What Is Surprising About Wave Function Collapse?

[naima]

Can we imagine real Turing machine which would not radiate heat in its environment. or which would have in its memories all the details of what is radiated? Rovelli writes that heat is what we feel when we have not access to the microscopic details.

 

[stevendaryl]

This statement is interesting. The standard example is with linearly polarized photons which pass through a polarizer at an angle α with respect to their polarization plane. But how do "I construct my apparatus so that it makes the photon pass through or not, with a probability cos²α?" It's not, instead, that I construct an apparatus and I simply observe it works in that way but don't know why, in the sense that don't know why a single photon passes or not?

The way that I think of measurements working is this: We set things up so that a microscopic variable, such as the spin of a particle, interacts with a macroscopic variable, such as the presence or absence of a dark spot on a photographic plate. By observing the macroscopic variable, we learn something about the microscopic variable. So in a sense, measurement involves amplification, so that microscopic differences are magnified to become macroscopic differences.

The fact that macroscopic variables have only a single value (as opposed to microscopic values, which can be in a superposition of values) is part of the mystery of the measurement process.

 

[vanhees71]

It's no mystery, because macroscopic observables can be described with overwhelming accuracy by classical physics (decoherence!).

 

[stevendaryl]

It's no mystery, because macroscopic observables can be described with overwhelming accuracy by classical physics (decoherence!).

I would say that there is still a pretty big mystery. If you take quantum mechanics seriously (that is, if you assume that it actually applies to arbitrarily large collections of particles), then an interaction between a microscopic variable in a superposition of states and a macroscopic variable should lead to a superposition of macroscopic states. Now, what is true about macroscopic superpositions is that, because of decoherence, interference effects are undetectable. And a superposition with undetectable interference effects is indistinguishable from a mixed state. And a mixed state can be interpreted as classical probability, which always has an ignorance interpretation: The system is REALLY in some state or another, but we just don't know which, and we use probabilities to quantity our uncertainty.

It all works, but it involves pretending something is true that is actually contrary to QM: that superpositions can evolve into mixed states where probabilities arise through ignorance.

 

[lightarrow]

The way that I think of measurements working is this: We set things up so that a microscopic variable, such as the spin of a particle, interacts with a macroscopic variable

Does this microscopic variable really exist or not, for you? Or maybe you intended that it's the quantum system prepared in a certain way (and so described by a precise state) that interacts with that other quantum system (called measurement apparatus) in a certain way?

such as the presence or absence of a dark spot on a photographic plate. By observing the macroscopic variable, we learn something about the microscopic variable. So in a sense, measurement involves amplification, so that microscopic differences are magnified to become macroscopic differences.

The fact that macroscopic variables have only a single value (as opposed to microscopic values, which can be in a superposition of values) is part of the mystery of the measurement process.

Yes. But some of this mystery can be in the mere fact that reality is quantized: we cannot detect "parts of a photon" but only entire photons (so we can't detect light on both parts of a beam splitter if a single photon is sent through it) or that spin components are quantized (we can't detect silver atoms in between the two screen' spots of a Stern-Gerlach apparatus), or that charge is quantized (we can't detect a single electron in two different points of a photographic plate).

--
lightarrow

 

[vanhees71]

One should reflect about what "observable" really means. In this case you can take the word literally: It's something you can observe in the real world, i.e., and for physicists this even means you can quantify it (the more precise the better). The spin of particles is a quite difficult concept, because it has no classical analogy. In the quantumtheoretical formalism it is defined in a quite abstract way, involving pretty advanced mathematics (group representation theory).

