Many-worlds true quantum event generator

[rodsika]

Hi, what cheap device is available where a quantum choice can be made.. for example.. particle that goes to left or right path or other similar? I'd like to experience what it is like to split myself between going to work or stay at home. According to Many World Interpretation, when I observe the device. A part of me would be entangled with the particle that goes to left, and the other part of me would be on the right particle.. and two worlds will split off and evolve separately...

How do you make or time it such that say the left particle is entangled to my decision to go to office (and actually doing it).. and the other particle (right or other configuration choices) staying at home?

Also in the present of a true quantum event generator.. would there always or automatically be a split in our parts in each of the quantum choice of the devices?

 

[Fyzix]

If some version of MWI were true, you'd be splitting non stop 24/7, so no need to conduct any such experiment if you would like to "experience the splitting"...

However, MWI is very likely not true, atleast not in it's current form so I wouldn't get attached to living like it is.

 

[JesseM]

No. We'd only split if there are quantum device choices available.

It has nothing to do with "devices", all the particles that make up your body and the world around it obey quantum laws, and all possible states for any quantum system must be manifested in the MWI.

 

[rogerl]

It has nothing to do with "devices", all the particles that make up your body and the world around it obey quantum laws, and all possible states for any quantum system must be manifested in the MWI.

Many Worlds appear silly, ain't it. But how come so many physicists believe it. How many percentage of them really believe it? 50%? 80%?

 

[JesseM]

Many Worlds appear silly, ain't it. But how come so many physicists believe it. How many percentage of them really believe it? 50%? 80%?

Why do you call it silly? Just because it's counterintuitive? At a theoretical level it seems more elegant to me, as it says that measuring devices are governed by the same laws as systems being measured, and all systems follow the same quantum laws at all time, but it doesn't require the addition of any new hidden variables as in Bohmian mechanics. Historically theoretical elegance has tended to be a better guide in physics than "common sense" intuitions about what predictions seem weird to us.

 

[rodsika]

It has nothing to do with "devices", all the particles that make up your body and the world around it obey quantum laws, and all possible states for any quantum system must be manifested in the MWI.

Hi, in a typical day, how many worlds does a single human spawn? Hundreds or billions? Also what is the smallest living thing that can create worlds? Bacteria or ants?

 

[ExecNight]

Well MWI suggests for every random event, the universe splits into available options. I think "Random Event" is the key here. Because some things can't be mathematically modeled right now doesn't mean they are random.

Actually i will go as far as saying, almost everything above atomic level can be very well mathematically modeled from the beginning of the universe. Your conciousness is a product of this material world, so considering your actions as random is absurd :)

 

[JesseM]

Hi, in a typical day, how many worlds does a single human spawn? Hundreds or billions? Also what is the smallest living thing that can create worlds? Bacteria or ants?

There aren't really clearly-differentiated "worlds" as I understand it, just a single wavefunction for the entire universe which can be seen (in the same way as any normal quantum wavefunction) as a superposition of different position states, a superposition of different momentum states, etc. How familiar are you with the standard (non-MWI) idea that every quantum system is modeled as having a single state vector which can be expressed as a sum (superposition) of eigenvectors for any observable like position or momentum? The basic idea behind the MWI is that we should use the same rules for the entire universe as the rules we use when modeling the evolution of quantum systems between measurements, that measurement itself shouldn't involve any special new rules like "wavefunction collapse".

 

[JesseM]

Well MWI suggests for every random event, the universe splits into available options. I think "Random Event" is the key here. Because some things can't be mathematically modeled right now doesn't mean they are random.

Actually i will go as far as saying, almost everything above atomic level can be very well mathematically modeled from the beginning of the universe. Your conciousness is a product of this material world, so considering your actions as random is absurd :)

But any chaotic system will exhibit sensitive dependence on initial conditions, which should mean that if you turned history back a bit and made some tiny micro change at the atomic level, then when you played history forward again with the altered initial condition, the new history would eventually start to diverge macroscopically from the original version.

