What will happen when we have a Theory of Everything?

[Varon]

What does |u>+|v> mean (in the mainstream view)?

1. |u>+|v> means that the there are (at least) two copies of the system, one of which is in state |u> and the other in state |v>?

2. 2. |u>+|v> doesn't actually represent the properties of the system, but is just a part of a mathematical formalism that can be used to calculate probabilities of possible results of experiments.

3. What else?

 

[SpectraCat]

What does |u>+|v> mean (in the mainstream view)?

1. |u>+|v> means that the there are (at least) two copies of the system, one of which is in state |u> and the other in state |v>?

2. 2. |u>+|v> doesn't actually represent the properties of the system, but is just a part of a mathematical formalism that can be used to calculate probabilities of possible results of experiments.

3. What else?

1. I don't think it ever means that
2. I wouldn't express it that way, but I guess that is correct
3. Usually that notation is used to express that a wavefunction is in a superposition of those two states.

 

[Varon]

1. I don't think it ever means that
2. I wouldn't express it that way, but I guess that is correct
3. Usually that notation is used to express that a wavefunction is in a superposition of those two states.

But what does it really mean that it is in superposition of those two states? For you, does each state vector describes all the properties of the system it represents?

 

[SpectraCat]

But what does it really mean that it is in superposition of those two states? For you, does each state vector describes all the properties of the system it represents?

Ah .. you want interpretation. I cannot supply one beyond what you already know .. that the superposition represents a mathematical description of how that system sill behave when measurements are performed on it.

 

[Varon]

Ah .. you want interpretation. I cannot supply one beyond what you already know .. that the superposition represents a mathematical description of how that system sill behave when measurements are performed on it.

Fredrik is saying that Copenhagen is really Many Worlds in disguised or at least Statistical Interpretation and nothing else. See his other thread https://www.physicsforums.com/showthread.php?t=500698&page=3 . Hope others who see a flaw in Fredrik thinking can comment and elaborate.

 

[Fredrik]

The only entirely uncontroversial thing that can be said about wavefunctions/state vectors is that they represent statistical properties of ensembles of systems that have been subjected to the same preparation procedure. Most interpretations say that they also represent something else.

As for the CI, it's hard to find two people who define it the same way, but most people insist that it includes the assumption (1) that the state vector is a complete description of all properties of the system. In the other thread, I argue that this assumption makes many worlds unavoidable. I would say that this makes all flavors of the CI that include the assumption mentioned above and the assumption (2) that there's only one world logically inconsistent.

I would never define the CI as a many-worlds interpretation, so rather than just dropping (2) and say that the CI is many-worlds in disguise, I would drop both (1) and (2) and say that the CI is the statistical/ensemble interpretation in disguise.

 

[Varon]

The only entirely uncontroversial thing that can be said about wavefunctions/state vectors is that they represent statistical properties of ensembles of systems that have been subjected to the same preparation procedure. Most interpretations say that they also represent something else.

As for the CI, it's hard to find two people who define it the same way, but most people insist that it includes the assumption (1) that the state vector is a complete description of all properties of the system. In the other thread, I argue that this assumption makes many worlds unavoidable. I would say that this makes all flavors of the CI that include the assumption mentioned above and the assumption (2) that there's only one world logically inconsistent.

I would never define the CI as a many-worlds interpretation, so rather than just dropping (2) and say that the CI is many-worlds in disguise, I would drop both (1) and (2) and say that the CI is the statistical/ensemble interpretation in disguise.

By believing in the statistical/ensemble interpretation. It's just being pragmatist, meaning you just care what is QM and how experiments results can be predicted by the theory. You don't care the rest or its ontology. So this statistical/ensemble interpretation is just a "shut up and calculate" thing. You may as well state you hold to this "shut up and calculate" approach.

 

[Fredrik]

By believing in the statistical/ensemble interpretation. It's just being pragmatist, meaning you just care what is QM and how experiments results can be predicted by the theory. You don't care the rest or its ontology. So this statistical/ensemble interpretation is just a "shut up and calculate" thing. You may as well state you hold to this "shut up and calculate" approach.

Don't tell me what I care about. You clearly don't know. "Shut up and calculate" is an attitude, not an interpretation. I don't share that attitude at all.

