What if the Bohmian model turned out to be correct?

[Ken G]

Bell makes you throw out realism or locality, but not necessarily both. Bohm throws out locality.

And science allows you to adopt them both at your whim, depending on the question being asked and the phenomenon being probed. What I'd like to know is, from whence comes one single shred of scientific evidence that the axiomatic substructure employed by science is now, or ever has been, any different than that? In other words, from whence comes this constant reemergence, like the phoenix, of the idea that our goal is to find "the real axioms", instead of "the axioms that help us predict an experiment, or organize existing experimental data, in regard to the phenomenon of interest"? The answer must account for why the vast majority of physics publications employ axioms that are "false" if taken as philosophical truths.

 

[Ken G]

To further it, Newton had the Golden Snitch far longer than Bohr did. Bohm's just trying to give it back to its rightful owner. :)

But I think reilly's question, if I'm not mistaken, is why is Bohm "trying" to do anything of the sort? Should our effort not be to understand existing experimental evidence and use it to plan and predict new experiments, rather than building a soothing mental picture including phenomena that have not been observed at the expense of economy of understanding of those that have? It seems we should "get out of the way" of our science, or we repeat the errors of ancient natural philosophy.

 

[peter0302]

And science allows you to adopt them both at your whim, depending on the question being asked and the phenomenon being probed. What I'd like to know is, from whence comes one single shred of scientific evidence that the axiomatic substructure employed by science is now, or ever has been, any different than that? In other words, from whence comes this constant reemergence, like the phoenix, of the idea that our goal is to find "the real axioms", instead of "the axioms that help us predict an experiment, or organize existing experimental data, in regard to the phenomenon of interest"? The answer must account for why the vast majority of physics publications employ axioms that are "false" if taken as philosophical truths.

I think it goes back to the sort of Einsteinian goal of finding "the final answer" to everything. Einstein used to write of finding or understanding "the Old One" (or something to that effect). Clearly he wanted to do more than predict outcomes; he wanted to get into the mind of nature itself. I'm sure that's why QM was so distasteful to him, I think that's also what motivates those in the search for the "real axioms" s you put it.

But, there's also a practical motive, which is that if you can find different axioms that explain everything we've seen so far, but make new predictions that the old ones don't, and those predictions turn out to be correct, then you've done the world a great service. This is basically what Einstein did with relativity. Maybe Bohmian mechanics isn't the best example of this but there's no reason to believe continued searching for better axioms of QM won't be of value or will never result in anything new.

But I think reilly's question, if I'm not mistaken, is why is Bohm "trying" to do anything of the sort? Should our effort not be to understand existing experimental evidence and use it to plan and predict new experiments, rather than building a soothing mental picture including phenomena that have not been observed at the expense of economy of understanding of those that have? It seems we should "get out of the way" of our science, or we repeat the errors of ancient natural philosophy.

You're definitely right that nothing should be clung to just for comfort's sake. On the flip side, something that has been so successful for hundreds of years should not be thrown out on a whim if it need not be. If you have two possible interpretations of QM, one which is not consistent with prior theory, and one which is, and there is no particular reason to favor one over the other, why would you not choose the one that was consistent with what came before?

And, along those lines, suggesting that Bohmian mechanics is flawed because it is not the most convenient method with which to perform calculations misses the mark I think. Mathematical formalisms can always be adapted to make calculations easier. QM had to develop a whole new notation and concept of "state vector" just to be manageable.

What we're talking about here are the benefits to the fundamental ideas underlying Bohm's theory, and everyone here seems to agree that those ideas, if correct, could lead to some pretty radical breakthroughs, therefore I don't see why some are so eager to dismiss them.

I think it bears repeating that it took a long time for Newton's theory of light to result in new physics, let alone be widely accepted. We expect fast results in the 21st century but I think we're just spoiled like that. And QED and QFT have been so successful that I think a lot of people simply don't see the need or desire to pursue a radically different approach. These are all perfectly understandable circumstances, but they don't require the conclusion that interpretations or metaphysics or whatever you want to call it are not important.

That's why the quiddich analogy is so good. QFT can be the most successful theory in history (as Newton's was until 100 years ago) - but let's not forget that it hasn't explained everything. There's several candidates for "the snitch" (quantum gravity, dark matter, etc.) that, if a new theory explaining them came along tomorrow, would make QFT fare no better than Newton did.

 

[Ken G]

I think it goes back to the sort of Einsteinian goal of finding "the final answer" to everything.

I'd say it goes back to the ancients Greeks, but I think you're pointing out that after Galileo pretty much knocked that approach on its keester, it has made fitful comebacks, first with Newton and most recently Einstein. Whatever vestiges of Einstein's approach survived quantum mechanics are still in play today, it's true.

Einstein used to write of finding or understanding "the Old One" (or something to that effect). Clearly he wanted to do more than predict outcomes; he wanted to get into the mind of nature itself. I'm sure that's why QM was so distasteful to him, I think that's also what motivates those in the search for the "real axioms" s you put it.

Yes, I think that is completely correct. No one wants to be content with science, they all want to do natural philosophy. Feh.

But, there's also a practical motive, which is that if you can find different axioms that explain everything we've seen so far, but make new predictions that the old ones don't, and those predictions turn out to be correct, then you've done the world a great service. This is basically what Einstein did with relativity.

Absolutely true, but note that Einstein was working in an environment of considerable unexplained data. That is generally the case in science, as opposed to natural philosophy, and I would say accounts for their spectacularly different "shooting percentages".

Maybe Bohmian mechanics isn't the best example of this but there's no reason to believe continued searching for better axioms of QM won't be of value or will never result in anything new.

But is Bohm doing science, or natural philosophy? We've already heard of his great science works, so perhaps he felt justified in delving a little into the realm of the philosophical. I have no problem with that-- as long as we can clearly make the distinction and not mix it with science.

