Exploring the Relationship Between Schroedinger and Bohm's Quantum Mechanics

[vanesch]

When do complex numbers arise?
Is there a well established theory already for what type of equations produce complex numbers as solutions?

One should study things in order
You talk about quantum gravity and then you ask the above question ; I don't want to sound offending, but it is a bit as if you subscribed to Formula 1 contests, and ask the technician on the starting line, what do people mean by "changing gears" ?
But I can understand that this comes from reading lots of popular science books. There is a not to be underestimated pleasure to be gained in doing things in the right order. Do you know real calculus ? (integrals, differentials etc...) We can take that maybe as a starting point.

cheers,
Patrick.

 

[Rothiemurchus]

vanesch:
But I can understand that this comes from reading lots of popular science books. There is a not to be underestimated pleasure to be gained in doing things in the right order. Do you know real calculus ? (integrals, differentials etc...) We can take that maybe as a starting point.

Rothie M:
It might surprise you to know that I know calculus of variations, Hamilton's principle,
how to solve differential equations and just about any useful mathematical procedure you can think of that relates to classical mechanics.I also know much of the maths of relativity - general and special relativity.I have studied complex numbers in detail - years ago - but I do not think they provide a reasonable or satisfactory description of reality.Physics is about ideas - not mathematics.Einstein said the maths will always follow from a good idea.
A mastery of mathematics does not guarantee an understanding of anything.
The trouble with quantum mechanics is this -
It has taken causality away from the world.It is de a defeatist point of view:it says " there are some things that just can't be understood in terms of the commonsense world."
Where is the proof of this? The most important question to ask about qm - in my opinion - is this:why is Max Born's guess ( that the wavefunction x complex conjugate of wavefunction is proportional to the probability of finding a particle at a certain position in space) so useful - what is a wavefunction? It must be something physical like Bohm's pilot wave.
There is a way to resolve the problem's associated with Bell's Theorem
and to restore causality to the world and that is to assume a signal exists that travels faster than light.But because such an idea shakes the foundations of relativity people will not get their heads around it.
But there was a time when nobody would have believed that the speed of a light wave catching up with the Earth equals the speed of a light wave approaching the Earth.

 

[vanesch]

Rothie M:
It might surprise you to know that I know calculus of variations, Hamilton's principle,
how to solve differential equations and just about any useful mathematical procedure you can think of that relates to classical mechanics.I also know much of the maths of relativity - general and special relativity.I have studied complex numbers in detail - years ago - but I do not think they provide a reasonable or satisfactory description of reality.

Well I then offer my apologies, but you have to understand that it is somehow contradictory to read the above, and:

When do complex numbers arise?
Is there a well established theory already for what type of equations produce complex numbers as solutions?

Do you see what I mean ?

cheers,
Patrick.

 

[ZapperZ]

The trouble with quantum mechanics is this -
It has taken causality away from the world.It is de a defeatist point of view:it says " there are some things that just can't be understood in terms of the commonsense world."

But you see nothing wrong in demanding that the world behaves only in ways that you approve DESPITE of all the experimental observations?

Where is the proof of this? The most important question to ask about qm - in my opinion - is this:why is Max Born's guess ( that the wavefunction x complex conjugate of wavefunction is proportional to the probability of finding a particle at a certain position in space) so useful - what is a wavefunction? It must be something physical like Bohm's pilot wave.
There is a way to resolve the problem's associated with Bell's Theorem
and to restore causality to the world and that is to assume a signal exists that travels faster than light.

I can play the same game as you do and ask you "Where is the proof of this"?

We didn't just make things up just so we can feel good about it and sleep comfortably at night. If you insist that there ARE signals traveling faster than light, then describe the nature of the signal so that it can be measured and proven to exist, and then be proven that it DOES travel faster than c. Till then, you're just making things up as you go along.

But because such an idea shakes the foundations of relativity people will not get their heads around it.
But there was a time when nobody would have believed that the speed of a light wave catching up with the Earth equals the speed of a light wave approaching the Earth.

