## Monday, May 22, 2006

### Nonlocality

I am relieved to see that Germany is still Germany. The weather is rainy, people drive like nuts, and everyone is unfriendly. Each time I come back for a visit I find it harder to localize my interactions. Crossing the street without being run over has become a challenge. The currency looks funny. Where do I get coffee to go, or aspirin on a Sunday afternoon? I go through the aisles in the grocery store, mumbling 'excuse me, thank you' and people stare at me with wonder. Not so much because I excuse, but because there is nothing to excuse for. And have avocados always been green?

Besides this, Germany is going nuts because of the soccer world cup. No street corner without advertisements, no magazine without reports, no good German without excitement. Glad to say, I leave before the fun starts.

I mentioned some time ago that I stumbled across this paper:

Relational EPR
Authors: Matteo Smerlak, Carlo Rovelli
quant-ph/0604064

We argue that EPR-type correlations do not entail any form of "non-locality", when viewed in the context of a relational interpretation of quantum mechanics. The abandonment of strict Einstein realism advocated by this interpretation permits to reconcile quantum mechanics, completeness, (operationally defined) separability, and locality.

It took me some while to make up my mind, but here is a rough summary of my understanding and my opinion.

The so-called collapse of the wave-function, caused by the measurement process in quantum mechanics, is commonly considered to be a problem because it is non-local. Even though such collapse does not allow to actually transmit information between observers, it is unpretty.

Take a box with two particles, about which you know that the total spin is zero. Then divide your system into two particles, sending one to observer A, one to observer B. Quantum mechanics tells you the state is entangled before any further measurement is made, meaning you can't say what the spin of each particle is. When observer A has made his measurement, the outcome has to be either + or - 1. Let's say, it is +1. Since the total spin is zero, the other particle then has to go into state with spin -1. Instantaneously.

Now the claim of the relational interpretation is that in the above it was omitted to take into account that the measurement device, or the observer himself, also are subject to quantum mechanics. Therefore, strictly speaking, the outcome +1 of the measurement for A is not global. It is +1 as seen by observer A, it is a measurement relative to A.

The main statement is that there is no need for a non-local collapse of the wave-function if one takes this quantum mechanical relativeness of observers really serious. Drop the assumption of the non-locality, and assume instead that A measures something, and B measures something. As long as observer A and B don't compare their measurements, there is no problem. But if they do, their comparison is an interaction, subject to quantum mechanics, and has to be treated like such. As shown in the paper, if you describe the comparison as an quantum mechanical interaction, both observers will always agree on their description of the experiment. "It is clear that everybody sees the same elephant."

As I understand it, this means roughly the following. If A measures +1 and B -1, or vice versa, there is no problem. But if that always were the case then we were back to the collapse. Now the new thing is, let A measure +1, and B measure +1. That doesn't worry us as long as they don't compare their measurements. When they do (back in causal contact) B will find A's measurement in agreement with his, meaning 'A as seen by B' is -1, and also A will find B's measurement in agreement with his 'B as seen by A' is -1.

Should I badly have misinterpreted this, I would be very grateful if someone could enlighten me.
You might also want to look up Alejandro's blog, Christine's blog and the Physicsforums.

It seems to me that this might be possible to write down on a paper. But I can't make too much sense out of it. In particular, I have a problem with the above elephant, alias, the classical limit. As long as they are not in causal contact, observer A and B make up their own stories about what is happening. Yet, when they talk to each other, they both always agree. Not because their stories are identical, but because they interpret to other observer's story through some measurement as being identical to their own story.

But suppose A has a dog, and he agrees with B to kill it when he measures +1. A and B separate, are out of causal contact. Both measure +1. A kills the stupid dog.

Then he comes back into causal contact with B, and of course he takes the dog, which is nothing but a macroscopic result of a quantum measurement. But no matter what, B will always have to find that the dog is alive.