Physically, however, at least for charged particles, it leads to something very concrete: The particle, e.g., an electron has a magnetic dipole moment. So you can think of the electron (in a rough way) as a charged point particle which is at the same time a tiny premanent magnet. Performing an experiment with a single electron in order to measure it's dipole moment is not so easy, because usually its motion in electromagnetic fields is dominated by the charge and the electric field. So in 1923 Stern and Gerlach performed an experiment with neutral silver atoms. It was already then known that the silver atom is built in a way that to a good accuracy its magnet moment is that of its single valence electron, but as a whole the silver atom is electrically neutral. So the idea was to measure the magnetic moment of silver atoms by running them through an inhomogeneous magnetic field, which has a large nearly constant component in one direction (usually taken as the $z$ direction of a coordinate system) and a piece varying rapidly in space. The latter component leads to a force acting on the silver atom (as known from classical physics!). In the classical picture, the constant component of the magnetic field leads to a rapid rotation of the components of the dipole moment perpendicular to the magnetic field's direction, i.e., the $z$ direction. Thus, for the much slower motion of the silver atom, the force according to these perpendicular components averages to 0, and what's left is the motion of a dipole magnetic with the dipole directed along the $z$ direction. This means the silver atom is reflected by the force due to the inhomogeneous magnetic field to the one or the other direction perpendicular direction due to the $z$-component of the dipole moment. In a classical picture this dipole moment can have any value, and thus one expects a broad spot when measuring many silver atoms running through this Stern-Gerlach apparatus, but what came out in this very important experiment was totally different! The beam of silver atoms split into two distinct lines registered on a photographic plate (which worked, by the way, only thanks to the cheap cigars smoked by Stern and Gerlach during their experiment, helping to better the contrast of these "photographs" due to a large amount of sulfur contained in the cigar smoke ;-)). This finding implied that the spin-z component is quantized, i.e., it can take only two values. In 1923 the correct quantum theory of spin and the related magnetic moment was not known and thus the experiment not fully understood from our modern point of view. Funnily enough two wrong implications of the then known Bohr-Sommerfeld model of atoms canceled out and lead to the right prediction for the "quantization of direction", as the phenomenon was dubbed then. Nowadays we know that within modern QT the explanation is a bit more abstract, because it is due to the half-integer spin of the electron (it has spin 1/2) and the socalled gyrofactor which is close to 2 for an electron (the latter is a relativistic effect; a naive non-relativistic treatment leads to a prediction of a gyrofactor of 1, but that's another story).

The very amusing story about the Stern-Gerlach experiment can be found in a nice Article by Herschbach et al in Physics Today:

http://scitation.aip.org/content/aip/magazine/physicstoday/article/56/12/10.1063/1.1650229

 

[vanhees71]

One should reflect about what "observable" really means. In this case you can take the word literally: It's something you can observe in the real world, i.e., and for physicists this even means you can quantify it (the more precise the better). The spin of particles is a quite difficult concept, because it has no classical analogy. In the quantumtheoretical formalism it is defined in a quite abstract way, involving pretty advanced mathematics (group representation theory).

Physically, however, at least for charged particles, it leads to something very concrete: The particle, e.g., an electron has a magnetic dipole moment. So you can think of the electron (in a rough way) as a charged point particle which is at the same time a tiny premanent magnet. Performing an experiment with a single electron in order to measure it's dipole moment is not so easy, because usually its motion in electromagnetic fields is dominated by the charge and the electric field. So in 1923 Stern and Gerlach performed an experiment with neutral silver atoms. It was already then known that the silver atom is built in a way that to a good accuracy its magnet moment is that of its single valence electron, but as a whole the silver atom is electrically neutral. So the idea was to measure the magnetic moment of silver atoms by running them through an inhomogeneous magnetic field, which has a large nearly constant component in one direction (usually taken as the $z$ direction of a coordinate system) and a piece varying rapidly in space. The latter component leads to a force acting on the silver atom (as known from classical physics!). In the classical picture, the constant component of the magnetic field leads to a rapid rotation of the components of the dipole moment perpendicular to the magnetic field's direction, i.e., the $z$ direction. Thus, for the much slower motion of the silver atom, the force according to these perpendicular components averages to 0, and what's left is the motion of a dipole magnetic with the dipole directed along the $z$ direction. This means the silver atom is reflected by the force due to the inhomogeneous magnetic field to the one or the other direction perpendicular direction due to the $z$-component of the dipole moment. In a classical picture this dipole moment can have any value, and thus one expects a broad spot when measuring many silver atoms running through this Stern-Gerlach apparatus, but what came out in this very important experiment was totally different! The beam of silver atoms split into two distinct lines registered on a photographic plate (which worked, by the way, only thanks to the cheap cigars smoked by Stern and Gerlach during their experiment, helping to better the contrast of these "photographs" due to a large amount of sulfur contained in the cigar smoke ;-)). This finding implied that the spin-z component is quantized, i.e., it can take only two values. In 1923 the correct quantum theory of spin and the related magnetic moment was not known and thus the experiment not fully understood from our modern point of view. Funnily enough two wrong implications of the then known Bohr-Sommerfeld model of atoms canceled out and lead to the right prediction for the "quantization of direction", as the phenomenon was dubbed then. Nowadays we know that within modern QT the explanation is a bit more abstract, because it is due to the half-integer spin of the electron (it has spin 1/2) and the socalled gyrofactor which is close to 2 for an electron (the latter is a relativistic effect; a naive non-relativistic treatment leads to a prediction of a gyrofactor of 1, but that's another story).

