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Everybody sees the same elephant (says Carlo Rovelli)

by marcus
Tags: carlo, elephant, rovelli, sees
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hossi
#91
Apr20-06, 08:34 PM
P: 198
Hi Dimitri,

well, the LQG people like to claim their approach is much older, not newer. I can toally relate to your not-liking of LQG, it's definitly not appealing. Anyway, what I wanted to say...

...what did I want to say...

...sorry, long day...

...essentially: anything is better than nuclear physics and solid state

Best,

B. (gotta go home get some sleep )
Kalimaa23
#92
Apr21-06, 05:39 AM
P: 307
Quote Quote by hossi
...essentially: anything is better than nuclear physics and solid state
Amen!
Kea
#93
Apr21-06, 10:19 PM
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To come back to the Elephant, although an extravagance perhaps, consider this quote from 1943:

The only possible alternative is simply to keep to the immediate experience that consciousness is a singular of which the plural is unknown; that there is only one thing and that, what seems to be a plurality, is merely a series of different aspects of this one thing, produced by a deception (the Indian Maya); the same illusion is produced in a gallery of mirrors, and in the same way Gaurisankar and Mt Everest turned out to be the same peak seen from different valleys.

There are, of course, elaborate ghost-stories fixed in our minds to hamper our acceptance of such simple recognition.
Erwin Schroedinger, What is life? 1943

This is taken from a set of lectures given by Schroedinger in Dublin, which became very well known and were subsequently read by Watson and Crick and others hot on the trail of the mystery of genes.

many worlds but one elephant

marcus
#94
Apr21-06, 11:25 PM
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nice quote from Schrödinger

this Kea koan not bad either

many worlds but one elephant
marcus
#95
May1-06, 11:18 AM
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found this on the web, Matt Liefer, a guy at Perimeter, had it on his blog
http://mattleifer.wordpress.com/2006...hilbert-space/

http://www.perimeterinstitute.ca/per...mmandments.pdf

in quoting I dropped some technical notation---the link has Liefer's original
=========quote========

TEN COMMANDMENTS OF THE CHURCH OF THE SMALLER HILBERT SPACE

With apologies to Charlie Bennett and, of course, God.

1. I am ρ , your state, who brought you out of wavefunction realism, the place of orthodox dogmatism.

2. Do not have any other states except Me. Do not represent states by false purifications, conceived as ontological states of the Platonic forms above, of reality below, or of the space-time foam underlying reality. Do not bow down to such states or worship them. I am ρ your state, a state that demands exclusive belief.

3. Do not announce your state ρ in vain. ρ will not allow the one who announces it in vain to go unpunished by a Dutch bookie.

4. Remember the CP-map E to keep dynamics meaningful. You can work things out using six different Kraus decompositions or Steinspring dilations and do all your tasks. But the CP-map E is an equivalence class to ρ your state. Do not do anything that attaches meaning to the arbitrary tools you choose to work with. This includes your Hilbert Space basis..., your purifications...

5. Honor your forefathers by using the Hilbert space algorithm they handed down to you to calculate your expected utilities. You will then live long on the land that ρ your state describes your beliefs about.

6. Do not commit murder, since there is no other “branch of the wavefunction” in which your victim will survive.

7. Do not adulterate the Schrödinger equation by adding nonlinear terms designed to cause collapse.

8. Do not steal from classical physics by insisting that particle position or field configuration variables must evolve deterministically.

9. Do not testify as a false witness to the existence of histories of events that do not appear in the empirical records.

10. Do not be envious of your neighbor’s state σ. Do not be envious of your neighbor’s dynamical CP-map ..., his POVM elements..., his update CP-maps..., his Kraus operators..., his donkey, or anything else that is your neighbor’s, for they only describe his beliefs (except for the donkey), which naturally differ from yours.

===endquote===
marcus
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May24-06, 07:15 PM
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Bee has introduced another animal into the picture, this time a dog.

A number of people were discussing this at her blog and I posted twice already and still have a bit more to say, so I will say it here.

In Bee's story there are two experimenters A and B and they agree to take their entangled electrons to separate places and on a certain day each perform an measurement. Let's make them women for a change.

They agree to point the machines to the East and read the spin.

Each person has a hilbertspace and each person has a wavefuntion or state in that space which describes what they have learned about life so far, and about the universe, like what to expect if you go out with Italian men---what to do if you see an elephant, and so on.

A and B are well-educated so they expect that one of them will get +1 and one get -1. Everything is crystal clear to them. Off they go to their respective stations, which are quite far apart.

the day arrives and A does her measurement and she gets -1, so she applies the appropriate projection operator and collapses part of her wavefunction to show the new information she has about HER electron.

She also has in her wavefunction or state vector some experience of how RELIABLE the other experimenter, B, is. And how often B's location is hit by hurricanes. In the hypothetical situation that B is TOTALLY reliable, always remembers to do what she is supposed to, TOTALLY competent, always gets her lab machines to work perfectly, and NEVER hit by hurricanes, then of course B would be expected to be reading +1 right now, because the spins on a given axis add up to one.

But that would not be realistic. So A does not commit herself right away, she doesnt collapse the wavefunction in her state space that codes the outcome of the distant measurement because she doesnt have that information yet.

Before she does that she will at least telephone, or maybe even go and check out the other station, where B is. Before recording any information about B's electron, she has to get in CAUSAL CONTACT.

