What if the Bohmian model turned out to be correct?

[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

<br /> 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)<br />

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

<br /> 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)<br />

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.

 

[Ken G]

Can you summarize that essence, with the intention of interesting me (or others) in it enough to go look it up and dig deeper?

 

[akhmeteli]

Even if you are not saying it, from your interpretation it follows that pair creation without field interactions is possible.

Not really, for the simple reason that, as I said, there are always field interactions, even if they are somewhat hidden in one-particle theories.

Therefore, the predictions resulting from your interpretation are necessarily different from those of the conventional information, without regard whether you say this or not.

Not really, because there can be no predictions of the conventional interpretation (I guess that's what you meant?) for the case of the absence of field interactions - again, for the simple reason that there are always field interactions.

... your interpretation, just like mine, can, in principle, be distinguished from the conventional interpretation.

It may be so, but I am not aware of any convincing specific arguments.

 

[akhmeteli]

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.

Whether I must agree with that or not, I fail to see what this is supposed to prove. If you believe this proves that the predictions of BI and CI differ in the relativistic case, I just cannot imagine how your argument can prove that, as the argument is, on the face of it, equally correct or wrong both for the relativistic and the nonrelativistic case, and I believe you agree that in the nonrelativistic case the predictions of BI and CI coincide.

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.

No offence, but my knowledge or lack thereof is irrelevant, unless you believe I wrote something terribly wrong because of my ignorance. If you do believe that, could you please indicate what it is? So far you just said that my interpretation, while also logical, predicts something different from what CI does (I don't exactly disagree, but neither do I see reasons to agree) and does not appeal to you (and this is a matter of opinion, not of me being ignorant or knowledgeable). Again, all I'm saying is your arguments fail to convince me, and I tried to explain why.

 

[Demystifier]

Can you summarize that essence, with the intention of interesting me (or others) in it enough to go look it up and dig deeper?

I have presented a short review in the Appendix of
http://xxx.lanl.gov/abs/quant-ph/0208185 [Found.Phys.Lett. 17 (2004) 363]
For more details see also the references cited at the beginning of this Appendix.

 

[Demystifier]

Whether I must agree with that or not, I fail to see what this is supposed to prove.

It is supposed to explain why the dotted trajectories are ignored, or better to say, why they are modified by the position measurement, in a manner that forbids them to join the dashed trajectories. As it is essential, I will not comment other points until we clear this up.

 

[Demystifier]

Not really, for the simple reason that, as I said, there are always field interactions, even if they are somewhat hidden in one-particle theories.

The predictions that depend on the value of the interaction constant cannot be the same as those that do not depend on it. I do not see how the interaction (except the mass and wavefunction renormalization that cannot explain particle creation) could be "hidden" in one-particle theories. Do you?

 

[Schrodinger's Dog]

http://arxiv.org/abs/quant-ph/0303156

S. Goldstein, working with D. Dürr, R. Tumulka, and physicist N. Zanghi of the University of Genoa in Italy.

http://arxiv.org/abs/0707.3487

W. Struyve and H. Westman.

2 recent papers on Bohm interpretation.

This may also be of interest.

http://arxiv.org/abs/hep-th/0610032

A. Valentini

Here's a brief excerpt from the article that set me to thinking about Bohmian mechanics. Like I said at the start I'm not convinced like many people but it did get me to looking into this model.

http://www.newscientist.com/article/mg19726485.700-quantum-randomness-may-not-be-random.html"

Quantum randomness may not be random

AT ITS deepest level, nature is random and unpredictable. That, most physicists would say, is the unavoidable lesson of quantum theory. Try to track the location of an electron and you'll find only a probability that it is here or there. Measure the spin of an atom and all you get is a 50:50 chance that it is up or down. Watch a photon hit a glass plate and it will either pass through or be reflected, but it's impossible to know which without measuring it.

Where does this randomness come from? Before quantum theory, physicists could believe in determinism, the idea of a world unfolding with precise mathematical certainty. Since then, however, the weird probabilistic behaviour of the quantum world has rudely intruded, and the mainstream view is that this uncertainty is a fundamental feature of everything from alpha particles to Z bosons. Indeed, most quantum researchers celebrate the notion that pure chance lies at the foundations of the universe.

