Accurate equations vs. accurate models in QM

[jon4444]

In QED, Feynman says: "The situation today is, we haven't got a good model to explain partial reflection by two surfaces; we just calculate..."

I've been frustrated in that I'm still not clear if this is the case (is there still no model to explain the behavior). A similar dynamic seems to come up in a lot of discussion threads (e.g., decoherence and entanglement)--when people say "this is understood," are they meaning that there's experimental evidence for a certain conceptual frame-work, or do they just mean, "there's a way of calculating that."

I guess I'm looking for a link-up between interpretation and mathematical accuracy. To use Feynman's statement as an example, he's saying there's high level of mathematical accuracy, but no reasonable interpretation. Was Feynman just alone in his perspective? (I.e., Are other physicists just satisfied in getting math that works?)

 

[Jolb]

The answer is that physics is the business of calculating. Numerical predictions are what we test in physics. So yes, physicists are more concerned with getting "the right answer" from a theory than having a nice interpretation for that theory. Elementary quantum mechanics still has issues in its interpretation (e.g. copenhagen vs. manyworlds), and quantum field theory is much worse.

Feynman himself, though renowned as an "intuitionist", obviously cared more about getting accurate predictions than having a nice interpretive picture. Though a Feynman diagram looks somewhat intuitive, its real mathematical structure is not very easy to interpret, and his work is filled with places where he "throws away" infinite contributions to the answer the diagrams would predict--what is their physical interpretation? [A lot of work, e.g. Ken Wilson's work on renormalization, was motivated by trying to find a physical reason for the infinite terms in QFT calculations that Feynman was unable to satisfactorily explain.] A more fundamental example: What is the physical interpretation of the "vacuum energy" that lurks in any quantum field theory?

The philosophy is called "shut up and calculate," and many physicists will tell you that the math is actually the only accurate description; the pictures are imprecise tools that hardly ever reflect the full physics contained in the math.P.S. Even though it is the dogma on physicsforums, don't believe anyone who says "decoherence is understood." Anyone who says that is fooling themselves into believing in a very speculative (and possibly nonscientific) theory, probably because they want to hang onto whatever physical picture they prefer. There's a bit of literature on decoherence, but it is speculation motivated by trying to tackle a genuinely unresolved problem. It is not a closed case.

 

[jon4444]

Well thanks for that--helpful background.

There does seem an extra wrinkle in the case of partial reflection--I understand Feynman to say that the theory can calculate what will happen (for any given set of parameters in a controlled experiment), but there's no model that predicts the phenomenon in the first place. This seems different than theories like Special and General Relativity, which predict that certain (qualitative) phenomenon will exist based on an underlying model.

 

[Jano L.]

You have to take into account the context in which Feynman says such things. Can you provide exact citation?

In the book QED: Strange theory... Feynman takes a particular point of view on the theory of light and matter: a view in which there are only particles and the theory is concerned only with calculating probabilities that particle at point 1 will get to point 2. The message was that quantum electrodynamics is an interesting and successful set of calculation rules, but without clear physical picture. This is to communicate to the public what is the situation in the theory he helped to develop, not to say there is not an intuitive picture at all.

Fortunately there are other theories, which are much better in this respect. In electromagnetic theory, the process of reflection of light from two surfaces is easily imagined in space and time, and calculations based on this theory give accurate predictions of light intensity (treated often in wave optics courses). In the Lorentz electron theory, even what happens at the surfaces with electrons can be modeled. These theories are also immensely successful, but they also have other drawbacks.

 

[physwizard]

. So yes, physicists are more concerned with getting "the right answer" from a theory than having a nice interpretation for that theory.physical interpretation of the "vacuum energy" that lurks in any quantum field theory?

From a practical point of view what you say may be true. But physicists are not just mere engineers who are interesting in just being able to calculate results. Of course having a model which gives the right results is a good first step. And it is better than not having anything at all. But a physicist should always try to seek a deeper and more satisfying level of understanding. Of course answering one 'Why?' question may give rise to another 'Why?' and the chain may be endless. But if you can replace five 'Why's with a single 'Why' then you have made progress.
I don't know what you mean by 'interpretation of a theory' but a theory should make sense at some level. If something is open to multiple interpretations I would still view it as either incomplete or not well formulated - for eg. if some aspects are formulated in a vague way(which allows many interpretations) or by making more assumptions than are necessary.

 

[Jolb]

I don't know what you mean by 'interpretation of a theory' but a theory should make sense at some level.

What I mean by an 'interpretation of a theory' is a handy analogy or mental picture that helps you to make sense of the mathematics that define the theory. I believe these are all synonyms for what you're calling an "understanding."

From a practical point of view what you say may be true. But physicists are not just mere engineers who are interesting in just being able to calculate results. Of course having a model which gives the right results is a good first step. And it is better than not having anything at all. But a physicist should always try to seek a deeper and more satisfying level of understanding.

I agree; physicists should try to have an intuitive understanding of the theories they work with. There are many physicists who are very good at math and can solve many physics problems but don't actually understand the physical meaning of such theories, and I don't approve of them. (They should call themselves applied mathematicians.) Most of the new theories that are created come from some sort of physical picture the physicist has, so it really is a prerequisite for a good physicist.

But not all theories come from a nice mental picture. Take for example the inventors of quantum theory: Planck was merely trying to fit a curve to a plot, and Heisenberg's creation of matrix mechanics was basically the same thing--trying to get the arithmetic to work. Quantum theory didn't come from any sort of intuition or picture--it's so counterintuitive that the only way to stumble upon it is basically the way Planck and Heisenberg did. So even though having a good "picture" of what a theory means is important for being a physicist, the aim of physics as a science is to get the right numerical predictions, and sometimes they come from theories without a nice intuitive analogy.