 

[cgk]

Why do you call it silly? Just because it's counterintuitive? At a theoretical level it seems more elegant to me, as it says that measuring devices are governed by the same laws as systems being measured, and all systems follow the same quantum laws at all time,

I was of the impression that almost all interpretations (except maybe for the Kopenhagen one) have these features.

but it doesn't require the addition of any new hidden variables as in Bohmian mechanics.

...you mean apart from the states of all split worlds themselves? Also, I don't think the hidden variables are the problem people care about... (rather the lack theirof). But in Bohmian mechanics they again have a somewhat counterintuitive nature (pilot wave etc) and their violate locality. On the other hand, there is little reason to believe that a quantum theory interpretation should be fully local (think of EPR-type entanglement).

Historically theoretical elegance has tended to be a better guide in physics than "common sense" intuitions about what predictions seem weird to us.

While that is certainly true, I'm somewhat doubtful about MWI being called elegant. It's a far stretch.

I also wonder if really a majority of physicists believe it. If I hear about it, it's usually in the sense of a discussion about a kind of novelty thing (aka ``see, interpretations are so free, we can't even exclude the MWI on a rational basis...'')

 

[ExecNight]

But any chaotic system will exhibit sensitive dependence on initial conditions, which should mean that if you turned history back a bit and made some tiny micro change at the atomic level, then when you played history forward again with the altered initial condition, the new history would eventually start to diverge macroscopically from the original version.

Yes but for the butterfly effect, you first need to send a butterfly back in time. That's not possible, so there goes the chaos theory :)

Every initial condition starts from a single condition in our universe. These initial conditions are one, so every outcome can be mathematically modeled. Including this message you are reading right now.

 

[JesseM]

I was of the impression that almost all interpretations (except maybe for the Kopenhagen one) have these features.

Copenhagen (or 'shut up and calculate', which also involves wavefunction collapse) is the default one that all other interpretations want to argue against, I think. And from what I understand the only alternative interpretations that are mathematically well-defined and taken seriously by a lot of physicists are variants of the MWI (including decoherent histories) or variants of Bohm's interpretation, other alternatives like the transactional interpretation are mostly just conceptual and don't have any clear mathematical definition.

...you mean apart from the states of all split worlds themselves?

Typically a hidden variable is defined as any information about the state of a system beyond what's in the wavefunction, the MWI is understood not to have anything but a single universal wavefunction so it doesn't have hidden variables.

Also, I don't think the hidden variables are the problem people care about... (rather the lack theirof).

But I was talking about theoretical elegance--a theory that doesn't contain extra hidden variables is simpler at a theoretical level than one that doesn't, even if it's more complicated in terms of the number of real-world entities are supposed to exist.

But in Bohmian mechanics they again have a somewhat counterintuitive nature (pilot wave etc) and their violate locality. On the other hand, there is little reason to believe that a quantum theory interpretation should be fully local (think of EPR-type entanglement).

Well, MWI advocates do argue that their interpretation allows locality to be restored, since Bell assumed in his proof that each measurement would have a unique outcome but this is obviously no longer true in the MWI.

While that is certainly true, I'm somewhat doubtful about MWI being called elegant. It's a far stretch.

Again, just at the theoretical level of equations and such, not in terms of predictions about what exists in the world. But as I said history has tended to show that theoretical elegance is a better guide than trying to minimize the number of entities that exist in the real world, for example if you cared about minimizing the number of real-world entities you'd have been led to favor the view that our galaxy was an isolated "island universe" surrounded by empty space over the view that it's just one of a vast number of galaxies (perhaps infinite) whose existence have very little effects on our lives on Earth.

I also wonder if really a majority of physicists believe it. If I hear about it, it's usually in the sense of a discussion about a kind of novelty thing (aka ``see, interpretations are so free, we can't even exclude the MWI on a rational basis...'')