Until now, that is. A series of recent papers show that the idea of a deterministic and objective universe is alive and kicking. At the very least, the notion that quantum theory put the nail in the coffin of determinism has been wildly overstated, says physicist Sheldon Goldstein of Rutgers University in New Jersey. He and a cadre of like-minded physicists have been pursuing an alternative quantum theory known as Bohmian mechanics, in which particles follow precise trajectories or paths through space and time, and the future is perfectly predictable from the past. "It's a reformulation of quantum theory that is not at all congenial to supposedly deep quantum philosophy," says Goldstein. "It's precise and objective - and deterministic."

If these researchers can convince their peers, most of whom remain sceptical, it would be a big step towards rebuilding the universe as Einstein wanted, one in which "God does not play dice". It could also trigger a search for evidence of physics beyond quantum theory, paving the way for a better and more intuitive theory of how the universe works. Nearly a century after the discovery of quantum weirdness, it seems determinism may be back.

 

[Demystifier]

Here's a brief excerpt from the article that set me to thinking about Bohmian mechanics. Like I said at the start I'm not convinced like may people but it did get me to looking into this model.

http://www.newscientist.com/article/mg19726485.700-quantum-randomness-may-not-be-random.html"

A larger part of this paper recently published in New Scientist is copied here:
http://www.groupsrv.com/science/post-2760759.html

 

[Schrodinger's Dog]

A larger part of this paper recently published in New Scientist is copied here:
http://www.groupsrv.com/science/post-2760759.html

Hehe that neatly avoids the legal complications by passing the buck. Thanks Demystifier.

 

[akhmeteli]

It is supposed to explain why the dotted trajectories are ignored, or better to say, why they are modified by the position measurement, in a manner that forbids them to join the dashed trajectories. As it is essential, I will not comment other points until we clear this up.

Now that you mentioned the dashed trajectories, I understand that I mixed up the dotted and the dashed trajectories, saying that "I am not enthusuastic about "ignoring the dotted trajectories" in your paper." I should have said that "I am not enthusuastic about the phrase "The dashed one is unphysical because it is assumed that only one particle exists" in your paper." I do apologize for this mix-up. However, this does not mean that now I find the arguments convincing. Specifically, I am not ready to accept the assumption that one-particle relativistic quantum equations, such as the Klein-Gordon equation, describe just one particle (however natural and even tautological that assumption may look, on the face of it), as I believe that travel-back-in-time trajectories describe pair creation.
Also, I am not sure that it is important whether the dotted lines join the dashed lines after measurement.

 

[akhmeteli]

The predictions that depend on the value of the interaction constant cannot be the same as those that do not depend on it. I do not see how the interaction (except the mass and wavefunction renormalization that cannot explain particle creation) could be "hidden" in one-particle theories. Do you?

Actually, I do. The mass and wavefunction renormalization that you mention are a direct result of particle creation. Maybe they cannot "explain" particle creation, but for the same reason that an effect cannot "explain" its own cause. Anyway, particle creation does take place in one-particle theories, if only through wave function/mass renormalization. On the other hand, a particle mass is created (whether partially or totally, is not important here), by the particle's field, and thus depends "on the value of the interaction constant". So there are always field interactions, whether explicit or implicit. And again, if an experiment yields a result incompatible with the predictions of, say, the Dirac equation, but compatible with those of QED, that will not be very exciting.

 

[Demystifier]

1. Specifically, I am not ready to accept the assumption that one-particle relativistic quantum equations, such as the Klein-Gordon equation, describe just one particle (however natural and even tautological that assumption may look, on the face of it), as I believe that travel-back-in-time trajectories describe pair creation.

2. Also, I am not sure that it is important whether the dotted lines join the dashed lines after measurement.

1. In my view, these are merely two ways to say the same thing. As long as there is only ONE CONTINUOUS CURVE in spacetime, it does not matter whether we call it one particle that can move backwards in time, or many particles that can be created and destructed.

2. Well, if they don't join, then you have a problem.
Assume first that they do. Then, even with your many-particle interpretation, the positions of all these particles are determined by ONLY ONE initial particle position. This differs from the n-particle state in the usual sense, which (in the Bohmian interpretation) requires n initial particle positions.
Now assume that they don't. If these two parts of the curve are not joined, then how do you know that they actually belong to the same curve? If you simply say that they do not belong to the same curve, which indeed is in the spirit of your many-particle interpretation, then how do you know that one particle must be accompanied with another one?

