B So can I use "wave particle duality?"

[Bianca Meske]

Some sources say wave particle duality is very much a principal, others say it's oversimplified and not exactly true but still okay to use in order to explain things, and many say it's flat out wrong... so who's right? Can I say "wave particle duality" when talking quantum mechanics or no?

 

[PeterDonis]

Some sources say wave particle duality is very much a principal

Can you give a specific example?

others say it's oversimplified and not exactly true but still okay to use in order to explain things

Can you give a specific example?

and many say it's flat out wrong

Can you give a specific example?

 

[Bianca Meske]

well I just see it a lot in articles detailing superposition or explaining light's behavior but other sites say it's wrong or not completely accurate so if that were true why is it still being used to explain bigger concepts?

 

[PeterDonis]

I just see it a lot in articles detailing superposition or explaining light's behavior but other sites say it's wrong or not completely accurate so if that were true why is it still being used to explain bigger concepts?

I don't know since you haven't given any specific examples.

 

[Bianca Meske]

Well I guess the example would just be the definition of wave particle duality or the idea that a particle can have the properties of both a particle and a wave. I'm just wondering if that's true or not.

 

[weirdoguy]

This still is not a specific example. Anyway, there are a few threads here discussing this issue, eg. : https://www.physicsforums.com/threads/why-does-wave-particle-duality-not-exist-anymore.910647/

 

[CHOP]

Some sources say wave particle duality is very much a principal, others say it's oversimplified and not exactly true but still okay to use in order to explain things, and many say it's flat out wrong... so who's right? Can I say "wave particle duality" when talking quantum mechanics or no?

Whose right? What a time to ask! We don't understand QM yet.
Which is kind of like superposition (which you are working on).
Whose right is like whose got spin up.
Everyone is right until the facts are known.

No, but in a more serious way, if you want to give people the 'most safe, most correct' picture of things, it's a good bet to stay away from wave-particle topic. Who is your audience?

If you don't care to give the 'most safe, most correct' picture of things, then I think you could use it (it might make things easier), but it's important to tell the people that you are just explaining in a fun way, and that it is thought by many to be not how things actually are.

 

[vanhees71]

Well, you can forget about wave-particle duality. It's an outdated idea, which is resolved by modern quantum theory (Heisenberg, Born, Jordan 1925, Schrödinger 1926, and Dirac 1926).

It's also not true that we don't understand quantum theory yet. To the contrary quantum theory is the best theory we have today to describe the behavior of all observed matter. Onfortunately also in this forum we still discuss more about philsophy rather than physics when it comes to quantum theory, but that's not how QT is used in the physics community at all. There it's rather a well-understood theoretical tool to make sense of (so far all) experiments and observations made in the lab.

It includes an understanding of the properties of matter around us and also some quite exotic manifestations like superfluids, super conductors, ultracold gases in traps (condensed-matter physics; mainly non-relativistic many-body theory/QFT) and high-energy particle and nuclear physics (mainly relativistic QFT in vacuo, describing scattering processes of usually two particles in the initial state, producing many partcles and as many-body theory, including the understanding of exotic matter as it occurs in compact stars, in heavy-ion collisions as the socalled quark-gluon plasma and hot and/or dense hadronic matter, and the medium inhabiting the very early universe during the fist few $\mu \text{s}$ after the Big Bang).

The only big things we really do not understand is the quantum theory of the gravitational interaction as well as the nature of dark matter and dark energy.

 

[haushofer]

I don't agree. We don't understand the ontology of the wavefunction, hence all the different interpretations. Although ontology sounds like 'mere philosophy', it's not. It's imho a crucial piece of physics, unless one sees physics as sophisticated bookkeeping.

So no, in my opinion we don't understand quantum mechanics. We understand how to model experimental outcomes with it.

I also don't understand why exactly the wave-particle duality is outdated. If you'd like to say something like that, it's merely because the particle picture is something which emerges if we measure individual 'quantum particles/entities/whatever you want ti call it') while the wavefunction is something we don't have a clear ontology for (unless you prefer ontological interpretations of qm, like Bohm).

I think this superficial separation of 'physics' and 'philosophy' is a big mistake, and a sign of how physics has emphasized mathematical modeling and neglects interpretational issues. The origin of this lies in the confusion of early qm-development and the influence of people like Bohr.