I've often seen physicists express the view that it's the simplest theoretically, but remain agnostic about whether the other terms in the universal superposition really "exist" in exactly the same sense we do (see Stephen Hawking's comments in the last paragraph of the 'Reception' section here for example)

 

[JesseM]

Yes but for the butterfly effect, you first need to send a butterfly back in time. That's not possible, so there goes the chaos theory :)

Every initial condition starts from a single condition in our universe. These initial conditions are one, so every outcome can be mathematically modeled. Including this message you are reading right now.

But QM only allows you to model a wavefunction, which assigns different amplitudes to different position/momentum states in a giant superposition, but doesn't pick one out as the "real" state. And your original comment was about the MWI, was it not? Do you disagree that in the context of the MWI, starting from a system in a specific position state, the future evolution would lead to a superposition of different position states for the particles, and that small early differences in particle positions for different elements of the superposition should later lead (via the butterfly effect) to bigger differences at the macro-scale for different terms in the superposition?

 

[ExecNight]

But QM only allows you to model a wavefunction, which assigns different amplitudes to different position/momentum states in a giant superposition, but doesn't pick one out as the "real" state. And your original comment was about the MWI, was it not? Do you disagree that in the context of the MWI, starting from a system in a specific position state, the future evolution would lead to a superposition of different position states for the particles, and that small early differences in particle positions for different elements of the superposition should later lead (via the butterfly effect) to bigger differences at the macro-scale for different terms in the superposition?

Like i said, everything above atomic level can be mathematically modeled. How is wavefunction relevant here? Yes well, we can't calculate exact positions of particles and so use probabilities.

Also yes, these probabilities create a superposition. And no real state is picked, true. Can you be more specific how does any of this creates a butterfly effect? In the sense of being a random and unexpected event in the mathematical model of the universe.

 

[Demystifier]

At a theoretical level it seems more elegant to me, as it says that measuring devices are governed by the same laws as systems being measured, and all systems follow the same quantum laws at all time, but it doesn't require the addition of any new hidden variables as in Bohmian mechanics. Historically theoretical elegance has tended to be a better guide in physics than "common sense" intuitions about what predictions seem weird to us.

Even though MWI does not require additional variables, it does require additional postulates (and there is no consensus on - which ones) in order to explain/derive the Born rule. So it is not really simpler than Bohmian mechanics.

 

[Dmitry67]

I would rather say, there is no acceptable definition of Born rule in MWI, because Born rule talks about the propabilities while MWI is deterministic.

But there is at least some hope that the 'apparent probability' would somehow 'emerge' from the behavior of the complex (and may be conscious) systems. So there is a hope that QM as we know it is complete already (or course, without gravity/very high energy stuff)

 

[Fyzix]

Dmitry, you know that your consciousness hypothesis has no foundation, so saying that it gives rise to hope that the current MWI is correct, is a little bit misleading.

I can also say that there is hope that there will emerge a completely local and deterministic quantum interpretation that will have no problem with Bells Theorem.
Does this statement give hope to this?

Besides MWI also got problems with relativity (check Jeffrey A Barrett)

 

[Dmitry67]

1. My hope has some foundation. For example, most of the scientific community agree on Block Time, hence there is nothing special in the moment of time called "NOW". The "NOW" phenomenon is not explained by physics, but is moved the the realm of the yet-to be-explained consciousness.

2. When I google
Jeffrey A Barrett mwi relativity
I find this thread and few links to Barrett works
what exactly are you talking about
Could you provide a description of that "problem"?

 

[rodsika]

My interests in the Many World was brought about by this movie I just watched called Source Code. If you still haven't seen it. Go watch it this sunday. It's incredibly good and very poignant. The movie is about Many World Interpretation. A train exploded in the morning. Then hours later, a man consciousness was sent back in time into a parallel Many World to determine the name of the bomb detonator. He did it several times.. visiting different Many World branches in the process. Of course I won't tell you the end to avoid spoiler but if you watch it, it will surely spark you interests in Many World Interpreation and combination with General Relativity as well as Consciousness Reseach. There is a possibility the movie may even be true.. it's because consciousness is still*a mystery. What if consciousness can be sent across Many World branches using some help from GR. That is what the movie is all about. It can happen. Give comment about Many Worlds after after you watch it!