This reminds me of some conversations I have with my grandmother. Being almost deaf she just hears what agrees with her story of the universe. I goes somewhat like this

Me: "I hear his mom is really worried"

My granny: "It's so great he's getting married!"

Me: "No, I mean, they split up recently."

My granny: "Yes, that's how it's supposed to be."

Me: "But he left - HE HAS MOVED OUT."

My granny: "She has every reason to be proud."

I admit that I envy my granny for her ability to make up her own reality. The bottomline of the relational interpretation is essentially, that we all have our own reality, and no matter how hard we try to talk to each other, we will never agree. But we will never notice that we don't. On a philosophical level, I find that to depressing to like it. In addition, I feel specifically non-local today. Looking forward to your feedback, B.

This used to be my playground
This used to be my childhood dream
This used to be the place I ran to
Whenever I was in need
Of a friend
Why did it have to end
And why do they always say
Don't look back
Keep your head held high
Don't ask them why
Because life is short
And before you know
You're feeling old

~Madonna

#### 31 comments:

1. Uncle Al postulates that Bundesautobahn vehicles' speeds are conjugate to the non-locality of Geschwindigkeitsbegrenzung printed a readable road sign.

2. "As long as they are not in causal contact, observer A and B make up their own stories about what is happening. Yet, when they talk to each other, they both always agree. Not because their stories are identical, but because they interpret to other observer's story through some measurement as being identical to their own story."

It seems to me that this is exactly the problem. Especially when you use actions rather than words for their stories -- your idea of the dead dog. It seems like "Rovelli's dog" is in a worse state than SchrÃ¶dinger's cat: it is not merely unkown whether he's dead or alive, but A will believe him dead (and try to bury him, maybe) and B will be sure he's alive (and try to stop A from burying -- or, no, because A is not burying the dog, as seen from B's perspective... now i'm realy confused).

Dennis Dieks said in his foudnations of QM course that the non-locality seen in EPR does not mean there is action at a distance - you cannot use it to send a signal - but only 'passion at a distance'. (This may be a quote from someone else, I don't recall.) Well, I'd rather have some regular 'passion at a distance' than this 'everyone their own reality' stuff.

3. was that McD really your playground?

4. Hi uncle al,

which speed limit? Here is my favourite road sign: it means End of all restrictions.

Best,

B.

5. Hi chris,

indeed, 15 years ago the whole industrial area was green meadows and trees.

They paved paradise, and put up a parking lot

~Bob Dylan

Best,

B.

6. Hi florine,

It is not really clear to me whether the question of Schroedinger's cat or Rovelli's dog is merely one of personal taste, or whether the relational approach would actually make different predictions in certain situations. I suspect though that one can't really tell without having an understanding of the measurement process anyway.

If that is the case, it seems to me for interpretational questions you just have the choice between non-locality or 'everyone their own reality'.

I also found this on the arxiv

Action and Passion at a Distance: An Essay in Honor of Professor Abner Shimony
Authors: Sandu Popescu, Daniel Rohrlich

Quantum mechanics permits nonlocality---both nonlocal correlations and nonlocal equations of motion---while respecting relativistic causality. Is quantum mechanics the unique theory that reconciles nonlocality and causality? We consider two models, going beyond quantum mechanics, of nonlocality---``superquantum" correlations, and nonlocal ``jamming" of correlations---and derive new results for the jamming model. In one space dimension, jamming allows reversal of the sequence of cause and effect; in higher dimensions, however, effect never precedes cause.

Best,

B.

7. Hey Bee.

I concur fully with your comment on relational EPR, and that it seems to imply this sort of ultra soliplism.

I think Rovelli disagrees on this point, or at least this is not the scenario he wishes to describe/create.

8. The correlations of the EPR paradox depenend on being able to reliably compare the arrival times of particles and the angles between the polarized filters.

EPR experiments cxarefully control just that uncertainty.

Now if the detectors and polarizers were accelerated or even moving close to the speed of light I don't see why the correlations should be maintained.