The difference being that there were existing TANGIBLE, experimental observations that simply did not fit the old notion of how light speed behave. These were not based on simply a matter of tastes, which is all you have stated. There have been NOTHING, no clear experimental observation, to indicate violation of any of SR's postulates so far. You should not equate what have been done to advance our knowledge of light with what you are trying to do here, because they are not even close to being the same.

Zz.

 

[Rothiemurchus]

Zapper Z:
But you see nothing wrong in demanding that the world behaves only in ways that you approve DESPITE of all the experimental observations?


Rothie M:

I do not doubt that the mathematical predictions of qm match experiment and
that any theory challenging qm must explain why.
As for my piece on superluminal signals:are we left with any alternative to them to
explain what Einstein called " ghostly action at a distance."
Everything else seems to have been tried.
I would say that your attitude is "I think that unfortunately the world is just
incomprehensible at some level."
That could be true but there is no harm in challenging it.
And as you have said previously people test qm all the time - just in case.
And people were very surprised by the results of Michelson and Morley
on the speed of light relative to the Earth.

Vanesch:
No need to apologise, I do have a habit of asking what people call
"naive" questions.

 

[selfAdjoint]

There are no signals, according to QM. The particle is not "told" what attribute to assume from afar; the projection of its state to an eigenvalue tells it just as with any particle. The fact that the state was complicated and the projection contingent doesn't change this.

 

[ZapperZ]

I do not doubt that the mathematical predictions of qm match experiment and
that any theory challenging qm must explain why.
As for my piece on superluminal signals:are we left with any alternative to them to
explain what Einstein called " ghostly action at a distance."
Everything else seems to have been tried.
I would say that your attitude is "I think that unfortunately the world is just
incomprehensible at some level."
That could be true but there is no harm in challenging it.
And as you have said previously people test qm all the time - just in case.
And people were very surprised by the results of Michelson and Morley
on the speed of light relative to the Earth.

And you're forgetting that for the MM expt. to be designed, we must first know WHAT it is that we're trying to measure. The old ether theory CLEARLY stated the kinds of influences it exert on light and how it should change. In other words, it had something CONCRETE that we can measure. It didn't just say "oh, there must be an ether", and left it at that, the way YOU did. You can't just say "oh, there must be something moving faster than c" without describing WHAT it is that is moving, and what property does it have for us to be able to measure AND detect its speed.

As an experimentalist, I am SELDOM satisfied with being told "oh, that's just the way it is". However, I have no qualm in settling for the POSSIBILITY that the quantum world is NOTHING like what we are familiar with. I make NO DEMANDS that it should. Unfortunately, from your complaints, you WANT and insisit that it must conform to your classical perception of the world. I find that highly irrational.

Zz.

Vanesch:
No need to apologise, I do have a habit of asking what people call
"naive" questions.[/QUOTE]

 

[Rothiemurchus]

Zapper Z:
You can't just say "oh, there must be something moving faster than c" without describing WHAT it is that is moving, and what property does it have for us to be able to measure AND detect its speed.

Rothie M:
I will set up a website sometime for you to look at the details of what I had in mind.
They are the kind of details you want!

 

[humanino]

I know (...) any useful mathematical procedure you can think of that relates to classical mechanics

You need humility Rothie. I seriously doubt. You just demonstrated that you are not aware of the gigantic field of mathematics. I know some, and I am aware that is so few.

The last person considered to know all mathematics at his time is Poincare. That is what we say in France. Today, it simply impossible, even in a narrow field.

If I am wrong about you needing humility, you are a authentic genius in math. Above any in history.

 

[ZapperZ]

Zapper Z:
You can't just say "oh, there must be something moving faster than c" without describing WHAT it is that is moving, and what property does it have for us to be able to measure AND detect its speed.

Rothie M:
I will set up a website sometime for you to look at the details of what I had in mind.
They are the kind of details you want!

Oh no! Not one of those!

If you think you have anything authentic and valid, then please send it for publication in a peer-reviewed journal. If you don't, then you are no better than the tons of quackery we find on Crank Dot Net.

