Ballentine's Ensemble Interpretation Of QM

[Jano L.]

Correct me if I am wrong but if electrons moved in trajectories around the nucleus, covalent bonds between atoms would be impossible and a big chunk of quantum chemistry would go out the window(e.g. H has just one electron and it's shared in the H2O molecule).

I do not understand how you can derive such conclusion. The theory of chemical bond is based on Schroedinger's equation for point-like charged particles. It is not based on rejection of existence of trajectories. Sure, it does not use the concept, but it also does not disprove it.

Covalent bond involves sharing of electrons and the probability distribution for positions is spread all over the molecule, so the natural way to imagine this is that electrons move all around the molecule, visiting randomly all the nuclei in the vicinity. Since electrons are negatively charged and with greatest probability in between the nuclei, they attract positive nuclei and keep them in some average distance despite their mutual repulsion. If some atoms are very attractive to electrons, they can leave some other atoms without the bonding electrons for long periods of time and the glueing effect of the latter may cease - hence the dissociation of polar molecules into ions that happens in solvents. I believe this is quite standard picture adopted in theoretical chemistry (see works by John Slater, David Cook, ...) It may not calculate exact trajectories, but for sure it does not disprove them either.

 

[kith]

For example, the probability for volume $\Delta V$

$$
P(\Delta V) = \int_{\Delta V} |\psi(\mathbf r, t)|^2\,dV
$$

is simply the probability that the particle is at $\Delta V$, not that "it will be measured to be in $\Delta V$".

How could an experiment distinguish between these two statements?

The SG-like experiments measuring spin projections along different axes refute such idea [...]

Why can't we apply the same logic to a measurement sequence of position, momentum, position, ... ?

 

[Ken G]

But surely a classical picture is quite clunky, because the guts of quantum mechanics is that the classical action per mode of excitation is in some sense both quantized and bounded below at h. I'd have a hard time seeing how this clearly universal principle can arise from a picture of chaotic classical buffeting by some zero-point field. Why quantized? Why always h? Maybe it can be done, but only by bending over backward, at best. Rather than reverse-engineering a classical picture to work in a domain where it is clearly not well suited, it would seem better to embrace the new picture of wave mechanics and the straightforward path to quantization that it presents.

 

[Jano L.]

How could an experiment distinguish between these two statements?

You cannot measure configuration of electronic position vectors in an atom. If you try that by light of wavelength comparable to the size of the atom, the radiation will have great immediate impact on its configuration, and the analysis of the scattered radiation is very hard. X-ray scattering study of electronic frequency density around nuclei of some molecule crystals of many such molecules to accumulate the signal, and it provides only frequency distribution averaged over these many molecules. Currently it is not possible to measure positions of electron in an individual molecule on the scale of its typical size.

The Born rule for $|\psi(\mathbf r)|^2$ used in treatment of atoms and molecules is not a rule to predict results of measurements of their configuration. It is a way to make sense of $\psi$, independently of such measurements, a very important thing since they cannot currently be performed.

Why can't we apply the same logic to a measurement sequence of position, momentum, position, ... ?

When we measure spin projection along some axis $\mathbf o$ chosen beforehand, the atoms split into two different trajectories and we label these by 1/2, -1/2. These two trajectories depend on the axis $\mathbf o$ chosen, so also the resulting value $\sigma =1/2$ or $\sigma=-1/2$ refers to this axis; it has no meaning without it. The actually measured value of projection $\sigma$ refers to the axis $\mathbf o$ and thus could not have existed in the atom before this axis was chosen.

This kind of reasoning does not apply in the case of position or momentum, because their meaning does not refer to any variable setting of the measurement apparatus.

When we measure position of a particle, we let the particle impinge on a detector screen. We do not choose any variable analogous to $\mathbf o$, and the result of measurement $\mathbf r$ (center of the spot left by the particle, for example, a photo grain or charged CCD pixel) has direct meaning of position, independently of any choice in the setting of the detector screen.

We cannot rotate the axis $\mathbf o$ of the position detector, show that positions will be different and conclude that they too cannot exist before the orientation of the detector was chosen. Rotating position detector has no such effect.

In short, the position has always the same thing, irrespective of how we measure it, in contrast to spin projection, which depends on how we orient the axis of the measuring magnet.

 

[Maui]

Covalent bond involves sharing of electrons and the probability distribution for positions is spread all over the molecule, so the natural way to imagine this is that electrons move all around the molecule, visiting randomly all the nuclei in the vicinity. Since electrons are negatively charged and with greatest probability in between the nuclei, they attract positive nuclei and keep them in some average distance despite their mutual repulsion. If some atoms are very attractive to electrons, they can leave some other atoms without the bonding electrons for long periods of time and the glueing effect of the latter may cease - hence the dissociation of polar molecules into ions that happens in solvents. I believe this is quite standard picture adopted in theoretical chemistry (see works by John Slater, David Cook, ...) It may not calculate exact trajectories, but for sure it does not disprove them either.

You seem to misunderstand what I asked. In the H2o(water) molecule, each of the two H atoms has just 1 electron. That 1 electron is shared between the atoms and the only possible case where that would be plausible is when the electron is spread out over the volume of two atoms at the same time, i.e. when the electron does not sit on a trajectory(at least not a on a single trajectory). If the single electron in the H atom of the H2O molecule had a trajectory, the covalent bond would fall apart and water would turn to H and O.

 

[Sugdub]

Spoken like a true empiricist! ... Yes, this is a vivid statement of the core of empiricism-- ... The empiricist hat that you are describing so accurately seems to fit me best, but I can put on the other hat too, and see reasons and places where I might want to do that.

I'm not an empiricist, far from it, but I know and I explained the value of keeping the empiricist view as a reference for distinguishing what is true (experimentally verified irrespective of any kind of interpretation) from what is added value, genuine physics if you wish, but can only be seen as a metaphoric part of our simulation of the world, I mean something that is neither verifiable nor refutable experimentally, but can be assessed in terms of its efficiency.

That's an interesting way to frame the measurement problem, I will cogitate on it!

You are welcome. More inputs on this approach in #28 and #43 of this thread: Mathematically what causes wavefunction collapse?

 

[Jano L.]

Rather than reverse-engineering a classical picture to work in a domain where it is clearly not well suited, it would seem better to embrace the new picture of wave mechanics and the straightforward path to quantization that it presents.

That has been a reasonable approach, and it has been very successful, I know, but along the way much nonsense was invented and accepted in the outbreak of enthusiasm. After 90 years, we are still having these painful debates about what's going on down there.

We can do calculations of magnetic moment that fit the experimental value to 18 decimal places, but still have no reasonable conceptual scheme such calculation would fit it. Virtual particles are real objects to some people, and artefacts of perturbation theory to others. They cannot agree on whether the theory is about particles or fields. It involves spurious operations with infinities, which even after renormalization group does not appear as a consistent theory with no loose ends. Apparently one can do 18-decimal calculations without any solid theory at all. And smart philosophers muddled the problem with complementarity and wave-particle duality.