You're definitely right that nothing should be clung to just for comfort's sake. On the flip side, something that has been so successful for hundreds of years should not be thrown out on a whim if it need not be. If you have two possible interpretations of QM, one which is not consistent with prior theory, and one which is, and there is no particular reason to favor one over the other, why would you not choose the one that was consistent with what came before?

Because that is not the only difference that separates them, as per "reilly's challenge".

And, along those lines, suggesting that Bohmian mechanics is flawed because it is not the most convenient method with which to perform calculations misses the mark I think. Mathematical formalisms can always be adapted to make calculations easier. QM had to develop a whole new notation and concept of "state vector" just to be manageable.

But such a new notation was indeed developed, and widely used. There must be a reason for that.

What we're talking about here are the benefits to the fundamental ideas underlying Bohm's theory, and everyone here seems to agree that those ideas, if correct, could lead to some pretty radical breakthroughs, therefore I don't see why some are so eager to dismiss them.

The one way that I could see it being useful is if it motivates a new experiment we might not have thought of otherwise. That has been true for a long time now. So far I have only seen experiments that agreed with standard quantum mechanics, including Bell's work and EPR type work. So to say "imagine a new experiment gave results consistent with Bohm and nothing else" is pretty much to assume what is to be shown. I don't deny its possibility, I just don't see any reason to see it as more than a guess. The only reason I can see that it draws more attention than any other guess is that it restores an unsupported reliance on determinism, but that concept was already scientifically limited even in Newton's day, as thermodynamics indicates.

I think it bears repeating that it took a long time for Newton's theory of light to result in new physics, let alone be widely accepted.

That is true, but the issue with Bohm is not the amount of time, it is the lack of empirical support. Newton could point to simple experiments, it just wasn't being looked at by others. Quantum mechanics has been addressed from every conceivable angle with some of the most elaborate and expensive machines humanity can create.

We expect fast results in the 21st century but I think we're just spoiled like that. And QED and QFT have been so successful that I think a lot of people simply don't see the need or desire to pursue a radically different approach.

I can't deny that there's no telling how this overall landscape may have changed looking back in a thousand years. I wish I was going to be there, but I won't, unless the many-worlds people who accept "quantum immortality" turn out to be right.

There's several candidates for "the snitch" (quantum gravity, dark matter, etc.) that, if a new theory explaining them came along tomorrow, would make QFT fare no better than Newton did.

True enough. My personal prediction is that data will precede such a theory, not the other way around, but I suppose it can't hurt to try.

 

[peter0302]

So much agreement! Are we in the right forum?

By the way, was a single Quiddich game ever won _without_ someone getting the snitch?

 

[DrChinese]

Bell makes you throw out realism or locality, but not necessarily both. Bohm throws out locality.

Sure. But there is no "predetermined values" for all possible measurement settings in a Bell test. So what is the point? And GHZ doesn't require the assumption of locality anyway. It is merely based on the assumption of realism. So my point is that how does BM really qualify as realistic? I understand that it is non-local.

 

[akhmeteli]

In order to answer the question what would happen, if the Bohmian model turned out to be correct, we should first know that how precisely would it have turned out to be correct? What enabled scientists to verify it?

I think that hypothetically the Bohmian interpretation (BI) can prevail in one of two quite different ways. The first one is if BI makes predictions that differ from those of the Copenhagen interpretation (CI), and experiments confirm BI's predictions. So far predictions of BI do not differ from those of CI for the nonrelativistic case. It is difficult to say if the same is true for the relativistic case, as there is no generally recognized BI for that case AFAIK. Demystifier believes that BI and CI may have different predictions for the relativistic case, and he may be right, but his specific arguments, with all due respect to his research, cannot convince me.

The other way is if BI offers a description that is more appealing to physicists than that of CI. One of the problems with BI is that people just don't like it. There is a famous Bopp's phrase: "We say that Bohm's theory cannot be refuted, adding however, that we don't believe it." Einstein, who was no fan of CI, nevertheless said that Bohm's way is "too cheap". Smolin wrote: "In Bohm’s theory the ontology includes both the particle positions and the wavefunction, both of which live in the classical configuration space. If one believes that the particles are real one must also believe the wavefunction is real because it determines the actual trajectories of the particles. This allows us to have a realist interpretation which solves the measurement problem, but the cost is to believe in a double ontology."

Let me give an example of how an interpretation can prevail just because it's more beautiful and simple, without any experimental results that favor it. Copernicus' description of the world prevailed over the Ptolemeus' description not because experiments favored the former. One can correctly describe motion of planets using the Earth as the system of reference. True, such description would be complex and ugly. So Copernicus eventually prevailed. The question is then: can BI offer a nicer description than now? I think this is possible. For example, for a Klein-Gordon field interacting with electromagnetic field, the wavefunction can be eliminated in a natural way, and the electromagnetic 4-potential replaces the quantum potential as the guiding field (http://arxiv.org/abs/quant-ph/0509044 ).

 

[Ken G]

Let me give an example of how an interpretation can prevail just because it's more beautiful and simple, without any experimental results that favor it. Copernicus' description of the world prevailed over the Ptolemeus' description not because experiments favored the former.

Actually, that isn't true. Ptolemy's model had several elements that were fully refuted by Galileo's observations, and Tycho's observations as well. They included the motion of Venus, and moons clearly orbiting Jupiter not Earth. If not for these empirical facts, and others, I doubt Copernicus would have prevailed, given the flaws in that theory as well. I don't know of any modern-science theory that replaced a widely accepted one without new and unexplained observations, and I think it's kind of a myth that science is theory or philosophy driven.

True, such description would be complex and ugly. So Copernicus eventually prevailed.

I don't think you are talking about the Greek models, you are talking about geocentric models like Tycho's. But his was never a prevailing theory, because the real lesson of Galileo's observations was that the Earth is not special, not that the Earth is not at the center. That was the primary impetus behind much of the geocentric philosophy. So to me, the real lesson in the Copernicus vs. Ptolemy issue is, don't use philosophy to do science. That would make it a poor example to bolster the Bohmian approach, but of course I cannot say that approach is wrong.