SO THE COLLAPSE OF A's wavefunction is LOCAL. Somebody had to get in somebody else's lightcone, or even go over and stand next to them at the same spot, for it to happen.
marcus
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May24-06, 07:28 PM
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I guess the point is that even if A knows B to be admirable in every respect---very reliable and competent in the lab etc.---maybe B is just then having an argument with her boyfriend, or maybe she has a hangover, or there has been a supernova explosion, or it just simply isn't her day. This happens sometimes. So you can't be sure.

the advice to A is, DONT COLLAPSE YOUR WAVEFUNCTION UNTIL YOU SEE THE WHITES OF THEIR EYES and you have definite information, dont go collapsing it based on some suppostion about somewhere you are not in causal contact with, some spacelike separated place where you cant have any idea what is happening there.

so now what about the DOG???

Well Sabine ups the narrative stakes by having B take along a dog to her station, and if her reading comes out +1 then B should SHOOT THE DOG. And conversely if the measurment comes out -1 then she should not shoot the dog.

There is a picture of the dog, which is an unpleasant overweight bulldog which it would be tempting to shoot regardless how the experiment turned out. I will get a link so you can go read further discussions of this

http://backreaction.blogspot.com/

http://backreaction.blogspot.com/200...nlocality.html
vanesch
#98
May30-06, 03:57 PM
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Quote Quote by marcus
A and B are well-educated so they expect that one of them will get +1 and one get -1. Everything is crystal clear to them. Off they go to their respective stations, which are quite far apart.

the day arrives and A does her measurement and she gets -1, so she applies the appropriate projection operator and collapses part of her wavefunction to show the new information she has about HER electron.

She also has in her wavefunction or state vector some experience of how RELIABLE the other experimenter, B, is. And how often B's location is hit by hurricanes. In the hypothetical situation that B is TOTALLY reliable, always remembers to do what she is supposed to, TOTALLY competent, always gets her lab machines to work perfectly, and NEVER hit by hurricanes, then of course B would be expected to be reading +1 right now, because the spins on a given axis add up to one.

But that would not be realistic. So A does not commit herself right away, she doesnt collapse the wavefunction in her state space that codes the outcome of the distant measurement because she doesnt have that information yet.

Before she does that she will at least telephone, or maybe even go and check out the other station, where B is. Before recording any information about B's electron, she has to get in CAUSAL CONTACT.

SO THE COLLAPSE OF A's wavefunction is LOCAL. Somebody had to get in somebody else's lightcone, or even go over and stand next to them at the same spot, for it to happen.
Yes, this is a perfectly all right view from a "solipsist" viewpoint: there is only ONE observer in this world, in casu "A". We never talk about the experience "B" lives, we only talk about what A OBSERVES from "B"s state.

As such, one can indeed see quantum theory as the theory that explains A's experience: first A sees her local result (local collapse of A's state), then A encounters B (local collapse of A's experience of B's state)...
So collapse occurs when A becomes, say, consciously aware of something.
This is all fine and well.

The problem arrives when we want the theory to describe at the same time also what B experiences, from its viewpoint.
Now, you can of course say that we should now apply the formalism on B's side, but there's a problem.
When A became aware of her result, and locally collapsed HER wavefunction, what can we say on B's side, from B's point of view ?
If you have A's wavefunction collapse from B's side too, then we are in contradiction with what we tried to establish, namely only "local collapse upon local becoming aware of the result". But if A's wavefunction DIDN'T collapse from B's point of view, then WE'VE LOST THE POTENTIAL LINK WITH A's experienced world.

From A's PoV:

State before A measures:
|a+>(u |b-> + v |b+>) + |a-> (x |b+> + y |b->)

A measures and "experiences" the result, it is +:

--> collapse (for A) into |A+>(u |b-> + v |b+>)

B might measure far away, but A doesn't know yet...

A meets B, and "measures" B's state, result of B is +:

--> collapse (for A) into |A+> | B+>

fine.

From B's PoV:

State before A measures:

|a+>(u |b-> + v |b+>) + |a-> (x |b+> + y |b->)


A measures, but this doesn't change anything to B yet.

B measures now, finds -

--> Collapse on B's side: (u |a+> + y |a->) |B->

B meets A, finds -:

--> Collapse on B's side: |A->|B->

All this is nice and well, except that from A's PoV, A and B got + and +, while from B's PoV, they both got - and -


This can be solved in a MWI scenario, by replacing collapse by "branch is consciously observed by"

Take # the "is conscious state by A" tag, and * the "is conscious state by B" tag, then we just have the state:

Before measurement, all states are still part of the "relative state" of A and of B:
|a+#*>(u |b-#*> + v |b+#*>) + |a-#*> (x |b+#*> + y |b-#*>)

A does a measurement, and found +, only changes the accessible states of A ; we remove what is NOT anymore part of "A's conscious world" (is projected out by the "collapse according to A":

|a+#*>(u |b-#*> + v |b+#*>) + |a-*> (x |b+*> + y |b-*>)

B does a measurement and found -:

|a+#*>(u |b-#*> + v |b+#>) + |a-*> (x |b+> + y |b-*>)

Now, A and B meet.
First, A "measures" B (that is, A learns about the "B" state) A learns that B saw +, so this gives:

|a+#*>(u |b-*> + v |b+#>) + |a-*> (x |b+> + y |b-*>)

About at the same time, B measures A, that is, B learns that "A saw -":

|a+#>(u |b-> + v |b+#>) + |a-*> (x |b+> + y |b-*>)

What now emerges is that, in "A's mental world", symbolized by #, the state of the first particle is seen to be a+ and the state of the b particle is seen to be b+. In "B's mental world", symbolized by *, the state of particle a is -, and the one of b is - too.