I hope you see that the arguments in 2. show that a single-particle interpretation has certain advantages (even if you are still not completely convinced).

 

[Demystifier]

The mass and wavefunction renormalization that you mention are a direct result of particle creation.

In a sense you are right, but the theoretical origin of this "particle creation" differs significantly from "particle creation" in relativistic Bohmian mechanics. The former is related to virtual particles that make sense only in the perturbative method of calculation based on Feynman diagrams. The latter makes sense only in the Bohmian interpretation, irrespective of the method of the calculation. If two things look similar (though not identical), but have different theoretical origins, then it does not seem very likely that they are actually the same.

 

[Demystifier]

And again, if an experiment yields a result incompatible with the predictions of, say, the Dirac equation, but compatible with those of QED, that will not be very exciting.

As far as we know, all effects of QED on the single-particle Dirac equation is a renormalization of the parameters of the Dirac equation. An example is a correction of g, which for free Dirac equation is g=2. The QED correction of this value is one of the most remarkable triumphs of QED.

 

[Demystifier]

Akhmetely, one additional remark. At the beginning, I was also hoping, using similar arguments that you do, that motions backwards in time could be related to genuine particle creation. Nevertheless, by using arguments that I presented above, I have concluded that it was not possible (or at least very unlikely).

However, a truly amazing result was when I recently realized that the Bohmian motions backwards in time ARE related to genuine particle creation - in string theory.
See my preprints arXiv:hep-th/0702060 and arXiv:0705.3542 (I am not giving the direct links because ZZ does not allow to do that for papers that are not yet published). See in particular Fig. 1 in the first paper that summarizes various views of particle creation.

 

[akhmeteli]

As far as we know, all effects of QED on the single-particle Dirac equation is a renormalization of the parameters of the Dirac equation.

I guess you mean the free Dirac equation? Because the Lamb shift does not look like a renormalization of parameters of the Dirac equation.

An example is a correction of g, which for free Dirac equation is g=2.

I am not sure g is a parameter of the free Dirac equation. So what parameter is renormalized in this case?

 

[Demystifier]

Akhmetely, see also the most convincing argument that motions backwards in time of particles cannot be sufficient to explain particle creation. It certainly cannot explain the creation of new kinds of particles, that is, kinds of particles that were not present in the initial state. For example, there are no particle trajectories of electrons that could explain the creation of photons.
Note also that this problem is elegantly avoided in string theory, because in string theory different kinds of particles are nothing but different states of the same object - the string. Therefore, a string can continuously transit from an electron to a photon. A particle cannot do that. See also Fig. 1 mentioned in my previous post.

 

[Demystifier]

I guess you mean the free Dirac equation? Because the Lamb shift does not look like a renormalization of parameters of the Dirac equation.

I am not sure g is a parameter of the free Dirac equation. So what parameter is renormalized in this case?

You are right: strictly speaking g has an operational physical meaning only when the interaction with the magnetic field is also present. Nevertheless, when the magnetic field is treated classically, g (or more precisely the magnetic moment mu) can be viewed as a parameter of the Dirac equation in a classical magnetic field, but a parameter that can be expressed in terms of other parameters (mass and charge). But this is not really important for our main discussion, is it?

 

[akhmeteli]

You are right: strictly speaking g has an operational physical meaning only when the interaction with the magnetic field is also present. Nevertheless, when the magnetic field is treated classically, g (or more precisely the magnetic moment mu) can be viewed as a parameter of the Dirac equation in a classical magnetic field, but a parameter that can be expressed in terms of other parameters (mass and charge). But this is not really important for our main discussion, is it?

I fully agree, it is not important for the discussion.

I cannot reply to your other post(s) now, I'll try to do it in the evening (Pacific time). Take care.

 

[Demystifier]

I cannot reply to your other post(s) now, I'll try to do it in the evening (Pacific time). Take care.

I am looking forward!

 

[Schrodinger's Dog]

Isn't a photon even in QM the most fundamental of particles. I always thought the reason everything would end up under an infinitely expanding universe as photons and then as the fundamental sea of the vacuum because, that form of energy is the lowest common denominator of all matter. A particle and antiparticle pair is as far as it goes, excluding string theory, which I'm not a fan of anyway atm.

 

[Demystifier]

Isn't a photon even in QM the most fundamental of particles. I always thought the reason everything would end up under an infinitely expanding universe as photons and then as the fundamental sea of the vacuum because, that form of energy is the lowest common denominator of all matter. A particle and antiparticle pair is as far as it goes, excluding string theory, which I'm not a fan of anyway atm.