The very amusing story about the Stern-Gerlach experiment can be found in a nice Article by Herschbach et al in Physics Today:

http://scitation.aip.org/content/aip/magazine/physicstoday/article/56/12/10.1063/1.1650229

Now comes my presonal opinion on the interpretation/measurement issue in connection with this experiment:

The SG experiment is one of the very few, which can (on this most simple level) be fully understood by nearly analytic solution of the appropriate wave equation (the Pauli equation, which generalizes the Schrödinger equation to an equation for particles with spin). As it turns out, just taking the probability interpretation of the wave function a la Born in the sense of the minimal interpretation, no mystery remains: You expect two distinct lines of silver atoms, and the silver atoms are sorted in (nearly) perfectly prepared spin-$z$-component eigenstates with $\sigma_z \in \{-\hbar/2,\hbar/2 \}$. The macroscopic measure for the spin-$z$ component is thus the location of the silver atoms itself, and there's a 100% correlation between this position and the spin-$z$ value because here we have an example for a perfect entanglement between this spin-$z$ component (microscopic variable) and the position of the silver atom (macroscopic variable). Nowhere do you have to envoke any classical process called "collapse" or other esoterics. In this sense, it's a paradigmatic example for an ideal von Neumann filter measurement.

I'm, however, pretty sure that other physicists reading this thread have a different opinion concerning this interpretation. My only excuse is that the minimal interpretation is the simplest one, sticking clearly to the physics content of the quantum theoretical formalism without adding metaphysical or philosophical additions to it.

 

[Demystifier]

The macroscopic measure for the spin-z component is thus the location of the silver atoms itself

Here you assume that there is such thing as silver atom itself and that the atom itself is not the same thing as wave function of the atom. Am I right? I find it perfectly reasonable, but then you should be aware that it is the same as saying that there are hidden variables, even if you do not want to say that explicitly because you do not want to sound like a philosopher.

The collapse is for those who want to consistently insist that there is nothing else but the wave function. As long as you admit that there is something else (even if you don't tell what) you don't longer need collapse, but then you are adherent of a general idea of hidden variables (even if you refuse to admit it).

 

[stevendaryl]

Now comes my presonal opinion on the interpretation/measurement issue in connection with this experiment:

The SG experiment is one of the very few, which can (on this most simple level) be fully understood by nearly analytic solution of the appropriate wave equation (the Pauli equation, which generalizes the Schrödinger equation to an equation for particles with spin). As it turns out, just taking the probability interpretation of the wave function a la Born in the sense of the minimal interpretation, no mystery remains: You expect two distinct lines of silver atoms, and the silver atoms are sorted in (nearly) perfectly prepared spin-$z$-component eigenstates with $\sigma_z \in \{-\hbar/2,\hbar/2 \}$. The macroscopic measure for the spin-$z$ component is thus the location of the silver atoms itself, and there's a 100% correlation between this position and the spin-$z$ value because here we have an example for a perfect entanglement between this spin-$z$ component (microscopic variable) and the position of the silver atom (macroscopic variable). Nowhere do you have to envoke any classical process called "collapse" or other esoterics. In this sense, it's a paradigmatic example for an ideal von Neumann filter measurement.

Yes, there's nothing mysterious about this level of description of the SG experiment. It's easily understood by assuming that each electron starts off in one of two states, spin-up in the z-direction, or spin-down in the z-direction. But Bell's inequalities show that that's not true. That's where the mystery, and the idea of "collapse" comes from. (Well, obviously, the idea of "collapse" preceded Bell, but the reason for hypothesizing such a thing was the belief that particles don't have definite values for dynamic variables until those variables are measured.)

 

[vanhees71]

No, it's not assuming that the silver atom starts off in a certain spin-$z$ state. The incoming beam is rather in a thermal state given that the beam is extracted from a little oven of hot silver vapor!

 

[vanhees71]

Here you assume that there is such thing as silver atom itself and that the atom itself is not the same thing as wave function of the atom. Am I right? I find it perfectly reasonable, but then you should be aware that it is the same as saying that there are hidden variables, even if you do not want to say that explicitly because you do not want to sound like a philosopher.