 

[ExecNight]

Your conciousness isn't something magical. Its electrical and chemical reactions to stimuli. Therefore while the stimuli remains the same, it will stay where it is. Plain and simple.

Can anyone please tell me about something in this universe that is purely random and is not a product of the big bang(initial condition).

I can't comprehend this thought process. For examples sake; How come weather activity is random? It is not, its just very complex and too many variables are in effect (Butterfly Effect) it doesn't mean its random.. It just means we can't calculate it.

Now this belongs to the Quantum Forum, as the question is, like i asked before how superposition and wavefunction probability calculations affect the macro world. Do they create randomness? How?

 

[JesseM]

Like i said, everything above atomic level can be mathematically modeled.

And like I said, a chaotic system cannot be precisely predicted without knowledge of the exact state of the "atomic level".

Also yes, these probabilities create a superposition. And no real state is picked, true. Can you be more specific how does any of this creates a butterfly effect? In the sense of being a random and unexpected event in the mathematical model of the universe.

Are we talking in terms of the MWI or not? If we are, do you disagree that if we have a model of, say, weather patterns, then if we run the model twice with slight differences "at the atomic level" the large-scale behavior of the weather patterns will eventually be quite different on the two runs? Do you disagree that in the MWI these slight difference "at the atomic level" would actually be manifested in different terms of the superposition (different 'worlds')?

 

[ExecNight]

And like I said, a chaotic system cannot be precisely predicted without knowledge of the exact state of the "atomic level".

Being unable to predict the system doesn't mean the system is random. It just means we don't have the variables and the means. There is no Chaos :)

Are we talking in terms of the MWI or not? If we are, do you disagree that if we have a model of, say, weather patterns, then if we run the model twice with slight differences "at the atomic level" the large-scale behavior of the weather patterns will eventually be quite different on the two runs? Do you disagree that in the MWI these slight difference "at the atomic level" would actually be manifested in different terms of the superposition (different 'worlds')?

I disagree with MWI because what i am trying to say is, no matter how many times you start the same system with same inital condition. It will always end up giving you the same result. Because i suggest that in this system there are no random events. So while there won't be any difference at all no different world will spawn.

 

[JesseM]

Being unable to predict the system doesn't mean the system is random. It just means we don't have the variables and the means. There is no Chaos :)

Chaos has nothing to do with randomness and I never said it did, so why do you bring it up?

I disagree with MWI because what i am trying to say is, no matter how many times you start the same system with same inital condition. It will always end up giving you the same result.

The MWI is deterministic, but what is evolving deterministically is a wavefunction which includes a superposition of multiple position states. Do you disagree that if we start a quantum system with the same initial conditions multiple times, then the wavefunction will evolve into a superposition of different position states, even if the initial state was a position eigenstate where every particle had a precise position to begin with? Do you disagree that if the system is a chaotic one, then even if the different elements of the superposition had only small "microscopic" differences a short time after the initial state, after a longer time the different elements of the superposition would inevitably start to have sizeable macroscopic differences due to the butterfly effect?

 

[ExecNight]

The MWI is deterministic, but what is evolving deterministically is a wavefunction which includes a superposition of multiple position states. Do you disagree that if we start a quantum system with the same initial conditions multiple times, then the wavefunction will evolve into a superposition of different position states, even if the initial state was a position eigenstate where every particle had a precise position to begin with?

Yes all agreed.

Do you disagree that if the system is a chaotic one, then even if the different elements of the superposition had only small "microscopic" differences a short time after the initial state, after a longer time the different elements of the superposition would inevitably start to have sizeable macroscopic differences due to the butterfly effect?

This is the point we disagree it seems. So i should ask you, for QM to be effective in Macro World the particles we are talking about need to be in a non-isolated state. And if i got this all correct if there is no isolation the wavefunction collapses.

When the wavefunction collapses there is only one observable outcome left in the Macro World as a particle. This is what we observe.

So for discussion's sake, you claim that this observation comes from a random event. I don't know if this is proven. Is it? Or the particle we observe is exactly what we would expect how a particle behave instead of a wavefunction would in the first place?