Meanwhile, people like Schroedinger, Jaynes, or Marshall and Boyer have shown that the quantization is often quite a superfluous operation; and explained that what was thought to be a "non-intuitive quantum phenomenon" is just something that can be predicted and described in simple terms, be it with Schroedinger equation or Maxwell's equation coupled with Newtonian equations of motion.

So I suspect that "the new picture of wave mechanics and the straightforward path to quantization that it presents" is only one possible philosophy to do physics. There are many more, one of which is the rational point of view of physics before 1905. They did not have "interpretation problems" in those days, which I suspect are also mainly communication problems. Maybe something worth considering.

Do not get me wrong - I do not claim classical physics from 19th century will finally explain everything from Maxwell's and Lorentz's equations, but I do believe its $standard~of~argument$ can help us to throw light on some basic questions, especially in situations where much of wild quantum fundamentalism gets in the way.

 

[Jano L.]

You seem to misunderstand what I asked. In the H2o(water) molecule, each of the two H atoms has just 1 electron. That 1 electron is shared between the atoms and the only possible case where that would be plausible is when the electron is spread out over the volume of two atoms at the same time, i.e. when the electron does not sit on a trajectory(at least not a on a single trajectory). If the single electron in the H atom of the H2O molecule had a trajectory, the covalent bond would fall apart and water would turn to H and O.

Well, hydrogens contribute with 2 electrons, oxygen with 8 electrons. They all move somewhere around the nuclei, and they all play the same role (the probability density is symmetric with respect to transposition of electrons). The covalent bond consist of strong correlation of the motion of the nuclei. It is maintained by the attractive force from the electrons, and has only as much stability as allowed by their motion. The stability of the bond in chemical bond theory based on Schr. equation is only probabilistic (tunnel effect...). The fact that the nuclei are close to each other does not break down immediately as some electron goes little bit farther from the hydrogen. The nuclei are very heavy and have great inertia with respect to the electrons; the hydrogen nucleus is 1836 times more heavier.

Of course, occasionally it may happen that this effect plus external forces lead to separation of hydrogen from the rest - there is some OH$^{-}$ in the water too, but there is no obvious reason why motion along trajectories should break all the molecules into collection of isolated atoms.

 

[kith]

This kind of reasoning does not apply in the case of position or momentum, because their meaning does not refer to any variable setting of the measurement apparatus.

What's wrong with a measurement apparatus which contains a rotatable axis with the settings "position" (e.g. a CCD) and "momentum" (e.g. an electromagnetic calorimeter)?

I think this is mainly a question of terminology and not necessarily a fundamental difference between position / momentum and spin x / spin y. It becomes fundamental only if you make the assumption that position is always well-defined while other observables are contextual. This is a matter of taste. I think I prefer Bohr's view that all observables get their meaning from the context of their measurements.

 

[Ken G]

Bernard d’Espagnat (in his book "on Physics and Philosophy") seems to forcefully describe the ensemble theory as requiring the existence of hidden variables.

I get the impression this issue relates to how the meaning of the "ensemble theory" has evolved. bhobba pointed out that Ballentine had to backtrack a bit on his original views of the ensemble theory, when it became clear that imagining the quantum system already had certain attributes prior to the interaction with the macro apparatus was untenable for his project. So perhaps we can say that the "ensemble theory" is a hidden variables theory, so sounds a lot like deBroglie-Bohm, but the "ensemble interpretation" is merely a language for attributing meaning to "the probability that preparation X leads to measurement Y," which takes the perspective that the way to attribute that meaning is to take a frequentist interpretation of the meaning of probability (as outlined in bhobba's posts). I think bhobba makes a good case that the ensemble interpretation of QM is more or less equivalent to the frequentist interpretation of a probability, the defining feature of which is that a probability really only takes on semantic meaning when considered in the context of an ensemble. Presumably this comes with an attitude that a "subjective sense" of the magnitude of a probability in an individual outcome really has no independent meaning from imagining you could repeat the experience many times, and select any individual outcome randomly from that set.

To me this has the same flavor of much of quantum statistical mechanics, in which a probability of a given outcome requires enumerating a large set of possibilities, each equally likely, from which the given outcome is selected. In that sense, the only probability that has meaning independently from an ensemble is a concept of "equally likely" (or "equally weighted" if we wish to avoid "likeliness" issues that could lead to circularity). Once that concept is obtained, which is more or less a symmetry principle, all other probability concepts are about measures within ensembles. An interesting point that arises, which we may not have considered enough in this discussion yet, is that physical ensembles are necessarily discrete, so a frequentist/ensemble interpretation requires thinking about probabilities in terms of discrete countings of equally-weighted possibilities, whereas more general probability measures do not embrace this discreteness requirement. I don't know what important theorems are different on a discrete set, but it may be worth attention.

 

[Jano L.]

What's wrong with a measurement apparatus which contains a rotatable axis with the settings "position" (e.g. a CCD) and "momentum" (e.g. an electromagnetic calorimeter)?

I think this is mainly a question of terminology and not necessarily a fundamental difference between position / momentum and spin x / spin y. It becomes fundamental only if you make the assumption that position is always well-defined while other observables are contextual. This is a matter of taste. I think I prefer Bohr's view that all observables get their meaning from the context of their measurements.

Please read my explanation more carefully, I tried hard to explain it and think I did get the main point there. The conclusion from spin projection measurements is that the spin projection does not have meaning independent of the choice of the measurement axis. In the case of position, there is no such experiment and no such conclusion.

There is one version of wave mechanics, called Bohmian mechanics, where the particles move along trajectories derived from $\psi$. It is generally acknowledged that that theory reproduces the same predictions as theory where there are no trajectories. I do not think the trajectories are that simple as those in the Bohmian mechanics, but they are viable and useful alternative to the fuzzy Copenhagen view.

Of course, if you use the word observable, you have to use the word measurement. However consider that nobody ever measured position of electron to verify Schroedinger wave functions for atoms and molecules. It is not currently possible to do such measurements. There are some simple diffraction experiments on larger scale, but neither these prove electrons acquire positions only as a result of doing the measurement. Such conception creates much confusion - if electron localized only through the measurement, how does it come about that it localizes to such a small region where it does? What mechanism collapses its wave function? And similar stuff. This should have never been introduced. Electrons are assumed point-like particles in Schr. equation, the function $\psi$ is not point-like, and does not collapse to point nor to a region smaller than the atom.

It is very tempting to throw spin and position in one bag, but it is a temptation one should resist to get at the faithful description of things.

 

[Ken G]

So I suspect that "the new picture of wave mechanics and the straightforward path to quantization that it presents" is only one possible philosophy to do physics. There are many more, one of which is the rational point of view of physics before 1905. They did not have "interpretation problems" in those days, which I suspect are also mainly communication problems.

