I have a question for you but I decided to use the slow comment box since it seems... more direct. Anyway, I wanted to know your opinion on something.
I've read that the Broglie-Bohm theory makes the same predictions that the normal quantum randomness theory makes but the latter was chosen because it was conceived first. Do you believe this is true or is there some kind of hard evidence that the Broglie-Bohm theory has some kind of problem with it. Thanks. It's bothering me since I can't seem to get a straight answer from anyone on it and I usually trust your opinions.
1) irrelevant for science because it is concerned with a historical curiosity
2) is historically incorrect.
Concerning the first point, people can have various theories in the first run. But once they have all possible alternative theories, they can compare them.
Second, it is not true that the probabilistic interpretation was conceived "first". Quite on the contrary. Technically, it's true that de Broglie wrote his pilot wave theory in 1927, one year after Max Born proposed the probabilistic interpretation, but the very idea that the wave connected with the particle was "real" was studied for many years that preceded it. Both de Broglie (1924) and Schrödinger (1925) explicitly believed that the wave was real which is incorrect. Moreover, I believe that pretty much every theorist - including me - initially believed that the "wave was real" and it took him some time to accept and get convinced that it can't be so.
Third, it is not true that the de Broglie-Bohm theory gives the same predictions in general. It can be arranged to do so in the case of one spinless particle. But in the real quantum theories we find relevant today, such as quantum field theory, de Broglie-Bohm theory cannot be constructed to match probabilistic QFT exactly, and one can see that its very framework contradicts observable facts.
First of all, the "real wave" would have to be defined in an infinitedimensional space. Second, the choice of the "particle coordinates" is not well-defined and universal because the "classically behaving" degrees of freedom emerge from a general quantum theory depending on the context, and one can't surely say that some of them are universal. For example, for the electromagnetic quantum field, the classical electromagnetic fields emerge as a natural classical limit, while for fermions, it's the positions and momenta of particles.
However, even for electrons, you can have situations such as superconductivity where the correct classical quantities to describe the system are waves. Moreover, you can see that the value of the spin can't be really classical because the projection of a spin is a "quantum bit". If there also existed a classical bit associated with it, one would have to choose a preferred axis/basis in which the qubit is projected from the very beginning, and such a choice would clearly break the rotational invariance.
De Broglie-Bohm theories universally break the Lorentz invariance, anyway. That's because Bell's theorems imply that a deterministic theory of this sort simply can't be local if it should respect the observed high correlations in many experiments. However, nonlocality implies Lorentz symmetry breaking. The ideas of some promoters of the Hohmian picture that this failure could be fixed in some sense are nothing else than a wishful thinking.
Thank you Lubos. Though while I was reading the comments for your post on John Conway's 70th birthday, Maaneli Derakhshani wrote some criticism of your ideas and I wanted to know your response to it so I can get a more solid understanding of this concept. Here's the comment minus the insults:
"I would like to take you to task on a particular point of confusion you seem to have regarding nonlocal hidden variables. You like to repeatedly claim that nonlocal HV theories like Bohm's are "incompatible" with Lorentz invariance, and then rant and tirade about how you think any deviation from orthodox probabilistic QM is foolish. It seems you do not really understand what "incompatible" means. The empirical predictions of relativistic de Broglie-Bohm pilot wave theory are in fact PERFECTLY consistent with Lorentz invariance. LI is a statistical symmetry in this quantum theory, not a fundamental symmetry on the level of the "be-ables" which are the particles with trajectories. This is what is meant when some people say that "nonlocal HV's are incompatible with LI", that LI is not a fundamental symmetry, but only a statistical symmetry, in spite of the empirical equivalence of relativistic Bohmian mechanics and field theory (yes there are field theoretic extensions that are also empirically equivalent) and orthodox relativistic QM. One can of course introduce a preferred foliation of spacetime hypersurfaces to reintroduce LI for the Bohmian particle trajectories - but this does not in any way change the empirical predictions of the theory, either for better or worse. It should also be mentioned that not everyone who works on these issues thinks this lack of LI on the BE-ABLE level is a problem to even worry about, because this is how the physical world "really is". Finally, it should also be stated that there actually is no proof of impossibility for LI on the be-able level, without a preferred frame (in spite of the claims of Conway and Kochen). And in fact there currently are counterexample models to such a claim.
By the way, you should better also understand that nonlocal HV's in this theory do have other virtues, not the least of which is the fact that the Born rule postulate is DERIVED from the statistical mechanics of Bohmian particles, as well as the entire orthodox quantum measurement formalism, and the APPEARANCE of wave function collapse. Moreover, Bohmian quantum theory is fully compatible with the decoherence formalism and in a very canonical way."
thanks for your new question and the filtering of the manifestly unscientific parts of the text of the other side.
The Lorentz symmetry is verified to be a symmetry of Nature not only statistically but even at the fundamental level.
If there were a preferred reference frame or foliation, at least in principle, as your other correspondent indicates, it would be possible to operationally find it and prove that the Lorentz symmetry doesn't hold.
There would also exist new friction forces that would try to align all moving objects with the preferred frame - a new kind of aether. That's simply because the entropy of a mass M object of some kind (a logarithm of a very complicated number of microstates and/or volume of phase space) would depend on its velocity because no symmetry would protect the velocity-independence. The v=0 frame would clearly be either miminized or (more likely) maximized, forcing all objects to slow down to v=0.
In other words, when the symmetry is only said to hold "statistically", one can arrange situations in which the statistics (number of events) is limited and in these experiments, the measurements would inevitably reveal violations of the Lorentz invariance "by a lot".
Any kind of a small symmetry violation must be controlled by a small parameter. Because the Bohmian picture qualitatively chages the quantum picture of physics into something else, it is not a small modification but a change of order one or 100%, if you wish. So all conclusions that follow from the quantum relativistic theories are modified by terms of order 100%.
The tests of Lorentz symmetry may also be combined with EPR-like entanglement experiments in such a way that if the Lorentz symmetry exactly holds in one event, a perfect correlation will be observed. It's very clear that if the Lorentz symmetry doesn't hold fundamentally, for every event, so to say, a violation of the perfect correlation would be observed. All these experiments are qualitatively analogous to normal experiments that people can do, so if the Lorentz violations were predicted in the former, they would also be predicted in the latter. One can dream about the statistical cancellations of some symmetry violations in one kind of an experiment but if the symmetry is violated at the fundamental level, it is always possible to design another type of experiment where the cancellation doesn't occur.
The very concept of a symmetry emerging "statistically" in quantum mechanics (or a theory "replacing it") is therefore fundamentally misguided. Any violation of the Lorentz symmetry at the fundamental level inevitably leads to Lorentz-non-invariant probability predictions for individual events and therefore, by statistics, to Lorentz-non-invariant statistics of most experiments.
Because, by experiments - for example from billions of collisions at Fermilab - it is known that the Lorentz symmetry is an extremely accurate property of the real world around us, it is clear that a correct theory of Nature must be extremely close to a Lorentz-symmetric theory. The Bohmian theories are clearly not fundamentally close to a Lorentz-invariant theory, there exists not a single argument why they should be, and any claims of their (approximate) consistency with the Lorentz symmetry are pure wishful thinking combined with the idea that the successes of any other theory can be "automatically mimicked".
Well, they cannot. The successful reproduction of some symmetry features of kinematics and dynamics by relativistic theories is a success of these relativistic theories, not a success of non-relativistic theories.
The other statement that the Lorentz violation is not even needed is even more preposterous, given those 104 years of detailed tests of special relativity. At least those people are happy if they can use meaningless philosophical pseudo-words such as "be-ables".
Conway and Kochen are completely correct and I've explained why previously.
Partly because of the would-be "revolutionary" statements contradicting relativity and partly because of your other correspondent's frequent usage of the spelling with all capital letters, your other correspondent - whose name I've never heard of - would probably have Baez index exceeding 100.
Out of sheer luck, I just came across your post about my comments to Lubos Motl, and his (very late!) response to you and me.
Briefly, LM makes a number of claims that are simply false and based on what seem to be very basic misunderstandings (or perhaps sheer lack of knowledge) of how the nonrelativistic de Broglie-Bohm theory (AKA "Bohmian Mechanics") works, and for that matter, the details of its relativistic and field theoretic extensions. I don't say any of that to be rude or inflammatory, but simply honest.
I recall that I included a number of published papers in my previous post, which explain not only the basics of nonrelativistic de Broglie-Bohm (deBB) theory, but also exactly how Lorentz symmetry emerges in the deBB measurement theory, and why the correct empirical predictions are always preserved (so long as the Born rule distribution is satisfied). I highly recommend studying at least one of those papers, because you will immediately see where many of the claims LM makes are false.
I'll just make one quick correction to LM's false claim that nonrelativisitic deBB only applies to spin-less particles. The deBB theory easily incorporates spin 1/2 particles through the use of spinor wavefunctions. To see this for yourself, construct the quantum continuity equation from the Pauli equation and its complex-conjugate (it follows the same procedure as in the Schroedinger case). You then see it has the form
-d(rho)/dt = div(rho*J),
where J is defined in terms of the spinor-valued psi and psi^bar. The deBB guidance (velocity) equation for the point particles is just defined as the ratio of the quantum probability current, J, to the quantum probability density, rho, or
where psi and psi^bar are spinors. Thus, spin is trivially included in the theory as a property of the wavefunction not the particles, and it preserves the empirical predictions. One can also take the nonrelativistic limit of the Dirac probability current under Gordon decomposition; in that case, the guidance equation has an extra term added of the form curl(J_spin). However, this extra term does not change the empirical predictions because, as you can see from the continuity equation, the divergence of the curl of a vector is zero. Nonetheless, the point should be clear that one can easily construct the guidance equation for deBB particles to include spin-1/2 properties. By the way, this incorporation of spin was done by Bohm as early as 1952 in his original papers.
For further discussion of the theory, I refer you to any number of introductory papers, but perhaps these two will do:
What you always wanted to know about Bohmian mechanics but were afraid to ask Oliver Passon Journal-ref. Physics and Philosophy 3 (2006) quant-ph/0611032 http://eprintweb.org/S/authors/All/pa/Passon/2
Understanding Bohmian mechanics: A dialogue Roderich Tumulka American Journal of Physics 72(9) (2004) 1220-1226 arXiv:quant-ph/0408113 http://arxiv.org/PS_cache/quant-ph/pdf/0408/0408113v1.pdf
For an even more comprehensive discussion of these details, I also recommend acquiring Bohm and Hiley's book, "The Undivided Universe", as well as Holland's book, "The Quantum Theory of Motion" (Holland presents a more complicated theory of spin through a rigid-rotator model, based on the idea that the particle should literally be like a spinning top, instead of spin being a property of the wavefunction - but his approach is mathematically much more complicated, and yields the same empirical results anyway). They will also dispel all the false claims that LM makes about deBB theory. In particular, they contain detailed discussions about relativistic spin-1/2 extensions of deBB.
I realize that's a fair bit of information to work through; but in the field of quantum foundations, the only way to have a reliable knowledge about anything (and not be misinformed or fall prey to factual inaccuracies) is to do the hard work and understand things for yourself. Also, it's not very convenient to write more complicated equations in this blog format.