The collapse is for those who want to consistently insist that there is nothing else but the wave function. As long as you admit that there is something else (even if you don't tell what) you don't longer need collapse, but then you are adherent of a general idea of hidden variables (even if you refuse to admit it).

Well, have you ever seen a wave function somewhere in the "real world"? I don't. This is just the language used to describe what's going on. Like a table is not a word made up of characters but a real object we call table to describe some thing in the real world. The only difference between common everyday-language and mathematics is that the latter is much more precise in describing (certain aspects) of the world.

 

[Demystifier]

Well, have you ever seen a wave function somewhere in the "real world"? I don't. This is just the language used to describe what's going on. Like a table is not a word made up of characters but a real object we call table to describe some thing in the real world. The only difference between common everyday-language and mathematics is that the latter is much more precise in describing (certain aspects) of the world.

I agree. All I want is to provoke you to say: "Yes, I think there are hidden variables, and I don't care if I someone will think that I sound as a philosopher."
But you are tough. You don't want to say it explicitly, even though it is obvious that you think so.
(By the way, I also think that there are hidden variables. But I don't have a problem with saying it explicitly.)

 

[vanhees71]

I don't think that there are hidden variables. How do you come to this conclusion? To the contrary, I'm a "minimalist", i.e., there is the quantum-theoretical formalism including Born's rule and the operational definition of states as preparation processes and measurements linking the formal objects of the theory with the observations in the real world. I don't think that physics is about ontology but just about the description of the (objectively comprehensible part of the) world.

 

[stevendaryl]

No, it's not assuming that the silver atom starts off in a certain spin-$z$ state. The incoming beam is rather in a thermal state given that the beam is extracted from a little oven of hot silver vapor!

I know it's not really in a definite state of $s_z$, but I don't see how it makes sense to consider the experiment a "filtering" experiment, if the atoms don't have a definite spin state.

 

[stevendaryl]

I don't think that there are hidden variables. How do you come to this conclusion?

For an experiment such as the Stern-Gerlach experiment to be a matter of "filtering", then doesn't the quantity have to exist in order to filter based on its value?

 

[vanhees71]

After they run through the magnetic field, you can filter out one of the partial beams, and the atoms in the remaining beam are (with arbitrary accuracy) in a definite $\sigma_z = \pm \hbar/2$ state. This is the whole point of my argument: You don't need a collapse to prepare a beam of silver atoms definite spin component; you just let the silver atoms run through a magnetic field, and the quantum dynamics explains why each of the partial beams are prepared in a definite spin-z-component state.

 

[vanhees71]

For an experiment such as the Stern-Gerlach experiment to be a matter of "filtering", then doesn't the quantity have to exist in order to filter based on its value?

No, why? With standard quantum dynamics you can show that the beam splits in two partial beams of silver atoms with well-prepared $\sigma_z$!

 

[stevendaryl]

No, why? With standard quantum dynamics you can show that the beam splits in two partial beams of silver atoms with well-prepared $\sigma_z$!

Yes, and that's what people are referring to when they speak of the "collapse of the wave function". Prior to passing through the device, the particle does not have a definite spin. Afterward, it does have a definite spin. That's a change. Either it's a physical change, or its an epistemological change (a change in our knowledge of the situation). You seem to be denying both alternatives, and they seem exhaustive to me.

 

[atyy]

Now comes my presonal opinion on the interpretation/measurement issue in connection with this experiment:

The SG experiment is one of the very few, which can (on this most simple level) be fully understood by nearly analytic solution of the appropriate wave equation (the Pauli equation, which generalizes the Schrödinger equation to an equation for particles with spin). As it turns out, just taking the probability interpretation of the wave function a la Born in the sense of the minimal interpretation, no mystery remains: You expect two distinct lines of silver atoms, and the silver atoms are sorted in (nearly) perfectly prepared spin-$z$-component eigenstates with $\sigma_z \in \{-\hbar/2,\hbar/2 \}$. The macroscopic measure for the spin-$z$ component is thus the location of the silver atoms itself, and there's a 100% correlation between this position and the spin-$z$ value because here we have an example for a perfect entanglement between this spin-$z$ component (microscopic variable) and the position of the silver atom (macroscopic variable). Nowhere do you have to envoke any classical process called "collapse" or other esoterics. In this sense, it's a paradigmatic example for an ideal von Neumann filter measurement.