 

[Dadface]

Is there any empirical evidence that can give the MWI any credence?

 

[JesseM]

This is the point we disagree it seems.

So you agree that the system will be in a superposition of different position states where the position of individual particles differ slightly, but you disagree that the butterfly effect implies that in a chaotic system, if you run it forward from different states where the position of individual particles differs slightly, these small initial differences lead to large differences later on?

So i should ask you, for QM to be effective in Macro World the particles we are talking about need to be in a non-isolated state. And if i got this all correct if there is no isolation the wavefunction collapses.

Huh? Not in the MWI, the whole point is it rules out the idea of "collapse" under any circumstances. And with no collapse, all macro systems would be like the Schroedinger's cat thought-experiment (where we imagine an entire cat can be kept totally isolated from the outside environment until the box it's in is opened), in giant superpositions of macroscopically different states (like "alive cat" and "dead cat").

When the wavefunction collapses there is only one observable outcome left in the Macro World as a particle. This is what we observe.

You're talking about the Copenhagen interpretation, not the MWI. But we can still discuss the issue of chaotic systems in this context, as long as we are willing to have a thought-experiment like Schroedinger's cat where a large macroscopic system can remain totally isolated for a while, until it is finally observed and "collapses". My assertion would be that if the cat's brain is sufficiently chaotic for sensitive dependence on initial conditions to apply (plausible given how many nonlinear effects there are in brains), then even if the experiment is not specifically designed so the cat lives or dies based on the decay of a radioactive particle, it would still be true that if enough time is left between the moment the cat is sealed in the box and the moment it's opened, then at the moment before the box is opened and the cat's wavefunction is collapsed, according to QM the cat would be in a superposition of macroscopically distinct states, like "sitting in North corner", "sitting in South corner", "walking in the middle of the box", "sleeping in the middle", etc.

So for discussion's sake, you claim that this observation comes from a random event.

What "observation"? I said nothing about observation, and again there is no concept that anything special happens upon observation in the MWI.

 

[rodsika]

There aren't really clearly-differentiated "worlds" as I understand it, just a single wavefunction for the entire universe which can be seen (in the same way as any normal quantum wavefunction) as a superposition of different position states, a superposition of different momentum states, etc. How familiar are you with the standard (non-MWI) idea that every quantum system is modeled as having a single state vector which can be expressed as a sum (superposition) of eigenvectors for any observable like position or momentum? The basic idea behind the MWI is that we should use the same rules for the entire universe as the rules we use when modeling the evolution of quantum systems between measurements, that measurement itself shouldn't involve any special new rules like "wavefunction collapse".

Are you saying that this idea of worlds splitting whenever there are quantum choices are wrong? No version of Many World that uses this concept? I was reading a book called "Schroedinger Rabbits: The Many worlds of quantum" and I came across these passages:

"According to Everett, you see a single version of reality because the countless divergent versions of patterns of neuron firings in your brain very rapidly cease to affect one another, just as 2,345- Angstrom calculations in the computer described above are affected only by light very close to that particular wavelength. Other versions of reality - which of course include other versions of your brain - quicly become imperceptible to your own version.

However, thanks to de Witt, the false image of universes actually splitting quickly became associated with many-worlds. Famously, John Wheeler ultimately rejected his pupil Everett's theory has having too much conceptual baggage. Perhaps the notion of the universe repeatedly splitting was the major part of that baggage."

 

[JesseM]

Are you saying that this idea of worlds splitting whenever there are quantum choices are wrong? No version of Many World that uses this concept?

I wouldn't say "no version" involves such a notion of splitting worlds, but I don't think most MWI advocates imagine any clearly-defined distinct "worlds", talking about worlds is usually more like an approximate way of talking about the fact that the wavefunction contains a superposition of macroscopically different states. See for example the Stanford Encyclopedia article on MWI which says:

The MWI consists of two parts:

A mathematical theory which yields evolution in time of the quantum state of the (single) Universe.
A prescription which sets up a correspondence between the quantum state of the Universe and our experiences.
Part (i) is essentially summarized by the Schrödinger equation or its relativistic generalization. It is a rigorous mathematical theory and is not problematic philosophically. Part (ii) involves "our experiences" which do not have a rigorous definition.