 

[Hurkyl]

What does |u>+|v> mean (in the mainstream view)?

One thing in particular is that + is an operation on kets, but is very much not an operation on states.

For example, in a typical way to use kets to describe spin states, all four of the kets $\pm|z-\rangle$ and $\pm i |z-\rangle$ represent the same state: spin down along the z-axis. However:

• $|z+\rangle + |z-\rangle$ is a ket representing spin up along the x-axis
• $|z+\rangle + i|z-\rangle$ is a ket representing spin up along the y-axis
• $|z+\rangle - |z-\rangle$ is a ket representing spin down along the x-axis
• $|z+\rangle - i|z-\rangle$ is a ket representing spin down along the y-axis

 

[Varon]

Don't tell me what I care about. You clearly don't know. "Shut up and calculate" is an attitude, not an interpretation. I don't share that attitude at all.

After spending many hours reading your messages in many threads months apart. I think what you are trying to say is that if wave function describes single system, it's Many Worlds. If multiple system, it's Ensemble Interpretation.

However I have problem understanding about single system with no Many worlds. In one buckyball at a time double slit experiment. What happens if you are the buckyball and only one experimental run is set up. Would you pass thru the left or right slit randomly or would you be pushed by a quantum potential force or would you become like a ghost passing thru both slits?

You know why Bohr, Schroedinger, von Neumman, Dirac, Heisenberg, Pauli, etc. didn't push for the statistical interpretation. Because they knew that someday we have to understand what went on in single system. So they just went straight to the problem. They had one thing in common. They were all Nobel Prize winners. They have amazing insight that can see far into the future. Supposed you Fredrik were the founder of quantum mechanics back in the 1920 and you emphasized on the statistical interpretation. Maybe it's sufficient for a century. Someday. People would still need to start to try to understand what went on in individual system and instead of 2020 as the year we discovered how it works. It would be year 2100 had you started us on the path of the ensemble back in 1920. Our quantum grandfathers were not Nobel Prize winners for nothing. They have amazing insight. Here in this paragraph I defended why QM based on a single system is justifiable.

 

[Varon]

One thing in particular is that + is an operation on kets, but is very much not an operation on states.

For example, in a typical way to use kets to describe spin states, all four of the kets $\pm|z-\rangle$ and $\pm i |z-\rangle$ represent the same state: spin down along the z-axis. However:

• $|z+\rangle + |z-\rangle$ is a ket representing spin up along the x-axis
• $|z+\rangle + i|z-\rangle$ is a ket representing spin up along the y-axis
• $|z+\rangle - |z-\rangle$ is a ket representing spin down along the x-axis
• $|z+\rangle - i|z-\rangle$ is a ket representing spin down along the y-axis

So how do you interpret them?

1. |u>+|v> means that the there are (at least) two copies of the system, one of which is in state |u> and the other in state |v>?

2. 2. |u>+|v> doesn't actually represent the properties of the system, but is just a part of a mathematical formalism that can be used to calculate probabilities of possible results of experiments.

3. What else do you have in mind that is different from the above two?

 

[kith]

Just to add fuel to the flames of your attempt to understand quantum mechanical superpositions: you seem to approach them always in a fixed basis, so you implicitly have chosen what observable you will measure. If you allow for arbitrary measurements, every quantum mechanical state is a superposition. Namely in the basis formed by the eigenstates of the corresponding observable.

 

[Hurkyl]

So how do you interpret them?

1. |u>+|v> means that the there are (at least) two copies of the system, one of which is in state |u> and the other in state |v>?

2. 2. |u>+|v> doesn't actually represent the properties of the system, but is just a part of a mathematical formalism that can be used to calculate probabilities of possible results of experiments.

3. What else do you have in mind that is different from the above two?

Your cases #1 and #2 seem to imply a desire to think of the state described by |u>+|v> in terms of the states described by |u> and by |v>. (well, #1 is explicit in its desire)

So it follows I interpret them as #3, where what I have in mind is pretty much any interpretation of quantum mechanics I have ever encountered.

 

[Fredrik]

However I have problem understanding about single system with no Many worlds. In one buckyball at a time double slit experiment. What happens if you are the buckyball and only one experimental run is set up. Would you pass thru the left or right slit randomly or would you be pushed by a quantum potential force or would you become like a ghost passing thru both slits?