And regarding the comment about the Conway-Kochen theorem, it is irrelevant because it does not affect the empirical predictions of deBB or GRW being consistent with Lorentz invariance - it only proves that interacting GRW particles cannot have a covariant evolution in between measurement interactions - this tends to create philosophical discomfort for some people in QM foundations, but again, it doesn't affect the empirics. Also, there do exist GRW theories for noninteracting particles, and which are relativistic on a fundamental level, and therefore circumvent the Conway-Kochen theorem:
Comment on "The Free Will Theorem" Roderich Tumulka Foundations of Physics 37 (2007) 186-197 arXiv:quant-ph/0611283 http://www.maphy.uni-tuebingen.de/members/rotu/papers/freewilly.pdf
Finally, Lubos, the reason you have never seen or heard my name before is because I am still a student (pursuing graduate studies to be exact) in physics. That may not impress you, but it certainly does not diminish the logical validity of what I say above.
I have no problem with your being a student. I have a problem with your complete inability to see that the mathematical masturbations you exercise don't solve an infinitesimal piece of the problems that they have to solve in order to be relevant for physics.
You explicitly proved this point in the case of the spin that you "solved trivially" by saying that the spin is a "property of the wave functions". Well, it surely is. But the wave functions have to have the probabilistic interpretation they have in ordinary quantum mechanics, otherwise you either contradict facts about the measurement of the spin itself or you violate the rotational symmetry of the theory.
Your equations about "X" are completely irrelevant for the measurement of the spin. The problem is not when one wants to measure "X". Indeed, the measurement of "X" might occur analogously to its measurement in the spinless case. The problem occurs when one actually wants to measure the spin itself.
The projection of the spin j_z is an observable that can have two values, in the spin 1/2 case, either +1/2 or -1/2. It is a basic and completely well-established feature of QM that one of these values must be measured if we measure it.
How is your 17th century deterministic theory supposed to predict this discrete value? Like with "X", it must already have a classical value for this quantity. Except that in this case, it has to be discrete, so it can't be described by any continuous equation.
QM has no problem of this kind because it only describes probabilities, not the "actual reality". The probabilities for spin being +1/2 or -1/2 are obtained from squared wave functions and these wave functions follow continuous equations.
But the actual "classical" value of the spin can't be doing anything of the sort. That's why any deBB-like deterministic description of reality inevitably contradicts the fact that many observables in QM must actually be measured with discrete spectrum.
It picks "X" are a privileged observable but there is nothing privileged about "X", and there are actually much more natural quantities that describe e.g. the interactions of atoms in chemistry.
If you tried anything like classical probabilities - different from the complex quantum wave functions - that would be describing the odds for spin up or down, you would fail, too, because there are no real 2-dimensional representations of SO(3). It is essential that the amplitudes are complex (2-dimensional complex reps of spin(3)), that they are interpreted probabilistically, and that one accepts the rest of the basic QM framework, too. There is no other conceptually different solution to match the data.
Preemptively: you might also argue that any actual measurement of the spin reduces to a measurement of "X". But it's not true. I can design gadgets that either absorb or not absorb the electron depending on its j_z. So they measure j_z directly. deBB theories of all kinds will inevitably fail, not being able to predict that with some probability, the electron is absorbed, and with others, they're not. This has nothing to do with "X" or some driving ways. It is about the probability of having the spin itself.
Please learn your basic quantum mechanics and don't try to fool yourself that your elementary ignorance about concepts like the spin is a virtue.
Indeed I understand the basics of standard QM quite well thank you. But you don't seem to realize that I am not primarily talking about standard QM here, but a different theory, called de Broglie-Bohm theory, which you first have to understood *on its own terms*, before you start comparing it to standard QM. For this reason, I will present you with an account of the Stern-Gerlach (SG) experiment from the POV of deBB, and thus answer your question of how discrete spin measurements can be possible in the theory (which is a fine question on its own), and at the same time dispel the other false characterizations you make of the theory.
As I mentioned before, the Pauli wavefunction that defines the particle guidance equation (in the spin-1/2 case) is a spinor of the form psi(x) = [psi_1(x), psi_2(x)], which gets mixed under rotations according to the action on it by the Pauli matrices sigma = (sigma_x,sigma_y,sigma_z). The wavefunction now satisfies the Pauli equation with the Pauli term, sigma*B, in the Hamiltonian, which represents the coupling of the spin with an external magnetic field. Focus now on a SG "measurement" of M = sigma_z. An inhomogeneous magnetic field is established in a neighborhood of the origin, by means of a suitable arrangement of magnets. This magnetic field is effectively oriented in the positive z-direction, and is increasing in this direction. Also assume that the arrangement is invariant under translations in the x-direction, i.e., that the geometry of the setup doesn't depend on x-coordinate. An electron, with a fairly definite momentum, is directed towards the origin along the negative y-axis. Its passage through the inhomogeneous B field then generates a vertical deflection of its spinor-valued wavefunction away from the y-axis, which for deBB leads to a similar deflection of the particle's trajectory. More precisely, if the wavefunction were initially an eigenstate of sigma_z, of eigenvalue +1 or -1, or
psi = |up>*phi_0
or psi = |down>*phi_0,
where |up> = (1,0) and |down> = (0,1),
then the deflection would be in the positive (or negative) z-direction, by a rather definite angle. For a more general initial wavefunction, passage through the B field will, by linearity, split the wave function into an upward deflected piece (proportional to |up>) and a downward deflected piece (proportional to |down>), with corresponding deflections of the possible particle trajectories.
The outcome is registered by detectors placed in the way of these two electron “beams.” Thus, of the four possible outcomes (i.e. “pointer positions”), we have a) the occurrence of no detection defines the null output, b) simultaneous detection is irrelevant (since it doesn't occur if the experiment is performed 1 particle at a time), and c) the two relevant outcomes corresponding to registration by either the upper or the lower detector.
Thus, the calibrated outcomes for a measurement of z is s_up = 1 and s_down = −1, while for a measurement of the z-component of the spin angular momentum itself the calibrated outcomes is the product of s_up and s_down by hbar/2.
Note that in deBB, one can completely understand whats going on in this SG experiment without invoking any additional property of the electron, (i.e., its "actual" z-component of spin that is revealed in the experiment). As John Bell pointed out (read his book "Speakable and Unspeakable in QM" where he presents an elegant discussion of the deBB theory and accurately treats the SG experiment from the deBB POV), unlike position, spin is not primitive, meaning no actual discrete degrees of freedom analogous to the actual positions of the particles, are added to the state description in order to deal with “particles with spin.” Spin is merely in the wave function as a symmetry of its dynamics. At the same time, as just said, “spin measurements” are completely clear in deBB and merely reflect the way spinor wavefunctions are incorporated (via the guidance equation) into a description of the motion of the particle configurations. Moreover, because the particle configurations corresponding to spin up and down are determined by the spinor-valued wavefunction, it is obvious that the statistical distributions of the particles will be rho(X,t) = |psi(X,t)|^2, and thus match the statistical predictions of the standard QM theory (indeed this is obvious from the fact that they share the same quantum continuity equation!).
You mentioned that deBB assumes the position, X, is privileged as the only ontological property, while others such as "spin" or "energy" or "momentum" are not. Close, but not quite there. Momentum measurements do obtain the asymptotically deBB particle velocities. Thus, the only properties of the deBB particle are its *position and velocity*. All other measured properties, such as "spin", are *Contextual* (meaning the property corresponding to spin "up" or "down" depends on the measurement interaction in the experiment, and is not a pre-existing property of the system) in the standard QM measurement theory language; moreover, it is precisely this Contextuality in deBB that allows it to easily circumvent no-go theorems for nonlocal "hidden-variables" like Kochen-Specker.
Also, you present this example below as a "preemptive" attempt to argue that not all experiments can be reduced to position measurements:
<< I can design gadgets that either absorb or not absorb the electron depending on its j_z. So they measure j_z directly. deBB theories of all kinds will inevitably fail, not being able to predict that with some probability, the electron is absorbed, and with others, they're not. >>
What you (surprisingly) fail to realize is that the absorption of the election by your gadget is reducible to a position measurement in itself, and is therefore easily subsumed in the analysis I presented above. And again, you also have to take into account the measurement interaction, in the prediction of what spin value will be observed. Once you take into account the measurement apparatus, deBB theories easily predicts (depending on the initial particle positions), through the guidance equation, what particle configurations will correspond to what particular "spin" value via the analysis above. Moreover, because the guidance equation just specifies the current velocity in the quantum continuity equation, it is ensured that the statistical distribution for the particle configurations will be |psi(x,t)|^2, and thus guaranteed to match the standard QM statistical predictions for all times.
Finally, just so we're clear, are you familiar with the "measurement problem/paradox"? If you claim so, please briefly tell us what your understanding of it is. The reason I ask you to do this is because I am not yet convinced that you understand the measurement problem, and because the main point of deBB theory is to solve the measurement problem (which it does) by removing operationally and mathematically vague postulates about "measurements" and "observables" in the textbook QM formalism, or even the standard Copenhagen interpretation of it, and replacing them with a clear ontology for the outcomes of experiments, and a mathematically precise equation of motion for that ontology that does not require ad-hoc and anthropocentric notions of "wavefunction collapse". This is probably the best way for most physicists like yourself to appreciate the utility of the deBB theory.
Indeed I understand the basics of standard QM quite well thank you. But you don't seem to realize that I am not primarily talking about standard QM here, but a different theory, called de Broglie-Bohm theory, which you first have to understood *on its own terms*, before you start comparing it to standard QM. For this reason, I will present you with an account of the Stern-Gerlach (SG) experiment from the POV of deBB, and thus answer your question of how discrete spin measurements can be possible in the theory (which is a fine question on its own), and at the same time dispel the other false characterizations you make of the theory.
As I mentioned before, the Pauli wavefunction that defines the particle guidance equation (in the spin-1/2 case) is a spinor of the form psi(x) = [psi_1(x), psi_2(x)], which gets mixed under rotations according to the action on it by the Pauli matrices sigma = (sigma_x,sigma_y,sigma_z). The wavefunction now satisfies the Pauli equation with the Pauli term, sigma*B, in the Hamiltonian, which represents the coupling of the spin with an external magnetic field. Focus now on a SG "measurement" of M = sigma_z. An inhomogeneous magnetic field is established in a neighborhood of the origin, by means of a suitable arrangement of magnets. This magnetic field is effectively oriented in the positive z-direction, and is increasing in this direction. Also assume that the arrangement is invariant under translations in the x-direction, i.e., that the geometry of the setup doesn't depend on x-coordinate. An electron, with a fairly definite momentum, is directed towards the origin along the negative y-axis. Its passage through the inhomogeneous B field then generates a vertical deflection of its spinor-valued wavefunction away from the y-axis, which for deBB leads to a similar deflection of the particle's trajectory. More precisely, if the wavefunction were initially an eigenstate of sigma_z, of eigenvalue +1 or -1, or
psi = |up>*phi_0
or psi = |down>*phi_0,
where |up> = (1,0) and |down> = (0,1),
then the deflection would be in the positive (or negative) z-direction, by a rather definite angle. For a more general initial wavefunction, passage through the B field will, by linearity, split the wave function into an upward deflected piece (proportional to |up>) and a downward deflected piece (proportional to |down>), with corresponding deflections of the possible particle trajectories.
