Stephen Tashi]

Why is the concept of the collapse of a wave function any more (or any less) of a problem in logical consistency than other applications of probability theory where there are probabilities of various outcomes followed by only one of the outcomes happening?

Mathematical probability theory (based on measure theory) says nothing about events actually happening and has no axiom stating that it is possible to take take random samples. Taking random samples (i.e. "realizing" the outcome of a random variable) is a topic for applications of probability theory, so it involves an interpretation of probability theory not explicitly given in the mathematical axioms.

Sure, that's why I said we're dealing with vague ordinary language. I'm not trying to put a specific definition on the word "real". I'm just trying to say that, as far as I can tell, people who espouse Case 1 interpretations consider the quantum state to be like probabilities, and in common ordinary language usage probabilities do not describe the physically real state of anything; they just describe our knowledge (or the limitations thereof). If it helps, substitute "case 1 says the quantum state is like probabilities" for "case 1 says the quantum state is not real".

It's controversial whether probabilities (in physics) represent a state of knowledge or whether they are objective. However, your make it clear that your definition of "physically real" excludes a quantity that represents a probability.

Case 2 interpretations of QM do not say a physically real state produces a deterministic outcome (that would contradict stan; they just say the quantum state is physically real. So I don't see how this helps to clarify anything relevant to this discussion.

To make a classical analogy, suppose we take a coin with uniform mass density and bend it in the middle at angle theta. When used in a coin toss experiment, the angle theta may affect the probability that the coin lands heads. In your view, the angle theta is a "physically real" aspect of the coin and the probability of the coin landing heads is not.

Is that a good analogy, from your point of view?

 

[PeterDonis]

It's controversial whether probabilities (in physics) represent a state of knowledge or whether they are objective.

Yes, agreed; but as you note, for purposes of this discussion I am using the term in the former sense.

In your view, the angle theta is a "physically real" aspect of the coin and the probability of the coin landing heads is not.

Yes.

 

[Auto-Didact]

No - its perfectly consistent.
... But be my quest - post the exact inconsistency. Schrodinger's equation is a deterministic equation about something (the wavefunction) that determines probabilities - there is no inconsistency in that.

There is nothing mathematically inconsistent about the Schrodinger equation itself. What is mathematically inconsistent about QM is that half the formalism (measurement process) has completely different mathematical properties than the other half (Schrodinger equation). Its even worse than that since the measurement process has not even actually been fully formalized. There is no other physical theory which suffers from these problems.

I think an actual inconsistency is impossible to prove because one half of the quantum formalism is informal: The notion of what it means to measure a quantity.

Exactly my point.

This is only a definition of what an observable is, not a definition of what it means to have measured something. (The link addresses only the classical situation, where this actually can be modeled, in principle.)

Arnold, as usual, hits the nail on the head.

Meaning - of course that's something different that the math bypasses. Of course - it's what an observable is - not the MEANING of to measure/observe. That however is a minefield if you want to pin it down exactly - but almost trivial in use.

Application is of course trivial, but that is misunderstanding the problem at hand here. One of the goals and duties of mathematical and theoretical physicists is to be able to demonstrate mathematical consistency of a physical theory by being to able to derive a theory entirely from first principles; QM is just another physical theory and thus not an exception to this. As the theory stands today, since its conception, this full derivation is not yet possible; no other accepted physical theory suffers from this. (NB: QFT has foundational issues as well, but that's another discussion).

The same in QM - if you look at it very deeply its a morass (just one obvious thing - since observations occur here in the macro world how does a theory that assumes such in the first place explain it - a lot of progress has been made - I think the answers we now know are just fine - others disagree) - if not its rather obvious. Its a matter of taste if you think such questions are worthwhile. I happen to think going too deep into it isn't that worthwhile - but not everyone agrees.

With all due respect, but your personal opinion or the opinion of large groups of physicists on what is or isn't worthwhile figuring out with respect to theories lacking proper foundations yet being able to generate predictions, should not be given too much weight. Actually putting too much weight on the experts opinion is doing a disservice to science, because doing this leads to the creation of a perpetuation of dogma among the young practitioners who often lack the experience or courage to properly analyse the expert's points. The incessant upholding of expert opinion and promulgating of obscurantist dogma is equivalent to relaxing or removing the capability of a science to spontaneously self-correct.