I'm, however, pretty sure that other physicists reading this thread have a different opinion concerning this interpretation. My only excuse is that the minimal interpretation is the simplest one, sticking clearly to the physics content of the quantum theoretical formalism without adding metaphysical or philosophical additions to it.

Once again, this is simply wrong. Here you only refer to one measurement.

 

[vanhees71]

But this example shows that there is ONLY quantum dynamics, no collapse, necessary to do this state preparation! It's physical, what else?

 

[Jimster41]

Now comes my presonal opinion on the interpretation/measurement issue in connection with this experiment:

The SG experiment is one of the very few, which can (on this most simple level) be fully understood by nearly analytic solution of the appropriate wave equation (the Pauli equation, which generalizes the Schrödinger equation to an equation for particles with spin). As it turns out, just taking the probability interpretation of the wave function a la Born in the sense of the minimal interpretation, no mystery remains: You expect two distinct lines of silver atoms, and the silver atoms are sorted in (nearly) perfectly prepared spin-$z$-component eigenstates with $\sigma_z \in \{-\hbar/2,\hbar/2 \}$. The macroscopic measure for the spin-$z$ component is thus the location of the silver atoms itself, and there's a 100% correlation between this position and the spin-$z$ value because here we have an example for a perfect entanglement between this spin-$z$ component (microscopic variable) and the position of the silver atom (macroscopic variable). Nowhere do you have to envoke any classical process called "collapse" or other esoterics. In this sense, it's a paradigmatic example for an ideal von Neumann filter measurement.

I'm, however, pretty sure that other physicists reading this thread have a different opinion concerning this interpretation. My only excuse is that the minimal interpretation is the simplest one, sticking clearly to the physics content of the quantum theoretical formalism without adding metaphysical or philosophical additions to it.

What is controlling the shape of the probability wave, and how? Why isn't it just a Gaussian distribution in the z direction?

 

[vanhees71]

Once again, this is simply wrong. Here you only refer to one measurement.

I don't understand what you mean by this. Of course, here I measure $\sigma_z$ of silver atoms, nothing else. It's one measurement. So what?

 

[vanhees71]

What is controlling the shape of the probability wave, and how? Why isn't it just a Gaussian distribution in the z direction?

The shape of the probability wave is determined by its initial condition and the quantum dynamics, described by the Pauli equation. The solution is unique.

 

[atyy]

I agree. All I want is to provoke you to say: "Yes, I think there are hidden variables, and I don't care if I someone will think that I sound as a philosopher."
But you are tough. You don't want to say it explicitly, even though it is obvious that you think so.
(By the way, I also think that there are hidden variables. But I don't have a problem with saying it explicitly.)

It is very hard to undo the damage of Ballentine. It has been noticed that some who claim to use a minimal interpretation are secretly using another interpretation like MWI or hidden variables. http://arxiv.org/abs/quant-ph/0209123: "In fact, experience shows that defenders of the correlation point of view, when pressed hard in a discussion to describe their point of view with more accuracy, often express themselves in terms that come very close to the Everett interpretation (see § 6.5); in fact, they may sometimes be proponents of this interpretation without realizing it!" [bolding mine]

 

[atyy]

I don't understand what you mean by this. Of course, here I measure $\sigma_z$ of silver atoms, nothing else. It's one measurement. So what?

Collapse requires two measurements, because collapse is what one needs to calculate the conditional probability - the probability of an outcome B given poutcome A. So there are two outcomes, and two measurements.

 

[vanhees71]

Well, to check my claims, you only need one measurement: put another Stern-Gerlach apparatus into one of the partial beams to verify that these particles have a definite spin-$z$ component. So you have a preparation procedure (first SG apparatus). For collapse proponents the collapse has appeared here. For me it's simply not looking at particles in one of the partial beams but only in the other. So for me there's no collapse. The measurement of $\sigma_z$ (2nd SG apparatus) then confirms that the particles in that beam have a definite $\sigma_z$ component. You can of course measure any other $\sigma_z$ component with an accordingly directed SG apparatus, which doesn't have a determined value, and all QT predicts is the probability to find $\pm \hbar/2$ for the measured component. Again separating out one of the two beams prepared in that way, you have particles prepared such that the corresponding spin-component has a definite value, again just due to quantum dynamics but no collapse mechanism outside of that dynamics.

