I won't debate on the wavefunction collapse

[vanesch]

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.

But the difficulty resides in the following: suppose I give you the physical description of an apparatus. What's the physical description of an apparatus ? I would say, a beginning state vector and a corresponding hamiltonian, no ? That's the quantum mechanical description of an apparatus. Now, given that, and only that, how do you deduce WHICH KIND OF MEASUREMENT BASIS goes with that apparatus ?

One can in fact do that, by fully assuming quantum theory all the way. One will then see that the interaction hamiltonian is such, that certain subspaces of states of the "system-under-study" couple with subspaces of states of the "measurement apparatus" in a kind of coarse-grained Schmidt decomposition of the overall state. Furthermore, if one introduces a quantum description of the environment (thermodynamical heat reservoir), usually, these couples ("subspace of states of measurement apparatus" and "subspace of states of system-under-study") remain stable against interaction with the environment ; again, by assuming that all this has a quantum description and that we don't leave the quantum-domain or the schroedinger equation. If one calls these subspaces of states of the measurement apparatus "the pointer states", then one can see that they are close to "classical states with different outcomes".
The whole above story is called "decoherence" and singles out specific subspaces of states of "macroscopic systems" which remain stable against interaction with the environment. From it, one can derive as such the "stable pointer states" and from this, and the interaction hamiltonian, one can then derive the "measurement basis" that the apparatus applies to the system.
But in order to do all this, we cannot collapse the wavefunction and we have to assume that quantum interactions and state descriptions are valid all the way up.

There is of course a way out, and that is by saying that there IS a preferred measurement basis, which is "position measurement". All measurements are then position measurements. When you do that, you can arrive at Bohmian mechanics, but the interpretational issues of Bohmian mechanics are not as simple as one might think at first, because the Bohmian ontology consists of two interacting worlds: the particle/position world (which we are used to from Newton), and on the other hand the quantum-mechancal wavefunction world which continues to evolve with superpositions and all that, just as in non-collapsing MWI quantum theory. This last world influences the former (the particle world), but not vice versa: the particle positions have no influence on the wave world. The problem as many people see it with Bohmian mechanics (except, of course, proponents of this view), is that the interaction between the wave world and the particle world is not relativistically invariant.

 

[Hurkyl]

In my opinion, it is too grandiose vision of the role of physics,

But I'm sure you understand that some people don't give up so easily.

and all paradoxes of quantum mechanics are clear evidence (for me) that this is not what theoretical physics is about.

By the way, to the best of my knowledge there are no paradoxes in quantum mechanics -- only pseudoparadoxes. Much like the twin pseudoparadox of special relativity, you only run into problems if you make unwarranted assumptions.

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.
...
There is no need for a description of the measuring apparatus, neither quantum nor classical description.
...
Of course, if we like, we can decide to include the measuring apparatus as a part of the physical system

You contradict yourself.

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.

It's not the wavefunction that takes that into account. The wavefunction has no idea what we're measuring. It's the choice of representation that takes into account what we're measuring.

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.

I take a wholly different lesson -- quantum mechanics emphasizes, more so than any other theory, the need to stick to experimentally meaningful questions when studying physics.

 

[vanesch]

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.

In a way I agree with you: I think one should remain modest and most probably our understanding of nature is still very remote from what is needed to get an overall universal picture. So all this is "running with the legs we have". However, I extend "theoretical physics" to "there's a banana on the table" too: it is a primitive form of theoretical physics!

So this is my point: once we have learned from quantum mechanics (and we already got a warning shot from relativity) that "theoretical physics" (in other words, trying to make sense of our observations) is not going to be a smooth ride in understanding the meaning of life, the universe and everything, and given that all intellectual activity related to observations is, in one way or another "theoretical physics", then we can only conclude that we don't know ANYTHING about the world and never will. We then realize that we don't even know whether that part of "theoretical physics from kindergarten" which tells us that there is a banana on the table has any sense.

So, or we try to make sense, in as much as we can, about all of it, or we simply say that nothing we ever deduced from observations has any sense, and we can just as well dwell in mysticism. Most people seem to prefer to place some "sane cut" somewhere, between "what's obviously true" on one hand, and what's "just theoretical constructs" on the other hand, but any such cut runs sooner or later in difficulties of logic, because of the grey zone.

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.

That's where the difficulty resides: the clear separation between the measurement apparatus and the observed system. Even von Neumann realized this already in 1932. It is especially important for an instrumentalist, who is to study the physical interaction between the measurement apparatus and the system under study! For the instrumentalist, the "system under study" is the measurement apparatus. It's maybe because I'm an instrumentalist, that I take on this stance, btw

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.