QM doesn't answer that. Some interpretations do, but there's no reason to think any of them can supply the right answer.

 

[Varon]

Your cases #1 and #2 seem to imply a desire to think of the state described by |u>+|v> in terms of the states described by |u> and by |v>. (well, #1 is explicit in its desire)

So it follows I interpret them as #3, where what I have in mind is pretty much any interpretation of quantum mechanics I have ever encountered.

But according to Fredrik (I got those two statements from him). Quantum Mechanics only produce those two possibilities. Either Many Worlds or Ensemble Interpretation. Meaning if QM describes single system, it's Many worlds, if ensemble. Then statistical (ensemble) interpretation. The rest are artificial and vague and inconsistent. What do you think?

 

[Hurkyl]

But according to Fredrik (I got those two statements from him). Quantum Mechanics only produce those two possibilities.

You sure you didn't misunderstand? What you state as #1 doesn't resemble any interpretation I know. And while I can imagine reasonable positions being described by #2, the position I think you are actually describing is not one.

 

[Varon]

You sure you didn't misunderstand? What you state as #1 doesn't resemble any interpretation I know. And while I can imagine reasonable positions being described by #2, the position I think you are actually describing is not one.

I was reading Fredrik messages over the past few months to try to understand his mind. Then I came across the following:

Someone wrote him "In double slit. The particle never enter both slits as in Many Worlds.. but they are just possibilities. So in von Neumann Interpretation, Macroscopic superposition means every state just exists as possibilities.."

and Fredrik (Aka Wolverine) answered:

"I don't think it makes sense to say that the components of a superposition "exist only as possibilities" without explaining what that means. I only see two things that it can mean: 1. |u>+|v> means that the there are (at least) two copies of the system, one of which is in state |u> and the other in state |v>. 2. |u>+|v> doesn't actually represent the properties of the system, but is just a part of a mathematical formalism that can be used to calculate probabilities of possible results of experiments.

The first option is some kind of MWI, regardless of whether von Neumann thought of it in those terms or not."

So Hurkyl, what do you think? What do you think is wrong with Fredrik statement?

 

[Chopin]

Just to add fuel to the flames of your attempt to understand quantum mechanical superpositions: you seem to approach them always in a fixed basis, so you implicitly have chosen what observable you will measure. If you allow for arbitrary measurements, every quantum mechanical state is a superposition. Namely in the basis formed by the eigenstates of the corresponding observable.

Varon, having seen a few of the threads you've started to try to understand quantum superposition, I think that thinking about kith's suggestion may help you. Understanding the fact that even a pure eigenstate can be regarded as a superposition is a tricky concept, but once you get it, you can see that a superposition isn't really as mysterious a concept as it sounds.

An easy example is light polarization. If you measure light along the horizontal and vertical axes, you get a two-state system. That is, light can either be horizontally polarized, vertically polarized, or a superposition of the two. However, you can also measure light along a 45 degree axis--either +45 degrees, or -45 degrees. These two directions also form a perpendicular set, just like the horizontal/vertical set.

Understanding how to project a state into these two bases gives a lot of insight into QM. For instance, say that you measure a photon and it's horizontally polarized. We'll call that state $|H\rangle$. Now, if you try to measure it again in the horizontal direction, you'll have a 100% chance of it being horizontal, and a 0% chance of it being vertical. We say that horizontal and vertical measurements are "orthogonal".

Now, if you take that same horizontal photon and measure it in the +45/-45 degree system, you'll find that it has exactly a 50% chance of being +45, and 50% chance of being -45. That is, you can say that $|H\rangle = \frac{1}{2}|+45\rangle + \frac{1}{2}|-45\rangle$. In other words, the "pure" state of "horizontally polarized" can just as easily be considered a superposition of two other states, "+45 polarized" and "-45 polarized". The reverse is also true--a "+45 polarized" photon can be considered to be an equal superposition of "horizontally polarized" and "vertically polarized".

This is just like looking at a unit vector that is straight along the X axis--its coordinates will be $(1,0)$. This vector might seem "purer" in some way than a diagonal vector like $(\frac{\sqrt 2}{2},\frac{\sqrt 2}{2})$ , but there's really no difference. If you take that diagonal vector, and interpret it in a coordinate system that is at a 45 degree angle to the first one, then all of a sudden the vector's coordinates are $(1,0)$ again. So whether or not a state is a superposition is just a function of the coordinate system that you look at it in--there's actually nothing special about the state itself.