This is no new phenomenon here either, the other sciences are absolutely rife with this problem, precisely because almost all their theories have not ever reached the stage of being sufficiently formalized such that it can be fully derived from first principles, in stark contrast with theories in physics. In the history of physics however, it is precisely such fundamental inconsistencies in theories as we see here in QM which have ended up unraveling centuries long accepted theories and research programmes, e.g. Aristotelian mechanics, Ptolemaic epicycle theory and Newtonian gravity. In each of the above cases, the experts and practitioners also tended to agree that the theories worked marvelously and relooking at the foundations of their theory wasn't a worthwhile endeavor, sometimes even dogmatically insisting on not doing so and so delaying scientific progress for centuries. These invaluable insights into science as a human process, which itself can be studied in a scientific manner, are important lessons easily gained purely by taking the history and philosophy of science, and in particular that of physics, to heart.

 

[David Halliday]

I understand that you were primarily contrasting two (2) interpretations (alluding to something like a third, or so), but there are a whole lot more than just a few interpretations that can be "cubbyholed" into the dichotomy you presented. (Basically, there are additional choices and other "dimensions" that can differ as well.)

However, your conclusion that "the best we can do at this point is to accept that reasonable people can disagree on QM interpretations and leave it at that" still holds firm!

 

[PeterDonis]

there are additional choices and other "dimensions" that can differ as well

Can you give some examples?

 

[Quandry]

The question is "Does God really play dice?"

Maybe the real question is, does God know where the particle is?

 

[Fra]

But how it can be coherent? What happens in every local measurement is choice between variants of the whole universe, while QM is telling about a limited experimental system.

Posting past midnight isn't a good thing but here is a simplified view of what i think of as an "inference interpretation", which is a highly twisted version of Peter Donis (1) version of the interpretation.

Coherence requires unifying unitary evolution with information updates, in the sense that in the unitary description by O3 of [O1 observing O2] must have a hamiltonian describing the internation interactions of the O1-O2 system that as per the inside view, is information updates. The problem is that if O1 is not a classical observer, the current theory does not apply. This is conceptually incoherent.

1) "Observer equivalence"
A coherent theory of physical inference must somehow apply to any observers inference on its environment. Not only to classical observers, because the difference is simply a matter of complexity scale(mass?). Current theory provides almost NO insight into the inferences of non-classical observers(*)

2) "Inferrability"
An inference itself contains premises and some rule of the inference. This rule can be a deductive rule such as hamiltonian evolution, or it can be a random walk. The other premises are typicaly initial conditions or priorly prepared states. Now from the point of view of requiring that only inferrable arguments enter the inference, we end up with the conclusion that we must treat information about initial conditions, no different than information about the rules. Ie. a coherent theory should unify state and law.

=> The inference systems itself, is inferred, and thus evolves. We natuarally reach a paradigm of evolution of physical law.

(*) This ultimately relates to unifying the interactions. To unify forces, and to understand how the hamiltonian or lagrangian of the unified interactions look like, is the same problem as to understand how all physical interactions in the standard model can be understood as the small non-classical observers making inferences and measurements on each other.

Once this is "clear", the task is to "reinvent" the mathematical models we need:
My mathematical grip on this, is that i have started a reconstruction of an algorithmic style of inference, implemented as random processes guided by evolving constraints. Physical interactions will be modeled a bit like "interacting computers", where the computer hardware are associated with the structure of matter. Even the computers evolve, and if this is consistent, one should get predictions from stable coexisting structures, that match the standard model. All in a conceptually coherent way.

Conventional models based on continuum mathematics should also correspond to steady states. In particular certain deductive logical system are understood as emergent "stable rules" in an a priori crazy game. In this sense we will see ALL interactions as emergent.

The big problem here is that the complexity here is so large, that no computer simulation can simulated the real thing, because the computational time actually relates to time evolution and tehre is simply no way to "speed up time". But theere is on exploit that has given me hope, and that is to look at the simplest possible observers, it would be probably doable to simulate parts of the first fractions of the big bang for one reason - the rules from the INSIDE are expected to be almost trivially simple at unification scale. They just LOOK complicated from the low energy perspective. But the task is huge indeed. But its not just a philosophical mess at all! Its rather a huge task of trying to reconstruct from this picture all spacetime and matter properties.