So both "relative views" intermixed is simply a many worlds view where the "objective" wavefunction didn't collapse, but where "the awareness of a state" narrowed down its scope as a function of what it was made aware off, to the piece of the overall wavefunction that corresponds to its measurement results.

As such, the Rovelli flavor of the relative state view is the "one-observer" version of the many worlds view (where many observers are considered in parallel).
vanesch
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May30-06, 03:58 PM
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Quote Quote by marcus
A and B are well-educated so they expect that one of them will get +1 and one get -1. Everything is crystal clear to them. Off they go to their respective stations, which are quite far apart.

the day arrives and A does her measurement and she gets -1, so she applies the appropriate projection operator and collapses part of her wavefunction to show the new information she has about HER electron.

She also has in her wavefunction or state vector some experience of how RELIABLE the other experimenter, B, is. And how often B's location is hit by hurricanes. In the hypothetical situation that B is TOTALLY reliable, always remembers to do what she is supposed to, TOTALLY competent, always gets her lab machines to work perfectly, and NEVER hit by hurricanes, then of course B would be expected to be reading +1 right now, because the spins on a given axis add up to one.

But that would not be realistic. So A does not commit herself right away, she doesnt collapse the wavefunction in her state space that codes the outcome of the distant measurement because she doesnt have that information yet.

Before she does that she will at least telephone, or maybe even go and check out the other station, where B is. Before recording any information about B's electron, she has to get in CAUSAL CONTACT.

SO THE COLLAPSE OF A's wavefunction is LOCAL. Somebody had to get in somebody else's lightcone, or even go over and stand next to them at the same spot, for it to happen.
Yes, this is a perfectly all right view from a "solipsist" viewpoint: there is only ONE observer in this world, in casu "A". We never talk about the experience "B" lives, we only talk about what A OBSERVES from "B"s state.

As such, one can indeed see quantum theory as the theory that explains A's experience: first A sees her local result (local collapse of A's state), then A encounters B (local collapse of A's experience of B's state)...
So collapse occurs when A becomes, say, consciously aware of something.
This is all fine and well.

The problem arrives when we want the theory to describe at the same time also what B experiences, from its viewpoint.
Now, you can of course say that we should now apply the formalism on B's side, but there's a problem.
When A became aware of her result, and locally collapsed HER wavefunction, what can we say on B's side, from B's point of view ?
If you have A's wavefunction collapse from B's side too, then we are in contradiction with what we tried to establish, namely only "local collapse upon local becoming aware of the result". But if A's wavefunction DIDN'T collapse from B's point of view, then WE'VE LOST THE POTENTIAL LINK WITH A's experienced world.

From A's PoV:

State before A measures:
|a+>(u |b-> + v |b+>) + |a-> (x |b+> + y |b->)

A measures and "experiences" the result, it is +:

--> collapse (for A) into |A+>(u |b-> + v |b+>)

B might measure far away, but A doesn't know yet...

A meets B, and "measures" B's state, result of B is +:

--> collapse (for A) into |A+> | B+>

fine.

From B's PoV:

State before A measures:

|a+>(u |b-> + v |b+>) + |a-> (x |b+> + y |b->)


A measures, but this doesn't change anything to B yet.

B measures now, finds -

--> Collapse on B's side: (u |a+> + y |a->) |B->

B meets A, finds -:

--> Collapse on B's side: |A->|B->

All this is nice and well, except that from A's PoV, A and B got + and +, while from B's PoV, they both got - and -


This can be solved in a MWI scenario, by replacing collapse by "branch is consciously observed by"

Take # the "is conscious state by A" tag, and * the "is conscious state by B" tag, then we just have the state:

Before measurement, all states are still part of the "relative state" of A and of B:
|a+#*>(u |b-#*> + v |b+#*>) + |a-#*> (x |b+#*> + y |b-#*>)

A does a measurement, and found +, only changes the accessible states of A ; we remove what is NOT anymore part of "A's conscious world" (is projected out by the "collapse according to A":

|a+#*>(u |b-#*> + v |b+#*>) + |a-*> (x |b+*> + y |b-*>)

B does a measurement and found -:

|a+#*>(u |b-#*> + v |b+#>) + |a-*> (x |b+> + y |b-*>)

Now, A and B meet.
First, A "measures" B (that is, A learns about the "B" state) A learns that B saw +, so this gives:

|a+#*>(u |b-*> + v |b+#>) + |a-*> (x |b+> + y |b-*>)

About at the same time, B measures A, that is, B learns that "A saw -":

|a+#>(u |b-> + v |b+#>) + |a-*> (x |b+> + y |b-*>)

What now emerges is that, in "A's mental world", symbolized by #, the state of the first particle is seen to be a+ and the state of the b particle is seen to be b+. In "B's mental world", symbolized by *, the state of particle a is -, and the one of b is - too.

So both "relative views" intermixed is simply a many worlds view where the "objective" wavefunction didn't collapse, but where "the awareness of a state" narrowed down its scope as a function of what it was made aware off, to the piece of the overall wavefunction that corresponds to its measurement results.