The outcome is registered by detectors placed in the way of these two electron “beams.” Thus, of the four possible outcomes (i.e. “pointer positions”), we have a) the occurrence of no detection defines the null output, b) simultaneous detection is irrelevant (since it doesn't occur if the experiment is performed 1 particle at a time), and c) the two relevant outcomes corresponding to registration by either the upper or the lower detector.
Thus, the calibrated outcomes for a measurement of z is s_up = 1 and s_down = −1, while for a measurement of the z-component of the spin angular momentum itself the calibrated outcomes is the product of s_up and s_down by hbar/2.
Note that in deBB, one can completely understand whats going on in this SG experiment without invoking any additional property of the electron, (i.e., its "actual" z-component of spin that is revealed in the experiment). As John Bell pointed out (read his book "Speakable and Unspeakable in QM" where he presents an elegant discussion of the deBB theory and accurately treats the SG experiment from the deBB POV), unlike position, spin is not primitive, meaning no actual discrete degrees of freedom analogous to the actual positions of the particles, are added to the state description in order to deal with “particles with spin.” Spin is merely in the wave function as a symmetry of its dynamics. At the same time, as just said, “spin measurements” are completely clear in deBB and merely reflect the way spinor wavefunctions are incorporated (via the guidance equation) into a description of the motion of the particle configurations. Moreover, because the particle configurations corresponding to spin up and down are determined by the spinor-valued wavefunction, it is obvious that the statistical distributions of the particles will be rho(X,t) = |psi(X,t)|^2, and thus match the statistical predictions of the standard QM theory (indeed this is obvious from the fact that they share the same quantum continuity equation!).
You mentioned that deBB assumes the position, X, is privileged as the only ontological property, while others such as "spin" or "energy" or "momentum" are not. Close, but not quite there. Momentum measurements do obtain the asymptotically deBB particle velocities. Thus, the only properties of the deBB particle are its *position and velocity*. All other measured properties, such as "spin", are *Contextual* (meaning the property corresponding to spin "up" or "down" depends on the measurement interaction in the experiment, and is not a pre-existing property of the system) in the standard QM measurement theory language; moreover, it is precisely this Contextuality in deBB that allows it to easily circumvent no-go theorems for nonlocal "hidden-variables" like Kochen-Specker.
Also, you present this example below as a "preemptive" attempt to argue that not all experiments can be reduced to position measurements:
<< I can design gadgets that either absorb or not absorb the electron depending on its j_z. So they measure j_z directly. deBB theories of all kinds will inevitably fail, not being able to predict that with some probability, the electron is absorbed, and with others, they're not. >>
What you (surprisingly) fail to realize is that the absorption of the election by your gadget is reducible to a position measurement in itself, and is therefore easily subsumed in the analysis I presented above. And again, you also have to take into account the measurement interaction, in the prediction of what spin value will be observed. Once you take into account the measurement apparatus, deBB theories easily predicts (depending on the initial particle positions), through the guidance equation, what particle configurations will correspond to what particular "spin" value via the analysis above. Moreover, because the guidance equation just specifies the current velocity in the quantum continuity equation, it is ensured that the statistical distribution for the particle configurations will be |psi(x,t)|^2, and thus guaranteed to match the standard QM statistical predictions for all times.
Finally, just so we're clear, are you familiar with the "measurement problem/paradox"? If you claim so, please briefly tell us what your understanding of it is. The reason I ask you to do this is because I am not yet convinced that you understand the measurement problem, and because the main point of deBB theory is to solve the measurement problem (which it does) by removing operationally and mathematically vague postulates about "measurements" and "observables" in the textbook QM formalism, or even the standard Copenhagen interpretation of it, and replacing them with a clear ontology for the outcomes of experiments, and a mathematically precise equation of motion for that ontology that does not require ad-hoc and anthropocentric notions of "wavefunction collapse". This is probably the best way for most physicists like yourself to appreciate the utility of the deBB theory.
Dear Maaneli, if the requirement that we should understand your pet theory "on its own terms" means that we should forget what we know about QM, then sorry, I won't be doing that.
QM describes all phenomena that have been observed and it is surely possible to look at every new theory as a specific modification of QM and discuss whether the specific features where you modify QM are correct or incorrect, natural or unnatural, predictive or unpredictive, consistent or inconsistent.
You're clearly not doing it. Instead, you are trying to impress others with Pauli's equation or Dirac's equation and link them with your pet theory. But your pet theory has nothing to do with the important equations of physics per se. These are equations that belong to the essential toolbox of the canonical quantum mechanics, and you are just giving all these objects and equations wrong, unnatural, and inconsistent interpretations that would be unpredictive (beyond QM) even if they were consistent.
I can read a popular book by a John Bell but that won't change the fact that the things you write about the spin being radically different from the position, not being "primitive", and so on are complete nonsense a deep misunderstanding of physics.
Spin is as "primitive" as the position, both of them can be effectively discrete or effectively continuous in various contexts, both of them carry the information, both of them can be measured, both of them are associated with probability amplitudes for various outcomes. In fact, there are even dualities between the spin and the position-like degrees of freedom. They can also transform to one another: if the spin of a large atom becomes large, this degree of freedom can be reinterpreted as a function of the positions of electrons inside it. It's simply not true that one can be "primitive" while the other is "nonprimitive".
Every approach that treats the spin and the position as qualitatively different things ontologically is manifestly wrong.
Once again, it is simply not true that every measurement of the spin must reduce to a measurement of the position (or velocity). You try to pretend that you don't hear this important fact, and instead, you continue to generate your 17th century pseudoscience that contradicts this fact.
To give you another manifest example showing very explicitly how much wrong you are, let me mention that all of quantum mechanics, including x,p observables, can be emulated, with any accuracy, by a quantum computer that contains nothing else than spins (qubits). It is manifest that if you won't have any "classical" degrees of freedom associated with these qubits, there will never be anything behaving classically in your pet theory.
The only thing how position (and/or momentum) is privileged is that they're usually the degrees of freedom that describe the states that decohere from each other. But that's not true in general. One must actually compute the rates of decoherence to see which degrees of freedom want to behave classically and which microstates decohere. For example, in my quantum computer that emulates the external world, it is the observables that mimick "x" and "p" - even though they're constructed out of spins - that decohere.
Your pet theory is simply unable to describe any spin-dependent process, the probability of absorption of a particle as a function of its spin, and so forth, even though such things are actually essential in the physics of spin. But even if you were unable to see that your theory is wrong, you should be - Jesus Christ - able to see that your theory is extremely unnatural if it gives totally different interpretations to randomly chosen subsets of observables that are treated in the same qualitative way in orthodox quantum mechanics.
Spin, position, and velocity are just three examples of observables, three examples of operators that have their eigenvalues with different probability amplitudes, and these things can be predicted. Can't you see that you're clearly doing something wrong if you say that some of them are "primitive" while others are not?
If x,v are primitive, the orbital angular momentum is associated with a "really existing" classical variable in your pet theory, too. Agreed? But the spin is not, agreed? But the spin is nothing else than another term in the total angular momentum, and the separation of the total angular momentum into these two parts actually depends on the effective theory we take.
The effective theory of the hydrogen atom may treat all of its angular momentum as internal discrete spin. But a description in terms of protons and electrons treats a major term in the angular momentum as a result of the orbital motion, the "x cross p" expression. Can't you see that there simply can't be any "universal" segregation of these angular momenta into the real "primitive" ones and some "invisible ones" that must reduce to the primitive ones?
The more microscopic description one takes, the higher part of the angular momentum is described in the orbital-like way. For example, the spin of massive particles (at the string scale) comes from the internal vibrations of the strings, so it gets reduced to the "orbital" rules. (Let me emphasize, in advance, that in this setup, it is irrelevant whether string theory is the right theory of this world; what matters and is sufficient here is that it is a consistent theory of observed-like phenomena).
On the other hand, for a chemist, all atoms are indivisible and all of their angular momenta are discrete spins. Do you think you can still argue that these spins don't exist "separately" from someone's positions and velocities? It is absurd.
The electron might be too confusing for you and you might think that the failure of your theory is OK because the spinors are hard. Why don't you try photons? Photons also carry helicity - spin with respect to the direction of motion. It is possible to design polarizers that absorb x-polarized photons but not y-polarized ones. Is the x-polarization primitive or not? Is the left-handed/right-handed polarization primitive? I could add all these questions but whatever segregation into two groups you make, it's trivial to show the segregation can't survive basic physical processes. The observables that you consider "primitive" are often directly evolving, transforming, or are dual to observables that you consider "nonprimitive". Any separation of physics into these two groups is manifest shit, a rudimentary misunderstanding of some rules of QM that have been firmly established by experiments.
<< if the requirement that we should understand your pet theory "on its own terms" means that we should forget what we know about QM, then sorry, I won't be doing that. >>
1) It's not my "pet theory" anymore than textbook QM is your pet theory. It's originators and leading proponents, I'll remind you ,were Louis de Broglie, David Bohm, and John Bell. I bet you didn't know that about Bell or that the nonlocality in deBB theory is what got him thinking about how to quantify QM nonlocality and construct his famous theorem named after him. I bet you also didn't know that deBB theory is what led Bell to consider the basic possibility of quantum computing.
2) The point (which any intellectually fair person would do) is to develop a basic enough understand of the theory you are criticizing and insulting before criticizing and insulting it. You clearly haven't spared the time to do this; instead, it sounds like all you've done is had random conversations with your colleagues and people you don't like about the deBB theory, and think that's enough to know about it, because you're "too cool for school" to actually pick up a book or review article and be patient enough to read through it on your own. Yeah, imagine if someone were to criticize string and M theory based on that same amount of laziness.
<< QM describes all phenomena that have been observed and it is surely possible to look at every new theory as a specific modification of QM and discuss whether the specific features where you modify QM are correct or incorrect, natural or unnatural, predictive or unpredictive, consistent or inconsistent. >>
Indeed, and this is not at all in contradiction with what I said.
<< You're clearly not doing it. Instead, you are trying to impress others with Pauli's equation or Dirac's equation and link them with your pet theory. But your pet theory has nothing to do with the important equations of physics per se. >>
Sorry, you're just plain wrong. Or more precisely, you are in denial. Just so you know, those equations (as well as the Schroedinger and Klein-Gordon equations) have an equivalent representation in the Hamilton-Jacobi-Madelung form (which are the Euler equations for a quantized, nonlocal fluid), and there you have a very natural justification for the deBB ontology, as Bohm and de Broglie pointed out in their first papers.
<< These are equations that belong to the essential toolbox of the canonical quantum mechanics, and you are just giving all these objects and equations wrong, unnatural, and inconsistent interpretations that would be unpredictive (beyond QM) even if they were consistent. >>
Indeed those equations are essential to the toolbox of standard QM and other interpretations and formulations of QM. But you're just plain wrong to claim the deBB use of them are somehow inconsistent; and I pretty much debunked that notion in my previous post.
<< I can read a popular book by a John Bell but that won't change the fact that the things you write about the spin being radically different from the position, not being "primitive", and so on are complete nonsense a deep misunderstanding of physics. >>
1) That book by John Bell is a collection of all his published and unpublished technical writings on the foundations of quantum mechanics and field theory.
2) You still are conflating the textbook QM formalism with the deBB formalism. They are quite different theories in terms of how they explain the quantum world, and you still fail to appreciate that.