Just my 2 cents.

 

[vanhees71]

Physics is about what's objectively observable. Theoretical physics uses the empirical fact that the observations can be described quantitatively with mathematical theories and models, but it doesn't provide an ontology at all. Philosophers provide different ontological interpretations of QT, QFT, and GR, but there's no conclusive ontology they can agree upon.

 

[phinds]

Can I say "wave particle duality" when talking quantum mechanics or no?

If you are writing a pop-science article, sure. It's done all the time even though it's wrong. If you are talking to any serious physicist who has not been in a coma for the last 90 years, then no, it would be a bad idea.

 

[DarMM]

Philosophers provide different ontological interpretations of QT, QFT, and GR

Let's be clear though.

It's not just philosophers, in fact it's not even mostly philosophers, who speculate on the ontology of QM. Unless Wheeler, Feynman, Einstein, Gell-Mann, Bell, Weinberg, Zurek, Zeilinger, Aspect, Gisin, Deutsch, Pauli (and I could list far more) are just philosophers.

Also there is a reason there is far more discussion on the ontology of QM than of GR. Ontology of GR is just the discussion of the blockworld by a small few basically.

 

[Demystifier]

Can I say "wave particle duality" when talking quantum mechanics or no?

Some experimentalists still use that term, but a better term for the essentially same thing is which path vs interference complementarity.

 

[Demystifier]

Physics is about what's objectively observable.

Physics is about what people with physics degree publish papers about. This includes ontological questions of QM.

Check also https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_physics#General_physics/quantum_physics
especially the second item in 1.1.

Or if you just google for "greatest unsolved problems in physics" or something like that, you will find that most lists contain some version of the problem of interpretation of QM.

 

[haushofer]

Physics is about what's objectively observable. Theoretical physics uses the empirical fact that the observations can be described quantitatively with mathematical theories and models, but it doesn't provide an ontology at all. Philosophers provide different ontological interpretations of QT, QFT, and GR, but there's no conclusive ontology they can agree upon.

Sure, there are also debates about the ontology of spacetime in GR. I'm well acquinted with them; in the past I've read a lot of Norton's (and others) papers about it. But the matter of ontology in QM is, in my experience, much worse.

Ask a physicist what (classical) spacetime is, and you probably get something like "a manifold endowed with a metric", with some comments that the inclusion of the metric is important due to the hole argument, no metric no nothing etc. etc.

Ask a physicist what the wavefunction represents, and you get a lot of widely spread answers. The operational answer is that it gives, via Born, probabilities. But imho that's not ontology. Different interpretations have very different ontologies; look e.g. at the way the quantity "spin" is defined in Bohmian mechanics.

I've made the comparison before, but let me say it again: the geocentric model of Ptolemeus can describe planetary motion very accurately, due to epicycles and (as we now know) Fourier analysis. But it's wrong. My gut feeling tells me that QM-wise we're in a similar position. Sure, we can reproduce numbers and experimental outcomes. But without a clear ontology I'm regarding that as sophisticated bookkeeping.

I guess it all falls down to what you see as "explanation". I'm not complaining about the weirdness of QM; I'm remarking that QM, as it now stands, is more of a cooking recepy than a physical explanation, like Kepler's laws. Somehow my gut-feeling is that we're missing the "Newtonian gravity explanation of Kepler" for QM.

But maybe I'm wrong and have wrong expectations. Who knows.

 

[haushofer]

Let's be clear though.

It's not just philosophers, in fact it's not even mostly philosophers, who speculate on the ontology of QM. Unless Wheeler, Feynman, Einstein, Gell-Mann, Bell, Weinberg, Zurek, Zeilinger, Aspect, Gisin, Deutsch, Pauli (and I could list far more) are just philosophers.

Also there is a reason there is far more discussion on the ontology of QM than of GR. Ontology of GR is just the discussion of the blockworld by a small few basically.

Yes. Somehow I have the feeling that some physicists are just fed up with the measurement/interpretational problem and throw it away, shrugging the shoulders and believe that modern-day physicists who are still debating interpretations are just romantic people longing back to the days of classicality. Move on, move on, don't waste your time on "philosophy", nothing to see here. For me, that's one reason why still a lot of physicists (in my experience) believe that Bohmian mechanics is an attempt to get a deterministic theory, similar to classical mechanics.