Again, except if you want to study the physics of a measurement apparatus!

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.

Right, and where do we stop ? With the "ultimate observation", which is nothing else but subjective experience. Even that, von Neumann realized.

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.

I agree with you. But I take this even further: the limited role of ANY knowledge and not only of physics. Quantum mechanics, IMO, showed us up to what point things that we thought we knew, are in fact up to a certain level, imaginary constructions of the mind. It depends or not whether you want to keep a "sanity cut" and keep insisting on the reality of the banana on the table (taking granted the logical difficulties that this will induce), or whether you're willing to just throw up the arms in the air and say that in the end, we don't know ANYTHING for sure (partly my position), or whether you say that whatever strange things your most complete formal knowledge gives you, it must somehow more be related to any "reality" than whatever intuitive idea you had of it (also partly my position).

So I'm in a kind of quantum superposition of the three views on reality and I won't collapse in either.

 

[jostpuur]

By the way, to the best of my knowledge there are no paradoxes in quantum mechanics -- only pseudoparadoxes. Much like the twin pseudoparadox of special relativity, you only run into problems if you make unwarranted assumptions.

Seems redundant terminology. Aren't all paradoxes pseudoparadoxes?

 

[Count Iblis]

Vanesch, that's also how I think about this issue. I.m.o. MWI + decoherence is the most natural thing to assume. If one proposes a real collapse of the wave function then there should be experimental evidence for that to motivate this. One has to demomonstrate that the time evolution of an isolated system is not exactly unitary. Some time ago I read about a proposal to look for such effects in observatons of neutrinos from astrophysical sources. Neutrino oscillations lead to neutrinos of one flavor evolving into a superposition of the three flavors. But if a pure neutrino state evolves into a mixed state then that can be detected as it affects the relative probabilities for detecting the three flavors.

 

[meopemuk]

It's not the wavefunction that takes that into account. The wavefunction has no idea what we're measuring. It's the choice of representation that takes into account what we're measuring.

Yes, I agree.

I take a wholly different lesson -- quantum mechanics emphasizes, more so than any other theory, the need to stick to experimentally meaningful questions when studying physics.

Yes, that's what I wanted to say.

Eugene.

 

[meopemuk]

then we can only conclude that we don't know ANYTHING about the world and never will.
[...] or we simply say that nothing we ever deduced from observations has any sense, and we can just as well dwell in mysticism.

Why such pessimism? We do know something don't we?

Right, and where do we stop ? With the "ultimate observation", which is nothing else but subjective experience. Even that, von Neumann realized.

The place to stop is determined by the concrete experimental situation. Ask the experimentalist conducting the experiment where is the boundary physical system/measuring device and you'll get a pretty accurate answer.

Eugene.

 

[Hurkyl]

Seems redundant terminology. Aren't all paradoxes pseudoparadoxes?

No. In a pseudoparadox, the contradiction is the fault of the arguer; typically he makes a subtle mistake or unwarranted assumptions. In a paradox, the contradiction is the fault of the system.

Examples of actual paradoxes are the Liar's paradox of 'naive' formal logic and Russell's paradox of 'naive' set theory.

 

[Count Iblis]

Hmmm, is there always something "naive" about a system allowing for a paradox? What about the Banach-Tarski Paradox

 

[Count Iblis]

Actually, the Banach-Tarski could be called a pseudoparadox...

 

[strangerep]

[...] I read about a proposal to look for [non-unitary evolution] effects in observatons of neutrinos from astrophysical sources. Neutrino oscillations lead to neutrinos of one flavor evolving into a superposition of the three flavors. But if a pure neutrino state evolves into a mixed state then that can be detected as it affects the relative probabilities for detecting the three flavors.

That's accounted for by flavor eigenstates not coinciding with mass eigenstates.
Where is the non-unitarity?

- strangerep.

 

[Count Iblis]

That's accounted for by flavor eigenstates not coinciding with mass eigenstates.
Where is the non-unitarity?

- strangerep.

That's right. However, decoherence would yield an extra measurable effect. See e.g. this article

 

[vanesch]

Why such pessimism? We do know something don't we?

That's not pessimism. It is realising up to what point we don't have any absolute knowledge, but only relative mental constructs which are useful. That's good enough reason to keep them, but we mustn't over-estimate the absolute character of any form of knowledge. There's no problem in living with the knowledge that our "knowledge" is up to a point arbitrary, conventional and probably even wrong. In fact, it frees oneself of dogmatic "holdons" which generate difficulties in thinking freely. But, as I said, there's no reason to *discard* our "shaky" knowledge, as it is still the best we can do.

