What is the value of "delayed choice" experiments?

[MichPod]

What is the value of "delayed choice" experiments?

Disclaimer: I do realize that nearly any experiment deserves to be performed even to make sure the QM theory predicts the results of such experiment right. So I have no objections to the work of people which implemented these sorts of experiments in their labs.
The other problem bothers me. If we consider the original works of Wheerler and his thought experiments... I could really understand and appreciate if such works had appeared in 1920-1930ies, that was IMO the right time for these dilemmas, but not 1970ies when these thought experiments were actually proposed. Did anybody think or claim at this time that the electron of photon may "know" ahead the configuration of the experiment and behave accordingly? Was it still the time when people were concerned with wave-particle duality and thought that may be the photon behaves "like a particle" from the beginning if we just remove the 2nd wave spliter in M-Z interferometer?

So, forgive me my polemic style above (I do realize I may have very wrong understanding of subtleties of QM and its history) but could somebody explain what was the way of thinking of people who designed and valued these experiments, Wheeler included? What did they try to prove or disprove which was not yet already well known in that time in QM? What is the value of these thought experiments for today?

2nd Disclaimer: my own understanding of these experiments is along the collapse interpretation, I think. I.e. until the particle is detected, it propagates like a wave, then on the detection/measurement the collapse happens according to the Born rule, so that the wave function of one particle (or of two entangled particles) is projected onto the eigenstates defined by measuring device(s). This, I think, gives rather full description (as full as QM currently may give) of what happens in delayed choice experiment of Wheeler with M-Z interferometer, "quantum eraser" of Walborn, "delayed choice quantum eraser" of Kim. Again, I understand, this my understanding may be in some parts wrong, I am just sharing it here so that you know what is in my head.

 

[DrChinese]

There are a lot of viewpoints on your questions. First, scientists are actually questioning whether the future somehow affects the past. QM seems to allow cases - such as delayed choice experiments - in which that is what appears to occur. Second, there are a variety of interpretations of QM that explain the phenomena in other ways.

In general, I would say that keeping an open mind on what is occurring behind the scenes is a good approach here. There are certainly advanced experiments that call our usual understanding of causality into question.

 

[MichPod]

Yet these experiments do not demonstrate that the future affects the past (unless we start to apply semi-classical (as for my point of view) terms and ideas like wave-particle duality, complimentarity etc.) Interestingly, this is what I am seeing in many sources discussing these experiments, including contemporary sources. IMO they use the wrong terms from the start, including the idea that a photon may behave like a particle from the start if the device is not built to show its wave nature. Then they conclude that Wheeler's experiments prove these terms and ideas poorly applicable. On the other side, if we follow the normal QM formalism (whatever the interpretation is, let me suppose), the results of these experiments look for me to fully comply with QM.

I would understand if Wheeler experiments would help to reject some mainstream or major interpretation of QM of 1970th. But it looks for me they reject just some reasoning which could be considered as poor even in that time. ( I understand I may be wrong here. That is why I am writing this thread - to clarify and correct this my view).

Now, I fully agree with you that we need to keep an open mind. These experiments may look counterintuitive for some people. May be for some students. May be even for some working physicists. But they IMO fit properly into QM of 70th. Then what was the motivation to invent them? And what is the motivation to value them today other then just for being instructive for students/physicists and for retesting the behavior which the QM theory clearly predicts?

. There are certainly advanced experiments that call our usual understanding of causality into question.

Do you mean Wheeler's experiments or something else? Do delayed choice experiments challenge our understanding of causality more that regular experiments with entangled particles (say, Bell/Aspect experiment)?

 

[DrChinese]

Do you mean Wheeler's experiments or something else? Do delayed choice experiments challenge our understanding of causality more that regular experiments with entangled particles (say, Bell/Aspect experiment)?

Something else. You can entangle particles after they have already been measured/detected. I'd say that is pretty amazing, and certainly hints at retrocausation. There are other (more traditional) interpretations that explain this as well.

https://arxiv.org/pdf/quant-ph/0201134.pdf
Middle of page 5 is the entangle-swap after detection: "... Alice’s measurement projects photons 0 and 3 into an entangled state after they have been measured."