The cut between philosophy and physics is just as artificial as the cut between classical and quantum systems.

 

[vanhees71]

Let's be clear though.

It's not just philosophers, in fact it's not even mostly philosophers, who speculate on the ontology of QM. Unless Wheeler, Feynman, Einstein, Gell-Mann, Bell, Weinberg, Zurek, Zeilinger, Aspect, Gisin, Deutsch, Pauli (and I could list far more) are just philosophers.

Also there is a reason there is far more discussion on the ontology of QM than of GR. Ontology of GR is just the discussion of the blockworld by a small few basically.

Well, some physicists turn to philosophy when they get older. Some even commit this sin when they are younger. That's even worse than when philosophers do that, because at least the philosophers are trained in their subject. I think, Weinberg and Feynman would very much protest against the idea to think their physical (!) work on the foundations of QT is philosophy. For them it's an insult to call their work philosophical. Also Einstein had mostly (valid!) physical arguments against some parts of the Copenhagen interpretations, particularly against collapse. That the EPR paper is unfortunately very philosophical is not Einstein's fault, who didn't like this paper very much, because it hides his arguments "behind erudition". What becomes very clear in a later writing from 1948 is that Einstein's point was the inseparability due to entanglement. Bell's work and its experimental test shows that Einstein was wrong on this point, because QT accurately describes the stronger-than-classical long-ranged correlations predicted by QT entanglement.

 

[vanhees71]

Ask a physicist what the wavefunction represents, and you get a lot of widely spread answers. The operational answer is that it gives, via Born, probabilities. But imho that's not ontology. Different interpretations have very different ontologies; look e.g. at the way the quantity "spin" is defined in Bohmian mechanics.

I've made the comparison before, but let me say it again: the geocentric model of Ptolemeus can describe planetary motion very accurately, due to epicycles and (as we now know) Fourier analysis. But it's wrong. My gut feeling tells me that QM-wise we're in a similar position. Sure, we can reproduce numbers and experimental outcomes. But without a clear ontology I'm regarding that as sophisticated bookkeeping.

I guess it all falls down to what you see as "explanation". I'm not complaining about the weirdness of QM; I'm remarking that QM, as it now stands, is more of a cooking recepy than a physical explanation, like Kepler's laws. Somehow my gut-feeling is that we're missing the "Newtonian gravity explanation of Kepler" for QM.

But maybe I'm wrong and have wrong expectations. Who knows.

Hm, well, of course, as any theory also QT is perhaps not the "last word", but all we have (in my opinion) is the QT formalism with the minimal probabilistic interpretation to make contact what's observed. You may well be of the opinion that this description is incomplete (and I think indeed it is, but not for philosophical reasons, but because we have no consistent quantum theory of gravitation yet), but it's pointless since we don't have a "better" theory.

At Kepler's time his empirical 3 laws were the best the physicists had figured out about planetary motion. It was an observation without even a working theory at hand. This came with Newton's works, which enabled the physicists to derive the 3 Keplerian laws from a far more comprehensive theory than just to collect the facts for this very special case of planetary motion around our Sun. That's progress of science, but as this example pretty clearly shows, it's unlikely to make progress of such a calliber without clear foundations kin and guidance by empirical facts. Usually, theories get improved, because a clear empirical contradiction to the existing theories can be established. That's why physicists at the LHC are so eager to find "deviations from the Standard Model", because they are "lost in math" in their attempt to find a better theory (maybe explaning the nature of dark matter by yet unknown particles) without any clear discovery of "physics beyond the Standard Model".

 

[Demystifier]

Well, some physicists turn to philosophy when they get older. Some even commit this sin when they are younger. That's even worse than when philosophers do that, because at least the philosophers are trained in their subject.

You still assume that there is a sharp borderline between physics and philosophy, which there isn't.

 

[DarMM]

Well, some physicists turn to philosophy when they get older. Some even commit this sin when they are younger. That's even worse than when philosophers do that, because at least the philosophers are trained in their subject. I think, Weinberg and Feynman would very much protest against the idea to think their physical (!) work on the foundations of QT is philosophy. For them it's an insult to call their work philosophical

I think Bell, Aspect, Gisin, Pauli, Zurek, Zeilinger, etc would think the same, that's my point. I don't see what you're using to separate physics and philosophy in this regard aside from personal preference.