Would all observers be able to agree on arrival times and angles between polarizers if the system was accelerating?

9. Hiyah,

My first post: Greetings. I really like your blog (I came to it from al's reality conditions), he's a friend at nottingham. I too am very interested in Rovelli and Smerlak's approach, although I am relatively happy with it. The only thing I don't really like is thier definition of observer because I take a different view as expressed in quant-ph/0604201. But I see nothing wrong with a relational definition of elements of reality (isn't this almost what Einstein suggested with his spacetime coincidences...). Another relational way to get rid of problems with nonlocality is hinted at in quant-ph/0605142. And I'm presently writing a new paper based on this hint. I'm quite new to blogging, but I hope my shameless self promotion won't be considered rude! :o) I will try and make some useful, and less shameless, comments soon.

I especially liked your post on liver physics!

Tom Marlow (Nottingham)

10. insightaction said:

The correlations of the EPR paradox depenend on being able to reliably compare the arrival times of particles and the angles between the polarized filters.

[...]

Would all observers be able to agree on arrival times and angles between polarizers if the system was accelerating?

hmmm, if the system was accelerating they wouldn't even agree on what a particle is to begin with...

11. Hi Tom, welcome. Thanks for the nice words :-)

anonymous said: But I see nothing wrong with a relational definition of elements of reality (isn't this almost what Einstein suggested with his spacetime coincidences...).

Well, I didn't say there is something wrong. Just that I am not sure what the gain is of such a re-interpretation to get rid of the non-local collapse. It it worth the mind-twisting?

12. Maybe this is just a philosophical comprise but I have come to think of spin entanglement experiments as not so much measureing spin of particles but rather measuring the average angle between detectors.

The correlations are not a function of cause and effect, after all who detects first is relative to the observer, but rather a result indicating that the anlge between the detectors is a well defined quantity.

The logical tool I have used to work this through is by imagining a third observer who receives a bit stream from both detectors. The third observer then can say he has observered an average angle between the detectors as given by the inverse cosine of the correlation coefficient.

Until someone builds a spin entanglement experiment where all the elements of the experiment are truly and completely isolated from each other we cannot eliminate the possibilty that the particles at the moment of emission have an a priori reaction to the angle between the detectors. Whether this is mediate through a vector potential (like an Aarhnov-Bohm effect) or gravity or other fields.

And I still don't know where the socks went!

13. I don't think the relational interpretation implies solipsism. It is only if A and B is in absolute causal isolation, that they can disagree about a measurement. Like if A is behind a black hole horizon. In most other cases, information about the measurement will have reached from A to B via decoherence processes.
That's what I think anyway.

I also think you have a nice blog.

14. Hi Bee

Thanks for pointing me to the article!

I kind of expect that RQM will not give different predictions than other interpretations of QM, that it is "merely" a way to interpret the predictions. So you could say that it's a matter of personal taste...

In that case, I opt for non-locality over everyone his own reality.

15. Hahaha, I'd rather think that nonlocality is more brain twisting! Relationalism is a pragmatic philosophy that ensures that only the most obvious rational elements of a theory, ones that we can justify, are used to formulate the theory itself---what can be less brain twisting than that?! We can justify that observer's only have partial information but we cannot justify that there exist observers with information about everything. Nonlocal theories seem to require the latter brain-twisting assumption.

Tom

Tom

16. ** Now the new thing is, let A measure +1, and B measure +1. **

unrealistic assumption, I think, Sabine. so that your critique from that point on does not apply

you asked for help understanding the paper which I will try to give, as well as I can (pretending to no special understanding myself!).

I think the point is simply that there is no non-local collapse of anybody's wavefuntion!

A's wavefunction about the OTHER electron does not collapse until he actually hops a jet and GOES to where B is.