 

[Demystifier]

I challenge Dr. Nikolic or anyone else to do some real problems in the Bohmian way:

1.Calculate the the LS and other relativistic corrections for hydrogen.

2. Work out the temporal interference pattern of the neutral K meson system;

3. Work out the radiative corrections to coincidence detection high energy electron-proton scattering.

4. Calculate the electron's magnetic moment to 13 decimal places.

5.With all spin and isospin factors in a relativistic format, show that the so-called 3-3 resonance exists in pion-nucleon scattering, with the partial wave approach, and estimate the mass of the resonance.

6. (Too much scattering?) Do superconductivity.

With the exception of number 4 and 6 these are all relatively straightforward to formulate with conventional field theory. The magnetic moment problem is very difficult, but it can be and has been done. And 2-6 have been done during the last 50 years; number 1 was done in the 1930s.

These will provide a very minimal test of the Bohm approach to do real physics.

It is trivial to do this minimal test of the Bohm approach. Just as it is trivial to show that standard quantum mechanics (QM) is consistent with observed motions of planets.

BM is NOT an alternative to standard QM. Instead, it is supposed to be an improvement of standard QM. But does standard QM really needs an improvement? Adherents of standard QM think that it doesn't. Nevertheless, in the relativistic case it does need an improvement and BM offers a possible solution:
http://xxx.lanl.gov/abs/quant-ph/0406173 [Found.Phys.Lett. 18 (2005) 549]
http://xxx.lanl.gov/abs/0705.3542

It is true that, at the moment, there is no experimental proof that the Bohmian interpretation is correct.
But there is also no experimental proof that the Copanhagen interpretation is correct either.
(Note that I distinguish the Copanhagen interpretation from the standard "shut-up-and-calculate" interpretation.)

 

[Demystifier]

Demystifier believes that BI and CI may have different predictions for the relativistic case, and he may be right, but his specific arguments, with all due respect to his research, cannot convince me.

Can you explain why?

 

[ZapperZ]

Let me give an example of how an interpretation can prevail just because it's more beautiful and simple, without any experimental results that favor it. Copernicus' description of the world prevailed over the Ptolemeus' description not because experiments favored the former. One can correctly describe motion of planets using the Earth as the system of reference. True, such description would be complex and ugly. So Copernicus eventually prevailed. The question is then: can BI offer a nicer description than now? I think this is possible. For example, for a Klein-Gordon field interacting with electromagnetic field, the wavefunction can be eliminated in a natural way, and the electromagnetic 4-potential replaces the quantum potential as the guiding field (http://arxiv.org/abs/quant-ph/0509044 ).

It is trivial to do this minimal test of the Bohm approach. Just as it is trivial to show that standard quantum mechanics (QM) is consistent with observed motions of planets.

BM is NOT an alternative to standard QM. Instead, it is supposed to be an improvement of standard QM. But does standard QM really needs an improvement? Adherents of standard QM think that it doesn't. Nevertheless, in the relativistic case it does need an improvement and BM offers a possible solution:
http://xxx.lanl.gov/abs/quant-ph/0406173 [Found.Phys.Lett. 18 (2005) 549]
http://xxx.lanl.gov/abs/0705.3542

It is true that, at the moment, there is no experimental proof that the Bohmian interpretation is correct.
But there is also no experimental proof that the Copanhagen interpretation is correct either.
(Note that I distinguish the Copanhagen interpretation from the standard "shut-up-and-calculate" interpretation.)

This is a heads up. Please use published references only. Unlike BTSM and High Energy Physics forums where arXiv preprints are commonly used, the rest of the physics forums (based on the practice of the respective fields) still favor heavily on only published papers.

I know some of the arXiv preprints have been published. So please include the exact reference. If not, they should not be used in here.

Zz.

 

[Ken G]

It is trivial to do this minimal test of the Bohm approach.

Do you mean by this that it is trivial to show that the Bohm approach is equivalent to QM, and then carry out the challenge using regular QM? If so, is that the same thing as meeting the challenge with the Bohm approach itself? Unless I'm mistaken, which I well may be, this argument sounds a little like proving that Shakespeare can be written in piglatin by showing there is a simple one-to-one transformation between that and English. But is such a transformation really the same as writing that great prose in piglatin from the outset? "Otay ebay or otnay otay ebay..."

Just as it is trivial to show that standard quantum mechanics (QM) is consistent with observed motions of planets.

To do that, wouldn't you have to treat a planet as a "quantum"? Can we claim that doing so is really within the axioms that make QM a "correct" theory? My point is that we pretend we are using an axiomatic system, but then in real applications we replace some of the axioms with any old thing we like in order to get an answer. Well, if we are going to do that, why pretend we have a self-consistent theory in the first place?

BM is NOT an alternative to standard QM. Instead, it is supposed to be an improvement of standard QM.

That is in interesting point, and I am inclined to take your word for that, but you may color me terribly unimpressed by a scientific theory that is "supposed" to be an improvement on purely philosophical grounds, yet has no experimental justification that is not pure guesswork. Why should we pay any attention to what a theory is "supposed" to be? That merely confirms what I said earlier that if I tack a periscope onto my car, and I can say that it is now supposed to be a submarine.

But there is also no experimental proof that the Copanhagen interpretation is correct either.
(Note that I distinguish the Copanhagen interpretation from the standard "shut-up-and-calculate" interpretation.)

Yes, the aspects of the Copenhagen interpretation that go beyond the "shut up and calculate" level are equally superfluous and we have no reason to pay any attention to them either. Are we empowering ourselves to do science, or philosophy here? I'll admit that the exercise can guide is to finding experiments that can test where the philosophies take us, but I'm not actually seeing any of those tests being done, so I tend to feel that all we are doing is trying to pretend we know more than we do-- a hallmark of unscientific paths to truth.