<< Spin is as "primitive" as the position, both of them can be effectively discrete or effectively continuous in various contexts, both of them carry the information, both of them can be measured, both of them are associated with probability amplitudes for various outcomes. In fact, there are even dualities between the spin and the position-like degrees of freedom. They can also transform to one another: if the spin of a large atom becomes large, this degree of freedom can be reinterpreted as a function of the positions of electrons inside it. It's simply not true that one can be "primitive" while the other is "nonprimitive". >>
Those mathematical transformations do indeed exist in *between* "measurement" events in the textbook QM formalism. But what you're not appreciating is that decoherent measurement interactions do in fact privilege position over spin (your speak of probability amplitudes from spin and position degrees of freedom is irrelevant because it doesn't specify a theory of measurement processes). Indeed, this is a *basic* result of even quantum decoherence theory - that decoherent measurement interactions suggest position as a privileged observable. Indeed that's how environmental decoherence solves the *preferred basis* problem - it selects position as the preferred basis, and it guarantees its uniqueness via the tridecompositional uniqueness theorem. If you're unfamiliar with the basic quantum decoherence description of measurement interactions (and it sounds like you are), let me suggest an introductory reference by one of the leaders in the field:
Decoherence, the measurement problem, and interpretations of quantum mechanics Authors: Maximilian Schlosshauer Journal reference: Rev.Mod.Phys.76:1267-1305,2004 http://arxiv.org/abs/quant-ph/0312059
See section 3 titled "Implications for the preferred basis problem" on page 14. Also see section 4 titled "Pointer basis vs instantaneous Schmidt states". So you see, any consistent theory of measurement (and deBB theory naturally incorporates decoherence theory on its wavefunctions) already privileges a position basis. This is even so when you combine quantum decoherence theory with the textbook QM formalism. DeBB differs from decoherence theory only in that the former assumes there is a literal particle that picks out a particular eigenstate branch as the experimentally observed one and explains why position is the preferred basis, while the latter only takes all the highly localized eigenstate branches to explain why position is the preferred basis (but decoherence then has the problem of explaining why we only see one eigenstate in an experiment as opposed to another, and for this reason it is not alone sufficient to solve this aspect of the measurement problem called *the problem of definite outcomes*).
<< Once again, it is simply not true that every measurement of the spin must reduce to a measurement of the position (or velocity). You try to pretend that you don't hear this important fact, and instead, you continue to generate your 17th century pseudoscience that contradicts this fact. >>
Once again, it simply IS true that every measurement of the spin must reduce to a measurement of the position (or velocity). You try to pretend that you don't hear this important fact, and instead, you continue to generate your 17th century pseudoscience that contradicts this fact.
<< The only thing how position (and/or momentum) is privileged is that they're usually the degrees of freedom that describe the states that decohere from each other. But that's not true in general. One must actually compute the rates of decoherence to see which degrees of freedom want to behave classically and which microstates decohere. For example, in my quantum computer that emulates the external world, it is the observables that mimick "x" and "p" - even though they're constructed out of spins - that decohere. >>
That's a bit of a misleading account of decoherence theory. As Schlosshauer points out, for all times greater than the characteristic timescale t_D (in fact for all physically realistic timescales, i.e. those observed in real experiments), the position basis will come to be preferred by the rapid diagonality of the reduced density matrix. Read the Schlosshauer paper above.
<< Your pet theory is simply unable to describe any spin-dependent process, the probability of absorption of a particle as a function of its spin, and so forth, even though such things are actually essential in the physics of spin. >>
So I guess you just chose to ignore role of the Pauli wavefunction in the mathematics of the guidance equation. It also sounds like you didn't closely read the Stern-Gerlach example in my previous post. Well then what can I say.
<< But even if you were unable to see that your theory is wrong, you should be - Jesus Christ - able to see that your theory is extremely unnatural if it gives totally different interpretations to randomly chosen subsets of observables that are treated in the same qualitative way in orthodox quantum mechanics. >>
1) Jesus Christ never existed.
2) The deBB theory is quite self-consistent and empirically equivalent to the standard textbook QM, and its assumption of position as the preferred basis is supported by the insights of decoherence theory, and its particle ontology yields the mathematically simplest solution to the problem of definite outcomes. Also, the Madelung representations of all the quantum wave equations naturally suggest a deBB particle ontology, coupled with the fact that all we see in real physical experiments are scintillation points on detectors, i.e. particles!
<< The effective theory of the hydrogen atom may treat all of its angular momentum as internal discrete spin. But a description in terms of protons and electrons treats a major term in the angular momentum as a result of the orbital motion, the "x cross p" expression. Can't you see that there simply can't be any "universal" segregation of these angular momenta into the real "primitive" ones and some "invisible ones" that must reduce to the primitive ones? >>
Dude, it's really not that complicated. Just look at the damn equations of deBB!
<< The more microscopic description one takes, the higher part of the angular momentum is described in the orbital-like way. For example, the spin of massive particles (at the string scale) comes from the internal vibrations of the strings, so it gets reduced to the "orbital" rules. (Let me emphasize, in advance, that in this setup, it is irrelevant whether string theory is the right theory of this world; what matters and is sufficient here is that it is a consistent theory of observed-like phenomena). >>
I would like to first see you construct a string decoherence theory of measurement that does not privilege a particular pointer basis. Then we can pursue this example further. Also, it is quite possible to construct a deBB version of string theory.
<< On the other hand, for a chemist, all atoms are indivisible and all of their angular momenta are discrete spins. Do you think you can still argue that these spins don't exist "separately" from someone's positions and velocities? It is absurd. >>
Actually, most physical chemists, especially those that numerically simulate the quantum dynamics of atoms and molecules, use the deBB formalism:
LANL/CNLS Workshop on Quantum Trajectories http://cnls.lanl.gov/qt/Agenda.html
Overview: Dynamics with Quantum Trajectories http://cnls.lanl.gov/qt/QT_talks/wyatt_overview.pdf
Hydrodynamic Methods for Ultrafast Quantum Dynamics, Quantum Transport, and Dissipation http://www.math.univ-toulouse.fr/~nanolab/Contents/Invited2.pdf (Quantum hydrodynamics (\Bohmian mechanics") [1] has recently been introduced in molecular physics as a new type of quantum-dynamical simulation technique [2], rather than in its previous role as a purely interpretative tool.)
<< Why don't you try photons? Photons also carry helicity - spin with respect to the direction of motion. It is possible to design polarizers that absorb x-polarized photons but not y-polarized ones. Is the x-polarization primitive or not? Is the left-handed/right-handed polarization primitive? I could add all these questions but whatever segregation into two groups you make, it's trivial to show the segregation can't survive basic physical processes. >>
I already have done this with photons. One can take the Schroedinger/Pauli equations for photons (which certainly do exist in quantum optics), and construct guiding equations for the photons in the momentum basis. And from it, one can account for polarization effects. Remember, polarization (like spin) is a property of the wavefunction, not necessarily the particle itself (although recall that I showed how spin can be incorporated as a literal degree of freedom for the particle via the NR limit of the Dirac current - but the point was that in the nonrelativistic theory, it is not necessary to do this for the sake of reproducing the experimental observations). The deBB theory tells us that we infer properties such as spin and polarization through the trajectories and experimental observations of point particles.
Dear Maaneli, indeed, QM is "my pet theory", if you wish. But unlike you, I would never object if it were called in this playful way.
I just wrote an article about Bohmism here, so you may want to move the discussion over there.
Of course that I have always known that Bell constructed his inequalities because he wanted to prove exactly the opposite than what he proved at the end. He was unhappy until the end of his life. Bad luck. Nature doesn't care if some people can't abandon their prejudices.
I won't allow further arrogant and stupid comments of yours lying about my knowledge about your pet theory.
You must know very well that I understand both its equations, achievements, and critical bugs much more than you do (or the authors of the popular physics books - that you ludicrously try to sell as sources of scientific authority - do) so why the f*ck are you writing something else? It's just plain disgusting. You're just a stupid student who has serious trouble to understand quantum mechanics, so where does your heavenly self-confidence come from?
The Hamilton-Jacobi rewriting of the quantum equations is clearly possible but it is not terribly deep; it is only useful in the classical limit; and even in the classical limit, one must be damn careful not to interpret the objects in these equations incorrectly because the correct interpretation of all underlying terms is and must be still quantum, and every other acceptable interpretation must be a derivable approximation of quantum mechanics.
Your attempts to compare yourself to the critics of M-theory is preposterous because your pet theory is rubbish while string/M-theory is the most crucial part of the contemporary theoretical high energy physics. In fact, many of the critics of string theory - like Lee Smolin - promote the same rubbish about quantum mechanics as you do. Neither of you really understands the real world - especially its quantum aspects.
I appreciate you putting me on the spot like that by linking my name to the article. Now I'm gonna have to worry about people I know reading this exchange, and all the subsequent flak I'll get for it. O well.
Forgot to add Brian Greene (of all people!) to the list of string theorist who doubt the standard interpretation of QM. In fact, Greene and his students are currently working on Bohmian field theories!
I'm just mentioning Brian Greene, not as an argument for the validity of deBB theory, but as an example of an eminently reasonable physicist and competent string theorist who takes the theory seriously. Most physicists will give more credence to an idea if someone they know of and respect takes it seriously too. That was all.
Interesting that you're exchanging emails with him about the theory. I'm curious what you think of his understanding of QM. ;)
<< The fact that Brian Greene is inclined to believe the Bohmian pictures doesn't remove the lethal flaws of that theory. >>
Of course, Brian Greene and I would disagree about the so-called "lethal flaws". Do you think any less of Brian Greene for his inclination to believe deBB theory?
Of course I do, how could I not? Or was your question just a rhetorical question where only one answer is polite or politically correct?
I have a tremendous respect for Brian Greene - for all kinds of reasons - but of course, his incomplete understanding of the meaning of quantum mechanics contributes negatively to my respect for him.
"Most physicists will give more credence to an idea if someone they know of and respect takes it seriously too. That was all."
I am sorry but if some physicists use this group-think recipe of yours, they are not behaving as scientists and their (sociologically driven) opinion cannot be counted as a relevant independent scientific argument.
If I actually understand the science of some topic, I don't have to pay any attention to the names of those who don't understand the topic.
Of course, once again, Brian Greene doesn't quite understand all the issues that decide about the correct and incorrect interpretations of quantum mechanics.
One qualification to add in my comments. Most physicists will give further credence to an idea if someone they know of and respect takes it seriously, and if they themselves don't very much about it.
I agree with you about the sociology issue being a problem; but unfortunately I have experienced it on numerous occasions in other branches of physics.
Due to some breathtaking recent expenses related to my free expression, I really need your material help... Also try PayPal.me/motls (EUR,CZK avoid a fee)
snail feedback (21) :
Dear Lubos,
I have a question for you but I decided to use the slow comment box since it seems... more direct. Anyway, I wanted to know your opinion on something.
I've read that the Broglie-Bohm theory makes the same predictions that the normal quantum randomness theory makes but the latter was chosen because it was conceived first. Do you believe this is true or is there some kind of hard evidence that the Broglie-Bohm theory has some kind of problem with it. Thanks. It's bothering me since I can't seem to get a straight answer from anyone on it and I usually trust your opinions.
squeehunter@gmail.com
Very addictive! ha!
