I won't debate on the wavefunction collapse

[Hurkyl]

There is a deep reason for using complex amplitudes in quantum mechanics instead of probabilities.

There's an algebraic path as well. Quantum states are, by definition, things that produce values for observables. (Which we call the 'expectation' of that observable)

This means that quantum states are a certain kind of functional on the algebra of observables. It is known that such functionals can be represented as vectors in a suitable unitary representation of your algebra of observable.

In fact, if we assume each observable has a bounded spectrum, then every possible algebra of observables is isomorphic to an algebra of operators on some Hilbert space. (I'm not as familiar with the theory of unbounded spectra)


In other words, no matter what we choose for our algebra of observables, and no matter what our state space is... everything can be represented in the Hilbert space formalism. And since the Hilbert space formalism is rather convenient, we might as well use it!

 

[meopemuk]

You are certainly entitled to your own opinion. But it's another thing entirely to foist that opinion upon others... especially when you make it sound as if it's an objective truth!

I am sorry for creating this wrong impression. Everything I am writing here is just my personal opinion. If this opinion happens to coincide with objective truth, it's just a coincidence. I am adding qualifiers like "I think", "in my opinion" in my posts. Possibly, I should do it more often.

Sure, we haven't observed the superposition of a dead and alive cat, but we have seen photons, electrons, and even macroscopic currents in superpositions of our favorite basis states.

I don't agree with that. When we observe a single electron we always find it in a definite state, not in a superposition. For example, when the electron interacts with a scintillating screen it hits one particular point on the screen and does not create a diffuse image. The idea of superposition and wave function arises only when we need to explain theoretically why different electrons hit different places on the screen. This is a purely theoretical idea. In my opinion.

Eugene.

 

[Hurkyl]

I don't agree with that. When we observe a single electron we always find it in a definite state, not in a superposition.

Of course, a definite "spin up about the z axis" is a superposition of "spin up about the x axis" and "spin down about the x axis".

For example, when the electron interacts with a scintillating screen it hits one particular point on the screen and does not create a diffuse image. The idea of superposition and wave function arises only when we need to explain theoretically why different electrons hit different places on the screen. This is a purely theoretical idea. In my opinion.

But you agree, at least, that there is a real 'interference' pattern produced when I fire thousands of electrons through the double slit, right? The superposition hypothesis has a real, observable effect that differs from the lack of superposition hypothesis.

 

[meopemuk]

But you agree, at least, that there is a real 'interference' pattern produced when I fire thousands of electrons through the double slit, right? The superposition hypothesis has a real, observable effect that differs from the lack of superposition hypothesis.

Yes, of course, the theory of quantum superposition is, in my opinion, the best creation of theoretical physics in the 20th century. It would be silly to deny that. But I tried to make a different point. I tried to reply to vanesch who (if I understood correctly) was surprised that superposed states (of individual systems, not ensembles) are not seen in experiments. I wanted to say that individual systems can be only found in a definite state (dead or alive; spin up or spin down) and they are never found in a complex superposition. The idea of quantum superposition is needed only when we try to describe an ensemble of identically prepared states and to "explain" why measurements in such an ensemble are not reproducible (sometimes we find a dead cat other times the cat is alive; sometimes we measure spin up and other times the spin is down).

Quantum mechanics doesn't say that it is possible to see half-dead half-alive cat. This superposition is a necessary and important ingredient of theory, but not something that can be directly observed. I hope I made myself clear now.

Eugene.

 

[vanesch]

Yes, of course, the theory of quantum superposition is, in my opinion, the best creation of theoretical physics in the 20th century. It would be silly to deny that. But I tried to make a different point. I tried to reply to vanesch who (if I understood correctly) was surprised that superposed states (of individual systems, not ensembles) are not seen in experiments.