As such, the Rovelli flavor of the relative state view is the "one-observer" version of the many worlds view (where many observers are considered in parallel).
marcus
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May30-06, 04:34 PM
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**But if A's wavefunction DIDN'T collapse from B's point of view, then WE'VE LOST THE POTENTIAL LINK WITH A's experienced world.
**
I think we didnt lose the possible linkage because
a two-way link occurs when the two are in the same place----linkage (one way or two way)follows causal contact

there is more on this at Bee's blog. To my considerable pleasure and surprise she indicates agreement to some extent. I don't know how far her agreement goes, so you'd best consult the blog or her directly.

Im happy for you to totally disagree! I just can't take the time to discuss this too much. I imagine Rovelli would consider his picture "multiple-observer" and "single world". Rovelli picture is multiple-observer in the sence that it ALLOWS for having one or more observers. You can have one, or you can have 100. You have as many hilbertspaces as you do observers. Objective reality arises from the AGREEMENT of these guys. I personally see no connection with "many worlds".

But if you see a connection with "many worlds" that is fine!
vanesch
#101
May31-06, 03:27 AM
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Quote Quote by marcus
I imagine Rovelli would consider his picture "multiple-observer" and "single world".
Well, "multiple-observer/single world" is of course what we all would like to see because it fits much better with our intuitive concept of how the world ought to be (how many times have people not said "how the world ought to be" ), but it is now clearly established that QM's predictions for a multiple observer/single world are such that if there is to be given an objective picture behind this, that this picture is necessarily non-local (that's Bell's result in a nutshell). It is in essence the approach of Bohmian mechanics, or of "standard" von Neuman quantum theory (with collapse upon observation), if one assigns some objective reality to the wavefunction (which represents your single world). All of these approaches violate Lorentz invariance in their inner workings (in other words, require non-local mechanisms to act upon the object that is supposed to represent the single world).

An exception to this are the approaches that consider quantum theory as just a technique to calculate probabilities of outcomes of experiments, but I'd classify that rather as "multiple observers / no world" because these approaches explicitly forbid you to think of any of the mathematical constructions to represent an objective reality.

Rovelli picture is multiple-observer in the sence that it ALLOWS for having one or more observers. You can have one, or you can have 100. You have as many hilbertspaces as you do observers. Objective reality arises from the AGREEMENT of these guys. I personally see no connection with "many worlds".
If you have "a hilbert space for each observer", then what goes wrong is the following, if one assumes that each hilbert space is an "independent generator for probabilities", and if one assumes a continuity in an observer's knowledge (that is, if at a point t1 on his world line, observer A measured result A+, then at a point t2>t1 on his world line, he will not suddenly conclude that back at t1 he measured finally A- when learning about another result).

Assume that the initial state is u |a+> |b-> + v |a->|b+> with u much smaller than v, and assume that A and B measure their particle's state "simultaneously" (in some frame), without contact.
This means, that in A's hilbert space, with an overwhelming probability, he's going to find A-, and in B's hilbert space, he's going to find B+. So indeed most of the time, after they meet, they will be in agreement.
But for the rare cases where A, in his hilbert space, finds A+, and registers this along his world line, there is no reason why B, in his *independent* hilbert space, will have to obtain the rare event B-. If B's hilbert space is independent of A's, then B will most of the time, project on the B+ state (independent of what A found).
In the same way, in those rare cases where B projects upon B- in his independent hilbert space, there's no reason why A should not project on A- most of the time.
The individual statistics are all right of course, but when they meet, something goes wrong, if there is continuity of their registered measurement results, AT LEAST IF THERE IS ONLY ONE "WORLD" (that is, if each observer has his own, single, outcome). Because the single B that is around cannot "forget" having seen B+ when he meets A having seen A+.

This is exactly the problem that a many world approach fixes: from A's PoV, there are TWO "B" observers, one of which he'll meet, and from B's PoV, there are TWO "A" observers, one of which he'll meet. And during the meeting, only those "versions" of observers can interact that are in agreement (that is, in the rare cases A has seen the A+ outcome, he'll only interact with the version of the B observer that has seen the B- outcome).

But these two meetings are not the SAME two observers: hence two different "worlds". This is what "goes wrong" with many worlds: the hard-to-swallow idea (however, entirely in agreement with subjective observation) that, when we "see an outcome" that this is just one of the several "me's" that sees an outcome, and that there all other possibilities are realised also, with "other me's". We'd intuitively like to have the case that there's only one "me" and that there's only one outcome.

However, if you restrict yourself to only one observer (say A) then all this is fine, because B is not really an observer, but just a quantum system as any other. As such, B has no "definite result" upon interacting with particle b, and B's state is simply a kind of copy of the state of particle b, which is waiting to be observed by A to take on a definite result - which is how I understand Rovelli: that, from A's PoV, B has not yet a definite result until it is observed by A. This is fine.

You cannot, however, require B NOT to have a definite result from A's PoV, and (1) B to HAVE a definite result from B's PoV, have these results being generated in (2) *independent* hilbert spaces, and hope that (3) the correlations upon meeting will come out all right. Something has to give.
If it is (1), well clearly we have only a single observer (B has no result) ;
If it is (2), well then there IS an "action at a distance" in some way in the inner workings to make the two hilbert spaces "dependent",
and if it is (3) then we're not reproducing the standard quantum theory correlations.