The resulting entanglement can be + or - (correlated or anti-correlated). But the decision to entangle - or not - is decided after detection. Of course, there is no signalling possible with this scheme, as the projection of the specific entangled state is itself random (and out of control of the experimenter). And of course everything is predicted by standard QM.

 

[Demystifier]

In my (rather cynical) opinion, the value of delayed choice experiments is to justify publication in the highest-impact journals of experimental results the real value of which is nothing but a development of experimental techniques. It's not that development of those techniques is not important, but without the "delayed choice cover" they would look boring to most physicists so highest impact journals would not publish them.

And of course, delayed choice is not the only cover used for that purpose. Other popular covers are weak values, cheshire cats, ...

 

[MichPod]

In my (rather cynical) opinion, the value of delayed choice experiments is to justify publication in the highest-impact journals of experimental results the real value of which is nothing but a development of experimental techniques

I must agree (if I am allowed to, having rather little knowledge of the topic).
Yet my original question was more about Wheeler and his time, that is what troubles me...

 

[Cthugha]

What is the value of "delayed choice" experiments?

Disclaimer: I do realize that nearly any experiment deserves to be performed even to make sure the QM theory predicts the results of such experiment right. So I have no objections to the work of people which implemented these sorts of experiments in their labs.
The other problem bothers me. If we consider the original works of Wheerler and his thought experiments... I could really understand and appreciate if such works had appeared in 1920-1930ies, that was IMO the right time for these dilemmas, but not 1970ies when these thought experiments were actually proposed. Did anybody think or claim at this time that the electron of photon may "know" ahead the configuration of the experiment and behave accordingly? Was it still the time when people were concerned with wave-particle duality and thought that may be the photon behaves "like a particle" from the beginning if we just remove the 2nd wave spliter in M-Z interferometer?

Have you actually read any of the original publications that have been published between the 80s and the mid-90s? Some of them state the motivation pretty clearly. Complementarity had been known for some time and the same was true for the Heisenberg uncertainty relation. So naturally the question arose, whether complementarity (as in which-way information vs. visibility of interference patterns) is a consequence of Heisenberg uncertainty or more fundamental. Most of the old ideas about complementarity such as the recoiling double slit were based on the Heisenberg uncertainty relation, so people at that time were looking for an experiment to demonstrate complementarity, which is not based on position-momentum uncertainty. This was the basis for Scully's famous quantum eraser Gedankenexperiment using emission from Rydberg atoms (Nature 351, 111–116 (1991)), where he argued that complementarity is more general than the limitied Heisenberg uncertainty relation. However, others argued that any kind of which-way experiment will always provide a momentum perturbation (Storey et al., Nature 375, 368 (1995)) , which in turn resulted in further comments and suggestions to settle the issue (e.g. Wiseman and Harrison, Nature 377, 584 (1995)). The delayed choice part then appeared as a natural extension to include a separation in time between the different important parts of the experiment. Of course I am not sure what Wheeler had in mind when he had his ideas, but the experimental interest was guided by the question of complementarity vs uncertainty. These 90s papers I mentioned above are actually also quite an interesting read from the historical point of view.

In my opinion the insight that complementarity is a very general phenomenon and that there are other pairs of complementary properties that are not as obvious as position and momentum (e.g. first-order coherence and entanglement, see Phys. Rev. A 63, 063803 (2001)) is quite remarkable.

 

[Lord Jestocost]

Of course I am not sure what Wheeler had in mind when he had his ideas,...

“The dependence of what is observed upon the choice of experimental arrangement made Einstein unhappy. It conflicts with the view that the universe exists “out there” independent of all acts of observation. In contrast Bohr stressed that we confront here an inescapable new feature of nature, to be welcomed because of the understanding it gives us. In struggling to make clear to Einstein the central point as he saw it, Bohr found himself forced to introduce the word “phenomenon.” In today’s words Bohr’s point — and the central point of quantum theory — can be put into a single, simple sentence. “No elementary phenomenon is a phenomenon until it is a registered (observed) phenomenon.” It is wrong to speak of the “route” of the photon in the experiment of the beam splitter. It is wrong to attribute a tangibility to the photon in all its travel from the point of entry to its last instant of flight. A phenomenon is not yet a phenomenon until it has been brought to a close by an irreversible act of amplification such as the blackening of a grain of silver bromide emulsion or the triggering of a photodetector.”