I'm not sure they didn't have interpretation problems-- maybe they just didn't get the same press, or have been forgotten. We tend to teach our students that a trajectory is a perfectly clear and natural thing for a particle to follow, but wave mechanics is weird and open to interpretation. I don't think that's really true-- a particle following a trajectory is just as inscrutable as a particle being told what to do in a statistical way by a wave. The inscrutability of a trajectory centers on the question, how does the particle know to keep doing what it was doing before, when no forces act on it? Relativity shows us that the momentum of a particle is probably not an attribute of the particle, it is more like, rationalistically, a property of the context with which we, the physicists, are conceptualizing that particle, and empirically, a property of the reference frame of the measuring apparatus. But if the momentum of a particle is not an attribute of the particle, how can we treat it like an attribute of the particle when we do classical physics? We were always kind of lying to ourselves when we imagined that a particle can follow a trajectory, since the concept of a trajectory must be embedded in a richer interpretative matrix being imposed by the reference frame of the observer, and indeed the very conceptualization of the physicist. In brief, classical physics already had a "measurement problem," it just chose to ignore it. And like all measurement problems, it stemmed from the same source-- physics has no idea how to include the physicist.

Do not get me wrong - I do not claim classical physics from 19th century will finally explain everything from Maxwell's and Lorentz's equations, but I do believe its $standard~of~argument$ can help us to throw light on some basic questions, especially in situations where much of wild quantum fundamentalism gets in the way.

And I can agree that completely rejecting the classical picture may not be advisable either, since it does speak more closely to our daily intuition. I am a generalist, who says, let's look at the lessons that the successes and failures of any and all interpretations have to teach us. So I think it is a good addition to the conversation to talk about what classical interpretations can still do. But I don't ascribe to the view that just because something is closer to our daily experience, it presents us with a more plausible account of happenings we do not experience.

 

[Jano L.]

... Relativity shows us that the momentum of a particle is probably not an attribute of the particle, it is more like, rationalistically, a property of the context with which we, the physicists, are conceptualizing that particle, and empirically, a property of the reference frame of the measuring apparatus. But if the momentum of a particle is not an attribute of the particle, how can we treat it like an attribute of the particle when we do classical physics? We were always kind of lying to ourselves when we imagined that a particle can follow a trajectory, since the concept of a trajectory must be embedded in a richer interpretative matrix being imposed by the reference frame of the observer, and indeed the very conceptualization of the physicist.
In brief, classical physics already had a "measurement problem," it just chose to ignore it. And like all measurement problems, it stemmed from the same source-- physics has no idea how to include the physicist.

I am not sure I see the problem you refer to. The trajectory in mechanics in calculations is eventually always talked about in terms of some concrete reference body, although the latter is not always explicitly stated. In different r.f., we have different trajectories.

Planck has a good account of the role of physicist in physics, in his Columbia lectures. Initially, physics was about what our senses and organs told us. We have ears - physics of hearing, acoustics. Eyes - physics of vision and light. Heat receptors - physics of heat and temperature. Muscles - mechanics.

But as the science evolved, the physicist as basic object played lower and lower role in it. As the mathematics and theory developed, the effort of most scientists was rather in the direction of finding non-subjective knowledge, to clean science of subjective and antropomorphic aspects. And that is a good thing ! Modern description of mechanics or electromagnetic theory has no need for the concepts of observers or measurements, on the basic level. True, to explain the stuff to students, these words are useful, but the goal we strive in CM and EM courses is a formulation that is not dependent on them.

 

[kith]

Please read my explanation more carefully, I tried hard to explain it and think I did get the main point there. The conclusion from spin projection measurements is that the spin projection does not have meaning independent of the choice of the measurement axis. In the case of position, there is no such experiment and no such conclusion.

I appreciate your effort and I think I understand quite well what you are saying. But I don't agree. To me, two orthogonal spin axes correspond to two different measurement apparatuses of conjugated observables just like a position and a momentum measurement apparatus. It is not clear why the fact that we can go from spin x to spin y by a rotation of the measurement apparatus implies that position is not contextual. As I already said I can also build an apparatus where a rotation takes us from a position to a momentum measurement.

However, I think my statement that observables get their meaning only from measurements was probably too strong. If we have a cold gas, most of the atoms are in the ground state where the electrons are localized quite well near the nucleus. I agree that this makes position special in a sense. But this doesn't imply that we have to assign this special role to position via an additional assumption. It is the interactions in the system which lead to this. IIRC, Zurek related decoherence in the position basis to the Coulomb potential.

 

[kith]

But as the science evolved, the physicist as basic object played lower and lower role in it. As the mathematics and theory developed, the effort of most scientists was rather in the direction of finding non-subjective knowledge, to clean science of subjective and antropomorphic aspects.

It is not self-evident that science can remove the observer from the scene because all knowledge is derived from interactions between the observer and the system. True, it works in CM but I think QM shows exactly the limit of this approach. Interacting entities become entangled which means that the full state cannot be separated into a state of the system and a state of the observer. There are a number of reformulations of this but none of them can get around the fact that the observed outcome is not uniquely determined by the observable state of the system.

 

[bhobba]

How is the interpretation of the quantum state as an ensemble at an arbitrary later time t dependent on a (future) measurement context?

The interpretation does not address how - it just is. The state is not given an interpretation except in measurement context - that's it - that's all. At the time of observation - but at no other time - the interpretation assumes an element of a conceptual ensemble of observational outcomes and state is selected. The ensemble is state and measurement apparatus so it does not even make sense in that interpretation to give a state an interpretation otherwise.

Now we are getting into why I prefer the ensemble interpretation with decoherence - it explains why its only given meaning in measurement context, and indeed exactly what a measurement is - its when decoherence has occurred. For example a few stray photons from the CBMR is enough to decohere a dust particle and give it a definite position (yes I know its a bit more complex than that) so we can say that, and many many similar things, have properties independent of an actual measurement with a device.

Thanks
Bill

 

[Jano L.]

What's wrong with a measurement apparatus which contains a rotatable axis with the settings "position" (e.g. a CCD) and "momentum" (e.g. an electromagnetic calorimeter)?

Aha, now I see your point kith. Sorry for the quick-and-loose answer above. I'll try to explain better what I think:

In the case of spin projection, we know that for any pure spin ket $|S\rangle$ there is exactly one direction in space $\mathbf o_S$ such that when the SG magnet is oriented to measure spin projection along it, we will obtain the projection $+1/2$ with probability 1. This characterization makes it quite plausible that when prepared into spin state $|S\rangle$, the atom has inner angular momentum vector $\hbar/2 \mathbf o_S$.

If that is the case, the inner angular momentum vector cannot point along any other direction $\mathbf o'$.


Question: Could angular momentum projections along other directions $\mathbf o'$ be determined for such system before their measurement by their appropriate SG magnet ?


