Question on observer created reality [Archive]

vanesch

Jul12-05, 10:48 AM

In other words the particles have no position until the observer decides to measure position at which time the particles then aquire position. So my question still is what gives the observer the ability to create its reality.

This is the Copenhagen view of things, and its obvious problems. One of the reasons NOT to adhere to Copenhagen :yuck:

But there are other ways of viewing quantum theory. First one has to make a big choice: is there an existing, real world out there or not ? This can sound like a completely crazy question from a physicist, but its answer is not so obvious.

A) there is a real world out there.

B) there's no real world.

Let's deal with B. What can it possibly mean ? It means that all there is, is "observation", and "knowledge". In that respect, quantum theory just tells us about relationships between observations (of nothing :-) and your knowledge (of nothing :-). I'd say that here we are in Alice in Wonderland: anything goes.
There's a variant: there is a real world out there all right, but it is not described by any laws ; all we are allowed to know and observe is given by quantum theory which doesn't describe it, but just gives us relationships between our observations and knowledge.

So let's go for A: there is some real world of some kind or other out there. What are the possibilities ?

1) there is only partly a real world, and some Alice in Wonderland. The real world is ruled by classical mechanics, and the microworld doesn't exist, and is ruled by quantum theory (that's Copenhagen, essentially). When certain aspects of that quantum world "go classical" they become real. I find that a very disturbing view, just as disturbing as B.

2) there is a real, classical world out there, and quantum theory is just a kind of statistical mechanics dealing with it. That was Einstein's view. Although it is not excluded, this classical world violates very, very fundamental properties in that case, like causality. Choices you will make tomorrow influence things today.

3) there is a real world out there, ruled by (unitary) quantum mechanics, and observers only observe part of it (one term of the wavefunction). It is this partial observation which introduces the apparent randomness. That's many worlds (comes in many subtle flavors). It's my favorite.

4) quantum theory + collapse are real phenomena ; certain processes do cause collapse, we simply haven't figured out the details yet. This is the von Neuman view. It suffers a bit from the same problems as 2), in that whatever causes collapse, is also non-causal.

My personal view is 3) with some hope for a subtle 4).

cheers,
Patrick.

selfAdjoint

Jul12-05, 12:35 PM

vanesch

Jul12-05, 01:40 PM

selfAdjoint

Jul12-05, 03:56 PM

What's the difference with (my favorite) 3) ??

cheers,
Patrick

(BTW, I'm looking at that relational paper, but I still have to wrap my mind around it...)

Umm, there's no difference, I guess. Just that it's important to stress that we can't be confident quantum theory shows us all the behavior of nature. It shows us what it is adapted to showing us. And that the reason we always come around to mind in interpreting QM is that QM is specifically designed to do that. To put a boundary between the world and "us".

Of course this all sounds Kantian, but I think any way we might interpret is going to sound like some philosopher - they seem to have covered all the bases between them!

But I'm eager to hear what you think about the relational paper.

seratend

Jul12-05, 04:46 PM

How about (4) There is a real world out there but quantum theory doesn't describe it; quantum theory describes our relationship to it. This is why there is a "boundary" in interpreting QM, somewhere between the world and us. The world behaves non-classically on the other side of the boundary and we behave, "sort of classically" on our side, and the only thing that can cross the boundary is a probability. Any quantum setup we make is just constructing a window to look at the world through quantum theory glass.

This is almost equivalent to define a case C): we do not care (if there is a real world or not): out of the scope of physics (the epistemic view).

I think one should accept that the existence of a real world or not does not change the results of a physical theory: it is first a logical description (and prediction) of some phenomena with a domain of validity. Any extrapolation from this point is, in my opinion, somewhat the domain of philosophy or metaphysics.

Accepting this point may help in simplifying the interpretation scope of a physical theory such as QM.

Seratend.

seratend

Jul12-05, 05:37 PM

Lets take the position attribute. To my understanding this attribute does not exist until it is measured.

For one moment forget about reality and try to focus on the properties needed to describe logically the reality (what we normally do when we describe an experiment and its results).

As with mathematics an object does not exist until it is defined. However, interpreting that the object exists because I have written it on a piece of paper (i.e. it does not exist before) is of the scope of mathematics (in this context).

Now, why do you need to say that the position attribute (I prefer to call it a property or proposition) does not exist until it is measured?
You just need to say that a given "experiment" has a given property, that's all. The logical definition of a given experiment defines the context (the domain of validity) of the property => different properties mean different experiments.
A "dynamical property" is a property (e.g. position x at time t) and an experiment may have a collection of properties (that defines a single property): this is the reformulation of the consistent histories formalism (i.e. stochastic processes).

Now if you take into account this logical description of experiments, the things should be simplified and most of yours problems should disappear.

For example, rewrite your box example taking into account this logical approach. To do that, you must understand, logically, that the box without the detectors is neither the box with detectors nor a box without detectors before time to and with detectors after time to etc ... (implicitly different logical contexts). In other words, the observer is also part of the context of the experiment for the given property (the "measurement result").

Seratend.

Nacho

Jul12-05, 10:30 PM

In other words, the observer is also part of the context of the experiment for the given property (the "measurement result").

Yeah, but take this setup .. Take a beam of electrons through a Stern-Gerlach magnet setup. Observer (A) sees 1/2 of them deflect up and 1/2 will deflect down. Take the "down" electrons and send it through the exact same setup and that same Observer (A) will see all of those electrons will deflect down.

You are Observer (B), and you take those "down" electrons and funnel over to Observer (C) who is doing the same thing as Observer (A), but Observer (C) is not aware of Observer (A) or what you are doing (also Observer (A) is not aware of you or Observer (C)).

Now let Observer (C) view those "down" electrons through his exact same Stern-Gerlach magnet setup as Observer (A). And then later you bring all three people together and discuss what yall observed.

Question: What does observer (C) see the electrons doing?

I don't know the answer. I suppose there is an outside chance 1/2 would defect up and 1/2 would deflect down. I doubt it.

I'd suppose he'd see them deflecting down. If so, he couldn't have created any reality in that experiment. Maybe either Observer (A) or you created the reality when you made the observation? I doubt it, because that would mean reality (in the context of "observer creating reality") is transferable from one person to another.

Or maybe it means that once reality is created by Observer (A), it is reality for all 3 Observers. If so, that begs the question: What "resets reality" so that Observer (A) is able to see of an initial beam of electrons, 1/2 deflect up and 1/2 deflect down? It can't be that he just got a sample of electrons that already were 1/2 "up" and 1/2 "down" electrons. We've come full circle in this "reality/observer part of the experiment" thing.

vanesch

Jul12-05, 11:38 PM

This is almost equivalent to define a case C): we do not care (if there is a real world or not): out of the scope of physics (the epistemic view).

That was my case B): if you do not care whether there is some real world, you can just as well assume it doesn't exist, because all you're talking about then, are relationships between knowledge and observations (of nothing :-). This is what I referred to as Alice in Wonderland. I have some difficulties with this view, even if purely from a mathematical point of view. It seems to be equivalent, say, to having an atlas with coordinate patches, but "not to care" whether it describes an underlying manifold or not. I think that that does not make much sense: you'd have a geometrical description of a non-existent geometry! It is going to be difficult to do any meaningful work there, no ?

cheers,
Patrick.

seratend

Jul13-05, 03:14 AM

That was my case B): if you do not care whether there is some real world, you can just as well assume it doesn't exist, because all you're talking about then, are relationships between knowledge and observations (of nothing :-).

Ok, so your case B) is "case A) is not true".
Beware, "nothing" is meaningless in case B).

This is what I referred to as Alice in Wonderland. I have some difficulties with this view, even if purely from a mathematical point of view. It seems to be equivalent, say, to having an atlas with coordinate patches, but "not to care" whether it describes an underlying manifold or not. I think that that does not make much sense: you'd have a geometrical description of a non-existent geometry! It is going to be difficult to do any meaningful work there, no ?

cheers,
Patrick.

Think on your logical meaning of meaningful as I think what you call meaningful is different from what I call meaningful (~ mainly the ability to do logical deductions/assertions).

Do you care if I say a natural number is for example peculiar subset of real numbers or a collection of potatoes or an inductive construction based the empty set, if the properties of natural numbers are preserved?

Think on the logical way to describe the reality: we have mainly a collection of properties (cat, black, eyes, speed ...) and a choice in the association of these properties with the properties of a mathematical theory in order to verify the consistency of the properties (e.g. mainly by a logical comparison with reference objects).

You can add your own reality property to the cat example above as long as it does not change the consistency of the other properties. Does it make the cat more meaningful than a simple collection of consistent properties?

What is the most important (anthropomorphic view)?: the consistency of the properties we attach to reality or their ontology?

Seratend.

vanesch

Jul13-05, 03:52 AM

Do you care if I say a natural number is for example peculiar subset of real numbers or a collection of potatoes or an inductive construction based the empty set, if the properties of natural numbers are preserved?

This is slightly different, because the natural numbers are a mathematical concept, not yet part of any physical theory as such. Now, if you want to know my view on THAT issue (which is not the one in physics), I do associate a kind of ontology (Platonic existence) to the natural numbers, irrespective of whether I use representations of that concept based upon structures in set theory, or potatoes, or drops of dried ink on a sheet of paper.

Think on the logical way to describe the reality: we have mainly a collection of properties (cat, black, eyes, speed ...) and a choice in the association of these properties with the properties of a mathematical theory in order to verify the consistency of the properties (e.g. mainly by a logical comparison with reference objects).

You can add your own reality property to the cat example above as long as it does not change the consistency of the other properties. Does it make the cat more meaningful than a simple collection of consistent properties?

The ontology of "cat" is then the underlying Platonic existence of the mathematical structure (worked out in a specific representation) that we associate to "cat". Call it your collection of properties: we have to associate an underlying mathematical structure with them, or better, a REPRESENTATION of such an underlying structure (this representation can take on different forms, and only represent partly the whole structure: whether it is just a point in 3-dim Euclidean space "my cat is on the roof of that building" ; or something more sophisticated, up to "|psi> is the wavefunction of my cat"). All these things are representations of a mathematical object that is supposed to be my cat (in the same way as we have representations of abstract groups with matrices in n-dimensional vector spaces).
What I'm claiming is that there needs to be such an underlying mathematical object, and that there is a real (Platonic) ontology to be associated to this object. You seem to accept the existence of the different "properties" without them to be a representation of an underlying mathematical object.

It is what I tried to depict with "having an atlas without a manifold".

What is the most important (anthropomorphic view)?: the consistency of the properties we attach to reality or their ontology?

I'd say that from the latter follows the former !
(and probably from the former follows the latter)

cheers,
Patrick.

seratend

Jul13-05, 04:07 AM

Yeah, but take this setup .. Take a beam of electrons through a Stern-Gerlach magnet setup. Observer (A) sees 1/2 of them deflect up and 1/2 will deflect down. Take the "down" electrons and send it through the exact same setup and that same Observer (A) will see all of those electrons will deflect down.

You are Observer (B), and you take those "down" electrons and funnel over to Observer (C) who is doing the same thing as Observer (A), but Observer (C) is not aware of Observer (A) or what you are doing (also Observer (A) is not aware of you or Observer (C)).

Now let Observer (C) view those "down" electrons through his exact same Stern-Gerlach magnet setup as Observer (A). And then later you bring all three people together and discuss what yall observed.

Question: What does observer (C) see the electrons doing?

I am not sure to understand your experiment. Can you make a small illustration?

e.g. this is the beginning of your description, after I am lost (i.e. I am not sure to understand what you mean)

+---|+>--------------
| |
| V
-->-[SG]+ [obs A]
^ | ^
| | |
| +---|->--------------+
| |
+----<------------------+

Seratend.

Igor_S

Jul13-05, 04:21 AM

2) there is a real, classical world out there, and quantum theory is just a kind of statistical mechanics dealing with it. That was Einstein's view. Although it is not excluded, this classical world violates very, very fundamental properties in that case, like causality. Choices you will make tomorrow influence things today.

How can classical world violate causality?

vanesch

Jul13-05, 04:31 AM

How can classical world violate causality?

Ok, that was a shortcut. If you insist on a classical existance of observation results, and EPR situations, you obviously have faster-than-light influences. Now, if you accept SR on an everyday scale (where it is amply tested), this means that you have some "back in time" influence.
Mind you, I didn't say "signalling". But clearly the classical process that determines what's going to happen to your photon in the polarizer right now at 12 AM, depends upon what Alice will do on Jupiter on 12:05, in certain reference frames. If you insist upon a classical mechanism, that is.

Igor_S

Jul13-05, 05:09 AM

Yeah, this is the tricky part. :smile: There are 2 kinds of influences: one of them is real or I would say "causal", but in the sense of deliberate, real (not sure what word to use, sorry), influence - they produce observable effects, the other is "ethereal"[1]. "Ethereal" influences would be the kind you talked about. I don't see real problem with them, since you cannot really tell did Alice at 12:05 measure something or not (nor can she). In that sense casuality is not a problem. It's not the usual effect preceeded cause, but more subtle, non-detectable one, so for some people, not really fundamental a problem. :smile:

[1] (that's the word Griffiths used in his book)

seratend

Jul13-05, 05:31 AM

This is slightly different, because the natural numbers are a mathematical concept, not yet part of any physical theory as such. Now, if you want to know my view on THAT issue (which is not the one in physics),

Yes, I do. :biggrin:

I do associate a kind of ontology (Platonic existence) to the natural numbers, irrespective of whether I use representations of that concept based upon structures in set theory, or potatoes, or drops of dried ink on a sheet of paper.

So you like complications :wink: and the risk of inconsistencies they carry. You have two jobs: using the properties of natural numbers and defining another externally consistent property on them (whatever it could be).

Logically I will say, ok fine. What kind of additionnal usefull information do you get from this additionnal property?

The ontology of "cat" is then the underlying Platonic existence of the mathematical structure (worked out in a specific representation) that we associate to "cat".

Note: "that we *choose* to associate to the cat".

Do you require a one to one mapping (between the mathematical structure and the cat "real" properties)?

Do you think that these properties define a single object or simply a class of different objects that cannot be distiguished from this collection of properties?

What I'm claiming is that there needs to be such an underlying mathematical object, and that there is a real (Platonic) ontology to be associated to this object.

Why do you say "there is a need". Personnally I do not requrie such a need, whatever it could be: I accept it if it is logically compatible with a choosen description.

You seem to accept the existence of the different "properties" without them to be a representation of an underlying mathematical object.

I am not assuming the a priori existence of properties (in the mathematical sense), just a formal choice of a collection of properties for a given object that is itself defined by a property.

What is the most important (anthropomorphic view)?: the consistency of the properties we attach to reality or their ontology?

I'd say that from the latter follows the former !
(and probably from the former follows the latter)

If you say that, you have to verify the logical consitency between the two concepts, i.e. you like the difficulties : ).
I prefer to say, I choose (formal choice) the former and I do not care of the later as, for me, it is not well defined mathematically.

Seratend.

vanesch

Jul13-05, 06:40 AM

Using the properties of natural numbers and defining another externally consistent property on them (whatever it could be).
Logically I will say, ok fine. What kind of additionnal usefull information do you get from this additionnal property?

You have of course much more formal liberty in mathematics than in physics, so what I'm going to say about the natural numbers will sound a bit artificial. But it is my belief that the "natural numbers" somehow have a platonic existence, irrespective of whether we define them or not. We can define certain mathematical constructs, and they can, or cannot, be a representation for that intangible concept of natural number. If they are, well, then they are, and if they aren't well, eh, they aren't and we are doing something else.
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).

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 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. 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" ? Now, someone who only looks at the formalism, like you, will probably say that it exists if the proof is written down. But that's something funny then. Let's say that Wiles' proof is correct. So the theorem exists. But did it exist back at the time of Fermat ? And did it exist in the time of Diophantine ? Now, let us assume that we are now all convinced that it exists, and 100 years from now, someone discovers an error in Wiles' proof. Does suddenly the theorem not exist anymore ? After a life of about 100 years ?
No, you probably take the view that the theorem EXISTS (whether we have a proof for it or not), or DOESN'T (can be undecidable or false), and this is a "timeless" and "inspiration less" thing.
So, somehow, mathematical concepts have a kind of existence of their own, independent of whether we have discovered them or not, and written down a formal representation of it.

But as I said, the *mathematical* existence of concepts (in the Platonic world) is of course less "tangible" than the *physical* existence of concepts. So let's switch to physics instead.

Note: "that we *choose* to associate to the cat".

Do you require a one to one mapping (between the mathematical structure and the cat "real" properties)?

No, not a 1-1 mapping of course. Just a representation. A group representation doesn't have to be faithful.

Do you think that these properties define a single object or simply a class of different objects that cannot be distiguished from this collection of properties?

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.

I am not assuming the a priori existence of properties (in the mathematical sense), just a formal choice of a collection of properties for a given object that is itself defined by a property.

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. In the same way, that collection of possible cat properties describes finally nothing else but an underlying physical (mathematical) concept, which is nothing else but "my cat" and has an ontological (platonic) existence, independent of exactly how I decided to define its properties etc...

If you say that, you have to verify the logical consitency between the two concepts, i.e. you like the difficulties : ).
I prefer to say, I choose (formal choice) the former and I do not care of the later as, for me, it is not well defined mathematically.

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 !
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). We can think of other faithful representations, like decimal expansions with repeating sequences, or continued fractions, or whatever. So we see that we were simply DISCOVERING a mathematical concept, namely the rational numbers, in ONE OF ITS POSSIBLE FORMAL REPRESENTATIONS.
In the same way, we were discovering just different properties of our cat, but it was there all right, even before we started to write down its list of properties.

cheers,
Patrick.

selfAdjoint

Jul13-05, 08:42 AM

But it is my belief that the "natural numbers" somehow have a platonic existence, irrespective of whether we define them or not. We can define certain mathematical constructs, and they can, or cannot, be a representation for that intangible concept of natural number. If they are, well, then they are, and if they aren't well, eh, they aren't and we are doing something else.

"Der liebe Gott hat die ganzen Zahlen gemacht. Alle anderes ist menschenwerk." Or that's how I remember itl; Was it Kummer who said that?

George Jones

Jul13-05, 09:43 AM

"Der liebe Gott hat die ganzen Zahlen gemacht. Alle anderes ist menschenwerk." Or that's how I remember itl; Was it Kummer who said that?

Or was it the guy who helped drive Cantor bonkers?

Personally, I'm a whole-hearted enough Platonist that I like:

"... and there is no sort of agreement about the nature of mathematical reality among either mathematicians or philosophers. Some hold that it is 'mental' and that in some sense we construct it, others that it is outside and independent of us ... I believe that mathematical reality lies outside of us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our 'creations', are simply our notes of our observations."

G. H. Hardy

Regards,
George

vanesch

Jul13-05, 10:47 AM

"Der liebe Gott hat die ganzen Zahlen gemacht. Alle anderes ist menschenwerk."

I'd go further, and claim some platonic existence for just any well-defined mathematical concept. But I was driven into this point without me wanting so, because we were not arguing about an ontology about *mathematical* objects, but about *physical* objects.
My point was simply that physical ontology is (at least) the platonic existence of the mathematical concept that corresponds to our physical world, whether it is a manifold, a Hilbert space or whatever, but that something is out there and corresponds to a mathematical concept, of which our physical theories and our observations are (meager ?) representations. I have difficulties with just a bunch of observations and knowledge if it is not somehow related to an underlying concept.

cheers,
Patrick.

Nacho

Jul13-05, 11:55 AM

ShalomShlomo

Jul14-05, 01:19 AM

Originally Posted by Igor_S
How can classical world violate causality?

If you insist on a classical existance of observation results, and EPR situations, you obviously have faster-than-light influences.

It's important, so let's get this clear (for some reason, this hasn't been grasped properly yet across our community).....

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.

HowSo ?

In the famous EPR thought experiment, two entangled photons are sent in
opposite directions, say, to two planets distant from each other, with the
photon generator somewhere between them.
At each of the two planets, the photon travels through a polarised filter
held at a certain angle before being measured.

If the two polarisation filters on the two planets are held at the same
angle, then since the photons are entangled the same measurement will be
recorded at the two planets.
EPR (Einstein, Podolsky & Rosen) derived that since the photon can't know
what angle the polarisation filter will be held at on each planet, and since
the results have to match if the filters are held at the same angle,
therefore the photon must leave the photon generator knowing what result to give for each angle that the filter will be held at.

Then in the 1964 John Bell came and disproved this incorrect derivation, and
showed that the result at each planet depended upon the angle that the
filter on the other planet was held at, and that the angle of the filter on
the other planet was always known to the photon instantaneously even though the planets was separated by large spatial distances.

But the implications of Bell's discovery to time and causality haven't been
fully spelled out. We know from Special Relativity that neither filter is
positioned first. To one observer travelling in a spaceship, the filter on
planet A is positioned first. To another observer travelling in a different
spaceship in a different direction, the filter on planet B is positioned
first. And yet each filter causes a change in the measurement at the other
planet. It is clearly evident that measurments do affect the past, and we are forced to narrow our definition of causality significantly. Indeed, only because no information capable of being interpreted is passed between the filters does any form of causality remain at all.

Consequences of the above:

1) We remain with a macro-causality but have to abandon causality on a Quantum level
2) Everything depends on what we understand 'Time' to be. We don't really understand what Time is, and since everything hinges on 'Time', our understanding of physics is ignorant
3) Given the fact that QM itself is proven causality-breaking, many of the objections to the classical view of QM have been removed, and this view ought to get a lot more attention than it does.

Shalom Shlomo

Igor_S

Jul14-05, 08:05 AM

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.

I would againt not use that word (but I think the rest of your post shows that we're talking about the same thing, eg.:

It is clearly evident that measurments do affect the past, and we are forced to narrow our definition of causality significantly

), because observer in the past cannot really tell if he is being influenced. Bell showed that QM breaks locality (and "soft" breaks :smile: causality). Nonlocality is connected with unseparability of the wave function which has deep physical meaning and that leads us to a statement you wrote later:

2) Everything depends on what we understand 'Time' to be. We don't really understand what Time is, and since everything hinges on 'Time', our understanding of physics is ignorant

I think this is really important problem to be solved.

vanesch

Jul14-05, 09:07 AM

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.