J. A. Wheeler in "Quantum Theory and Measurement“ (edited by John Archibald Wheeler and Wojciech Hubert Zurek), Princeton, New Jersey 1983, page 184

 

[vanhees71]

In my (rather cynical) opinion, the value of delayed choice experiments is to justify publication in the highest-impact journals of experimental results the real value of which is nothing but a development of experimental techniques. It's not that development of those techniques is not important, but without the "delayed choice cover" they would look boring to most physicists so highest impact journals would not publish them.

And of course, delayed choice is not the only cover used for that purpose. Other popular covers are weak values, cheshire cats, ...

Well, I think the experiments themselves are important since one should check the foundations of physics with the highest accuracy possible to eventually find reproducible failures of the theories to make progress.

Of course, I'm also very worried about the possibility to publish in journals of highest reputation like Nature or Science (sometimes also PRL) esoterical interpretations in connection with these experiments rather than using the standard interpretation that is esoterics free and fully accounts for the observed phenomena. That's NOT the way to empirically finding flaws in our contemporary models. For that you have to exclude all interpretations of the experiments using conservative, i.e., standard-theory analyses. AFAIK this has not yet been achieved, but all these fascinating experiments confirm standard QT (including relativistic local microcausal QFT) with an astonishing significance.

 

[DrChinese]

1. ...That's NOT the way to empirically finding flaws in our contemporary models.

2. For that you have to exclude all interpretations of the experiments using conservative, i.e., standard-theory analyses.

1. Actually, no one knows where the next great breakthrough is coming from, or how it will be discovered. The history of science is pretty clear on that point.

2. Were this generally accepted, we wouldn't be having discussions on interpretations. And yet, here we are. Obviously, most scientists believe that a better interpretation will eventually lead to better predictive/explanatory power. Some even take an interpretation and look to see if it leads to a difference relative to "conservative" analyses. Much like string theorists look to improve upon existing theory. There is no one path to a better idea. Sort of like "sum over paths".

 

[Strilanc]

QM seems to allow cases - such as delayed choice experiments - in which that is what appears to occur.

I disagree pretty strongly with this idea, for three reasons.

First, delayed choice experiments don't demonstrate retrocausal effects. The explanation people normally give is simply backwards. The delayed measurement's outcome doesn't cause the screen hit position, the screen hit position causes the delayed measurement's outcome. To be even more correct, neither causes the other; they are correlated.

Second, delayed choice experiments don't even demonstrate FTL effects. The delaying introduces a signalling loophole. It is trivial to reproduce the same qualitative results classically. You use different mechanisms, since entanglement is not available, but the banded-if-chosen outcomes still show. Close the signalling loophole and it is no longer a delayed choice experiment (ideally it would become a Bell test).

Third, retrocausality allows too much. It doesn't make specific predictions, it is a framework for making whatever predictions you want. Sort of like how every time we discover a new weird thing in astronomy, people say "aliens!". That's fun and all, but it's not really useful.

 

[DrChinese]

I disagree pretty strongly with this idea, for three reasons.

First, delayed choice experiments don't demonstrate retrocausal effects. The explanation people normally give is simply backwards. The delayed measurement's outcome doesn't cause the screen hit position, the screen hit position causes the delayed measurement's outcome. To be even more correct, neither causes the other; they are correlated.

Second, delayed choice experiments don't even demonstrate FTL effects. The delaying introduces a signalling loophole. It is trivial to reproduce the same qualitative results classically. You use different mechanisms, since entanglement is not available, but the banded-if-chosen outcomes still show. Close the signalling loophole and it is no longer a delayed choice experiment (ideally it would become a Bell test).

Third, retrocausality allows too much. It doesn't make specific predictions, it is a framework for making whatever predictions you want. Sort of like how every time we discover a new weird thing in astronomy, people say "aliens!". That's fun and all, but it's not really useful.

First, the delayed choice experiments don't "prove" the future changes the past; and I never said otherwise. But certainly they suggest as much - that's the whole point. So yes, other interpretations provide other explanations.

Second, delayed choice experiments are not designed to demonstrate non-local effects. But certainly some can demonstrate either non-local effects or retrocausal effects in a single experiment (again depending on interpretation). For example, delayed choice entanglement swapping.