It seems that such determination for all directions $\mathbf o'$ would amount to description via a strange discontinuous function defined on the sphere with function values $+1/2,-1/2$, plus the ludicrous problem what does it mean that angular momentum vector is $\hbar/2 \mathbf o_S$ and yet its projections along the other axes $\mathbf o'$ are again of the same magnitude $\hbar/2$.

So I think the most reasonable answer is: no, the angular momentum projections along other axes are not part of the atomic state prior their measurement. The only angular momentum projection that allows natural presence prior its measurement is that inferred from $|S\rangle$, that is the projection along $\mathbf o_S$.

For those other directions $\mathbf o'$, surely it is the process of measurement who creates the observed scatter of values from $+1/2,-1/2$.

Now, why is this any different from the measurement of position/momentum?


The difference is, that in the case of position or momentum measurement, there is no wave function $\psi(\mathbf r)$ that would be equivalent to $|S\rangle$ in the sense that upon measurement of position(or momentum) we would get the same value $\mathbf r_\psi (\mathbf p_\psi)$ with certainty. There is no way to attach position $\mathbf r_\psi$ to the wave function $\psi$ analogously to how we attached angular momentum vector $\hbar/2 \mathbf o_S$ to the spin ket $|S\rangle$. There will always be some spread in the wave function, so we expect (and should get) scattered positions of positions / momenta for any $\psi$, due to continuous nature of quantities like position or momentum.

This prevents us to identify a position $\mathbf r_\psi$ with the wave function $\psi$ and derive non-presence of $\mathbf r'$ from the exclusive presence of $\mathbf r_{\psi}$.
​

In short: the ability to prepare definite spin states allows us to make the presence of other spin projections prior their measurement implausible. But the non-existence of definite position/momentum centred $\psi$ functions prevents us from doing the same for position/momentum.


OK, I admit the argument is bit difficult and has some debatable parts, but at least I managed to write it down:-) What do you think ?

 

[Ken G]

I am not sure I see the problem you refer to. The trajectory in mechanics in calculations is eventually always talked about in terms of some concrete reference body, although the latter is not always explicitly stated. In different r.f., we have different trajectories.

But that's the problem. No particle has "a" trajectory, nor can the laws of physics by themselves explain any trajectory we would perceive. The laws only explain part of what we observe. Classical physics only provides the mappings between some initial and final conditions, separated by some proper time, and all that information is completely observer independent, but not the initial and final conditions themselves. The evolutionary "guts" have no measurement problem, the measurement problem appears because no physical law can say why the initial conditions (and by association, final conditions) are what they are, all we can "explain" is the observer-independent piece. Since the preparation of all systems are always observer dependent (there is no observer-independent way to say how a system is prepared), preparation involves measurement in ways that appears in no physical theory whatsoever.

Similarly, in quantum mechanics, all we get to explain is the evolution of the observer-independent part, but the outcome of any particular observation is dependent on the preparation in ways we can never explain, we have to actually generate it with a fundamentally inscrutable observing apparatus to say that we have prepared it such-and-such. In a deBroglie-Bohm interpretation, that's where all the indeterminacy comes in, in other interpretations QM adds additional uncertainties in the outcome of the measurement that an observer perceives which cannot be explained within the theory. But it's not that big a deal to add unexplainable observer-dependent aspects to something which is already not explainable in an observer-independent way!

But as the science evolved, the physicist as basic object played lower and lower role in it.

Perhaps that is true of the observer's physical apparatuses, but it leaves out the most important observer-dependent function of all-- our brains. Our brains do crucial things like declare "the initial preparation is such-and-such," a step that cannot be done without in any brand of physics. Sure the preparation itself can happen without this step, but we are not talking about what happens, we are talking about how physics explains what happens. You always at least need to say "let the initial preparation be X", or you can't account for what happens next. The very act of saying that already invokes a measurement problem, and indeed deBroglie-Bohm doesn't invoke any other measurement problems (indeed my criticism of deBroglie-Bohm has always been that it does not actually get rid of the measurement problem, it just pushes it "out of view.").

Modern description of mechanics or electromagnetic theory has no need for the concepts of observers or measurements, on the basic level.

That is exactly the claim that I do not think is congruent with the facts of doing physics.

 

[kith]

The interpretation does not address how - it just is. The state is not given an interpretation except in measurement context - that's it - that's all. At the time of observation - but at no other time - the interpretation assumes an element of a conceptual ensemble of observational outcomes and state is selected. The ensemble is state and measurement apparatus so it does not even make sense in that interpretation to give a state an interpretation otherwise.

That's not how I read Ballentine's book. Sure, he says he uses the ensemble interpretation because in measurements, superpositions get amplified into the macroscopic domain which is a problem for single system interpretations. But this is just the reason why he interprets the quantum state the way he does. It doesn't limit the interpretation to measurements.

 

[kith]

Aha, now I see your point kith. Sorry for the quick-and-loose answer above.

No offense taken. ;-)

Your argument raises an interesting point. |S> is a state of definite spin wrt the spin operator in direction of o_S. For a wavepacket ψ(x), we can construct analoguous observables mathematically. If ψ(x) is an eigenfunction of a self-adjoint operator A, our system is in a definite state wrt to A.

We can for example imagine a wavepacket observable (WO) whose eigenfunctions are wavepackets with intermediate spread in both position and momentum space. We can also consider a family of such observables which reaches from a WO with very sharply localized wavepackets in position space over a WO with intermediately localized wavepackets to a WO with sharply localized wavepackets in momentum space. So we have kind of a gradual transition from the position to the momentum operator. This is very similar to the gradual rotation of the spin operator from the x- to the y-direction.

The question is, can we construct the measurement apparatuses which correspond to these WOs? The eigenstates of an observable need to be stable wrt the interactions between the system and its environment. If Zurek is right with his connection between the position basis and the Coulomb potential, it might well be the case that we can't construct these measurement apparatuses. But this difference between spin and position/momentum would not be a fundamental difference but a result of the dynamics.

 

[Maui]

Well, hydrogens contribute with 2 electrons, oxygen with 8 electrons. They all move somewhere around the nuclei, and they all play the same role (the probability density is symmetric with respect to transposition of electrons). The covalent bond consist of strong correlation of the motion of the nuclei. It is maintained by the attractive force from the electrons, and has only as much stability as allowed by their motion. The stability of the bond in chemical bond theory based on Schr. equation is only probabilistic (tunnel effect...). The fact that the nuclei are close to each other does not break down immediately as some electron goes little bit farther from the hydrogen. The nuclei are very heavy and have great inertia with respect to the electrons; the hydrogen nucleus is 1836 times more heavier.

Of course, occasionally it may happen that this effect plus external forces lead to separation of hydrogen from the rest - there is some OH$^{-}$ in the water too, but there is no obvious reason why motion along trajectories should break all the molecules into collection of isolated atoms.

