Everybody sees the same elephant (says Carlo Rovelli)

[marcus]

Hey brainy guys,

me and my dwarves, we would really like to play your adult's games. But I still did not get the point.

.

Hi Biene, I am glad that you did not get too offended by my beginning that story about Hossi and the Seven Dwarves. It seemed charming at that moment and then later I was afraid it was too unserious.

Anyway now it IS Easter, happy easter everybody, and you remember that today is the day that Hossi looks at the spin of her particle!

She measures it in EastWest direction and Ach! Behold! it is East, as is just right for Easter.

BUT the confusion-loving dwarf, Careful John, has meanwhile distracted the other six Dwarves so that they have FORGOTTEN what direction they want to measure spin. they have totally forgotten everything, those poor Dwarves!

So they just measure their particle spin in any old random direction!

What do you think? They do this year after year and the spin of the dwarfs particle is always acting just as if random. Because you see they DO NOT KNOW that their friend Hossi has observed hers. And they do not Know what is their friend's result.

TO BE CONTINUED

(in case anyone did not see the beginning, this is a continuation of post #44 story
https://www.physicsforums.com/showthread.php?p=963986#post963986 )

 

[marcus]

Recap of what the thread is about

To recapitulate, this thread is about Rovelli RQM (relational quantum mechanics).

RQM was defined by Rovelli in 1996 in the first paper he wrote about it, a paper called, appropriately enough Relational Quantum Mechanics
quant-ph/9609002
So to have a clear authoritative idea of what the term means (and not just what this or that person might SAY it means) I can think of nothing better than simply to read the first paragraph of Rovelli 1996

---quote Rovelli 1996 RQM paper---
I. A REFORMULATION OF THE PROBLEM OF THE INTERPRETATION OF QUANTUM MECHANICS

In this paper, I discuss a novel view of quantum mechanics. This point of view is not antagonistic to current ones, as the Copenhagen [Heisenberg 1927, Bohr 1935], consistent histories [Griffiths 1984, Griffiths 1996, Omnes1988, Gell-Mann and Hartle1990], many-worlds [Everett 1957, Wheeler 1957, DeWitt 1970], quantum event [Huges1989], many minds [Albert and Lower 1988, 1989, Lockwood 1986, Donald1990] or modal [Shimony 1969, van Fraassen 1991, Fleming 1992] interpretations, but rather combines and complements aspects of them.

This paper is based on a critique of a notion generally assumed uncritically. As such,it bears a vague resemblance with Einstein’s discussion of special relativity, which is based on the critique of the notion of absolute simultaneity.

The notion rejected here is the notion of absolute, or observer-independent, state of a system; equivalently, the notion of observer-independent values of physical quantities.

The thesis of the present work is that by abandoning such a notion (in favor of the weaker notion of state-–and values of physical quantities–-relative to something), quantum mechanics makes much more sense.

This conclusion derives from the observation that the experimental evidence at the basis of quantum mechanics forces us to accept that distinct observers give different descriptions of the same events.

From this, I shall argue that the notion of observer-independent state of a system is inadequate to describe the physical world beyond the hbar->0 limit, in the same way in which the notion of observer-independent time is inadequate to describe the physical world beyond the c->oo limit.

I then consider the possibility of replacing the notion of absolute state with a notion that refers to the relation between physical systems.
-------endquote-------

So you get the idea of what RQM is about. The main idea is to get rid of the notion of an absolute state---an official right set of facts or measurements.

The RQM point is that it is not realistic to expect nature to provide one official right list of facts (any more than it is realistic to expect all observers to agree on the sequence in which some events occurred and which ones were simultaneous). So since it isn't realistic to expect that, we need to get over it---and adjust our expectations to be in line with what QM has been trying to tell us Lo these many years.

That is just my paraphrase of what he's saying. If you want to be more sure what Rovelli is saying please read the paper---it is just 20 pages or so, and not difficult.