Dear Squeehunter,
the hypothesis you write is
1) irrelevant for science because it is concerned with a historical curiosity
2) is historically incorrect.
Concerning the first point, people can have various theories in the first run. But once they have all possible alternative theories, they can compare them.
Second, it is not true that the probabilistic interpretation was conceived "first". Quite on the contrary. Technically, it's true that de Broglie wrote his pilot wave theory in 1927, one year after Max Born proposed the probabilistic interpretation, but the very idea that the wave connected with the particle was "real" was studied for many years that preceded it. Both de Broglie (1924) and Schrödinger (1925) explicitly believed that the wave was real which is incorrect. Moreover, I believe that pretty much every theorist - including me - initially believed that the "wave was real" and it took him some time to accept and get convinced that it can't be so.
Third, it is not true that the de Broglie-Bohm theory gives the same predictions in general. It can be arranged to do so in the case of one spinless particle. But in the real quantum theories we find relevant today, such as quantum field theory, de Broglie-Bohm theory cannot be constructed to match probabilistic QFT exactly, and one can see that its very framework contradicts observable facts.
First of all, the "real wave" would have to be defined in an infinitedimensional space. Second, the choice of the "particle coordinates" is not well-defined and universal because the "classically behaving" degrees of freedom emerge from a general quantum theory depending on the context, and one can't surely say that some of them are universal. For example, for the electromagnetic quantum field, the classical electromagnetic fields emerge as a natural classical limit, while for fermions, it's the positions and momenta of particles.
However, even for electrons, you can have situations such as superconductivity where the correct classical quantities to describe the system are waves. Moreover, you can see that the value of the spin can't be really classical because the projection of a spin is a "quantum bit". If there also existed a classical bit associated with it, one would have to choose a preferred axis/basis in which the qubit is projected from the very beginning, and such a choice would clearly break the rotational invariance.
De Broglie-Bohm theories universally break the Lorentz invariance, anyway. That's because Bell's theorems imply that a deterministic theory of this sort simply can't be local if it should respect the observed high correlations in many experiments. However, nonlocality implies Lorentz symmetry breaking. The ideas of some promoters of the Hohmian picture that this failure could be fixed in some sense are nothing else than a wishful thinking.
Best wishes
Lubos
Thank you Lubos. Though while I was reading the comments for your post on John Conway's 70th birthday, Maaneli Derakhshani wrote some criticism of your ideas and I wanted to know your response to it so I can get a more solid understanding of this concept. Here's the comment minus the insults:
"I would like to take you to task on a particular point of confusion you seem to have regarding nonlocal hidden variables. You like to repeatedly claim that nonlocal HV theories like Bohm's are "incompatible" with Lorentz invariance, and then rant and tirade about how you think any deviation from orthodox probabilistic QM is foolish. It seems you do not really understand what "incompatible" means. The empirical predictions of relativistic de Broglie-Bohm pilot wave theory are in fact PERFECTLY consistent with Lorentz invariance. LI is a statistical symmetry in this quantum theory, not a fundamental symmetry on the level of the "be-ables" which are the particles with trajectories. This is what is meant when some people say that "nonlocal HV's are incompatible with LI", that LI is not a fundamental symmetry, but only a statistical symmetry, in spite of the empirical equivalence of relativistic Bohmian mechanics and field theory (yes there are field theoretic extensions that are also empirically equivalent) and orthodox relativistic QM. One can of course introduce a preferred foliation of spacetime hypersurfaces to reintroduce LI for the Bohmian particle trajectories - but this does not in any way change the empirical predictions of the theory, either for better or worse. It should also be mentioned that not everyone who works on these issues thinks this lack of LI on the BE-ABLE level is a problem to even worry about, because this is how the physical world "really is". Finally, it should also be stated that there actually is no proof of impossibility for LI on the be-able level, without a preferred frame (in spite of the claims of Conway and Kochen). And in fact there currently are counterexample models to such a claim.
By the way, you should better also understand that nonlocal HV's in this theory do have other virtues, not the least of which is the fact that the Born rule postulate is DERIVED from the statistical mechanics of Bohmian particles, as well as the entire orthodox quantum measurement formalism, and the APPEARANCE of wave function collapse. Moreover, Bohmian quantum theory is fully compatible with the decoherence formalism and in a very canonical way."
How would you anwser that? Thanks again.
Dear squeehunter,
thanks for your new question and the filtering of the manifestly unscientific parts of the text of the other side.
The Lorentz symmetry is verified to be a symmetry of Nature not only statistically but even at the fundamental level.
If there were a preferred reference frame or foliation, at least in principle, as your other correspondent indicates, it would be possible to operationally find it and prove that the Lorentz symmetry doesn't hold.
There would also exist new friction forces that would try to align all moving objects with the preferred frame - a new kind of aether. That's simply because the entropy of a mass M object of some kind (a logarithm of a very complicated number of microstates and/or volume of phase space) would depend on its velocity because no symmetry would protect the velocity-independence. The v=0 frame would clearly be either miminized or (more likely) maximized, forcing all objects to slow down to v=0.
In other words, when the symmetry is only said to hold "statistically", one can arrange situations in which the statistics (number of events) is limited and in these experiments, the measurements would inevitably reveal violations of the Lorentz invariance "by a lot".
Any kind of a small symmetry violation must be controlled by a small parameter. Because the Bohmian picture qualitatively chages the quantum picture of physics into something else, it is not a small modification but a change of order one or 100%, if you wish. So all conclusions that follow from the quantum relativistic theories are modified by terms of order 100%.
The tests of Lorentz symmetry may also be combined with EPR-like entanglement experiments in such a way that if the Lorentz symmetry exactly holds in one event, a perfect correlation will be observed. It's very clear that if the Lorentz symmetry doesn't hold fundamentally, for every event, so to say, a violation of the perfect correlation would be observed. All these experiments are qualitatively analogous to normal experiments that people can do, so if the Lorentz violations were predicted in the former, they would also be predicted in the latter. One can dream about the statistical cancellations of some symmetry violations in one kind of an experiment but if the symmetry is violated at the fundamental level, it is always possible to design another type of experiment where the cancellation doesn't occur.
The very concept of a symmetry emerging "statistically" in quantum mechanics (or a theory "replacing it") is therefore fundamentally misguided. Any violation of the Lorentz symmetry at the fundamental level inevitably leads to Lorentz-non-invariant probability predictions for individual events and therefore, by statistics, to Lorentz-non-invariant statistics of most experiments.
Because, by experiments - for example from billions of collisions at Fermilab - it is known that the Lorentz symmetry is an extremely accurate property of the real world around us, it is clear that a correct theory of Nature must be extremely close to a Lorentz-symmetric theory. The Bohmian theories are clearly not fundamentally close to a Lorentz-invariant theory, there exists not a single argument why they should be, and any claims of their (approximate) consistency with the Lorentz symmetry are pure wishful thinking combined with the idea that the successes of any other theory can be "automatically mimicked".
Well, they cannot. The successful reproduction of some symmetry features of kinematics and dynamics by relativistic theories is a success of these relativistic theories, not a success of non-relativistic theories.
The other statement that the Lorentz violation is not even needed is even more preposterous, given those 104 years of detailed tests of special relativity. At least those people are happy if they can use meaningless philosophical pseudo-words such as "be-ables".
Conway and Kochen are completely correct and I've explained why previously.
Partly because of the would-be "revolutionary" statements contradicting relativity and partly because of your other correspondent's frequent usage of the spelling with all capital letters, your other correspondent - whose name I've never heard of - would probably have Baez index exceeding 100.
Best wishes
Luboš
love it!
Dear squeehunter,
Out of sheer luck, I just came across your post about my comments to Lubos Motl, and his (very late!) response to you and me.
Briefly, LM makes a number of claims that are simply false and based on what seem to be very basic misunderstandings (or perhaps sheer lack of knowledge) of how the nonrelativistic de Broglie-Bohm theory (AKA "Bohmian Mechanics") works, and for that matter, the details of its relativistic and field theoretic extensions. I don't say any of that to be rude or inflammatory, but simply honest.
I recall that I included a number of published papers in my previous post, which explain not only the basics of nonrelativistic de Broglie-Bohm (deBB) theory, but also exactly how Lorentz symmetry emerges in the deBB measurement theory, and why the correct empirical predictions are always preserved (so long as the Born rule distribution is satisfied). I highly recommend studying at least one of those papers, because you will immediately see where many of the claims LM makes are false.
I'll just make one quick correction to LM's false claim that nonrelativisitic deBB only applies to spin-less particles. The deBB theory easily incorporates spin 1/2 particles through the use of spinor wavefunctions. To see this for yourself, construct the quantum continuity equation from the Pauli equation and its complex-conjugate (it follows the same procedure as in the Schroedinger case). You then see it has the form
-d(rho)/dt = div(rho*J),
where J is defined in terms of the spinor-valued psi and psi^bar. The deBB guidance (velocity) equation for the point particles is just defined as the ratio of the quantum probability current, J, to the quantum probability density, rho, or
dX/dt = J/rho = (hbar/m)*Im{psi^bar*grad(psi)}/psi^bar*psi,
where psi and psi^bar are spinors. Thus, spin is trivially included in the theory as a property of the wavefunction not the particles, and it preserves the empirical predictions. One can also take the nonrelativistic limit of the Dirac probability current under Gordon decomposition; in that case, the guidance equation has an extra term added of the form curl(J_spin). However, this extra term does not change the empirical predictions because, as you can see from the continuity equation, the divergence of the curl of a vector is zero. Nonetheless, the point should be clear that one can easily construct the guidance equation for deBB particles to include spin-1/2 properties. By the way, this incorporation of spin was done by Bohm as early as 1952 in his original papers.
For further discussion of the theory, I refer you to any number of introductory papers, but perhaps these two will do:
What you always wanted to know about Bohmian mechanics but were afraid to ask
Oliver Passon
Journal-ref. Physics and Philosophy 3 (2006)
quant-ph/0611032
http://eprintweb.org/S/authors/All/pa/Passon/2
Understanding Bohmian mechanics: A dialogue
Roderich Tumulka
American Journal of Physics 72(9) (2004) 1220-1226
arXiv:quant-ph/0408113
http://arxiv.org/PS_cache/quant-ph/pdf/0408/0408113v1.pdf
For an even more comprehensive discussion of these details, I also recommend acquiring Bohm and Hiley's book, "The Undivided Universe", as well as Holland's book, "The Quantum Theory of Motion" (Holland presents a more complicated theory of spin through a rigid-rotator model, based on the idea that the particle should literally be like a spinning top, instead of spin being a property of the wavefunction - but his approach is mathematically much more complicated, and yields the same empirical results anyway). They will also dispel all the false claims that LM makes about deBB theory. In particular, they contain detailed discussions about relativistic spin-1/2 extensions of deBB.
I realize that's a fair bit of information to work through; but in the field of quantum foundations, the only way to have a reliable knowledge about anything (and not be misinformed or fall prey to factual inaccuracies) is to do the hard work and understand things for yourself. Also, it's not very convenient to write more complicated equations in this blog format.