ShalomShlomo

Jul14-05, 01:35 PM

...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

Jul15-05, 12:37 AM

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.

Miserable

Jul15-05, 05:42 AM

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.

seratend

Jul15-05, 06:23 AM

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.

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 ...).

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).

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.

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.

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 ; ).

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).

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.

seratend

Jul15-05, 06:53 AM

Seratin:

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

--- (+) ------
|
---->(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).

Nacho

Jul15-05, 09:45 AM

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).

Nacho

Jul15-05, 10:08 AM

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.

seratend

Jul15-05, 04:05 PM

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.

Nacho

Jul15-05, 04:52 PM

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

Jul16-05, 12:13 AM

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.

seratend

Jul16-05, 03:50 AM

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).

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).

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.

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.

seratend

Jul16-05, 04:26 AM

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).

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

Jul16-05, 01:13 PM

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.

ShalomShlomo

Jul16-05, 02:27 PM

...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

seratend

Jul17-05, 04:48 AM

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).

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.

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:

selfAdjoint

Jul17-05, 08:24 AM

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.

gptejms

Jul17-05, 12:59 PM

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 \Delta x 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

Jul17-05, 01:24 PM

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

Jul17-05, 01:33 PM

you just reduce the \Delta x 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.

Nicky

Jul17-05, 04:17 PM

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

Jul17-05, 11:11 PM

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.

gptejms

Jul18-05, 12:40 AM

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

Jul18-05, 01:02 AM

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.

Nicky

Jul18-05, 07:25 AM

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.

vanesch

Jul18-05, 07:40 AM

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.

I don't see what you mean (not pejorative: please explain). I thought that the quantum potential was a function of the actual positions of the particles (which are well-defined in Bohm's theory), and the wavefunction (the same as the one in quantum theory, and which continues to evolve according to unitary QM: that's why it has some MWI aspects). Both evolve smoothly and are not influenced particularly by a measurement, no ? A measurement (in Bohm's theory, there is only one kind of measurement possible, namely a position measurement ; hence the preferred basis problem is solved this way as there is explicitly a preferred basis: the position) just gives us information about what trajectory (from a statistical ensemble which had an initial Born rule given distribution: the deux ex machina in Bohm :-) we had.

The only objection one can have against Bohmian mechanics is its blunt violation of SR (the expression of the quantum potential) - ok, and the deux ex machina that the initial uncertainty on particle positions has to be given by the Born rule... If one is willing to let go SR, I think it is one of the finest resolutions of the measurement problem that exist. However, I find a violation of SR too gross to take it seriously.

cheers,
Patrick.

seratend

Jul18-05, 07:42 AM

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
I think so (for the impression). I am a fan of what I call the minimalist interpretation: the consistent logical content of QM formalism, especially the collapse postulate (hence, I hope it should be included in any consistent interpretation). I am sure it is not far from the logical content of MWI.

I think the main difference in our views seem to be your search for a reality behing the descriptive view given by QM. Personnally, I do not care if there is a concrete "reality", I can continue to appreciate good wine, and the rest, without that ; ))).

I have difficulties with a purely epistemological view because *something* exists (a la Descartes, also from cheese and wine fame).

So you think we do not live in the matrix? :biggrin:
Ok, I understand what you mean (would like to have).

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.

I agree with that (all what I say is around this). QM formalism is, formally, a descriptive tool (in space and time). It does not require or assume other properties to work logically.
I would like to get a clear separation between the descriptive part (what we currently have) and the search of ontological properties or anything else (further improvements). The different posts we find in this forum highlights the confusion resulting from this mixture (especially concerning the collapse postulate and the HUP).
Moreover, most of the different existing interpretations participate to this confusion in mixing (by a lack of a clear separation in the formulation) the equivalent mathematical reformulation of the formalism (e.g. bohmian meachanics) together with the definition of external ontological properties (e.g. the path of a bohmian particle). MWI suffers from this default (e.g. especially by the choice of "many worlds", I would have chosen instead the ensemble interpretation ; ).

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.

The main consistency problem with this interpretation relies on the , may be implicit, meaning "before" "after" and "still" words.
Collapse postulate just defines a property (description and not prediction of what a system is and not what it would be or may be, etc ...). Collapse postulate does not reject "ontology" nor it assumes it: (all properties may be assumed to be "real" as long as we keep the logical consistency of the description). The only interpretational problem comes from assuming the system had a different property "before" the property given by the measurement result (i.e. the state before the measurement and the state "after" the measurement).
Concerning this aspect, the consistent histories formalism allows one to understand better how the things work when we consider the measurement results on space and time: a measurement result is, formally, part of a collection of measurement results (which is also a "measurement result"). (A good introduction to general stochastic processes)

Seratend.

vanesch

Jul18-05, 07:59 AM

So you think we do not live in the matrix? :biggrin:

Even that is ontological. It is in fact pretty close to the view I'm advocating.

Concerning this aspect, the consistent histories formalism allows one to understand better how the things work when we consider the measurement results on space and time: a measurement result is, formally, part of a collection of measurement results (which is also a "measurement result"). (A good introduction to general stochastic processes)

Yes, exactly. When we learned something about a system at time t1, say: that the system was in state a|1> + b|2> and we found, at t1, that the result was "1", we are allowed to work with the state |1> alone (projection postulate) because all FURTHER measurement results are conjunct with "and at t1, the result was equal to 1". So a second measurement, at t2, with result U, is not an independent result but is a CORRELATION with "and at t1 we had result = 1". The possibility doesn't exist anymore of performing the measurement at t2, INDEPENDENT of what was the result at t1: we irreversibly HAVE that result.
This is in fact what allows us to apply unitary evolution and only apply the Born rule "at the end of the day", but this time with the measurement result "at t1 we had result 1 and at t2 we had result U". It will implicitly lead to the projection, first, of |1> and then of |U>
This is indeed the same as considering the entire history of measurement results as one single measurement.

cheers,
Patrick.

Nicky

Jul18-05, 08:48 AM

[...] I thought that the quantum potential was a function of the actual positions of the particles (which are well-defined in Bohm's theory), and the wavefunction (the same as the one in quantum theory, and which continues to evolve according to unitary QM: that's why it has some MWI aspects). Both evolve smoothly and are not influenced particularly by a measurement, no ? [...]

I am no expert in Bohmian mechanics, so maybe you are right. I read some criticism of Bohm's account of wavefunction collapse, but it was just informal commentary on the 'net, not a serious analysis.

On the other hand, I would point out where Bohm invokes some more "deus ex machina" as you call it. In second of two papers where Bohm lays out his theory (Phys Rev 85, p. 180 (1952)), the talk of "violent and extremely complicated fluctuations" in the wavefunction is a bit vague to me. Also he seems to take the Born rule as given:

Because the probability density is equal to |psi|^2, we deduce that the apparatus variable [...] must finally enter one of the packets and remain with that packet thereafter [...] Thus, for all practical purposes, we can replace the complete wave function [...] by a new renormalized wave function
But maybe he explains this better elsewhere. I still have not understood the whole paper.

vanesch

Jul18-05, 08:55 AM

I am no expert in Bohmian mechanics, so maybe you are right.

I found http://plato.stanford.edu/entries/qm-bohm/ a very useful and readable introduction. Don't mind Bohm's original papers, after all, the originator of an idea doesn't always, at that moment, have the clearest view and explication of it (it is still brand new and has to be digested: as well by himself as by others).

cheers,
Patrick.

George Jones

Jul18-05, 11:05 AM

What about the Kochen-Specker theorem? This says, roughly, that quantum systems do not, in general, possess properties.

Consider the measurement of S_z of a spin-1 particle. If the state is psi = |1> just before measurement, then, with certainty, the result of the measurement is S_z = 1, and it seems to make sense that S_z = 1 was a property of the particle before measurement. Now suppose that the state is psi = (sqrt(3)|-1> + |1>)/2 just before the measurement, and that the result of the measurement is S_z = 1. Is it possible, within the framework of standard quantum theory, to say that the particle had the property S_z = 1 before the measurent? In other words, is possible that to say that the observable S_z possessed the value 1 before the measurent?

Now generalize this. Let A be an observable for a quantum system. Is it possible that a value function V that takes as input an observable and a state of the system, and spits out, say V(A ,psi), for the value of the observable A when the system is in state psi?

No one has ever thought of a way of doing this. Is this because no one has been able to hit on the right idea, or is it because it is impossible? If it were possible to do this, many of the ontological "problems" associated with quantum theory would disappear, and realists, like Patrick (I think) and me, would be happier campers :-). The Kochen-Specker theorem says that for quantum systems having state spaces of dimension 3 or higher, no value function (with reasonable properties) exists. :-(

This one of the things that makes a "disturbance" interpretation of the uncertainty principle difficult. If a system doesn't possess a particular property, how is it possible to disturb that property.

Nice discussions of the Kocken-Specker theorem can be found in Lectures on Quantum Theory: Mathematical and Structure Foundations by Chris Isham, and in The Structure and Interpretation of Quantum Mechanics by R.I.G.Hughes. Hughes is a philosopher, and some philosophy he espouses in his preface is particularly interesting: "Having thus outlined my program and declared my allegiances, I leave the reader to decide whether to proceed further, or to open another beer, or both."

The Kochen-Specker theorem makes life somewhat difficult for realists, but positivists probably have no problem with it. Isham says "... very effective professionally without needing to lose any sleep over the implications of the Kochen-Specker theorem or the Bell inequalities. However, in the last twenty years there has been a growing belief among physicists from many different specialisations that even if modern quantum theory works well at the pragmatic level, it simply cannot be the last word on the matter."

Patrick, this is essentially your hope, isn't it? Maybe a subtle 4).

Isham says further "... there are now any any physicists who feel that any significant advance will entail a radical revision in our understanding in the meaning and significance of the categories of space, time and substance."

To me, this seems to point towards quantum gravity, which is no surprise coming from Isham. Many physicists would disagree this, but I am inclined to believe that a theory of quantum gravity might have interesting things to say about these issues. Unfortunately, despite claims by various camps to the contrary, I see no viable candidate for a quantum theory of gravity. Also, such a theory could bring forth new interpretational issues just as thorny as any it alleviates.

Regards,
George

gptejms

Jul18-05, 12:06 PM

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.

The potential was introduced to give an idea of what might be happening.The wavefunction changes by the introduction of a potential(in this case it gets localized).This at least makes the measurement process less mysterious.In any case I also mentioned the interaction of the photon field with the electron field to be fully quantum--this is more difficult to calculate,but I think it is worth exploring(and my guess is that the 'potential' mimics this effect well).With my little knowledge of QFT,I am not in a position to do it---but you or other QFTists in the forum can certainly do a small calculation--may be localization comes out of such two interacting fields.

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).

I agree with this totally--when you sum up over the bath coordinates,you are in a way already using the Born rule.But what I am saying is different--you are introducing a quantum interaction(mimicked roughly by a potential)when you do a measurement and this localizes the wavefunction.I think sudden introduction of a potential has merit in the following sense---evolution is unitary in the absence of the potential as well as when you have the potential 'on',but in between these two phases is the evolution unitary?May be not,but I need to think about this.

vanesch

Jul18-05, 12:36 PM

I think sudden introduction of a potential has merit in the following sense---evolution is unitary in the absence of the potential as well as when you have the potential 'on',but in between these two phases is the evolution unitary?May be not,but I need to think about this.

According to QM, of course it is unitary ! There is nothing else that can give you a time evolution. A time-dependent hamiltonian still gives you a unitary time evolution.
I think the problem in your approach is that you refuse to see the "thing that applies the potential" as a quantum object. I agree with you that FOR ALL PRACTICAL PURPOSES you can do that, by restricting your attention to the "system", and find a quite good approximation to the quantum evolution of the system alone ; also you wouldn't find much of a difference for a "full" quantum treatment IF AT ANY POINT YOU APPLY THE BORN RULE. But *applying the Born rule* means that you switch to a classical world, and unitary evolution doesn't apply there. That's the essential contents of the Copenhagen view: that there is a macroscopic, classical world, and that there is a microscopic quantum world and that both "communicate" by the Born rule (micro -> macro) and the projection postulate (macro -> micro). But this means that there is a barrier separating the two. So the macroscopic world is then NOT subject to quantum theory, which would be, in itself, an amazing statement: we don't have the same laws, and it is not exactly clear what objects obey what set of rules.
If you refuse that, and you say that EVERYTHING is ruled by quantum theory however, then you are stuck with your unitary evolution all the way up. This is the case I was considering.

cheers,
Patrick.

gptejms

Jul19-05, 01:31 AM

According to QM, of course it is unitary ! There is nothing else that can give you a time evolution. A time-dependent hamiltonian still gives you a unitary time evolution.

When I wrote that I had a step function kind of a potential in mind--a potential that's introduced all of a sudden.Say the particle is free to begin with and has a wavefunction \exp[\iota(k_1 x - \omega_1 t)] .Now a potential is introduced say at time t_1 which to begin with we take to be constant.The wavefunction now readjusts(over some time) to \exp[\iota(k_2 x - \omega_2 t)] ,where the new variables take care of the change in energy.What happens at t=t_1 :-do the two wavefunctions merge?No they don't---there is some funny wavefunction during the readjustment phase which is a mixture of the two.Can you derive it from the Schrodinger equation?Can you give me the readjustment/response time?

Another problem:-Say the potential introduced is that of a harmonic oscillator,so the wavefunction not only goes from a plane wave to a Hermite Gauss function(if I remember correctly),but also the particle now falls into the nearest eigenstate i.e. it gains or loses some energy--can you describe this process thoroughly through unitary evolution/Schrodinger equation?May be you can,I need to think about these things.

I think the problem in your approach is that you refuse to see the "thing that applies the potential" as a quantum object. I agree with you that FOR ALL PRACTICAL PURPOSES you can do that, by restricting your attention to the "system", and find a quite good approximation to the quantum evolution of the system alone ; also you wouldn't find much of a difference for a "full" quantum treatment IF AT ANY POINT YOU APPLY THE BORN RULE. But *applying the Born rule* means that you switch to a classical world, and unitary evolution doesn't apply there. That's the essential contents of the Copenhagen view: that there is a macroscopic, classical world, and that there is a microscopic quantum world and that both "communicate" by the Born rule (micro -> macro) and the projection postulate (macro -> micro). But this means that there is a barrier separating the two. So the macroscopic world is then NOT subject to quantum theory, which would be, in itself, an amazing statement: we don't have the same laws, and it is not exactly clear what objects obey what set of rules.
If you refuse that, and you say that EVERYTHING is ruled by quantum theory however, then you are stuck with your unitary evolution all the way up. This is the case I was considering.

On the contrary I am taking everything to be quantum.What I am stressing is this:--what a measurement does is not to yield a particle with a definite x and a definite p.When you have made a measurement say by Heisenberg's microscope at one of the slits,you still observe a particle with some \Delta x and a \Delta p i.e. it is still a wavefunction--the orignal wavefunction corresponding to the two slits has now shrunk,but it's still a wavefunction or a quantum particle(without a definite x or p) that you observed when you made a measurement.I think the mistake one does is to think that 'since the particle has been observed,it must have a definite x and a definite p' and then one starts questioning how this mysterious collapse(of the wavefunction) comes out of unitary evolution.But if you keep in mind that all you do is to localize the wavefunction when you make a measurement,you can argue that the measurement process is akin to the introduction of a potential.

vanesch

Jul19-05, 03:56 AM

Another problem:-Say the potential introduced is that of a harmonic oscillator,so the wavefunction not only goes from a plane wave to a Hermite Gauss function(if I remember correctly),but also the particle now falls into the nearest eigenstate i.e. it gains or loses some energy--can you describe this process thoroughly through unitary evolution/Schrodinger equation?May be you can,I need to think about these things.

First of all, I'd like to re-iterate my remark that there is no *interaction* between two systems that introduces a "potential" in the Schroedinger equation. You only introduce INTERACTION TERMS in the product hilbert space, and if the initial (product) state of both systems is not an eigenstate of that interaction term (which it most probably isn't), this will give rise to a time evolution of the total state which is an entangled state of both systems.

But now to come to your specific problem of the sudden introduction of a harmonic potential: clearly the particle will NOT evolve to an energy eigenstate, for the following simple reason:
at t0- (just before the potential is introduced), we assume that the particle is, say, in a plane wave state. Of course, we require continuity of the wavefunction (otherwise the schroedinger equation doesn't make sense: it is a second order differential equation), so at t0+ the particle is now still in this plane wave state. We now rewrite that plane wave state as a superposition of eigenstates of the harmonic potential (the Hermite functions). Clearly we do not have just one term !
Given that each individual term is a stationary state, the time evolution from t0+ onward is given by the hamiltonian of the harmonic potential, so each term (stationary state) just gets a phase factor exp(-i E_n t).
No term will "decay". So we remain in this superposition for ever.

cheers,
Patrick

gptejms

Jul20-05, 07:27 AM

First of all, I'd like to re-iterate my remark that there is no *interaction* between two systems that introduces a "potential" in the Schroedinger equation. You only introduce INTERACTION TERMS in the product hilbert space, and if the initial (product) state of both systems is not an eigenstate of that interaction term (which it most probably isn't), this will give rise to a time evolution of the total state which is an entangled state of both systems.

You introduce a 'nucleus' and say you your system of interest is an electron--don't the two things interact?You mean the nucleus just introduces a potential?!

But now to come to your specific problem of the sudden introduction of a harmonic potential: clearly the particle will NOT evolve to an energy eigenstate, for the following simple reason:
at t0- (just before the potential is introduced), we assume that the particle is, say, in a plane wave state. Of course, we require continuity of the wavefunction (otherwise the schroedinger equation doesn't make sense: it is a second order differential equation), so at t0+ the particle is now still in this plane wave state. We now rewrite that plane wave state as a superposition of eigenstates of the harmonic potential (the Hermite functions). Clearly we do not have just one term !

Again I take the example of an electron approaching a nucleus.Take for the moment the electron to be a classical particle.Depending on its speed,it should either fall into a circular orbit(rather spiral into the nucleus) or be scattered off.In a quantum scenario,if it is scattered off, it doesen't remain the same plane wave--its wavevector changes.If,as you say, the plane wave remains as it is,the electron should merrily pass on away from the nucleus with the same momentum and in the same direction as if nothing has happened--obviously this is not correct.In the case the electron gets trapped by the nucleus,the wavefunction again changes.

Let's however remain focused on the central issue.I stated that when you 'observe' a particle you are just observing a shrunk form of the wavefunction--the particle is still quantum and has a delta x and a delta p.The only thing a measurement does is to give you this shrunk form which comes out very well from quantum mechanics itself.Need to see some comments on this.

seratend

Jul20-05, 08:18 AM

Again I take the example of an electron approaching a nucleus.Take for the moment the electron to be a classical particle.Depending on its speed,it should either fall into a circular orbit(rather spiral into the nucleus) or be scattered off.In a quantum scenario,if it is scattered off, it doesen't remain the same plane wave--its wavevector changes.

Attention, you are attaching a reality to the wave function (in the same way you may speak wrongly about the path of particle in a double slit experiment). Try to think with the heisenberg view where the wave function is a constant in time in order to avoid false deductions.
Note that in the quantum as well as in the classical scenario, a particle may be scattered of or captured by the scatterer (it depends on the interactions).

Seratend.

vanesch

Jul20-05, 08:28 AM

Again I take the example of an electron approaching a nucleus.

Ok, it is an interesting example.

Take for the moment the electron to be a classical particle.Depending on its speed,it should either fall into a circular orbit(rather spiral into the nucleus) or be scattered off.

Let us more say that the speed is fixed, and that we work with the impact parameter b (the distance between the straight line on which the incoming electron moves, and the nucleus) in the classical case.

Indeed, for a large impact parameter, the particle almost goes straight through, while for smaller and smaller impact parameters, first the particle track bends lightly, a bit and finally, for small enough values, the particle scatters under large angles. Let us not consider the case of capture. The nucleus will undergo the appropriate recoil for momentum to be conserved.

In a quantum scenario,if it is scattered off, it doesen't remain the same plane wave--its wavevector changes.If,as you say, the plane wave remains as it is,the electron should merrily pass on away from the nucleus with the same momentum and in the same direction as if nothing has happened--obviously this is not correct.In the case the electron gets trapped by the nucleus,the wavefunction again changes.

In a semi-quantum scenario (incoming particle quantum, nucleus classical), if the particle's momentum is well known, it is an incoming plane wave, and hence it "contains" all impact parameters at once. The nucleus being considered classical, we can replace it by a potential in the electron's schroedinger equation. We now solve that Schroedinger equation, and out will come a rather complicated looking wavefront. If we apply the Born rule to it (meaning, we make a transition to classical), it gives us the probability of the particle to scatter under a certain angle. From that *classical* result, we can then find the corresponding probability of the nucleus to recoil with a certain momentum.

In the full quantum scenario, the initial state of the nucleus-electron system is a product state |nucleus> |electron> in which the nucleus corresponds to some localized lumpy wavefunction, and the electron an incoming plane wave. Now, there is no external potential, but an interaction term in the hamiltonian over the hilbert space of the two particles, which describes their Coulomb interaction. If we apply this hamiltonian's time evolution to
|nucleus> |electron>, this product state will evolve in an entangled state, which I intuitively think will take on something like:

|psi_final> = Integral db f(b) |nucleus-plane-wave-p(b)> |electron-plane-wave-p(b)>

Here, f(b) is some complex number as a function of a variable which I call b, because it more or less corresponds to some impact parameter, and the two states correspond to a product state of a plane wave with momentum p(b) for the nucleus and a plane wave with momentum - p(b) for the electron.

I'm not sure about this, I just guess it: it is my guess for the form of the solution of the schroedinger equation (in Schmidt decomposition).