I'm not really "surprised", but it is the "surprise" of the theory in a way, when we think too naively that what we observe is real and is all there is. As, according to the theory, there is a "superposition" of outcomes, then the "naive" question that arrises is "then why don't I see them ?" ; but as Einstein said: it is the *theory* that says what is to be observable and what isn't. So one can clearly understand why we can't, at the same time, *observe* a superposition of outcomes and at the same time be subject to a linear dynamics, and have an "illusion of free will". Indeed, otherwise it would be possible to (have the illusion that we can) change the evolution according to the different observed superpositions, which would imply a non-linear time evolution.
To make this clear, imagine that I could somehow subjectively observe both branches, in which a state (|a> + |b>) evolved (after measurement interaction) into (|a>|pointer1> + |b> |pointer2>). That means that subjectively I would be able to observe both pointer1 and pointer2 outcomes. I could now decide to push the red button when I see BOTH outcomes, but push the green button when I only see ONE outcome.
But that would mean that I somehow have an evolution:
(|a> + |b>) ---> |red button>
|a> ----> |green button>
|b> ----> |green button>

This cannot be linear and unitary. As such, the price to pay for my subjective observation and my illusion of free will means that I will never be able to subjectively experience the superposition of states in a unitary evolution dynamics.

I wanted to say that individual systems can be only found in a definite state (dead or alive; spin up or spin down) and they are never found in a complex superposition.

Consider polarisation states. Is |45 degrees> a superposition of |90 degrees> and |0 degrees > ? Is "spin along X" not a superposition of "spin along z up" and "spin along z down" ? Isn't "short light pulse" not a superposition of "red light" "green light" "blue light", "yellow light" ... ?

The idea of quantum superposition is needed only when we try to describe an ensemble of identically prepared states and to "explain" why measurements in such an ensemble are not reproducible (sometimes we find a dead cat other times the cat is alive; sometimes we measure spin up and other times the spin is down).

No, not really. In 100% destructive interference, you cannot explain, without superposition, why the particle NEVER hits a certain place, for instance.

Quantum mechanics doesn't say that it is possible to see half-dead half-alive cat. This superposition is a necessary and important ingredient of theory, but not something that can be directly observed. I hope I made myself clear now.

I agree with you that quantum mechanics (together with some other hypotheses, such as the illusion of free will) explains why macroscopic superpositions are not experienced as such. It only comes as a naive "surprise" when we stop taking quantum theory seriously along the path and think that somehow we should have a "god's eye" viewpoint on "what is" and exclude our proper observation from a quantum-mechanical description.

Mind you, I don't say that nature is "really" like that ; but quantum theory, when taken seriously all the way (which is maybe a good or a bad thing to do) explains entirely consistently WHY we don't observe "superpositions". As such, the very fact that we don't observe macroscopic superpositions is NOT an argument against taking quantum mechanics as ontological hypothesis. You may, for other reasons, have other arguments not to do so. But the fact that we don't see superpositions of macroscopic classical states isn't an argument. Quantum theory, by itself, is entirely capable of explaining WHY we don't see them.

 

[Mentz114]

Vanesch, your posts are well argued and backed by knowledge and understanding. But I have one question I'd like to raise,

But the fact that we don't see superpositions of macroscopic classical states isn't an argument. Quantum theory, by itself, is entirely capable of explaining WHY we don't see them.

Is quantum theory the first physical theory where things exist consistently within the theory ( probability amplitude, superposed states ..) but which, the theory itself tells us, cannot be observed ? Does this very idea not conflict with the notion of objective reality ?

 

[meopemuk]

Consider polarisation states. Is |45 degrees> a superposition of |90 degrees> and |0 degrees > ? Is "spin along X" not a superposition of "spin along z up" and "spin along z down" ? Isn't "short light pulse" not a superposition of "red light" "green light" "blue light", "yellow light" ... ?

Yes. "Spin along x" state in quantum mechanics is a superposition of "spin along z up" and "spin along z down" states. But what this superposition means for experiment? Does it mean that somehow we can see both "spin along z up" and "spin along z down" states simultaneously? No, not at all. That's not what quantum mechanics says. It says that if we perform measurements in the "spin along x" state, then sometimes we will find its "spin along z" up and sometimes the "spin along z" will be down. We will always find a definite value of "spin along z". However, it is impossible to say which of the two possible values (up or down) will be found each time. We can only predict the probabilities by taking squares of superposition coefficients.

This is what we see in experiment. Now you may say: "these experiments indicate that before the spin has been measured it was in a superposition state in which both "spin along z up" and "spin along z down" states coexisted together. Our measurement induced a random collapse of this superposition state to one of its components." This is Copenhagen interpretation. It tells you something about the system before the measurement was performed. So, you have a good reason to be sceptical about this statement, because it is impossible to verify it experimentally, even in principle.

Eugene.