 

[Hurkyl]

So Hurkyl, what do you think? What do you think is wrong with Fredrik statement?

I think the most probable situation is that you discounted the importance of some bit of context and left it out of your description. e.g. I would think his #1 would be eminently reasonable if we first assumed {|u>, |v>} was some sort of pointer basis and the state would promptly decohere.

But taken literally and on its own, I think it is misleading at best.

 

[Fredrik]

1. |u>+|v> means that the there are (at least) two copies of the system, one of which is in state |u> and the other in state |v>?

2. 2. |u>+|v> doesn't actually represent the properties of the system, but is just a part of a mathematical formalism that can be used to calculate probabilities of possible results of experiments.

I was quite surprised to see that this was an exact quote from one of my posts. Here. I didn't recognize it when I saw it in this thread. I think it requires some clarification.

I was talking about the two possible answers to the question "Does a state vector represent all the properties of a single system?" Obviously, there are only two answers: yes and no. I've been arguing that "yes" implies many worlds. This is the most recent version of the argument. Item #1 in that quote was an attempt to explain the significance of a superposition in the context of a many-worlds interpretation.

I have also been arguing that "no" defines the statistical/ensemble/Copenhagen interpretation. (In posts 50-55 in the same thread, I was arguing that the CI is either nonsense, or the SI in disguise, depending on which of the many definitions we choose). Item #2 in that quote was an attempt to explain the significance of a superposition in the context of the statistical interpretation.

I could probably have worded both #1 and #2 better. The wording of #2 was motivated by the fact that if state vectors don't represent all the properties of single systems, and just represent all the statistical properties of an ensemble of identically prepared systems, then QM can't be said to describe reality at all. It's just a set of rules that tells us how to calculate probabilities of possible results of experiments.

 

[Fredrik]

I think the most probable situation is that you discounted the importance of some bit of context and left it out of your description. e.g. I would think his #1 would be eminently reasonable if we first assumed {|u>, |v>} was some sort of pointer basis and the state would promptly decohere.

Looks like that was actually my fault. I made some comments about that sort of thing in that thread, but not in that post.

 

[Varon]

Varon, having seen a few of the threads you've started to try to understand quantum superposition, I think that thinking about kith's suggestion may help you. Understanding the fact that even a pure eigenstate can be regarded as a superposition is a tricky concept, but once you get it, you can see that a superposition isn't really as mysterious a concept as it sounds.

An easy example is light polarization. If you measure light along the horizontal and vertical axes, you get a two-state system. That is, light can either be horizontally polarized, vertically polarized, or a superposition of the two. However, you can also measure light along a 45 degree axis--either +45 degrees, or -45 degrees. These two directions also form a perpendicular set, just like the horizontal/vertical set.

Understanding how to project a state into these two bases gives a lot of insight into QM. For instance, say that you measure a photon and it's horizontally polarized. We'll call that state $|H\rangle$. Now, if you try to measure it again in the horizontal direction, you'll have a 100% chance of it being horizontal, and a 0% chance of it being vertical. We say that horizontal and vertical measurements are "orthogonal".

Now, if you take that same horizontal photon and measure it in the +45/-45 degree system, you'll find that it has exactly a 50% chance of being +45, and 50% chance of being -45. That is, you can say that $|H\rangle = \frac{1}{2}|+45\rangle + \frac{1}{2}|-45\rangle$. In other words, the "pure" state of "horizontally polarized" can just as easily be considered a superposition of two other states, "+45 polarized" and "-45 polarized". The reverse is also true--a "+45 polarized" photon can be considered to be an equal superposition of "horizontally polarized" and "vertically polarized".

This is just like looking at a unit vector that is straight along the X axis--its coordinates will be $(1,0)$. This vector might seem "purer" in some way than a diagonal vector like $(\frac{\sqrt 2}{2},\frac{\sqrt 2}{2})$ , but there's really no difference. If you take that diagonal vector, and interpret it in a coordinate system that is at a 45 degree angle to the first one, then all of a sudden the vector's coordinates are $(1,0)$ again. So whether or not a state is a superposition is just a function of the coordinate system that you look at it in--there's actually nothing special about the state itself.