I don't read, nor do I pay any degree of emphasis on stuff that can only see the light of day on someone's website.

Zz.

 

[nrqed]

There are no signals, according to QM. The particle is not "told" what attribute to assume from afar; the projection of its state to an eigenvalue tells it just as with any particle...

But the particle *is* "told" in what state to collapse even though the measurement might have been made on the other side of the universe.

I am not saying that QM is wrong or that Nature should obey rules that are intuitive.

What I *am* saying is that it seems to me that the standard presentations of QM and SR can't be the whole story. For example, the measurement problem. We say "take the measurement of that particle here and *then* the wavefunction collapses. There is , imho, something obviously flawed here. In the case of two entangled photons separated by timelike intervals, the order of the measurements is frame dependent. So in one frame it's observer A which makes the wavefunction collapse, in another frame it's observer B. So it does not make sense to talk about a measurement making the wavefunction collapse. That means that, imho, the standard picture can't be right. The usual way used to describe QM measurements would have to be changed.


Just one example to be more specific: You have two entangled photons separated by timelike intervals. Their polarizations are measured by two observers.

Question 1: you are in a frame where measurement A is taken first. Compute the probabibilities of each measurement of A and then the proabilities of each measurement obtained by B. In the standard presentations, the results of A would be 50/50 and then the result of B would be determined at 100%.

Question 2: Now you are in another frame where B is measured first. Then the standard answer would be quite different than the first, it would be 50/50 for B, then entirely determined for A.

Obviously, there is no way to distinguish one interpretation from the other experimentally. But still, I think it would be important to rephrase the standard interpretation. It sounds to me that the correct phrasing would be to abandon completely the collapse part and to phrase things in a way that is from the start symmetric between the two cases. One should consider the measurements grouped together, with no notion of time delay between the two or of collapse of the wavefunction for that matter. One should then say:

A and B make measurements. There are two possible outcomes: A measures this type of polarization and B measures this other type of polarization, with a probability of 50%. OR the other way around with prob 50%.

That's it, no mention of spacetime interval, no collapse, no time delay, no space separation.

I guess that most people already think that way and see no big deal to it. But if we take his seriously, we should apply the same point of view to all QM measurements. For example, you measure the position of a particle, and then 10 hours later you measure its momentum. In the standard approach, the first measurement caused a collapse of the wavefunction. Then we time evolve the state to find the prob of different momentum measurements 10 h later. But maybe we whould never think of it that way and use the above, symmetric prescription. Then we should say that it's also equivalent to see the second measurement (the momentum one) as causing the collapse and specifying, back in time, the possible results of the x measurement.

My point is : if we adopt a point of view for some measurements, we should adopt the same point of view for all. It feels to me that people treat implicitly treat differently EPR type measurements then other types of measurements. That's what bothers me.

Pat

 

[vanesch]

So it does not make sense to talk about a measurement making the wavefunction collapse. That means that, imho, the standard picture can't be right. The usual way used to describe QM measurements would have to be changed.

Hi Pat,

What you write here bothered me also quite a while, until I realized that collapse of the wavefunction does make sense as long as it is an observer-bounded concept. This is a viewpoint which is somewhat intermediate in between the standard interpretation and MWI. Indeed, thanks to decoherence, you cannot distinguish between a measurement that gives rise to a true collapse, and one that just "decoheres".
So if you have two entangled particles, A and B, and you have two observers, P and Q, P which observes A and Q which observes B (and we assume these observation interactions to be spacelike separated - you write everywhere timelike but I suppose you mean spacelike), let us then take the point of view of P.
When P observes A, this is a true observation for P. But at that point, he doesn't know anything about B or Q, so it doesn't make sense for P to talk about a collapse of the state at Q. When Q travels to P to tell him the result of his measurement, P just considers this message from Q as another measurement (P makes a measurement on Q). All this is completely local at P, and his successive measurements (with collapse) make completely sense.
Q can do exactly the same, but then of course we have different quantum discriptions according to the observers.
I didn't work this out, maybe one can think of a propagating collapse wavefront going out from each observer ; or one considers that there is only one true observer in the universe, namely me :-)

cheers,
Patrick.