...

The concept of "world" in the MWI belongs to part (ii) of the theory, i.e., it is not a rigorously defined mathematical entity, but a term defined by us (sentient beings) in describing our experience. When we refer to the "definite classically described state" of, say, a cat, it means that the position and the state (alive, dead, smiling, etc.) of the cat is maximally specified according to our ability to distinguish between the alternatives and that this specification corresponds to a classical picture, e.g., no superpositions of dead and alive cats are allowed in a single world.

On the other hand, DeWitt did seem to have a more technical definition of a "world" in terms of a choosing a preferred basis (like the position basis) and then considering each possible eigenstate of that basis to be a distinct "world" even if the differences were microscopic--see this section on DeWitt's version from another Stanford Encyclopedia article on variants of Everett's interpretation. Note though the section on the difficulty of choosing which basis should be the preferred one (starting with the paragraph that begins "The preferred basis problem is arguably a more serious problem for a splitting-worlds reading of Everett").

 

[rodsika]

I wouldn't say "no version" involves such a notion of splitting worlds, but I don't think most MWI advocates imagine any clearly-defined distinct "worlds", talking about worlds is usually more like an approximate way of talking about the fact that the wavefunction contains a superposition of macroscopically different states. See for example the Stanford Encyclopedia article on MWI which says:

On the other hand, DeWitt did seem to have a more technical definition of a "world" in terms of a choosing a preferred basis (like the position basis) and then considering each possible eigenstate of that basis to be a distinct "world" even if the differences were microscopic--see this section on DeWitt's version from another Stanford Encyclopedia article on variants of Everett's interpretation. Note though the section on the difficulty of choosing which basis should be the preferred one (starting with the paragraph that begins "The preferred basis problem is arguably a more serious problem for a splitting-worlds reading of Everett").

About this Prefered Basis problem, the question is why we get observables like position, momentum, spin and related. Why. What other observables can we get from Hilbert Space.. are you talking about observables like position-size, momentum-color, etc as the weird combination of observables that can be acquired (in any combination)*in*Hilbert Space? Pls. give other valid examples of what weird observables possible which we don't get in our world but available in Hilbert Space.
*
But then reading about preferred basis problem. I came across it in*Max*Tegmark article that says Decoherence has solved why things appear*classical, which I presumed is related to the preferred basis problem?* (see the thread "Predictivity Sieves questions" which*came as a result of my research in your preferred basis connection)*Can you share a very good site that introduced the preferred basis problem? Thanks.

 

[JesseM]

About this Prefered Basis problem, the question is why we get observables like position, momentum, spin and related. Why. What other observables can we get from Hilbert Space.

No, the point is that some observables like position and momentum don't commute, so you have to decide whether the position basis or the momentum basis is to be "preferred" in order to break down the universal state vector into a set of eigenstates which you call "worlds" in DeWitt's version of the MWI.

But then reading about preferred basis problem. I came across it in*Max*Tegmark article that says Decoherence has solved why things appear*classical, which I presumed is related to the preferred basis problem?* (see the thread "Predictivity Sieves questions" which*came as a result of my research in your preferred basis connection)*Can you share a very good site that introduced the preferred basis problem? Thanks.

You could take a look at this thread, and there's some discussion of the preferred basis problem starting on p. 9 of this paper. But you can find more references just by typing the words "preferred basis everett" (not in quotes) into google scholar or google books.

 

[JDude13]

Hi, what cheap device is available where a quantum choice can be made..

A flourescent light flickering is performing a quantum experiment.
However most things are quantum experiments. There could be minute changes in the brightness of an incandescant bulb which are too small to differentiate between.

Any electronic device which generates a random number can be dependant on a few if not one quantum mechanical factor.