So that is what RQM is. RQM is not NOTATION. It has the same equations as usual old Copenhagen. It calculates the same numbers as any normal version of QM. And it is not an imagining of some MECHANISM by which probabilities come about, as by branching which explore alternative lives in alternative universes. It does not add any novel mechanisms to believe in. It doesn't add anything that I can see: it just THROWS OUT SOMETHING. It discards the notion of an absolute or observerindependent state----it chucks out what i suspect is an UNREASONABLE EXPECTATION.

So here is a good test to see what SOME OTHER PROPOSAL MIGHT HAVE IN COMMON with RQM. If some other other person's proposal for adapting how we think about, i.e. interpret, QM is primarily focused on DUMPING THE ABSOLUTE STATE then that other interpretation is fundamentally similar. If it is not aimed at discarding the absolute state then it may be superficially similar, but does not capture the essential.

It is the essential of RQM that I want to focus on in this thread, although some people may wish also to talk about superficial resemblances with this or that. ROVELLI HIMSELF talks in the paper about some overlaps with other interpretations---which is fine, it just doesn't interest me especially

 

[koantum]

In the Quantum Physics Forum there is a thread called https://www.physicsforums.com/showthread.php?p=965424&nojs=1#goto_threadsearch".

 

[Chronos]

Rovelli's relational quantum states proposition is very attractive. I think it also yields testable predictions. The concept of observer independent quantums states is intuitively wrong, IMO.

 

[vanesch]

I have observers A and B, measuring alpha and beta when not in causal contact. That does not neccessarily have to be the same time (which is not well defined anyway), but let's say in whatever slicing its the same time t_0. We know the total spin is zero. Let us say they measure

S_A,alpha = 1
S_B,beta = 1

I think that the point of Rovelli is, that you have to look at things from the point of view of one observer at a time. As there is no SINGLE observer who can see both S_A and S_B at this moment (in whatever frame), it doesn't make sense for him to talk about "S_A has measured 1 and S_B has measured 1". You have to put yourself into the skin of A OR of B because there's no single observer seeing both.

So, S_A ONLY knows about "A saw 1", not about B and vice versa.

which is not a problem, because they have not compared their stuff.

Exactly.

Now go to time t_1 when they are in causal contact and measure the other part of the previously entangled state. They find

S_A,beta = 1 [note: I corrected this, think it was a typo to say -1]
S_B,alpha = -1

Now, I would have thought S_B,beta is what B has measured for beta at t_0. According to Rovelli, the important thing is now to let A ask at t_1 what B has measured. This is

S_AB = S_A,beta = -1

which is not what B has measured at t_0. Has B changed his mind concerning the measurement of beta from 1 to -1? Or has he not changed his mind but A always hears the answer he wants to hear? If so, does that make sense macroscopically?

Again, I think you have to see things from the PoV from ONE single observer, even when they meet.
Let's pick A. Back when A did his measurement, A knew of HIS result, but didn't know anything about B, so from A's PoV, B was in a superposition of states. And when A met B, this resulted in a kind of collapse, which put B into one definite state. So first A had his result (+1), and next, he meets B which has a result (-1). No problem. The -1 of B comes from the collapse of the superposition of B (before measurement by A) and its measurement by A.

So from A's PoV everything is ok.
You could do a similar reasoning from B's point of view.

And this is what I've been claiming all along: if you step back, and you consider ALL of these PoV's together, you have MWI.

Because from B's PoV, we first had +1. Ok. And from B's PoV, A was in a superposition until they met. So B will "measure" A in the -1 state when he meets. But that means that the "B" of the second story is NOT THE SAME B as the B in the first story (written from A's PoV).
In other words, they are in different branches. But as long as you look upon things from a single observer viewpoint, you don't have to think about this and this is what Rovelli does. He works from the PoV of ONE observer, for which the second observer is still in a superposition until he's observed by the first observer. And then he says that this is not something that happens to that second observer, but a description from the PoV of the first observer. This argument comes close to "Wigner's friend" (Eugene Wigner, 60ies).