You familiar with Many worlds Intepretation? How do you formulate the above in Many worlds?
Does the case of $|H\rangle = \frac{1}{2}|+45\rangle + \frac{1}{2}|-45\rangle$ mean $\frac{1}{2}|+45\rangle$ is in one world, the second $\frac{1}{2}|-45\rangle$ is in another world?

 

[Varon]

I was quite surprised to see that this was an exact quote from one of my posts. Here. I didn't recognize it when I saw it in this thread. I think it requires some clarification.

I was talking about the two possible answers to the question "Does a state vector represent all the properties of a single system?" Obviously, there are only two answers: yes and no. I've been arguing that "yes" implies many worlds. This is the most recent version of the argument. Item #1 in that quote was an attempt to explain the significance of a superposition in the context of a many-worlds interpretation.

But for Neumaer or others. I think he believes that "Does a state vector represent all the properties of a single system?" can be yes yet not involving Many worlds. Neumaier superior mathematics seem to answer it. I hope he can share what he means. I believe it is possible that this mathematician Neumaier is the new von Neumann of the 21th century and about to rewrite history.

I have also been arguing that "no" defines the statistical/ensemble/Copenhagen interpretation. (In posts 50-55 in the same thread, I was arguing that the CI is either nonsense, or the SI in disguise, depending on which of the many definitions we choose). Item #2 in that quote was an attempt to explain the significance of a superposition in the context of the statistical interpretation.

I could probably have worded both #1 and #2 better. The wording of #2 was motivated by the fact that if state vectors don't represent all the properties of single systems, and just represent all the statistical properties of an ensemble of identically prepared systems, then QM can't be said to describe reality at all. It's just a set of rules that tells us how to calculate probabilities of possible results of experiments.

Even if this were true, that QM is just a set of rules that tells us how to calculate probabilities of possible results of experiments, one still has to understand the stage trick behind the magic. Maybe you'll say it is a law like Einstein EFE. But one still has to take into account the behavior of a single system. The great mystery is why is destructive interference regions are entirely void of particles even if you send one particle a day at the double slit. Ensemble explanation can't explain how this regions of destructive interference are avoided. This is the central mystery that the ensemble interpretation wants to hide under the rug.

 

[Varon]

I think the most probable situation is that you discounted the importance of some bit of context and left it out of your description. e.g. I would think his #1 would be eminently reasonable if we first assumed {|u>, |v>} was some sort of pointer basis and the state would promptly decohere.

But taken literally and on its own, I think it is misleading at best.

Can you please elaborate what you meant when you said that "I would think his #1 would be eminently reasonable if we first assumed {|u>, |v>} was some sort of pointer basis and the state would promptly decohere."??

I was reading so many messages in old archives and maybe got confused a bit.

 

[Varon]

Can you please elaborate what you meant when you said that "I would think his #1 would be eminently reasonable if we first assumed {|u>, |v>} was some sort of pointer basis and the state would promptly decohere."??

I was reading so many messages in old archives and maybe got confused a bit.

Btw.. I know what pointer basis meant... Many worlds can only branch out if preferred basis is chosen. So you are saying that the states can only be many worlds if they are pointer basis? This means other kinds of superposition can never be decomposed into many worlds. Can you give an example of such? thanks.

 

[Chopin]

You familiar with Many worlds Intepretation? How do you formulate the above in Many worlds?
Does the case of $|H\rangle = \frac{1}{2}|+45\rangle + \frac{1}{2}|-45\rangle$ mean $\frac{1}{2}|+45\rangle$ is in one world, the second $\frac{1}{2}|-45\rangle$ is in another world?

Sort of, but not quite. This is where people start to get confused about Many Worlds, and ascribe all kinds of mystical concepts to it that aren't actually part of it at all. All that MWI says is that the measuring device is a quantum object just like anything else in the universe, so just like the photon, it can also be in a superposition of states. The act of measuring doesn't collapse a wavefunction, or disturb the particle, or even interact with it in any way, all that it does is entangle the measuring device with the particle.

