Question on observer created reality

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vanesch

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ShalomShlomo said:
Bell showed that QM itself formally breaks causality.
ie whether QM is Classical, Copenhagen, Many Worlds, Bohmiam, etc all describe a QM that violates causality because QM itself violates causality.
This is not true, and it is one of the merits of Many Worlds to allow QM to respect locality and causality. If you want to know the details, I put it in my journal, but the point is essentially this:
when Alice performs her "measurement", with respect to Bob, she's just in a superposition, and got entangled with her photon, BUT ACCORDING TO BOB, THERE WASN'T ANY RESULT AT ALICE'S. It is only when Bob LEARNS about Alice's result that he in fact chooses in which branch he lives, but this happens of course when he's in local (causal) contact with Alice, or with a messenger of Alice.
So that's the way how many worlds gets around Bell's theorem: there simply WASN'T A RESULT at Alice's and at Bob's, so you cannot talk about the probability of Alice to have observed something, from Bob's point of view.

It is described in much more detail in my journal (collection of old posts on the subject).

cheers,
Patrick.
 
vanesch said:
...one of the merits of Many Worlds to allow QM to respect locality and causality.
Sorry, Vanesch. You are right. I blithely included the wacky Many Worlds interpretation of QM amongst the rest, and forgot that of course it does not suffer from the normal problems, and it answers all normal questions and doubts.

I'm sorry.

It's just such a wacky theory, I find it difficult to be professional and take it seriously as we all need to. I am at fault in this.

So it's either throw out causality (keeping only soft-causality) or Many Worlds.

Shalom Shlomo
 

vanesch

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ShalomShlomo said:
So it's either throw out causality (keeping only soft-causality) or Many Worlds.
I'll pretend not having noticed a certain sarcasm in your post :biggrin:, but what you write above is essentially the choice we have, at least if we stick to special relativity. Everything which induces a real collapse, and which considers that there is an ontology to the measurement results of Bob and Alice, and which accepts SR cannot escape the throwing out of causality, thanks to Bell's theorem.
In fact it is worse: your theory is even not lorentz invariant !
So if I have to choose between a "wacky theory" but which is lorentz invariant, local, causal, and explains all my *subjective* observations, or a theory which is not "wacky", but violates locality, lorentz invariance and causality, but allows me to associate my subjective observations to objective facts in a 1-1 relationship (I think that that is what "wacky" means, no ?), I opt for causality, and if unwackyness has to go, then so be it :tongue2:

There might be an intermediate way out, in that *some* violations of unwackyness are allowed on "small enough scales", and that on "larger scales", unwackyness is restored, and there are deviations from unitary QM. My hope is that gravity does such a thing, but it might very well not, and then I don't see how to save unwackyness :cool:

But the message of all this is simply that jumping to the conclusion that Bell's theorem NECESSARILY implies non-causality is wrong: there's a counter example and that's Many Worlds (even if you don't like it). In the same way as saying that Bell's theorem doesn't allow for a hidden variable model of QM: Bohm's mechanics is an example (even if you don't like it).

cheers,
Patrick.
 
Nacho said:
Seratin:

I'm not going to be too good at this .. but here goes:

Code:

--- (+) ------ | ---->(SG)--->| | --- (-) ----->(SG)--->| | ------ (-) --- ( input to (C) )



That is what Observer (A) sees .. the electrons going into the first SG magnet. 1/2 are deflected UP (+), 1/2 are deflected down (-). The "down" electrons are sent through another SG magnet, same setup as the 1st SG magnet. All of them will deflect down (-), as they are "already measured".

Now, Observer (B), unbeknownest to (A) or (C), takes those down (-) electrons and shoves those through a SG magnet that (C) is watching. The SG magnet is oriented exactly the same as the 2 SG magnets that (A) is observing.