Well, that is wrong. A photon is not more (and not less) fundamental than an electron. The standard model of elementary particle contains a LOT of equally elementary particles (photons, gluons, W bosons, Z bosons, electrons, muons, tau, e-neutrinos, mu-neutrinos, tau-neutrinos, 6 types of quarks, Higgs). In fact, one of the main motivations for string theory is to derive all these seemingly "elementary" particles from a SINGLE elementary object - the string.

 

[Schrodinger's Dog]

Well, that is wrong. A photon is not more (and not less) fundamental than an electron. The standard model of elementary particle contains a LOT of equally elementary particles (photons, gluons, W bosons, Z bosons, electrons, muons, tau, e-neutrinos, mu-neutrinos, tau-neutrinos, 6 types of quarks, Higgs). In fact, one of the main motivations for string theory is to derive all these seemingly "elementary" particles from a SINGLE elementary object - the string.

By that I meant ultimately (under the infinitely expanding model) all matter in the Universe will end up as photons and then vacuum energy, and without strings the idea that a photon can become an electron is meaningless. Rather than it was more elementary than an electron. If I'm getting this straight though your points only make sense if you believe string theory to be more than a hypothesis, if not then they are meaningless, yes? If so carry on, I won't interfere again unless the subject changes.

I'm well aware quarks are more fundamental, that wasn't my point.

 

[Demystifier]

1. By that I meant ultimately (under the infinitely expanding model) all matter in the Universe will end up as photons and then vacuum energy,

2. and without strings the idea that a photon can become an electron is meaningless.

1. Even if that was true (which wasn't), so what? I do not understand your point at all.

2. It is not meaningless if you allow quantum jumps (whatever that means). But if all changes are continuous and if particles are pointlike objects, which is what Bohmian mechanics claims, then yes, it becomes meaningless.

 

[Demystifier]

If I'm getting this straight though your points only make sense if you believe string theory to be more than a hypothesis, if not then they are meaningless, yes?

Let me put it this way. If string theory is wrong, then Bohmian mechanics has problems that cannot be solved in a simple way (but can in a complicated, ugly way). If string theory is correct, then these problems of Bohmian mechanics are resolved automatically, in a simple way.

 

[Schrodinger's Dog]

1. Even if that was true (which wasn't), so what? I do not understand your point at all.

2. It is not meaningless if you allow quantum jumps (whatever that means). But if all changes are continuous and if particles are pointlike objects, which is what Bohmian mechanics claims, then yes, it becomes meaningless.

I'm sorry but yes it is.

The Big Freeze is a scenario under which continued expansion results in a universe that is too cold to sustain life. It could, in the absence of dark energy, occur only under a flat or hyperbolic geometry, because such geometries then are a necessary condition for a universe that expands forever. With a positive cosmological constant, it could also occur in a closed universe. A related scenario is Heat Death, which states that the universe goes to a state of maximum entropy in which everything is evenly distributed, and there are no gradients — which are needed to sustain information processing, one form of which is life. The Heat Death scenario is compatible with any of the three spatial models, but requires that the universe reach an eventual temperature minimum.

http://en.wikipedia.org/wiki/Big_Freeze

The Dark Age - from 10100 years until 10150 years

All Black Holes now Disintegrated: 10150 years

The remaining black holes evaporate: first the small ones, and then the supermassive black holes. All matter that used to make up the stars and galaxies has now degenerated into photons and leptons.

[edit] The Photon Age - 10150 years and Beyond

The Universe Achieves Low-Energy State: 1010³ years and beyond

The Universe now reaches an extremely low-energy state. What happens after this is speculative. It's possible a Big Rip event may occur far off into the future, or the Universe may settle into this state forever, achieving true heat death. Extreme low-energy states imply that localized quantum events become major macroscopic phenomena rather than negligible microscopic events because the smallest perturbations make the biggest difference in this era, so there is no telling what may happen to space or time. It is perceived that the laws of "macro-physics" will break down, and the laws of "quantum-physics" will prevail.

In this scenario where the Universe continues to expand more and more rapidly.

I agree with your second point.