So if you had a photon that was in a superposition of states, say $|H\rangle + |V\rangle$, and you measure it with a detector, then you entangle the detector with the photon, and the detector is itself in a superposition as well. That is, instead of the states being "photon is horizontal" and "photon is vertical", the states are now "photon is horizontal AND detector indicates horizontal" and "photon is vertical AND detector indicates vertical". We could call the states something like $|H, D_H\rangle$ and $|V, D_V\rangle$. So the state of the system is now a superposition of these two states, instead of the original two states: $|H, D_H\rangle + |V, D_V\rangle$.

Since each of these states describes both parts of our little "world" (the photon and the detector), you could view this superposition as meaning that there are now two different worlds, and the system is in a superposition of them. But that's really just semantics, and like I said before, it tends to put some funny ideas in peoples' heads that aren't really part of the theory. A clearer way to think about it is just to say that the quantum system now includes both the observer and the observed object, and they are both in a superposition together. In this way, MWI removes the special role of the observer--it's just another quantum object that can be in a superposition like anything else.

 

[Varon]

Sort of, but not quite. This is where people start to get confused about Many Worlds, and ascribe all kinds of mystical concepts to it that aren't actually part of it at all. All that MWI says is that the measuring device is a quantum object just like anything else in the universe, so just like the photon, it can also be in a superposition of states. The act of measuring doesn't collapse a wavefunction, or disturb the particle, or even interact with it in any way, all that it does is entangle the measuring device with the particle.

So if you had a photon that was in a superposition of states, say $|H\rangle + |V\rangle$, and you measure it with a detector, then you entangle the detector with the photon, and the detector is itself in a superposition as well. That is, instead of the states being "photon is horizontal" and "photon is vertical", the states are now "photon is horizontal AND detector indicates horizontal" and "photon is vertical AND detector indicates vertical". We could call the states something like $|H, D_H\rangle$ and $|V, D_V\rangle$. So the state of the system is now a superposition of these two states, instead of the original two states: $|H, D_H\rangle + |V, D_V\rangle$.

Since each of these states describes both parts of our little "world" (the photon and the detector), you could view this superposition as meaning that there are now two different worlds, and the system is in a superposition of them. But that's really just semantics, and like I said before, it tends to put some funny ideas in peoples' heads that aren't really part of the theory. A clearer way to think about it is just to say that the quantum system now includes both the observer and the observed object, and they are both in a superposition together. In this way, MWI removes the special role of the observer--it's just another quantum object that can be in a superposition like anything else.

Come to think of it... in the Dirac Equation.. positrons are not just in the equations. It is describing something really out there. Similarly in Many worlds, there are actually two worlds.. meaning the quantum states are describing something really out there. In one world (which could be this world), contains "photon is horizontal AND detector indicates horizontal", in the other world contains "photon is vertical AND detector indicates vertical". Refute this.

 

[Chopin]

Come to think of it... in the Dirac Equation.. positrons are not just in the equations. It is describing something really out there. Similarly in Many worlds, there are actually two worlds.. meaning the quantum states are describing something really out there. In one world (which could be this world), contains "photon is horizontal AND detector indicates horizontal", in the other world contains "photon is vertical AND detector indicates vertical". Refute this.

I'm not sure what you're asking me to refute--what you've said is pretty much the description of MWI.

 

[Varon]

I'm not sure what you're asking me to refute--what you've said is pretty much the description of MWI.

I mean.. try to refute Many worlds. But it seems one can't refute or prove it.. I know.

The way you believe it. Do you think those states are, as Fredrik loves to say "just a set of rules that tells us how to calculate probabilities of possible results of experiments"?

But if they are just rule. How do you tie it up with the Bohr postulate that:

"In the absence of measurement to determine its position, a particle has no position".

Here Bohr was describing it literally... so the particle has literally no position before measurement, here it can't be just a set of rules, isn't it? What do you think? I think the truth is neither Many Worlds or Ensemble Interpretation.. but others.. but Fredrik seems to want to prove that there are no others.. as those others are just superficial attempt to be neither MWI or Ensemble but are really them in disguise.. and this statement haunts me for days.

 

[Fredrik]

Fredrik loves to say "just a set of rules that tells us how to calculate probabilities of possible results of experiments"?

But if they are just rule. How do you tie it up with the Bohr postulate that:

"In the absence of measurement to determine its position, a particle has no position".

