What does "multiple worlds" in MWI mean?

[entropy1]

Suppose that in Copenhagen, we measure one of the eigenvectors/eigenvalues ##e_x##, the outcome being ##M_x##. Now, in MWI, micro-outcome ##e_x## gets entangled with macro-outcome ##M_x##, right?

So, what does that mean in this case? If all outcomes are realized, should outcomes ##e_n## resp. ##M_n## remain in superposition? Because if they are not, what are they?

I expect the answer to be somewhere in the wavefunction.

Moreover, since matter is not being multiplied, why do we speak of multiple worlds? Is this even correct?

 

[PeterDonis]

I expect the answer to be somewhere in the wavefunction.

So have you tried to write down what the wave function is?

 

[PeterDonis]

since matter is not being multiplied, why do we speak of multiple worlds?

Because that's what some physicists who favored this interpretation (IIRC a key one was Bryce DeWitt) decided to call it decades ago and the name stuck.

 

[entropy1]

So have you tried to write down what the wave function is?

Not yet. But I understand it should be something like ##|e_1 \rangle|M_1 \rangle + |e_2 \rangle|M_2 \rangle##.

You might suggest I have to study QM formalism. I have trouble reading texts of any kind though. But QM keeps tugging me.

Product states appear kind of opportunistic to me, like "if we have ##e_1## we have ##M_1##, but if we have ##e_2## we have ##M_2##" (and perhaps vice-versa). But at this point I should really study QM

 

[PeterDonis]

I understand it should be something like ##|e_1 \rangle|M_1 \rangle + |e_2 \rangle|M_2 \rangle##.

Yes, that will do (strictly speaking it should be normalized, but that's not essential for this discussion).

Product states appear kind of opportunistic to me

The state you wrote isn't a product state. It's an entangled state. The measured system ##e## and the system ##M## that registers the result are entangled with each other. Each term in the entangled state you wrote down represents a "world" in MWI terms.

A product state would be, for example, ##|e_1 \rangle|M_1 \rangle ##, and is what an interpretation like Copenhagen would say you have after the measurement result has been registered.

 

[entropy1]

@PeterDonis I appreciate your reaction, but I think you know me better than that...

 

[PeterDonis]

@PeterDonis I appreciate your reaction, but I think you know me better than that...

I don't know what you mean. I wasn't "reacting" to anything. I was confirming that the wave function you wrote down is reasonable for this problem, and clarifying some terminology.

 

[entropy1]

I don't know what you mean. I wasn't "reacting" to anything. I was confirming that the wave function you wrote down is reasonable for this problem, and clarifying some terminology.

I know what a product state is and I understand that the whole equation represents an entangled state. I have several topics in which this is mentioned. I don't blame you if you haven't recalled this when you reacted.

Let's not make this too big an issue. It's my birthday and I have enjoyed some red wine.

 

[PeterDonis]

I know what a product state is and I understand that the whole equation represents an entangled state.

Ok. Your previous post did not make that at all clear.

I have several topics in which this is mentioned.

The fact that it was mentioned in previous threads that you posted does not necessarily mean you understand it.

 

[entropy1]

The fact that it was mentioned in previous threads that you posted does not necessarily mean you understand it.

That is true.

@PeterDonis Nevermind. Cheers!

 

[bobob]

Moreover, since matter is not being multiplied, why do we speak of multiple worlds? Is this even correct?

I think the acronym MWI would be better suited to mean "Many Words Interpretation," Since it requires many words to describe, really doesn't say anything physically meaningful and may be different than the many words someone else's MWI involves. Seriously, I ran across an article about a lecture on quantum mechanics given by Sidney Coleman a long time ago and this is what he had to say about interpretations of quantum mechanics that claim to be in some way "deeper" insights into quantum mechanics when confronted with things like the Bell inequalities:

"Why on Earth do people - I'm trying to see inside other people's heads which is always a
dangerous operation, but let me do it - why, why on Earth do people get so confused, so
wrong on such a simple point? Why do they write long books about quantum mechanics
and non-locality full of funny arrows pointing in different directions?"

"I think secretely, in their heart of hearts, deep down, it's really classical mechanics -
that we're putting something over on them - deep,deep down, it's really classical
mechanics."

He then goes on to make the point:

"Likewise, a similar error is being made here. The problem is not the interpretation
of quantum mechanics. That's just getting things backwards. The problem
is the interpretation of classical mechanics."

Basically, what he is saying is that when Newton came along, no one insisted on
explaining Newton's laws in terms Fire, Water, Air and Earth
to find some deeper meaning in Newton's laws consistent with what people believed
for a few thousand years. That would be backwards. So, fussing over what MWI
means is doing exactly that, which would be obviously ridiculous if you did this
with other theories that have subsumed previous theories.