It can't collapse because he doesnt know that B actually DID WHAT HE PROMISED. maybe a supernova or an exciting soccer playoff interupted him and he forgot to measure. or his machine broke. So A's wavefunction about B's electron cannot collapse until he actually gets information of what really happened.

the point is pretty simple, there is just no non-local collapse of ANYBODY'S wavefunction.

that's how I see it IMHO.

something in what you said suggested you might be picturing a THIRD observer who can somehow see both of them (I hope not instantaneously) in order to give operational meaning to the truth or falsity of some assumption about what happens to the two simultaneously before they get in contact. I don't know that the assumptions corresponds to something physical like an observable or performing some practical measurement. So I would rather keep it simple and NOT introduce the third observer.

If that is OK then maybe is the question settled? Correct me if I am mistaken or missing your point.

Your stories about grandmother and about the dog are funny but seem to be about something that never happens in what Smerlak and Rovelli are studying.

the blog gets better and better,

hello to florine,

regards

Who

17. Who said: I think the point is simply that there is no non-local collapse of anybody's wavefuntion!

A's wavefunction about the OTHER electron does not collapse until he actually hops a jet and GOES to where B is.

Hi Who, thanks for your comment. I get the point. It doesn't take a non-local collapse. The wave-function does not collapse non-locally. But a measurement of one observer still has to yield a specific state. In contrast to the usual QM interpretation, this measurement does not imply anything for the other observer.

The question is what happens if two observers come into causal contact after both of them have made measurements (you might want to call that two local collapses). They need to compare their local results. If you assume that both ALWAYS agree, then you have to explain that. This is the spooky non-locality. In case they don't you have to explain that. That is where my grandmother comes into play.

You might want to claim that nobody ever knows whether my granny is right or I am. Or maybe there is no right or wrong. But that doesn't solve the problem with the dead dog. It might be that for observer B (without the dog), observer A never had a collapse, and never made a measurement until they meet and compare their results. But if they eventually do meet, they have to agree. No matter what B thinks A does: measures +1,-1, does not measure anything, they will both have to come to the result that QM is right and the sum of their measurments is zero.

Best,

B.

18. What actually happened is that when it came time to do the experiment, B could not remember whether he was supposed to point the machine East or West. As a compromise, he points the machine North and measures the spin. He gets +1, so he shoots the dog.

After a while A, who is the principal investigator comes to check up on the results. When A hears what has happened he is completely exasperated and shouts "You imbecile, you killed the dog BUT FOR THE WRONG REASON!"

The moral of the story

Don't collapse your wave function until you see the whites of their eyes.

19. Hi Bee, our posts crossed. I was interupted at computer and sent my 4:30 while unaware of your 4:10 (times approximate).

I THINK I SEE YOUR POINT. It is here:

**They need to compare their local results. If you assume that both ALWAYS agree, then you have to explain that. This is the spooky non-locality.**

To me it is not spooky and it is something they discover AFTER THE FACT when they get together at their favorite espresso place and compare notes.

And the agreement is ALMOST always. And they say "Hey, yeah! I got a +1 and you got a -1. It adds up to zero! that is because the original system had spin adding to zero."

And this happy ending is only when everything went as planned and both of them remembered to point East and both machines worked etc.

they can only discover this happy ending and be sure of it when they get back in causal contact and sit down together, for a beer if you prefer.

So you definitely be right and I could be missing something, but right now I dont see anything spooky.

I dont see any non-local collapse of anybody's wavefunction----I see them sitting together comparing notes and happily collapsing their wavefunctions as they agree that everything worked right.

A's wavefunction represents A's information based on her experience of the world. Likewise B's is her accumulated information.

You only collapse your wavefunction, or do some projection operator on it, when you get some new information. You only get the new information when you actually see the evidence and are in causal contact. Otherwise everything is still suppositional and hypothetical ("if she really made the measurment and if the sucker was pointed in the right direction" and so on) so it doesnt count. So I see the collapse (which is you learning something about something) as always local.

Hey, this is your blog which first and foremost should be fun and about your ideas friends etc.
So I will not go on about this! Instead, I put this argument on the "elephant" thread at PF. So you can address it if you care to and not if you don't. No problemo either way. Wont pursue it here.