And regarding the comment about the Conway-Kochen theorem, it is irrelevant because it does not affect the empirical predictions of deBB or GRW being consistent with Lorentz invariance - it only proves that interacting GRW particles cannot have a covariant evolution in between measurement interactions - this tends to create philosophical discomfort for some people in QM foundations, but again, it doesn't affect the empirics. Also, there do exist GRW theories for noninteracting particles, and which are relativistic on a fundamental level, and therefore circumvent the Conway-Kochen theorem:
Comment on "The Free Will Theorem"
Roderich Tumulka
Foundations of Physics 37 (2007) 186-197
arXiv:quant-ph/0611283
http://www.maphy.uni-tuebingen.de/members/rotu/papers/freewilly.pdf
Finally, Lubos, the reason you have never seen or heard my name before is because I am still a student (pursuing graduate studies to be exact) in physics. That may not impress you, but it certainly does not diminish the logical validity of what I say above.
Peace,
Maaneli Derakhshani
Dear maaneli,
I have no problem with your being a student. I have a problem with your complete inability to see that the mathematical masturbations you exercise don't solve an infinitesimal piece of the problems that they have to solve in order to be relevant for physics.
You explicitly proved this point in the case of the spin that you "solved trivially" by saying that the spin is a "property of the wave functions". Well, it surely is. But the wave functions have to have the probabilistic interpretation they have in ordinary quantum mechanics, otherwise you either contradict facts about the measurement of the spin itself or you violate the rotational symmetry of the theory.
Your equations about "X" are completely irrelevant for the measurement of the spin. The problem is not when one wants to measure "X". Indeed, the measurement of "X" might occur analogously to its measurement in the spinless case. The problem occurs when one actually wants to measure the spin itself.
The projection of the spin j_z is an observable that can have two values, in the spin 1/2 case, either +1/2 or -1/2. It is a basic and completely well-established feature of QM that one of these values must be measured if we measure it.
How is your 17th century deterministic theory supposed to predict this discrete value? Like with "X", it must already have a classical value for this quantity. Except that in this case, it has to be discrete, so it can't be described by any continuous equation.
QM has no problem of this kind because it only describes probabilities, not the "actual reality". The probabilities for spin being +1/2 or -1/2 are obtained from squared wave functions and these wave functions follow continuous equations.
But the actual "classical" value of the spin can't be doing anything of the sort. That's why any deBB-like deterministic description of reality inevitably contradicts the fact that many observables in QM must actually be measured with discrete spectrum.
It picks "X" are a privileged observable but there is nothing privileged about "X", and there are actually much more natural quantities that describe e.g. the interactions of atoms in chemistry.
If you tried anything like classical probabilities - different from the complex quantum wave functions - that would be describing the odds for spin up or down, you would fail, too, because there are no real 2-dimensional representations of SO(3). It is essential that the amplitudes are complex (2-dimensional complex reps of spin(3)), that they are interpreted probabilistically, and that one accepts the rest of the basic QM framework, too. There is no other conceptually different solution to match the data.
Preemptively: you might also argue that any actual measurement of the spin reduces to a measurement of "X". But it's not true. I can design gadgets that either absorb or not absorb the electron depending on its j_z. So they measure j_z directly. deBB theories of all kinds will inevitably fail, not being able to predict that with some probability, the electron is absorbed, and with others, they're not. This has nothing to do with "X" or some driving ways. It is about the probability of having the spin itself.
Please learn your basic quantum mechanics and don't try to fool yourself that your elementary ignorance about concepts like the spin is a virtue.
Best wishes
Lubos
Dear Lubos,
Thanks for at least replying promptly this time.
Indeed I understand the basics of standard QM quite well thank you. But you don't seem to realize that I am not primarily talking about standard QM here, but a different theory, called de Broglie-Bohm theory, which you first have to understood *on its own terms*, before you start comparing it to standard QM. For this reason, I will present you with an account of the Stern-Gerlach (SG) experiment from the POV of deBB, and thus answer your question of how discrete spin measurements can be possible in the theory (which is a fine question on its own), and at the same time dispel the other false characterizations you make of the theory.
As I mentioned before, the Pauli wavefunction that defines the particle guidance equation (in the spin-1/2 case) is a spinor of the form psi(x) = [psi_1(x), psi_2(x)], which gets mixed under rotations according to the action on it by the Pauli matrices sigma = (sigma_x,sigma_y,sigma_z). The wavefunction now satisfies the Pauli equation with the Pauli term, sigma*B, in the Hamiltonian, which represents the coupling of the spin with an external magnetic field. Focus now on a SG "measurement" of M = sigma_z. An inhomogeneous
magnetic field is established in a neighborhood of the origin, by means of a suitable arrangement of magnets. This magnetic field is effectively oriented in the positive z-direction, and is increasing in this direction. Also assume that the arrangement is invariant under translations in the x-direction, i.e., that the geometry of the setup doesn't depend on x-coordinate. An electron, with a fairly definite momentum, is directed towards the origin along the negative y-axis. Its passage through the inhomogeneous B field then generates a vertical deflection of its spinor-valued wavefunction away from the y-axis, which for deBB leads to a similar deflection of the particle's trajectory. More precisely, if the wavefunction were initially an eigenstate of sigma_z, of eigenvalue +1 or -1, or
psi = |up>*phi_0
or psi = |down>*phi_0,
where |up> = (1,0) and |down> = (0,1),
then the deflection would be in the positive (or negative) z-direction, by a rather definite angle. For a more general initial wavefunction, passage through the B field will, by linearity, split the wave function into an upward deflected piece (proportional to |up>) and a downward deflected piece (proportional to |down>), with corresponding deflections of
the possible particle trajectories.
The outcome is registered by detectors placed in the way of these two electron “beams.” Thus,
of the four possible outcomes (i.e. “pointer positions”), we have a) the occurrence of no detection defines the null output, b) simultaneous detection is irrelevant (since it doesn't occur if the experiment is performed 1 particle at a time), and c) the two relevant outcomes corresponding to registration by either the upper or the lower detector.
Thus, the calibrated outcomes for a measurement of z is s_up = 1 and s_down = −1, while for a measurement of the z-component of the spin angular momentum itself the calibrated outcomes is the product of s_up and s_down by hbar/2.
Note that in deBB, one can completely understand whats going on in this SG experiment without invoking any additional property of the electron, (i.e., its "actual" z-component of spin that is revealed in the experiment). As John Bell pointed out (read his book "Speakable and Unspeakable in QM" where he presents an elegant discussion of the deBB theory and accurately treats the SG experiment from the deBB POV), unlike position, spin is not primitive, meaning no actual discrete degrees of freedom analogous to the actual positions of the particles, are added to the state description in
order to deal with “particles with spin.” Spin is merely in the wave
function as a symmetry of its dynamics. At the same time, as just said, “spin measurements” are completely clear in deBB and merely reflect the way spinor wavefunctions are incorporated (via the guidance equation) into a description of the motion of the particle configurations. Moreover, because the particle configurations corresponding to spin up and down are determined by the spinor-valued wavefunction, it is obvious that the statistical distributions of the particles will be rho(X,t) = |psi(X,t)|^2, and thus match the statistical predictions of the standard QM theory (indeed this is obvious from the fact that they share the same quantum continuity equation!).
You mentioned that deBB assumes the position, X, is privileged as the only ontological property, while others such as "spin" or "energy" or "momentum" are not. Close, but not quite there. Momentum measurements do obtain the asymptotically deBB particle velocities. Thus, the only properties of the deBB particle are its *position and velocity*. All other measured properties, such as "spin", are *Contextual* (meaning the property corresponding to spin "up" or "down" depends on the measurement interaction in the experiment, and is not a pre-existing property of the system) in the standard QM measurement theory language; moreover, it is precisely this Contextuality in deBB that allows it to easily circumvent no-go theorems for nonlocal "hidden-variables" like Kochen-Specker.
Also, you present this example below as a "preemptive" attempt to argue that not all experiments can be reduced to position measurements:
<< I can design gadgets that either absorb or not absorb the electron depending on its j_z. So they measure j_z directly. deBB theories of all kinds will inevitably fail, not being able to predict that with some probability, the electron is absorbed, and with others, they're not. >>
What you (surprisingly) fail to realize is that the absorption of the election by your gadget is reducible to a position measurement in itself, and is therefore easily subsumed in the analysis I presented above. And again, you also have to take into account the measurement interaction, in the prediction of what spin value will be observed. Once you take into account the measurement apparatus, deBB theories easily predicts (depending on the initial particle positions), through the guidance equation, what particle configurations will correspond to what particular "spin" value via the analysis above. Moreover, because the guidance equation just specifies the current velocity in the quantum continuity equation, it is ensured that the statistical distribution for the particle configurations will be |psi(x,t)|^2, and thus guaranteed to match the standard QM statistical predictions for all times.
Finally, just so we're clear, are you familiar with the "measurement problem/paradox"? If you claim so, please briefly tell us what your understanding of it is. The reason I ask you to do this is because I am not yet convinced that you understand the measurement problem, and because the main point of deBB theory is to solve the measurement problem (which it does) by removing operationally and mathematically vague postulates about "measurements" and "observables" in the textbook QM formalism, or even the standard Copenhagen interpretation of it, and replacing them with a clear ontology for the outcomes of experiments, and a mathematically precise equation of motion for that ontology that does not require ad-hoc and anthropocentric notions of "wavefunction collapse". This is probably the best way for most physicists like yourself to appreciate the utility of the deBB theory.
Best wishes,
Maaneli
Dear Lubos,
Thanks for at least replying promptly this time.
Indeed I understand the basics of standard QM quite well thank you. But you don't seem to realize that I am not primarily talking about standard QM here, but a different theory, called de Broglie-Bohm theory, which you first have to understood *on its own terms*, before you start comparing it to standard QM. For this reason, I will present you with an account of the Stern-Gerlach (SG) experiment from the POV of deBB, and thus answer your question of how discrete spin measurements can be possible in the theory (which is a fine question on its own), and at the same time dispel the other false characterizations you make of the theory.
As I mentioned before, the Pauli wavefunction that defines the particle guidance equation (in the spin-1/2 case) is a spinor of the form psi(x) = [psi_1(x), psi_2(x)], which gets mixed under rotations according to the action on it by the Pauli matrices sigma = (sigma_x,sigma_y,sigma_z). The wavefunction now satisfies the Pauli equation with the Pauli term, sigma*B, in the Hamiltonian, which represents the coupling of the spin with an external magnetic field. Focus now on a SG "measurement" of M = sigma_z. An inhomogeneous
magnetic field is established in a neighborhood of the origin, by means of a suitable arrangement of magnets. This magnetic field is effectively oriented in the positive z-direction, and is increasing in this direction. Also assume that the arrangement is invariant under translations in the x-direction, i.e., that the geometry of the setup doesn't depend on x-coordinate. An electron, with a fairly definite momentum, is directed towards the origin along the negative y-axis. Its passage through the inhomogeneous B field then generates a vertical deflection of its spinor-valued wavefunction away from the y-axis, which for deBB leads to a similar deflection of the particle's trajectory. More precisely, if the wavefunction were initially an eigenstate of sigma_z, of eigenvalue +1 or -1, or
psi = |up>*phi_0
or psi = |down>*phi_0,
where |up> = (1,0) and |down> = (0,1),
then the deflection would be in the positive (or negative) z-direction, by a rather definite angle. For a more general initial wavefunction, passage through the B field will, by linearity, split the wave function into an upward deflected piece (proportional to |up>) and a downward deflected piece (proportional to |down>), with corresponding deflections of
the possible particle trajectories.