As a side note, the mental pictures and analogies we use in the present time to understand quantum mechanics are mostly pictures you'd see in pure math classes (n-dimensional vector spaces, linear mappings, etc.) as well as the set of elementary quantum experiments (stern gerlach, double slit, 1-d tunneling, etc.) Contrast this with the pictures we use to understand the non-mathematically-obvious phenomena in classical mechanics: masses bouncing on springs, waves on the surfaces of fluids, gyroscopes precessing about, etc. --these are all analogies that use everyday experience as the reference point--but this really breaks down for quantum.

If something is open to multiple interpretations I would still view it as either incomplete or not well formulated - for eg. if some aspects are formulated in a vague way(which allows many interpretations) or by making more assumptions than are necessary.

I feel like you're just asserting some sort of personal feeling rather than making a scientific argument. Why should the universe be described by a set of rules that humans even understand (much less agree on the same interpretation of)? Quantum mechanics (always the best example) stands out as a super successful theory that still has multiple interpretations, and attempts (by Einstein no less) to show that it is incomplete have all failed.

 

[bhobba]

Even though it is the dogma on physicsforums, don't believe anyone who says "decoherence is understood." Anyone who says that is fooling themselves into believing in a very speculative (and possibly nonscientific) theory, probably because they want to hang onto whatever physical picture they prefer. There's a bit of literature on decoherence, but it is speculation motivated by trying to tackle a genuinely unresolved problem. It is not a closed case.

Sorry can't agree with that. Decoherence, to a large extent, is understood, and it is an experimentally verified fact.

The issue is not if it exists or is understood but rather if it resolves interpretational issues. It doesn't to everyone's satisfaction - and there is a substantial body of literature where both sides are examined from which anyone can form their own view. There are also some unresolved technical issues such as if the the preferred basis it singles out is merely an artifact of a systems decomposition and guys like me and Fredrik have discussed that. But to say its not understood in IMHO way off the mark. Still the literature is out there - anyone that wants check it out can and form their own view.

Thanks
Bill

 

[Jolb]

Sorry can't agree with that. Decoherence, to a large extent, is understood, and it is an experimentally verified fact.

The issue is not if it exists or is understood but rather if it resolves interpretational issues. It doesn't to everyone's satisfaction

I stand corrected. You are right--I didn't state it (sorry for jumping out of context), but I was referring to whether or not what is known about decoherence resolves interpretational issues. Yes, decoherence is a phenomenon that certainly exists, but often people use it to argue (or identify it with) a certain perspective on interpreting quantum mechanics.

However, I do think that on a general philosophical level, or the level of the layperson, that the most relevant context for the topic of "decoherence" has to do with interpretational issues.

- and there is a substantial body of literature where both sides are examined from which anyone can form their own view.

I'm not so sure there are only two sides to the interpretational issues.

 

[bhobba]

Are other physicists just satisfied in getting math that works?

Its a mathematical model:
http://en.wikipedia.org/wiki/Mathematical_model

They are used in many areas such as actuarial science to calculate all sorts of stuff. What the issue with QM is is its a model that doesn't have neat visualisable pictures. But why should nature be describable in terms of neat easy pictures? And why should it admit only one interpretation?

I think you might benefit watching Susskinds Lectures on Entanglement:
http://www.newpackettech.com/Resources/Susskind/PHY30/QuantumEntanglementPart1_Overview.htm

Thanks
Bill

 

[bhobba]

I'm not so sure there are only two sides to the interpretational issues.

On that I stand corrected as well - there are a myriad of views.

Thanks
Bill

 

[jon4444]

But why should nature be describable in terms of neat easy pictures? And why should it admit only one interpretation?

If you could indulge me in pushing just one step more on this. I'm trying to fully understand the implications of Feynman's statement. To that end, to what extent are the predictions made by the mathematical models of QED predicated more on empirical observations than other theories in Physics.

Of course, I realize all theories are based on empirical observation to some degree, but there are degrees. E.g., there's no widely accepted theory giving masses of elementary particles--we take those as a given based on observation--but people would prefer if there was a theory that predicted them based on more fundamental assumptions.

So, to what extent is QED like that--i.e., that it's predicated on observing that 96% of the photons in monochromatic light will be detected in a block of glass without really being able to explain that phenomenon in any coherent, solid fashion?

 

[bhobba]

So, to what extent is QED like that--i.e., that it's predicated on observing that 96% of the photons in monochromatic light will be detected in a block of glass without really being able to explain that phenomenon in any coherent, solid fashion?

The basic framework of QM was forced upon scientists by observation. That part is strongly influenced by what was observed such as the photoelectric effect.

Beyond that however, perhaps surprisingly, its very theoretical, based on symmetry and mathematically extremely beautiful, notably gauge symmetry. This is the reason when infinities were encountered it was so devastating - the theory was pretty well determined - there was virtually no wiggle room. Renormalization was discovered but it was ugly until greatly clarified by Wilson and others during the 70's. Nowadays everything is fine - but for a while there it really was bad with jokes like when you go into a theorists office have a look for the infinities swept under the rug. These days it is recognized that symmetry is really the rock bottom essence of physics and many such as myself believe there is some deep all pervading symmetry lying right at the foundation of the universe waiting to be discovered.

Thanks
Bill

 

[jon4444]

Again, very helpful.

And I'm still wondering whether the observation about 96% of photons is strictly from experiment or theoretically derived?

 

[bhobba]

And I'm still wondering whether the observation about 96% of photons is strictly from experiment or theoretically derived?

Strictly theory - QED has only a couple of experimentally determined parameters - the mass of the electron and the so called fine structure constant.

Thanks
Bill