 

[lightarrow]

I wanted to say that individual systems can be only found in a definite state (dead or alive; spin up or spin down) and they are never found in a complex superposition. The idea of quantum superposition is needed only when we try to describe an ensemble of identically prepared states and to "explain" why measurements in such an ensemble are not reproducible (sometimes we find a dead cat other times the cat is alive; sometimes we measure spin up and other times the spin is down).

Quantum mechanics doesn't say that it is possible to see half-dead half-alive cat. This superposition is a necessary and important ingredient of theory, but not something that can be directly observed. I hope I made myself clear now.

Eugene.

I agree with you and I would add: could a "measurement" have any meaning if it wouldn't be described by a well defined state?

 

[Hurkyl]

I agree with you and I would add: could a "measurement" have any meaning if it wouldn't be described by a well defined state?

Why not? I consider a CNOT gate to be the most basic example of a measuring device.

 

[lightarrow]

Why not? I consider a CNOT gate to be the most basic example of a measuring device.

Hello Hurkyl.
Sorry but I would ask you to explain better what exactly it's measured in that case.

 

[vanesch]

Is quantum theory the first physical theory where things exist consistently within the theory ( probability amplitude, superposed states ..) but which, the theory itself tells us, cannot be observed ?

No, the very first theory that did this was Newtonian mechanics, where the concept of force was introduced, but force cannot be observed, only displacement (and derivatives) can. It gave a lot of headaches to Newton himself, and his "action at a distance" which was so different than what one would intuitively think of a force, such as a push or a pull. So you could argue that Newtonian mechanics is just a tool which helps us calculate the observed displacements of objects, and uses a mathematical tool for that which is "force" (or one of its equivalents, potential energy, interaction, ...) but that this is nothing physical. We only observe displacements of things. Things don't really "interact" because we cannot observe directly their "interaction" but only their displacements, and it seems to be a convenient thing in the theory to talk about interactions (forces, or interaction potentials or whatever), but in "reality" the sun doesn't attract the Earth physically, and there is no force of gravity or electrical forces or whatever, all these are constructions of a theory. We only have that objects suffer displacements, period.
Newtonian theory tells us that forces cannot be observed. Only positions, velocities and accelerations can. The reason that a force cannot be observed in Newtonian physics, is that it suffers vector addition. As such, a force plus its opposite force has exactly the same consequence as no force at all. There's no "preferred decomposition" of zero force, and hence its components cannot have the slightest observable effect.

A stronger form of "non-observability", which prompted Einstein to his statement, is found in general relativity. The typical trap in doing GR is to take one's coordinate system too seriously, and to think that because one has introduced x,y,z,t, that these are things that can be observed. In GR, you cannot observe directly the spacetime manifold, and certainly not a coordinate system over it. You can only measure such things as eigentimes, and other intervals.

Does this very idea not conflict with the notion of objective reality ?

No, this idea conflicts with the notion of naive realism: that reality is what is observed, and that it is all there is to it.

 

[vanesch]

It tells you something about the system before the measurement was performed. So, you have a good reason to be sceptical about this statement, because it is impossible to verify it experimentally, even in principle.

This is true in a way. But the problem with that attitude is that, when applied to the extreme, you end up in solipsism. Indeed, the whole point of an ontological hypothesis is to have a claim of objective existence of something loose from observation. If you insist on only taking for real what is observation, then you run into the following problem: you cannot even take for real the banana on the table. Indeed, you don't observe "a banana", you only observe some yellow light in your eye. But then, you don't observe "yellow light in your eye", your brain only observes some nerve pulses coming from your eye.
You can say: yes but I can touch the banana. True. But how do you know that you touch the banana ? Because receptors under your finger skin send out nerve pulses to your brain. So you're not really observing the touch of the banana, your brain only observes nerve pulses from your fingers.
You can also eat the banana. You will taste it, but I can set up the same story, that the entire sensation of "eating a banana" is just the result of nerve pulses arriving in your brain. And then, do you really observe your brain ? Or do you assume you have a brain because you have read about it, and you've seen motion pictures or even bodies being dissected etc... ?