That's it .. but remember:

A is not aware of B or C.
C is not aware of B or A.
B is aware of what A and B is doing .. but I don't think it matters to the setup.
There is no problem with this- C will conclude that he was observing a bunch of electrons which had already been prepared in the down eigenstate in the direction of his SG. C's observation doesn't affect the electrons because they were not in an uncertain state (no superposition of up and down) before his measurement.
 
vanesch said:
But the concept of, say, the number "5" seems to exist, irrespective of whether we have the right definition for it. If we don't have it, we're simply talking about something else but the number 5. And if we have it, we simply have A FORMAL REPRESENTATION of the concept "5". There can be different formal representations of that same concept (with symbols on a sheet of paper, like with the set-theoretic construction, or with potatoes, or whatever), but if they are correct representations of that same concept, they are equivalent (that's somehow tautological).
You have implicitly choosen a context: the numbers.


vanesch said:
Now, it seems that people like you DO NOT believe in that underlying concept, and ONLY see the formal game. It is my not so humble opinion that you're then missing something :tongue:
I think you are missing the point, I have no belief, I am just using logic to make statements (with sometimes some logical errors : ) and up to now, I think both maths and physics have also made this choice.

I know I may always construct an underlying property assuming a set of all properties (E), I may call the [contextual] ontological property (e.g. belongs to P(E)). This is a formal logical construction and the equivalence between these 2 views through what can be viewed as a context (i.e. the set E). But this not a true ontological property (it depends on the choosen context). In addition, it requires some care to extend the equivalence to other mathematical objects larger than sets: it may leads to logical inconsistencies and in fine these new mathematical objects define a new context.

I just say that currently physics chooses to describe the “reality” objects by a set of logical propositions (a choice and not an obligation). The description by a reduced set of properties of a “real” object includes [i.e. is compatible with] the case where the object may have an “ontological reality” (it does not require the existence of such an ontological property). However, assuming an *ab initio* ontological status of the “reality” object may lead to logical inconsistencies as long as we are not able to prove logically the validity of the “ontology” property – whatever, it could be (hence my remark: you like the difficulties): QM is full of such examples (e.g. the improvements in the bohmian mechanics in order to keep the compatibility with QM result, etc ...).

vanesch said:
I can (by definition !) of course not give you a formal argument of why this is so, but I'm firmly convinced that the concept "5" exists, even if we don't have a nice formal definition for it.
If you look at the axiomatic set theory (e.g. ZF theory), you will see that the mathematical existence is one of the most difficult properties to obtain/understand (e.g. axiom of choice in set theory). It usually requires the formal statement of the existence of wider objects (usually the theory itself). What we can obtain more easily is the consistency of a logical construction: I do not know (logic) if a set exists (without a larger theory containing the set objects), I just know (logic) that the ZF, ZF+C and ZF not C is logically consistent, hence my claim: I do not care that “5” exists, I just want that the logical constructions I make with 5 are consistent (i.e. I usually choose the inductive construction of naturals numbers based on the ZF set theory).


vanesch said:
It existed in the time of the Romans, if you want to. We only DISCOVERED a formal representation of it in the relatively recent history.
There's a nice argument for this in Penrose (I admit being greatly influenced by the man). It goes as follows: take Fermat's last theorem. Does that theorem "exist" ?
One of the main problems of physicists: the mixture between the logical content of physics and the philosophical external extension (that should remain consistent with the logical content otherwise we have no more the same theory).
The following of this section of your post tries to give another meaning to the “existence” we have in the mathematical language => Once again, I say ok. You are free to choose your own definition. Everyone has this formal right (logical choice). However, as long as you are not able to give a formal logical meaning to this new definition, it is almost impossible to see the logical consistency of such affirmations.