So we end up with a global wavefunction for the nucleus and the electron, which is not a product state. If we now apply the Born rule to this system, measuring both momenta of nucleus and electron, we notice several things:

1) there is a very strong correlation between the momentum of the electron and the momentum of the nucleus (they are exactly opposite). That's what you obtained classically by imposing momentum conservation, but it will simply come out of the Schroedinger equation.

2) the probability distribution of the momenta of the electron-nucleus system will be VERY CLOSE to the probability distribution of the semiclassically obtained potential-scattering solution, where the nucleus was replaced by a potential.

I didn't claim that the wave function of the electron had to remain "as if nothing happened" ; after all there is an interaction with a nucleus ; and this entangles both wavefunctions, and transforms them unitarily. But you see again that no SINGLE scattering angle comes out of this: all angles are realised (that is: there is a term in the final wavefunction corresponding to each possible scattering angle for the electron) and to each angle for the electron, corresponds the matched angle for the nucleus.

Let's however remain focused on the central issue.I stated that when you 'observe' a particle you are just observing a shrunk form of the wavefunction--the particle is still quantum and has a delta x and a delta p.The only thing a measurement does is to give you this shrunk form which comes out very well from quantum mechanics itself.Need to see some comments on this.

If you mean that you got now entangled with that "shrunk part" (which is just a term in the overall wavefunction), then yes, I agree of course!
If you say that quantum theory by itself unitarily shrunk the wavefunction, I'm telling you that that is mathematically impossible for a unitary operator.

cheers,
Patrick.

vanesch

Jul20-05, 08:35 AM

I want to lift a potential confusion:

I said:

We now rewrite that plane wave state as a superposition of eigenstates of the harmonic potential (the Hermite functions). Clearly we do not have just one term !
Given that each individual term is a stationary state, the time evolution from t0+ onward is given by the hamiltonian of the harmonic potential, so each term (stationary state) just gets a phase factor exp(-i E_n t).
No term will "decay". So we remain in this superposition for ever.

However, this doesn't mean that, after t0+, the particle remains in a PLANE wave! This wavefunction will evolve now according to the harmonic potential hamiltonian, and this will "dephase" the different terms in the initial plane wave decomposition in Hermite functions, so that after a finite time, their recomposition will give you something else than a plane wave. I only showed you that whatever that complicated function is, it cannot decay into the ground state of the harmonic potential.

seratend

Jul20-05, 08:38 AM

If you say that quantum theory by itself unitarily shrunk the wavefunction, I'm telling you that that is mathematically impossible for a unitary operator.

Only for finite times. : ))

Seratend.

vanesch

Jul20-05, 09:45 AM

Only for finite times. : ))

I don't know exactly what you mean ? Do you allude to the result of DeWitt (I think) that all branches in which there is a serious deviation from the Born rule have a total (Hilbert) norm 0 for t-> Infinity ?
Or do you allude to the slightly imaginary slope given to the time axis to derive the LZH result (but that, to me, is just a sloppy trick) ?
Or still something else ?

cheers,
Patrick.

seratend

Jul20-05, 10:48 AM

I don't know exactly what you mean ? Do you allude to the result of DeWitt (I think) that all branches in which there is a serious deviation from the Born rule have a total (Hilbert) norm 0 for t-> Infinity ?
Or do you allude to the slightly imaginary slope given to the time axis to derive the LZH result (but that, to me, is just a sloppy trick) ?
Or still something else ?

cheers,
Patrick.
: ).

We just need to take any translation generator. We have (with the good units) <x|exp(-ip.a)|psi> = psi(x+a) for all finite a and all states |psi> but not necessarily for infinite a (a group is closed under finite operations and not necessarily for infinite operations) where everything is possible (without external properties on this limit, e.g. sigma additivity).
The rest is just application of this property (e.g. classical limits, decoherence etc ...).

Some formal applications of this result for the time (i.e. the unitary evolution) are used in the formal study of the boundary limit between classical world and quantum world especially in the decoherence area . If you are interested on this aspect I recommend the excellent paper of of N.P. Landsman "Between Classical and quantum" quant-ph/0506082 (especially section 6.6 and 7 that deals with the results of infinite time on measurements).
(Note: it requires some knowledge on the C*-algebra formalism results, but it has a lot of pointers).

(I hope you will appreciate this paper as it may also help you in your search for an ontological reality :biggrin: ).

Seratend.

P.S. My comment does not invalidate what you say, just that we need to take some care with the unitary evolution for the sake of consistency.

P.P.S. I hope you may have a new view on the scattering matrix and more precisely the “limit at t --> +oO”.

gptejms

Jul20-05, 12:22 PM

Attention, you are attaching a reality to the wave function (in the same way you may speak wrongly about the path of particle in a double slit experiment).

When you have shrunk the wavefunction to one slit,obviously the particle's path is certain to the the extent that the particle passes through this slit.

Try to think with the heisenberg view where the wave function is a constant in time in order to avoid false deductions.

Good suggestion.If the wavefunction is a constant,obviously no operator can cause the particle to pass through one slit only.However when you suddenly introduce a potential,you can no longer continue to work with the old wavefunction.

Note that in the quantum as well as in the classical scenario, a particle may be scattered of or captured by the scatterer (it depends on the interactions).

Of course, and I have mentioned the latter case also.

gptejms

Jul20-05, 12:58 PM

If we apply this hamiltonian's time evolution to |nucleus> |electron>, this product state will evolve in an entangled state, which I intuitively think will take on something like:

|psi_final> = Integral db f(b) |nucleus-plane-wave-p(b)> |electron-plane-wave-p(b)>

Here, f(b) is some complex number as a function of a variable which I call b, because it more or less corresponds to some impact parameter, and the two states correspond to a product state of a plane wave with momentum p(b) for the nucleus and a plane wave with momentum - p(b) for the electron.

I'm not sure about this, I just guess it: it is my guess for the form of the solution of the schroedinger equation (in Schmidt decomposition).

Ok,the nucleus is now entangled with the electron.You will use this to argue that the measuring apparatus also gets entangled with the system being measured etc. etc. and finally give only a 'conscious' observer the authority to break the superposition(by MW splitting) and that too to your own consciousness only and not that of a cat or for that matter not even any other human--this is a kind of wishful thinking that I don't subscribe to.

If you mean that you got now entangled with that "shrunk part" (which is just a term in the overall wavefunction), then yes, I agree of course!
If you say that quantum theory by itself unitarily shrunk the wavefunction, I'm telling you that that is mathematically impossible for a unitary operator.

When you are entangled with the shrunk part,at least the electron passed through a particular slit--you are entangled with one slit only.Regarding the unitarity,I like seratend's suggestion of the Heisenberg picture.Read my response to him.

gptejms

Jul20-05, 01:16 PM

I want to lift a potential confusion:

I said:

However, this doesn't mean that, after t0+, the particle remains in a PLANE wave! This wavefunction will evolve now according to the harmonic potential hamiltonian, and this will "dephase" the different terms in the initial plane wave decomposition in Hermite functions, so that after a finite time, their recomposition will give you something else than a plane wave. I only showed you that whatever that complicated function is, it cannot decay into the ground state of the harmonic potential.

Say you have a plane wave \exp[i(kx-\omega t)] to start with.You Fourier analyze the x part of this to Hermite functions---the time dependence continues to be \exp(-i \omega t) !If you insist that you'll Fourier analyze the t part also into different frequencies,even then that grand sum will sum up to act like \exp(-i \omega t) only.Now you may say,you meant that the t part would change upon interaction--ok fine,but then you see that the energy has changed.In your model the x part has remained the same i.e. the momentum has not changed,whereas the energy has--I see no point in preserving the momentum.

vanesch

Jul20-05, 01:31 PM

If you are interested on this aspect I recommend the excellent paper of of N.P. Landsman "Between Classical and quantum" quant-ph/0506082 (especially section 6.6 and 7 that deals with the results of infinite time on measurements).
(Note: it requires some knowledge on the C*-algebra formalism results, but it has a lot of pointers).

(I hope you will appreciate this paper as it may also help you in your search for an ontological reality :biggrin: ).

Thanks for the reference ! I started (p 20) reading it (but it's LONG ! 100 p).

cheers,
Patrick.

vanesch

Jul20-05, 01:57 PM

Good suggestion.If the wavefunction is a constant,obviously no operator can cause the particle to pass through one slit only.However when you suddenly introduce a potential,you can no longer continue to work with the old wavefunction.

Of course you can ! The potential now just changes the evolution of the observables. "Suddenly introducing a potential" V(x) at time t0 just comes down to having a hamiltonian:

H(t) = H0 + h(t-t0) V(x)

(h(t) is the Heavyside step function)

U(t) is the solution to the equation:

hbar dU/dt = - i H(t)

and is a unitary operator

(the solution is not anymore exp(-i H/hbar t) because that only applies for time invariant hamiltonians).

Given your (time independent) waverfunction psi (which, say, coincides with the Schroedinger view at t = ta), we have now:
x(t) = U(t)U_dagger(ta) x U_(ta) U_dagger(t)
and the same for p(t),
with x and p the Schroedinger position and momentum operators, and x(t) and p(t) the Heisenberg position and momentum operators, evolving according to your hamiltonian with sudden potential.

psi remains always psi(ta).

cheers,
Patrick.

seratend

Jul20-05, 02:01 PM

vanesch

Jul20-05, 02:03 PM

Say you have a plane wave \exp[i(kx-\omega t)] to start with.You Fourier analyze the x part of this to Hermite functions---the time dependence continues to be \exp(-i \omega t) !

No, it doesn't of course ! This time dependence is what you get for the free hamiltonian ; this time dependence was correct as long as the potential was not switched on (for t < t0, say). But when the hamiltonian changes (it is a time-dependent hamiltonian, because some potential is switching on at t = t0), all these different hermite functions get DIFFERENT omegas (namely E_n / hbar).

cheers,
Patrick.

vanesch

Jul20-05, 02:20 PM

Ok,the nucleus is now entangled with the electron.You will use this to argue that the measuring apparatus also gets entangled with the system being measured etc. etc. and finally give only a 'conscious' observer the authority to break the superposition(by MW splitting) and that too to your own consciousness only and not that of a cat or for that matter not even any other human--this is a kind of wishful thinking that I don't subscribe to.

Apart from your last statement, yes, you captured my thought :-) HOW do you "break the superposition" ? My hope is that gravity will, somehow, do so, because I'd also rather not subscribe to this view, but I simply don't know how to avoid it if unitary QM is correct, and we're talking here about how to interpret unitary QM.

However, you missed a point: I'm not saying that *my* consciousness somehow breaks the superposition, as some objective thing it does to the state of the universe, as if I were somehow a special physical or devine construction. The superposition is still there ; my consciousness just only observes one term of it. Now, of course, TO ME, that comes down to exactly the same thing (and that's why the projection postulate WORKS FAPP) - epistemologically. The problem only exists if you say that there is a real world out there (ontologically) and that its objective state is given by the wavefunction ; if QM is correct on all levels, this wavefunction cannot do anything else but evolve according to a Schroedinger equation, and if it does, there's no way to break the superposition.
(except if one is going to introduce infinities and so on, but if we take it that the universe has only a finite, but very large, number of degrees of freedom, I don't see how this is going to solve the issue).
As not one single physical interaction in the universe (possessing a hamiltonian) can break the superposition, clearly something unphysical has to do it when our subjective observations are to be explained.
Again, IF unitary QM is correct.

gptejms

Jul20-05, 11:18 PM

?? What do you mean?
If the potential is bounded, you still have your constant state.

Seratend.

If what you say is right,no atom should radiate!The wavefunction remains a constant and no amount of interaction causes it to change--think about it.

vanesch

Jul20-05, 11:39 PM

If what you say is right,no atom should radiate!The wavefunction remains a constant and no amount of interaction causes it to change--think about it.

The wavefunction of the atom alone ? But then it is not interacting with something ! Or do you mean, the wavefunction of the atom + the EM field ?

But if you are talking about the Heisenberg picture, the wavefunction there is constant by construction, so I do not see how it ever could do something else but "remain constant": it is not a function of time !

gptejms

Jul21-05, 12:17 AM

U(t) is the solution to the equation:

hbar dU/dt = - i H(t)

and is a unitary operator

Given your (time independent) waverfunction psi (which, say, coincides with the Schroedinger view at t = ta), we have now:
x(t) = U(t)U_dagger(ta) x U_(ta) U_dagger(t) .....(1)
and the same for p(t),
with x and p the Schroedinger position and momentum operators, and x(t) and p(t) the Heisenberg position and momentum operators, evolving according to your hamiltonian with sudden potential.

psi remains always psi(ta).

Your expression (1) above is not right.There is another term i \hbar U^\dagger \dot U which you have missed out.Let's start afresh.Say your hamiltonian is
H(t) = H_0 + \Theta(t-t_0)V(x)

U(t) = \exp\frac{-i \int_0^t [{H_0 + \Theta(t^\prime-t_0)V(x)}]dt^\prime}{\hbar} = \exp(-iH_0 t/ \hbar) \exp[-i V(x)(t-t_0)/ \hbar]

Now x(t) is something like this:-

x(t) = \exp[-i/\hbar(....)] x(0) \exp[i/\hbar(....)])]+i\hbar U^\dagger(t).\dot U (t) ,

where \dot U(t) has terms like:-
H_0(..) + V(x)(..) + V^\prime(x) \dot x(t)(...)

Work out what this leads to---I am already tired of writing in tex.

gptejms

Jul21-05, 12:24 AM

No, it doesn't of course ! This time dependence is what you get for the free hamiltonian ; this time dependence was correct as long as the potential was not switched on (for t < t0, say). But when the hamiltonian changes (it is a time-dependent hamiltonian, because some potential is switching on at t = t0), all these different hermite functions get DIFFERENT omegas (namely E_n / hbar).

cheers,
Patrick.

Vanesch,again you have not chosen to comment on the x part---do you accept that it won't remain as such,it would change?

In any case my point was that the energy of the particle changes when it is trapped by the nucleus and its wavefunction also changes to be that correponding to the introduced potential---this is a point you were not accepting earlier.

vanesch

Jul21-05, 03:31 AM

Your expression (1) above is not right.There is another term i \hbar U^\dagger \dot U which you have missed out.Let's start afresh.Say your hamiltonian is
H(t) = H_0 + \Theta(t-t_0)V(x)

U(t) = \exp\frac{-i \int_0^t [{H_0 + \Theta(t^\prime-t_0)V(x)}]dt^\prime}{\hbar} = \exp(-iH_0 t/ \hbar) \exp[-i V(x)(t-t_0)/ \hbar]

????

If H0 and V don't commute, you can't do that ! What you write is not the general solution to the operator differential equation. Check out "Dyson series".

Now x(t) is something like this:-

x(t) = \exp[-i/\hbar(....)] x(0) \exp[i/\hbar(....)])]+i\hbar U^\dagger(t).\dot U (t) ,

I have no idea where this comes from.

If U(t) (let us take ta = 0) is the time evolution operator (solution of the Schroedinger equation), then the Heisenberg operator is nothing else but
O_H(t) = U(t)_dagger O_S U(t).

You can check this easily: O_H defined in this way satisfies the Heisenberg evolution equation
i hbar d O_H/dt = [O_H(t), H(t)]

So where does this extra term you give, come from ???
(I think I put the dagger on the wrong side in my previous post)

cheers,
Patrick.

vanesch

Jul21-05, 04:29 AM

Vanesch,again you have not chosen to comment on the x part---do you accept that it won't remain as such,it would change?

Of course it will change, that was not the point. You wanted it to evolve into the ground state, something that won't happen.

In any case my point was that the energy of the particle changes when it is trapped by the nucleus and its wavefunction also changes to be that correponding to the introduced potential---this is a point you were not accepting earlier.

It is difficult to say what you mean by the "energy of the particle" in this situation, and we are making different points simultaneously, which may lead to confusion.

The point I tried to make was, that if you treat EVERYTHING quantum-mechanically, including the measurement apparatus, the environment, your body, etc... then a "measurement" is nothing else but an interaction of the measurement apparatus with the system, and simply leads to the overall wavefunction of the entire system to be a non-product state of the system, and the apparatus and all the rest, so there is no MEANING attached anymore to "the wavefunction of the apparatus" or "the wavefunction of the system": the overall wavefunction is not a product state anymore which would be necessary to talk about the individual wavefunctions of the subsystems. There is no escaping of this, when you consider all these interactions to be described by a hermitean hamiltonian, which automatically leads to a unitary evolution operator.

However, you can also work semi-classically, by considering the measurement apparatus and everything classically, and imposing a wavefunction onto the system (this is how people use quantum theory in practice, and corresponds to the Copenhagen view of things). Mind you, this means that part of the universe DOES NOT FOLLOW THE LAWS OF QUANTUM THEORY.
Now, as the measurement apparatus has a classical description (no hilbert space, but a phase space) and the quantum system has a quantum description (a hilbert space, no phase space), the interaction between both needs to go through a "bridge". This bridge is THE POTENTIAL you introduce in the hamiltonian of the quantum system, and THE BORN RULE and PROJECTION postulate, which then introduces an effective potential in the classical equations of motion of the measurement system.

I tried to point out that the introduction of the potential alone is not sufficient to make a system "fall to its ground state" in the cases you mentionned. However, there is some on-going work in looking how coupled classical-quantum systems, with added noise, CAN do this. Nevertheless, this approach NECESSARILY places you outside of quantum theory: part of the universe is to be considered NOT subject to quantum mechanics. So even if this work is successfull, it doesn't contradict my statement that WITHIN QM, as it stands, you can never obtain this.

It is the essence of the Copenhagen view, to which I do not subscribe AS SUCH. Of course, in practice, everybody who uses QM works with it this way. But I find it fundamentally disturbing that quantum mechanics somehow stops to be valid, and classical theory takes over, and that's it. I'd rather see then both theories as limiting cases of a more fundamental theory.

cheers,
Patrick.

gptejms

Jul21-05, 04:29 AM

If H0 and V don't commute, you can't do that ! What you write is not the general solution to the operator differential equation. Check out "Dyson series".

That's right.I am being a bit sloppy here,but the idea was to show that x(t) is significantly altered by the introduction of a potential--thus the path of an electron through a double slit arrangement would be altered and may be reduced to be 'through one slit' by a suitable potential(even in the Heisenberg picture).I agree this is easier said than done,but you get the basic idea.

I have no idea where this comes from.

If U(t) (let us take ta = 0) is the time evolution operator (solution of the Schroedinger equation), then the Heisenberg operator is nothing else but
O_H(t) = U(t)_dagger O_S U(t).

You can check this easily: O_H defined in this way satisfies the Heisenberg evolution equation
i hbar d O_H/dt = [O_H(t), H(t)]

So where does this extra term you give, come from ???
(I think I put the dagger on the wrong side in my previous post)

The formula I have given you is right.I don't have the books with me(I left physics 9 years back as soon as I submitted my Ph.D. thesis)--but I remember it's there in Merzbacher's QM.

seratend

Jul21-05, 04:55 AM

That's right.I am being a bit sloppy here,but the idea was to show that x(t) is significantly altered by the introduction of a potential--thus the path of an electron through a double slit arrangement would be altered and may be reduced to be 'through one slit' by a suitable potential(even in the Heisenberg picture).I agree this is easier said than done,but you get the basic idea.

I think I do not understand you at all. Double slit experiment is the plain old toy model used to explain why we cannot have the two properties: "electron passes through one slit" and "interference pattern on the screen".
Therefore, I do not see how you can reduce the "path" of an electron to the one through one slit and still have the interference pattern.

Seratend.

Igor_S

Jul21-05, 05:12 AM

gptejms

Jul21-05, 05:20 AM

I think I do not understand you at all. Double slit experiment is the plain old toy model used to explain why we cannot have the two properties: "electron passes through one slit" and "interference pattern on the screen".
Therefore, I do not see how you can reduce the "path" of an electron to the one through one slit and still have the interference pattern.

Seratend.

My model is this:-a measurement process is like the introduction of a potential.In absence of the potential(i.e. when we do not make a measurement) of course we see an interference pattern and the wavefunction of the electron(or whatever) spans both the slits.This broad wavefunction gets affected when we introduce the potential--what I am proposing here is that the potential is such that the wavefunction shrinks to span only one slit(of course the interference pattern is destroyed).The question being discussed is if this model is right or not.

vanesch

Jul21-05, 05:50 AM

The formula I have given you is right.I don't have the books with me(I left physics 9 years back as soon as I submitted my Ph.D. thesis)--but I remember it's there in Merzbacher's QM.

I'm sorry but it just doesn't make sense.
i hbar U-dagger dU/dt = U-dagger (i hbar dU/dt) = U-dagger H U.
so this means that you add to each observable in the Heisenberg picture, U-dagger H U. Now let us consider a trivial observable, namely I (the unit operator). It simply means that any state is an eigenvector of I with eigenvalue 1. As such, it is a good observable. Now, clearly, no matter what happens to the system, I will always measure "1" with this trivial observable.

But with your formula, its Heisenberg representation (which should also just be I) is given by:

I_H = U-dagger I U + U-dagger H U
= I + U-dagger H U

Clearly, for many states now, the expectation value of I_H, given by:

<psi_H | I_H | psi_H> = <psi_H | I | psi_H> + <psi_H | U-dagger H U | psi_H>
= 1 + <psi_S|H|psi_S>
= 1 + <H>

This cannot be: the expectation value in the Heisenberg picture cannot be different from 1.

cheers,
Patrick.

vanesch

Jul21-05, 06:01 AM

seratend

Jul21-05, 06:26 AM

I think you can, according to Bohm's interpretation. Interference pattern is created by introduction of some (really) strange quantum potential - which (I think) contains stohastic part. I know very little about it and personally don't like Bohm's interpretation. If I remember correctly he claims that 1s electron in hydrogen atom is not moving at all; he is just standing there (not sure how is missing el. dipole moment is then explained, but I don't want to go offtopic).

However if you dismiss existence of quantum potential, then you surely cannot have electron passing through one particular hole and have interference (as you said).