So why do you think that there really is a banana on the table ? Because it is a (small piece of) theory which is consistent with all your observations. You have the theory "there's a banana on the table" and that theory gives rise to some ontology (a REAL banana on a REAL table), and from it, you can deduce a lot of observations: if you touch it, you will feel something that feels like a banana ; if you look at it, you will see some yellow light ; if you eat it, it will taste like a banana etc...
So this theory "there's a banana on the table" explains very well, in a consistent way, many observations. As such, it is a good theoretical construct. But of course, it is only that: a construct. You could just as well argue that "banana's" are of course useful theoretical constructs, which are very useful to explain observations, but that they are only that, and don't, of course, correspond to a genuine ontology, because you can never verify experimentally that a banana really exists! You can only verify experimentally that you have subjective experiences which probably result from nerve pulses on something you probably have, which is a brain. But there's no way that the observation of these nerve pulses proves that there is really a banana on the table.

 

[Mentz114]

Vanesch:

No, this idea conflicts with the notion of naive realism: that reality is what is observed, and that it is all there is to it.

Agreed.

No, the very first theory that did this was Newtonian mechanics, where the concept of force was introduced, but force cannot be observed, only displacement (and derivatives) can.

I'd like to say that a quantity that can be calculated using experimental data is 'observable'. For instance by measuring times, distances and masses, I can in principle put a number on F=ma for a given situation.

Is it not the case that in principle there is no experiment that would allow me to calculate what the quantum phase was at the time of measurement ?

So why do you think that there really is a banana on the table ? Because it is a (small piece of) theory which is consistent with all your observations. You have the theory "there's a banana on the table" and that theory gives rise to some ontology (a REAL banana on a REAL table), and from it, you can deduce a lot of observations: if you touch it, you will feel something that feels like a banana ; if you look at it, you will see some yellow light ; if you eat it, it will taste like a banana etc...
So this theory "there's a banana on the table" explains very well, in a consistent way, many observations. As such, it is a good theoretical construct. But of course, it is only that: a construct. You could just as well argue that "banana's" are of course useful theoretical constructs, which are very useful to explain observations, but that they are only that, and don't, of course, correspond to a genuine ontology, because you can never verify experimentally that a banana really exists! You can only verify experimentally that you have subjective experiences which probably result from nerve pulses on something you probably have, which is a brain. But there's no way that the observation of these nerve pulses proves that there is really a banana on the table.

No, I don't like this. It is sophisticated ( in the worse sense) and goes against experience. There's an easy test for the reality/existence of a banana.

 

[Hurkyl]

Is it not the case that in principle there is no experiment that would allow me to calculate what the quantum phase was at the time of measurement ?

You can't get complete information, but you can get partial information.

No, I don't like this. It is sophisticated ( in the worse sense) and goes against experience.

That doesn't make it wrong.

There's an easy test for the reality/existence of a banana.

Please elaborate: propose an experiment that distinguishes between a real banana and the solipsist hypothesis.

 

[Mentz114]

Hurkyl:

You can't get complete information, but you can get partial information.

Ok. I'm doing some reading about this.

No, I don't like this. It is sophisticated ( in the worse sense) and goes against experience.

That doesn't make it wrong.

But it doesn't make it physics.

Please elaborate: propose an experiment that distinguishes between a real banana and the solipsist hypothesis.

You cannot be serious ! Solipsism is a ridiculous idea and not worth discussing.

My point is that QM is different from earlier theories, that's all, but we stray into pure philosophy. We have to accept that we can believe our senses and that there is an objective reality or physics has no meaning or purpose.

Another thing worth mentioning about the original topic 'wave function collapse' is that it is possible to start with the SE and correctly predict the dynamics of quantum particles without mentioning probablity amplitudes, Hilbert space or wave function collapse. So these things do not have the special position they seem to have assumed.

 

[Hurkyl]

But it doesn't make it physics.

If we were discussing physics, the discussion would have ended with "QM predicts superpositions, and is supported by empirical evidence". This has been a debate of metaphysics for quite some time.

You cannot be serious ! Solipsism is a ridiculous idea and not worth discussing.

You're the one who claimed that there was an easy test to tell the difference between the solipsist hypothesis and the real banana hypothesis.

 

[vanesch]

You cannot be serious ! Solipsism is a ridiculous idea and not worth discussing.

Mmmm... doesn't sound like a very convincing argument to me

My point is that QM is different from earlier theories, that's all, but we stray into pure philosophy. We have to accept that we can believe our senses and that there is an objective reality or physics has no meaning or purpose.