In mathematics, we have theorems and proofs about these theorems. A proof may be wrong. Depending on the assumptions (formal choices), we have different conclusions, and these conclusions may be also false or inconsistent . That’s all we can say in general when we *choose* to use logic.

vanesch said:
A class of course, UNTIL we finally hit upon a faithful representation: in that case we hit upon a mathematical structure which can serve as an ontology.
That's what I tried to illustrate: a cat corresponds to a complicated thing, but it center of gravity is a point in 3-dim euclidean space (unless you really do nasty things with your cat). So there's a (non-faithful) representation from the complicated mathematical object "cat" onto E^3. And that can be sufficient for my purpose (like when I say that my cat sits on the roof), or not. If I want to describe a bit more my cat, there's another (non-faithful) representation into the simply connected subspaces of E^3, and now I can talk about the form of my cat, etc...
But I do assume that there's an underlying concept, "my cat", which has an ontological existence irrespective of what representation I CHOOSE to use of it. ?
So as long as you are not able to prove the existence of an “underlying concept” irrespective of what interpretation you choose, you follow the epistemic view : )).
Does that mean you choose (logical choice) to reduce the collection of possible representations to the ones compatible with the existence of such an underlying concept?

Don’t you think the above question defines an implicit context of the underlying concept and hence is not strictly compatible with the ontology.

vanesch said:
Yes, you can define "my cat" as just the collection of all thinkable properties that you could possibly attribute to it. But my claim is that this collection of properties is like all possible atlases in differential geometry: in the end it describes an underlying mathematical concept, namely a differentiable manifold, which has, in my view, a platonic existence *INDEPENDENT* of how we chose to represent (define) it formally.
For a given context (e.g. choice of a given set of properties), you may have a common denominator, that you may call a representation. However, for another context, you may have another representation. These representations may be logically incompatible (e.g. the incompatible observables in QM, or if you prefer one proposition true in one context may be false in another context) => to get a common representation compatible with these 2 incompatible representations you will need to define an ad-hoc external mathematical object (e.g. Boolean lattices vs non Boolean lattices in QM).

I do not know if this inductive construction is always possible (i.e. consistency) and I do not see what additional information it brings (my remark: you like complications ; ).


vanesch said:
I would say that it is somehow much more reassuring on the consistency side to HAVE an underlying concept from which we deduce properties (have representations), than just randomly have a set of properties.
After all, if your set of properties is to be a consistent thing, I do not see what it can be else but a mathematical object !
You have a context: the set of properties hence an underlying concept valid for this context. For me an ontological property that depends on the context is not really ontological (once again, it depends on the logical content of the ontological concept).
If you accept a context (e.g. a given mathematical theory) to define the consistency of your properties, you are implicitly rejecting the ontology (in the sense: independent of the context).

vanesch said:
As a simple example: let us take fractions. I claim that "fractions have a mathematical existence". You just say that fractions are "pairs of integers over which we defined an equivalence relation, because that's how they are formally defined". But if you define stuff like the sum of two fractions, and so on, more and more you get away from that "pair of integers ..." and you work more and more with Q, the set of rational numbers.
And you can begin to start to see that this "pair of integers with an equivalence relation" is not really the DEFINITION of rational numbers, but a REPRESENTATION (a faithful representation).
Yes an implicitly contextual representation: the numbers.

Seratend.
 
Nacho said:
Seratin:

I'm not going to be too good at this .. but here goes:

Code:
             --- (+) ------
             |
---->(SG)--->|
             |
             --- (-) ----->(SG)--->|
                                   |
                                   ------ (-) --- ( input to (C) )
That is what Observer (A) sees .. the electrons going into the first SG magnet. 1/2 are deflected UP (+), 1/2 are deflected down (-). The "down" electrons are sent through another SG magnet, same setup as the 1st SG magnet. All of them will deflect down (-), as they are "already measured".

Now, Observer (B), unbeknownest to (A) or (C), takes those down (-) electrons and shoves those through a SG magnet that (C) is watching. The SG magnet is oriented exactly the same as the 2 SG magnets that (A) is observing.

That's it .. but remember:

A is not aware of B or C.
C is not aware of B or A.
B is aware of what A and B is doing .. but I don't think it matters to the setup.
Ok (sorry for the late answer). What is for you the logical content of an observer?
For me, you are implicitly choosing an observer with 2 properties:
a) an observer may interact with the experiment: with QM I describe it through an hamiltonian interaction (property: the hamiltonian)
b) the result of a given experiment (the eigenvalue of an observable or more precisely the property for a given experiment, i.e. an electron with spin down at time t within a given finite area).