Whether or not this qualifies as being a hidden proponent of the Everett interpretation I cannot say, because I've never understood what makes this idea different from the minimal interpretation. At least as far as I understand it, there's no difference in the prediction of observable probabilistic statements about the outcome of measurements. So I don't see a difference between Everet's and the minimal interpretation from a physical point of view. You may believe or not that the universe splits in different branches at each measurement act (whatever this might be); it doesn't change any testable prediction of QT concerning objective observations.

 

[Jimster41]

The shape of the probability wave is determined by its initial condition and the quantum dynamics, described by the Pauli equation. The solution is unique.

I get that it is a solution to the wave equation. The part that seems surprising to me is that the solution (a specifically symmetrical periodic solution) is enforced by nature, for each silver thingy.

To the point about one experiment vs many. If it was one, and the silver thingy was classical, wouldn't it be a randomly curved path? If many, then a normal distribution of randomly curved paths? But what is seen are specific "eigenvalues", as I think you said. What is enforcing that?

 

[rubi]

I agree. All I want is to provoke you to say: "Yes, I think there are hidden variables, and I don't care if I someone will think that I sound as a philosopher."
But you are tough. You don't want to say it explicitly, even though it is obvious that you think so.
(By the way, I also think that there are hidden variables. But I don't have a problem with saying it explicitly.)

Why should we make ontological commitments as long as we aren't forced to? Why not just stay agnostic about it?

For an experiment such as the Stern-Gerlach experiment to be a matter of "filtering", then doesn't the quantity have to exist in order to filter based on its value?

I would say the word "filtering" is just a metaphor and one shouldn't take it too seriously.

 

[Demystifier]

I don't think that there are hidden variables. How do you come to this conclusion? To the contrary, I'm a "minimalist", i.e., there is the quantum-theoretical formalism including Born's rule and the operational definition of states as preparation processes and measurements linking the formal objects of the theory with the observations in the real world. I don't think that physics is about ontology but just about the description of the (objectively comprehensible part of the) world.

So when you say e.g. "the atoms in the remaining beam", you don't really think that there are really atoms there in the ontological sense? For you, atoms are merely an abstract operational description of observations?

I could understand such a view too. But then I could not understand why are you so much against collapse, not in the ontological sense, but also in the sense of an abstract operational description of observations. Therefore I think you really think atoms are there, and that's, by definition, is a belief in hidden variables.

 

[Jimster41]

Well, to check my claims, you only need one measurement: put another Stern-Gerlach apparatus into one of the partial beams to verify that these particles have a definite spin-$z$ component. So you have a preparation procedure (first SG apparatus). For collapse proponents the collapse has appeared here. For me it's simply not looking at particles in one of the partial beams but only in the other. So for me there's no collapse. The measurement of $\sigma_z$ (2nd SG apparatus) then confirms that the particles in that beam have a definite $\sigma_z$ component. You can of course measure any other $\sigma_z$ component with an accordingly directed SG apparatus, which doesn't have a determined value, and all QT predicts is the probability to find $\pm \hbar/2$ for the measured component. Again separating out one of the two beams prepared in that way, you have particles prepared such that the corresponding spin-component has a definite value, again just due to quantum dynamics but no collapse mechanism outside of that dynamics.

Whether or not this qualifies as being a hidden proponent of the Everett interpretation I cannot say, because I've never understood what makes this idea different from the minimal interpretation. At least as far as I understand it, there's no difference in the prediction of observable probabilistic statements about the outcome of measurements. So I don't see a difference between Everet's and the minimal interpretation from a physical point of view. You may believe or not that the universe splits in different branches at each measurement act (whatever this might be); it doesn't change any testable prediction of QT concerning objective observations.

I think I agree that at one level, the fact that fundamental things have always been observed to be something specific, and not random, or changing, is not mysterious or surprising. How else could it be? What is interesting to me is the way the mechanism that enforces that factitious fact is sitting there in the future, which surely is a thing in the world, though not precisely observable, doing a bunch of apparently non-local work - dictating eigenvalues across space-time, organizing the Lie group, maintaining the wave-equation.

 

[Demystifier]

Why should we make ontological commitments as long as we aren't forced to? Why not just stay agnostic about it?

I answered it in post #99. I cannot understand how can someone simultaneously be both a) agnostic about ontology and b) non-agnostic about collapse.

 

[atyy]

Why should we make ontological commitments as long as we aren't forced to? Why not just stay agnostic about it?