But if you see a connection with "many worlds" that is fine!
As I said, I see Rovelli's idea as the "single observer/single world" version of the "many observers/many worlds" view. I'm not sending out any critique, but I'm just saying that these ponderings are already around for at least 40 years, in several different forms and presentations.
selfAdjoint
#102
Jun3-06, 07:05 PM
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Quote Quote by vanesch
if there is to be given an objective picture behind this, that this picture is necessarily non-local (that's Bell's result in a nutshell)
Well, this is the crux of the whole disagreement. Your understanding of "objective" is different from the relational one. Your view, call it QM with a priviledged observer, or QMPO says that before the PO "observes" the observed system it has no definite values in spacetime but after that priviledged act it does. RQM on the other hand says there are no priviledged observers and no priviledged values, but only interacting quantum systems. Bell and many since have conceiled this possibility from the reader by appeals to traditional classical images, and the tendency to talk about observers as people and give them names like Alice and Bob reinforces this misdirection.

If there is nothing but quantum interactions and those interaction are symmetric, changing the quantum state of both interacting systems, can there be any real objectivity? Smerlak and Rovelli say that thanks to QM the answer is yes!


SInce it is key to this discussion I have quoted the entire section 4.3 of the paper:

4.3. Consistency. Let us bring B back into the picture. It is far from the spirit of RQM to assume that each observer has a “solipsistic” picture of reality, disconnected from the picture of all the other observers. In fact, the very reason we can do science is because of the consistency we find in nature: if I see an elephant and I ask you what you see, I expect you to tell me that you too you see an elephant. If not, something is wrong. But, as claimed above, any such conversation about
elephants is ultimately an interaction between quantum systems. This fact may be irrelevant in everyday life, but disregarding it may give rises to subtle confusions, such as the one leading to the conclusion of nonlocal EPR influences. In the EPR situation, A and B can be considered two distinct observers, both making measurements on α and β. The comparison of the results of their measurements, we have argued, cannot be instantaneous, that is, it requires A and B to be in causal contact. More importantly, with respect to A, B is to be considered as a normal quantum system (and, of course, with respect to B, A is a normal
quantum system). So, what happens if A and B compare notes? Have they seen the same elephant?

It is one of the most remarkable features of quantum mechanics that indeed it automatically guarantees precisely the kind of consistency that we see in nature [5]. Let us illustrate this assuming that both A and B measure the spin in the same direction, say z, that is n = n′ = z.
Since B is a quantum system, there will be an observable [tex]S^n_{AB}[/tex] corresponding to B’s answer (at time t1) to the question “which value of the spin have you measured?”. That is, [tex]S^n_{AB}[/tex] is the observable describing the pointer variable in the detector B. Then consistency demands that:
(i) If A measures [tex]S^n_{AB}[/tex] after having measured [tex]S^n_{A\beta}[/tex] she will get

(4) [tex]S^n_{AB} = S^n_{A\beta}[/tex].

(ii) If a third observer C, who has the prior information that measurements have been performed by A and B, measures at a later time the two
pointer variables: [tex]S^n_{CA}[/tex]and [tex]S^n_{CB}[/tex] then

(5) [tex]S^n_{CB} = S^n_{CA}[/tex]

But this follows from standard QM formalism, because an interaction between β and B that can be interpreted as a measurement is an interaction such that the state (1) and the initial state of α, β and B evolve into the state (relative to A)

(6) [tex]|\psi>^(A)_{\alpha+\beta+B} = \frac{1}{\sqrt{2}} (|\downarrow>_{\alpha} |\uparrow>_{\beta} |\uparrow>_B − |\uparrow>_{\alpha} |\downarrow>_{\beta} |\downarrow>_{B}) [/tex]

with obvious notation. Tracing out the state of α that plays no role here, we get the density matrix

(7)[tex]\rho^{(A)}_{\beta+B} = \frac{1}{2} (|\uparrow>_{\beta} |\uparrow>_B <\uparrow|_{\beta} <\uparrow|_B + |\downarrow>_{\beta} |\downarrow>_B <\downarrow|_{\beta} <\downarrow|_{B}) [/tex] .

from which (4) follows immediately. Similarly, the state of the ensemble of the four systems α, β,A,B, relative to C evolves, after the two nteractions at time t0 into the state

(8)[tex]|\psi^{(C)}_{\alpha+\beta+A+B} = \frac{1}{\sqrt{2}}(|\downarrow>_{\alpha} |\uparrow>_{\beta} |\downarrow>_A |\uparrow>_B−|\uparrow>_{\alpha} |\downarrow>_{\beta} |\uparrow>_A |\downarrow>_{B})[/tex]

again with obvious notation. Tracing out the state of α and β, we get the density matrix

(9) [tex]\rho^{(C)}_{A+B} = \frac{1}{2}( |\downarrow>_A |\uparrow>_B <\downarrow|_A <\uparrow|_B+|\downarrow>_A |\uparrow>_B <\downarrow|_A <\uparrow|_{B} )[/tex].

which gives (5) immediately. It is clear that everybody sees the same elephant. More precisely: everybody hears everybody else stating that they see the same elephant he sees. This, after all, is the best definition of objectivity.
Note that the particle states have been traced away in computing the density matrix. Only the observer states remain.
marcus
#103
Jun4-06, 10:18 AM
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sA,
missing a minus sign in equation (5)
sometimes those things don't copy and paste right
worked pretty well though!

also in eqns. (6) and (8) the symbol "8722;" did not translate to a minus sign
(at least for me) but the reader can easily make that substitution

sA and vE, I will save a post by commenting on #104 here:
[EDIT]
Rovelli does not use the term "branch" and the term has no intuitive or widely understood meaning in the context of a discussion of the paper. Therefore we can test the logic of any comment on the paper by replacing every occurrence of the word "branch" by a neutral word like BLEXO.