So in a certain sense, Rovelli's viewpoint, that quantum states (using projection and all that) have only a meaning relative to an observer, is very similar to saying that coordinates in relativity have only a meaning relative to an observer. This is very true of course. But in relativity, one doesn't reject, because of that, the *underlying* geometrical object of spacetime, which is simply differently explored by different observers. So it is not because Rovelli rightly gives us a view on how "standard quantum theory with projection" is something which is relative to an observer, that this implies that the underlying objective structure does not exist.

And in an MWI view, that's exactly what happens. So it seems that Rovelli says something which is the equivalent of "(x,y,z,t) coordinates are to be seen relative to the observer" and MWI says the equivalent of "there is an underlying geometry from which we can derive that for each observer, things appear in an (x,y,z,t) coordinate frame".

 

[marcus]

Hi hossi and vanesch, BTW an incidental observation about coordinates.
In Gen Rel coordinates (t,x,y,z) do not have physical reality.
Events do though.

Rovelli has an interesting discussion of this in his book, including some quotes from Einstein. One could find it by looking up "Hole Argument", I expect, in either the index or the TOC.

I seem to recall some AE quote like "the princ. of gen. covariance removes the last vestige of physical reality from points of spacetime"
something like that. Anyway coordinates are just something you compute with, and have no real meaning: only events matter. (and the gravitational field, which is defined as an equivalence class making it coordinate-free)

I imagine that side observation is thoroughly familiar to you both, but let's not worry about coordinates. I think they are probably even off topic

 

[hossi]

But that means that the "B" of the second story is NOT THE SAME B as the B in the first story (written from A's PoV).
In other words, they are in different branches. But as long as you look upon things from a single observer viewpoint, you don't have to think about this and this is what Rovelli does.

Hi vanesh, thanks for the explanation. I think I finally get it. The observers can indeed have different measurements, but they agree whenever they exchange information, because that implies a quantum measurement. Can't say I like it.

B.

PS: I don't get your typo correction, the total spin is zero, and A measures =1 for particle alpha, then he should measure -1 for particle beta, when they come in causal contact, no?

 

[marcus]

dear Bee, my condolences to the federal republic for not catching a fine fish with the bright bait of an Emmy Noether. but it was just one month and some stiff-necked bureaucrat that screwed them out of it. you would have looked very nice in hamburg---in my way of thinking better there even than on the beach at SanBa
it is one of the world's good cities and also I like the freihaffen where I worked for a little while unloading ships
anyway it is all extremely sad and I am sorrier for them than for you.

 

[hossi]

dear Bee, my condolences to the federal republic for not catching a fine fish with the bright bait of an Emmy Noether.

Dear marcus,

thanks for the nice words. It's good to hear someone not telling me that I am stupid. I still hope that they are able to fill my position with someone else. It would be too bad, when the opportunity to build a group on phenomenological quantum gravity would be lost in Germany! There are just too little people working on physics beyond the standard model and quantum gravity.

I am kind of afraid, the priorities set for physics research in German are completely missing the importance of the field.

Anyway, I certainly don't regret going to PI

Take care,

B.

 

[marcus]

Dear marcus,


Anyway, I certainly don't regret going to PI

Take care,

B.

Hey! CONGRATULATIONS HOSSI!

 

[marcus]

I watched the video of your talk at PI, and I was wondering...when a person goes somewhere and gives a seminar talk then often later there could be discussions and a possible offer...but I don't read everything and I hadnt heard. I was just wondering.

this is GREAT NEWS!

and at least now we have gotten you off the beach at Santa Barbara

I was afraid you would be turning into a real California-German. Northerners should experience freezing weather on a regular basis and Waterloo Ontario will do fine.

==========================

about them not succeeding in putting together a Hamburg QG phenomenology team, that sux.