In this case what does mean "not aware"? Do you see that this decomposition of the "observer" allows to split the problem into the time evolution of the state defining the probability law of a collection of compatible properties (the results)?
Do you understand that these results are not predictive ones but just reflect (acknowledge) what a peculiar experiment gives? (i.e. they do not exist outside the experiment that has - and not will have- these properties).

If you choose a collection of properties that have a zero probability (for a given context), you will have a zero probabiltiy to *find* an experiment with such results. That's all you can say.

Seratend.

P.S. Answer to your post, if I asume the good interactions, spin down for (C).
 
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Miserable,

There is no problem with this- C will conclude that he was observing a bunch of electrons which had already been prepared in the down eigenstate in the direction of his SG. C's observation doesn't affect the electrons because they were not in an uncertain state (no superposition of up and down) before his measurement.
I agree, but that was just the setting up of the experiment to show some subtilies of how a person tries to explain away the measurement/reality problem.

As you answered, C's participation in the experiment couldn't have introduced/made any reality into the outcome of the experiment. So, I think that on least some measurements you (anybody) have to conclude that the observer doesn't create any reality.

Maybe you could come back and say reality is transferable to other observers, or once reality is made, all other persons would see that same reality. But, then if you still hold onto observer-creating-reality, look back to that very initial observation that "A" made .. where the electron beam split in two and examine that a bit.

The beam couldn't have split in two just because of randomness of a predetermined orientation of the electrons (I'm told that is not possible, and agree). And you (anybody) adhere to the thought that the observer creates the reality. How then did those electrons get "reset" from a previous observation on them to a state that your reality of observation can set them? Another person making an observation couldn't have done it. I think you (anybody) must conclude that "nature" resets them so that your observation can make the reality.

And if you conclude that, then "nature" itself can make a change in a state of reality .. an observer is not needed for at least some changes in reality. Then why is an observer needed to create any reality? Leave it all to be "nature" (particle interactions).
 
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Seratend,

My diagram was just a problem setup to explore some subtilies of the "reality" problem. It went further in my last post to "Miserable".

Of your response .. well, it appears to me that that is a QM/mathmatical description of what is happening. I'm not disagreeing with it, but I want to bear this out. QM/mathmatical interpretations don't really make any predictions about the reality aspects of an experiment. I think that is added on solely as a study in philosophy.
 
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Nacho said:
Seratend,

My diagram was just a problem setup to explore some subtilies of the "reality" problem. It went further in my last post to "Miserable".

Of your response .. well, it appears to me that that is a QM/mathmatical description of what is happening. I'm not disagreeing with it, but I want to bear this out.
Sorry, If you leave the light of mathematics and physics, I have nothing to say. I think this forum section and this thread are not the good ones to continue in this direction.

Seratend.
 
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Seratend,

Sorry, If you leave the light of mathematics and physics, I have nothing to say. I think this forum section and this thread are not the good ones to continue in this direction.
Maybe I misunderstood when you posted this:

In other words, the observer is also part of the context of the experiment for the given property (the "measurement result").
I took that to mean that you believed actions of the observer took part in the reality of measurements. Where did I go wrong there? I'm not necessarily wanting a discussion of the philosophy .. maybe just to show that how a person thinks about/interprets observer created reality is really a discussion in philosophy.
 

vanesch

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seratend said:
For a given context (e.g. choice of a given set of properties), you may have a common denominator, that you may call a representation. However, for another context, you may have another representation. These representations may be logically incompatible (e.g. the incompatible observables in QM, or if you prefer one proposition true in one context may be false in another context) => to get a common representation compatible with these 2 incompatible representations you will need to define an ad-hoc external mathematical object (e.g. Boolean lattices vs non Boolean lattices in QM).