 

[Demystifier]

I'll admit that the exercise can guide is to finding experiments that can test where the philosophies take us, but I'm not actually seeing any of those tests being done, so I tend to feel that all we are doing is trying to pretend we know more than we do-- a hallmark of unscientific paths to truth.

I agree with most of your remarks, especially with the one I cite above.

 

[peter0302]

Sure. But there is no "predetermined values" for all possible measurement settings in a Bell test. So what is the point? And GHZ doesn't require the assumption of locality anyway. It is merely based on the assumption of realism. So my point is that how does BM really qualify as realistic? I understand that it is non-local.

I'm not sure what mechanism the BI provides to explain Bell experiments. I believe it's some kind of non-local influence but I could be wrong. You're certainly right that there's no possible configuration of "predetermined values" that could explain the Bell correlations.

I was just pointing out that even accepting Bell's Theorem it's possible to have realism without locality.

To respond to some other comments, I have previously suggested performing Bell experiments with measurements made at relativistic speeds. Obviously the measurements would have to be somewhat indirect since it'd be hard to accelerate a photon detector to .9c. :) But if such an experiment could be devised it would at least eliminate the possibility that measurement outcomes are frame dependent.

 

[Demystifier]

I'm not sure what mechanism the BI provides to explain Bell experiments. I believe it's some kind of non-local influence but I could be wrong.

You are right.

 

[Demystifier]

But to carry your analogy further, there are problems that are easier to deal with in the Schrodinger picture, and then there are problems that are easier to handle in the Heisenberg picture. That's why we are taught both so that we can switch back and forth. Are there any such examples we can attribute to the Bohm picture? If there is, then it will illustrate very clearly the usefulness of Bohmian QM.

The same can be said of your analogy of classical and quantum mechanics. There are definitely situations when one is more appropriate to be used versus the other. In what type of problems would an analogous situation arises between CI and Bohm?

I think BM is very useful when one needs to think about "paradoxes" related to the delayed choice type of experiments. The CI, with its wave function collapse, may be misleading. I am not saying that such experiments cannot be interpreted correctly with CI, but thinking in terms of wave function collapse may easily cause a mistake in thinking. On the other hand, in BM it is clear that there is no true wave function collapse, so with BM it is simpler to get to the right conclusion. Of course, I am talking about conceptual simplicity, not about technical simplicity.

 

[ZapperZ]

I think BM is very useful when one needs to think about "paradoxes" related to the delayed choice type of experiments. The CI, with its wave function collapse, may be misleading. I am not saying that such experiments cannot be interpreted correctly with CI, but thinking in terms of wave function collapse may easily cause a mistake in thinking.

How does this "mistake" translates into a wrong result? If it doesn't, this this isn't a "mistake" in the physical sense, and I think, in my case, that's all that matters. Anything beyond that, as I've mentioned, is simply a matter of tastes.

Besides, there's nothing here that says that it is a mistake, since nothing contradictory has been shown. Maybe that is how the universe works. I'm not saying it is, but since we are entertaining all the various, non-testable scenarios, there's nothing here to eliminate CI either.

Zz.

 

[akhmeteli]

Can you explain why?

In my previous posts, I tried to explain why I have doubts about your specific arguments (that are supposed to prove that BI and CI may have different predictions for relativistic quantum theory) as follows:
"I see the travel-back-in-time parts of trajectories somewhat differently (as an anti-particle moving ahead in time), and am not quite sure Kopenhagen and Bohm give different predictions for that case." "...Whether neutral particles can be called their own anti-particles, is not important, IMO. It is important, though, that creation and annihilation of pairs of neutral particles is possible, as far as I understand. So for time-space trajectories with travel-back-in-time sections, it is possible that at some point in time they describe three particles, not one. Therefore, acting on one of those particles, you cannot change the past for the other two particles, only the future."

 

[akhmeteli]

Actually, that isn't true. Ptolemy's model had several elements that were fully refuted by Galileo's observations, and Tycho's observations as well. They included the motion of Venus, and moons clearly orbiting Jupiter not Earth. If not for these empirical facts, and others, I doubt Copernicus would have prevailed, given the flaws in that theory as well. I don't know of any modern-science theory that replaced a widely accepted one without new and unexplained observations, and I think it's kind of a myth that science is theory or philosophy driven.

I don't think you are talking about the Greek models, you are talking about geocentric models like Tycho's. But his was never a prevailing theory, because the real lesson of Galileo's observations was that the Earth is not special, not that the Earth is not at the center. That was the primary impetus behind much of the geocentric philosophy. So to me, the real lesson in the Copernicus vs. Ptolemy issue is, don't use philosophy to do science. That would make it a poor example to bolster the Bohmian approach, but of course I cannot say that approach is wrong.

I am not going to tell you that I have read Ptolemy - my Greek is terrible (and I am not even sure his work is available in Greek :-) - maybe it is only known in arabic translations). But I remember since school that his was a geocentric system. I went to school long ago, but the following link seems to confirm this: http://plato.stanford.edu/entries/copernicus/
I readily admit though that I don't know much about Ptolemy's system. However, it follows from what you wrote that Copernicus' system was not perfect either. What is important is that it is possible to build astronomy with the Earth as the system of reference, and it will be equally correct and precise. However, in most cases this is awkward.
As for "don't use philosophy to do science", a few days ago you praised the Occam's razor as "the very beating heart of science", and I might even agree with that, but Occam's razor is philosophy, pure and simple, if you ask me. Please, no offence, I really like your posts, even if we often disagree. I think it is difficult to do science efficiently without philosophy. I believe Heisenberg's philosophy greatly facilitated his epic achievements, although I don't like his philosophy. Dirac said that "physical laws must have mathematical beauty" or something like that. This is also philosophy. I do avoid lengthy discussions of philosophy in this forum, but it is because they require a lot of time and in general seem inappropriate here.

 

[jtbell]

I readily admit though that I don't know much about Ptolemy's system. However, it follows from what you wrote that Copernicus' system was not perfect either. What is important is that it is possible to build astronomy with the Earth as the system of reference, and it will be equally correct and precise. However, in most cases this is awkward.