 

[selfAdjoint]

Patrick, it seems you have the esssence of a sound view here, if you will just lose the "propagating wavefront". Necessarily such a wavefront would be unphysical, since experiment has proved that the time between observations P and Q can be less than the distance between them in light units, i.e. the events showing the correlation can be spaclike. What I think is correct is that the correlation was born, though not yet physical, when the particles were produced entangled, and has spread with the particles; so the cause of the correlation lies in the past light cones of both particles. The only thing that happens at the later time is that the correlation becomes physically manifest at the first measurement; and if the measurements are spacelike related it is impossible to say meaningfully which one came first, since no one can view both of them, except historically.

 

[cepheid]

Again, this is an example on why, if one did not learn from the ground up, things will seem to appear out of nowhere.

We have gone over this in other threads of the importance of calculus of variation, and in particular the principle of least action. This is the only means of understanding the origin of the Lagrangian/Hamiltonian approach to classical mechanics. I strongly suggest you look this up.

Zz.

Cool, I'm learning this stuff just now, in a course called PHYS 350...Applied Classical Mechanics. My prof said the formulation is far more fundamental than the Newtonian formulation of mechanics in that it applies more universally and draws together many branches of physics. We've already seen things like Fermat's Principle of Least Time in optics. But both that course and this one are very difficult to understand.

Another funny anecdote. When the same prof (the 350 one) tried to show how the Hamiltonian/Lagrangian approach applied more broadly, he asked our class, "Have you studied quantum mechanics?" When he eventually got the sense that our sole exposure to QM in a previous course (Intro to Modern Phys.) consisted of being dumped with the Schrodinger Equation, and shown how to solve certain problems with it, his exact words were:

"You mean to say they never even went over the history of how the theory arose?" That's pathetic!"

I couldn't have agreed more. It was pathetic. I'm starting to realize that some of the treatment of physics for us in Engineering Physics might be lacking compared to the treatment in the pure physics programme. Still...*hopes fervently that QM makes more sense the second time 'round*

EDIT: Thanks for that link you gave us back on the 1st page Zz! That should help...

 

[ttn]

What I think is correct is that the correlation was born, though not yet physical, when the particles were produced entangled, and has spread with the particles; so the cause of the correlation lies in the past light cones of both particles. The only thing that happens at the later time is that the correlation becomes physically manifest at the first measurement; and if the measurements are spacelike related it is impossible to say meaningfully which one came first, since no one can view both of them, except historically.

Actually, if I understand you correctly, your view here is precisely what is shown by Bell's theorem to be impossible. If you assume that "the correlation lies in the past light cones of both particles" (i.e., that the particles get their properties correlated at birth) and if you assume that the outcomes of the two measurements depend only on that total, joint two-particle state (and not on the setting or outcome of the distant experiment) then you get Bell's inequality, which is violated by experiment. So the quantum correlations cannot be explained by any (local) model like the kind (I think) you have in mind.

But then, I'm not entirely sure what you meant by saying that "the correlation becomes physically manifest at the first measurement." If this allows for the first measurement to causally affect the state of the distant particle (or, more generally, the probability distribution for possible outcomes of the distant measurement) then this would be consistent with experiment. But it would of course be non-local.

 

[selfAdjoint]

I didn't mean to suggest classical movement of the correlation, or the quantum state. They evolve outside of spacetime. But the state _mmmm_, "pro-exists" where the two particles are, in the sense that it is available to provide probabilities to the experimenters. All of this - the essence of QM - is outside classical physics, and it is classical physics that yields the Bell inequality. It is nevertheless true that the extended state carries the information "If one of the particles is found to be in the "DOWN" state, the other will be in the "UP" state, and vice versa". And that state subsists in spite of separation, until a measurement is made. The collapse of the state, or its projection onto its spacetime eigenvalues, conveys the values appropriate value to both particles and doesn't need to travel from one to the other because it is available at both and its link is outside of spacetime, as all states are in QM.