Third: This is one I really don't get. Why is any interpretation too much? Other than as a personal preference, I mean. MWI may be too much for me personally, but that really isn't an argument against MWI for someone who thinks non-locality is too much.

 

[jerromyjon]

MWI may be too much for me personally, but that really isn't an argument against MWI for someone who thinks non-locality is too much.

I used to think MWI solved everything but it just shuffles the incongruity to other universes that never exist.
All interpretations leave us with something missing. I think that might be one common belief, but I only care about my own opinion.
I bet @bhobba might think everything that needs to be explained, is. And I don't disagree at all. The DCQE and entanglement swapping experiments don't illuminate anything new in QM. They merely shift the logical discontinuity to other points of view and reconfirm the same quantum behavior per Bell and all the others. Making the observation is the only pertinent moment and any conflicting possibilities of occurrence are results of quantum behavior. When or what or if are not altering the actual results, which cannot be classical.

 

[bhobba]

I bet @bhobba might think everything that needs to be explained, is. And I don't disagree at all.

You hit it in one.

Every theory has assumptions - every single one. You can find equivalent assumptions, or conjecture on things that might explain those assumptions, but unless you get experimental support what have you gained? Yes - understanding things better - but aside from that, even if you are proven correct by experiment - all you have done is replaced one set of assumptions with another - and so it goes. Nothing is actually gained in an overall sense. Of course you have gotten a deeper knowledge of the world - and doing that is the very essence of science -- but are no closer in answering those questions some seem really concerned about here - the reason is they are more philosophical than scientific eg what is reality etc etc.

The delayed choice experiments do show how one uses QM to solve an apparent mystery - that's its value. But its just seems to go on and on - to what gain? We know the answer - so why keep on about it? Of course anyone has the right to keep investigating anything they feel like and who knows may discover something of great value - we do not know - but its not a central mystery - we know very well what's going on.

Thanks
Bill

 

[bhobba]

Third: This is one I really don't get. Why is any interpretation too much? Other than as a personal preference, I mean. MWI may be too much for me personally, but that really isn't an argument against MWI for someone who thinks non-locality is too much.

Mystery to me as well.

But boy does it generate a lot of 'verbosity'.

MWI is too much for me - just like you; and I think a lot of physicists - however mathematically its very beautiful. I remember a long personal conversation with a person much more into philosophy than me who only occasionally posts here. He wanted me to elucidate more clearly why I don't like MW. I did. But he said that didn't wash with him. I then said I like green - and I am sure you like some color as well. Tell me why with exact reasons. He never got it.

Thanks
Bill

 

[Vanadium 50]

. Obviously, most scientists believe that a better interpretation will eventually lead to better predictive/explanatory power.

I'm going to do something I rarely do and disagree with you. I think most physicists are not terribly interested in the "one true interpretation". I think this because a) the number working on this is small - could it possibly be as large as 100? b) all interpretations predict the same experimental results (otherwise they are not interpretations but different theories)

 

[bhobba]

In my opinion the insight that complementarity is a very general phenomenon

Well I think its time we got to the bottom of this complementary thing.

I don't even understand it, I understand Ballentine and other advanced QM texts, any of which contain more than enough about QM to explain any known QM phenomena - it has never been found wanting. But never a mention of Complementary.

I don't understand it, never have understood it, and consider it a leftover from Bohrs more philosophical musings about QM. I think his very good friend Einstein understood what he meant, but a lot has passed under the bridge since then and it has long outlived its usefulness.

To see what I mean let's clearly state Copenhagen at about the time of Einstein and Bohr:

1. A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)
2. The description of nature is essentially probabilistic, with the probability of an event related to the square of the amplitude of the wave function related to it. (The Born rule, after Max Born)
3. It is not possible to know the value of all the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)
4. Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.
5. Measuring devices are essentially classical devices, and measure only classical properties such as position and momentum.
6. The quantum mechanical description of large systems will closely approximate the classical description. (The correspondence principle of Bohr and Heisenberg)

Lets look at 4:
Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.

Really - does the hydrogen atom, particle in the well, and harmonic oscillator show both particle and wave properties? If you believe that one I have same real estate with 360% ocean views you may like (sorry I couldn't resist it).

