Everybody sees the same elephant (says Carlo Rovelli)

marcus

hello hawk, Sabine suggested several things to read. If you still want some ideas of beginning reading in QG, just say. someone will come up with more suggestions. I would try to think of some, if you want. but you may be quite content with what Sabine already mentioned.

I assume that you live in China, from what you said in your post, and have studied physics at college or university level (you may have introduced yourself to others but I didnt see---I dont read everything at the forum)

there are quite a few people at Beijing who do Loop Quantum Gravity and also a lot who do superstring theory (the majority field). In the summer of 2006, in fact quite soon, there will be a String conference at Beijing.

If you live in China perhaps you know what the two large university in Beijing are called. As a foreigner I call the one which has QG physics group by the name "Beijing Normal University". Probably you have a different name.

Kalimaa23

Quote by hossi

Nice that you are so optimistic. I will keep you updated but I wouldn't put my hopes too high. The Germans are pretty conservative, and quantum gravity is *uhm* no butter and bread physics

(not yet, not in europe).

Then why are half the theoretical physics groups in Belgium working on String Theory?

marcus

Quote by Dimitri Terryn

Then why are half the theoretical physics groups in Belgium working on String Theory?

Could it be that they feel obliged to imitate the Americans?

hossi

Quote by Dimitri Terryn

Then why are half the theoretical physics groups in Belgium working on String Theory?

oh well, sorry, I consider string theory to be conservative

B.

Kalimaa23

@Marcus

@Hossi : I can see what you mean... but being newer doesn't mean it's "better". Don't get me wrong, I'm no Motl-type LQG hater, but I must admit that the more I read about it the less appealing it seems. Not that I think ST has the answers though... As a MS student in the field I'm taking the current pragmatic attitude that String Theory is a useful tool to learn about QFT, new mathematics, and who knows, will maybe show the way to true quantum gravity.

hossi

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

Quote by hossi

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

Amen!

Kea

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

nice quote from Schrödinger

this Kea koan not bad either

many worlds but one elephant

marcus

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

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

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

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

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

**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

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

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.

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hossi	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 )

marcus Recognitions: Gold Member Science Advisor	nice quote from Schrödinger this Kea koan not bad either many worlds but one elephant