Sorry, I don't see how your explanation shows that two electrons that are shared and on unique trajectories between two atoms can hold the two atoms together. The assertion that electrons follow unique trajectories(i.e. they are not in superposition of states) in atoms must be one of the wrongest claims I've read on this forum and reminds of early 20th century physics and Rutherford's model of the atom, which has been known to be wrong for a century(the paper you referenced that claims that background radiation keeps atoms from falling apart is wild speculation, not fact). There are areas where high levels of cosmic or environmental radiation are very unlikely to be found(e.g. the Earth's core) and yet the Earth is not know to have fallen apart.

 

[Ken G]

Isn't the deBroglie-Bohm interpretation of quantum mechanics, generally viewed as a successful interpretation, based on the concept of quasi-classical trajectories? Sure there's a pilot wave, instead of buffeting by EM effects, but the same basic idea of a highly chaotic trajectory that goes all over the covalent bond would seem to be an appropriate picture in the deBB-B interpretation. I think the bottom line is that clever people can always reverse-engineer an interpretation that allows them to continue to hold whatever basic picture they like best, and it usually ends up being something of a matter of taste.

 

[Maui]

The Bohmian Interpretation, may God forgive it, was a beautiful theory but it died when superpositions of states were observed.

http://physicsworld.com/cws/article/news/2010/mar/18/quantum-effect-spotted-in-a-visible-object

It was just another case(of many) of quantum weirdness overriding classical intuition. But I can understand where the motivation for fairy tales comes from.

 

[Ken G]

I have no doubt that followers of deB-B can reconcile that kind of observation, but that is a neat picture.

 

[Maui]

It seems impossible without introducing particles' clones. You must somehow detect a single particle guided by a wave in two or more places at once. So you would need additional particles, more than you would have if you actually counted them before they were isolated and cooled down. But the interpretation makes no such claims as far as I know and if it did, it would revert back to standard qm.

 

[Len M]

Planck has a good account of the role of physicist in physics, in his Columbia lectures. Initially, physics was about what our senses and organs told us. We have ears - physics of hearing, acoustics. Eyes - physics of vision and light. Heat receptors - physics of heat and temperature. Muscles - mechanics.

But as the science evolved, the physicist as basic object played lower and lower role in it. As the mathematics and theory developed, the effort of most scientists was rather in the direction of finding non-subjective knowledge, to clean science of subjective and antropomorphic aspects. And that is a good thing ! Modern description of mechanics or electromagnetic theory has no need for the concepts of observers or measurements, on the basic level. True, to explain the stuff to students, these words are useful, but the goal we strive in CM and EM courses is a formulation that is not dependent on them.

Planck I think represents an outmoded paradigm within physics, though many seem still adhere to it. This is what Walter Moore said about Planck in his book on “Schrodinger, Life and Thought”:

Max Planck belonged to a scientific generation just prior to that of Schrodinger. As a young man, his view of science was completely different from that which would prevail thirty years later. He believed the outside world is something independent from man, something absolute. He said "the quest for the laws that apply to this absolute appeared to me to be the most sublime scientific pursuit in life"

I hesitate to label you with any particular flavour of realism, though I would surmise it is close to the above quote, but that aside, whatever position you take up regarding realism I think it important to qualify that position as being a philosophical one. Perhaps you do, in which case there is nothing more to be said, other than perhaps it could be of benefit to a wider audience if this were more transparent.

However if you don’t see it as a philosophical stance but rather as a legitimate default assumption that the human can be separated from the objects of physics, then I would take issue with that. What we take as strong objectivity within the classical realm is a philosophical stance. In fact, philosophically speaking, such "strong objectivity" that we associate with classical physics may be in “appearances” only.

Essentially, all we have to work with is phenomena and if we take the bottom line of physics as being connected with measurement and observation, then that bottom line is a product of phenomena. This doesn’t detract from the physics in creating the mathematical predictive models, but to extrapolate those models to an arena that separates mind from the object departs from the legitimate “truth” of a predictive model in terms of physics proper and enters an area of enquiry that involves a philosophical stance of realism. The former takes place within empirical reality, the later takes place within a “chosen” flavour of realism. Nothing wrong with that of course as long as we all keep track of what we are doing, especially when imparting such models to a wider audience.

Everything in our reality is phenomena and the mechanisms at play within and between that phenomena are what we subject physics to, but we don’t have any scientific means (following the scientific method invoking testability) in which to investigate what lay outside of phenomena (if there is anything, idealists would say there is only phenomena). The use of mathematics still has to ultimately be referenced to phenomena if we are to label the discipline as physics. Even if the verification is not possible now, we still expect to somehow, in principle to be able to apply that mathematics to the scrutiny of observation and measurement and once we agree to that principle then we are invoking phenomena.

The above premise can be established through pure philosophy, and indeed has been by many philosophers, but the subjective elements of QM provide scientific support for this premise. Now you seem to take issue with this subjective element to some degree, though I’m not entirely sure about this, so apologies if that is not the case. In any event I certainly am unable to comment on the technicalities you invoke regarding this issue. However I have studied Bernard d’Espagnat’s writings in his books “Conceptual foundations of Quantum Mechanics” and “Veiled Reality”. The former is considered a classic and I am inclined to assume there is genuine substance to the book. It is d’Espagnat’s opinion that QM supports the view that the product of physics is empirical reality rather than a mind independent reality. He says in his book “Veiled Reality”:

“ what physics can be expected to describe is not Reality-per-se (mind independent reality) in its totality and its details but primarily the phenomena as they get manifested to the community of all human beings”.

Everything I have studied and read on this matter has not changed my complete agreement with this.

 

[The_Duck]

The Bohmian Interpretation, may God forgive it, was a beautiful theory but it died when superpositions of states were observed.

What? The Bohmian interpretation is entirely equivalent, observationally, to any other interpretation. It can't be ruled out by experiment without ruling out quantum mechanics altogether.

It seems impossible without introducing particles' clones. You must somehow detect a single particle guided by a wave in two or more places at once. So you would need additional particles, more than you would have if you actually counted them before they were isolated and cooled down. But the interpretation makes no such claims as far as I know and if it did, it would revert back to standard qm.

You seem to think that experiments actually detect particles in two places at once? They never do. If you measure the position of anything, you only ever find it in one single place. So Bohm does fine without any need to introduce extra particles.

 

[Maui]

You seem to think that experiments actually detect particles in two places at once? They never do. If you measure the position of anything, you only ever find it in one single place. So Bohm does fine without any need to introduce extra particles.

Did you see the link in the post you quoted? It's been a while since superpositions were observed for the first time. You are coming in somewhat late or do you prefer to have a fully functional quantum computer to believe it?

http://www.futurity.org/quantum-computer-built-inside-diamond/

http://www.nature.com/nature/journal/v484/n7392/abs/nature10900.html

What? The Bohmian interpretation is entirely equivalent, observationally, to any other interpretation. It can't be ruled out by experiment without ruling out quantum mechanics altogether.