Before the discussion in the thread "Do particles have well-defined positions at all times?", I thought what Bohr said in that quote was the only possibility. But it seems that QM is neutral on the issue of whether particles have positions. So now I think the right way to think isn't what Bohr said there, but rather "Since QM doesn't say that particles have positions, there's no reason to think that they do".

I think the truth is neither Many Worlds or Ensemble Interpretation.. but others.. but Fredrik seems to want to prove that there are no others.. as those others are just superficial attempt to be neither MWI or Ensemble but are really them in disguise.. and this statement haunts me for days.

There's still hope if you want to believe that there's something else. For example, it seems that the assumption that particles do have positions can be added to QM without causing any inconsistencies or changing the theory's predictions. This would have some weird implications about the ways particles move (see the discussion in the positions thread), and we would need something like Bohmian mechanics to provide the details. In my opinion, that's what an interpretation should be: A set of statements that provide ontological details that QM doesn't.

Also, my analysis of the situation is heavily influenced by the specific list of axioms that I think of as the definition of "QM". If someone can come up with a different set of axioms that give us the same predictions about results of experiments, and that set doesn't include any axioms that can be removed without changing the predictions, then we have another theory that has just as much right to be called "QM" as the theory I call QM. For example, suppose that we replace the Born rule with a rule ("the ABL rule") that tells us the probability of each possible result of a measurement at time t, given the state of the system at two times t₁ and t₂, with t₁<t<t₂. This is probably the simplest change we can make to the theory. This version of QM can of course be "just a set of rules" too, but now it looks like the main alternative to the ensemble interpretation would be a version of consistent histories, rather than a version of the MWI.

My point here is that different sets of axioms suggest different ways to interpret QM as a description of what actually happens. Of course, I still have to point out that there's no good reason to think any of them is correct, but there's also no really convincing reason to think that they're all wrong. The best reason I have is just that QM looks so much like a toy theory that someone invented just to show that it's possible to assign non-trivial probabilities to possible results of experiments. It looks like it should be the simplest possible theory of that kind actually.

 

[Varon]

Before the discussion in the thread "Do particles have well-defined positions at all times?", I thought what Bohr said in that quote was the only possibility. But it seems that QM is neutral on the issue of whether particles have positions. So now I think the right way to think isn't what Bohr said there, but rather "Since QM doesn't say that particles have positions, there's no reason to think that they do".


There's still hope if you want to believe that there's something else. For example, it seems that the assumption that particles do have positions can be added to QM without causing any inconsistencies or changing the theory's predictions. This would have some weird implications about the ways particles move (see the discussion in the positions thread), and we would need something like Bohmian mechanics to provide the details. In my opinion, that's what an interpretation should be: A set of statements that provide ontological details that QM doesn't.

Also, my analysis of the situation is heavily influenced by the specific list of axioms that I think of as the definition of "QM". If someone can come up with a different set of axioms that give us the same predictions about results of experiments, and that set doesn't include any axioms that can be removed without changing the predictions, then we have another theory that has just as much right to be called "QM" as the theory I call QM. For example, suppose that we replace the Born rule with a rule ("the ABL rule") that tells us the probability of each possible result of a measurement at time t, given the state of the system at two times t₁ and t₂, with t₁<t<t₂. This is probably the simplest change we can make to the theory. This version of QM can of course be "just a set of rules" too, but now it looks like the main alternative to the ensemble interpretation would be a version of consistent histories, rather than a version of the MWI.

My point here is that different sets of axioms suggest different ways to interpret QM as a description of what actually happens. Of course, I still have to point out that there's no good reason to think any of them is correct, but there's also no really convincing reason to think that they're all wrong. The best reason I have is just that QM looks so much like a toy theory that someone invented just to show that it's possible to assign non-trivial probabilities to possible results of experiments. It looks like it should be the simplest possible theory of that kind actually.