/Fredrik

 

[bhobba]

One of the goals and duties of mathematical and theoretical physicists is to be able to demonstrate mathematical consistency of a physical theory by being to able to derive a theory entirely from first principles; QM is just another physical theory and thus not an exception to this. As the theory stands today, since its conception, this full derivation is not yet possible; no other accepted physical theory suffers from this. (NB: QFT has foundational issues as well, but that's another discussion).

Ballentine has two axioms

1. Outcomes of observations are the eigenvalues of some operator.
2. The Born Rule.

Everything is derived from that except some things that in physics is usually accepted eg you can find the derivative of a wave-function and the POR.

So I have zero idea where you are getting this from - its certainly not from textbooks that carefully examine QM. Textbooks at the beginner/intermediate level sometimes have issues - but they are fixed in the better, but unfortunately, more advanced texts.

There are other misconceptions - but that's the one that stood out to me.

Thanks
Bill

 

[bhobba]

Why is the concept of the collapse of a wave function any more (or any less) of a problem in logical consistency than other applications of probability theory where there are probabilities of various outcomes followed by only one of the outcomes happening?

Of course it isn't - leaving aside that collapse isn't really part of QM - only some interpretations. In fact QM is simply a generalization of ordinary probability theory:
https://arxiv.org/abs/1402.6562

Mathematical probability theory (based on measure theory) says nothing about events actually happening and has no axiom stating that it is possible to take take random samples. Taking random samples (i.e. "realizing" the outcome of a random variable) is a topic for applications of probability theory, so it involves an interpretation of probability theory not explicitly given in the mathematical axioms.

Exactly - and that's where the morass I previously spoke about comes into it. If you push it too deeply you run unto unresolved philosophical issues of a formidable nature - even in ordinary probability theory when you apply it they rear their ugly head. But its usually bypassed by simple reasonableness criteria such as for all practical purposes. An example is the issue I mentioned, since QM is a theory about observations that appear here in an assumed macro world (we will exclude strange interpretations like consciousness creates the external world and causes collapse and stick with what most consider reasonable and not 'mystical') how can it explain that world? We have made a lot of progress in that but if you really push it, it still has issues eg decoherence models show that interference terms very quickly decay to zero - but usually never quite reach it - but are so small to be irrelevant. Some do not accept that (ie it must be zero to truly explain it) - which is OK - but then you are stuck, as I put it in a very deep morass of complex issues. Physics has long made reasonableness assumptions - if you don't do that then you are unlikely to get anywhere - although occasionally you can find something very deep and powerful such as in figuring out what that damnable Dirac Delta Function really is you create distribution theory that has wide applicability. But often you get nowhere.

BTW QM can be done the same way as probability theory ie simply an elaboration of axioms like the Kolmogerov axioms without applications entering into it - that's the intent of the previous mentioned book:
https://www.amazon.com/dp/0387493859/?tag=pfamazon01-20

But as Dr Neumaier correctly points out, exactly as for ordinary probability theory, you run into interpretive issues when applying it. That's why an axiomatic treatment is usually more along the lines of Ballentine that mixes applied and pure together. Its like Hilbert's Euclidean axioms and the usual ones - the usual ones leave it to our intuition things like between etc - Hilbert is exact - but abstract.

This is a point I have been emphasizing a lot in discussions about the meaning of QM - it's just the typical meaning stuff you get when you use applied math and not stick to just pure math. Its even in good old Euclidean geometry - defining precisely what points and lines are in an applied sense a minefield - but nobody has any issue in doing it.

Is that a good analogy, from your point of view?

Of course.

Thanks
Bill

 

[bhobba]

What is mathematically inconsistent about QM is that half the formalism (measurement process) has completely different mathematical properties than the other half (Schrodinger equation). Its even worse than that since the measurement process has not even actually been fully formalized. There is no other physical theory which suffers from these problems.

I have a couple of minutes spare before going to the dentist so can answer some of the other issues raised.

Remember what I said before: 'Imagine you have a coin that has a predictable mechanism inside it so its bias deterministically varies in time. You can write a deterministic equation giving the probabilities of getting heads or tales if flipped.'