Currently, the only consistent bohmian interpretation I know may be reduced to "when you know result, e.g. a position at time t, you may infer the position at any time t<to if this position is not measured during the experiment. The rest is a play of words.
Yes, you can say that when the electron hits the screen it has crossed 10 times all the universe and passed through a given slit as long it is not measured or the electron is a human being before it is measured as long as these propositions are compatible with QM results.
If this discussion concerns physically non verifiable properties, I have nothing to say. However one who uses such description must first prove it is consistent with QM formalism.
Bohmian mechanics is a perfect example of this problem: as long as we do not require a reality of the bohmian particle, everything is ok. When we require some interpretation, well consistency is no more guaranteed: since its first publication in 1952, the interpretation has continuously evolved in order to keep the consistency with the results issued by the QM formalism.

Seratend.

seratend

Jul21-05, 06:42 AM

My model is this:-a measurement process is like the introduction of a potential.In absence of the potential(i.e. when we do not make a measurement) of course we see an interference pattern and the wavefunction of the electron(or whatever) spans both the slits.This broad wavefunction gets affected when we introduce the potential--what I am proposing here is that the potential is such that the wavefunction shrinks to span only one slit(of course the interference pattern is destroyed).The question being discussed is if this model is right or not.

For the slit plate of the double slit experiment, you may say you have the measurement given by this projector: P_slit= |slit1><slit1|+|slit2><slit2| and you still have the interference pattern that is given by the projector P_int=|interference><interference|.
These 2 projectors do not require the introduction of additional potentials to the ones already present (the interaction of the plate and of the screen). However, I may say: I have the results P_slit and P_int for each electron or P_int or P_slit.

With QM formalism, you are always able to do that: a clear separation between the [quantum] interactions of the system (the unitary evolution) and the measurement results (i.e. the projectors). To break the unitary evolution [of a closed system], you need to define a new theory that is no more QM theory: that's what Patrick tries to tell you.

Seratend.

ZapperZ

Jul21-05, 06:45 AM

ZapperZ

Jul21-05, 06:50 AM

It is the essence of the Copenhagen view, to which I do not subscribe AS SUCH. Of course, in practice, everybody who uses QM works with it this way. But I find it fundamentally disturbing that quantum mechanics somehow stops to be valid, and classical theory takes over, and that's it. I'd rather see then both theories as limiting cases of a more fundamental theory.

I should have just let this slip by, but I can't help myself. :)

Why do you find this "disturbing"? Discontinuity in understanding and discontinuity in description happens all the time. At a first order phase transition, practically all bets are off. What you used to describe in one phase simply cannot be extrapolated into the other phase. There's an abrupt discontinuity in a number of state variables. So you switch gears and adopt a different set of description and properties.

My point here is that if you live by a principle where you are disturbed by this abrupt change, then you should also be disturbed by many more phenomena than just QM-classical boundary. So are you? :)

Zz.

gptejms

Jul21-05, 06:52 AM

I'm sorry but it just doesn't make sense.

ok,my formula applies to the transformation of a hamiltonian under a time dependent unitary transformation.

gptejms

Jul21-05, 07:38 AM

You can do this, but only if you allow for a stochastic potential. Some people work on this.

Why stochastic?Can you give the references?

I am now throwing in another idea.In terms of QFT:-the principle of microscopic causality tells you that the measurement of the field at place 1 and subsequently at place 2(time-like separated) doesen't give you the same result as measurement at place 2 first and then at place 1(non-commutation).What this implies is that when I make a measurement at place 1,I create a disturbance which travels at the speed of light and the whole field readjusts to some new values.This is precisely what is happening in the 2-slit experiment(or for that matter any other experiment)--you measure the field or find an electron at slit 1,the field readjusts at slit 2 to no electron(if one electron comes at a time) and the field at the screen also readjusts to 'no interference pattern'.

vanesch

Jul21-05, 12:25 PM

My point here is that if you live by a principle where you are disturbed by this abrupt change, then you should also be disturbed by many more phenomena than just QM-classical boundary. So are you? :)

What is disturbing in the QM-classical boundary is that it is "slippery". It is not defined, and you cannot deduce its location (at least, according to standard QM - I'm not talking about speculative extensions). If QM, in its unitary version, applies "all the way up", it should be *in principle* possible to UNDO about just any measurement result, and have "notebooks, people and all that" interfere quantummechanically. For the moment, we are technologically only able to do that for systems of 2 or 3 photons or so.
So whereever you put physically the QM - classical boundary, it is *in principle* possible, if QM applies all the way up, to transgress it, which would then show that the QM-classical boundary is not yet reached.

What I mean is the following:

If you have a system S, in the famous state a|1> + b|2>, and you have a measurement apparatus M and we do the "pre-measurement" interaction thing a la von Neumann, we end up with
|psi> = a |1> |M1> + b |2> |M2>

Now, as long as M1 and M2 are very complicated states, which are going to stay essentially orthogonal (so that the entanglement is "for ever"), if you take a "relative observer position" to be the measurement apparatus, then you can say that the measurement apparatus has "irreversibly" recorded the result.
But if we are technologically advanced enough to subject this complicated apparatus M to such an evolution that at a certain time M1 and M2 evolve towards the same state MX (this is unitarily possible, because we can "compensate" on the system: it is in essence the INVERSE measurement interaction), then we arrive back at |psi> = (a |1'> + b|2'>) |MX>. We could now perform an experiment on the system S IN ANOTHER BASIS, and observe quantum interference.
This is the essence of a quantum erasure experiment (although all papers about it formulate it in a much more spooky way about "forgetting" and "not violating the heisenberg uncertainty relations" etc...).
We can do it with photons and even with more sophisiticated stuff.
If we would have thought that the interaction of M with the system was a "measurement" (was the "phase transition" between quantum and classical), we would have been proven wrong, because this quantum erasure could not happen anymore. In density matrix language: once the non-diagonal elements have been set to 0 (the quantum-classical transition: the Born rule), there's no way to put them back.
There is *in principle* no indication in current quantum theory that M cannot include the laboratory, the experimenter, the solar system, the galaxy etc... (except, except... for gravity - but I stick to non-speculative, current, quantum theory). So you can push back this "quantum-classical" transition in principle to beyond "M" systems the size of our galaxy.
To do that experimentally of course would require a mind-bogglingly sophisticated technology, but there is nothing in current quantum theory (except for our ignorance of how to treat gravity) that indicates that it cannot be done in principle.
Once you've pushed back the QM-classical transition far beyond the scale of humans and laboratories, it doesn't matter anymore: we clearly have then bodystates in a superposition, of which we consciously only observe ONE term.
This infinite possible "pushing back" is not present in the thermodynamical examples of phase transitions.

cheers,
Patrick.

vanesch

Jul21-05, 12:42 PM

ok,my formula applies to the transformation of a hamiltonian under a time dependent unitary transformation.

Can't be !
Let us have for simplicity a time-independent Hamiltonian (it should be valid for that case too, right ?)

So you claim that:

H_H = U_dagger H_S U + U_dagger H_S U

(because we still have: hbar U-dagger dU/dt = U-dagger (i hbar dU/dt) = U-dagger H U)

So H_H = 2 U_dagger H_S U

However, in the case of a time-independent hamiltonian, you can easily find out that U = exp(- i hbar H_S), which commutes of course with H_S

So we find that H_H = 2 H_S ????

Expectation values of energy in the Heisenberg picture are twice as big as those in the Schroedinger picture ??

cheers,
Patrick.

vanesch

Jul21-05, 12:55 PM

Why stochastic?Can you give the references?

Have a look at "decoherence and the appearance of a classical world in quantum theory" (by Joos, Zeh et al). The last 3 chapters (which I haven't studied in detail myself) are: 7. Open quantum systems (by Kupsch), 8. Stochastic collapse models (by Stamatescu) and 9. Related concepts and methods (by Zeh).
Look for the model of Ghirardi, Rimini and Weber (non-hamiltonian evolution) or Barcheilli, Lanz and Prosperi who build a model with "continuous approximate position measurement".

But I'm not very knowledgeable of all this stuff - I don't like the approach: it is introducing small "fudge terms" in the Schroedinger equation which aren't there in standard QM, so that the evolution is non-unitary, and then trying to find values for the free parameters so that at small scales, the effect of the terms is neglegible, and at large scales, it introduces a projection. It is not based upon some grand a-priori principle, and that's what I don't like about it.

you measure the field or find an electron at slit 1,the field readjusts at slit 2 to no electron(if one electron comes at a time) and the field at the screen also readjusts to 'no interference pattern'.

This won't work in all generality: you need faster-than-light propagation to do so. Ok, Bohm's theory does exactly this, but it has instantaneous action at a distance terms in it.

cheers,
Patrick.

gptejms

Jul21-05, 01:46 PM

Can't be !
Let us have for simplicity a time-independent Hamiltonian (it should be valid for that case too, right ?)

So you claim that:

H_H = U_dagger H_S U + U_dagger H_S U

(because we still have: hbar U-dagger dU/dt = U-dagger (i hbar dU/dt) = U-dagger H U)

So H_H = 2 U_dagger H_S U

However, in the case of a time-independent hamiltonian, you can easily find out that U = exp(- i hbar H_S), which commutes of course with H_S

So we find that H_H = 2 H_S ????

Expectation values of energy in the Heisenberg picture are twice as big as those in the Schroedinger picture ??

cheers,
Patrick.

Why don't you use tex?The math notation you write is not so readable--e.g. what is U-dagger?

Since you are insisting on knowing the origin of this formula,I have worked it out.No,you are not in the Heisenberg picture(my mistake if I gave that impression) here--make a transformation |\psi^\prime(t)> =U(t)|\psi (t)\rangle
Differentiating the above(plus using the Schrodinger equation) you get
H^\prime(t) = U(t)H(t)U^\dagger(t) + i \hbar U^\dagger(t)\dot U(t)

gptejms

Jul21-05, 01:55 PM

This won't work in all generality: you need faster-than-light propagation to do so. Ok, Bohm's theory does exactly this, but it has instantaneous action at a distance terms in it.

Why do you need ftl propagation?The field readjusts after the measurement at one place at the speed of light i.e. the disturbance is communicated to other places at the speed of light--for typical experimental dimensions this happens very very fast.

vanesch

Jul21-05, 03:32 PM

Why don't you use tex?The math notation you write is not so readable--e.g. what is U-dagger?

I used to write in pure ASCII, from the good old days when news forums were pure ascii :-)

Since you are insisting on knowing the origin of this formula,I have worked it out.No,you are not in the Heisenberg picture(my mistake if I gave that impression) here--make a transformation |\psi^\prime(t)> =U(t)|\psi (t)\rangle
Differentiating the above(plus using the Schrodinger equation) you get
H^\prime(t) = U(t)H(t)U^\dagger(t) + i \hbar U^\dagger(t)\dot U(t)

This formula is right. But that's not what you were saying ! You were claiming (post 78) that in my transformation from a Schroedinger picture operator into its Heisenberg equivalent, I missed a term, when I wrote:

A_H(t) = U^\dagger(t) A_S U(t)

The above formula is part of the definition of the Heisenberg picture, so I don't see how "a term can be missing".

Now, i \hbar dU/dt = H_S(t) , it is the DEFINITION of the Hamiltonian (see chapter 2 of Sakurai for instance).

From these two equations follows:
i \hbar d A_H(t) / dt = [A_H(t), H_H(t)]

with H_H the Hamiltonian in the Heisenberg picture, and given by
H_H(t) = U^\dagger(t) H_S(t) U(t)

If all H_S(t) commute for all values of t, then H_S commutes with U and hence H_H = H_S, but this is not the case in all generality.

But I didn't need this point at all. I just wanted to show that a unitary evolution operator U exists, whether you switch on a potential or not, that this allows you to go to the Heisenberg picture, and that there, by definition, the state of the system is given by a constant ket. Hence, switching on a potential doesn't affect the constant ket at all.

vanesch

Jul21-05, 03:40 PM

Why do you need ftl propagation?

EPR situations require this, for instance. But you do not need to set up things so complicated: imagine a light beam, hitting a beam splitter, and the two resulting beams are diverging. When they are at a reasonable distance of a few meters, say, you make the thing such that you can, or cannot, "watch the photon" (say, by guiding the beam in a local detector or not) in each arm.
Next, you let the beams (with mirrors and so on) come together again, and form an interference pattern.
If you switch the arm detectors quickly enough "in and out" the beam, there's not enough time to propagate from one arm to the other to go and tell what you did. We're in the measurable 10 ns range here for a few meters distance.

cheers,
Patrick.

gptejms

Jul22-05, 01:23 AM

But I didn't need this point at all. I just wanted to show that a unitary evolution operator U exists, whether you switch on a potential or not, that this allows you to go to the Heisenberg picture, and that there, by definition, the state of the system is given by a constant ket. Hence, switching on a potential doesn't affect the constant ket at all.

It will be nice if you can do this exercise:-show that the atom radiates in the Heisenberg picture-should be possible.
You have so far not commented on the x-part of the plane wave.

gptejms

Jul22-05, 01:46 AM

But you do not need to set up things so complicated: imagine a light beam, hitting a beam splitter, and the two resulting beams are diverging. When they are at a reasonable distance of a few meters, say, you make the thing such that you can, or cannot, "watch the photon" (say, by guiding the beam in a local detector or not) in each arm.
Next, you let the beams (with mirrors and so on) come together again, and form an interference pattern.
If you switch the arm detectors quickly enough "in and out" the beam, there's not enough time to propagate from one arm to the other to go and tell what you did. We're in the measurable 10 ns range here for a few meters distance.

Has an experiment of above nature been done?I find this idea so appealing--do a measurement at one place and the quantum field readjusts everywhere else within some time dictated by the velocity of light(and this arises naturally out of the commutation properties of the quantum field(microscopic causality))--I don't feel like giving it up!But yeah EPR is non-local,there may be other non-local experiments too--are QM(non-rel.) and QFT in contradiction here..???Is the principle of microscopic causality being violated in such experiments..??

gptejms

Jul22-05, 02:19 AM

But yeah EPR is non-local,there may be other non-local experiments too--are QM(non-rel.) and QFT in contradiction here..???Is the principle of microscopic causality being violated in such experiments..??

Answering my own question--in EPR situations you are just measuring the polarization--so the principle of microscopic causality doesen't come in in any way.The other experiment where you detect a photon in one of the arms and there is not enough time for the other arm to know what you did--well you have made a measurement of the field at one of the arms--now your contention is that the message can't go fast enough to the other arm to readjust to 'no photon'--but that's not required.After all you look at the screen,see that the interference pattern is destroyed and then conclude positively that the photon passed through one arm only--for the message to pass to the screen to readjust the field to 'no interference pattern',there is enough time.

vanesch

Jul22-05, 04:00 AM

It will be nice if you can do this exercise:-show that the atom radiates in the Heisenberg picture-should be possible.

It surely is very difficult if you want the full treatment in QFT, for many reasons. The physical picture behind it is the the E-fields in the right transition mode(s) in QFT are non-zero even in vacuum (the expectation values of the squares of the amplitudes of these modes are not zero), and it is the interaction of the electon of the atom with these modes that makes that the stationary states of the atom when calculated, taking purely into account the coulomb interaction with the nucleus, are NOT stationary states anymore when taking into account the dynamical EM field (as a quantum field). As such, the atom will get entangled with the EM field, and the transition amplitude for doing so can be calculated perturbatively, but in all these calculations, approximations are made. Even this treatment is quite complicated, and I'm not aware of a "frontal attack" of the problem in full, non-perturbative QED.
Nevertheless, there ARE calculations of the rate of decay of excited atoms following the idea I outlined very roughly above, and as far as I know, they fit with observations. I don't have references handy as such, but some stuff on this must be found in Mandel and Wolf in their "bible" on quantum optics, I'm sure.

You have so far not commented on the x-part of the plane wave.

I did, in post 81.

Incoming "plane wave" for t<t0 (free hamiltonian)

At t1 < t0, the incoming wave is exp(i k x), so solving for the time evolution in the Schroedinger picture with the free hamiltonian, will give us a time dependence which is:

exp(i k x) exp(- i omega t)
up to t = t0.
Note that for the free hamiltonian, the plane wave exp(i k x) is a stationary state.

So at t = t0, the wavefunction is exp(i k x - i omega t0).
Now, the potential is switched on, but this doesn't immediately change the wavefunction which is supposed to evolve continuously.

So simply said, for t>t0, we have to solve the Schroedinger equation with the new hamiltonian, with as a starting wave function, exp(i k x - i omega t0).
But note now that this function of x is not a stationary state anymore, so this time, the time evolution will not simply add a phase factor.
A way to solve this, is to expand exp(i k x - i omega t0) in the Hermite-Gauss functions (the new stationary states), so you will find:

exp(i k x - i omega t0) = a H0(x) + b H1(x) + c H2(x) + ...
(where H0, H1, etc... are the new stationary states)

The time evolution will now do the following thing:

at t = t2 > t0, we have that the wave function equals:

psi(x) = a H0(x) exp(-i E0 t2) + b H1(x) exp(- i E1 t2) + c H2(x) exp(- i E2 t2) ....

This will of course now not take on the aspect any more of a plane wave.

cheers,
Patrick.

vanesch

Jul22-05, 04:15 AM

are QM(non-rel.) and QFT in contradiction here..?

No, not at all, but even experimented particle physicists let themselves mislead by this apparent conflict, and that's because they are less used to make the distinction between the unitary dynamics (say, the properties of the hamiltonian), and quatum superposition.
The unitary dynamics in QFT satisfies the SR light cone conditions, in that observables (which are function of spacetime parameters) which are on spacelike intervals, commute. This prevents a DYNAMICAL interaction that is FTL.
However, nothing stops you from considering superpositions of states which ENTANGLE parts of the fields which are spacelike separated. As such, there can be no DYNAMICAL influence, but all the EPR like stuff still remains valid in QFT. But QFT is so complicated already with all Feynman integrals, renormalization schemes and so on, that these situations are rarely considered. Moreover, in typical particle physics experiments, one works from the beginning to the end in the momentum basis, so there are usually no "quantum interference" experiments (you need to change basis to observe quantum interference) done in that domain ; so QFT as usually practiced, usually "looks" very classical. But the whole machinery is there, even if not used !

I'll try to think up a simple "analogy".
Consider the free non-relativistic hamiltonian of 2 particles. We could think of an equivalent of "relativity" that forbids us to have dynamical interaction between the two particles (instead of between spacelike separated parts of quantum fields). This would be formalized by imposing commutation between all observables that relate to particle 1 and all observables that relate to particle 2 in the Heisenberg picture. So as long as we work with product states (in the Schroedinger picture) we remain in product states.
But this doesn't stop us from considering entangled states ! And then suddenly we do find EPR like correlations between both. Is this incompatible with our imposed absence of dynamical interactions between both ?
No, it is just a property of the quantum theory.
In the same way, the absence of dynamics between different, spacelike separated parts of a quantum field do not forbid you to have them entangled, and as such find EPR correlations between them.

cheers,
Patrick.

tdunc

Jul22-05, 04:39 AM

good thread ;)

gptejms

Did you answer Zappers question or did I miss that? I was about to ask the same thing. What is the nature of this potential? - That is introduced. There are only 2 things you could say, I want to here you say what.

vanesch #94

The QM - Classical boundary solution lies with the wavefunction(s) amplitude of a given construct. Mass is explicitly related to this function, such that the less mass an "object" has the greater the potential wavelength attributes and thus the greater the probability of P and M. Once you reach a certain density of a collection of wavefunctions in a given construct - more mass - the "object" ceases to have a QM wavefunction when considering in context of a whole object. It is at the size of molecules and compound atoms that the wavefunction amplitude of the whole decreases to a point where the molecules probability of location is almost certain.

Ask yourself, could a neutron for example, qualify for wavelengths attainable by photons based on its mass alone? I think not, and the reason being because its mass does not allow it such degree of freedom. It has as it is, a well defined position because of its larger mass and any change in momentum is bounded by such mass.

The question is, a what point when mass equals near zero does the wavelength have almost unlimited wavelength potential? The photon of course, radio waves are extremely large and qualify as one of the least massive objects we know of. Going up several notches to gamma rays we see that its wavelength amplitude is far more focused - a more well defined position, reason being because it has more mass but instead in the form of "energy" as found in Einstiens famous mass energy equations.

Now that Ive said that, when we talk about measurements on massive objects we know that it has Already a well defined almost absolute position, not quite so in the QM world as things evolve more rapidly then we are able to observe them. There is no such thing as a collapse of the wavefunction in the classical macro world, because the wavefunction is already collapsed (reduced) to a point where it effectivly has none. Interference cant be considered because interference requires the interference of wavefunctions of individual particles, when an object doesnt Have a wavefunction ... you get the idea. Covalent bonds are the process by which atoms collectively combined their individual normal mode wave resounaces to form a new wavefunction as a compound atom, a superposition perhaps but not in the normal sense.

gptejms

Jul22-05, 05:09 AM

It surely is very difficult if you want the full treatment in QFT, for many reasons. The physical picture behind it is the the E-fields in the right transition mode(s) in QFT are non-zero even in vacuum (the expectation values of the squares of the amplitudes of these modes are not zero), and it is the interaction of the electon of the atom with these modes that makes that the stationary states of the atom when calculated, taking purely into account the coulomb interaction with the nucleus, are NOT stationary states anymore when taking into account the dynamical EM field (as a quantum field).

Not QFT,I wanted to see it in the Heisenberg picture of non-rel. QM.Anyway, the points you have raised are good.

The time evolution will now do the following thing:

at t = t2 > t0, we have that the wave function equals:

psi(x) = a H0(x) exp(-i E0 t2) + b H1(x) exp(- i E1 t2) + c H2(x) exp(- i E2 t2) ....

This will of course now not take on the aspect any more of a plane wave.