 

[ttn]

I didn't mean to suggest classical movement of the correlation, or the quantum state. They evolve outside of spacetime. But the state _mmmm_, "pro-exists" where the two particles are, in the sense that it is available to provide probabilities to the experimenters. All of this - the essence of QM - is outside classical physics, and it is classical physics that yields the Bell inequality. It is nevertheless true that the extended state carries the information "If one of the particles is found to be in the "DOWN" state, the other will be in the "UP" state, and vice versa". And that state subsists in spite of separation, until a measurement is made. The collapse of the state, or its projection onto its spacetime eigenvalues, conveys the values appropriate value to both particles and doesn't need to travel from one to the other because it is available at both and its link is outside of spacetime, as all states are in QM.

So... when Alice makes a measurement on one side, Bob's particle is affected -- but the "information" that let's Bob's particle "know" to do this doesn't propagate through regular space, instead taking a detour outside of space and time on its way there?

Is this supposed to be consistent with relativity?! Or maybe you didn't intend it to be. But surely if it's really true that, according to QM, all states are "outside of spacetime", then QM is simply not consistent with relativity. This is a nice illustration of the point I made earlier in this thread: it's wrong to criticize Bohmian mechanics on the basis of its violating relativity's prohibition on superluminal causation, if one's favored alternative is to reject altogether the idea of micro-physical events unfolding on a space-time stage. The fact is, *no* sharp formulation of quantum mechanics is consistent with relativity. It's not just true because Bell said it, but he did say it, and it is true... and it seems like it's time people started recognizing this.

Also, what you said about the inputs to Bell's theorem isn't correct. The inequality is in no way based on "classical physics." I challenge you to point out any place in any of Bell's papers where he brings in something from classical physics. In fact, the inequality isn't based on *any* kind of physics. It's just pure statistics (plus some assumptions about what's allowed to depend on what, i.e., a locality assumption).

 

[vanesch]

Patrick, it seems you have the esssence of a sound view here, if you will just lose the "propagating wavefront". Necessarily such a wavefront would be unphysical, since experiment has proved that the time between observations P and Q can be less than the distance between them in light units, i.e. the events showing the correlation can be spaclike.

Yes I understood that of course. What I'm saying is that from P's point of view, Q doesn't make a measurement. It is only P who makes two measurements: first on particle A and second on "pseudoobserver Q" which remains itself in a decohered superposition until P (the only true observer in the universe) observes Q. P can only start to observe Q's results (Q's entanglement with B) when Q is in the past lightcone of P after the entanglement took place at Q.

So my point is that there is not necessarily a collapse at Q when P makes his first measurement. It is only when Q is in the past lightcone of P after the entanglement with B that potentially P can observe Q's results and hence that there must be a projection.

You can ask: and what about Q ? Well, Q is a different observer, and hence lives in a different quantum observer world. So he can observe completely different things, P can never find out. P can only make measurements on Q, and then P's measurements will be coherent with other measurements P made in his history record. This is the same issue as how different people perceive the color blue. When presented with something blue, both say that it is blue because told so since they were a child. But you'll never find out if what you perceive as "blue" isn't perceived as "orange" by the other person.

As I said before, this is very strange to me too! But it is the only way I found to have peace of mind with SR and QM, the way they are formulated.

cheers,
Patrick.

 

[Rothiemurchus]

Humanino:
You need humility Rothie. I seriously doubt. You just demonstrated that you are not aware of the gigantic field of mathematics. I know some, and I am aware that is so few.

Rothie M:
I was just emphasising that I am not completely ignorant of mathematics used in physics! You are right to say it is hard for anyone to know
all mathematics .In fact Feynamn went out of his way to learn only maths he thought would be useful.

Zapper Z:
Oh no! Not one of those!

If you think you have anything authentic and valid, then please send it for publication in a peer-reviewed journal.