Of course it doesn't. So you change it to something like - well sometimes it acts like a wave and sometimes it acts like a particle. Yes that's true - but I say so? We have a coin - one side with the picture of the queen, the other the picture of an emu. Well then it sometimes is like an emu, and others like the queen. They are complementary. Yea - true - but you know what - its really neither - its money. The same with QM its actually neither its QM stuff - whatever that is. Its a trite statement of zero value IMHO. Fine in Bohr's time - but these days - well to be blunt useless, confusing and not even understandable at advanced levels - as illustrated by books like Ballentine, correctly, never even mentions it.

The best advice I can give forget it - it's useless.

Thanks
Bill

 

[vanhees71]

1. Actually, no one knows where the next great breakthrough is coming from, or how it will be discovered. The history of science is pretty clear on that point.

2. Were this generally accepted, we wouldn't be having discussions on interpretations. And yet, here we are. Obviously, most scientists believe that a better interpretation will eventually lead to better predictive/explanatory power. Some even take an interpretation and look to see if it leads to a difference relative to "conservative" analyses. Much like string theorists look to improve upon existing theory. There is no one path to a better idea. Sort of like "sum over paths".

Ad 1) Of course, I also don't know, where the next great breakthrough is coming from (otherwise I'd publish it in a peer reviewed journal), but I'm very sure that it comes either from a well-reproducible empirical observation contradicting our present theories rather than some philosophical speculation without a solid foundation in the scientific method.

Ad 2) Well, we have these discussion on interpretations in certain circles because of the unfortunate way QT was introduced by part of the founding fathers (most notably Bohr and Heisenberg). Early on there have been papers and textbooks presenting QT as a scientific theory rather than some esoterical philosophy (most notably Sommerfelds "Quantenmechanischer Ergänzungsband" zu "Atombau und Spektrallinien", Dirac's "Principles of QM", and Pauli's Encyclopedia article on "Wellenmechanik"). I clearly regard the latter as the way we should present physics.

Also string theory is a good example for a failed attempt to make progress towards a more comprehensive theory without having clear foundations in observations. There's not a single prediction (nor even postdiction) of String Theory of any observable phenomenon yet, although from a mathematical esthetical point of view it might have some appeal.

 

[Lord Jestocost]

Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.

What a tremendous misunderstanding! Complementarity refers to the manner how classical terms and visualizations can continue to be used in quantum theory.

Listen to Carl Friedrich von Weizsäcker in “The Structure of Physics”:

For quantum theoretical complementarity Bohr found it decisive that we must describe every actual measurement by means of classical concepts. About this thesis Bohr remained unrelenting.

Langauge is necessary, as there is no science if we cannot say what we know. To Einstein’s “God does not play dice” Bohr replied: “It is not relevant whether God plays dice or not, but whether we know what we mean when we say that God is throwing dice or not.” For this reason Bohr liked to explain the necessity of complementary concepts as being due to limitations of our means of expression. “We are suspended in language” he used to say in his conversations with Aage Petersen. He was talking that way long before linguistic philosophy had become fashionable. Admittedly he never made the structure of the language itself an object of investigation. In the linguistic explanation of complementarity he only pointed out that in the description of phenomena “we always depend on expressing ourselves by means of word-paintings.” If we do not have a word which unambiguously describes a phenomenon we then have to use several approximate words with mutually exclusive scopes.

 

[vanhees71]

Well, v. Weizsaecker is strongly influenced by his academic teacher Heisenberg and later on turned completely to philosophy. The adequate language to talk about physics is, of course, mathematics. There is no way to describe quantum phenomena in a classical way, and complementarity means something else: It refers to the fact that in QT the complete preparation of the state doesn't imply the definiteness of all observables (but only of the complete set of compatible observables determined by this preparation). About the outcome of general measurements you can only make probabilistic statements, and the ideas subsumed by Bohr under "complementarity" are completely resolved by modern QT and applying Born's rule. There's no need to mention complementarity anymore!

 

[bhobba]

What a tremendous misunderstanding! Complementarity refers to the manner how classical terms and visualizations can continue to be used in quantum theory..

Well here we face an issue. I want a precise concise statement of the principle. I found one and show it falls to pieces. You say it was Bohr's way of saying what it is can't be expressed in English and this was an attempt to try and convey something of its mystery in English. But the math tells us exactly what it is. Just use that - forget wishy washy 'slogans' that fall to pieces when looked at closely. Maybe that's why Bohr and Dirac clashed.