Bell's theorem seems like physics to me. Zurek's investigations of the subtleties of decoherence seem like physics to me. Zeilinger's foundational work in quantum information seems like physics to me. And so on. Some of them were quite young when they did this stuff and most of it was an attempt to investigate the ontology and foundations of QM.

 

[Demystifier]

Some of them were quite young when they did this stuff and most of it was an attempt to investigate the ontology and foundations of QM.

Moreover, now it's normal to do a PhD in quantum foundations at a physics department. Perhaps it was not normal 20 years ago, but now it is. The definition of "physics" in the 21st century differs from that in the 20th century. Someone may not like research in quantum foundations, just as someone may not like research in string theory or quantum gravity, but it doesn't mean that it's not physics. It means that the scope and definition of physics evolves with time, whether one likes it or not.

 

[Lord Jestocost]

Or if you just google for "greatest unsolved problems in physics" or something like that, you will find that most lists contain some version of the problem of interpretation of QM.

Why is the interpretation of QM one of the "greatest unsolved problems in physics"? From whose perspective?

One of the characteristics of physics is that it is an exact science. In exact sciences, one studies sets of measurement outcomes and connects them with other measurement outcomes. Thus, the aim of physics is to match mathematics to measurements, everything else would be baseless speculations.

QM is the mathematical theory that accounts for the facts, and these facts are measurement outcomes. One should not extend “interpreting speculations" beyond the range of experiments. In case an interpretation provides no experimentally testable predictions, it shouldn’t be regarded as a matter of exact science. In in such a case, interpretations are usually only based upon personal ideological beliefs, personal “theories” about oneself and of oneself’s experience of observations.

 

[A. Neumaier]

The cut between philosophy and physics is just as artificial as the cut between classical and quantum systems.

Yes!

Newton's main physics work was even called Philosophiæ Naturalis Principia Mathematica!

 

[vanhees71]

Physics is about observable quantitative facts in nature and their (mathematical) description. Everything else is philosophy, and there's no doubt that there is some value in philosophy to get a bigger picture about the cultural meaning of established (sic!) theories. To get good philosophy about physics, you first need to get the physics strate. There's no way to get good philosophy from wrong assumptions (as, e.g., the idea that QT implies wave-particle duality, because that's a notion of an ill-defined historical step, usually called "old quantum theory", leading to QT and is abandoned by the now established QT).

Indeed, it's the great merit of Bell's work to have brought the ill-defined gibberish of EPR to a clear physical statement or better said a clear physical question to nature. A physical statement or question is a hypothesis that can be empirically justified. For me Bell's work and the subsequent experimental work following from, all of which in my opinion are of Nobel-prize caliber, is the only really valuable physics contribution arising from these socalled interpretational problems. The same holds for the various investigations on decoherence.

For me the upshot of all this is that QT is the best theory we have, including the facts (and these are facts precisely due to the quoted experimental work!) due to entanglement, which some people seem still to find "weird". The idea that these facts are weird, for me is (bad) philosophy. Since QT is an intrinsically consistent framework in terms of a physical theory (at least in the minimal statistical interpretation, for non-relativistic QT also Bohmian mechanics is a physically equivalent deterministic interpretation) there's nothing weird. It's just progress in our understanding of how nature observationally behaves in realms, for which our socalled "common sense" is not trained. Whether or not this is "sufficient ontology" is to everybody's personal taste, but it's not a question important to physics. Physical theories are epistemic anyway. Everything beyond this is metaphysics or even religion but not physics.

That Newton's physics book is called "philosophiae naturalis" is due to the simple historical fact as at this time physics didn't exist as a well-separated discipline, and everything connected with what we call "natural sciences" today was part of philosophy, namely philosophia naturalis. The clear distinction between the disciplines (most roughly in humanities, natural sciencs, and structural sciences) has been established only later when it turned out that specialization is nessary for all these different disciplines to get further into more complicated issues and knowledge. That's why it is so important to keep these realms strictly separated!

 

[A. Neumaier]

QT is an intrinsically consistent framework in terms of a physical theory (at least in the minimal statistical interpretation

In its minimal statistical interpertation, it is not consistent since, unlike classical mechanics, it cannot be applied to huge quantum systems such as the solar system or the whole unvierse. At least Peres, whose book champions the minimal interpretation, thinks so.