Rothie M:
There is no real opportunity for alternative theories on this website
that is why I suggested setting up my own.A journal is the right place though.

 

[Rothiemurchus]

Photon correlations have been determined over a distance of 10 km.
If a particle or wave of some sort traveled from one photon to another,
then perhaps at a greater distance the second photon would be absorbed by the detecting apparatus before the correlating signal reached it.I think that it is important
to keep testing these correlations over greater distances.No doubt people will.

 

[Roberth]

You are not alone - Pat

I am apparently almost alone in this . It sounds as if most people just say "well, no information (in the usual sense) is transmitted, no energy is transmitted so everything is fine. End of story. Whereas I think that a more fundamental theory would present a more clear picture of the measurement process, of the collapse of the wavefunction, etc.

But it seems that people have got so used to the weirdness of QM that it does not elicit much desire to dig deeper.

Pat

You almost said exactly the same thing that I said at the General Physics about "Speed of Gravity".

Here is an extract:

My point is this: Quantum entanglement shows non-locality, hence there is something that is not bound by the speed of light. This 'something' causes entanglement. I believe that our known "Physics" is only a subpart of a larger structure and entanglement or the Aharanov-Bohm effect are evidence of that structure.

The fact that you cannot transmit information via entanglement is always used to 'save' locality (ie. the speed of light barrier). However, it does not matter whether you can use it to send meaningful information. The fact remains that there is an action that has a physical effect which acts faster than the speed of light.

Roberth

 

[selfAdjoint]

No I keep saying that in orthodox QM there is no signal between the particles, non3e at all, let alone an FTL one. In QM the correlation is caused by the extended entangled state, which does not exist in spacetime, and so does not have anything to do with relativity or "sending". What the state "is" truly is of course problematical, but that doesn't affect the truth of this statement.

 

[Roberth]

But this is my point

No I keep saying that in orthodox QM there is no signal between the particles, non3e at all, let alone an FTL one. In QM the correlation is caused by the extended entangled state, which does not exist in spacetime, and so does not have anything to do with relativity or "sending". What the state "is" truly is of course problematical, but that doesn't affect the truth of this statement.

I am not saying that there is a 'signal' as such in the conventional way. Your comment about spacetime is exactly what I meant in this other post.

Most likely, there is a higher dimensional (5-dimensional or higher) space above Minkowsky space where symmetry considerations are observed and they act instantly. Minkowsky space is then a sub-space of this higher dimensional 'order'.

You can think of it as something like a Hawking´s wormhole, if you like (although I do not believe that it is a wormhole). The 'information of the entanglement' does not go through our spacetime but ' cuts' through it.

Now, how could one start with a more 'flesh on the bone' theory? A candidate would be a group theoretical approach and see if there is a symmetry that must be observed in order to explain the result of the spin entanglement. The problem with that is, however, that group theory is also an epistemological and not ontological approach, similarly to the major parts of QM.

Bohm at least tried to acknowledge that there is something, ie. his quantum potential. This could be in the right direction but must probably be explained from an upper-dimensional level to forecast new physics.

Roberth

 

[nrqed]

Hi Pat,

What you write here bothered me also quite a while, until I realized that collapse of the wavefunction does make sense as long as it is an observer-bounded concept. This is a viewpoint which is somewhat intermediate in between the standard interpretation and MWI. Indeed, thanks to decoherence, you cannot distinguish between a measurement that gives rise to a true collapse, and one that just "decoheres".
So if you have two entangled particles, A and B, and you have two observers, P and Q, P which observes A and Q which observes B (and we assume these observation interactions to be spacelike separated - you write everywhere timelike but I suppose you mean spacelike),

Yes, sorry about that. For some reason I was thinking "spacelike" and typed timelike throughout the post

let us then take the point of view of P.
When P observes A, this is a true observation for P. But at that point, he doesn't know anything about B or Q, so it doesn't make sense for P to talk about a collapse of the state at Q. When Q travels to P to tell him the result of his measurement, P just considers this message from Q as another measurement (P makes a measurement on Q). All this is completely local at P, and his successive measurements (with collapse) make completely sense.
Q can do exactly the same, but then of course we have different quantum discriptions according to the observers.