The outcome is registered by detectors placed in the way of these two electron “beams.” Thus,
of the four possible outcomes (i.e. “pointer positions”), we have a) the occurrence of no detection defines the null output, b) simultaneous detection is irrelevant (since it doesn't occur if the experiment is performed 1 particle at a time), and c) the two relevant outcomes corresponding to registration by either the upper or the lower detector.
Thus, the calibrated outcomes for a measurement of z is s_up = 1 and s_down = −1, while for a measurement of the z-component of the spin angular momentum itself the calibrated outcomes is the product of s_up and s_down by hbar/2.
Note that in deBB, one can completely understand whats going on in this SG experiment without invoking any additional property of the electron, (i.e., its "actual" z-component of spin that is revealed in the experiment). As John Bell pointed out (read his book "Speakable and Unspeakable in QM" where he presents an elegant discussion of the deBB theory and accurately treats the SG experiment from the deBB POV), unlike position, spin is not primitive, meaning no actual discrete degrees of freedom analogous to the actual positions of the particles, are added to the state description in
order to deal with “particles with spin.” Spin is merely in the wave
function as a symmetry of its dynamics. At the same time, as just said, “spin measurements” are completely clear in deBB and merely reflect the way spinor wavefunctions are incorporated (via the guidance equation) into a description of the motion of the particle configurations. Moreover, because the particle configurations corresponding to spin up and down are determined by the spinor-valued wavefunction, it is obvious that the statistical distributions of the particles will be rho(X,t) = |psi(X,t)|^2, and thus match the statistical predictions of the standard QM theory (indeed this is obvious from the fact that they share the same quantum continuity equation!).
You mentioned that deBB assumes the position, X, is privileged as the only ontological property, while others such as "spin" or "energy" or "momentum" are not. Close, but not quite there. Momentum measurements do obtain the asymptotically deBB particle velocities. Thus, the only properties of the deBB particle are its *position and velocity*. All other measured properties, such as "spin", are *Contextual* (meaning the property corresponding to spin "up" or "down" depends on the measurement interaction in the experiment, and is not a pre-existing property of the system) in the standard QM measurement theory language; moreover, it is precisely this Contextuality in deBB that allows it to easily circumvent no-go theorems for nonlocal "hidden-variables" like Kochen-Specker.
Also, you present this example below as a "preemptive" attempt to argue that not all experiments can be reduced to position measurements:
<< I can design gadgets that either absorb or not absorb the electron depending on its j_z. So they measure j_z directly. deBB theories of all kinds will inevitably fail, not being able to predict that with some probability, the electron is absorbed, and with others, they're not. >>
What you (surprisingly) fail to realize is that the absorption of the election by your gadget is reducible to a position measurement in itself, and is therefore easily subsumed in the analysis I presented above. And again, you also have to take into account the measurement interaction, in the prediction of what spin value will be observed. Once you take into account the measurement apparatus, deBB theories easily predicts (depending on the initial particle positions), through the guidance equation, what particle configurations will correspond to what particular "spin" value via the analysis above. Moreover, because the guidance equation just specifies the current velocity in the quantum continuity equation, it is ensured that the statistical distribution for the particle configurations will be |psi(x,t)|^2, and thus guaranteed to match the standard QM statistical predictions for all times.
Finally, just so we're clear, are you familiar with the "measurement problem/paradox"? If you claim so, please briefly tell us what your understanding of it is. The reason I ask you to do this is because I am not yet convinced that you understand the measurement problem, and because the main point of deBB theory is to solve the measurement problem (which it does) by removing operationally and mathematically vague postulates about "measurements" and "observables" in the textbook QM formalism, or even the standard Copenhagen interpretation of it, and replacing them with a clear ontology for the outcomes of experiments, and a mathematically precise equation of motion for that ontology that does not require ad-hoc and anthropocentric notions of "wavefunction collapse". This is probably the best way for most physicists like yourself to appreciate the utility of the deBB theory.
Best wishes,
Maaneli
Dear Maaneli, if the requirement that we should understand your pet theory "on its own terms" means that we should forget what we know about QM, then sorry, I won't be doing that.
QM describes all phenomena that have been observed and it is surely possible to look at every new theory as a specific modification of QM and discuss whether the specific features where you modify QM are correct or incorrect, natural or unnatural, predictive or unpredictive, consistent or inconsistent.
You're clearly not doing it. Instead, you are trying to impress others with Pauli's equation or Dirac's equation and link them with your pet theory. But your pet theory has nothing to do with the important equations of physics per se. These are equations that belong to the essential toolbox of the canonical quantum mechanics, and you are just giving all these objects and equations wrong, unnatural, and inconsistent interpretations that would be unpredictive (beyond QM) even if they were consistent.
I can read a popular book by a John Bell but that won't change the fact that the things you write about the spin being radically different from the position, not being "primitive", and so on are complete nonsense a deep misunderstanding of physics.
Spin is as "primitive" as the position, both of them can be effectively discrete or effectively continuous in various contexts, both of them carry the information, both of them can be measured, both of them are associated with probability amplitudes for various outcomes. In fact, there are even dualities between the spin and the position-like degrees of freedom. They can also transform to one another: if the spin of a large atom becomes large, this degree of freedom can be reinterpreted as a function of the positions of electrons inside it. It's simply not true that one can be "primitive" while the other is "nonprimitive".
Every approach that treats the spin and the position as qualitatively different things ontologically is manifestly wrong.
Once again, it is simply not true that every measurement of the spin must reduce to a measurement of the position (or velocity). You try to pretend that you don't hear this important fact, and instead, you continue to generate your 17th century pseudoscience that contradicts this fact.
To give you another manifest example showing very explicitly how much wrong you are, let me mention that all of quantum mechanics, including x,p observables, can be emulated, with any accuracy, by a quantum computer that contains nothing else than spins (qubits). It is manifest that if you won't have any "classical" degrees of freedom associated with these qubits, there will never be anything behaving classically in your pet theory.
The only thing how position (and/or momentum) is privileged is that they're usually the degrees of freedom that describe the states that decohere from each other. But that's not true in general. One must actually compute the rates of decoherence to see which degrees of freedom want to behave classically and which microstates decohere. For example, in my quantum computer that emulates the external world, it is the observables that mimick "x" and "p" - even though they're constructed out of spins - that decohere.
Your pet theory is simply unable to describe any spin-dependent process, the probability of absorption of a particle as a function of its spin, and so forth, even though such things are actually essential in the physics of spin. But even if you were unable to see that your theory is wrong, you should be - Jesus Christ - able to see that your theory is extremely unnatural if it gives totally different interpretations to randomly chosen subsets of observables that are treated in the same qualitative way in orthodox quantum mechanics.
Spin, position, and velocity are just three examples of observables, three examples of operators that have their eigenvalues with different probability amplitudes, and these things can be predicted. Can't you see that you're clearly doing something wrong if you say that some of them are "primitive" while others are not?
If x,v are primitive, the orbital angular momentum is associated with a "really existing" classical variable in your pet theory, too. Agreed? But the spin is not, agreed? But the spin is nothing else than another term in the total angular momentum, and the separation of the total angular momentum into these two parts actually depends on the effective theory we take.
The effective theory of the hydrogen atom may treat all of its angular momentum as internal discrete spin. But a description in terms of protons and electrons treats a major term in the angular momentum as a result of the orbital motion, the "x cross p" expression. Can't you see that there simply can't be any "universal" segregation of these angular momenta into the real "primitive" ones and some "invisible ones" that must reduce to the primitive ones?
The more microscopic description one takes, the higher part of the angular momentum is described in the orbital-like way. For example, the spin of massive particles (at the string scale) comes from the internal vibrations of the strings, so it gets reduced to the "orbital" rules. (Let me emphasize, in advance, that in this setup, it is irrelevant whether string theory is the right theory of this world; what matters and is sufficient here is that it is a consistent theory of observed-like phenomena).
On the other hand, for a chemist, all atoms are indivisible and all of their angular momenta are discrete spins. Do you think you can still argue that these spins don't exist "separately" from someone's positions and velocities? It is absurd.
The electron might be too confusing for you and you might think that the failure of your theory is OK because the spinors are hard. Why don't you try photons? Photons also carry helicity - spin with respect to the direction of motion. It is possible to design polarizers that absorb x-polarized photons but not y-polarized ones. Is the x-polarization primitive or not? Is the left-handed/right-handed polarization primitive? I could add all these questions but whatever segregation into two groups you make, it's trivial to show the segregation can't survive basic physical processes. The observables that you consider "primitive" are often directly evolving, transforming, or are dual to observables that you consider "nonprimitive". Any separation of physics into these two groups is manifest shit, a rudimentary misunderstanding of some rules of QM that have been firmly established by experiments.
Best wishes
Lubos
Dear Lubos,
<< if the requirement that we should understand your pet theory "on its own terms" means that we should forget what we know about QM, then sorry, I won't be doing that. >>
1) It's not my "pet theory" anymore than textbook QM is your pet theory. It's originators and leading proponents, I'll remind you ,were Louis de Broglie, David Bohm, and John Bell. I bet you didn't know that about Bell or that the nonlocality in deBB theory is what got him thinking about how to quantify QM nonlocality and construct his famous theorem named after him. I bet you also didn't know that deBB theory is what led Bell to consider the basic possibility of quantum computing.
2) The point (which any intellectually fair person would do) is to develop a basic enough understand of the theory you are criticizing and insulting before criticizing and insulting it. You clearly haven't spared the time to do this; instead, it sounds like all you've done is had random conversations with your colleagues and people you don't like about the deBB theory, and think that's enough to know about it, because you're "too cool for school" to actually pick up a book or review article and be patient enough to read through it on your own. Yeah, imagine if someone were to criticize string and M theory based on that same amount of laziness.
<< QM describes all phenomena that have been observed and it is surely possible to look at every new theory as a specific modification of QM and discuss whether the specific features where you modify QM are correct or incorrect, natural or unnatural, predictive or unpredictive, consistent or inconsistent. >>
Indeed, and this is not at all in contradiction with what I said.
<< You're clearly not doing it. Instead, you are trying to impress others with Pauli's equation or Dirac's equation and link them with your pet theory. But your pet theory has nothing to do with the important equations of physics per se. >>
Sorry, you're just plain wrong. Or more precisely, you are in denial. Just so you know, those equations (as well as the Schroedinger and Klein-Gordon equations) have an equivalent representation in the Hamilton-Jacobi-Madelung form (which are the Euler equations for a quantized, nonlocal fluid), and there you have a very natural justification for the deBB ontology, as Bohm and de Broglie pointed out in their first papers.
<< These are equations that belong to the essential toolbox of the canonical quantum mechanics, and you are just giving all these objects and equations wrong, unnatural, and inconsistent interpretations that would be unpredictive (beyond QM) even if they were consistent. >>
Indeed those equations are essential to the toolbox of standard QM and other interpretations and formulations of QM. But you're just plain wrong to claim the deBB use of them are somehow inconsistent; and I pretty much debunked that notion in my previous post.
<< I can read a popular book by a John Bell but that won't change the fact that the things you write about the spin being radically different from the position, not being "primitive", and so on are complete nonsense a deep misunderstanding of physics. >>
1) That book by John Bell is a collection of all his published and unpublished technical writings on the foundations of quantum mechanics and field theory.