That leads to exactly the same situation as QM - a deterministic equation describing a probabilistic quantity. Is that inconsistent too? Of course not. Inconsistency - definition: If there are inconsistencies in two statements, one cannot be true if the other is true. Obviously it can be true that observations are probabilistic and the equation describing those probabilities deterministic. There is no inconsistency at all,

And the measurement process has been fully formalized - its just after decoherence has occurred. The issue is not everyone agrees for reasons I have mentioned before. I will not argue they are wrong and I am correct - but saying that it has not been resolved is misrepresenting the situation. It just has not been resolved to everyone's satisfaction eg some want a 'formalization' where interference terms just don't decay to a very small value - but are actually zero. Most would say for all practical purposes (FAPP) it has been resolved - in fact probably many who think issues of defining remain will likely agree it has been resolved FAPP - they just want more than FAPP. I am not going to argue if they are right or wrong - I think everyone knows my opinion - but opinions are like bums - everyone has one - it does not make it correct. But this is in large part a philosophical morass - is FAPP good enough? It's part of what I mean if you push it too hard you are lead into a morass of issues.

And, as posted previously - its the same with many areas of applied math - push it too hard and you are lead down a path like Wittgenstein was led down. He was an excellent applied mathematician studying aeronautical science. He went to do his PhD but came under the influence of Bertrand Russell and wanted to know 'why' about issues with even basic arithmetic. He then became a philosopher. His view was very strange from a scientific viewpoint - he thought it all just convention. Was he correct - blowed if I know - all I can say to me its a very strange view.

Thanks
Bill

 

[vanhees71]

In my opinion, part of the reason there is such scope for interpretations is that nobody actually KNOWS what Ψ means. Either there is an actual wave of there is not, and here we have the first room for debate. If there is, how come nobody can find it, and if there is not, how come a stream of particles reproduce a diffraction pattern in the two slit experiment? No matter which option you try, somewhere there is a dead rat to swallow. As it happens, I have my own interpretation which differs from others in two ways after you assume there is an actual wave. The first, the phase exp(2πiS/h) becomes real when S = h (or h/2) - from Euler. This is why electrons pair in an energy well, despite repelling each other. Since it becomes real at the antinode, I add the premise that the expectation values of variables can be obtained there. The second is that if there is a wave, the wave front has to arrive at the two slits about the same time as the particle. If so, the wave must transmit energy (which waves generally do, but the dead rat here is where is this extra energy? However, it is better than Bohm's quantum potential because it has a specific value.) The Uncertainty Principle and Exclusion Principle follow readily, as does why the electron does not radiate its way to the nucleus. The value in this, from my point of view, is it makes the calculation of things like the chemical bond so much easier - the hydrogen molecule becomes almost mental arithmetic, although things get more complicated as the number of electrons increase. Nevertheless, the equations for Sb2 gave an energy within about 2 kJ/mol, which is not bad.

In real-world physics there's not much scope for interpretations. QT is just used as what it is, namely a mathematical description of what's observed in nature, and it is very well known what $\psi$ (or more generally quantum states) mean: It gives probabilities for the outcome of measurements on a system which is prepared in the corresponding state. The diffraction pattern is quite easily predicted by solving the Schrödinger equation. There's no "dead rat to swallow". I don't comment on your enigmatic claims on the phase etc.

 

[A. Neumaier]

Ballentine has two axioms

1. Outcomes of observations are the eigenvalues of some operator.
2. The Born Rule.

But he doesn't say what it means that one subsystem (an observer) of the physical system called the Earth has measured a property of another subsystem (a particle, say). This is the gap that makes all the interpretations vague when it comes to analyzing the measurement process as a physical process rather than as a metaphysical appearance of outcomes of observations from nowhere. It is filled by vague words about a collapse happening (when and where), worlds splitting (why and how?), etc..

 

[vanhees71]

Again, a theory book or scientific paper has not the purpose to tell how something is measured. That's done in experimental-physics textbooks and scientific papers! Of course, if you only read theoretical-physics and math literature you can come to the deformed view about physics that everything should be mathematically defined, but physics is no mathematics. It just uses matheamtics as a language to express its findings using real-world devices (including our senses to the most complicated inventions of engineering like the detectors at the LHC).

 

[A. Neumaier]

the deformed view about physics that everything should be mathematically defined, but physics is no mathematics.

I only asserted that the bridge between theoretical physics (mathematically defined) and experimental physics (operationally defined) is philosophy, and hence open to interpretation. Only what is theoretically precise can be subject to precise arguments.

 

[bhobba]

I only asserted that the bridge between theoretical physics (mathematically defined) and experimental physics (operationally defined) is philosophy, and hence open to interpretation. Only what is theoretically precise can be subject to precise arguments.

Yes - but its usually pretty obvious philosophy. If you get too deep about it you are led into very murky waters and really don't get anywhere.