It is meaningless if you accept string theory also I don't see what relevance it has to BM, not least because its a theory without any evidence and thus it shouldn't really be used to extrapolate except in philosophical terms . Personally I'd rather go with whatever theory is the most robust atm. String theory is a bit of a dead end IMO, unless something turns up soon, I think I'm personally going to consign it to the waste bin of nice ideas with no evidence. It's getting quite full actually.

 

[Demystifier]

I'm sorry but yes it is.

Oh, now I see the argument. OK, it is, provided two assumptions:
1. That Hawking radiation really exists (there is no proof yet).
2. That there are no other free massless particles except photons. (If, which is very likely, gravitons also exist, then Hawking radiation will produce gravitons as well.)

 

[Schrodinger's Dog]

Oh, now I see the argument. OK, it is, provided two assumptions:
1. That Hawking radiation really exists (there is no proof yet).
2. That there are no other free massless particles except photons. (If, which is very likely, gravitons also exist, then Hawking radiation will produce gravitons as well.)

Granted but at least we have some inferred evidence of black holes, so I'm willing to speculate on that. And actually knock your self out with string theory, pardon me being grumpy. This thread isn't exactly the least speculatory of threads anyway.

 

[akhmeteli]

1. In my view, these are merely two ways to say the same thing. As long as there is only ONE CONTINUOUS CURVE in spacetime, it does not matter whether we call it one particle that can move backwards in time, or many particles that can be created and destructed.

It took me quite some time to decide whether I should agree with this or not:-). OK, let us assume that I agree.

2. Well, if they don't join, then you have a problem.
Assume first that they do. Then, even with your many-particle interpretation, the positions of all these particles are determined by ONLY ONE initial particle position. This differs from the n-particle state in the usual sense, which (in the Bohmian interpretation) requires n initial particle positions.

Sorry, Demystifier, you just cannot have it both ways. You have just said that in this case "As long as there is only ONE CONTINUOUS CURVE in spacetime, it does not matter whether we call it one particle that can move backwards in time, or many particles that can be created and destructed."

Now assume that they don't. If these two parts of the curve are not joined, then how do you know that they actually belong to the same curve? If you simply say that they do not belong to the same curve, which indeed is in the spirit of your many-particle interpretation, then how do you know that one particle must be accompanied with another one?

I don't know (that they actually belong to the same curve), and I don't care. But it seems important to me that along with the first particle there is the second and the third ones, which are also real and can affect the first particle (as they are very close to it), so I 'm not over-enthusiastic when they are announced "unphysical" without bullet-proof arguments. How do I "know that one particle must be accompanied with another one"? I just take solutions of wave equations very seriously, and you are considering one of such solutions.

I hope you see that the arguments in 2. show that a single-particle interpretation has certain advantages (even if you are still not completely convinced).

You see, come to think of it, I don't really care whether the single-particle or multi-particle interpretation is correct. I can even tolerate the Wheeler's idea that there is just one electron in the Universe. I just cannot see any advantages in deeming that part of the trajectory unphysical. You may say that the advantage is that difference then arises between predictions of BI and CI. I think this can be an advantage only if experiments confirm that you are right. If, however, that does not happen, BI will suffer through no fault of its own. Ultimately, your arguments cannot convince me just because they contradict my physical intuition. I understand, however, that your arguments can eventually prove right, and my intuition - wrong. But that would surprise me immensely.

Another thing. In thirties, Landau and Peierls wrote that the achievable accuracy of coordinate measurement is even further limited in the relativistic case, as a hard enough photon used for such measurement can generate pairs, so you'll never know the coordinate of which particle you are measuring (by the way, maybe this is the ultimate source of the uncertainty relation even in the non-relativistic case). This is actually the case that we are considering.

 

[akhmeteli]

Akhmetely, one additional remark. At the beginning, I was also hoping, using similar arguments that you do, that motions backwards in time could be related to genuine particle creation. Nevertheless, by using arguments that I presented above, I have concluded that it was not possible (or at least very unlikely).

However, a truly amazing result was when I recently realized that the Bohmian motions backwards in time ARE related to genuine particle creation - in string theory.
See my preprints arXiv:hep-th/0702060 and arXiv:0705.3542 (I am not giving the direct links because ZZ does not allow to do that for papers that are not yet published). See in particular Fig. 1 in the first paper that summarizes various views of particle creation.

Again, no offence, but, as you admit in your article, the experimental status of string theory is problematic, to put it mildly, so no arguments based on string theory can convince me. Sorry.