The place to stop is determined by the concrete experimental situation. Ask the experimentalist conducting the experiment where is the boundary physical system/measuring device and you'll get a pretty accurate answer.

As I said, for the instrumentalist, this is not obvious!
For instance, in a photomultiplier, when is the "measurement" done ? By the freeing of an electron from the photocathode ? But if we study that in more detail, we do it with a quantum-mechanical description, and the photo-electric effect becomes a "system-under-study". Is it during the electron multiplication ? But then, the electron-metal interaction can also be accounted for quantum-mechanically...

Is it when the amplifier amplifies the signal on the anode ? But then, this amplifier has a fist stage with a FET transistor which can have a quantum-mechanical description...

Of course, at a certain point, the instrumentalist knows that a classical approximation will be good enough for the specific purpose, and places his "cut" there. But that's a matter of approximation, not something fundamental.

 

[vanesch]

That's accounted for by flavor eigenstates not coinciding with mass eigenstates.
Where is the non-unitarity?

The point is that it would probably be a lack of quantum interference there where it is expected and no decoherence effect can explain away the non-observation of the interference. In other words, it would be an attempt to falsify the applicability of quantum mechanics proper.

 

[vanesch]

Hmmm, is there always something "naive" about a system allowing for a paradox? What about the Banach-Tarski Paradox

Isn't this a bit like the counter-intuitive fact that an absolutely divergent series can always be re-arranged to yield any finite sum ?

 

[Count Iblis]

Isn't this a bit like the counter-intuitive fact that an absolutely divergent series can always be re-arranged to yield any finite sum ?

Yes, but the Banach-Tarski is much more counterintuitive (you only need to cut the ball into a finite number of pieces and reassemble them to make the new ball of twice the volume). I think that Banach and Tarski argued that the Axiom of Choice should be be dropped because of their theorem.

 

[Hans de Vries]

Personally, I don't find solipsism "unworthy of discussion" ; I only find it not a very useful ontology hypothesis, because we stop immediately.

If the solipsist physicist assumes that the universe is in some way the product of his own
mind, and this universe includes all the physics textbooks he owns, why does he have
to study these books year after year after year, when he himself is, in fact, the author?



Regards, Hans

 

[lightarrow]

If the solipsist physicist assumes that the universe is in some way the product of his own
mind, and this universe includes all the physics textbooks he owns, why does he have
to study these books year after year after year, when he himself is, in fact, the author?



Regards, Hans

Because he forgot his creation...

 

[Fra]

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.

I'm sorry for jumping into the late discussion and I'm not sure what you guys mean with solipsism in the context of physics, but I associate it closely to subjective reality in the sense that the local perception of reality needs a representation which I think is a relation to the environment, a sort of mirror. This I think is related to the subjective and relational interpretations of QM. The only reality for an observer is IMO represented by his relations to the environment. And a real observer or particle can most probably (I think) not keep infinite amounts of relations, the information capacity is bound to limit the relational complexity.

I personally don't think this is ridicilous. I rather think the opposite idea that there is an objective absolute reality is unfounded and overly speculative, whose purpose is to simplify the matter. But I think this simplification really produces inconsistencies.

OTOH if solipsism means physicists human MIND then it is a statement of insufficient scope, unless the concept of mind is also attributed to an arbitrary system, like particles "minds". But that terminology gets awkward and a bit silly I agree.

We have to accept that we can believe our senses and that there is an objective reality or physics has no meaning or purpose.

I disagree with this. It still has meaning. The fact that reality is relational and subjective is not the same as to say it's totally arbitrary. Also I think that one can find that communicating/interacting observers will mutually favour understanding, and this will render an effective objective reality as emergent, but I think it is not _fundamentally objective_ which I personally think is an extremely important distinction.

/Fredrik

 

[vanesch]

If the solipsist physicist assumes that the universe is in some way the product of his own mind, and this universe includes all the physics textbooks he owns, why does he have to study these books year after year after year, when he himself is, in fact, the author?

In the same way as you may not understand your dreams, I guess... If you dream that you are a detective who's working on a case and cannot find the murderer, then you could say the same thing: how can it be that you, as creator of your own dream, wouldn't know who's the guilty one.
The idea of solipsism is not somehow that you are fully knowledgeably your own "god and creator" or something, but rather that the only thing you can be sure of, is that you undergo subjective impressions and that those impressions do not necessarily have to come from an evident "outside reality".