But that's the whole point ! This is a statement that one should adhere to naive realism and that it is forbidden to think of the consequences of not doing so. Rather dogmatic, no ?

Personally, I don't find solipsism "unworthy of discussion" ; I only find it not a very useful ontology hypothesis, because we stop immediately. Ontology should be useful (although, and that is what the possibility of solipsism illustrates, up to a point arbitrary and fixed by convention). As such, the question is: what's the most useful ontology hypothesis that we can make, that helps us "understand" (= give us an intuitive feeling) for our subjective observations ?

"there's a banana on the table" is a very useful ontology hypothesis in daily life.
When doing quantum mechanics, what we take as "real" (to help our intuition) may be set differently.

Another thing worth mentioning about the original topic 'wave function collapse' is that it is possible to start with the SE and correctly predict the dynamics of quantum particles without mentioning probablity amplitudes, Hilbert space or wave function collapse. So these things do not have the special position they seem to have assumed.

Ah ? We can use the SE without the entire hilbert space mechanism ?

 

[meopemuk]

If you insist on only taking for real what is observation, then you run into the following problem: you cannot even take for real the banana on the table.

This example makes clear that one needs to carefully draw the line between what is considered observable effects and what is "stuff" of theory. You vividly demonstrated that drawing this line inside our brain leads to solipsism. But it would be just as silly to draw this line in such a way that all theoretical stuff gets promoted to the rank of observable effects. Shall we say that forces are real? what about electromagnetic fields? wave functions? Hilbert spaces? quantum fields? curved space-time..?

I think that you provided an excellent example of the separation observable/theoretical in your previous post:

Newtonian theory tells us that forces cannot be observed. Only positions, velocities and accelerations can.

I basically agree with this Newtonian philosophy: Experiment tells us about certain observables of material particles (position, velocity, spin, momentum,...). This is what objectively exists. The rest of physics (forces, wave functions, Hilbert spaces...) is just mathematical stuff that we invented to describe these observations.

Eugene.

 

[Mentz114]

From: Wiki

Solopsism is the philosophical idea that "My mind is the only thing that I know exists". Solipsism is an epistemological or metaphysical position that knowledge of anything outside the mind is unjustified.

A weak form of epistemological solipsism states that the agent has no proof of anything beyond the senses. This can be raw observation, at the level of "I see red", "I am not aware of a proof". A stronger form states "No proof exists", this is falsifiable in as far as anything is. In order to falsify it, a proof must be provided.

This is what I understand by Solopsism and I admit I only vaguely see what is meant, while finding it offensively ilogical. I don't want to get into metaphysics, not my bag.

You're the one who claimed that there was an easy test to tell the difference between the solipsist hypothesis and the real banana hypothesis.

No, you misunderstand me. I would not try and answer any question that relates to or involves Solopsism any more than count angels on pinheads.

Quote:
Originally Posted by Mentz114

You cannot be serious ! Solipsism is a ridiculous idea and not worth discussing.

Mmmm... doesn't sound like a very convincing argument to me.

You are right, of course. May I amend it to

"Solipsism is a ridiculous idea and not worth discussing further as a useful ontological model"

This is a statement that one should adhere to naive realism and that it is forbidden to think of the consequences of not doing so. Rather dogmatic, no ?

If Maxwell, Planck, Lorentz and Einstein were 'naive' realists, I'm proud to be counted in their company. What's wrong with being dogmatic in keeping physics grounded in experiment ?

Ah ? We can use the SE without the entire hilbert space mechanism ?

Well, yes. It's De Broglie-Bohm theory.

I appreciate the time and trouble you've taken to put me right on the metaphysics, it has been stimulating and edifying. Now it's back to the equations (reality !) for me.

 

[rewebster]

I basically agree with this Newtonian philosophy: Experiment tells us about certain observables of material particles (position, velocity, spin, momentum,...). This is what objectively exists. The rest of physics (forces, wave functions, Hilbert spaces...) is just mathematical stuff that we invented to describe these observations.

Eugene.

let's see---do I agree with Newtonian/Galilean philosophy, or is it that my philosophy is Newtonian/Galilean physics?