The Copernican model, as modified by Kepler to use elliptical orbits, can in turn be explained by Newton's law of universal gravitation, which can be tested directly in experiments here on Earth (Cavendish and his successors). IIRC it was Newton himself who showed that Kepler's laws of planetary motion could be derived from his law of gravitation.

I can't see how this would have been possible with the Ptolemaic model, except by assuming that Newtonian gravitation is not universal and does not apply to planetary motions.

 

[akhmeteli]

The Copernican model, as modified by Kepler to use elliptical orbits, can in turn be explained by Newton's law of universal gravitation, which can be tested directly in experiments here on Earth (Cavendish and his successors). IIRC it was Newton himself who showed that Kepler's laws of planetary motion could be derived from his law of gravitation.

I can't see how this would have been possible with the Ptolemaic model, except by assuming that Newtonian gravitation is not universal and does not apply to planetary motions.

What I mean is you can use an accelerating or even a rotating body as a system of reference, you just have to add several forces, such as -ma, or something like that, where a is the acceleration of the system of reference, the centrifugal force, and the Coriolis force.

 

[Ken G]

I am not going to tell you that I have read Ptolemy - my Greek is terrible (and I am not even sure his work is available in Greek :-) - maybe it is only known in arabic translations). But I remember since school that his was a geocentric system.

I have also not read Ptolemy, and indeed it was geocentric, but the point is that geocentric was not all it was! It was a detailed model involving complex cycles and epicycles, and it made specific predictions unrelated to its geocentrism that were falsified by Galileo. Of course there could always be cluges added to the theory to respect Galileo's constraints, but it was supposed to be correct as is, and too many cluges is no better than admitting it's wrong. Then, as jtbell pointed out, the advent of Newton's laws explained the basis for a Kepler's modifications to Copernicus, leaving no doubt as to the inadequacy of Ptolemy's model.

What is important is that it is possible to build astronomy with the Earth as the system of reference, and it will be equally correct and precise. However, in most cases this is awkward.

I do not dispute that, it is a central premise of general relativity. You might be interested in learning more about Tycho's model, rather than Ptolemy's, if you want to contrast sensible geocentric models with heliocentric ones. Tycho took the data that Kepler used, and was pretty close to correct if you choose a reference frame where the Earth is stationary (Tycho expected to be able to see stellar parallax if the Earth was in motion).

As for "don't use philosophy to do science", a few days ago you praised the Occam's razor as "the very beating heart of science", and I might even agree with that, but Occam's razor is philosophy, pure and simple, if you ask me.

I wondered if I would be called to make that clarification. One needs a "philosophy of science", of course, to define the very process itself. In the quote you cite, I meant philosophy in science, not philosophy of science, but that is an important distinction that you bring out. Ironically, I'm saying that it is the philosophy of science to restrict the inclusion of philosophy in science!

Please, no offence, I really like your posts, even if we often disagree.

No offense taken, I'm happy to have the opportunity to make that clarification. And I think disagreement is great-- we can learn nothing from people who agree with everything we think!

I think it is difficult to do science efficiently without philosophy.

That is most likely true, and indeed there are very simple philosophies we all apply almost automatically that are not strictly a part of science but make it closer to our own experiences. What I'm really saying is not that we shouldn't do that, it's that we should not fail to notice we are doing that. All philosophy in science should come with a disclaimer in small print, that's really what I'm saying-- yet instead we sometimes encounter an effort to elevate that philosophy to something higher than the science itself. That's unscientific, pure and simple.

Dirac said that "physical laws must have mathematical beauty" or something like that. This is also philosophy.

True, but again that is a philosophy about how and why we do science, it is not part of the chosen axiomatic structure itself. Imagine a proof like "now I adopt this equation on the basis of its beauty rather than its experimental effectiveness, citing the Dirac axiom." Instead, we say it is our philosophy to adopt the most parsimonious expression that leads to useful results, as defined by our needs, and the desire to achieve a soothing state of feeling like we understand more than we really do should not be one of those needs.

 

[Schrodinger's Dog]

Wow thanks guys this is exactly what I was looking for.

So for example we know that CI says that the wave function is not real since it is derived from imaginary numbers - I'm paraphrasing what Bohr said here - or at least we say it is not pictorial, even though it describes perfectly adequately experimental results. Could it be though that the measurement problem could be overcome and does anyone think if that happened, we would have an ability to finally define light in pictorial terms? Or given the CI this is unlikely to ever happen? What would we need to achieve this, and is it even possible?

 

[Ken G]

My problem with the realness of the wave function is not that it uses imaginary numbers, it's that "realness" isn't a scientific principle in the first place. Science doesn't know how to judge what is real, it only knows how to describe it. For example, we may have a hard time imagining the square root of -1, but we can easily imagine the concepts of magnitude and phase of some cycle-- and that's all one needs to have "complex numbers". The use of the square root of -1 is a mathematical convenience, not an essential part of a wave function, so I don't think we can rule on its realness on that basis.

The best we can do, if so inclined, is rule on the measurability of a concept, and there are weird applications in things like superconductivity where wave functions might seem to get pretty close to what one might think of as real. But that doesn't matter, I argue, because we don't sit in judgement of that, we only judge the value of our theories. It is too easy to mistake familiarity for understanding for us to start claiming that an electron is real but its wave function isn't, so I don't see exactly what you mean by "pictorial terms".

 

[Schrodinger's Dog]

My problem with the realness of the wave function is not that it uses imaginary numbers, it's that "realness" isn't a scientific principle in the first place. Science doesn't know how to judge what is real, it only knows how to describe it. For example, we may have a hard time imagining the square root of -1, but we can easily imagine the concepts of magnitude and phase of some cycle-- and that's all one needs to have "complex numbers". The use of the square root of -1 is a mathematical convenience, not an essential part of a wave function, so I don't think we can rule on its realness on that basis. The best we can do is rule on the measurability of a concept, and there are weird applications in things like superconductivity where wave functions might seem to get pretty close to what one might think of as real. But that doesn't matter, I argue, because we don't sit in judgement of that, we only judge the value of our theories. It is too easy to mistake familiarity for understanding for us to start claiming that an electron is real but its wave function isn't. I don't see the point, frankly, so I don't see exactly what you mean by "pictorial terms".