2) You still are conflating the textbook QM formalism with the deBB formalism. They are quite different theories in terms of how they explain the quantum world, and you still fail to appreciate that.
<< Spin is as "primitive" as the position, both of them can be effectively discrete or effectively continuous in various contexts, both of them carry the information, both of them can be measured, both of them are associated with probability amplitudes for various outcomes. In fact, there are even dualities between the spin and the position-like degrees of freedom. They can also transform to one another: if the spin of a large atom becomes large, this degree of freedom can be reinterpreted as a function of the positions of electrons inside it. It's simply not true that one can be "primitive" while the other is "nonprimitive". >>
Those mathematical transformations do indeed exist in *between* "measurement" events in the textbook QM formalism. But what you're not appreciating is that decoherent measurement interactions do in fact privilege position over spin (your speak of probability amplitudes from spin and position degrees of freedom is irrelevant because it doesn't specify a theory of measurement processes). Indeed, this is a *basic* result of even quantum decoherence theory - that decoherent measurement interactions suggest position as a privileged observable. Indeed that's how environmental decoherence solves the *preferred basis* problem - it selects position as the preferred basis, and it guarantees its
uniqueness via the tridecompositional uniqueness theorem. If you're unfamiliar with the basic quantum decoherence description of measurement interactions (and it sounds like you are), let me suggest an introductory reference by one of the leaders in the field:
Decoherence, the measurement problem, and interpretations of quantum mechanics
Authors: Maximilian Schlosshauer
Journal reference: Rev.Mod.Phys.76:1267-1305,2004
http://arxiv.org/abs/quant-ph/0312059
See section 3 titled "Implications for the preferred basis problem" on page 14. Also see section 4 titled "Pointer basis vs instantaneous Schmidt states". So you see, any consistent theory of measurement (and deBB theory naturally incorporates decoherence theory on its wavefunctions) already privileges a position basis. This is even so when you combine quantum decoherence theory with the textbook QM formalism. DeBB differs from decoherence theory only in that the former assumes there is a literal particle that picks out a particular eigenstate branch as the experimentally observed one and explains why position is the preferred basis, while the latter only takes all the highly localized eigenstate branches to explain why position is the preferred basis (but decoherence then has the problem of explaining why we only see one eigenstate in an experiment as opposed to another, and for this reason it is not alone sufficient to solve this aspect of the measurement problem called *the problem of definite outcomes*).
<< Once again, it is simply not true that every measurement of the spin must reduce to a measurement of the position (or velocity). You try to pretend that you don't hear this important fact, and instead, you continue to generate your 17th century pseudoscience that contradicts this fact. >>
Once again, it simply IS true that every measurement of the spin must reduce to a measurement of the position (or velocity). You try to pretend that you don't hear this important fact, and instead, you continue to generate your 17th century pseudoscience that contradicts this fact.
<< The only thing how position (and/or momentum) is privileged is that they're usually the degrees of freedom that describe the states that decohere from each other. But that's not true in general. One must actually compute the rates of decoherence to see which degrees of freedom want to behave classically and which microstates decohere. For example, in my quantum computer that emulates the external world, it is the observables that mimick "x" and "p" - even though they're constructed out of spins - that decohere. >>
That's a bit of a misleading account of decoherence theory. As Schlosshauer points out, for all times greater than the characteristic timescale t_D (in fact for all physically realistic timescales, i.e. those observed in real experiments), the position basis will come to be preferred by the rapid diagonality of the reduced density matrix. Read the Schlosshauer paper above.
<< Your pet theory is simply unable to describe any spin-dependent process, the probability of absorption of a particle as a function of its spin, and so forth, even though such things are actually essential in the physics of spin. >>
So I guess you just chose to ignore role of the Pauli wavefunction in the mathematics of the guidance equation. It also sounds like you didn't closely read the Stern-Gerlach example in my previous post. Well then what can I say.
<< But even if you were unable to see that your theory is wrong, you should be - Jesus Christ - able to see that your theory is extremely unnatural if it gives totally different interpretations to randomly chosen subsets of observables that are treated in the same qualitative way in orthodox quantum mechanics. >>
1) Jesus Christ never existed.
2) The deBB theory is quite self-consistent and empirically equivalent to the standard textbook QM, and its assumption of position as the preferred basis is supported by the insights of decoherence theory, and its particle ontology yields the mathematically simplest solution to the problem of definite outcomes. Also, the Madelung representations of all the quantum wave equations naturally suggest a deBB particle ontology, coupled with the fact that all we see in real physical experiments are scintillation points on detectors, i.e. particles!
<< The effective theory of the hydrogen atom may treat all of its angular momentum as internal discrete spin. But a description in terms of protons and electrons treats a major term in the angular momentum as a result of the orbital motion, the "x cross p" expression. Can't you see that there simply can't be any "universal" segregation of these angular momenta into the real "primitive" ones and some "invisible ones" that must reduce to the primitive ones? >>
Dude, it's really not that complicated. Just look at the damn equations of deBB!
<< The more microscopic description one takes, the higher part of the angular momentum is described in the orbital-like way. For example, the spin of massive particles (at the string scale) comes from the internal vibrations of the strings, so it gets reduced to the "orbital" rules. (Let me emphasize, in advance, that in this setup, it is irrelevant whether string theory is the right theory of this world; what matters and is sufficient here is that it is a consistent theory of observed-like phenomena). >>
I would like to first see you construct a string decoherence theory of measurement that does not privilege a particular pointer basis. Then we can pursue this example further. Also, it is quite possible to construct a deBB version of string theory.
<< On the other hand, for a chemist, all atoms are indivisible and all of their angular momenta are discrete spins. Do you think you can still argue that these spins don't exist "separately" from someone's positions and velocities? It is absurd. >>
Actually, most physical chemists, especially those that numerically simulate the quantum dynamics of atoms and molecules, use the deBB formalism:
LANL/CNLS Workshop on Quantum Trajectories
http://cnls.lanl.gov/qt/Agenda.html
Overview: Dynamics with Quantum Trajectories
http://cnls.lanl.gov/qt/QT_talks/wyatt_overview.pdf
Hydrodynamic Methods for Ultrafast Quantum Dynamics,
Quantum Transport, and Dissipation
http://www.math.univ-toulouse.fr/~nanolab/Contents/Invited2.pdf
(Quantum hydrodynamics (\Bohmian mechanics") [1] has recently been introduced in
molecular physics as a new type of quantum-dynamical simulation technique [2], rather
than in its previous role as a purely interpretative tool.)
<< Why don't you try photons? Photons also carry helicity - spin with respect to the direction of motion. It is possible to design polarizers that absorb x-polarized photons but not y-polarized ones. Is the x-polarization primitive or not? Is the left-handed/right-handed polarization primitive? I could add all these questions but whatever segregation into two groups you make, it's trivial to show the segregation can't survive basic physical processes. >>
I already have done this with photons. One can take the Schroedinger/Pauli equations for photons (which certainly do exist in quantum optics), and construct guiding equations for the photons in the momentum basis. And from it, one can account for polarization effects. Remember, polarization (like spin) is a property of the wavefunction, not necessarily the particle itself (although recall that I showed how spin can be incorporated as a literal degree of freedom for the particle via the NR limit of the Dirac current - but the point was that in the nonrelativistic theory, it is not necessary to do this for the sake of reproducing the experimental observations). The deBB theory tells us that we infer properties such as spin and polarization through the trajectories and experimental observations of point particles.
Best wishes,
Maaneli
Dear Maaneli, indeed, QM is "my pet theory", if you wish. But unlike you, I would never object if it were called in this playful way.
I just wrote an article about Bohmism here, so you may want to move the discussion over there.
Of course that I have always known that Bell constructed his inequalities because he wanted to prove exactly the opposite than what he proved at the end. He was unhappy until the end of his life. Bad luck. Nature doesn't care if some people can't abandon their prejudices.
I won't allow further arrogant and stupid comments of yours lying about my knowledge about your pet theory.
You must know very well that I understand both its equations, achievements, and critical bugs much more than you do (or the authors of the popular physics books - that you ludicrously try to sell as sources of scientific authority - do) so why the f*ck are you writing something else? It's just plain disgusting. You're just a stupid student who has serious trouble to understand quantum mechanics, so where does your heavenly self-confidence come from?
The Hamilton-Jacobi rewriting of the quantum equations is clearly possible but it is not terribly deep; it is only useful in the classical limit; and even in the classical limit, one must be damn careful not to interpret the objects in these equations incorrectly because the correct interpretation of all underlying terms is and must be still quantum, and every other acceptable interpretation must be a derivable approximation of quantum mechanics.
Your attempts to compare yourself to the critics of M-theory is preposterous because your pet theory is rubbish while string/M-theory is the most crucial part of the contemporary theoretical high energy physics. In fact, many of the critics of string theory - like Lee Smolin - promote the same rubbish about quantum mechanics as you do. Neither of you really understands the real world - especially its quantum aspects.
Best
Lubos
Dear Lubos,
I appreciate you putting me on the spot like that by linking my name to the article. Now I'm gonna have to worry about people I know reading this exchange, and all the subsequent flak I'll get for it. O well.
Best,
Maaneli
Forgot to add Brian Greene (of all people!) to the list of string theorist who doubt the standard interpretation of QM. In fact, Greene and his students are currently working on Bohmian field theories!
I know: we've exchanged quite a lot of e-mails about QM interpretations with Brian Greene.
Note that you always rely on sociological arguments - because sociology is on the side of the "materialist" interpretations: just the science is not.
The fact that Brian Greene is inclined to believe the Bohmian pictures doesn't remove the lethal flaws of that theory.
I'm just mentioning Brian Greene, not as an argument for the validity of deBB theory, but as an example of an eminently reasonable physicist and competent string theorist who takes the theory seriously. Most physicists will give more credence to an idea if someone they know of and respect takes it seriously too. That was all.
Interesting that you're exchanging emails with him about the theory. I'm curious what you think of his understanding of QM. ;)
<< The fact that Brian Greene is inclined to believe the Bohmian pictures doesn't remove the lethal flaws of that theory. >>
Of course, Brian Greene and I would disagree about the so-called "lethal flaws". Do you think any less of Brian Greene for his inclination to believe deBB theory?
~M
Of course I do, how could I not? Or was your question just a rhetorical question where only one answer is polite or politically correct?
I have a tremendous respect for Brian Greene - for all kinds of reasons - but of course, his incomplete understanding of the meaning of quantum mechanics contributes negatively to my respect for him.
"Most physicists will give more credence to an idea if someone they know of and respect takes it seriously too. That was all."
I am sorry but if some physicists use this group-think recipe of yours, they are not behaving as scientists and their (sociologically driven) opinion cannot be counted as a relevant independent scientific argument.
If I actually understand the science of some topic, I don't have to pay any attention to the names of those who don't understand the topic.
Of course, once again, Brian Greene doesn't quite understand all the issues that decide about the correct and incorrect interpretations of quantum mechanics.
One qualification to add in my comments. Most physicists will give further credence to an idea if someone they know of and respect takes it seriously, and if they themselves don't very much about it.
I agree with you about the sociology issue being a problem; but unfortunately I have experienced it on numerous occasions in other branches of physics.
~M
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