I finally understand your liking to live in N. America (california, waterloo etc.) it makes sense! Nice pictures.

20. Who said: Hey, this is your blog which first and foremost should be fun and about your ideas friends etc. [...] Wont pursue it here.

Hi Who, Thanks for your comments. Don't worry, I have fun with my blog :-) Reading your last post I think we do agree anyway. There is nothing spooky in the sense as there is never information transmitted non-locally. Also, the observers never directly notice any non-locality (as they are not in causal contact when it happens, should it happen).

Also, I don't see anything wrong with the relational interpretation, I just fail to see what it is good for.

Regarding the so-called collapse, think about the following: when A and B meet, they both have a history of events, including the measurement. The history might be: measured +1,-1 (relative to their detector), did not measure anything. The history comes with a time-line. In case they did not both make measurements before being in causal contact there is no problem. But what if they both made measurements? You then have to assure somehow that if they finally meet, their histories never disagree. Either because their measurements always agree (usual QM), or because their detectors are 'relative' and the comparison of their measurements is such that they always agree (relational).

I finally understand your liking to live in N. America (california, waterloo etc.) it makes sense! Nice pictures.

I hate to tell you, but I actually don't specifically like living in the US. I am very happy to move back into a civilized country soon. The difference between ucsb/santa barbara and pi/waterloo could hardly be more extreme, regarding climate as well as research.

Best,

B.

21. We are still side stepping the issue of how the observers are comparing the angles between the detectors.

Something very tricky is occuring there.

After all it is completely reasonable to compare the output from the detectors, and that comparison will yield any correlation between -1 and +1. The spooky part is that this number relates so nicely to the angle between the detectors.

So what exactly do we mean when we say the angle between the detectors is such and such? There are a host of implications in that statement that I don't think are being fairly accounted for.

---Warning: Long Ramble----

What EPR and Schrodinger's Cat point to is the difficult question of what a quantum state is defined over, is it all of space time? Or just a single light cone coincident with a observation at one point in space-time? or something completely different?

So lets digress to a very specific experiment. Imagine we have etched a pair of cyrogenic quantum dot arrays on silicon which are also physically and magnetically shielded from each other. We can sequentially populate the dots with spin entangled electrons. Now here is where we do something tricky, we move these arrays separately around space-time, we can theoretically move them to any point that we can access at less than the speed of light. Now in the first array we turn on a magnetic field and measure the spins using a polarized laser probe. Provided we have stabilized the arrays well enough we can wait as long as we like, and move the second array as far as we want before continuing the experiment. Which is where the really difficulties start. Silcon chips, even ones with a lot of cryogenics are pretty small things thus we can rotate them about in space as well, so when we turn on the magnetic field do we measure the field relative to the direction of the other field or do we measure relative to the orientation of the array? I'm pretty sure the only sensible answer is to say that we measure the field relative to the orientation of the array, but then that begs the question of how the array is changing the wave function so that the wave function maintains orientation relative to the array.

...So I think for a quantum system in equilibrium (don't ask for a definition) the state is defined through-out all of space-time. Unfortunately if the universe were described by a separable Hilbert space we wouldn't have enough spare dimesions to form the infinite sub-spaces necessary for independent observers (that is we would be returning to determinism) this leaves us with only one conclusion that the universe is describe by a Hilbert space not having a countable basis but rather an uncountable basis.

---End of rambling---

22. The problem lay in the fact A and B cannot be in a single space at the same instant. Being at two seperate locations, determines that observers cannot collapse "other" observer's frame of reference.

23. paul valletta said...

The problem lay in the fact A and B cannot be in a single space at the same instant. Being at two seperate locations, determines that observers cannot collapse "other" observer's frame of reference.

Hi paul,

I don't think that is where the problem comes from (if there is any). You are right that in the relational approach two observers at two locations should not collapse each others wave-function, but I don't see why sharing a common space-time point does imply both observers agree. I.e. I don't think it's the location that uniquely determines an observer. At the very least, the observer is not very well defined anyway. Best, B.