Well isn't i just a mathematical trick that links geometry with the imaginary plane. Is it really what we are representing, ie by pictorial Bohr meant is it a snapshot or photograph of what really happens.

Since I can probably not explain it better than Bohr, here is his explanation.

http://plato.stanford.edu/entries/qm-copenhagen/

I realize this is a philosophical treatise (so is CI to an extent) but I think it sums up his theory well enough, it may be out of date, but it's something I read.

Bohr's more mature view, i.e., his view after the EPR paper, on complementarity and the interpretation of quantum mechanics may be summarized in the following points:

1. The interpretation of a physical theory has to rely on an experimental practice.
2. The experimental practice presupposes a certain pre-scientific practice of description, which establishes the norm for experimental measurement apparatus, and consequently what counts as scientific experience.
3. Our pre-scientific practice of understanding our environment is an adaptation to the sense experience of separation, orientation, identification and reidentification over time of physical objects.
4. This pre-scientific experience is grasped in terms of common categories like thing's position and change of position, duration and change of duration, and the relation of cause and effect, terms and principles that are now parts of our common language.
5. These common categories yield the preconditions for objective knowledge, and any description of nature has to use these concepts to be objective.
6. The concepts of classical physics are merely exact specifications of the above categories.
7. The classical concepts—and not classical physics itself—are therefore necessary in any description of physical experience in order to understand what we are doing and to be able to communicate our results to others, in particular in the description of quantum phenomena as they present themselves in experiments;
8. Planck's empirical discovery of the quantization of action requires a revision of the foundation for the use of classical concepts, because they are not all applicable at the same time. Their use is well defined only if they apply to experimental interactions in which the quantization of action can be regarded as negligible.
9. In experimental cases where the quantization of action plays a significant role, the application of a classical concept does not refer to independent properties of the object; rather the ascription of either kinematic or dynamic properties to the object as it exists independently of a specific experimental interaction is ill-defined.
10. The quantization of action demands a limitation of the use of classical concepts so that these concepts apply only to a phenomenon, which Bohr understood as the macroscopic manifestation of a measurement on the object, i.e. the uncontrollable interaction between the object and the apparatus.
11. The quantum mechanical description of the object differs from the classical description of the measuring apparatus, and this requires that the object and the measuring device should be separated in the description, but the line of separation is not the one between macroscopic instruments and microscopic objects. It has been argued in detail (Howard 1994) that Bohr pointed out that parts of the measuring device may sometimes be treated as parts of the object in the quantum mechanical description.
12. The quantum mechanical formalism does not provide physicists with a ‘pictorial’ representation: the ψ-function does not, as Schrödinger had hoped, represent a new kind of reality. Instead, as Born suggested, the square of the absolute value of the ψ-function expresses a probability amplitude for the outcome of a measurement. Due to the fact that the wave equation involves an imaginary quantity this equation can have only a symbolic character, but the formalism may be used to predict the outcome of a measurement that establishes the conditions under which concepts like position, momentum, time and energy apply to the phenomena.
13. The ascription of these classical concepts to the phenomena of measurements rely on the experimental context of the phenomena, so that the entire setup provides us with the defining conditions for the application of kinematic and dynamic concepts in the domain of quantum physics.
14. Such phenomena are complementary in the sense that their manifestations depend on mutually exclusive measurements, but that the information gained through these various experiments exhausts all possible objective knowledge of the object.

Bohr thought of the atom as real. Atoms are neither heuristic nor logical constructions. A couple of times he emphasized this directly using arguments from experiments in a very similar way to Ian Hacking and Nancy Cartwright much later. What he did not believe was that the quantum mechanical formalism was true in the sense that it gave us a literal (‘pictorial’) rather than a symbolic representation of the quantum world. It makes much sense to characterize Bohr in modern terms as an entity realist who opposes theory realism (Folse 1987). It is because of the imaginary quantities in quantum mechanics (where the commutation rule for canonically conjugate variable, p and q, introduces Planck's constant into the formalism by pq − qp = ih/2π) that quantum mechanics does not give us a ‘pictorial’ representation of the world. Neither does the theory of relativity, Bohr argued, provide us with a literal representation, since the velocity of light is introduced with a factor of i in the definition of the fourth coordinate in a four-dimensional manifold (CC, p. 86 and p. 105). Instead these theories can only be used symbolically to predict observations under well-defined conditions. Thus Bohr was an antirealist or an instrumentalist when it comes to theories.

 

[Schrodinger's Dog]

My problem with the realness of the wave function is not that it uses imaginary numbers, it's that "realness" isn't a scientific principle in the first place. Science doesn't know how to judge what is real, it only knows how to describe it. For example, we may have a hard time imagining the square root of -1, but we can easily imagine the concepts of magnitude and phase of some cycle-- and that's all one needs to have "complex numbers". The use of the square root of -1 is a mathematical convenience, not an essential part of a wave function, so I don't think we can rule on its realness on that basis.

The best we can do, if so inclined, is rule on the measurability of a concept, and there are weird applications in things like superconductivity where wave functions might seem to get pretty close to what one might think of as real. But that doesn't matter, I argue, because we don't sit in judgement of that, we only judge the value of our theories. It is too easy to mistake familiarity for understanding for us to start claiming that an electron is real but its wave function isn't, so I don't see exactly what you mean by "pictorial terms".

I agree but what if what we are describing we don't have the ability to describe given our limitations? If we could would that make us able to describe it in deterministic terms or quantum terms? I think probably it is quantum, and that's why we fail to describe it; but as a virtual laymen with some physics knowledge but not as much as a graduate, I am of course only speculating on the ideas of others.