I do not know if this inductive construction is always possible (i.e. consistency) and I do not see what additional information it brings (my remark: you like complications ; ).
Well, I'd say: that's the point exactly. I think it would be seen by most physicists as a problem if we have 2 sets of properties (2 representations) of "nature" which are logically incompatible, if it is not in the context that at least one of them is known to be only "an approximation". This is exactly what "unification" is all about, no ?

However, I do not have any problem with "incompatible observables" in QM as logically incompatible: I do not assign something like a position property and a momentum property to a quantum particle ; if quantum theory is correct, its existence is given by a wavefunction in hilbert space, and I'm able to observe a component of that wavefunction, which can be in the position basis or the momentum basis, according to the experiment I try to perform.
Of course, this can all be wrong - after all physics is about DISCOVERING the laws of nature, not about formally setting them up. So it can be that QM is not correct.

cheers,
Patrick.
 
vanesch said:
Well, I'd say: that's the point exactly. I think it would be seen by most physicists as a problem if we have 2 sets of properties (2 representations) of "nature" which are logically incompatible, if it is not in the context that at least one of them is known to be only "an approximation".
This is the heart of the QM formalism and the interpretation problems it rises. QM postulates say that you can describe the "reality" properties through, e.g. the position or momentum filter => We obtain 2 incompatible descriptions and there is no approximation in these descriptions (we have, formally, "a particle at position x" or "a particle with momentum p" properties).

vanesch said:
However, I do not have any problem with "incompatible observables" in QM as logically incompatible: I do not assign something like a position property and a momentum property to a quantum particle ;
Yes you do. When you describe the results of an experiment, you implicitly have these properties. You can't avoid it (otherwise you cannot describe your experiment).

vanesch said:
if quantum theory is correct, its existence is given by a wavefunction in hilbert space, and I'm able to observe a component of that wavefunction, which can be in the position basis or the momentum basis, according to the experiment I try to perform.
You are not able to observe a component of that wavefunction. All you can say is that you may deduce a component of a peculiar wavefunction from the [observed] properties of a set of experiments. That's all what the formalism allow you to do (i.e. it is a choice of description). The rest is outside the theory content (i.e. interpretation) and may lead to some inconsistencies.

vanesch said:
Of course, this can all be wrong - after all physics is about DISCOVERING the laws of nature, not about formally setting them up. So it can be that QM is not correct.
Yes discovering (or may be describing the nature in a large sense), but with the use of logic : )).

Seratend.
 
Nacho said:
I took that to mean that you believed actions of the observer took part in the reality of measurements. Where did I go wrong there?
I think you attach to the observer more properties than I do (hence it lacks a minimum of mathematical rigor).

Nacho said:
I'm not necessarily wanting a discussion of the philosophy .. maybe just to show that how a person thinks about/interprets observer created reality is really a discussion in philosophy.
Ok. I think the main problem you have is that you do not seem to see that physics in general is a description of reality and not a creation of reality (whatever it could mean : )).
A description (e.g. a set of properties), may include the past the present and future (you need to think in space time and not in space or in time).

A description applies or not to a physical system but not "will apply" nor "will not apply". All QM formalism is based on this distinction and many paradoxes rise from this misunderstanding. (e.g. collapse postulate does not say how the things will be but how the things are).

The "observer" (when we remove the interaction part cf previous post reply) is formally a property (or a collection of= another property). A property is not a person (cloud, a stone, etc ...). However a person is a property or the property applies to this person.

Now you can add a creation of reality concept, but it is an additionnal object to the QM formalism description and hence may have a lot of inconsistencies until you proove it is formally consistent.

Seratend.
 

vanesch

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seratend said:
Yes you do. When you describe the results of an experiment, you implicitly have these properties. You can't avoid it (otherwise you cannot describe your experiment).
What's wrong with the view that the meaning of "and the result of the position measurement of particle A is x" comes down to: "I'm an observer which is now entangled with the particle A's part of the wavefunction which is an eigenstate of the position operator I've assigned to particle A", which says in the end more about my state as an observer, than about particle A. So particle A has absolutely not "a position x" or whatever, but I can pretend it to be in such a state.