 

[vanesch]

I'm sorry for jumping into the late discussion and I'm not sure what you guys mean with solipsism in the context of physics, but I associate it closely to subjective reality in the sense that the local perception of reality needs a representation which I think is a relation to the environment, a sort of mirror. This I think is related to the subjective and relational interpretations of QM. The only reality for an observer is IMO represented by his relations to the environment. And a real observer or particle can most probably (I think) not keep infinite amounts of relations, the information capacity is bound to limit the relational complexity.

I personally don't think this is ridicilous. I rather think the opposite idea that there is an objective absolute reality is unfounded and overly speculative, whose purpose is to simplify the matter. But I think this simplification really produces inconsistencies.

This is to me a very good representation of what "solipsism" in quantum interpretations means, and what is the scope of "a reality hypothesis".

 

[Mentz114]

Hello Fredrik, I would like to restate my personal view that solipsism is ridiculous. How can any rational being contemplate for a moment the absurdity that they ( him, her, it) is 'dreaming' the universe. There is no reason whatever to think this.

I rather think the opposite idea that there is an objective absolute reality is unfounded and overly speculative, whose purpose is to simplify the matter. But I think this simplification really produces inconsistencies.

In my view, utter rubbish. I hope that isn't considered too strong, but this is a physics forum, and someone is telling me that assuming an objective reality is a 'simplification' !
What inconsistencies are found from this assumption ?


If you continue to disagree with me - I'll undream you !

 

[friend]

Hello Fredrik, I would like to restate my personal view that solipsism is ridiculous. How can any rational being contemplate for a moment the absurdity that they ( him, her, it) is 'dreaming' the universe. There is no reason whatever to think this.

Reason is a manifestation of imagination just as dreaming is. The weird things would be to consider dreaming inside this dream.

 

[Hurkyl]

Hello Fredrik, I would like to restate my personal view that solipsism is ridiculous. How can any rational being contemplate for a moment the absurdity that they ( him, her, it) is 'dreaming' the universe.

A rational being wouldn't reject the possibility simply because they find it aesthetically displeasing.

There is no reason whatever to think this.

What reason is there to think otherwise?



As I understand it, solipsism's main practical use is as a counterexample, and for proof-by-contradiction-like arguments.


For example, as a being who instinctively rejects solipsism, you should therefore tend to reject any philosophical position that reduces to solipsism. For example, the position that all knowledge of the universe comes entirely from sensory experience.

(If our only knowledge comes from sensory experience, that means we cannot trust our theories and conceptions about what happens "beyond" our sensory apparatuses -- and thus all our knowledge of the 'external universe' is a mental fiction we've cooked up to organize our sensory experience)

 

[Mentz114]

If our only knowledge comes from sensory experience, that means we cannot trust our theories and conceptions about what happens "beyond" our sensory apparatuses -- and thus all our knowledge of the 'external universe' is a mental fiction we've cooked up to organize our sensory experience.

Hi Hurkyl, nothing important is happening beyond your sensory experiences. If important parts of actuality were not perceptable by us, we'd have unexplained, ie magic phenomena all the time. I have not seen convincing evidence that my senses are not telling me everything I need to know to do physics, and make machines that work.

For example, as a being who instinctively rejects solipsism, you should therefore tend to reject any philosophical position that reduces to solipsism. For example, the position that all knowledge of the universe comes entirely from sensory experience.

Not logical in view of what I said above. Why is it so wrong to assume my senses are correct and not deceiving me (by Occam) ?

 

[Hurkyl]

Hi Hurkyl, nothing important is happening beyond your sensory experiences. If important parts of actuality were not perceptable by us, we'd have unexplained, ie magic phenomena all the time.

I could take this statement several ways, depending on just what you mean by "perceptable". Choose the response that best fits your intent.

. If something was causing magic phenomena, then it wouldn't be imperceptable.

. Lots of important things aren't perceptable, and once really were unexplained. But that hasn't prevented us from postulating theories about them.

I have not seen convincing evidence that my senses are not telling me everything I need to know to do physics, and make machines that work.

But the question is whether there is really a machine out there, or if the existence of the machine is a concept you invented to organize your sensory experience.


The modern age has given us wonderful examples of the latter -- there is no 'real' object called an icon, but it is certainly a good descriptor of my visual experiences with my computer. Similarly my television set doesn't contain people or the land of Hyrule, nor does my stereo contain a symphony orchestra.

And yet, my mind still organizes this data as it would anything 'real'. I can see and manipulate the icon, I can recognize 'people' in my television, and can learn the physics of Hyrule, I can pick out the different instruments in my 'stereo', and so forth.

And it also gives examples of the inverse hypothesis too -- it gives examples where we infer existence in a decidedly intellectual way, rather than directly with our senses. We have all sorts of wonderful tools for measuring things we couldn't otherwise see. And I assume you believe that I exist; how did you infer that?