 

[Jehannum]

My answer to the original question:

If you take the equation of a wave, e.g. y = sin(x), where wavelength is known precisely, you don't get any positional information (the wave amplitude has a value at every position x). If you add in some uncertainty in the wavelength by adding similar waves, e.g. y = sin (0.9*x) + sin (x) + sin (1.1*x), the "beats" of the resultant wave look a lot like a particle because the amplitude is large at certain positions. This isn't wave-particle duality - there is no duality - it's wave behaviour. I think this is why people object to the term, but it's a case of "I know what you mean but I want to be pedantic". As long as you don't use it in a technical way the term's okay as a shorthand.

 

[Demystifier]

Why is the interpretation of QM one of the "greatest unsolved problems in physics"?

In case an interpretation provides no experimentally testable predictions, it shouldn’t be regarded as a matter of exact science.

The latter is a partial answer to your question. It is an unsolved problem precisely because it is not known how to solve it by experimental/exact methods. If you ask why is it a great problem, that's because it is deep, fundamental and difficult.

But I guess your true question is why is it a problem in physics? Well, it depends on definition of physics. If you want to adopt a narrow definition of physics according to which problems that cannot be solved by exact methods are not counted as physics, fine, but then you define physics by its method, rather than by its object of study. But one object can be studied by many methods. Sometimes exact methods do not answer all the questions one may ask about the object, in which case one can either ignore such questions (for the sake of being exact) or try to apply other, not so exact methods. When the problem is great (that is deep, fundamental and difficult), I would rather try to shed some light on it by non-exact methods than to completely ignore it.

 

[vanhees71]

In its minimal statistical interpertation, it is not consistent since, unlike classical mechanics, it cannot be applied to huge quantum systems such as the solar system or the whole unvierse. At least Peres, whose book champions the minimal interpretation, thinks so.

This is only what you claim. There's no doubt that QT in its minimal interpretation can very well applied to macroscopic systems. The whole universe, according to current theoretical understanding, cannot be observed even principally. That's why it's an empty phrase anyway. Where do you find the contrary statement by Peres?

 

[Demystifier]

Physics is about observable quantitative facts in nature and their (mathematical) description. Everything else is philosophy, and there's no doubt that there is some value in philosophy to get a bigger picture about the cultural meaning of established (sic!) theories.

I can agree with that, but I think the right question is the following. If everything else is philosophy, and not physics, then should physicists study it? I think they should, because (i) it, as you said, has a value and (ii) pure philosophers without a degree in physics cannot do it right. Physicists are too smart to be left dealing with physics only.

 

[Lord Jestocost]

If you want to adopt a narrow definition of physics according to which problems that cannot be solved by straightforward, exact and well understood methods are not counted as physics, fine, but then you define physics by its method, rather than by its object of study.[emphasis added by LJ]

QM is a theory to predict the probabilities of various directly observed macroscopic outcomes within a certain experimental setup, let’s say an “electron” diffraction experiment. If you like, you can now think of the “electron” as some kind of “real object” you are studying, but you are then entering the area of metaphysics. The reality** you experience is in the observations, not in the “electron”. And what will you gain by this step with regard to physics as exact science? Nothing, because only observations themselves and their correlations are handled in physics. Or, maybe, you will gain the extra trouble of digging your “real object” out again from your thinking.

** To be precise: At the end, your ultimate reality is the content of your consciousness

 

[Lord Jestocost]

Physics is about observable quantitative facts in nature and their (mathematical) description. Everything else is philosophy, and there's no doubt that there is some value in philosophy to get a bigger picture about the cultural meaning of established (sic!) theories. To get good philosophy about physics, you first need to get the physics strate. There's no way to get good philosophy from wrong assumptions (as, e.g., the idea that QT implies wave-particle duality, because that's a notion of an ill-defined historical step, usually called "old quantum theory", leading to QT and is abandoned by the now established QT).

Indeed, it's the great merit of Bell's work to have brought the ill-defined gibberish of EPR to a clear physical statement or better said a clear physical question to nature. A physical statement or question is a hypothesis that can be empirically justified. For me Bell's work and the subsequent experimental work following from, all of which in my opinion are of Nobel-prize caliber, is the only really valuable physics contribution arising from these socalled interpretational problems. The same holds for the various investigations on decoherence.