I was not referring to observations, but observations in special conditions where the BI fails.

 

[bohm2]

The claim is like non-euclidean geometry you can relax one of Kolmogorov's axioms and get a non standard version. However, you can be 100% guaranteed that the probabilities in the Born rule are assumed to obey these axioms.

Khrennikov's interpretation does predict violation of Born's rule:

Towards violation of Born's rule: description of a simple experiment
http://arxiv.org/pdf/1007.4677v2.pdf

 

[bohm2]

The Bohmian Interpretation, may God forgive it, was a beautiful theory but it died when superpositions of states were observed.

http://physicsworld.com/cws/article/news/2010/mar/18/quantum-effect-spotted-in-a-visible-object

Those experiments are fully consistent with the Bohmian Interpretation. This was discussed previously with other posters.

Do the SQUID experiments falsify Bohmian mechanics?
https://www.physicsforums.com/showthread.php?t=610085

A paper that discusses that paper and other similar experiments and showing that those experiments do not show what you say they show (Read the "2.3-Observation of macroscopic superpositions" and the 2.4-Summary of main issues):

Decoherence and definite outcome
http://arxiv.org/pdf/1208.0904.pdf

 

[Len M]

I get the impression this issue relates to how the meaning of the "ensemble theory" has evolved. bhobba pointed out that Ballentine had to backtrack a bit on his original views of the ensemble theory, when it became clear that imagining the quantum system already had certain attributes prior to the interaction with the macro apparatus was untenable for his project. So perhaps we can say that the "ensemble theory" is a hidden variables theory, so sounds a lot like deBroglie-Bohm, but the "ensemble interpretation" is merely a language for attributing meaning to "the probability that preparation X leads to measurement Y," which takes the perspective that the way to attribute that meaning is to take a frequentist interpretation of the meaning of probability (as outlined in bhobba's posts).

Thanks, that clarifies my confusion over the terms "theory" and "interpretation" with regards to QM ensembles.

 

[Maui]

Those experiments are fully consistent with the Bohmian Interpretation. This was discussed previously with other posters.

Do the SQUID experiments falsify Bohmian mechanics?
https://www.physicsforums.com/showthread.php?t=610085
[/url]

Yes, I brought up the issue in that thread. Observed superpositions of states are incompatible with Bohmian mechanics for the reason I stated earlier. The participants in that thread defended the position that superpositions have not been observed due to semantics, imprecise definitions, etc. but recent developments in quantum computing and macroscopic quantum effects prove they were all wrong. You should learn to differentiate opinions from facts, a lot of what is stated in this forum is wrong and personal opinion and at times goes unchallenged because those who actually know would not bother to engage in arguments. Superpositions are quite real but hard to maintain, that's all(if in doubt on an issue, seek second opinion in books/textbooks or stick to what the moderators say - they usually have the highest quality posts here - by far).

 

[Nugatory]

Superpositions are quite real but hard to maintain, that's all

I don't think that anyone has questioned that superpositions are real, nor that it is hard to maintain macroscopic objects in superpositions of macroscopically distinguishable states (microscopic, it's not so hard - give me a sideways-oriented Stern-Gerlach device and I'll give you superpositions of spin-up and spin-down all you want).

The disagreement is whether, if I observe a macroscopic system in a superposition of macroscopically distinguishable states A and B without a direct measurement of either, the system is physically/really/objectively both A and B. That doesn't seem to be the natural assumption for superpositions of microscopic systems (as in the spin example from the previous paragraph - superimposed up and down is not "both", it's pure sideways) but maybe the macroscopic systems are different.

If superposition does have that meaning for macroscopic systems, then the Bohmian interpretation is in trouble with the observation of macroscopic superpositions. But that meaning is itself an interpretation, and not justified by the observation of the macroscopic superpositions itself.
----
Hmmm... I have a queasy feeling that I'm just recapitulating that SQUID thread. I never did like calamari... but that's a matter of taste, just as is one's preference for interpretations...

De [STRIKE]gustibus[/STRIKE] interpretationes non est disputandum.

 

[Maui]

It's a direct measurement(not weak), sophisticated but non-invasive - quote from the link above:"In the experiment, Cleland's team reduce the amplitude of the vibrations in the resonator by cooling it down to below 0.1 K. The high frequency of the aluminium resonator was key to the experiment's success, because the temperature to which an object needs to be cooled in order to reach its ground state is proportional to its frequency. "A regular tuning fork, for example [with significantly lower frequency], would need to be cooled by another factor of a million to reach the same state," Cleland said.

Next, the team measured the quantum state of the resonator by connecting it electrically to a superconducting quantum bit or "qubit". The qubit acts, in fact, like a "quantum thermometer" that can identify just one quantum thermal excitation, or phonon. Once this has been done, the qubit can then be used to excite a single phonon in the resonator. This excitation can be transferred many times between the resonator and qubit.

In this way the researchers created a superposition state of the resonator where they simultaneously had an excitation in the resonator and no excitation in the resonator, such that when they measured it, the resonator has to "choose" which state it is in. "This is analogous to Schrödinger's cat being dead and alive at the same time," says Cleland.

"Unlike other measuring instruments, [the qubit] allowed us to measure the mechanical resonator while preserving all quantum effects," Cleland told physicsworld.com. "Most measuring instruments disturb the mechanical object by heating it up, and so destroy the very quantum effects being sought."

The experiments could have important implications for new quantum technologies, like quantum information processing, and for investigating the boundaries between the quantum and classical worlds – one of the least understood areas in physics.
http://physicsworld.com/cws/article/news/2010/mar/18/quantum-effect-spotted-in-a-visible-object

 

[bhobba]

The disagreement is whether, if I observe a macroscopic system in a superposition of macroscopically distinguishable states A and B without a direct measurement of either, the system is physically/really/objectively both A and B.

Exactly

In this way the researchers created a superposition state of the resonator where they simultaneously had an excitation in the resonator and no excitation in the resonator, such that when they measured it, the resonator has to "choose" which state it is in.

It was not observed to be in both states simultaneously - but since a superposition is simply another state, it's a pretty meaningless statement anyway. But since the experiment was not designed to detect the superposition state, it only detected what it was designed to detect - but flicked back and forth at high frequency. What it really did was simply confirm bog standard QM which predicts exactly that - an observation will yield one of the outcomes it was designed to detect - but only one - and if you think about it, it would be wildly ridicules if it did otherwise.

DBB cannot be falsified by experiment because it was deliberately cooked up to obey the formalism of QM. Falsifying it would falsify QM.

But to be fair I have to point out myself (and I don't really count) and others that know a lot more QM than I do at one time thought it was falsifiable, and some even did an experiment to disprove it - with the result it was supposedly disproved. But a careful analysis showed it was wrong - and if you think about it, it must be.