Thanks
Bill

 

[Lord Jestocost]

...some esoterical philosophy

In case somebody doesn't understand something doesn't mean that this something is some esoterical philosophy.

 

[bhobba]

In case somebody doesn't understand something doesn't mean that this something is some esoterical philosophy.

That's true. It is well known Bohr spoke softly, thought on his feet, retracted statements as he was thinking, and tried to be very careful and subtle about what he said. Without doubt Einstein, his good friend understood what Bohr meant but he never did express his thinking as clearly as Einstein. BTW Einstein wasn't always right - but he was clear. Bohr tried to be right but clarity was not his strong suit.

I have no doubt Bohr knew what he was trying to say, it just wasn't expressed in the way more mathematically oriented physicists would like. In fact he sometimes clashed with that type - he clashed with Feynman on one occasion (at Shelter Island where Feynman was explaining his methods) because he couldn't follow Feynman mathematically and didn't understand what he was saying. He totally clashed with Dirac.

Thanks
Bill

 

[DrChinese]

I'm going to do something I rarely do and disagree with you. I think most physicists are not terribly interested in the "one true interpretation". I think this because a) the number working on this is small - could it possibly be as large as 100? b) all interpretations predict the same experimental results (otherwise they are not interpretations but different theories)

My viewpoint probably isn't *that* much different than yours.

I would guess definitely more than 100 actively performing theoretical work on MWI, Bohmian Theories, RBW, etc.; but admittedly a very small group in total. And a much larger group nipping away experimentally at the fringes of various interpretations. And by that I mean *top* teams doing work on delayed choice, erasers, entanglement of particles that have not interacted in the past, and similar. Precisely the kinds of things that might eventually lead to ruling out an interpretation**. I would certainly say those teams, while not specifically favoring one interpretation over another, are quite interested in locating potential areas of subtle differences between interpretations. So in that sense, you're right, the group actively working on this is relatively a small proportion of physicists in total. That is no surprise in and of itself.

And I would certainly agree (with your basic idea) that past the above, few working physicists lose sleep at night over interpretations. Nonetheless, I stand by my comment that "most scientists believe that a better interpretation will eventually lead to better predictive/explanatory power." Simply for the fact that I think most scientists believe a better interpretation will one day arise. And in fact I think that has already happened, and continues to happen.

EPR's entanglement (1935) brought us to a stalemate on whether QM was a complete theory. Bell (1964) and Aspect (1981) broke that stalemate. And recent experiments (last 20 years) have created a new kind of EPR: Entanglement of particles that have never been in a common light cone (no causal contact). If only EPR/Einstein could have witnessed that! I'm sure that would have been inconceivable to both Einstein and Bohr.

Has the "standard" interpretation of QM changed in the last 80 years? I'd say so, and thus we really do have a better interpretation. And I would also say that some of the interpretations might be better classed as full-on theories anyway. (Although obviously the ability to predict consistent with "standard" theory is a critical factor.) I think better interpretations are around the corner, and there will be interpretations falling by the wayside going forward. Of course, that part is just my opinion. But I don't think it's really much different than the belief of many others either.**There are those, for example, that believe most Bohmian-type theories have been ruled out - but that is not universally accepted. And certainly not by Bohmians.

 

[bhobba]

Also string theory is a good example for a failed attempt to make progress towards a more comprehensive theory without having clear foundations in observations. There's not a single prediction (nor even postdiction) of String Theory of any observable phenomenon yet, although from a mathematical esthetical point of view it might have some appeal.

I have a book - Conceptual Developments in 20th Century Field Theories. It says progress comes from asking the right question - that's the key - finding the right question to ask. String theory certainly proved an interesting question to ask - and its still going - but I think its now generally believed its not the right one. It may eventually suggest the right one - but so far we are all waiting.

Thanks
Bill

 

[Lord Jestocost]

I have no doubt Bohr knew what he was trying to say, it just wasn't expressed in the way more mathematically oriented physicists would like. In fact he sometimes clashed with that type...

That's the point! As Carl Friedrich von Weizsäcker says in “The Structure of Physics”:

“Bohr’s thinking was never based on mathematical structures, on what physicists somewhat condescendingly call the formalism, but rather on the classical description of experience and an unrelenting examination of the meaning of concepts.”