 

[rodsika]

No, the point is that some observables like position and momentum don't commute, so you have to decide whether the position basis or the momentum basis is to be "preferred" in order to break down the universal state vector into a set of eigenstates which you call "worlds" in DeWitt's version of the MWI.
You could take a look at this thread, and there's some discussion of the preferred basis problem starting on p. 9 of this paper. But you can find more references just by typing the words "preferred basis everett" (not in quotes) into google scholar or google books.

I've read the threads you mentioned. But Collin Bruce seems to be describing it differently in Schroedinger Rabbit. He seemed to be saying that the problem of preferred basis is how to map the Hilbert space to the geometry of our own space-time. What has this got to do with momentum? Anyway he said (he was describing the Hilbert Space):

"... How to decide which way to draw the axes needed? Why should the directions of the various axes we chose correspond in any way to the directions of our particular three-dimensional space?

The matter gets even more puzzling if we take into account that, according to the mathematics, half the axes respresent imaginary numbers - numbers like the square root of minus one. This problem of deciding a preferred axes is called the problem of the preferred basis, and physicists wrangle fiercely over whether a unique preferred basis to map Hilbert space to the geometry of our own space-time arises naturally from the mathematics, or must be put in by hand"

Now pls. connect what he is saying to what you are saying above that "No, the point is that some observables like position and momentum don't commute, so you have to decide whether the position basis or the momentum basis is to be "preferred" in order to break down the universal state vector into a set of eigenstates which you call "worlds" in DeWitt's version of the MWI."

What do you mean by commute and what has this got to do with mapping Hilbert space to the geometry of our own space-time? I have actually studied about preferred basis problem years before and I thought it was just about why classical states are preferred (which was done alleged by Environmental Superselection). Many thanks.

 

[JesseM]

I've read the threads you mentioned. But Collin Bruce seems to be describing it differently in Schroedinger Rabbit. He seemed to be saying that the problem of preferred basis is how to map the Hilbert space to the geometry of our own space-time. What has this got to do with momentum? Anyway he said (he was describing the Hilbert Space):

"... How to decide which way to draw the axes needed? Why should the directions of the various axes we chose correspond in any way to the directions of our particular three-dimensional space?

Momentum and position eigenstates are axes in Hilbert space, each one forming a different "basis". It's like how in 3D space you can have coordinate system #1 made up of x-y-z axes, as well as coordinate system #2 made up of x'-y'-z' axes pointing in different directions, and you can use either coordinate system to describe points and vectors in that space.

What do you mean by commute and what has this got to do with mapping Hilbert space to the geometry of our own space-time?

If two observables commute (like position and spin), then one meaning of that is that in terms of the Hilbert space, you can find a set of basis vectors such that each vector is an eigenvector of both those observables. If they don't commute, then an eigenvector of one will be a superposition of different eigenvectors of the other, and vice versa. So, another way of stating the preferred basis problem is that you have to pick a complete set of commuting observables as your basis, if the vectors are position eigenvectors (definite position states) then they won't be momentum eigenvectors (each vector will be a superposition of different momentum states) and vice versa.

A more intuitive physical meaning of commuting vs. not commuting is that that if two observables commute, you can measure one without disturbing the value of the other--if you measure position, then immediately after that (a negligible time interval) measure spin, then immediately after that measure position again, then if the time between measurements is arbitrarily small the second position measurement will be arbitrarily close to the first one (in the limit as the time goes to infinity the change in position goes to zero). But if you measure position, then immediately measure momentum, then immediately measure position again, then no matter how small the time intervals the probability distribution for position will be significantly changed, by an amount which can be calculated from the position/momentum uncertainty relation.

 

[Dadface]

Let me rephrase my earlier question.Is there any experimental/observational evidence that supports these interpretations?

 

[Dmitry67]

My understanding is that to understand how world looks to YOU you break the symmetry and chose there preferred basic associated with YOU (your brain, measurement device), but there is no "objective" way to chose one basis or another. And that moment you fix the basic and frame of reference. I will check the links provided by JesseM to verify, to what extent I was right or wrong.