This is somehow a bit analoguous to: "and the x-coordinate of the astronaut is", and then saying a lot about incompatible results about x-coordinates from different possible observations (coordinate systems).
The x-coordinate is simply an observer-dependent property which is not "a property of the astronaute" but describes the relationship between the astronaute and the observer.

cheers,
Patrick.
 
vanesch said:
...a certain sarcasm in your post...
I wasn't being sarcastic.
Honest - I made a mistake and I was apologising.
I'm Sorry.
Shalom Shlomo
 
vanesch said:
What's wrong with the view that the meaning of "and the result of the position measurement of particle A is x" comes down to: "I'm an observer which is now entangled with the particle A's part of the wavefunction which is an eigenstate of the position operator I've assigned to particle A", which says in the end more about my state as an observer, than about particle A. So particle A has absolutely not "a position x" or whatever, but I can pretend it to be in such a state.
Basically nothing (wrong with the view). You have 2 different propositions that may be incompatible depending on the context where they are used.

The second proposition is equivalent to the state of the (observer, particle A) is "entangled state". Where we may attach a real value to "entangled state" to define a projector and hence we have a proposition "and the result of the position measurement of (observer, particle A) is the real value "entangled state" (we just recover a first proposition concerning a system "observer +particle A").
=> I do not see why you can say this proposition "says in the end more about my state as an observer, than about particle A". (May be I have not understood your example).

vanesch said:
So particle A has absolutely not "a position x" or whatever, but I can pretend it to be in such a state" without external data.
You are free to assign the propositions you want to a "real" system (in this case observer+particleA), this is a logical choice. However, if you do not compare the consistency of this proposition with deduced propositions from "real" systems (i.e. the "measurement results"), you have no more physics, just a mathematical theory (i.e. "disconnected from reality").

I think I am missing what you want to mean.


vanesch said:
This is somehow a bit analoguous to: "and the x-coordinate of the astronaut is", and then saying a lot about incompatible results about x-coordinates from different possible observations (coordinate systems).
The x-coordinate is simply an observer-dependent property which is not "a property of the astronaute" but describes the relationship between the astronaute and the observer.
It's funny. I am not sure I have understood at all this post (in a non pejorative way). In the previous posts, I understand you try to introduce an ontological view of reality and in this final post you just reintroduce, implicitly, an epistemic view through the observer. All what I say is that I have properties and these properties are defined (sometimes implicitly) within a context (that may be "an observer").

Seratend.

P.S. (astronaute vs astronaut => Parlez vous français et aimez vous le bon vin et le fromage qui sent pas bon? :tongue2: :biggrin: :biggrin:
 

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You are free to assign the propositions you want to a "real" system (in this case observer+particleA), this is a logical choice. However, if you do not compare the consistency of this proposition with deduced propositions from "real" systems (i.e. the "measurement results"), you have no more physics, just a mathematical theory (i.e. "disconnected from reality").
I think you have put your finger on the nub of the whole measurement problem. There is no physics associated with the observation/measurement. The "consciousness of the observer" is not a controlled or objectively observable system.
 
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collapse of the wavefunction

The following is what I wrote in one of the 'meataphysics and epistemology' threads('no observer no existence').Surprisingly it has received no comments,good or bad,there.So I am putting it up here with the hope that it generates at least a few replies:-

I think 'collapse of the wavefunction' is not such a mysterious thing as it is made out to be.What do you do when you do a measurement----you just reduce the [tex] \Delta x [/tex] or the position uncertainty of the particle(so that you know the position of the particle (reasonably well)),whereas the momentum uncertainty becomes high.So what you do when you make a measurement is simply this-------you reduce the particle's position uncertainty whereas you increase its momentum uncertainty(given any initial wavefunction)--it's 'as if ' you have a gamma ray microscope in your hands and you 'observe' the particle---in doing so you inevitably disturb the particle,so whatever interference/diffraction pattern you would have expected in absence of the measurement is disturbed.The 'collapse' is a literal collapse in the position sense---the problem is to show that this can come out of a unitary process.'If ' we can do that(may be we could take the measurement to be introduction of some sort of a potential which changes the wavefunction and localizes the particle in the position sense) then the need for mysterious things like consciousness,MWI etc. goes away--note the 'if' in the statement.
 