You have quantum mechanics, so that is at the bottom and classical mechanics
needs to be explained in terms of quantum mechanics instead of trying make
quantum theory conform to our inherently biased picture of the world in a
mechanistic classical way. MWI tries to solve a non-problem by making it complex
at a ridiculous level without contributing anything but a lot of confusing words.

 

[stevendaryl]

I think the acronym MWI would be better suited to mean "Many Words Interpretation," Since it requires many words to describe, really doesn't say anything physically meaningful and may be different than the many words someone else's MWI involves. Seriously, I ran across an article about a lecture on quantum mechanics given by Sidney Coleman a long time ago and this is what he had to say about interpretations of quantum mechanics that claim to be in some way "deeper" insights into quantum mechanics when confronted with things like the Bell inequalities:

"Why on Earth do people - I'm trying to see inside other people's heads which is always a
dangerous operation, but let me do it - why, why on Earth do people get so confused, so
wrong on such a simple point? Why do they write long books about quantum mechanics
and non-locality full of funny arrows pointing in different directions?"

"I think secretely, in their heart of hearts, deep down, it's really classical mechanics -
that we're putting something over on them - deep,deep down, it's really classical
mechanics."

He then goes on to make the point:

"Likewise, a similar error is being made here. The problem is not the interpretation
of quantum mechanics. That's just getting things backwards. The problem
is the interpretation of classical mechanics."

Basically, what he is saying is that when Newton came along, no one insisted on
explaining Newton's laws in terms Fire, Water, Air and Earth
to find some deeper meaning in Newton's laws consistent with what people believed
for a few thousand years. That would be backwards. So, fussing over what MWI
means is doing exactly that, which would be obviously ridiculous if you did this
with other theories that have subsumed previous theories.

You have quantum mechanics, so that is at the bottom and classical mechanics
needs to be explained in terms of quantum mechanics instead of trying make
quantum theory conform to our inherently biased picture of the world in a
mechanistic classical way. MWI tries to solve a non-problem by making it complex
at a ridiculous level without contributing anything but a lot of confusing words.

I don’t think that the analogy with Newtonian mechanics really works. The formalism of QM has the two aspects, the smooth evolution of the wave function according to Schroedinger’s equation, and the Born Rule for measurement. Since presumably a measurement is a physical interaction itself, this splitting seems artificial, something in need of further explanation. So quantum mechanics has an interpretation problem that is unlike Newtonian mechanics (or electromagnetism or General or Special Relativity). It’s an operational theory (do this, and you’ll see that), so to me, it cries out for interpretation. Is measurement revealing some pre-existing fact about the world, or does the measurement process create the result, or what? I don’t think it’s fair or accurate to say that the problem is trying to interpret things in Newtonian terms.

 

[bobob]

I don’t think that the analogy with Newtonian mechanics really works. The formalism of QM has the two aspects, the smooth evolution of the wave function according to Schroedinger’s equation, and the Born Rule for measurement. Since presumably a measurement is a physical interaction itself, this splitting seems artificial, something in need of further explanation.

OK, then why would one not choose to start with quantum theory to explain the classical world instead of interpreting away the quantum part? It seems to me that assuming all the probabilities are realized by creating new worlds in which duplicates of ourselves measured what we didn't is not really an explanation. It's a way to avoid the question without explaining anything. (At least, that's how I see it.) It was the same with inventing the ether. Because waves in media were familiar, lots of effort went into finding a medium for light to propagate in. That was backwards also. Electromagnetic waves were what is fundamental. Working backwards from elastic media wasn't a successful approach to understanding the propagation of those waves.

So quantum mechanics has an interpretation problem that is unlike Newtonian mechanics (or electromagnetism or General or Special Relativity). It’s an operational theory (do this, and you’ll see that), so to me, it cries out for interpretation.

How is that different from any other theory in physics apart from some bias about what is and isn't "real?" People just more readily accept those things as making more sense, although I'm not sure why that should be so. You cannot use Newton's laws to come up with any sensible description of what it means for billiard balls to collide, for example. All you can talk about are initial and final momenta, masses, etc. "Real" billiard balls are irrelevant because there is no way to explain what "collide" means. It's the same, "You do this and you'll see that," except in general that's not what happens and you have to come up with all sorts of macroscopic parameters to account for the real materials used to make billiard balls, and other things.

Is measurement revealing some pre-existing fact about the world, or does the measurement process create the result, or what?

In my opinion, quantum theory tells you what can be known about something in the form of a set of commuting observables. You get to choose the set in making a measurement (or preparing a state, which is pretty much the same thing). If you could keep using different incompatible observables to get more and more information, (first, they wouldn't be incompatible), there would be no limit to the amount of information contained in the measurement or stored in preparing a state. Interpretations like MWI simply discard what I would call the physically relavant part that doesn't allow you to do that, shuffle it off to an infinity of other worlds we can't observe and call it a day as if that isn't a lot less plausible than just getting rid of the interpretation.