Ie when we talk about the tensors or equations what we are really doing is fudging it based on a lack of knowledge of what is really going on? Is that clear? As you say we are not in a position to make claims beyond that which we know. But if we were?

 

[samalkhaiat]

The real and only challenge for the so-called Bohm's mechanics is the following exercise;
Derive Bohm's equations from the (p-representation) Schrodinger equation

$$i \partial_{t}\Phi (p,t) = \frac{p^{2}}{2m} \Phi (p,t) + \int d^{3} \bar{p} V(p , \bar{p}) \Phi ( \bar{p},t)$$

If one manages to do this, then one can say that the mathematical structure of Bohm's is equivalent to that of Schrodinger's. The point is this; we can choose to write (and solve) Schrodinger equation in the x-rep., the p-rep. or the whatever-representation, but we can not do the same thing with Bohm's equations, i.e., while QM is a representation-free theory, Bohm's is not. However, leaving this defficiency aside, Bohm's mechanics is still able to reproduce all the results of the non-relativistic QM.
In the relativistic domain, Bohm's approach does not function at all.

It seems to me that Bohm's mechanics stands somewhere between QM and CM (abit of each worlds). I also believe that Biology (which I do not know much about) lies in the same domain! Bohm's concepts such as "Nonseparability" and "Self-organisation" are (I believe) of great importance for Biological systems. It would be the greatest triumph of physics if BM turns out to be a good dynamical framework for describing protein-making processes. I believe one day equations of physics WOULD DO to biology what Schroginger equation DID to chemistry. Would those equations be Bohm's? Biophysicists should try their luck! I would be a very lucky man if my idea (speculation) turns out to be correct

regards

sam

 

[Ken G]

Well isn't i just a mathematical trick that links geometry with the imaginary plane. Is it really what we are representing, ie by pictorial Bohr meant is it a snapshot or photograph of what really happens.

OK, I understand what you mean by "pictorial" now, and the issue of the "realness" of the wave function, but I still don't see the argument involving i, because yes it is just a mathematical trick. It would not seem to be hard to write the Schrodinger equation without i by breaking it into two parts (parts that would have no point in being called "real" and "imaginary", as none of the predictions of quantum mechanics rely on that distinction).

http://plato.stanford.edu/entries/qm-copenhagen/

I realize this is a philosophical treatise (so is CI to an extent) but I think it sums up his theory well enough, it may be out of date, but it's something I read.

The article is good, and causes me to see just how much I agree with Bohr's view of the meaning of quantum mechanics-- and why it's not really what gets called the CI at all.

 

[Ken G]

I agree but what if what we are describing we don't have the ability to describe given our limitations?

Not a hypothetical question-- that seems to be just the case. The question is, should this state of affairs surprise us? Our technology for studying the world has vastly outstripped our intellect and experience, it is amazing we hang on as well as we do.

If we could would that make us able to describe it in deterministic terms or quantum terms?

Either, both, whatever works in whatever situation.

Ie when we talk about the tensors or equations what we are really doing is fudging it based on a lack of knowledge of what is really going on?

I would say it's worse than we lack the knowledge to know what's going on, we lack the very language that could provide meaning to the expression "what's really going on". It seems to me science is above all a set of rules for creating a language, and we should follow those rules instead of being beguiled into using a language that we cannot make scientific. I believe that is also what Bohr was saying, as I interpret it.

 

[Schrodinger's Dog]

Not a hypothetical question-- that seems to be just the case. The question is, should this state of affairs surprise us? Our technology for studying the world has vastly outstripped our intellect and experience, it is amazing we hang on as well as we do.

Either, both, whatever works in whatever situation.

I would say it's worse than we lack the knowledge to know what's going on, we lack the very language that could provide meaning to the expression "what's really going on". It seems to me science is above all a set of rules for creating a language, and we should follow those rules instead of being beguiled into using a language that we cannot make scientific. I believe that is also what Bohr was saying, as I interpret it.

The first question was meant to be rhetorical, accidentally put a question mark in I think.

Uncannily that's exactly how Bohr put it. If we do not even have the language to describe the quantum, then how do we expect to describe it. Paraphrasing again.

The real and only challenge for the so-called Bohm's mechanics is the following exercise;
Derive Bohm's equations from the (p-representation) Schrodinger equation

$$i \partial_{t}\Phi (p,t) = \frac{p^{2}}{2m} \Phi (p,t) + \int d^{3} \bar{p} V(p , \bar{p}) \Phi ( \bar{p},t)$$

Not related to Bohm per se but have you seen a 3d solution (technically 4d I suppose) to the shcrödinger equation, I'll fish out the paper if you're interested; maths degree level though, so was a bit above me, having only recently studied calculus. I guess that's as close to pictorial as you're likely to get atm? It was a link in the tutorial section IIRC supplied by HOI. I hope you won't mind if I pass up trying to solve that for the time being.

If one manages to do this, then one can say that the mathematical structure of Bohm's is equivalent to that of Schrodinger's. The point is this; we can choose to write (and solve) Schrodinger equation in the x-rep., the p-rep. or the whatever-representation, but we can not do the same thing with Bohm's equations, i.e., while QM is a representation-free theory, Bohm's is not. However, leaving this defficiency aside, Bohm's mechanics is still able to reproduce all the results of the non-relativistic QM.
In the relativistic domain, Bohm's approach does not function at all.

Well QM isn't entirely relativistic, so perhaps we're missing the language there too.

It seems to me that Bohm's mechanics stands somewhere between QM and CM (abit of each worlds). I also believe that Biology (which I do not know much about) lies in the same domain! Bohm's concepts such as "Nonseparability" and "Self-organisation" are (I believe) of great importance for Biological systems. It would be the greatest triumph of physics if BM turns out to be a good dynamical framework for describing protein-making processes. I believe one day equations of physics WOULD DO to biology what Schroginger equation DID to chemistry. Would those equations be Bohm's? Biophysicists should try their luck! I would be a very lucky man if my idea (speculation) turns out to be correct

regards

sam

I think a good analogy to biology would be to explain the homochirality of DNA and amino acids. One being left the other right handed. Seems a wonderfully odd way of working life into the equation.