vanesch

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seratend said:
B
It's funny. I am not sure I have understood at all this post (in a non pejorative way). In the previous posts, I understand you try to introduce an ontological view of reality and in this final post you just reintroduce, implicitly, an epistemic view through the observer. All what I say is that I have properties and these properties are defined (sometimes implicitly) within a context (that may be "an observer").

Seratend.

P.S. (astronaute vs astronaut => Parlez vous français et aimez vous le bon vin et le fromage qui sent pas bon? :tongue2: :biggrin: :biggrin:
First of all, yes, I like the good wine and the smelly cheese (and lots of other stuff around here :-) ; one of the reasons to stick to a certain ontology :-)

I have indeed the impression that we are talking next to eachother, and I'm affraid I'm not clear on your viewpoint as well.

I'm *for the moment* a kind of MWI fan, with the hope that I'm wrong :blushing:
I have difficulties with a purely epistemological view because *something* exists (a la Descartes, also from cheese and wine fame). Now, because we don't have anything better, the mathematical object that seems to be a representation of "what exists" (ontological view) is "the wavefunction". I'm fully aware that this can be wrong, but for the moment we don't have anything better. What I was trying to argue was that *some representation* of what is "really out there" must be part of a successfull physical theory. (why ? Because my bones (and Descartes) tell me so :-) Maybe QM is not such a theory and one day we will understand our confusion (that's my hope, in fact). But for the moment we don't have anything of the kind. So we'll have to do with it. Where does it lead us ?
If we take the wavefunction to be a representation of reality, clearly the collapse gives us a problem: how can a meager observation by a humble human change the state of the entire universe ?
So this "collapse" stuff must be something EPISTEMOLOGICAL.
And MWI shows you how:

System "before":
|ignorant me> (a |u> + b |v> )

System "after":

a |u> |the-me-i'm-aware-of> + b |v> |some-other-me-i-don't-know-about>

So through the "looking glasses of the observations I'm aware of" (call this epistemology if you want), the system is now in state |u> and I got there with probability |a|^2.

But when you look at the "ontology" (if that's what the wavefunction represents), this measurement did in fact more to me than to the system, which is still with amplitude a in |u> and with amplitud b in |v> except that it's now entangled with my bodystates ; that's what I meant.

cheers,
Patrick.
 

vanesch

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gptejms said:
you just reduce the [tex] \Delta x [/tex] or the position uncertainty of the particle(so that you know the position of the particle (reasonably well)),whereas the momentum uncertainty becomes high.
The classical argument against saying that "the wavefunction is a representation of the information we have about a system" is that hydrogen molecules exist, independent of the information we have about them, for instance. The binding energy of a hydrogen molecule (calculated from its wavefunction in the ground state) doesn't "change" because we know, or don't know, things about it.
That's different in classical statistical mechanics: if for one reason or another, you KNOW the microscopic state of, say, a gas in a container, this changes drastically the density in phase space (from the canonical ensemble, it becomes a delta-function), but that doesn't change any physical property of the gas.

The 'collapse' is a literal collapse in the position sense---the problem is to show that this can come out of a unitary process.'If ' we can do that(may be we could take the measurement to be introduction of some sort of a potential which changes the wavefunction and localizes the particle in the position sense) then the need for mysterious things like consciousness,MWI etc. goes away--note the 'if' in the statement.
I think it is easy to show that collapse cannot come from a unitary process. I showed it here already (it takes 5 lines or so). Unitarity implies linearity and conservation of hilbert norm, so you CANNOT collapse the wavefunction with a unitary operator. Even the decoherence people acknowledge this (sometimes :-).

cheers,
Patrick.
 