Added Later:

Check out:
http://www.scientificamerican.com/article.cfm?id=quantum-microphone
In a vibrating state each atom in the resonator only moves by an extremely small distance—less than the size of the atom itself. Thus, in the superposition of states the resonator is never really in two totally distinct places.

Thanks
Bill

 

[Maui]

It was not observed to be in both states simultaneously - but since a superposition is simply another state, it's a pretty meaningless statement anyway. But since the experiment was not designed to detect the superposition state, it only detected what it was designed to detect - but flicked back and forth at high frequency.

What a misleading statement. It was designed to flick according to the chosen state corresponding to the superposition of states of the resonator.

What it really did was simply confirm bog standard QM which predicts exactly that - an observation will yield one of the outcomes it was designed to detect - but only one - and if you think about it, it would be wildly ridicules if it did otherwise.

Great that it confirmed standard QM and I said so several times earlier but you seem to have missed it. Yes, QM predicts superpositions and the BI does not! So what was your point?

What kind of conspiracy would it take for the resonator to act like its in a superposition of states but is not?

 

[bhobba]

What a misleading statement. It was designed to flick according to the chosen state corresponding to the superposition of states of the resonator.

You are confused.

When observed it, exactly as QM, and by extension, DBB, predicts, it was found to be in one state or the other - it was not in both states simultaneously, but because of the way it was designed the original state was not destroyed like it usually is during measurement. This meant when you measured it again it did the same thing again.

Now that is not the interesting thing with this experiment, the interesting thing is it resonated at a very high frequency ie the outcome of the observation flicked back and forth but not randomly as an observation would do. This shows a lot more was going on than a simple analysis would indicate, and indeed it was.

The new link I posted shows it was not what you naively think it is - it was not really in two places at once - the effect was a lot more subtle than that.

Added Later:

Actually on further thought what you said makes no sense at all.

It was designed to be in a state that was a superposition of vibrating and not vibration ie of moving and not moving - it was not designed to flick according to some chosen state.

And after careful reading of the article again I am not sure they actually observed it in such a superposition - the resonance they observed was the vibrating state.

So basically ignore what I said above - it was mistaken based on what I read about the experiment before where the claim was when observed it 'toggled' between the two states. But that is not what the Scientific American article is saying.

Thanks
Bill

 

[bohm2]

or stick to what the moderators say - they usually have the highest quality posts here - by far).

Name 1 moderator that agreed with you that those experiments falsify Bohmian mechanics.

 

[DrChinese]

Great that it confirmed standard QM and I said so several times earlier but you seem to have missed it. Yes, QM predicts superpositions and the BI does not! So what was your point?

What kind of conspiracy would it take for the resonator to act like its in a superposition of states but is not?

I see your point, and note that there are a number of elements of dBB/BM/BI that seem to directly be contradicted by QM. An(other) example is the entanglement of photons AFTER they are already detected. This doesn't fit with the Bohmian idea that effects must follow cause (since the decision to entangle is made after the photons are detected as entangled).

And yet, as also pointed out, BM has been constructed to mimic the results of QM. The way I reconcile these different perspectives is to "let it be". (To be fair, there are also rabid BMers who insist that BM came before QM and there has been a massive conspiracy to suppress BM as the true theory.)

In fact, I don't even see the non-local character of BM as being particularly useful in explaining quantum non-locality. There is no obvious explanation as to why ALL OTHER interactions in the universe are canceled out so that entangled particles can behave as entangled ONLY with each other. A reasonable reading of BM says (to me at least) that every particle is both influencing AND influenced by every other particle. That sounds like a form of entanglement by definition. And yet we see no obvious evidence of that anywhere.

Although I should apologize for making a post that is relatively off topic.

 

[Ken G]

In my view, BM merely allows the "pilot wave" to have quasi-magical properties that assure QM predictions always happen. So as bhobba was saying, there's no experiment that can violate BM unless it discovers something that QM doesn't predict either. The real issue with BM is how "artificial" the pilot wave feels, and that's subjective. But anyone who thinks Bohm himself would have expected that experiment to come out any different than it did, probably doesn't understand BM. This is the key point that seems to be getting overlooked: everyone who "believed in" quantum mechanics expected that experiment to give exactly the result it did, regardless of their interpretation of QM. It is only people who felt QM is wrong in some way that would be surprised by that result, but the BM is not a way to say that QM is wrong, it is a way to make QM right while still retaining quasi-classical fundamental elements. It's strictly a matter of priorities-- proponents of BM say that the quasi-classical picture is the essential aspect we must always preserve (since that is more or less how our brains work), even at the cost of somewhat magical unobserved effects like the pilot wave or nonlocal interactions. Detractors of the BM say that if a quasi-classical picture seems artificial, it is time to drop it (in favor of improved mathematical elegance and simplicity). Personally, I say, vive la difference.

 

[Maui]

Name 1 moderator that agreed with you that those experiments falsify Bohmian mechanics.

You are taking my words out of the context. You still appear to not understand some very basic stuff like the factthat the BI is forced to mimic superpositions(act as if there were) and which, due to a multitude of experiments, are now widely accepted as real and are put to use(see link above on quantum computers). Quantum computing relies on quantum superposition and entanglement to work--qbits must exist in all states simultaneously before giving a particular result when observed. And in Bohmian mechanics there are no superpositions of states.

If you need an authority opinion how a quantum computer could be compatible with Bohmian mechanics(I don't see how it could), send a pm to the moderators. But it would have been better if you followed the 'picture' yourself instead of taking someone's word on faith.
The adaptation of Bohmian mechanics to superpositions requires the conspiracy to get bigger and funnier to explain qubits and quantum computing.

 

[Maui]

The real issue with BM is how "artificial" the pilot wave feels, and that's subjective.

It feels like a superposition of states. Oh wait, we are back to standard quantum mechanics.

 

[bohm2]

If you need an authority opinion how a quantum computer could be compatible with Bohmian mechanics(I don't see how it could), send a pm to the moderators.

This criticism was already addressed in a previous thread and some links provided:

Quantum computation from a de Broglie-Bohm perspective
http://xxx.lanl.gov/pdf/1205.2563v1.pdf

Quantum Computing in the de Broglie-Bohm Pilot-Wave Picture
http://xxx.lanl.gov/pdf/1012.4843v1.pdf

And also addressed on Physics Stack Exchange:

Generally, when you make a quantum calculation, you have to make some sort of measurement of the qubits at the end of the algorithm where the result you're looking for is a very probable (but not necessarily certain) result. In any interpretation that actually agrees with the basic results of quantum mechanics, these probabilities will still hold and the algorithm will still work.

If an interpretation is ruled out by the possibility quantum computing, then it's (probably) wrong because it contradicts quantum mechanics. To the best of my knowledge all of the interpretations you mentioned, while deterministic, still give results in agreement with quantum mechanics and can't be ruled out by the existence of a quantum computer.