Since (until defined) branch does not mean anything in connection with the paper it would have to be defined by the commentor in terms used in Rovelli's conceptual framework and shown to apply. one would need a definition of BLEXO and also to say what "same" BLEXO and "different" BLEXO mean.

In the Rovelli scheme all the observers are IN THE WORLD.
It is even meaningless to say they are IN THE "SAME" WORLD because there is just this world. There is not imagined to exist a different world so that one could meaningfully talk about "same" or "different".

The QM formalism as in Rovelli eqn (6) and (8) allows the individual observer to include different POSSIBILITIES in his or her state space but these do not correspond to REALITIES---possibilities in the Hilbertspace formalism are just a way of representing information and the lack thereof.
Let's now apply the test to see if this statement has anything to do with the Rovelli Smerlak paper:

"The consistency requirement that is worked out here in all detail, comes simply down to the MWI statement: observers in different blexo only learn about the answers of their peers in the SAME BLEXO."

I think if someone were to define for us (in another thread please) what a BLEXO is and what it means to be in a different Blexo and what it means to be in the same Blexo, that it might be quite interesting (for some people) to think about and discuss! But I regret to say that AFAICS talking about "branch" HAS NOTHING TO DO WITH ROVELLI'S PAPER.

He does not use the blexo concept. There is not even the "same" world: there is just the world

cordial thanks to all for the comments received so far on this paper!
vanesch
#104
Jun4-06, 10:32 AM
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Quote Quote by selfAdjoint
Well, this is the crux of the whole disagreement. Your understanding of "objective" is different from the relational one. Your view, call it QM with a priviledged observer, or QMPO says that before the PO "observes" the observed system it has no definite values in spacetime but after that priviledged act it does.
Well, I fail to see the "disagreement, Dick. In fact, I'm 100% "in sync" with what you quoted, and of course the essential point is when A "measures" the state of B with an observable that says "what did you, B, measure?"

The consistency requirement that is worked out here in all detail, comes simply down to the MWI statement: observers in different branches only learn about the answers of their peers in the SAME BRANCH.

In other words, if we end up with:

|alice+> |bob+> |stuffA> + |alice->|bob->|stuffB>

then this means that any such interaction when Alice asks bob what he measured, comes down to: alice+ will only hear from bob+, and alice- will only hear from bob- ; alice+ will never hear from bob-.

As such, indeed, "everybody" will see "the same elephant" ; that is, "alice+" will see the same elephant as bob+ (namely stuffA), and "alice-" will see the same elephant as bob-, namely stuffB.
It is implicitly assumed in MWI that this is the case of course, otherwise the view would be immediately falsified! The *entire idea* is indeed that though there is a "multiplication of worlds/branches/terms", nevertheless, each observer is "locked up" in its own term, ONLY being able to interact with its "peers" in the same branch, so that everything happens AS IF this branch was, to him, the only thing that existed, and the others "faded away".

It is my understanding that this is what is worked out in detail in the section you quoted: that observers in a branch only "see" their peers in the same branch, with "see" meaning: get their results through an interaction which is "what did you get as a result", and that they DON'T get any result of an observer in another branch. The wavefunctions in (6) and (8) are nothing else but what I write above here. That's really nothing
but the MWI version of the measurement situation, and that was what I tried to say here since the beginning: that Rovelli re-discovered MWI, or at least the aspect that each branch "only sees itself", and that there is a self-consistency in A measures system a, B measures system b, and then A measures B.

As to your comment, or I misunderstand you, or you misunderstand me :-)
In MWI, there is no "priviledged observer", because there are many copies of each observer, one in each branch. However, it was my understanding, maybe erroneously, that Rovelli takes it that there is only ONE version of each observer. Clearly that runs into troubles (and is in fact contradicted with his equations 6 and 8 from your quote): B cannot be "in a superposition wrt A" and have "a single and definite measurement" wrt itself (unless, and that's the entire MWI approach, B is dedoubled into two B's). So I took it that Rovelli saw everything from the PoV of observer A (which can then be thought of to be "single"), allowing B to be in superposition until A saw him (the kind of PO you are talking about). And from the PoV from B, we forget what we did for A, we now do things from the PoV of B, and now B is "single" and A is "in superposition".
Both viewpoints together of course correspond to A as well as B in "superposition" but agreement in the corresponding branches. Which is, to my understanding, nothing else but MWI...
selfAdjoint
#105
Jun4-06, 01:07 PM
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Quote Quote by vanesch
Well, I fail to see the "disagreement, Dick. In fact, I'm 100% "in sync" with what you quoted, and of course the essential point is when A "measures" the state of B with an observable that says "what did you, B, measure?"

The consistency requirement that is worked out here in all detail, comes simply down to the MWI statement: observers in different branches only learn about the answers of their peers in the SAME BRANCH.

In other words, if we end up with:

|alice+> |bob+> |stuffA> + |alice->|bob->|stuffB>

then this means that any such interaction when Alice asks bob what he measured, comes down to: alice+ will only hear from bob+, and alice- will only hear from bob- ; alice+ will never hear from bob-.