Very interesting, Patrick. That's the kind of ideas that Iwould like to see people discussing more, instead of just saying "well, no energy is transferred and the setup can't be used to transmit the results of a baseball game faster than the speed of light so there is no problem. End of story". I find it hard to understand how anybody could feel satisfied with the present status of QM and SR in light of Bell type experiments. Anyway, sorry for the rant...

You idea is a very very interesting one. But it brings up tricky issues...See below.

I didn't work this out, maybe one can think of a propagating collapse wavefront going out from each observer ; or one considers that there is only one true observer in the universe, namely me :-)

cheers,
Patrick.

hehehe...

Patrick added, in a later post:

What I'm saying is that from P's point of view, Q doesn't make a measurement. It is only P who makes two measurements: first on particle A and second on "pseudoobserver Q" which remains itself in a decohered superposition until P (the only true observer in the universe) observes Q. P can only start to observe Q's results (Q's entanglement with B) when Q is in the past lightcone of P after the entanglement took place at Q.

So my point is that there is not necessarily a collapse at Q when P makes his first measurement. It is only when Q is in the past lightcone of P after the entanglement with B that potentially P can observe Q's results and hence that there must be a projection.

You can ask: and what about Q ? Well, Q is a different observer, and hence lives in a different quantum observer world. So he can observe completely different things, P can never find out. P can only make measurements on Q, and then P's measurements will be coherent with other measurements P made in his history record. This is the same issue as how different people perceive the color blue. When presented with something blue, both say that it is blue because told so since they were a child. But you'll never find out if what you perceive as "blue" isn't perceived as "orange" by the other person.

As I said before, this is very strange to me too! But it is the only way I found to have peace of mind with SR and QM, the way they are formulated.

Ok, but here's a question: what is "observer Q" is a piece a paper on which the results of a polarization measurement are printed out. No human consciousness is involved there. So when P (who is human, let's say!) receives paper Q, what happens to the results printed on the paper? Would you say that the numbers on the paper are not well-defined before P reads it? It almost starts to sound like the question: if there is nobody in the forest, does a falling tree make any noise...

In any case, at least I appreciate the fact that you are struggling with these issues and trying to make sense of them, which seems to be th eexception rather than rule in the physics community.


Regards

Pat

 

[vanesch]

Would you say that the numbers on the paper are not well-defined before P reads it? It almost starts to sound like the question: if there is nobody in the forest, does a falling tree make any noise...

Well, if you take unitary evolution literally, such as MWI proponents do, then your piece of paper (and everything it potentially interacted with, so the whole universe within it's past lightcone) is in a superposition in exactly the same way as the original system was ; the "measurement" at Q is nothing else but an entanglement:

Piece of paper state |empty> (there exists 2 other states |+> and |->, when we've written respectively "+" and "-" on the paper)
System: |s0> = a |spin up> + b |spin down>

"measurement hamiltonian" gives rise to:
|spin up> x |empty> ----> |spin up> x |+>
|spin down> x |empty> ---> |spin down> x |->

so: |s0> x |empty> ----> a |spin up> x |+> + b |spin down> x |->

So the state of the paper simply entangled with the spin state, and it is only P who did the measurement with collapse:
probability |a|^2 to find a + sign and probability |b|^2 to find a - sign, and at this point, you can also say that the spin state is determined: because in the first case, the state is |spin up> x |+> ; remember that this collapse only happens when the paper arrives at P, so causality for the collapse of the (past) spin state at Q is preserved.

cheers,
Patrick.

 

[Rothiemurchus]

Vanesch:
When presented with something blue, both say that it is blue because told so since they were a child. But you'll never find out if what you perceive as "blue" isn't perceived as "orange" by the other person.

Rothie M:
Unless one day it is shown that perceiving a particular colour in the brain uses quanta of energy and that everyone's brain gets stimulated to use the same number of quanta.