24. InsightAction said...
We are still side stepping the issue of how the observers are comparing the angles between the detectors

Indeed we are. Think big: quantum mechanics is not merely measuring spins. What do you do with other experiments when up-down-left-right is not sufficient? Is the 'long ramble' enlightening for measuring interference patterns or P_T distributions? Best, B.

25. Think big-exactly! But then I would have to tamper with the most unfortunate of questions: What is measurement anyways? I strongly suspect that if I were to contemplate those sorts of questions I'd be bettter of teaching Yoga for a living.

I was thinking of interference patterns mostly, and the idea of storing and transporting entangled states. Could an etched quantum dot store a p_t distribution? I don't know.

26. Hi, again.

Take a single particle, within a SINGLE location,(box) seperate the particle, send the TWO half's to locations "outside" the initial box?

Neat trick I know, BUT you cannot create TWO detectors,(initial box containing two particles is observed by a single detector) unless one create's two "boxes" from the original One?

It surely makes no difference to observers, one observer can observe two particles in ONE box,Two observers can observe one particle in one box.

Two observers 'cannot' observe One particle, at two non-local reference frames in a single instant?

27. insightaction said...

What is measurement anyways? I strongly suspect that if I were to contemplate those sorts of questions I'd be bettter of teaching Yoga for a living.

Why? I find the question of how the measurement happens really important. I admit though that I can't relate to all the metaphysical crap that some people like to attach to the question. I think there must be some physical description of it. E.g. I liked (half of) the paper

Emergent Probabilities in Quantum Mechanics
Authors: Olaf Dreyer

I tried Yoga once. Definitly not my thing - too much sitting and breathing.

Anyway, relational QM or standard QM don't say anything about the measurment. I guess that's why I don't think it gets us anywhere. It's a reinterpretation of reality, much more like Yoga.

Best, B.

28. paul valletta said...

Take a single particle, within a SINGLE location,(box) [...]

you cannot create TWO detectors[...]

one observer can observe two particles in ONE box,Two observers can observe one particle in one box.

Two observers 'cannot' observe One particle, at two non-local reference frames in a single instant?

Hi paul,

the problem I have is that it's not clear what we are talking about in very many regards. What is a detection? What is an observer? What is a particle, what is a reference frame? Can a particle have a 'single' location? Can detectors be 'singled'? What do you mean with 'single instant'? One observer can certainly receive information about detection in two previous measurements that were not in causal contact.

I should add though that I do in principle agree to your view. I mentioned that earlier somewhere that the relational interpretation seems to imply that every location in spacetime comes with it's own 'private' (relative) history of events. Best,

B.

29. The Emergent Probabilities paper is pretty good, but noticably avoids the issue of non-commuting operators and the Hiesenberg Uncertainty relationships. I may be reading the paper wrong, but their logic would seem to allow for unlimited precision in measuring non-commuting operators simultaneously. There is more to quantum mechanics than merely probabilities.

30. There is another interesting aspect that can be further introduced, I made some comments re:
http://arxiv.org/abs/gr-qc/0403001

on the PF forum before I got banned(again!)..but I have extended the implications original post by Sabine, but will leave the link for now, and will hopefully place a simplistic overview of another thought experiment.

P.S PF poster Ranyart-Moorglade-Olias-Wave's_hand_particle..and last but not least-Spin Network. ;)

31. IIRC, A and B need to worry about more than each other's "particle-oriented" wavefunctions, they also need to avoid collapsing those into the "environmental" wavefunctions of their surroundings. I'm pretty sure that interactions with the dog would be enough to do that.

And consistency would be enforced via the static plenum -- that is, once "either end" of the wavefunction collapses, it constrains how the other end can collapse, because the 'waves" in question are properly considered as four-dimensional patterns within spacetime (In this case, the pattern might look something like a wishbone.)

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