As such, indeed, "everybody" will see "the same elephant" ; that is, "alice+" will see the same elephant as bob+ (namely stuffA), and "alice-" will see the same elephant as bob-, namely stuffB.
It is implicitly assumed in MWI that this is the case of course, otherwise the view would be immediately falsified! The *entire idea* is indeed that though there is a "multiplication of worlds/branches/terms", nevertheless, each observer is "locked up" in its own term, ONLY being able to interact with its "peers" in the same branch, so that everything happens AS IF this branch was, to him, the only thing that existed, and the others "faded away".

It is my understanding that this is what is worked out in detail in the section you quoted: that observers in a branch only "see" their peers in the same branch, with "see" meaning: get their results through an interaction which is "what did you get as a result", and that they DON'T get any result of an observer in another branch. The wavefunctions in (6) and (8) are nothing else but what I write above here. That's really nothing
but the MWI version of the measurement situation, and that was what I tried to say here since the beginning: that Rovelli re-discovered MWI, or at least the aspect that each branch "only sees itself", and that there is a self-consistency in A measures system a, B measures system b, and then A measures B.

As to your comment, or I misunderstand you, or you misunderstand me :-)
In MWI, there is no "priviledged observer", because there are many copies of each observer, one in each branch. However, it was my understanding, maybe erroneously, that Rovelli takes it that there is only ONE version of each observer. Clearly that runs into troubles (and is in fact contradicted with his equations 6 and 8 from your quote): B cannot be "in a superposition wrt A" and have "a single and definite measurement" wrt itself (unless, and that's the entire MWI approach, B is dedoubled into two B's). So I took it that Rovelli saw everything from the PoV of observer A (which can then be thought of to be "single"), allowing B to be in superposition until A saw him (the kind of PO you are talking about). And from the PoV from B, we forget what we did for A, we now do things from the PoV of B, and now B is "single" and A is "in superposition".
Both viewpoints together of course correspond to A as well as B in "superposition" but agreement in the corresponding branches. Which is, to my understanding, nothing else but MWI...
My use of the term priviliedged observer refers to the (originally Copenhagian) macroscopic observer who stands above and beyond the quantum world. Whether you have one or many of these chaps, they and the classical values they measure have really no place in a totally quantum view of the world.

S&M abandon this nonquantum fellow for a picture containing only interacting quantum systems ("the facts of the world are interactions", they say someplace in the paper). Some of these systems in a particular case function as "observation systems", i.e. they have pointer states. But critically these observer systems can be in superimposed states, entangled states, and so on, and they evolve quantally. This is how we can write the interacting state in terms of not only the evolving state of observed system (the "particle") but also including the observer state ("what the observational system records") in the state functions and density matrix calculations, which is the heart of their demonstration.

I recognize there are some problems to be dealt with in getting rid of the PO; notably if she goes, so does her watch, that external nonquantum clock that supplies the time parameter to QM. But people are working on that.
vanesch
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Jun4-06, 02:00 PM
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Quote Quote by selfAdjoint
S&M abandon this nonquantum fellow for a picture containing only interacting quantum systems ("the facts of the world are interactions", they say someplace in the paper). Some of these systems in a particular case function as "observation systems", i.e. they have pointer states. But critically these observer systems can be in superimposed states, entangled states, and so on, and they evolve quantally. This is how we can write the interacting state in terms of not only the evolving state of observed system (the "particle") but also including the observer state ("what the observational system records") in the state functions and density matrix calculations, which is the heart of their demonstration.
Uh, but that, to me, has always been the heart of any MWI view!

That an observation is a change in an observer state due to an interaction between the system and the observer ; now, if - as you rightly point out - these "observer degrees of freedom" - can be in superposed/entangled... states, then what becomes an "observer" now, with a specific 'observational record', is not the original degree of freedom (of which the quantum description, indeed, appears in superposition), but its single manifestation in ONE term. But that means that there are now "copies" of the observer (the different states, in the different terms=branches) around, each with different 'observational recordings' (a different one in each term).

So I fully agree with that. But I'm saying that this idea is the core idea of any MWI view. It is MWI's way to deal with the AND/OR problem: the fact that the observer is NOT the degree of freedom (= the device), but ONE of the different states in which this degree of freedom occurs (= one of the pointer states). An observer IS the pointer state, and not the apparatus, to put it rather bluntly. (and this leads me, in the case of human beings, to distinguish between the conscious observation of the pointer state, versus the entire bodystate)

THIS is, the way I understand it, the fundamental insight of an MWI view.

Now, I thought (maybe erroneously, I didn't read Rovelli's paper in all detail very thoroughly once I thought I recognized the main line), that Rovelli somehow thought he could get away with this "superposition of observer states" and hence solve the AND/OR problem by looking only at the measurement of A onto B and find out that everything is allright.

If Rovelli moreover recognizes this superposition of pointerstates, then I really don't see in what way his idea is different from the general idea of MWI. This is what I tried to say here from the beginning.

I recognize there are some problems to be dealt with in getting rid of the PO; notably if she goes, so does her watch, that external nonquantum clock that supplies the time parameter to QM. But people are working on that.
Yes, this is the famous "problem of time" which I understood was one of the principal difficulties in QG.
Note that in special relativity, as such, this is not necessarily an issue, because unitarity is conserved under a lorentz transformation, so you can "re-tell" the story along different timelike axes, the entire system is normally consistent.
vanesch
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Jun4-06, 02:32 PM
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Quote Quote by marcus
Rovelli does not use the term "branch" and the term has no intuitive or widely understood meaning in the context of a discussion of the paper.
But also in an MWI view, "branch" is a loosely used concept, which often introduces more confusion than anything else. As such, "branch" has no objective existence, but has only a kind of meaning WRT AN OBSERVER.