All this you've said earlier.My question was this:-the x-part of the plane wave is exp(ikx)-you decompose it into a sum of Hermite Gauss functions--this sum remains as such no matter how much you evolve it--so in your picture the momentum i.e. hbar k remains conserved--should it be?
Another thing:-the t part is exp(-i omega t)--you can't decompose a single frequency plane wave in terms of plane waves of other frequencies.

gptejms

Jul22-05, 05:24 AM

I'll try to think up a simple "analogy".
Consider the free non-relativistic hamiltonian of 2 particles. We could think of an equivalent of "relativity" that forbids us to have dynamical interaction between the two particles (instead of between spacelike separated parts of quantum fields). This would be formalized by imposing commutation between all observables that relate to particle 1 and all observables that relate to particle 2 in the Heisenberg picture. So as long as we work with product states (in the Schroedinger picture) we remain in product states.
But this doesn't stop us from considering entangled states ! And then suddenly we do find EPR like correlations between both. Is this incompatible with our imposed absence of dynamical interactions between both ?
No, it is just a property of the quantum theory.
In the same way, the absence of dynamics between different, spacelike separated parts of a quantum field do not forbid you to have them entangled, and as such find EPR correlations between them.

That's right.
Let me add that one has to give a mechanism/reason for the entanglement, which exists at the start(in an EPR experiment).And since it's just the polarization that's being measured,there's no violation of microscopic causality anyway(see my earlier post).

seratend

Jul22-05, 05:53 AM

All this you've said earlier.My question was this:-the x-part of the plane wave is exp(ikx)-you decompose it into a sum of Hermite Gauss functions--this sum remains as such no matter how much you evolve it--so in your picture the momentum i.e. hbar k remains conserved--should it be?

Before asking to the others, you should pay attention to what is written since the beginning (i.e. make an effort). If you do not want to accept/understand the mathematical results of more than 100 years of developpment in QM it will be difficult for you to make valid claims/interpretations.

Look at what Patrick has written in its post #104. This is a basic QM application. For example think on what the energy of a free particle is and what the energy of particle with a potential that depends on time is as well as the cost to have a pure plane wave at t=0 (for example think with the heisenberg view).

Seratend.

gptejms

Jul22-05, 06:18 AM

Before asking to the others, you should pay attention to what is written since the beginning (i.e. make an effort). If you do not want to accept/understand the mathematical results of more than 100 years of developpment in QM it will be difficult for you to make valid claims/interpretations.

I think you are the one who needs to pay attention to what is written--have you understood what's being discussed or what I asked vanesch--make an effort!If you do that you'll understand that no mathematical result of more than 100 years is being challenged.

seratend

Jul22-05, 06:43 AM

I think you are the one who needs to pay attention to what is written--have you understood what's being discussed or what I asked vanesch--make an effort!.

I make an effort. Reread and try to understand post #104 by yourself. If you make an effort to understand what is written, your question about the momentum should be answered.

Seratend.

gptejms

Jul22-05, 07:39 AM

Perhaps my using the word plane wave in the following has caused confusion.In post #107 I wrote:-
Another thing:-the t part is exp(-i omega t)--you can't decompose a single frequency plane wave in terms of plane waves of other frequencies.

Read this as:-
Another thing:-the t part is exp(-i omega t)--you can't decompose a single frequency sinusoid in terms of sinusoids of other frequencies.

Right,seratend?

vanesch

Jul22-05, 08:04 AM

Once you reach a certain density of a collection of wavefunctions in a given construct - more mass - the "object" ceases to have a QM wavefunction when considering in context of a whole object.

That is not standard QM. It may very well be right, but you have a whole lot of stuff to explain.

Ask yourself, could a neutron for example, qualify for wavelengths attainable by photons based on its mass alone? I think not, and the reason being because its mass does not allow it such degree of freedom. It has as it is, a well defined position because of its larger mass and any change in momentum is bounded by such mass.

Well, here's for example already a difficulty in exactly the thing you cite. Just at the other side of my office, there's a small angle neutron scattering machine, which produces interference patterns in neutron scattering due to density correlations over several micrometers. So clearly the neutron behaves as a quantum object at least over these distances.
We have quantum states of neutrons in a gravitational potential (ultracold neutrons), which extend over several tens of micrometers too.

And then there are of course collective quantum phenomena, such as superfluids, which have macroscopic masses.

It's not so easy to define a classical-quantum boundary!

cheers,
Patrick.

gptejms

Jul22-05, 11:33 AM

good thread ;)

gptejms

Did you answer Zappers question or did I miss that? I was about to ask the same thing. What is the nature of this potential? - That is introduced. There are only 2 things you could say, I want to here you say what.

The potential will depend on what measuring device you are using,what is the nature of the interaction etc.I don't want to introduce an ad-hoc potential and do a calculation--any potential would alter the wavefunction(and disturb the interference pattern)-we need a potential that shrinks the wavefunction to span one slit only and the potential should be realistic.The case I was considering was Heisenberg's microscope at one of the slits--so photons are interacting with the electron.The crudest way to formulate this could be to take the potential to introduce random kicks in time i.e. be a sum of delta functions in time(Sum_i V_i delta(t-t_i) where t_i 's are randomly distributed--may be V_i 's could be given some spatial dependence(?).Frankly I don't have a good model for this.

It's better to take recourse to QFT so that you are in a fully quantum scenario.A consequence of this is discussed in my earlier post titled 'QFT and the measurement problem'.Briefly--when you make a measurement say at one slit, you create a disturbance that travels at the velocity of light to other places and the field readjusts to new values corresponding to what is observed-no interference pattern at the screen.

gptejms

Jul22-05, 12:16 PM

ok vanesch I've just read what you wrote in post #104--I withdraw my question.

tdunc

Jul22-05, 09:28 PM

vanesch

Standard QM is not something that I am known for ;) I have a whole lot to explain do I? Sounds familiar..

Your examples did not contradicted my concept.

gptejms # 114

Well I was more concerned When and Where the "measurement" as you define it takes place, exactly before or after or at the 2-slit, knowingly or not. Or in another case you could have considered, as some do, the 2-slit to Be the measurement and measurement tool. Clearly though if you were to subject the particle to a measurement - a measuring device, you could do this at Any point, the results will be quite different mind you, thats why I wanted to clairify, but it all depends what concept of behavior you are trying to convey that we dont already know? Or what theory are you promoting, theres plenty of them.

"Briefly--when you make a measurement say at one slit, you create a disturbance that travels at the velocity of light to other places and the field readjusts to new values corresponding to what is observed-no interference pattern at the screen."

Right so? You are trying to convey that the collapse of the wavefunction is at the speed of light correct?

What if I said though that the speed of a photon moving forward - c, is not the same as the speed at which a photon oscillates? Because that is afterall the varible that will collapse, not the forward speed varible. Oh it Could be, but what says that it is? I can imagine that if I throw a baseball that wobbles slightly up and down as it goes, is the speed of the wobble (call it its wavefunction) the speed of forward propagation? no

What I might say though _for the time being_ is that the collapse of a photons wavefunction is Limited by the speed of light so that we can avoid any what if senerios that deal with very large spaces and superluminal collapse.

vanesch

Jul23-05, 01:34 AM

That's right.
Let me add that one has to give a mechanism/reason for the entanglement, which exists at the start(in an EPR experiment).

That mechanism (to obtain the entangled state from the start) is obtained by dynamical interaction when the two subsystems WERE interacting. Interaction (hamiltonian interaction) causes entanglement of the system.
When the subsystems get separated, they cannot interact dynamically anymore, but their global state is still entangled.
The interaction with a measurement apparatus can be seen exactly in the same way (it is the von Neumann "pre-measurement interaction").

cheers,
Patrick.

gptejms

Jul23-05, 01:56 AM

gptejms # 114

Or what theory are you promoting, theres plenty of them.

I am not promoting any theory here.I can tell you what my train of thought has been during this thread:-

1.Measurement is akin to introducing a potential which shrinks the wavefunction to one or the other slit--it's definitely 'one slit'(no interference pattern) now,my conscious knowledge of it is not important.It's just that when I go to observe,it's revealed to me that the particle went through this particular slit--I may go after 10 years to make an observation that there is no interference pattern and that the particle went through this particular slit.This does not mean that the particle was in a superposition of two slits all this while.Now one may ask how the potential shrinks the wavefunction sometimes to slit 1 and at other times to slit 2--well the potential has an element of randomness in it.The merit of this scheme is that measurement is explained via QM/unitary evolution itself.

2.Then to be in a fully quantum scenario,I thought why not look at this problem from the QFT aspect.There, from the principle of microscopic causality,it becomes clear that measurement at one place introduces a disturbance which causes the field at other places to readjust to new values within a time dictated by the velocity of light.This at least tells you that the so called collapse can't be at superluminal speeds.EPR is not in contradiction with this because you are not measuring the field,you are just measuring the polarizations which are correlated due to the entanglement.But one case stands out:-say you have a single particle in a box,you put a partition in the box,take one half to Pluto,keep the other half on earth,make a measurement on earth and find the particle.Now microscopic causality tells me that this information is not instantaneously passed on to Pluto--the field there will readjust to 'no particle' after some time gap.But if an observer on pluto makes a measurement before that,can he still find the particle?--I leave that unanswered.

3.Does the above i.e. microscopic causality solve the measurement problem.No,it doesen't.Now the wavefunction is a functional of the field.There is still a chance for the particle to be in this or that slit!Now I do not know enough QFT to introduce another field to interact with the particle field and to see what that leads to.I hope the QFTists here can shed some light on that.

gptejms

Jul23-05, 01:59 AM

That mechanism (to obtain the entangled state from the start) is obtained by dynamical interaction when the two subsystems WERE interacting. Interaction (hamiltonian interaction) causes entanglement of the system.
When the subsystems get separated, they cannot interact dynamically anymore, but their global state is still entangled.

Agree with this part.

gptejms

Jul23-05, 06:52 AM

Continuing with what I wrote to tdunc,here's point 4

4. In point no. 1,I said that the potential has an element of randomness in it.Now coming to QFT,the quantum field by its very nature is stochastic--the result of a measurement at one place has a probability attached with it.So let's use that to our advanatge--when I make a measurement at one of the slits,I sometimes find the electron and sometimes don't(in which case it's at the other slit)--this is exactly what the stochastic potential(in point no. 1) was supposed to do!

So I think a satisfactory picture is this:-if you don't make any measurement what-so-ever,it's better to think just in field terms--the two slits cause a field readjustment at the screen to form the interference pattern.When you make a measurement at one of the slits,the field is again disturbed and readjusts to 'no electron' at the other slit and 'no interference effect' on the screen.

It's just field all the way,only measurements/interactions are quantum.Appearance of the interference pattern by introduction of the two slits,the disturbance/destruction of this pattern by introducing the measurement device at one of the slits is just 'field readjustments' that proceed at the speed of light.I think it's not even justified to say that the electron passed through both slits--you can talk of 'an electron' only when you make a measurement at one of the slits and when you do that,there is no interference pattern.Remember complementarity--it's a perfectly sound principle.Think of the whole thing as just field readjustments(measurement or no measurement) and it's even better.

What do you all say to the above?

tdunc

Jul23-05, 07:45 AM

gptejms

"Now one may ask how the potential shrinks the wavefunction sometimes to slit 1 and at other times to slit 2--well the potential has an element of randomness in it."

How does the 'potential' shrink the wavefunction period. I could care less what slit it goes through and the fact that its random, I already know the mechanics of that.

Ok 2-slit experiment aside. We know that in the case of a "detection area" manifested by a measuring device the wavelength of a particle(s) is reduced to no more than the width of the detection area. If the displacement of the particle is already <= the width of the detection area, is does not collapse. If it is greater than, it collapses. Supposedly. Why and How? This was a lingering question I had not answered myself in the past.

found it

"A recent paper by Keller (6) demonstrated rigorously for a propagating particle that its wave function, as an amplitude for location in space, is collapsed by any detection. Using probability theory, he proved that the probability amplitude wave for location of the ongoing quantum particle immediately following the observation becomes limited to the observation area, in other words its effective size is collapsed to that of the observation area."

"AJP 1990 Joseph B. Keller "Collapse of wavefunctions and probability densities"

I cant read it because I dont have a subscription.

tdunc

Jul23-05, 08:12 AM

Radio antennas > collapse the wavefunction > to the area of detection - the antenna itself > limited by the speed of light. Do you have an explaination for this?

gptejms

Jul23-05, 10:52 AM

Patrick,would you like to comment on my post #120?

gptejms

Jul23-05, 10:59 AM

How does the 'potential' shrink the wavefunction period. I could care less what slit it goes through and the fact that its random, I already know the mechanics of that.

There are 4 points there,go through all of them and then comment.I need to see some comments on point 4,which is the most important.

"A recent paper by Keller (6) demonstrated rigorously for a propagating particle that its wave function, as an amplitude for location in space, is collapsed by any detection. Using probability theory, he proved that the probability amplitude wave for location of the ongoing quantum particle immediately following the observation becomes limited to the observation area, in other words its effective size is collapsed to that of the observation area."

"AJP 1990 Joseph B. Keller "Collapse of wavefunctions and probability densities"

I cant read it because I dont have a subscription.

I don't have a subscription either.

vanesch

Jul23-05, 12:17 PM

So I think a satisfactory picture is this:-if you don't make any measurement what-so-ever,it's better to think just in field terms--the two slits cause a field readjustment at the screen to form the interference pattern.When you make a measurement at one of the slits,the field is again disturbed and readjusts to 'no electron' at the other slit and 'no interference effect' on the screen.

It's just field all the way,only measurements/interactions are quantum.Appearance of the interference pattern by introduction of the two slits,the disturbance/destruction of this pattern by introducing the measurement device at one of the slits is just 'field readjustments' that proceed at the speed of light.I think it's not even justified to say that the electron passed through both slits--you can talk of 'an electron' only when you make a measurement at one of the slits and when you do that,there is no interference pattern.Remember complementarity--it's a perfectly sound principle.Think of the whole thing as just field readjustments(measurement or no measurement) and it's even better.

What do you all say to the above?

This is a "local realist" approach, and some people try to work it out ; for instance, the promotors of "stochastic electrodynamics" and so on. It is considered a bit "fringe" work (but that by itself doesn't matter).
The big difficulty is to make *explicit* models of what's going on, in order to obtain the same results as standard QM.
And the really nasty part are EPR situations (that's often why these people simply deny these experiments and try to find loopholes in it). They imply then always faster-than-light effects in whatever is the explicit "collapse" mechanism.
Mind you, I don't find this approach totally ridiculous - in fact my hope is that gravity does exactly this, on some level or other. But this would in any case mean a serious deviation from as well general relativity as from quantum theory as we know it.

One thing is clear, however: this approach is not completely compatible with quantum theory "all the way up".

gptejms

Jul23-05, 01:37 PM

This is a "local realist" approach, and some people try to work it out ; for instance, the promotors of "stochastic electrodynamics" and so on. It is considered a bit "fringe" work (but that by itself doesn't matter).

The kind of local realism I am talking of is dictated by the principle of microscopic causality(i.e.nothing but the commutation property of the field at two space-time points),which is the basic feature of QFT--how can anyone doubt it?And this kind of local realism dictated by microscopic causality does not contradict EPR situations as I have already said--in EPR you don't measure the field anywhere,you are just measuring polarization at two places (which due to entanglement leads to higher correlation than expected on classical grounds).

Mind you, I don't find this approach totally ridiculous - in fact my hope is that gravity does exactly this, on some level or other. But this would in any case mean a serious deviation from as well general relativity as from quantum theory as we know it.

Don't know what you are saying here.

vanesch

Jul24-05, 01:44 AM

The kind of local realism I am talking of is dictated by the principle of microscopic causality(i.e.nothing but the commutation property of the field at two space-time points),which is the basic feature of QFT--how can anyone doubt it?And this kind of local realism dictated by microscopic causality does not contradict EPR situations as I have already said--in EPR you don't measure the field anywhere,you are just measuring polarization at two places (which due to entanglement leads to higher correlation than expected on classical grounds).

The point is: if you try to obtain the "wave function collapse" by a dynamical process which obeys what you call microscopic causality, you should see that you then have a serious problem with EPR situations. I don't understand your remark: "are just measuring polarisation at two places, you don't measure the field" ? What else is polarization but an aspect of the field ??
But again, in QFT, the microscopic causality puts limits on the DYNAMICAL INTERACTIONS that can be present in the Hamiltonian ; they do not specify anything about what happens to the wave function, of which the collapse (if this collapse is considered real) is global and does not obey any microscopic causality. So I don't see how you are going to obtain the last one effectively based upon the first one.
The only way out (IMHO) is by keeping unitary evolution "all the way up" if you stick to microscopic causality, and to have an other explanation for the *apparent* collapse - at least if you want to stick some meaning to the wavefunction in the first place (which you don't have to in a purely epistemological view).
I really don't see how you are going to do the collapse thing unitarily (with a hamiltonian that obeys local causality). EPR for me seems to be a killer of that idea (although it is not the only one).

But I think it is even worse. As long as you accept unitary evolution, I don't see how you can get rid of the linearity that a |1> + b|2> will give you a result that is a |result_of_state_1> + b |result_of_state_2>.
And if |result_of_state_1> includes having the pointer of your voltmeter on 11V and |result_of_state_2> is having the pointer of your voltmeter on 23V, I don't see how you're going to get away with having sometimes 11 V and sometimes 23 V.

cheers,
Patrick.

gptejms

Jul24-05, 01:00 PM

The point is: if you try to obtain the "wave function collapse" by a dynamical process which obeys what you call microscopic causality, you should see that you then have a serious problem with EPR situations. I don't understand your remark: "are just measuring polarisation at two places, you don't measure the field" ? What else is polarization but an aspect of the field ??

There is a difference:-microscopic causality implies that 'field measurements'(field intensity)' at space-like intervals can't be correlated.An aspect of the field like polarization can be--polarizations can be entangled,the field intensities themselves can't be entangled for space-like intervals.

But again, in QFT, the microscopic causality puts limits on the DYNAMICAL INTERACTIONS that can be present in the Hamiltonian ; they do not specify anything about what happens to the wave function, of which the collapse (if this collapse is considered real) is global and does not obey any microscopic causality. So I don't see how you are going to obtain the last one effectively based upon the first one.
The only way out (IMHO) is by keeping unitary evolution "all the way up" if you stick to microscopic causality, and to have an other explanation for the *apparent* collapse - at least if you want to stick some meaning to the wavefunction in the first place (which you don't have to in a purely epistemological view).

Consider the following:-

There is a source of electrons and a screen a little away.Think of this as just a field,an 'electron field'.There is no pattern on the screen.You introduce the double slit in between the source and the the screen.You have imposed certain constraints,the field gets disturbed and readjusts to 'interference pattern' on the screen--this proceeds at the speed of light(consistent with microscopic causality).Till I do not make any measurement,I think of it as just a field--in fact I am not even allowed to think of it as particles,until I make a measurement and find a particle.In fact my assertion is that only interactions are quantum,otherwise it's just a field.When I make a measurement at one of the slits and find a particle,the field again is disturbed and readjusts to 'no particle' at the other slit(if one particle comes at a time) and 'no interference effects' on the screen.Now that I have found the particle,I am allowed to talk in terms of the particle picture--and I don't see any contradictions--there is no interference pattern on the screen.

The problem arises only when you think of it as a particle incident on the double slit--you write down a|1> + b|2> and think how this collapses by unitary evolution.I say that there's no particle until you make a measurement,till then it's all a field.It's as if the measurement 'creates the particle',before that it doesen't even exist.

Jagmeet Singh

Rake

Jul25-05, 01:48 AM

Before I begin I feel that I should state that I have only a passing amount of knowledge on the subject so if I've got something wrong let me know. My current understanding of QM is that certain atomic attributes are created through observation of these attributes. This seems to suggest that there are two values present in an observation, the observer and the reality created. So my question is what special properties does the observer possess that allows an observation to be made. Here's what I mean, when a reality is present an observer is necessarily present. However, if an observer is present it does not neccesitate the presence of a reality. Looked at from this perspective the observer can be considered real, in that regardless of observations being made the observer always exist's and that reality only exists in relation to the observer. This would mean that the constituent parts of the observer in no way find their primary causes in the reality which the observer creates. This means that the system the observer creates finds all its values in the observer. The observer on the other hand finds none of its initial values in the system it creates. This is what troubles me the most about QM, if there is no separation between observer and observed, and the observer finds its initial values bound up within a system it creates through observation how is anything ever observed? Please help.

I dont have any amount on the subject which probably explains why I dont have any formal training. Which probably explains why I dont understand 90% of the replies, but when I read your post, these thoughts came to minf.

1) This seems to suggest that there are two values present in an observation, the observer and the reality created."

A) I dont understand QM but I don't think that reality gets "created". When you mention 2 values, the first thing that comes to my mind is the space-time co-ordinate of the observer and the s-t co-ordinate of that which is being observed. The reason this came to mind is that the only way you can observe anything, or as you say, create reality is when a photon traverses s-t to go from that which is being observed directly into the retinae of the observer. But since each photon that is absorbed into the retina of an observer at a specific s-t co-ordinate is unique then I would think that "reality" as we define it is a one-of-a-kind but slightly inaccurate snapshot of an object's past state at a precise s-t co-oridinate. My logic for this definition is based on the following:

1) Its a past representation because as it traverses s it must also traverse t

2) Its inaccurate because

a) prior to leaving the object the photon imparts a recoiling force upon it which must displace it and hence change its state by an undeterminate factor.

b) The photon gets tugged upon by gravity and who knows what else as it traverses s-t to get to your retina.

3) Its one of a kind because

a) you can never have 2 photons strike an object exactly in the same spot, at the same velocity, same approach angle, same gravitational lensing, etc...

a) Even if you could have 2 exactly the same photons You will never get 2 brains that will extrapolate the same representation.

In this context, reality is relative to the observer, which is to say that essence precedes existance. I think therefore I am.

2) what special properties does the observer possess that allows an observation to be made. Here's what I mean, when a reality is present an observer is necessarily present. However, if an observer is present it does not neccesitate the presence of a reality

A) By properties I would say a pair of eyes connected to a brain that can take take in photons and extrapolate.