 

[Hurkyl]

This example makes clear that one needs to carefully draw the line between what is considered observable effects and what is "stuff" of theory. You vividly demonstrated that drawing this line inside our brain leads to solipsism. But it would be just as silly to draw this line in such a way that all theoretical stuff gets promoted to the rank of observable effects. Shall we say that forces are real? what about electromagnetic fields? wave functions? Hilbert spaces? quantum fields? curved space-time..?

It is because of this arbitrariness that I think all this talk of "existing" and "reality" is usually just an expression of cognative bias.

This is what I understand by Solopsism and I admit I only vaguely see what is meant, while finding it offensively ilogical. I don't want to get into metaphysics, not my bag.

If you don't want to get into metaphysics, then you shouldn't jump into a discussion about what is "real" and what isn't. It is physics to postulate entities that explain experiment, but it is metaphysics to postulate about the "reality" of those entities.

It's amazing how much QM inspires people to turn into metaphysicists. I suppose SR did the same thing, though.

 

[Count Iblis]

Another thing worth mentioning about the original topic 'wave function collapse' is that it is possible to start with the SE and correctly predict the dynamics of quantum particles without mentioning probablity amplitudes, Hilbert space or wave function collapse. So these things do not have the special position they seem to have assumed.

Thought experiment: A classical computer simulates an observer measuring the z-component of the spin of an electron in state \frac{1}{\sqrt{3}}\left |\uparrow\right\rangle+\frac{\sqrt{2}}{\sqrt{3}}\left |\downarrow\right\rangle

The computer numerically computes the time evolution of the many particle wave function of the observer as it interacts with the electron. Assuming functional artificial intelligence (the idea that an exact simulation of an observer generates a real conscious observer), what is the probability that the spin is found in the state \left |\uparrow\right\rangle ?

 

[meopemuk]

Another thing worth mentioning about the original topic 'wave function collapse' is that it is possible to start with the SE and correctly predict the dynamics of quantum particles without mentioning probablity amplitudes, Hilbert space or wave function collapse. So these things do not have the special position they seem to have assumed.

I disagree completely. Schroedinger equation allows you to calculate the wave function. However, the wave function does not "correctly predict the dynamics of quantum particles". It tells us only probabilities of this or that outcome. However, in real measurement only one outcome gets realized out of the whole range of possibilities. Nobody can tell (SE certainly doesn't tell that) which outcome will be realized. This choice is completely random and unpredictable. So, you cannot avoid talking about probability amplitudes and wave function collapse in quantum mechanics.

Eugene.

 

[Mentz114]

I disagree completely. Schroedinger equation allows you to calculate the wave function. However, the wave function does not "correctly predict the dynamics of quantum particles". It tells us only probabilities of this or that outcome. However, in real measurement only one outcome gets realized out of the whole range of possibilities. Nobody can tell (SE certainly doesn't tell that) which outcome will be realized. This choice is completely random and unpredictable. So, you cannot avoid talking about probability amplitudes and wave function collapse in quantum mechanics.

Eugene.

Hi Eugene,
my understanding of the dB-B theory is that given the initial conditions, the trajectory of the particle is determined. But the initial conditions ( like quantum phase) cannot be known completely. The theory is thus interpreted ensemble-wise. Given a distribution of initial conditions, the outcome is found to be the same as with Copenhagen. No probablitiy amplitudes, no imaginary numbers.

I myself don't have any preference for one or another interpretation of the SE as long as experiments are not contradicted.

 

[meopemuk]

Hi Eugene,
my understanding of the dB-B theory is that given the initial conditions, the trajectory of the particle is determined. But the initial conditions ( like quantum phase) cannot be known completely. The theory is thus interpreted ensemble-wise. Given a distribution of initial conditions, the outcome is found to be the same as with Copenhagen. No probablitiy amplitudes, no imaginary numbers.

I myself don't have any preference for one or another interpretation of the SE as long as experiments are not contradicted.

The fact is that experimental outcomes in quantum physics are random. No theory can predict them. Various "interpretations" try to "explain" this unpleasant fact and make it easier to swallow.

One interpretation says that the wave function collapses upon interaction with the measuring apparatus. Another interpretation says that this interaction creates a whole new world. Yet another interpretation says that the randomness occurs because of uncontrolled initial conditions. There are dozens of ways to invent excuses for our ignorance about nature's behavior, but none of them can go around the simple fact that measurements are random and unpredictable. I think that the easiest and the most honest "interpretation" is to say that we simply don't know the reason of this randomness, then shut up and calculate the probabilities.