Exactly what Demystifier said - if we do not make an ontological commitment, then we do have collapse. It is percisely because the wave function is not real, that collapse is needed. Also, vanhees71's philosophy is not very coherent, as Matt Leifer says, "given that we are not assigning ontological status to anything, let alone the state-vector, then you are free to collapse it, uncollapse it, evolve it, swing it around your head or do anything else you like with it. After all, if it is not supposed to represent anything existing in reality then there need not be any physical consequences for reality of any mathematical manipulation, such as a projection, that you might care to do." http://mattleifer.info/2007/01/24/what-can-decoherence-do-for-us/

Collapse is a standard part of the minimal interpretation. As we discussed before, one does not need it if one does not do successive measurements. However, vanhees71 has not yet rejected successive measurements.

Once again, I stress that vanhees71 is making a technical error, so this debate is not a matter of taste. He is rejecting the textbook formulation of quantum mechanics, eg. Nielsen and Chuang or Holevo or Weinberg.

 

[atyy]

Well, to check my claims, you only need one measurement: put another Stern-Gerlach apparatus into one of the partial beams to verify that these particles have a definite spin-$z$ component. So you have a preparation procedure (first SG apparatus). For collapse proponents the collapse has appeared here. For me it's simply not looking at particles in one of the partial beams but only in the other. So for me there's no collapse. The measurement of $\sigma_z$ (2nd SG apparatus) then confirms that the particles in that beam have a definite $\sigma_z$ component. You can of course measure any other $\sigma_z$ component with an accordingly directed SG apparatus, which doesn't have a determined value, and all QT predicts is the probability to find $\pm \hbar/2$ for the measured component. Again separating out one of the two beams prepared in that way, you have particles prepared such that the corresponding spin-component has a definite value, again just due to quantum dynamics but no collapse mechanism outside of that dynamics.

How can there be partial beams? That is assigning a definite trajectory to particles.

And again, I stress that in the minimal interpretation it is wrong to use a one measurement procedure to argue against collapse. In the minimal interpretation, there is no need for collapse if one does one measurement.

Whether or not this qualifies as being a hidden proponent of the Everett interpretation I cannot say, because I've never understood what makes this idea different from the minimal interpretation. At least as far as I understand it, there's no difference in the prediction of observable probabilistic statements about the outcome of measurements. So I don't see a difference between Everet's and the minimal interpretation from a physical point of view. You may believe or not that the universe splits in different branches at each measurement act (whatever this might be); it doesn't change any testable prediction of QT concerning objective observations.

The difference is that in Everett's view, it makes sense to talk about the "wave function of the universe". In the minimal interpretation, we don't know what the "wave function of the universe" means.

 

[Demystifier]

Collapse is a standard part of the minimal interpretation. As we discussed before, one does not need it if one does not do successive measurements. However, vanhees71 has not yet rejected successive measurements.

Exactly!

 

[vanhees71]

How can there be partial beams? That is assigning a definite trajectory to particles.

And again, I stress that in the minimal interpretation it is wrong to use a one measurement procedure to argue against collapse. In the minimal interpretation, there is no need for collapse if one does one measurement.
The difference is that in Everett's view, it makes sense to talk about the "wave function of the universe". In the minimal interpretation, we don't know what the "wave function of the universe" means.

No, beams are not trajectories of particles in a classical sense. That's the whole point of this example! After the magnet of a properly constructed SG apparatus, you have a sufficiently good separation of beam-like regions of space, where only silver atoms in FAPP pure $\sigma_z=+\hbar/2$ states are found. I wrote FAPP, because in fact there's always a tiny probability to find a silver atom at such a place with $\sigma_z=-\hbar/2$, but you can make this tiny probability as tiny as you wish. That's why I wrote FAPP. Just looking at silver atoms in this region of space is the only thing you need to have an ensemble of silver atoms prepared in a (FAPP) pure $\sigma_z=+1/2$ state. No collapse argument is necessary to make this preparation. Note that a collapse is necessary only for state preparations, not for measurements, which usually destroy the object observed (like a photon hitting a photo/CCD plate, a particle being absorbed in ALICES calorimeter, and so on), and you don't need to bother about what state it might be into be described for later measurements ;-).

In this example I don't need a "wave function of the universe", and in my opinion it is very hard to make sense of such a notion in a physical sense. Whatever I tell this wave function might be, you'll never be able to think about an experiment in the real world that can verify or falsify my claim of such a wave function. It's not even possible in principle to observe the entire universe! Here, I'm humbly talking about a SG apparatus as found in many labs for physics students around the world :-).