3) Here's what I mean, when a reality is present an observer is necessarily present.

A) As long as by reality you mean something that we observe. But even if it is not observed it must still exist. I understand that quantum mechanics says something else and so do a lot of others including Descartes, to whom I would counter: Nay Rene! Sum ergo cogito! And then maybe slap him with my glove for effect...

4) if an observer is present it does not neccesitate the presence of a reality

A) Again I would counter that simply because the only place I would think where reality is not present is anything outside the boundaries of our universe as defined by s-t. So anything that does not have an s-t co-ordinate cannot be considered "real". This does not include any s-t region that might be causally disconnected from us due to the fact that it is receding faster than the speed of light. Imo reality does not require c to give it essence or an s-t co-ordinate even though a photon from that co-ordinate will never reach the earth. Reality simply is. Which is really just a way of saying that then s is dependent on t but independent of v....which it must be because as soon as you get v involved then we're talking about that one-of-a-kind but slightly inaccurate space-time representation of reality and not the real reality (the real reality...I made a funny!) Another argument I would make is that if an observer is present, then the observer themselves define reality. Again, this is a case where existence precedes the essence of reality and not vice-versa (i.e. sum ergo cogito)

5) This means that the system the observer creates finds all its values in the observer. The observer on the other hand finds none of its initial values in the system it creates. This is what troubles me the most about QM, if there is no separation between observer and observed

A) Same argument. I can see why you are having trouble with it. I'm having a lot of trouble with it myself. Maybe I'm just not getting it (likely) but it seems to me like this is a case of human arrogance (unlikely because these humans are like 1000 times smarter th an me) to try to define reality through us. In this sense it almost seems like thir is a prescriptive approach rather than a descriptive one. I prefer the latter. But I have a sneaking suspicion that i am being fooled by my limited concept of reality and also not understanding what it is that QM is really saying. This is likely because I know that QM does not suggest that there is no separation between the observer and the observed because such a position goes against what that ice-berg lettuce guy said. (sorry sometimes I recall the mnemonic and not the memory which is like saying....that the....nevermind....)

gptejms

Jul25-05, 06:47 AM

In continuation of what I wrote in post #128,let me add the following:-

In QFT,what is the role of the wavefunction?Now, wavefunction is a functional of the field--what this just does is to give you the probability density of finding a certain field value(upon measurement) at a place.You can't have a superposition of this wavefunction at two places--we don't know what meaning to assign to it.We no longer have the wavefunction of a particle which leads to the measurement problem.

Now let me come to the Schrodinger equation which gave rise to the notion of a wavefunction(of a particle).Schrodinger equation is the non-relativistic limit of the K.G. equation or the Dirac equation which are field equations.Now does the field suddenly change into a wavefunction when the velocity is sufficiently lowered i.e. v/c < < 1? Of course not,it's still a field which obeys the continuity equation.It also satisfies microscopic causality and the wavefunction is still a functional of the field.Wavefunction of a particle is a notion that leads to all the problems--it should be replaced by 'field of a particle' or particle field.

Jagmeet

vanesch

Jul26-05, 01:13 AM

In QFT,what is the role of the wavefunction?Now, wavefunction is a functional of the field--what this just does is to give you the probability density of finding a certain field value(upon measurement) at a place.You can't have a superposition of this wavefunction at two places--we don't know what meaning to assign to it.We no longer have the wavefunction of a particle which leads to the measurement problem.

No, the wavefunction is indeed a functional of the field (in the rarely used Schroedinger picture of QFT), but it gives you the probability AMPLITUDE to have a CERTAIN ENTIRE CLASSICAL FIELD CONFIGURATION.
So you can have a superposition of the kind:

a |plane wave with wavevector k> + b |sphericalwave outward from A> + ...

You can have a superposition of different fields, for instance a field that has a bump at A, and another field that has a bump at B. This is not the same as a field that has both a bump at A and a bump at B.
Now, when a measurement establishes (in the first case) that we have a bump at A, then the collapse comes down to the component in the wave function (field with the bump at B) disappearing from the wavefunction, instantaneously. This is exactly the same situation as in non-relativistic QM, so I don't see how this "resolves" the measurement problem.

Now let me come to the Schrodinger equation which gave rise to the notion of a wavefunction(of a particle).Schrodinger equation is the non-relativistic limit of the K.G. equation or the Dirac equation which are field equations.Now does the field suddenly change into a wavefunction when the velocity is sufficiently lowered i.e. v/c < < 1? Of course not,it's still a field which obeys the continuity equation.

This view (Dirac's view) is known to be misguided now - although it took until the 50ies for people to fully realize this. The Schroedinger equation is not the NR limit of the KG equation or the Dirac equation in QFT. The KG or the Dirac equation play the role of Newton's equations of motion and the Schroedinger equation remains what it is: the dynamical prescription of the wavefunction in Hilbert space (which is now constructed over field states instead of particle positions).

It also satisfies microscopic causality and the wavefunction is still a functional of the field.Wavefunction of a particle is a notion that leads to all the problems--it should be replaced by 'field of a particle' or particle field.

"Field of a particle" in QFT is the CLASSICAL FIELD. And on this classical field, one applies now "the wavefunction" over all possible classical configurations of the field. The Dirac equation is NOT the relativistic version of the Schroedinger equation, it is the classical dynamical equation of the classical field that has to be quantized. It is the CLASSICAL field evolution equation (Dirac's equation) that satisfies microscopic causality, but this classical field is NOT the wavefunction.

cheers,
Patrick.

gptejms

Jul26-05, 02:15 AM

No, the wavefunction is indeed a functional of the field (in the rarely used Schroedinger picture of QFT), but it gives you the probability AMPLITUDE to have a CERTAIN ENTIRE CLASSICAL FIELD CONFIGURATION.

Right!Thanks,I stand corrected.

You can have a superposition of different fields, for instance a field that has a bump at A, and another field that has a bump at B. This is not the same as a field that has both a bump at A and a bump at B.

Why 'different fields'--you can have a superposition of two different field configurations,where the field is the same.

Now, when a measurement establishes (in the first case) that we have a bump at A, then the collapse comes down to the component in the wave function (field with the bump at B) disappearing from the wavefunction, instantaneously. This is exactly the same situation as in non-relativistic QM, so I don't see how this "resolves" the measurement problem.

Seems fine.But the difficulty is that this seems to violate microscopic causality(a property of any quantum field) namely that if you introduce a measurement/disturbance at A,the field at B can not get instantaneously readjusted. Before a measurement is made,the field at B could have been a bump or no bump,now it definitely is 'no bump' in zero time.

This view (Dirac's view) is known to be misguided now - although it took until the 50ies for people to fully realize this. The Schroedinger equation is not the NR limit of the KG equation or the Dirac equation in QFT. The KG or the Dirac equation play the role of Newton's equations of motion and the Schroedinger equation remains what it is: the dynamical prescription of the wavefunction in Hilbert space (which is now constructed over field states instead of particle positions).

See what I am asserting here is that the Schrodinger equation is the NR limit of the KG or Dirac field(quantum) equations--where the field is quantised.There is nothing like the wavefunction of a particle.Plus the field obeys microscopic causality.

It is the CLASSICAL field evolution equation (Dirac's equation) that satisfies microscopic causality, but this classical field is NOT the wavefunction.

What do you mean here?It's not the classical field,but the quantum field that obeys microscopic causality(commutation relations of the field).

Sherlock

Jul26-05, 02:51 AM

The problem arises only when you think of it as a particle incident on the double slit--you write down a|1> + b|2> and think how this collapses by unitary evolution.I say that there's no particle until you make a measurement,till then it's all a field.It's as if the measurement 'creates the particle',before that it doesen't even exist.

That's how I think of it. The measurement itself is the particle. It might
be reasonable in some situations to speak of particles or waves or
whatever existing independent of measurement, but, strictly speaking,
these terms refer to recorded instrumental phenomena (and values
in formalizations associated with instrumental preparations).

Precisely what might exist, and how it might behave, in some
'quantum realm' beyond or independent of macroscopic records
is an open question. With both slits open, there's currently
no way to tell whether an assumed quantum disturbance incident
on the double-slit went through both slits or only one.

In an unambiguous usage of terms, it isn't just "as if" the photon
or electron doesn't exist until a recorded measurement creates it -- it
really *doesn't exist* in the world (beyond mathematical form) of
physical interactions until it becomes physical evidence via some
instrumental change(s).

I'm thinking of the measurement problem as a real, physical
incapability on our part. Your proposed resolution to this problem
seems to me to be a metaphysical, and not satisfactory, one.

gptejms

Jul26-05, 05:26 AM

Now, when a measurement establishes (in the first case) that we have a bump at A, then the collapse comes down to the component in the wave function (field with the bump at B) disappearing from the wavefunction, instantaneously. This is exactly the same situation as in non-relativistic QM, so I don't see how this "resolves" the measurement problem.

Let me add here the following to what I already wrote in a part of post #132 as a response to the above.You are writing your wavefunction as a superposition of a 'field bump' at x1,t1 and a 'field bump' at x2,t1(i.e. two possible field configurations).Now your assertion is that when I make a measurement at x1,t1 and the bump appears there,the bump at x2,t1 is insatantaneously wiped off.

My assertion is that if at all you have to use your wavefunction for field superpositions,you can't use equal times at x1 and x2.At x2,the time must at least be (x2-x1)/c + t1 (in consistence with microscopic causality).

Let me repeat that the Schrodinger equation is an equation for a quantum field not for wavefunction.Wavefunction in the new picture(if I may say so) has a lesser role to play--you can't use it for superpositions in the way one did for the wavefunction of a particle.

gptejms

Jul26-05, 05:32 AM

In an unambiguous usage of terms, it isn't just "as if" the photon
or electron doesn't exist until a recorded measurement creates it -- it
really *doesn't exist* in the world (beyond mathematical form) of
physical interactions until it becomes physical evidence via some
instrumental change(s).

I'm thinking of the measurement problem as a real, physical
incapability on our part. Your proposed resolution to this problem
seems to me to be a metaphysical, and not satisfactory, one.

Would it be ok for you if I dropped the "as if" ?!Is that the only objection?Keeping it or dropping it is just a matter of taste--stick to whatever you like,it makes no difference.

vanesch

Jul26-05, 01:20 PM

Why 'different fields'--you can have a superposition of two different field configurations,where the field is the same.

Yes, of course I meant two different configurations of the same field (let us say, the electron field).

What do you mean here?It's not the classical field,but the quantum field that obeys microscopic causality(commutation relations of the field).

No, the classical field satisfies microscopic causality (because of the fact that the differential equation (KG or Dirac) that it obeys is Lorentz-invariant). From this, and the quantization procedure the quantum operator associated with the field value at the point (x,t), satisfies commutation relations which correspond to microscopic causality, in the Heisenberg picture. Translated in the Schroedinger picture, this means that the UNITARY evolution of the wavefunction satisfies microscopic causality. However, collapse, which is not a unitary evolution, does NOT. So you're going to have a hard time to model this collapse by a unitary evolution, and that's what I'm trying to tell you since the beginning of this thread.
The above dichotomy is simply because QFT is just another quantum theory, just like non-relativistic QM is. And the "immediate collapse" is not something that has to do anything with the specific model of the dynamics we're trying to quantize (non-relativisitic point particles in Euclidean space, or classical fields obeying relativistic equations such as Dirac or KG). It is part of the general quantum theory. Even string theory suffers from it. So it doesn't matter what conditions you impose upon the dynamics (such as Lorentz invariance, or microscopic causality, or non-interaction, or whatever you can think of).
Collapse happens in Hilbert space, not in any real 4-dim manifold on which the quantum dynamics is modelled.

cheers,
Patrick.

vanesch

Jul26-05, 01:43 PM

Let me add here the following to what I already wrote in a part of post #132 as a response to the above.You are writing your wavefunction as a superposition of a 'field bump' at x1,t1 and a 'field bump' at x2,t1(i.e. two possible field configurations).Now your assertion is that when I make a measurement at x1,t1 and the bump appears there,the bump at x2,t1 is insatantaneously wiped off.

My assertion is that if at all you have to use your wavefunction for field superpositions,you can't use equal times at x1 and x2.At x2,the time must at least be (x2-x1)/c + t1 (in consistence with microscopic causality).

No, this is not the case. The superposition (in a fixed reference frame) is at equal times.
Let us call f1(x,y,z) = N1 exp(-(x^2 + y^2 - 81) ), the field config 1 at t = t1 (bump around circle in xy plane of radius 9)
and f2(x,y,z) = N2 exp(-(z^2 - 141)), the field config 2 at t=t1. (bump around z = 12)

Both field configurations correspond to orthogonal kets in Hilbert space, which we denote by |1> and |2> respectively.

I can now have the quantum field, at t=t1, in the state a|1>+ b|2>

If I measure now at t=t1, that the particle was around z=12, then suddenly the state of the quantum field collapses into |2>.

It doesn't even matter what is the time evolution (the dynamics) of the quantum field, and what conditions (such as microcausality) it satisfies, because this only relates to how the state |1> will evolve from t1 to t2, and how the state |2> will evolve from t1 to t2 (and as such, we know also how the above state a|1> +b|2> will evolve).
For instance, it might be that the evolved |1> will not be a single classical field configuration anymore at t2, but can be now a superposition of classical field configurations (this is highly probable, if the field configurations are "spiked" and we cannot apply the classical evolution equations: QFT effects are then visible). BUT ALL THIS HAS NOTHING TO DO with the projection postulate, which acts upon the quantum state at a given time.

Let me repeat that the Schrodinger equation is an equation for a quantum field not for wavefunction.Wavefunction in the new picture(if I may say so) has a lesser role to play--you can't use it for superpositions in the way one did for the wavefunction of a particle.

Well, I'm sorry but you have it completely backwards here (at least in standard QM). The Schroedinger equation - which is just as valid in QFT as in ordinary QM - is the evolution equation of the wavefunction (= the quantum state of the system) in Hilbert space. However, except for the single 1-particle non-relativistic QM case, the Schroedinger equation IS NOT an equation of a field over the spacetime manifold.

cheers,
Patrick.

gptejms

Jul27-05, 12:11 AM

No, the classical field satisfies microscopic causality (because of the fact that the differential equation (KG or Dirac) that it obeys is Lorentz-invariant). From this, and the quantization procedure the quantum operator associated with the field value at the point (x,t), satisfies commutation relations which correspond to microscopic causality, in the Heisenberg picture. Translated in the Schroedinger picture, this means that the UNITARY evolution of the wavefunction satisfies microscopic causality. However, collapse, which is not a unitary evolution, does NOT. So you're going to have a hard time to model this collapse by a unitary evolution, and that's what I'm trying to tell you since the beginning of this thread.

Ok,so in QFT,in the Schrodinger picture the field has the same status as the spatial coordinates of a wavefunction in NR quantum mechanics.The field is classical,and you may superpose different field configurations.

gptejms

Jul27-05, 12:20 AM

Well, I'm sorry but you have it completely backwards here (at least in standard QM). The Schroedinger equation - which is just as valid in QFT as in ordinary QM - is the evolution equation of the wavefunction (= the quantum state of the system) in Hilbert space. However, except for the single 1-particle non-relativistic QM case, the Schroedinger equation IS NOT an equation of a field over the spacetime manifold.

Look at it this way--you have the K.G. or the Dirac (quantum)field equations to begin with.Now you go on reducing the velocity till v/c <<1.How does the quantum field now change into a wavefunction?At what point does the transition occur?I am asserting that it remains a quantum field--the wavefunction even in the NR limit is a functional of the field.

vanesch

Jul27-05, 01:35 AM

Look at it this way--you have the K.G. or the Dirac (quantum)field equations to begin with.Now you go on reducing the velocity till v/c <<1.How does the quantum field now change into a wavefunction?At what point does the transition occur?I am asserting that it remains a quantum field--the wavefunction even in the NR limit is a functional of the field.

It's a trick :-) In fact, it turns out that the wave function in the QFT Hilbert space (which can be identified with the Fock space), when reduced to the 1-particle subspace of Fock space, satisfies the same equation as the classical field. But you can already see the difference, for instance in the case of a real classical field: the field is supposed to be real, and the resulting NR Schroedinger equation gives you complex 1-particle wave functions! Another way to see it is: how does your field reduce to the wave function of TWO PARTICLES ? The field is function of (x,t) and the wave function is function of (x1,x2,t).

There is just a "mathematical coincidence" of the wave function equation (Schroedinger equation) in the 1-particle case and the classical field equation to have the same form. Of course there are reasons why this is so, but it is not because the equations are the same, in this particular case, that the *objects* (classical field over 4-manifold vs. wavefunction in hilbert space) are the same.
But people who get confused are in good company: it took until the 50ies for people to realise the difference.

gptejms

Jul27-05, 04:32 AM

No, the classical field satisfies microscopic causality (because of the fact that the differential equation (KG or Dirac) that it obeys is Lorentz-invariant).

By microscopic causality,I had loosely meant the commutation relation for the field at two spacetime points itself.I've just checked Bjorken and Drell for the definition of microscopic causality:-it says 'the condition of vanishing of the commutators for all space-like intervals,no matter how small,is referred to as the condition of microscopic causality".For a classical field the above should be satisfied for all intervals--I hope that is what you mean by microscopic causality for classical fields.

gptejms

Jul27-05, 04:38 AM

It's a trick :-) In fact, it turns out that the wave function in the QFT Hilbert space (which can be identified with the Fock space), when reduced to the 1-particle subspace of Fock space, satisfies the same equation as the classical field. But you can already see the difference, for instance in the case of a real classical field: the field is supposed to be real, and the resulting NR Schroedinger equation gives you complex 1-particle wave functions! Another way to see it is: how does your field reduce to the wave function of TWO PARTICLES ? The field is function of (x,t) and the wave function is function of (x1,x2,t).

Can you elaborate on the above--it's not quite clear to me.

vanesch

Jul27-05, 06:20 AM

By microscopic causality,I had loosely meant the commutation relation for the field at two spacetime points itself.

Yes, that is correct, but only makes sense in the Heisenberg picture of course, where the fields are Hilbert space operators, parametrized over the spacetime manifold.
The meaning behind it is of course that the value at one (x,t) point cannot be influenced by the value at another spacetime point (x2,t2) if the interval is spacelike. In the quantum version, this comes down to a condition on commutators, in the classical version, this comes down on a condition on the Green's function (propagator).

For a classical field the above should be satisfied for all intervals--I hope that is what you mean by microscopic causality for classical fields.

No, it wouldn't of course make sense to talk about commutators of the classical fields. What I meant was that the value of a classical field at an event (x1,t1) can only depend on initial values of the classical field which are within its past light cone ; which puts a condition on the Green's function. This is exactly what is re-worded in the quantum language.
I'm a bit out of my depth here, but I'd guess (someone correct me if I'm wrong) that the classical version of microscopic causality can be reformulated as Poisson brackets vanishing over spacelike intervals.

cheers,
Patrick.

gptejms

Jul27-05, 10:24 AM

Let's stick to Bjorken and Drell's definition of microscopic causality.

The interesting part is the non-zero commutator for time-like separations.
Measuring a field at spactime point 1 and then at spacetime point 2 does not give you the same result as measuring it first at point 2 and then at 1.I interpreted this in one of my earlier posts as due to the fact that when you make a measurement at 1(or 2),you create a disturbance which travels to 2(or 1) at the speed of light and readjusts the field there.Do you agree with this interpretation?You don't as we'll see below.In my model(the above interpretation) there's nothing instantaneous.A measurement at 1 can't instantaneously establish a field value at 2.

In your model when you make a measurement at 1,a certain field configuration is established in the whole of space(not just at 2)at once--of course it has some prob. attached with it.So when you measure at 1,you get some value 'a' and the value at 2 say 'b' is automatically established.If you do the reverse,that is measure at 2 you get some value 'c' which establishes the value at 1 say 'd'.So the disturbance model is out.Well yours is the official picture,can't overrule it--even though I find the disturbance model less disturbing!

vanesch

Jul27-05, 10:27 AM

Can you elaborate on the above--it's not quite clear to me.

I will try to find a reference...

cheers,
Patrick

vanesch

Jul27-05, 10:39 AM

[quote]
The interesting part is the non-zero commutator for time-like separations.
Measuring a field at spactime point 1 and then at spacetime point 2 does not give you the same result as measuring it first at point 2 and then at 1.

I'm sorry, but interchanging event (x1,t1) and (x2,t2) if t1 < t2 doesn't place suddenly the "second event before the first one". It is tricky to say what it means to "measure first at point 2" (which is an event, with a time coordinate!). So interpreting exactly what it means for NON-commuting observables at timelike separated events is tricky !
In fact, one usually talks about non-compatible observables AT EQUAL TIMES (in a certain reference frame). Time-like separated events are never at equal times in any frame, so it's going to be tricky.
It is in fact more instructive to say that space-like separated events have COMMUTING field operators - indeed, space-like separated events can be made equal-time events in a certain reference frame, and if you work in that frame, you can say that these field operators are dynamically independent.

I interpreted this in one of my earlier posts as due to the fact that when you make a measurement at 1(or 2),you create a disturbance which travels to 2(or 1) at the speed of light and readjusts the field there.Do you agree with this interpretation?You don't as we'll see below.In my model(the above interpretation) there's nothing instantaneous.A measurement at 1 can't instantaneously establish a field value at 2.

But entangled field states CAN be entangled at space-like separated events, and they do have space-like separated Bell-violating correlations. So this "field propagation" won't do. And it doesn't have to, in fact, because it is NOT the dynamics of individual field configurations that is at hand here (which have dynamics that is constrained by special relativity), but THE CHOICE BETWEEN DIFFERENT FIELD CONFIGURATIONS which is mastered by the quantum state (the wave function, if you want).

In your model when you make a measurement at 1,a certain field configuration is established in the whole of space(not just at 2)at once--of course it has some prob. attached with it.So when you measure at 1,you get some value 'a' and the value at 2 say 'b' is automatically established.If you do the reverse,that is measure at 2 you get some value 'c' which establishes the value at 1 say 'd'.So the disturbance model is out.Well yours is the official picture,can't overrule it--even though I find the disturbance model less disturbing!