Eugene.

 

[Mentz114]

Eugene, I agree with everything in your post #55 above. My point is that one can get a statistical interpretation without the mathematics of probability amplitudes, at least for simpler problems.

M

 

[meopemuk]

Eugene, I agree with everything in your post #55 above. My point is that one can get a statistical interpretation without the mathematics of probability amplitudes, at least for simpler problems.

I am sorry, I probably misinterpreted what you said. I am not intimately familiar with dB-B approach (is it de Broglie - Bohm?). So, you are saying that it can describe two-slit interference without adding at some point two complex numbers (the amplitudes for passing through the left and right slit) and taking their square? Interesting.

Eugene.

 

[Count Iblis]

I think that all that can be done is dropping a few postulates. Wavefunction collapse is, of course, a nonsensical postulate or a theory claiming to be a fundamental theory rather than just a phenomenological description of Nature.

The Born rule can be derived from a much weaker postulate. All you need is a postulate that says that if the wavefuntion is in an eigenstate of an observable, then measuring it will yield the corresponding eigenvalue with probability 1.

 

[vanesch]

The fact is that experimental outcomes in quantum physics are random. No theory can predict them. Various "interpretations" try to "explain" this unpleasant fact and make it easier to swallow.

This is in fact not the difficulty at all. The difficulty resides in the fact that quantum theory as it is usually formulated, needs an arbitrary "transition point" (also called, the Heisenberg cut) where the fundamental dynamical rules *completely change*. The Schroedinger equation stops working, amplitudes give rise to probabilities when the a priori vectorial quantity (the state vector) gets components "with a meaning", the so-called preferred-basis problem. There is no way to give, in this picture, a *physical explanation* of the functioning of a measurement device, and hence the measurement basis in which one has to expand the state vector in order to transform it in a list of probabilities. There is no fundamental way to explain why a "position measurement" apparatus actually measures positions! At a certain point, you have to decide that quantum theory is no longer working "the usual way", that the system (apparatus ...) no longer has a quantum description (state vector), and that you are in "the classical domain".
So you have to decide then that quantum theory is NOT applicable to certain systems, although they are build up of atoms and particles and all that which ARE described by quantum theory. This is very well possible, but this is not an "interpretation" of a theory, it is a modification of its applicability domain. And no-one succeeded in writing down a sensible way in which this transition might occur, without inducing a lot of other problems.

THIS is the difficulty ; not so much that nature is or isn't random at a certain level.

 

[meopemuk]

This is in fact not the difficulty at all. The difficulty resides in the fact that quantum theory as it is usually formulated, needs an arbitrary "transition point" (also called, the Heisenberg cut) where the fundamental dynamical rules *completely change*. The Schroedinger equation stops working, amplitudes give rise to probabilities when the a priori vectorial quantity (the state vector) gets components "with a meaning", the so-called preferred-basis problem.

I don't see it as a difficulty at all. It appears as a difficulty only for those who want to see quantum mechanics (or whatever theory of nature they have in mind) as a complete and comprehensive description of the world, which encompasses everything including physical systems, measuring devices, minds of observers, whole universe, etc. In my opinion, it is too grandiose vision of the role of physics, and all paradoxes of quantum mechanics are clear evidence (for me) that this is not what theoretical physics is about.

I believe that the role of theoretical physics is much more modest. Its goal is to describe and predict observations made on physical systems by measuring apparatuses. The idea is to produce numbers which can be compared with results of experiments. In each well-defined experiment there is a clear separation between the measuring apparatus and the observed physical system. Only the physical system needs to be described by the wave function. There is no need for a description of the measuring apparatus, neither quantum nor classical description. Actually, the wave function of the system already takes into account the kind of measuring device that is used in the experiment. For example, when we write the wave fuinction of an electron in the position representation we already use the fact that the electron is observed by a device measuring position.

Of course, if we like, we can decide to include the measuring apparatus as a part of the physical system and shift the "Heisenberg cut". But then we will be speaking about a different experimental setup, whose description requires a completely different wave function.

In my opinion, this understanding of the limited role of physics is the most important lesson of quantum mechanics. We could have dreamed about precise and comprehensive description of the whole world in the days of classical Laplacian determinism. After the discovery of quantum mechanics, we should forget such dreams.

Eugene.