If we believed in duty, to the Fatherland and to the Scientific Establishment and for the honor of the Human Mind and the Future of Colonies in Space, and things like that. If we believed in dark Gothic letters written PFLICHT. Then we might say that you have a HIGHER DUTY to, at all costs, make sure that the QG phenomenology team is formed.

But it is a no-brainer to build such a team and I feel somewhat confident that after a little fumbling they will go ahead and do it without you. Or even offer you part-time. It is such an obvious thing to do. An "idea whose time has come" than which nothing is more powerful as they say.

Good luck at perimeter! this is such excellent news! when do you go?

 

[hossi]

Then we might say that you have a HIGHER DUTY to, at all costs, make sure that the QG phenomenology team is formed.

I will find some way. With or without the Germans.

But it is a no-brainer to build such a team and I feel somewhat confident that after a little fumbling they will go ahead and do it without you. Or even offer you part-time. It is such an obvious thing to do. An "idea whose time has come" than which nothing is more powerful as they say.

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).

Good luck at perimeter! this is such excellent news! when do you go?

September. B.

 

[hawk00321]

CONGRATULATIONS TO HOSSI
I am very curious about QG.if I want to study it,how can I do ?Can u give me some advice.thank u very much in advanced.:-)

 

[hossi]

Hi hawk,

I have no idea - I don't even know what quantum gravity is.

Try to start with some of this and follow references therein, according to your interests:

"[URL Gravity
Enrique Alvarez[/URL]

"[URL Quantum Gravity
Dagny Kimberly, Joao Magueijo[/URL]

or, if you are really tough

"[URL Quantum Gravity
Carlo Rovelli [/URL]

Don't forget to have fun

B.

 

[hawk00321]

Dear hossi ,thanks

Hi hawk,

I have no idea - I don't even know what quantum gravity is.

I only know some QFT and QCD.

Try to start with some of this and follow references therein, according to your interests:

"[URL Gravity
Enrique Alvarez[/URL]

"[URL Quantum Gravity
Dagny Kimberly, Joao Magueijo[/URL]

or, if you are really tough

"[URL Quantum Gravity
Carlo Rovelli [/URL]

I think that I am tough enough but as like you said:quantum gravity is *uhm* no butter and bread physics of course ,it will be lost in China too.I am very sorry.

Don't forget to have fun

haha ,That's my dream in all life.U MUST BE A PRETTY GIRL

BEST WISHES FOR U

 

[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 don't 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]

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]

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]

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 definately 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



B. (gotta go home get some sleep :zzz:)

 

[Kalimaa23]

...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]

Ten Commandments Of The Church Of The Smaller Hilbert Space

found this on the web, Matt Liefer, a guy at Perimeter, had it on his blog
http://mattleifer.wordpress.com/2006/04/13/the-church-of-the-smaller-hilbert-space/

http://www.perimeterinstitute.ca/personal/mleifer/humor/commandments.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 doesn't collapse the wavefunction in her state space that codes the outcome of the distant measurement because she doesn't 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, don't go collapsing it based on some suppostion about somewhere you are not in causal contact with, some spacelike separated place where you can't 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/2006/05/nonlocality.html

 

[vanesch]

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 doesn't collapse the wavefunction in her state space that codes the outcome of the distant measurement because she doesn't 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]

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 doesn't collapse the wavefunction in her state space that codes the outcome of the distant measurement because she doesn't 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 sense 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]

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 sense 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 realized 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]

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 $$S^n_{AB}$$ corresponding to B’s answer (at time t1) to the question “which value of the spin have you measured?”. That is, $$S^n_{AB}$$ is the observable describing the pointer variable in the detector B. Then consistency demands that:
(i) If A measures $$S^n_{AB}$$ after having measured $$S^n_{A\beta}$$ she will get

(4) $$S^n_{AB} = S^n_{A\beta}$$.

(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: $$S^n_{CA}$$and $$S^n_{CB}$$ then

(5) $$S^n_{CB} = S^n_{CA}$$

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

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

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

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

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

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

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]

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]

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]

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.