 

[Demystifier]

In my previous posts, I tried to explain why I have doubts about your specific arguments (that are supposed to prove that BI and CI may have different predictions for relativistic quantum theory) as follows:
"I see the travel-back-in-time parts of trajectories somewhat differently (as an anti-particle moving ahead in time), and am not quite sure Kopenhagen and Bohm give different predictions for that case." "...Whether neutral particles can be called their own anti-particles, is not important, IMO. It is important, though, that creation and annihilation of pairs of neutral particles is possible, as far as I understand. So for time-space trajectories with travel-back-in-time sections, it is possible that at some point in time they describe three particles, not one. Therefore, acting on one of those particles, you cannot change the past for the other two particles, only the future."

I agree, this is also a logically possible interpretation. However, the predictions of such an interpretation would significantly differ from those of the conventional interpretation:
1. According to your interpretation, neutral particles (e.g. photon) would also have antiparticles that are NOT identical to particles, contradicting the conventional interpretation.
2. According to your interpretation, pair creation would be possible even without field interactions, contradicting the conventional interpretation. (This is directly testable.)

Further, your interpretation is mathematically less elegant than mine. Your interpretation requires a preferred time even for a 1-coordinate wave function. Mine does not.

In addition, I do not understand your last statement. What kind of "action on one of those particles" you have in mind? In a deterministic theory (and Bohmian mechanics is deterministic) an "action" (whatever that means in a deterministic theory) equally influences both the future and the past.

 

[akhmeteli]

I agree, this is also a logically possible interpretation. However, the predictions of such an interpretation would significantly differ from those of the conventional interpretation:
1. According to your interpretation, neutral particles (e.g. photon) would also have antiparticles that are NOT identical to particles, contradicting the conventional interpretation.

I did not say that antiparticles of neutral particles are not identical to particles. If you believe what I said implies that, could you explain how?

2. According to your interpretation, pair creation would be possible even without field interactions, contradicting the conventional interpretation. (This is directly testable.)

I am not saying that "pair creation is possible even without field interactions". However, there are always field interactions, so there is always pair creation. I am not sure this contradicts the conventional interpretation - such processes take place, say in QED, on the level of virtual particles - a "dressed" propagator includes loops. If, however, you have in mind a comparison with a one-particle quantum theory, then experimental differences between Bohm's interpretation and such a theory would not be very interesting, as long as the experimental results agree, say, with QED.

Further, your interpretation is mathematically less elegant than mine. Your interpretation requires a preferred time even for a 1-coordinate wave function. Mine does not..

I am not sure my interpretation requires a preferred time, not any more than special relativity. It is important whether one event is inside or on the future (past) light cone of the other event, or whether the events are spacelike. These three (or five:-) ) possibilities do not depend on preferred time.

In addition, I do not understand your last statement. What kind of "action on one of those particles" you have in mind? In a deterministic theory (and Bohmian mechanics is deterministic) an "action" (whatever that means in a deterministic theory) equally influences both the future and the past.

The "action" is some measurement that is performed in an experiment aiming to find differences between predictions in two different interpretations. As for influencing the past, I agree that Bohm's interpretation is nonlocal, furthermore, I wrote previously that you may be right stating that predictions of Bohm's interpretation for the relativistic case might be different from those of CI. However, as I said, I don't see convincing specific arguments in favor of this statement in your paper. I am not saying that you don't offer specific arguments, I am saying they fail to convince me. Specifically, I am not enthusuastic about "ignoring the dotted trajectories" in your paper.

Another thing. Many people believe that it is a drawback of the Bohmian interpretation that it (apparently) gives the same predictions as the standard quantum theory. It does not matter here whether this opinion is correct or wrong. However, proponents of BI who agree with this statement may be too eager to find some differences between the predictions. If they erroneously find such differences and experiments do not confirm their predictions, BI's status will suffer dramatically and unfairly. Again, I am not sure I am enthusiastic about BI, but if it is to be "kicked", better if it is kicked for its real faults, not imaginary ones.

 

[Demystifier]

I am not saying that "pair creation is possible even without field interactions".

Even if you are not saying it, from your interpretation it follows that pair creation without field interactions is possible. Therefore, the predictions resulting from your interpretation are necessarily different from those of the conventional information, without regard whether you say this or not. Of course, just as with my interpretation, in most practical cases these differences cannot be easily observed, so your interpretation does not seem to be in conflict with existing experiments. Nevertheless, your interpretation, just like mine, can, in principle, be distinguished from the conventional interpretation.

 

[Demystifier]

Another thing. Many people believe that it is a drawback of the Bohmian interpretation that it (apparently) gives the same predictions as the standard quantum theory. It does not matter here whether this opinion is correct or wrong. However, proponents of BI who agree with this statement may be too eager to find some differences between the predictions. If they erroneously find such differences and experiments do not confirm their predictions, BI's status will suffer dramatically and unfairly. Again, I am not sure I am enthusiastic about BI, but if it is to be "kicked", better if it is kicked for its real faults, not imaginary ones.

I understand your point. I am not saying that my version of relativistic Bohmian mechanics is the only possible one. Nevertheless, this version seems so simple and natural and elegant to me, that, if an experiment would rule out this particular version, I would no longer find the Bohmian approach so appealing and promising. But that's just me.

 

[Demystifier]

Specifically, I am not enthusuastic about "ignoring the dotted trajectories" in your paper.

But you must agree that measurement involves a (unitary) change of the wave function, so the trajectories must be different from those without the measurement. Are you familiar with the theory of quantum measurements in Bohmian mechanics? Do you understand how an effective wave function collapse takes place due to interaction with the measuring apparatus? If not, then you do not understand the essence of BM.