Do you notice all the interpretations or theories you favor support realism. That is. Many Worlds and Bohmian Mechanics support realism. Ensemble Interpretation is also realism (or more like the surface being exposed but the ontology undefined). But I think the true ontology shouldn't be realism. I think Bohr anti-realism view is more correct. This is because of the unreasonable effectiveness of mathematics which makes it appear like there is in some sense a platonic world of pure mathematics. Here ontology is superficial, realism is artificial. Yet Fredrik, you are arguing precisely opposite this.. that is.. you prefer realism.. and the only possibilities seem to be Many worlds, Bohmian mechanics, Ensemble. Can't you think of pure Bohr anti-realism interpretation that is plausible? That is.. Can't you think of one that makes sense? Fra conjectured that instead of the Many worlds, there are many observers interacting. Instead of main classical observer and small isolated system. You have all quantum stuff with different interacting observers and different Collapses interacting with information exchange and update. Model like this makes more sense than your realist stance. Know of any argument that can refute this? Bohr anti-realism model is more elegant. So pls. offer some of these.

 

[Hurkyl]

Can you please elaborate what you meant when you said that "I would think his #1 would be eminently reasonable if we first assumed {|u>, |v>} was some sort of pointer basis and the state would promptly decohere."??

In such a situation, one can say that the pure state |u>+|v> decohered into an equally weighted mixture of the |u> and |v> states.

If one was so inclined, one could describe this as the splitting of a world.

 

[Varon]

In such a situation, one can say that the pure state |u>+|v> decohered into an equally weighted mixture of the |u> and |v> states.

If one was so inclined, one could describe this as the splitting of a world.

What can you say about the following?

http://193.189.74.53/~qubitor/people/david/structure/Documents/Research%20Papers/CommentOnLockwood.html

"The point that theorists tend to miss is that the multiplicity of reality is not only, or even primarily, a consequence of quantum theory. It is quite simply an observed fact. Any interference experiment (such as the two-slit experiment),when performed with individual particles one at a time, has no known interpretation in which the particle we see is the only physical entity passing through the apparatus. We know that the invisible entities passing through obey the same phenomenological equations of motion (e.g. geometrical optics) as the single particle we do see. And we know from Einstein-Podolski-Rosen-type experiments, such as that of Aspect, that these not-directly-perceptible particles are arranged in extended ‘layers’ each of which behaves internally like an approximately classical universe. Admittedly all these observations detect other universes only indirectly. But then, we can detect pterodactyls and quarks only indirectly too. The evidence that other universes exist is at least as strong as the evidence for pterodactyls or quarks."

Hurtle, Pls. comment on the above. Also in a separate paragraph can you give a counterargument that wave function collapse is still possible? What I want to understand now is how to view it not just collapse on paper but a one to one correspondence or mapping between the collapse in paper and what actually happens in the system, presently, how do you see it that is not inconsistently with the math and the system behavior? Remember something is actually interfering in the system so one can't just say it is all a math trick and the particle is either on one side and we just don't know (here the experimental results would differ).

 

[Hurkyl]

What can you say about the foAsllowing?

Honestly, it looks somewhere between heavily biased and flat-out wrong.

What I want to understand now is how to view it not just collapse on paper but a one to one correspondence or mapping between the collapse in paper and what actually happens in the system

Something that answers the question "what actually happens in the system" is quite literally what it means for something to be an interpretation of quantum mechanics.

Your question seems to presume there is some prior notion of stuff happening in systems, and you want to reduce quantum mechanics into it. But that's exactly the opposite of how science works -- we use our theories tell us how reality works, rather than use our assumptions about reality to tell our theories how to work.

 

[SpectraCat]

Your question seems to presume there is some prior notion of stuff happening in systems, and you want to reduce quantum mechanics into it. But that's exactly the opposite of how science works -- we use our theories tell us how reality works, rather than use our assumptions about reality to tell our theories how to work.

I would only add that the way we know that our theories are good ones is that:

a) they can reproduce the results of known experiments

b) they can successfully predict the results of experiments that have yet to be performed.

Basically, anyone can come up with a theory, but unless that theory can be cast in the form of an experimentally falsifiable hypothesis or hypotheses, then it is of limited value to science. Or perhaps it is better to say that such a theory's value is only a fraction of what it would be if it could be experimentally tested. As I have mentioned to Varon before, that is why I am curious about interpretations of QM, but don't lose any sleep over which one is the best. Once they start making experimentally falsifiable predictions that can distinguish between the "internal pictures" posited by BM or CI or MWI or relational blockworld or whatever, then I will become a lot more interested.