With regard to Ballentine he does indeed analyse such things and uses the Ensemble interpretation. I won't argue if it's the right one, but its pretty simple and does provide a minimalist sort of link between the formalism and application.

It's like when you first learn the Kolmogorov axioms how to apply it ie what is meant by events etc is picked up with a bit of experience. They gave it meaning with a not too rigorous reference to the strong law of large numbers - which of course can't be fully detailed at the beginner level. Its fixed up later but the alternate Bayesian view isn't usually presented until Bayesian statistics. I don't think I ever formally studied the Cox axioms - l learned about it years later in my own reading.

Difficult interpretive issues are mostly deferred. Strangely though around here with beginners it seems to dominate. Interesting isn't it.

Thanks
Bill

 

[A. Neumaier]

Yes - but its usually pretty obvious philosophy. If you get too deep about it you are led into very murky waters and really don't get anywhere.

It is pretty obvious in classical mechanics but not in quantum mechanics. This is why the quantum measurement problem constitutes very murky waters, and nobody really gets anywhere, before it is made pretty obvious.

 

[vanhees71]

I only asserted that the bridge between theoretical physics (mathematically defined) and experimental physics (operationally defined) is philosophy, and hence open to interpretation. Only what is theoretically precise can be subject to precise arguments.

Well, you can call that philosophy, but it's constraint by the necessity for empirical testability, i.e., you have an idea of how to theoretically describe an experiment, including the preparation of the observed system and the measurement of the quantities of interest and then see whether the experiment agrees or disagrees with that prediction. Of course, it's not easy to analyze the errors in both experiment and theory etc. etc. E.g., the claim one might have discovered faster-than-light neutrinos at CERN could not immediately lead to giving up relativity but one had to exclude all sources of errors in the experimental setup first, and indeed after an independent control measurement in accordance with the theory and a long search one found two defects in the time-of-flight-measurement setup which finally explained the wrong findings etc. etc. This is all solid scientific work and not wild "philosophical" speculation.

 

[AlexCaledin]

Feynman would say measurement is done when "nature knows" the outcome - is this a wild speculation?

 

[vanhees71]

He'd not say this since it's an empty phrase, or what do you mean by "nature knows the outcome"?

 

[AlexCaledin]

- I mean just what any ordinary student must think, reading the Feynman's Lectures :

You do add the amplitudes for the different indistinguishable alternatives inside the experiment, before the complete process is finished. At the end of the process you may say that you “don’t want to look at the photon.” That’s your business, but you still do not add the amplitudes. Nature does not know what you are looking at, and she behaves the way she is going to behave whether you bother to take down the data or not.
. . .
...You may argue, “I don’t care which atom is up.” Perhaps you don’t, but nature knows...

http://www.feynmanlectures.caltech.edu/III_03.html

 

[bhobba]

Feynman would say measurement is done when "nature knows" the outcome - is this a wild speculation?

The quote you gave does not support what you said Feynman says. He was saying regardless of if you look or not if nature decides its up then its up.

Thsnks
Bill

 

[Fra]

I find the different perspectives interacting here truly entertaining.

This is all solid scientific work and not wild "philosophical" speculation.

We can probably agree that physics is not logic, nor mathematics, nor is it philosophy. But all ingredients are needed, this is why i think physics is so much more fun than pure math.

I think Neumaier said this already elsewhere but there is also a difference in progressing science or creating new sensible hypothesis, and applying mature science to technology. Its not a coincidence that the founders of quantum theory seemed to be very philosophical, and the people that some years later formalized and cleaned up the new ideas was less so. I think it is deeply unfair to somehow suggest that the founders like Bohr or Heisenberg was someone inferior physicists than those that worked out the mathematical formalism better in an almost axiomatic manner. This is not so at all! I think all the ingredients are important. (Even if no one said the word inferior, its easy to get almost that impression, that the hard core guys to math, and the others do philosophy)

On the other hand, RARE are those people that can span the whole range! It takes quite some "dynamic" mindset, to not only understand complex mathematics, but also the importance or sound reasoning and how to create feedback between abstraction and fuzzy reality. If you narrow in too much anywhere along this scale you are unavoidable going to miss the big picture.

As for "wild", I think for some pure theorists and philosophers even a soldering iron my be truly wild stuff! Who knows what can go wrong? You burn tables books and fingers. Leave it to experts ;-)

/Fredrik