Yes, except that the "disturbance model" doesn't explain EPR situations, which are supported by experiment as well as theory !

cheers,
Patrick.

vanesch

Jul27-05, 12:38 PM

I will try to find a reference...

Indeed, not many QFT books mention this, so I went through Peskin, Zee, Stone, Ryder to no avail, but Brian Hatfield, "Quantum Field theory of point particles and Strings" has a very illuminating chapter on it in the beginning (chapter 2).

cheers,
Patrick

gptejms

Jul27-05, 01:06 PM

I'm sorry, but interchanging event (x1,t1) and (x2,t2) if t1 < t2 doesn't place suddenly the "second event before the first one". It is tricky to say what it means to "measure first at point 2" (which is an event, with a time coordinate!). So interpreting exactly what it means for NON-commuting observables at timelike separated events is tricky !

No.The second part is hypothetical--a hypothetical observer at t2,disturbance going back in time followed by an observation at t1.Indeed,it's hypothetical,but it conveys the idea.

There's a footnote in Bjorken and Drell which says Bohr and Rosenfeld made a detailed analysis of the physical meaning of the commutation relations in terms of physical measurement in some obscure journal in 1933,and also in Phys. Rev,78,794(1950).Can you get hold of this---if yes,I'll be obliged if you can send me a copy.

Yes, except that the "disturbance model" doesn't explain EPR situations, which are supported by experiment as well as theory !

We have discussed EPR,polarizations can be entangled but not field intensities at space-like intervals.The former is not forbidden by the time-like commutator(I don't know what to call it,after reserving the term microscopic causality for space-like intervals,a la Bjorken & Drell!)

gptejms

Jul27-05, 01:11 PM

Indeed, not many QFT books mention this, so I went through Peskin, Zee, Stone, Ryder to no avail, but Brian Hatfield, "Quantum Field theory of point particles and Strings" has a very illuminating chapter on it in the beginning (chapter 2).

Thanks,but I am right now in a place where we get no physics books or journals.Kindly illuminate me on the contents of the illuminating chapter!

vanesch

Jul27-05, 01:23 PM

We have discussed EPR,polarizations can be entangled but not field intensities at space-like intervals.The former is not forbidden by the time-like commutator

I don't see why you make a difference between "intensities" and "polarizations" ? I mean, if we're talking about a vector field, then, can the x-component at A be entangled or not with the 45-degree component at B or not ? And can the x-component at A be entangled with the x-component at B ? And can the x-component at A be entangled with the y-component at B ?
Can the +45 component at A be entangled with the -45 component at A ? And at B ?

gptejms

Jul28-05, 12:52 AM

Patrick,let's look at the time-like part of the commutator in a different way.The commutator implies that \Delta E_1(x_1,t_1) \Delta E_2(x_2,t_2) \geq \hbar(...) ,i.e. field measurements E1 and E2 at two spacetime points follow the uncertainty principle.So if I make a measurement at x1,t1 and find a certain value,the value at x2,t2 is totally uncertain.But if I make a measurement at x2,t1 (or near about t1),the value of the field is certain.So you are also right and so is the disturbance model.

Sherlock

Jul28-05, 01:23 AM

Would it be ok for you if I dropped the "as if" ?!Is that the only objection?Keeping it or dropping it is just a matter of taste--stick to whatever you like,it makes no difference.

The usage of terms like photon and electron isn't just
a matter of tasete. The terms, photon and electron, have
specific meanings. Photons and electrons aren't what
produce measurement values. They *are* the measurement
values. It isn't known what (in terms of modeled behavior in
some quantum or submicroscopic 'realm') produces certain
measurement values. It's only known that certain experimental
setups yield certain results at certain rates. There might
be *lots* of 'models' for a given setup, and which model
one chooses to use is what is due to taste or convenience.

If we say that it's "as if" the photon or electron is created
via measurement, then it's "as if" the terms photon or electron
refer to something other than formal constructs related to
detection attributes. But photons and electrons don't have
any objective (ie., verifiable) existence other than as formal
constructs related to detection attributes -- and this is why the
photon and the electron are *neither* particle nor wave in
any classically analogous sense (and why, by definition, they
*can't* exist, as physical phenomena differentiated from yet
associated with formal constructs, prior to detection).

There is a source of electrons and a screen a little away.Think of this as just a field,an 'electron field'.There is no pattern on the screen.You introduce the double slit in between the source and the the screen.You have imposed certain constraints,the field gets disturbed and readjusts to 'interference pattern' on the screen--this proceeds at the speed of light(consistent with microscopic causality).Till I do not make any measurement,I think of it as just a field--in fact I am not even allowed to think of it as particles,until I make a measurement and find a particle.In fact my assertion is that only interactions are quantum,otherwise it's just a field.

In 'realistic' terms, the medium that is transmitting disturbances from one
oscillator (an emitting medium) to another (a detecting medium) is "just a field" unless
set in motion by an interaction of some sort. If the oscillations of the emitter are quantized,
then so must the associated oscillations of the transmitting medium be quantized. And, all
of this is inferred from the quantized oscillations of the detecting medium.

This is a wave picture of course, and wrt to the two-slit setup where interference
patterns are built up quantum by quantum there is the problem of explaining how/why
two wave fronts emerging from two open slits, and interferring with each other, produce
only a single detected point of interaction.

Of course, we don't know that there's two wave fronts (associated with a single
detection attribute) emerging from two open slits. Maybe there's just one wave front,
or some sort of bubble or whatever, emerging from just one of the two open slits -- and
while this would seem to account for the single detection points ,,, how could it happen
that way, and how could that produce interference if there's nothing for the
singular disturbance to interfere with?

One way to talk about the measurement problem is that it isn't known
how a submicroscopic or quantum 'realm' is behaving -- or even if there exists,
independent of instruments, a submicroscopic or quantum 'realm' of behavior.

And, I don't think that your approach is providing any new insight wrt
the problem. But maybe I've missed something.

The kind of local realism I am talking of is dictated by the principle of microscopic causality(i.e.nothing but the commutation property of the field at two space-time points),which is the basic feature of QFT--how can anyone doubt it?And this kind of local realism dictated by microscopic causality does not contradict EPR situations as I have already said--in EPR you don't measure the field anywhere,you are just measuring polarization at two places (which due to entanglement leads to higher correlation than expected on classical grounds).

Entanglement *refers to* ( at least wrt certain setups) a "higher correlation than expected
on classical grounds", doesn't it? That is, this is one way to test for the presence of
entanglement. However, if, as you seem to indicate, entanglement is the *cause* of the
higher correlations, then what is entanglement?

Anyway, it isn't EPR setups that are at odds with local realism. It's the Bell-Bohm-etc.
setups that evolved from the EPR considerations that pose a problem. I want to think
of the precondition (at a submicroscopic or quantum level) necessary for the global
correlations (predictably produced by variations in the Theta of the analyzing crossed
linear polarizers), as a relationship between opposite-moving paired emissions that
is produced at emission. But, Bell's analysis doesn't seem to allow this way of
thinking about it.

It isn't clear to me how your approach deals with this problem.

vanesch

Jul28-05, 02:43 AM

So if I make a measurement at x1,t1 and find a certain value,the value at x2,t2 is totally uncertain.But if I make a measurement at x2,t1 (or near about t1),the value of the field is certain.So you are also right and so is the disturbance model.

Not necessarily ! Commuting observables do not mean that their value IS, FOR ALL STATES, certain !! It means that THERE EXIST states for which both of their values can be certain (common eigenstates).
So it is not true in all generality that if I make a measurement of the field at x2, t1, that this means that now my value of the field at x1, t1 is certain. It might be, it might not be, and that depends upon the specific quantum state at hand I'm measuring. Most of the time, it will not be (Eigenstates are rare, your generic state isn't an eigenstate).

cheers,
Patrick.

gptejms

Jul28-05, 03:13 AM

Not necessarily ! Commuting observables do not mean that their value IS, FOR ALL STATES, certain !! It means that THERE EXIST states for which both of their values can be certain (common eigenstates).
So it is not true in all generality that if I make a measurement of the field at x2, t1, that this means that now my value of the field at x1, t1 is certain. It might be, it might not be, and that depends upon the specific quantum state at hand I'm measuring. Most of the time, it will not be (Eigenstates are rare, your generic state isn't an eigenstate).

From the wavefunction approach,I know that if I make a measurement of the field at x1,t1,I instantaneously establish a certain field configuration in the whole of space.My basic idea was that this is allowed for by the time-like commutator(I wish I had a better word for it),and if the measurement is made at x2,t2(where x2,t2 is time-like separated from x1,t1) the value is completely uncertain--this substantiates the fact that a disturbance has travelled from x1 to x2 at vel. of light.So the disturbance model is also right.

vanesch

Jul28-05, 03:30 AM

The usage of terms like photon and electron isn't just
a matter of tasete. The terms, photon and electron, have
specific meanings. Photons and electrons aren't what
produce measurement values. They *are* the measurement
values.

Yes, that's an epistemological view of nature. There's nothing really out there, we're just knowing about measurements, and our theories give us relationships between measurements. It is an acceptable view. However, I don't like it: I like to think that *something* is really out there (a certain ontology), and that our formalism maps onto that ontology in some way. The main reason for it is that it is an "inspiration killer" ! If you just think of physical theories as scratching symbols on a paper, and measurement apparatus as making pointers move on a dial, there's not much your imagination can cling on to try to see what grand principles underlie all of it. The theory "measurements happen" is also a good theory then.

If we say that it's "as if" the photon or electron is created
via measurement, then it's "as if" the terms photon or electron
refer to something other than formal constructs related to
detection attributes. But photons and electrons don't have
any objective (ie., verifiable) existence other than as formal
constructs related to detection attributes -- and this is why the
photon and the electron are *neither* particle nor wave in
any classically analogous sense (and why, by definition, they
*can't* exist, as physical phenomena differentiated from yet
associated with formal constructs, prior to detection).

Ok, that's the purely epistemological view concerning "particles".
But...

In 'realistic' terms, the medium that is transmitting disturbances from one
oscillator (an emitting medium) to another (a detecting medium) is "just a field" unless
set in motion by an interaction of some sort. If the oscillations of the emitter are quantized,
then so must the associated oscillations of the transmitting medium be quantized. And, all
of this is inferred from the quantized oscillations of the detecting medium.

This is a wave picture of course, and wrt to the two-slit setup where interference
patterns are built up quantum by quantum there is the problem of explaining how/why
two wave fronts emerging from two open slits, and interferring with each other, produce
only a single detected point of interaction.

We can now apply the same epistemology to "fields" and "waves" and say that they are just constructions according to our taste to explain measurements. They're not real either.

Of course, we don't know that there's two wave fronts (associated with a single
detection attribute) emerging from two open slits. Maybe there's just one wave front,
or some sort of bubble or whatever, emerging from just one of the two open slits -- and
while this would seem to account for the single detection points ,,, how could it happen
that way, and how could that produce interference if there's nothing for the
singular disturbance to interfere with?

In the same way as "particles" are attributes of a measurement, so are then "interference patterns", no ?

One way to talk about the measurement problem is that it isn't known
how a submicroscopic or quantum 'realm' is behaving -- or even if there exists,
independent of instruments, a submicroscopic or quantum 'realm' of behavior.

And, I don't think that your approach is providing any new insight wrt
the problem. But maybe I've missed something.

Entanglement *refers to* ( at least wrt certain setups) a "higher correlation than expected
on classical grounds", doesn't it? That is, this is one way to test for the presence of
entanglement. However, if, as you seem to indicate, entanglement is the *cause* of the
higher correlations, then what is entanglement?

In your view, "entanglement" is just another attribute of measurement results...

Anyway, it isn't EPR setups that are at odds with local realism. It's the Bell-Bohm-etc.

I'd say, if there is no reality, no point in discussing local realism !
"Measurements happen". See how it kills inspiration ? :smile:

cheers,
Patrick.

vanesch

Jul28-05, 03:45 AM

From the wavefunction approach,I know that if I make a measurement of the field at x1,t1,I instantaneously establish a certain field configuration in the whole of space.

No, because the measurement in ONE spacetime point doesn't fix all of the field configuration, there is still a lot of degeneracy. You only project upon the eigenspace of field configurations that have this result at (x1,t1). It is like if you measured, say, the x-component of a particle in NR QM. This doesn't mean that the y and z component are now completely established !
If the x-coordinate is not entangled with the y coordinate (the wave function is a product of a function of x and of y), then the measurement of x will not influence the measurement at y (they will be statistically uncorrelated). If the wavefunction is not a product, then the "x-coordinate" is entangled with "the y-coordinate" and the measurement of x will be correlated with the measurement of y. It doesn't have to FIX it. It might. In that case, we have 100% entanglement, and we are using compatible observables (x and y).
All this being an example in NR QM of course.

My basic idea was that this is allowed for by the time-like commutator(I wish I had a better word for it),and if the measurement is made at x2,t2(where x2,t2 is time-like separated from x1,t1) the value is completely uncertain--this substantiates the fact that a disturbance has travelled from x1 to x2 at vel. of light.So the disturbance model is also right.

It can explain the LACK of correlations WITHIN the lightcone of INCOMPATIBLE observables. It cannot explain the Bell-type correlations OUTSIDE of the light cone of COMPATIBLE observables.

cheers,
Patrick.

seratend

Jul28-05, 04:38 AM

Sherlock

Jul28-05, 04:46 AM

Yes, that's an epistemological view of nature. There's nothing really out there, we're just knowing about measurements, and our theories give us relationships between measurements. It is an acceptable view. However, I don't like it: I like to think that *something* is really out there (a certain ontology), and that our formalism maps onto that ontology in some way. The main reason for it is that it is an "inspiration killer" ! If you just think of physical theories as scratching symbols on a paper, and measurement apparatus as making pointers move on a dial, there's not much your imagination can cling on to try to see what grand principles underlie all of it. The theory "measurements happen" is also a good theory then.

I also think that *something* is really out there. My bit about
photons and electrons just had to do with how *those terms*
should be used -- to avoid confusion -- since we don't know the
physical characteristics of what corresponds *out there* to
photons and electrons.

We can now apply the same epistemology to "fields" and "waves" and say that they are just constructions according to our taste to explain measurements. They're not real either.

Of course they're real. Just like photons and electrons are
real. (But waves and particles are the only things mentioned
so far that have any meaning wrt our ordinary experience of
the world.) The only question is what are we referring to when we
use the terms. When we're talking within the context of an
instrumental theory like qm, then these terms have specific
meanings and don't refer to things *out there*. They refer
to specific instrumental configurations and formal constructs
associated with the instrumental configurations. What is
*out there* is a matter of speculation, and hopefully a
comprehensive picture of *out there* can eventually be
developed via the data and the many ways of interpreting it.

In the same way as "particles" are attributes of a measurement, so are then "interference patterns", no ?

Particles, waves and interference patterns refer to commonly
observable phenomena, and are often used interpretively, to help
develop a qualitative picture of *out there*.

In your view, "entanglement" is just another attribute of measurement results...

Quantum entanglement has a theory-dependent meaning.
It's not a cause, it's an effect.

I'd say, if there is no reality, no point in discussing local realism !
"Measurements happen". See how it kills inspiration ? :smile:

I think you've misunderstood my orientation. I'm very much a
local realist ... when possible. Very much interested in
the big picture of *out there*. :-)

vanesch

Jul28-05, 06:02 AM

So you think you need constraints to have inspiration (a kind of causality or masochism?)? :biggrin:

Yes, of course ! That's the whole point. If "anything goes" that's, as you point out, too much choice, hard to choose from. The "blank paper" experience.

Why do you seem to think an epistemic approach does not allow to build beautifull grand principles to describe reality?

It allows for it, but there's no reason for it. It could all be "a big lookup table" too.

Look at the power of the approach: it contains surely the ontological view (while i am not sure for the converse) and there may be not a single principle, but a collection of powerfull principles or no grand principle at all.

Indeed. So when looking for grand principles, it is disturbing to be in a mindset where there might very well not be such a grand principle. You'll be less good at your job. A bit like as if you are a suicide bomber, and you go for the 74 virgins, but you're not really sure about it. You'll be a less motivated bomber, than the one that is convinced those ladies are waiting for him :-)

cheers,
Patrick.

gptejms

Jul28-05, 07:13 AM

No, because the measurement in ONE spacetime point doesn't fix all of the field configuration, there is still a lot of degeneracy. You only project upon the eigenspace of field configurations that have this result at (x1,t1). It is like if you measured, say, the x-component of a particle in NR QM. This doesn't mean that the y and z component are now completely established !
If the x-coordinate is not entangled with the y coordinate (the wave function is a product of a function of x and of y), then the measurement of x will not influence the measurement at y (they will be statistically uncorrelated). If the wavefunction is not a product, then the "x-coordinate" is entangled with "the y-coordinate" and the measurement of x will be correlated with the measurement of y. It doesn't have to FIX it. It might. In that case, we have 100% entanglement, and we are using compatible observables (x and y).
All this being an example in NR QM of course.

You are the one,I thought,who believed in instantaneous establishment of the entire field configuration upon measurement(see post no. 146).If it dosen't happen generally(except in a limited way in cases of entanglement),it's even better for my case!I think the disturbance model is perfectly sound,it explains a lot of things and does not forbid EPR correlations(even though it doesen't explain it).Mind you,disturbance model is not something that I am proposing or propounding--it is a natural interpretation of the time-like part of the field commutator.

seratend

Jul28-05, 07:17 AM

Yes, of course ! That's the whole point. If "anything goes" that's, as you point out, too much choice, hard to choose from. The "blank paper" experience. .
If anything
Come on patrick :tongue2:. The blank paper view is as beautifull as the catholic paradise before the snake: it just illustrates the set of possibilities we have before and the difficulties we have after when we choose one of them o:) .

It allows for it, but there's no reason for it. It could all be "a big lookup table" too..
Interesting. As long as we use the set theoric approach, yes we can say it is a big look up table.

Seratend

vanesch

Jul28-05, 08:28 AM

You are the one,I thought,who believed in instantaneous establishment of the entire field configuration upon measurement(see post no. 146).

Hum, that was indeed a particular case in which the projection of the state upon the space spanned by all field configurations which are compatible with the measurement result, resulted in a single base vector (= a specific configuration).

If it dosen't happen generally(except in a limited way in cases of entanglement),it's even better for my case!I think the disturbance model is perfectly sound,it explains a lot of things and does not forbid EPR correlations(even though it doesen't explain it).Mind you,disturbance model is not something that I am proposing or propounding--it is a natural interpretation of the time-like part of the field commutator.

I still have the impression we're talking next to eachother. The disturbances and so on, ruled by unitary QM, tell us how field configurations evolve in other field configurations, or in superpositions of other field configurations.
The measurement, on the other hand, projects instantaneously out those field configurations that are compatible with the measurement and eliminates all other terms from the wavefunction. How can you consider the latter to be a special case of the former ?
Now, in many cases, this "projecting out" doesn't correlate measurements. But in some cases it does. The very fact that there are SOME cases when the "propagation of the effect" technique doesn't work, should make you accept that this is NOT the explanation in general, no ?

I mean, it is as if you said that gravity propagates through sound waves in air, and point to many experiments involving gravity, that happened in air. I point out to a few experiments where gravity was observed in vacuum, and you say, ok, then, "I think the air gravity model is perfectly sound, it explains a lot of things and does not forbid gravity working in vacuum (even though it doesn't explain it). Mind you,the air gravity model is not something that I am proposing or propounding--it is a natural interpretation of how gravity works around us."

vanesch

Jul28-05, 10:33 AM

The blank paper view is as beautifull as the catholic paradise before the snake

This must be the quote of the day :smile:

gptejms

Jul28-05, 11:16 AM

Hum, that was indeed a particular case in which the projection of the state upon the space spanned by all field configurations which are compatible with the measurement result, resulted in a single base vector (= a specific configuration).

In which particular case of measurement does it become a single base vector and when not?

The disturbances and so on, ruled by unitary QM, tell us how field configurations evolve in other field configurations, or in superpositions of other field configurations.

other field configurations--are you introducing interactions here?

The measurement, on the other hand, projects instantaneously out those field configurations that are compatible with the measurement and eliminates all other terms from the wavefunction.

I put this question to you.Why is the measurement so different from interactions?What special quality does it have,which other interactions don't have?

Now, in many cases, this "projecting out" doesn't correlate measurements. But in some cases it does. The very fact that there are SOME cases when the "propagation of the effect" technique doesn't work, should make you accept that this is NOT the explanation in general, no ?

I didn't offer the disturbance model as a panacea for all measurement problems.All I can say is it does not forbid EPR correlations.

I mean, it is as if you said that gravity propagates through sound waves in air, and point to many experiments involving gravity, that happened in air. I point out to a few experiments where gravity was observed in vacuum, and you say, ok, then, "I think the air gravity model is perfectly sound, it explains a lot of things and does not forbid gravity working in vacuum (even though it doesn't explain it). Mind you,the air gravity model is not something that I am proposing or propounding--it is a natural interpretation of how gravity works around us."

I think this is making light of the whole thing.BTW what interpretation do you give to the TFC(time-like part of the field commutator!)--do you agree with my disturbance model?If yes,how do you reconcile it with EPR?If you don't agree,give me your interpretation of TFC.

vanesch

Jul28-05, 12:37 PM

In which particular case of measurement does it become a single base vector and when not?

When, in the superposition of field configurations (the quantum state written out in the "field configuration" basis), there is only ONE SINGLE term that satisfies the measured value of the field at the given event.