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vanesch said:
Unitarity implies linearity and conservation of hilbert norm, so you CANNOT collapse the wavefunction with a unitary operator. Even the decoherence people acknowledge this (sometimes :-).
Does that mean, therefore, that if wavefunction collapse is "real", there must be some nonlinearity in the time evolution operator?
 

vanesch

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Nicky said:
Does that mean, therefore, that if wavefunction collapse is "real", there must be some nonlinearity in the time evolution operator?
Yes. Some people try to add some tiny non-linearities and some noise to the Schroedinger equation, with the hope that it doesn't change most of what works in QM, and that it induces a genuine collapse.

The problem I have with that approach is that it is "fiddling" and that it destroys completely the mathematical structure of QM without replacing it with another fundamental principle. What we also know is that, given the EPR results, those terms will have to violate SR too.
In fact, if you allow for all that, there's no point in looking further, there IS already a theory which does that, correctly: Bohmian mechanics !

My uninformed gut-feeling is that if we are to do that, it should be by a modification of GR based upon some or other general principle, and not just by adding a fudge term in some equation.

cheers,
Patrick.
 
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vanesch said:
I think it is easy to show that collapse cannot come from a unitary process. I showed it here already (it takes 5 lines or so). Unitarity implies linearity and conservation of hilbert norm, so you CANNOT collapse the wavefunction with a unitary operator. Even the decoherence people acknowledge this (sometimes :-).
I realize that but at the same time I am against a special role for consciousness in the measurement process.Say you have a double slit experiment(with electrons) and you look for photons with a gamma ray microscope at one of the slits.What I am saying is that this measurement process may be pictured as the introduction of 'some potential' which localizes the wavefunction--the potential would necessarily change the wavefunction and in this case localizes it to one of the slits.In other words,one could picture the measurement process here as the interaction between two fields, the electron field and the photon field and somehow this interaction forces the electrons to appear at one or the other slit.
 

vanesch

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gptejms said:
Say you have a double slit experiment(with electrons) and you look for photons with a gamma ray microscope at one of the slits.What I am saying is that this measurement process may be pictured as the introduction of 'some potential' which localizes the wavefunction--the potential would necessarily change the wavefunction and in this case localizes it to one of the slits.In other words,one could picture the measurement process here as the interaction between two fields, the electron field and the photon field and somehow this interaction forces the electrons to appear at one or the other slit.
In order to say so, you have to consider the measurement system "classical", in that you put a "classical" potential in the Schroedinger equation of the electron. In doing so, you've neglected the quantum nature of the microscope. Of course, in practice this works in many occasions (semi-classical models work very well in different fields) ; after all that is the correspondence principle.
But doing so puts you in a Copenhagen view (the "macroscopic, classical, ontological" world vs the "microscopic, quantum, epistemological" world) already, and you have again to explain what differentiates both.
If you insist on all the atoms and so on of the gamma ray microscope to be described quantum-mechanically, and the EM field of the gamma ray microscope also through QFT, then the gamma ray microscope doesn't introduce "a potential" in the electron schroedinger equation, but both systems (electron + microscope) are COUPLED through an interaction term in the overall product hilbertspace.
And if you do that, again, you do not obtain a projection, but an entanglement.

As with all resolutions of the projection postulate without modifying the unitary part of QM that I've come across: the projection postulate follows naturally if you have sneaked it in through the back door :tongue2:
That is the case in Copenhagen (you POSTULATE a classical macroscopic world, and its (fuzzy) transition from the quantum world by projection), that's true for those who think that decoherence solves the problem (they use the density matrix, which itself is based upon the Born rule and the projection postulate), it is even true for Deutsch (who introduces some "reasonable assumptions" for his rational deciders which comes down to the Born rule).

cheers,
Patrick.
 
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vanesch said:
In fact, if you allow for all that, there's no point in looking further, there IS already a theory which does that, correctly: Bohmian mechanics !
I was under the impression that Bohmian mechanics does not explain well the collapse of wavefunctions, i.e. the sudden discontinuity in Bohm's "quantum potential" after measurement.
 

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