The problem MWI tries to address (one of the core problems in the measurement problem) is the AND/OR problem: How do you go from a superposition of pointer states to one (with a probability given by the Born rule). In Copenhagen/von Neumann, this is "solved" by the projection postulate, but this introduces fundamental difficulties (one is: WHY/WHEN does it happen - what sets an "observation" apart from a "physical interaction" ; the other is its non-local character).
MWI wants no such projection postulate, and is then confronted with the AND/OR problem. Its proposed solution is then purely "conceptual": instead of saying that the outcome is "in the apparatus" (with the different pointer states), say that the outcome "is in the pointer state".
That seems like a cheap trick of course, what have we gained ?
Well, FROM THE POINT OF VIEW OF AN OBSERVER (= a pointer state = a container of measurement record) we can say that HIS world did split in many branches: BEFORE the measurement, there was ONE pointer state (the pre-measurement state of the apparatus), so there was ONE observer associated with the apparatus, and AFTER the measurement there were as many DIFFERENT observers associated with the apparatus as there were used pointerstates. And "the" observer is just ONE of the many pointer states.
"Branches"(wrt the observer) are simply these different pointerstates that evolved out of one. Again, it is not an objective concept, it is observer-related.

It's because it is intuitively as if "the single observer" branched now into many (the single pre-measurement pointer state evolved into many) that we talk about "branches". But you do not even need to talk about branches in MWI. You simply say that observers are pointer states ; are "records of observation". While we usually think of observers as degrees of freedom (apparatus/bodies...).

The QM formalism as in Rovelli eqn (6) and (8) allows the individual observer to include different POSSIBILITIES in his or her state space but these do not correspond to REALITIES---possibilities in the Hilbertspace formalism are just a way of representing information and the lack thereof.
Well, up to a point, even in MWI, that's open to interpretation. Do you call a "reality" the record of an observer (= a pointer state), or do you call "reality" the entire unitary structure ?
One is inclined to say that the former is a "subjective reality" and the latter an "objective reality".

Let's now apply the test to see if this statement has anything to do with the Rovelli Smerlak paper:

"The consistency requirement that is worked out here in all detail, comes simply down to the MWI statement: observers in different blexo only learn about the answers of their peers in the SAME BLEXO."

I think if someone were to define for us (in another thread please) what a BLEXO is and what it means to be in a different Blexo and what it means to be in the same Blexo, that it might be quite interesting (for some people) to think about and discuss! But I regret to say that AFAICS talking about "branch" HAS NOTHING TO DO WITH ROVELLI'S PAPER.
Well, "branch or world or Blexo" for several observers is then simply the term in the wavefunction corresponding to their entirely entangled pointer states. It is the consistent set of records which "survive in interaction between different observers".

For instance, if we are in the state (where a and b are two measurement apparatus):
|a+>(|b+> + |b->) + |a->(|b+>-|b->)

we cannot yet talk about a "common world for a and b" ; however, we can talk about the two branches wrt a, namely the one with a+ (a pointer state, where clearly a has a definite record of observation, namely +) and another "branch" with a-.
We now say that there are TWO a-observers now (each with their branch).

After a and b interact (exchange information), then the above state cannot exist anymore. We have now:

|a++>|b++> + |a+->|b-+> + |a-+>|b+-> - |a-->|b-->

(because a now has ALSO the information of b, and vice versa).

So now there are FOUR a observers (= a-pointer states = a-branches = a observation records), and there are FOUR b observers with CONSISTENT records with their a observer.
We now have that the 4 a pointer states=observers correspond to the 4 b pointer states, and we COULD, if we wanted to, talk about FOUR DIFFERENT WORLDS.
However, for each of these a-observers, there is a SPECIFIC record, and it is IN AGREEMENT with the accessible record of his "associated" b-observer (that's the consistency requirement that SA pointed us to).

In how much we have to talk about "realities" or "possibilities" does not really matter, it is semantics. The straightforward interpretation is that the 4 different possibilities correspond to an "objective" reality, and each of the observers, with his record, his peers with which he's in interaction... lives in his "subjective reality". But these are just words.

It was my understanding that Rovelli simply never stated these things EXPLICITLY but somehow assumed them (by keeping observer B in a "superposition wrt A as long as A didn't measure B"), and just concentrated on "one term" from a single pointer state's point of view.
selfAdjoint
#108
Jun4-06, 05:32 PM
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Quote Quote by vanesch
That an observation is a change in an observer state due to an interaction between the system and the observer ; now, if - as you rightly point out - these "observer degrees of freedom" - can be in superposed/entangled... states, then what becomes an "observer" now, with a specific 'observational record', is not the original degree of freedom (of which the quantum description, indeed, appears in superposition), but its single manifestation in ONE term. But that means that there are now "copies" of the observer (the different states, in the different terms=branches) around, each with different 'observational recordings' (a different one in each term).
But all that happens is that the observer pointer state goes into some value. Where is it demanded that they go into all possible values on different branches? The mathematics traces over all those values intermediately in calculating the density matrix, but all you have at the end of the day for a result is the reconciled value, determined by yet another interaction way down in the future light cones of all the experiment interactions, which the quantum analysis in the paper, and you say you agree with it, says will come out as it should.

Is there some reification (sorry, "ontological") issue I am missing?


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