For me the upshot of all this is that QT is the best theory we have, including the facts (and these are facts precisely due to the quoted experimental work!) due to entanglement, which some people seem still to find "weird". The idea that these facts are weird, for me is (bad) philosophy. Since QT is an intrinsically consistent framework in terms of a physical theory (at least in the minimal statistical interpretation, for non-relativistic QT also Bohmian mechanics is a physically equivalent deterministic interpretation) there's nothing weird. It's just progress in our understanding of how nature observationally behaves in realms, for which our socalled "common sense" is not trained. Whether or not this is "sufficient ontology" is to everybody's personal taste, but it's not a question important to physics. Physical theories are epistemic anyway. Everything beyond this is metaphysics or even religion but not physics.

That Newton's physics book is called "philosophiae naturalis" is due to the simple historical fact as at this time physics didn't exist as a well-separated discipline, and everything connected with what we call "natural sciences" today was part of philosophy, namely philosophia naturalis. The clear distinction between the disciplines (most roughly in humanities, natural sciencs, and structural sciences) has been established only later when it turned out that specialization is nessary for all these different disciplines to get further into more complicated issues and knowledge. That's why it is so important to keep these realms strictly separated!

I can agree with most, but when hearing “minimal statistical interpretation”, I just cannot get rid of the thought that behind this interpretation there lurks the idea that quantum mechanics must be supplemented by some kind of hidden variables operating from behind the scenes.

 

[DarMM]

Physics is about observable quantitative facts in nature and their (mathematical) description. Everything else is philosophy, and there's no doubt that there is some value in philosophy to get a bigger picture about the cultural meaning of established (sic!) theories

You're not wrong from a certain perspective, but I think we have to keep in mind what motivates people. I doubt Einstein was motivated by explaining the measurement statistics of ensembles of equivalence classes of suitably prepared astronomical observation equipment when he came up with GR. He wanted to understand how the world worked, i.e. the ontology.

There is a good argument that QM forces a very positivist view of physics and that the searching for an ontology for it is misguided, but this is a bit of a break from why most people get into physics. Perhaps you're just more empircally disciplined than the rest of us!

 

[stevendaryl]

QM is a theory to predict the probabilities of various directly observed macroscopic outcomes within a certain experimental setup, let’s say an “electron” diffraction experiment. If you like, you can now think of the “electron” as some kind of “real object” you are studying, but you are then entering the area of metaphysics. The reality** you experience is in the observations, not in the “electron”. And what will you gain by this step with regard to physics as exact science? Nothing, because only observations themselves and their correlations are handled in physics. Or, maybe, you will gain the extra trouble of digging your “real object” out again from your thinking.

But presumably, the only reason that it is possible to make observations is because we are ourselves systems described by physics, and we interact with the thing we're studying through physical interactions. Treating observations as primary seems like solipsism, to me. As if humans were disembodied minds.

It's kind of funny; in my mind, the people who most strongly object to "philosophical" discussions are the ones who have the most rigid philosophical systems.

Science, to me, is about understanding the world. That's the reason that people are interested in science. They see rainbows and want to know what are they. They see magnets work, and wonder how that is possible. They see the stars and wonder what they are, and how they are powered. Understanding the universe is the goal of science, in my opinion (or probably in the opinion of anyone who ever was interested in science, before they became indoctrinated in the anti-philosophy philosophy). Being able to make predictions about measurement results is a test of understanding. That's what's so great about empirical science, is that mistakes can be corrected. But making predictions isn't the reason that people are interested in science. To me, that's like saying that the point of studying mathematics is to be able to pass mathematics tests.

 

[DarMM]

But presumably, the only reason that it is possible to make observations is because we are ourselves systems described by physics, and we interact with the thing we're studying through physical interactions. Treating observations as primary seems like solipsism, to me. As if humans were disembodied minds

I think most of the views of QM where observation is a primary concept take it as a primitive of the theory, but not of the world. Sort of like how decision theory has an agent as a primitive, but that doesn't mean you think an "agent" is an irreducible physical property.

 

[PeterDonis]

This is way too much argument about the philosophy of QM for a "B" level thread.

It looks like a fair "B" level summary would be that, while there might be some limited ways in which the concept of "wave-particle duality" is useful, it's probably better to ignore it.

And with that, this thread is closed.