Is measurement revealing some pre-existing fact about the world, or does the measurement process create the result, or what? I don’t think it’s fair or accurate to say that the problem is trying to interpret things in Newtonian terms.

Then what else could be the problem? If you aren't taking quantum theory and working your way up to a classical regime, you're starting with a classical picture and trying make it quantum theory. That's what I say is backwards. I haven't seen any interpretation that doesn't have the objective of eliminating the quantum part by handing it off to something that (also) can't be measured, can't make any different predictions and which relies on NOT making any different predictions to justify its existence.

 

[EPR]

In my opinion, quantum theory tells you what can be known about something in the form of a set of commuting observables. You get to choose the set in making a measurement (or preparing a state, which is pretty much the same thing). If you could keep using different incompatible observables to get more and more information, (first, they wouldn't be incompatible), there would be no limit to the amount of information contained in the measurement or stored in preparing a state. Interpretations like MWI simply discard what I would call the physically relavant part that doesn't allow you to do that, shuffle it off to an
Then what else could be the problem? If you aren't taking quantum theory and working your way up to a classical regime, you're starting with a classical picture and trying make it quantum theory. That's what I say is backwards. I haven't seen any interpretation that doesn't have the objective of eliminating the quantum part by handing it off to something that (also) can't be measured, can't make any different predictions and which relies on NOT making any different predictions to justify its existence.

What do you suggest should be done so that QT can recover classical mechanics and the macro world?
It seems we are 1000 years away from accomplishing this feat.
Accepting the situation for what it is is a definite start.

 

[stevendaryl]

OK, then why would one not choose to start with quantum theory to explain the classical world instead of interpreting away the quantum part?

I don’t think it’s a matter of classical versus quantum. Quantum mechanics just considered by itself doesn’t have a clear interpretation. It has an operational meaning, but that’s different from an interpretation.

 

[stevendaryl]

Then what else could be the problem? If you aren't taking quantum theory and working your way up to a classical regime, you're starting with a classical picture and trying make it quantum theory. That's what I say is backwards.

I’m not doing either one of those.

 

[stevendaryl]

In my opinion, quantum theory tells you what can be known about something in the form of a set of commuting observables.

That seems incoherent to me. What dies it mean to “know” something? Presumably, you know something when there is a representation of that knowledge in your brain that has been developed through sensory inputs and reasoning. It’s a very complicated concept. Saying noncommuting observables limit what we can know is just buzzwords. Quantum mechanics has noncommuting operators, which is nothing new to QM. The operators x and -i d/dx failed to commute before quantum mechanics was invented. The connection between operators and observables comes through the postulate that measurements result in an eigenvalue of the corresponding operator. But that’s just a heuristic, a rule of thumb. A measurement really amounts to an interaction between a microscopic system and a macroscopic system that results in the macroscopic state revealing some aspect of the microstate.

I am perfectly happy with QM as an operational theory, but it seems to me that measurements and observables are not primitive entities. They are complex things involving devices and persistent records, etc. A coherent theory shouldn’t make complex entities into primitives. Presumably physics worked before there were humans around to be observers...

 

[entropy1]

If all outcomes are realized, should outcomes ##e_n## resp. ##M_n## remain in superposition? Because if they are not, what are they?

So have you tried to write down what the wave function is?

If the wave function is for example ##|e_1 \rangle|M_1 \rangle + |e_2 \rangle|M_2 \rangle##, does that require the outcomes to be in superposition (the two product states), or is that not required?

 

[PeterDonis]

If the wave function is for example ##|e_1 \rangle|M_1 \rangle + |e_2 \rangle|M_2 \rangle##, does that require the outcomes to be in superposition (the two product states), or is that not required?

What do you mean by "the outcomes in superposition"? The state you wrote down is an entangled state, so neither of the subsystems, ##e## or ##M##, have a definite state by themselves; only the total system does.

 

[entropy1]

What do you mean by "the outcomes in superposition"? The state you wrote down is an entangled state, so neither of the subsystems, ##e## or ##M##, have a definite state by themselves; only the total system does.

I mean the terms in the entangled state, ##|e_x \rangle |M_x \rangle##; e and M are associated with each other, but I mean to ask if those product states as mentioned are in superposition of each other (eg. ##A+B##).

 

[PeterDonis]

I mean the terms in the entangled state, ##|e_x \rangle |M_x \rangle##; e and M are associated with each other

In the sense that the ##e## and ##M## kets in each term refer to states that go together (the ##M## state is the state that describes the appropriate measurement result for the corresponding ##e## state), yes.

I mean to ask if those product states as mentioned are in superposition of each other (eg. ##A+B##).

It makes no sense to ask whether different terms in an entangled state are "in superposition of each other".