Does quantum computing rely on particular interpretations of quantum mechanics?
http://physics.stackexchange.com/qu...rticular-interpretations-of-quantum-mechanics

Personally, I find the arguments presented by those who propose that quantum theory itself is emergent from a deeper, more exact theory on a sub-quantum level as the most reasonable view, but we're not there yet, so I guess we're kind of debating which is the best means to achieve that goal (if achievable). Maybe it doesn't matter as Ken G argues. Maybe it does. But interpretations/foundations may shed light or spawn other areas of research that may shed light as pointed out by people like Lucien Hardy, Spekkens, Leifer, etc.

there are a number of elements of dBB/BM/BI that seem to directly be contradicted by QM. An(other) example is the entanglement of photons AFTER they are already detected.

Those experimental results are further evidence against local theories not dBB.

 

[kye]

You misunderstand. The ensemble is state and observational apparatus.

The interpretation says nothing about the interpretation of the state independent of measurement context.

Thanks
Bill

Can others confirm if Ballentine believe this too??

Because if he does. This is not different from Copenhagen Interpretation. Ballentine just focus on the ensemble and even if A and B was literally in superposition in real time. He doesn't care because his reasoning being that you only detect one at a time, so may well call it Ensemble without saying anything about the interpretation of the state independent of measurement context.

Also can Ballentine's convincingly explained violations of Bell's Theorem too and the contextual somewhat non-local nature of it?

 

[bhobba]

Can others confirm if Ballentine believe this too??

Its in his book, and so fundamental its in the early pages as well.

However in his 1970 paper he explicitly stated it was an actual value prior to observation and was reliant on a not spelled out sub quantum process, or hidden variable theory.

And no its not that different to CI, a point I have been trying to make. But that is fairly well known these days eg:
http://en.wikipedia.org/wiki/Ensemble_interpretation
'The standard Copenhagen Interpretation (CI) is no different in this respect. A fundamental principal of QM is that only probabilistic statements may be made, whether for individual systems/particles, a simultaneous group of systems/particles, or a collection (ensemble) of systems/particles. An identification that the wave function applies to an individual system in standard CI QM, does not defeat the inherent probabilistic nature of any statement that can be made within standard QM. To verify the probabilities of quantum mechanical predictions, however interpreted, inherently requires the repetition of experiments, i.e. an ensemble of systems in the sense meant by the ensemble interpretation. QM cannot state that a single particle will definitely be in a certain position, with a certain momentum at a later time, irrespective of whether or not the wave function is taken to apply to that single particle. In this way, the standard CI also “fails” to completely describe “single” systems.'

Plus, and probably even more importantly, its exactly what a little thought would show.

In his book Ballentine goes deeply into Bells stuff.

His book has not attained the status as one of the finest, if the not finest, books to learn QM from without good reason. It is by a LONG, LONG way the best book I have read. You may not hold to the ensemble interpretation after reading it, but you will understand it, as well as a lot of QM's foundational issues - that's one of its strengths - it goes deeply into it. IMHO its the anti Griffiths book which is very cookbook like - not to run down Griffiths - it's good - but Ballentine is WAY ahead IMHO. Still its at graduate level (ie assumes a certain level of math maturity) and Griffith is at undergrad level. Griffith is a good prep for Ballentine though.

Thanks
Bill

 

[kye]

Electron spin acts in abstract space.. because two revolutions made one turn. It has no correlate to physical world. In the same way. I wonder if configuration space or Hilbert space in a single quantum system is like the electron spin... no physical correlate.. I guess this is one reason one turn to Ballentine's because the other choices are bohemians and many worlds, right?

Mass is always definite in a quantum system. There is no superposition of mass. So I guess the higgs field which couples to the lepton field conspire together to make themselves undetectable in position but not in mass. I guess this is a problem quantum gravity can solve.. noting that mass curves spacetime.. and we still don't know how mass and spacetime are coupled as we don't know the physics of the Planck size. So do you believe quantum gravity is related to the foundational problems in QM or unrelated (and what's arguments they are unrelated?)

 

[atyy]

Mass is always definite in a quantum system. There is no superposition of mass.

http://www.slac.stanford.edu/econf/C040802/papers/L004.PDF
"This superposition of mass eigenstates is called the neutrino of flavor."

So do you believe quantum gravity is related to the foundational problems in QM or unrelated (and what's arguments they are unrelated?)

They are not necessarily related, since string theory, which is a plausible theory of quantum gravity for some universe (not necessarily ours) uses standard QM.

 

[kye]

http://www.slac.stanford.edu/econf/C040802/papers/L004.PDF
"This superposition of mass eigenstates is called the neutrino of flavor."



They are not necessarily related, since string theory, which is a plausible theory of quantum gravity for some universe (not necessarily ours) uses standard QM.

In the future if the higgs boson is made to pass through double slit.. it would also interfere with itself? Remember the higgs boson is the only (and first) scalar particle discovered in nature... what is the mathematical arguments scalar particles also obey quantum mechanics or QM don't care about spins?

I wonder what Ballentine says about the higgs.

 

[Ken G]

It feels like a superposition of states. Oh wait, we are back to standard quantum mechanics.

Yes, of course, that's why it is called an interpretation of standard quantum mechanics.

 

[Cthugha]

Quantum computing relies on quantum superposition and entanglement to work--qbits must exist in all states simultaneously before giving a particular result when observed.

This is simply wrong. QC relies solely on the math, not on its interpretation. The math is interpreted as a "real" superposition in standard qm, but there is no need to do that for QC to work. All Bohmian mechanics does is dividing the physics into something considered a real particle and a guiding wave. Shifting the math part which leads to superposition in standard QM to the guiding wave does not change a single prediction - even without superposition.

If you need an authority opinion how a quantum computer could be compatible with Bohmian mechanics(I don't see how it could), send a pm to the moderators.

The literature on that is relatively scarce. Aaronson investigated hidden variables in general from a quantum computing perspective (http://pra.aps.org/abstract/PRA/v71/i3/e032325) and I think there is some PhD or MSc thesis from Valentinis group on quantum computing in the Bohmian picture. But I do not know that for sure. I am not really a fan of Bohmian mechanics.

But it would have been better if you followed the 'picture' yourself instead of taking someone's word on faith.

The scientific standard on what to accept is still set by peer review. So if you insist on claiming that Bohmian mechanics is ruled out by quantum computing, please provide some peer reviewed article backing your opinion. BM may seem arbitrary, but personal liking or disliking is fortunately not a factor in deciding what is acceptable in science. Personally, for example, I think that imposing any kind of interpretation on quantum computing makes papers more horrible and that physicsworld link on superposition is one of the most horrible proofs of that I have read. It is that pop-sci stuff trying to visualize things for laymen which brings up that stuff. Real experimental papers rarely bother (or even have the space) to talk about interpretations. The math speaks for itself. See, e.g. Berthold-Georg Englerts "On quantum theory" (http://arxiv.org/abs/1308.5290) for an essay trying to make clear where physics ends and where philosophy starts.