Why is it so wrong to assume my senses are correct and not deceiving me by Occam.

Nobody said your senses are deceiving you. If you take the position that your senses are all that you can trust, then the conclusion is that your mind is deceiving you. Raw sensory data doesn't tell you that apple exists. You simply see an image. It is your mind that processes that image and declares that there is a real apple out there.

So, if you take the position that you can only trust your senses, that means you cannot trust your mental constructs. You can trust that you saw an image, but you cannot trust the inference that there is an apple out there.



Of course, most people when they say "sensory experience", they usually mean "sensory experience and all of the mental constructs that I like to use". And that's an incredibly important philosophical distinction.

 

[friend]

...If important parts of actuality were not perceptable by us, we'd have unexplained, ie magic phenomena all the time. I have not seen convincing evidence that my senses are not telling me everything I need to know to do physics...

Actually, the path integral formulation of QM requires us to account for an infinity of other possibilities that we do not observe/preceive. We seem to have to make an assumption about things we do not preceive in order to account for things we do see/observe. This is very interesting. Is reality (things we observe) really the result of presuming without evidence/observation an infinite number of other possiblities? Does reality consist of just our musings about other possibilities we will never observe? I'm not sure what to make of all this.

 

[Mentz114]

But the question is whether there is really a machine out there, or if the existence of the machine is a concept you invented to organize your sensory experience.

Suppose there is no machine out there, then where am I and why do I have senses ?
Am I the machine ? This looks like a conspiracy-theory philosophy.

If there's no objective reality, then surely I cannot exist either.

That clinches it for me.

The modern age has given us wonderful examples of the latter -- there is no 'real' object called an icon, but it is certainly a good descriptor of my visual experiences with my computer. Similarly my television set doesn't contain people or the land of Hyrule, nor does my stereo contain a symphony orchestra.

I disagree. The icon does exist, as a collection of coloured pixels on the screen. The music exists as ordered information stored on disc or whatever even when you're not playing it, and when it is playing the air vibrates as well, and your eardrums.

So, if you take the position that you can only trust your senses, that means you cannot trust your mental constructs. You can trust that you saw an image, but you cannot trust the inference that there is an apple out there.

I don't take that position. Yes I can and do trust my mental constructs. I can test the inference by eating the apple. It's never failed, it was an apple every time.

Hurkyl, respectfully, you do a good argument but it's tiring and I have better things to do. I don't want to be a last worder - so, I wonder if there's anything we can agree on?

Regards,
M

Friend:

Actually, the path integral formulation of QM requires us to account for an infinity of other possibilities that we do not observe/preceive. We seem to have to make an assumption about things we do not preceive in order to account for things we do see/observe.

There's nothing strange going here - it's because probability is involved.
Whenever we work out a probability we do so over a range of possible outcomes, only one of which we will see per throw ( so to speak). But things which won't happen must be included in the calculation.

 

[Hurkyl]

Hurkyl, respectfully, you do a good argument but it's tiring and I have better things to do. I don't want to be a last worder - so, I wonder if there's anything we can agree on?

Well, let's recall how this tangent even started! meopemuk, vanesch, and I were debating over what really exists -- meopemuk was taking the position that labelling some things (like spots on a scintillating screen) as being "directly observable", and thus real, whereas he labelled other things (like superposition) as not being "directly observable", and thus unreal.

And so, vanesch presented the usual derivation of solipsism from meopemuk's hypothesis that only what is "directly observable" is real -- vanesch demonstrated that the notion of a banana is a mental construct. The implication is that if meopemuk really insists on his hypothesis, then he must consider the banana unreal.

This is where you chimed in with your remark that there is an easy test to see if the banana is real.


But you and I agree that the banana is a mental construct -- that is the important point. If everyone agrees the banana is a mental construct, and also that the banana is real, then we see that the quality of being a mental construct does not render something unreal, and so meopemuk's argument loses most of its force.

 

[friend]

Friend:
There's nothing strange going here - it's because probability is involved.
Whenever we work out a probability we do so over a range of possible outcomes, only one of which we will see per throw ( so to speak). But things which won't happen must be included in the calculation.

This gets into the question as to whether mere possibilities can be actually real that we have to account for them in our theoretical models. In QM mere possibilities actually have a real effect in interference patterns, etc. We know that possibilities are a real consideration in the mind of those who are trying to decide what to do because they are uncertain as to what is real. But that nature itself seems to consider the possibilities begs the question to whether there really is some objective reality or whether it's all in our heads.