Consider the quantum state:

|psi(t1)> = a |fieldconf1> + b |fieldconf2> + c |fieldconf3>

Imagine that we measure F = 15.3 at (x1,t1). Now, fieldconf1(x1,t1) = 15.3, fieldconf2(x1,t1) = 15.3 and fieldconf3(x1,t1) = 18.8

That means that after measurement (using the projection postulate - so I'm NOT doing some MWI here), we have the state:

|psi(t1+epsilon)> = Normfactor (a |fieldconf1> + b |fieldconf2> )

However, imagine that we measured F = 18.8 at (x1,t1). Then it means that we now have the state:

|psi(t1+epsilon)> = |fieldconf3>

because there was only one single fieldconfiguration term in |psi(t1)> that satisfied the measurement result, namely fieldconf3.

I put this question to you.Why is the measurement so different from interactions?What special quality does it have,which other interactions don't have?

Ha, well, it ISN'T any different (except for the fact that YOU are taking part in it). But to recognize this in quantum theory, you need to put the projection postulate in the dustbin, and you end up in a Many Worlds interpretation.
All collapse models do at least one of both things: set "measurements" apart as interactions, and/or violate special relativity in their workings.

All I can say is it does not forbid EPR correlations.

This is what I don't understand. If effects of measurements ("effective collapse", say) are to propagate within the light cone, how can you then have Bell-violating correlations at space-like intervals ??

BTW what interpretation do you give to the TFC(time-like part of the field commutator!)--do you agree with my disturbance model?If yes,how do you reconcile it with EPR?If you don't agree,give me your interpretation of TFC.

I have to say I don't really know how to interpret the TFC. I'd say that a priori, a generic couple of operators DOES NOT commute, and it is rather the exception that they DO. So the thing I find interesting is that SPACELIKE field operators DO commute, which means that explicit dynamical influence (capable, say, of sending information) over spacelike intervals is prohibited ; a necessary condition to satisfy special relativity.
Why timelike commutators vanish or not doesn't have a deep message, to me.
But quantum superposition by itself, and the "effect of collapse" is not something that has to do with the specific dynamics of the quantized model at hand ; it is build into quantization itself, and independent of the underlying dynamics. It becomes 'spectacular' when something forbids any underlying dynamics to do the correlations for us ; we then suddenly realize the difference between the dynamics of the underlying model, and the strangeness of quantum theory by itself. But the strangeness was there alright from the start, only, we could trick ourselves into believing we saw "dynamical links".

cheers,
Patrick.

gptejms

Jul28-05, 02:05 PM

Consider the following:-

There is a classical field(deterministic) superimposed on a random noise field(say white noise) in a certain region of space.My measuring device is such that I can not resolve field strength differences less than a certain value(call it a 'quantum')--so my measurements of field strengths are n quanta,m quanta etc.(in an approximate sense).Now on this mixture field,I impose the condition from outside(i.e. hypothetical condition) that whenever I measure it or introduce an interaction at x1,t1,the same affects the entire field at the velocity of light.The entire field gets readjusted.Now I can also introduce the notion of a wavefunction and say that the wavefunction is a functional of the field and at any given time,there could be field-config1 or field-config2 or field-config3 etc.The field satisfies commutator relations too,in a way.

The above is not a complete representation of the quantum field.But it's a good analogy.I wonder if the wavefunction of quantum mechanics has a very different role than the above.Feeling quite sleepy,will write more tomorrow(err..today morning).

vanesch

Jul28-05, 02:26 PM

There is a classical field(deterministic) superimposed on a random noise field(say white noise) in a certain region of space.My measuring device is such that I can not resolve field strength differences less than a certain value(call it a 'quantum')--so my measurements of field strengths are n quanta,m quanta etc.(in an approximate sense).Now on this mixture field,I impose the condition from outside(i.e. hypothetical condition) that whenever I measure it or introduce an interaction at x1,t1,the same affects the entire field at the velocity of light.The entire field gets readjusted.Now I can also introduce the notion of a wavefunction and say that the wavefunction is a functional of the field and at any given time,there could be field-config1 or field-config2 or field-config3 etc.The field satisfies commutator relations too,in a way.

The above is not a complete representation of the quantum field.But it's a good analogy.I wonder if the wavefunction of quantum mechanics has a very different role than the above.Feeling quite sleepy,will write more tomorrow(err..today morning).

What you are describing is very close to Stochastic Electrodynamics, an attempt to modify classical electromagnetics by adding "universal noise" so as to mimick quantum effects. I don't know all of it (I think its originator is De Santos or Dos Santos or something). What I know is that it DOES mimick quite a lot of quantum effects of QED. However, on true EPR situations, it breaks its neck. It does, however, have the potential to explain "inefficient" EPR experiments, as are in fact all EPR experiments today. When I say "has the potential to explain", it still means you have to build awkward photon detector models made on purpose to trick us into believing EPR situations. This is the difference with standard QM, which predicts EPR results without any ambiguity or "fiddling on purpose", and which explains also without fiddling how a photodetector works.
There are other, deeper problems with Stochastic Electrodynamics, such as the appearance of particle-like properties of electrons and so on ; but nevertheless it is a nice attempt, and what you describe makes me think of it.

gptejms

Jul28-05, 11:22 PM

Imagine a photon detector at one of the slits.Further imagine that it's conscious.Now the photon detector has to describe its interaction with the particle(better imagine yourself to be the photon detector).When the observer is part of the observed,can it write down the wavefunction,is the evolution still unitary?See,as long as you give yourself all the importance and write down the wavefunction,whatever interactions I may introduce,whatever picture(field/particle) I may use,if you come in in the last and write down the wavefunction,evolution is going to be unitary.I want to change that.A part interacting with the whole,and the part describing its own dynamics.I feel this evolution would not be unitary.

gptejms

Jul29-05, 12:20 AM

What you are describing is very close to Stochastic Electrodynamics, an attempt to modify classical electromagnetics by adding "universal noise" so as to mimick quantum effects. I don't know all of it (I think its originator is De Santos or Dos Santos or something). What I know is that it DOES mimick quite a lot of quantum effects of QED. However, on true EPR situations, it breaks its neck. It does, however, have the potential to explain "inefficient" EPR experiments, as are in fact all EPR experiments today.

I am surprised,whatever I have come up with during this thread,whether potential or stochastic potential,the role of TFC/microscopic causality in measurements or the classical + random noise field picture,someone has thought of it and worked on it.I wonder what Bohr & Rosenfeld have written in their paper on TFC.
I found the following abstract when I googled for 'stochastic electrodynamics santos' :-

Stochastic optics: A local realistic analysis of optical tests of Bell inequalities
Trevor W. Marshall
Department of Mathematics, University of Manchester, Manchester M13 9PL, United Kingdom

Emilio Santos

Departamento de Física Moderna, Universidad de Cantabria, Santander, Spain

Received 22 November 1988
Stochastic optics may be considered as simply a local realistic interpretation of quantum optics and, in this sense, it is a first step in the reinterpretation of the whole of quantum theory. However, as it is not possible to interpret all the details of quantum theory in a local realistic manner, as shown by Bell's theorem, minor changes are introduced in the formalism with the consequence that the new theory makes different predictions in some special cases. In stochastic optics, the quantum-operator formalism is simply considered a formal way of dealing with stochastic fields. In particular, the quantum zero point is taken as a real random electromagnetic radiation filling the whole of space. This radiation noise has the same nature as light signals, the only difference being the greater intensity of the latter. We assume that photon detectors have an intensity threshold just above the level of the noise, thus detecting only signals. Transmission of radiation through polarizers follows Malus's law, but the interplay of signal and noise leads quite naturally to the prediction that the detection probability of some signals is enhanced, which is known to be a necessary condition for the violation of the empirically tested Bell inequalities. In our view, correlated photon pairs are pairs of light signals supercorrelated in polarization, in the sense that, as well as the signal, the accompanying noise is also correlated. Thus stochastic optics allows predictions for the empirical correlations very close, but not identical, to the quantum ones. The theory is applied to the analysis of all experiments designed to test the Bell inequalities by measuring polarization correlations of photon pairs. The predictions agree with quantum optics and experiments within statistical errors, except for the Holt-Pipkin experiment. In this case, the experimental results agree with stochastic optical predictions within two standard deviations while violating quantum optics by four.

©1989 The American Physical Society

vanesch

Jul29-05, 01:38 AM

I am surprised,whatever I have come up with during this thread,whether potential or stochastic potential,the role of TFC/microscopic causality in measurements or the classical + random noise field picture,someone has thought of it and worked on it.

This has been my problem too during all of my career ! It's not so much that I cannot solve the problems I'm presented with, it's that the way I solve them, I discover usually afterwards, has been done already... It's so difficult to have a truely NEW idea, isn't it ! :grumpy:

DaTario

Jul29-05, 03:20 AM

The Group in Spain is one of the few that sustain this idea. One remarkable result of this theory, I should say fantastic result, is that if you take the quantum vaccum inside a very large box, its energy can be cast in the form:
[tex]
E = \Sum_{{i = 0}^infty \frac{1}{2}\hbar \omega_i
[\tex]

which contains all possible frequencies for the radiation field. Notice that this expression allows one to obtain the vaccum spectrum.

Now, if you look for a classical field which must be invariant under a Lorentz transformation, i.e., which looks the same whether you are at rest relatively to some intertial referential or at constant velocity, the spectrum is the same as the one obtained from de expression above. Therefore, according to those spanishes of stochastic electrodynamics, what we quantum mechanically call vacuum, they call "the state of the EM field which doesn't change with your moving perspective". This is a very beautiful definition of vaccum in my opinion.

gptejms

Jul29-05, 04:01 AM

This has been my problem too during all of my career ! It's not so much that I cannot solve the problems I'm presented with, it's that the way I solve them, I discover usually afterwards, has been done already... It's so difficult to have a truely NEW idea, isn't it ! :grumpy:

Right,but keep at it.May be,you come up with something truly original one day! I think you've got it in you to make it.

gptejms

Jul29-05, 04:08 AM

The Group in Spain is one of the few that sustain this idea. One remarkable result of this theory, I should say fantastic result, is that if you take the quantum vaccum inside a very large box, its energy can be cast in the form:

E = \sum_{i = 0}^\infty \frac{1}{2}\hbar \omega_i

which contains all possible frequencies for the radiation field. Notice that this expression allows one to obtain the vaccum spectrum.

Now, if you look for a classical field which must be invariant under a Lorentz transformation, i.e., which looks the same whether you are at rest relatively to some intertial referential or at constant velocity, the spectrum is the same as the one obtained from de expression above. Therefore, according to those spanishes of stochastic electrodynamics, what we quantum mechanically call vacuum, they call "the state of the EM field which doesn't change with your moving perspective". This is a very beautiful definition of vaccum in my opinion.

Just to correct your tex!

gptejms

Jul29-05, 11:02 AM

The usage of terms like photon and electron isn't just
a matter of tasete. The terms, photon and electron, have
specific meanings. Photons and electrons aren't what
produce measurement values. They *are* the measurement
values. It isn't known what (in terms of modeled behavior in
some quantum or submicroscopic 'realm') produces certain
measurement values. It's only known that certain experimental
setups yield certain results at certain rates. There might
be *lots* of 'models' for a given setup, and which model
one chooses to use is what is due to taste or convenience.

If we say that it's "as if" the photon or electron is created
via measurement, then it's "as if" the terms photon or electron
refer to something other than formal constructs related to
detection attributes. But photons and electrons don't have
any objective (ie., verifiable) existence other than as formal
constructs related to detection attributes -- and this is why the
photon and the electron are *neither* particle nor wave in
any classically analogous sense (and why, by definition, they
*can't* exist, as physical phenomena differentiated from yet
associated with formal constructs, prior to detection).

In 'realistic' terms, the medium that is transmitting disturbances from one
oscillator (an emitting medium) to another (a detecting medium) is "just a field" unless
set in motion by an interaction of some sort. If the oscillations of the emitter are quantized,
then so must the associated oscillations of the transmitting medium be quantized. And, all
of this is inferred from the quantized oscillations of the detecting medium.

I think you have contradicted yourself here.You say 'photons and electrons don't have any objective (ie., verifiable) existence other than as formal
constructs related to detection attributes' and then you conclude that 'oscillations of the transmitting medium are quantized'.I think the resolution lies in understanding that quantization aspect is revealed to you only upon measurement--and then to avoid the contradiction say 'before that the photons/electrons don't exist'(though I prefer the 'as if').

Entanglement *refers to* ( at least wrt certain setups) a "higher correlation than expected
on classical grounds", doesn't it? That is, this is one way to test for the presence of
entanglement. However, if, as you seem to indicate, entanglement is the *cause* of the
higher correlations, then what is entanglement?

The disturbance model does not explain EPR,but why should it?It's just an interpretation that I have given to TFC(time-like part of field commutator).It gives you a new way of looking at some of the things--when you introduce a double slit in between a source of electrons and a screen,you've given rise to a disturbance in the field,which propagates(at vel. of light) and readjusts the field at the screen to 'interference pattern'.When you make a measurement at one of the slits,it again gives rise to a disturbance that propagates and causes the field at the other slit to correspond to 'no electron' and at the screen to 'no interference effects'.I think it's a beautiful way of looking at things.I can only tell you that this disturbance model does not contradict EPR results--EPR results are tested or arrived at at space-like intervals.Your measurement at '1' has not had sufficient time to travel to '2' and affect the measurement there.

If you think my disturbance interpretation of TFC is wrong,you must tell me why and give me an alternate interpretation.

gptejms

Jul30-05, 12:59 AM

No one is writing any more.So I think I must sum up,at least, what my thinking is at the moment(the same has developed/evolved from points 1 to 4 mentioned in a couple of replies/posts to tdunc above to the one below,call it point 5):-

5.I think what I wrote in post #168 is not very different from the decoherence approach:-after writing it,I think decoherence is a good approach to the measurement problem.One can't do much more than that:-when the 'observer' is also a part of the observed,if you write down a wavefunction you are introducing a 3rd person in the picture(in whose frame of reference the evolution is unitary)--so the wavefunction is not a way for handling things from the perspective(or the frame of reference) of the 'observer'.In order to do that,it's ok to introduce a 3rd person,write down a wavefunction,sum over the reservoir('observer') degrees of freedom to describe the particle/system being observed.In summing up over these degrees of freedom(which can not be described by a unitary operator),you are introducing the necessary non-unitarity.
The disturbance interpretation of TFC describes the Heisenberg picture of measurement,rather what happens upon a measurement.It does not explain measurement,it tells you what happens upon measurement.It does not explain EPR results(but does not violate it either).I wish somebody could put EPR in the Heisenberg picture--i.e. show how entanglement arises from the Heisenberg picture.
Regarding the classical field + random noise field picture in post #166--looks good but need to think more.

Sherlock

Jul30-05, 10:28 AM

I think you have contradicted yourself here.You say 'photons and electrons don't have any
objective (ie., verifiable) existence other than as formal constructs related to detection
attributes' and then you conclude that 'oscillations of the transmitting medium are quantized'.

It seems like a reasonable conclusion, doesn't it? But, I have no way of *knowing* if
it's an accurate description of what is happening in the experimental setup prior
to detection. I can *know* whether or not a photon or an electron has been
produced, because these terms have verifiable operational meanings -- and the
physical effects (the data) that they refer to don't exist until detecting instruments
produce them. So, there's no contradition to resolve.

Having said that, I must say that I find it to be a rather unsatisfying way of talking
about things. I believe that the medium between emitters and detectors
is behaving in a real, quantized way that is directly related to the recording of
individual quantum measurement values. However, the qualitative characteristics
of whatever it is that is moving from emitter to detector, and eventually producing
a photon or electron, aren't known.

I think the resolution lies in understanding that quantization aspect is revealed to you
only upon measurement--and then to avoid the contradiction say 'before that the
photons/electrons don't exist' (though I prefer the 'as if').

If you say "as if", then you're using the terms 'photon' and 'electron' in a
way that requires you to clarify exactly what you mean.

The disturbance model does not explain EPR, but why should it? It's just an interpretation
that I have given to TFC (time-like part of field commutator). It gives you a new way of looking
at some of the things -- when you introduce a double slit in between a source of electrons and
a screen, you've given rise to a disturbance in the field,which propagates (at vel. of light) and
readjusts the field at the screen to 'interference pattern'. When you make a measurement at
one of the slits, it again gives rise to a disturbance that propagates and causes the field at the
other slit to correspond to 'no electron' and at the screen to 'no interference effects'. I think it's
a beautiful way of looking at things.

Two open slits transmit two disturbances which interfere with each other.
One open slit transmits one disturbance which has nothing to interfere with
on the other side. But, how to account for the single localized
detection when both slits are open? Maybe the two open slits transmit a single
disturbance. How does that happen, and if that *is* what is happening, then
what is that single disturbance interfering with to produce the interference pattern
observed with both slits open? I don't think you've solved *the problem*. If you do,
then that will indeed be beautiful and you will probably get a some sort of prize.

I can only tell you that this disturbance model does not contradict EPR results -- EPR results
are tested or arrived at at space-like intervals. Your measurement at '1' has not had sufficient
time to travel to '2' and affect the measurement there.

What does your model have to do with Bell test (EPR) results? And, what does this part of
your reply have to do with my question about your use of the term 'entanglement'?
Quantum entanglement is an observed effect (eg. Bell inequality violating correlations).
But you were using the term as a *cause* -- so I was asking what you meant by the
term wrt that usage.

gptejms

Jul30-05, 12:43 PM

Having said that, I must say that I find it to be a rather unsatisfying way of talking
about things. I believe that the medium between emitters and detectors
is behaving in a real, quantized way that is directly related to the recording of
individual quantum measurement values.

Why do you bring in the medium here?The medium is not behaving in a quantized way,it's the field that does(that too upon measurement).

If you say "as if", then you're using the terms 'photon' and 'electron' in a
way that requires you to clarify exactly what you mean.

I prefer the "as if" partly because of conditioning:-we are conditioned to believe that that things(table, chair etc.) are out there even if we don't observe them--that my observation plays no crucial role in it.That does not work for electrons and photons.The other reason is that even if I don't observe an electron,something is out there(otherwise what are we describing)--it exists as a potential reality.Even the use of the words 'potential reality' is a projection of my measurement--since I observed an electron,it must be out there in some form when I didn't observe it.See, you can't segregate the observer and the observed(though physicists are used to working in that way--and that leads to the conceptual problems in QM).

Two open slits transmit two disturbances which interfere with each other.
One open slit transmits one disturbance which has nothing to interfere with
on the other side. But, how to account for the single localized
detection when both slits are open? Maybe the two open slits transmit a single
disturbance.

There is nothing like one disturbance or two disturbances--a disturbance is a disturbance,that's it.The nature of disturbance may vary.

I don't think you've solved *the problem*.

The problem is more in our heads than out there!

What does your model have to do with Bell test (EPR) results?

Nothing.In fact it's not even my model(or anyone's model)--TFC is in the structure of QFT and it implies propagation effects.

vanesch

Jul31-05, 02:36 AM

No one is writing any more.

Don't interpret that as a victory :biggrin:
I'm visiting some family so it's more difficult to be at the computer the whole evening, but next week, as Schwarzenegger used to say, "I'll be back" o:)

cheers,
Patrick.

Sherlock

Aug1-05, 03:13 AM

Why do you bring in the medium here?The medium is
not behaving in a quantized way, it's the field that does(that too upon measurement).

I'm using the word 'medium' as being more or less synonymous
with 'field'. We're saying the same thing essentially.

I prefer the "as if" partly because of conditioning:-we are conditioned to believe that that things(table, chair etc.) are out there even if we don't observe them--that my observation plays no crucial role in it.That does not work for electrons and photons.

I realize I'm maybe being too nitpicky about this. I believe that
there is an 'out there' (a quantum or submicroscopic realm) that
our senses and instruments can't track (not just that we're not
looking at it). Chairs and tables and photons and electrons have
physical referents that we *can* track, and have some sort of
qualitative apprehension of -- that is, they have meaning,
verifiable objective existence in the world of our sensory
experience. Photons and electrons are operationally defined.
They don't exist independent of the operations that create
them (except symbolically of course).

So, it really isn't correct to say that a photon was emitted, or
was transmitted by a slit, or a double-slit, or a polarizing filter
or a beamsplitter or whatever. It just isn't known what was
emitted, or what was transmitted by some filter, or what
hit a barrier or how it interacted with it or how whatever it
was that was initially emitted is behaving anywhere along the
transmission line from (and including) emission to the recording
of some data bit. Everything except the raw data and
the hardware preparation steps is an inference or assumption
of some sort.

Anyway, by definition, photons and electrons don't exist
independent of the processes that produce them. They're
defined in a certain way, and that's what they mean. What's
'out there' in quantumrealityland is still anybody's guess.
On the other hand, it would be silly to say that a chair
or table or photon or electron doesn't exist simply because
we're not looking at it.

The other reason is that even if I don't observe an electron,something
is out there (otherwise what are we describing)--it exists as a potential reality.

I also believe that something is out there doing it's thing
in submicroscopicville. We just don't know what it is out
there (wrt where the meaning of the word 'reality' is quite
ambiguous) that corresponds to what we call photons
and electrons here in ordinarysensoryexperienceland (where
the meaning of the word 'reality' is relatively unambiguous).

Even the use of the words 'potential reality' is a projection of my measurement--since I observed an electron,it must be out there in
some form when I didn't observe it.See, you can't segregate the
observer and the observed (though physicists are used to working
in that way--and that leads to the conceptual problems in QM).

'Potential reality' is a very hazy term.

There are conceptual problems because what is out there
is only indirectly accessible to us. There's an insufficient
qualitative understanding of quantum-level phenomena, which
means more data is needed.

There is nothing like one disturbance or two disturbances--a
disturbance is a disturbance,that's it.The nature of disturbance
may vary.

Let's say the disturbance (speaking 'realistically' now about
what is 'out there') is a wavefront propagating from an emitter
to a double-slit. The double-slit transmits two wavefronts,
and these two wavefronts interfere to produce more
wavefronts. I'm thinking of all these different wavefronts as
different 'disturbances' in the medium.

The problem is more in our heads than out there!

I would say that we have questions in our heads
about what is happening out there -- and we get
closer to answering those questions mainly by
sampling or probing the behavior of what is out there.