Question about Many Worlds branching in Quantum Mechanics

[Michael Price]

Of course, every branch is equally rare. The thing you refer to is that quantum outcomes themselves appear to violate statistical predictions of QM. Accordingly, an observer in such a world might conclude spin up is the outcome of EVERY measurement rather than being a 50-50 proposition, as we observe. (Or maybe they see it as 60-40.)

I agree there are a few branches as you describe - as stevendaryl also says. Out of the many times greater branches that yield normal statistics. So what? Certainly, in any experimental situation, you might be part of an environment that gives a "biased" answer as compared to some other environment.

Honestly, that part of MWI doesn't bother me as it does you. My question is: where are the other branches? Are they accessible?

The other branches occupy the same space as our branch, at least as long as we ignore quantum gravity. Inaccessible, by the rules of quantum physics (linearity).

 

[DrChinese]

The other branches occupy the same space as our branch, at least as long as we ignore quantum gravity. Inaccessible, by the rules of quantum physics (linearity).

That's the idea, I know, but how much sense does it really make? Or is it simply by assumption?

For example, and as you mention: we ignore gravity (which no one knows whether there is quantum gravity or not). On the other hand, maybe that dark matter we can't otherwise explain is actually those other worlds.

 

[Michael Price]

Forget about dark matter being other worlds or timelines. DM is about explaining galactic rotation velocities, not the double slit experiment or Schrödinger's cat.
The linearity is not an assumption, though, it is part and parcel of all quantum mechanics, independent of any intepretation.

 

[stevendaryl]

Yes - Wallace deals with that and explains why it must be like that. Of course in some sequence of observations there are very low probability sequence outcomes - but that is in the formalism itself. If it s 50-50 and the observation the the count of say the number of 1's then of course the probability will be small for all 1's. That's the central limit theorem.

Yes, so most "worlds" (using the Born measure to give a definition of "most") will have relative frequencies that approach the probabilities given by the Born rule. But some worlds will have relative frequencies that differ from those predicted by the Born rule.

 

[Mentz114]

The other branches occupy the same space as our branch, at least as long as we ignore quantum gravity. Inaccessible, by the rules of quantum physics (linearity).

[]
The linearity is not an assumption, though, it is part and parcel of all quantum mechanics, independent of any intepretation.

Can a linear quantum theory of gravity be ruled out ? I thought classically non-linear processes can be modeled with infinitessimal linear contact transformations.

 

[DrChinese]

Forget about dark matter being other worlds or timelines. DM is about explaining galactic rotation velocities, not the double slit experiment or Schrödinger's cat.
The linearity is not an assumption, though, it is part and parcel of all quantum mechanics, independent of any intepretation.

I wasn't proposing anything about dark matter. But obviously: postulating an increasingly large number of universes co-resident with ours (without testable consequence) is not something that neither explained nor predicted by orthodox quantum mechanics. It's an interpretation, and like all has its own (as of this time) assumption(s).

One question being discussed is what people in those far, far "outlier" universes would conclude after getting all 1's in their quantum experiments. Of course, when they wake up and repeat those experiments tomorrow, the vast, vast majority will suddenly see the normal mix of 1's and 0's we do. They would be checking their instruments to see why yesterday's results don't match today's.

But as I am NOT inhabiting one of those outlier universes, and so I am NOT checking my instruments today. Instead, I am searching for my quantum twin who is forever just out of reach...

 

[Michael Price]

Can a linear quantum theory of gravity be ruled out ? I thought classically non-linear processes can be modeled with infinitessimal linear contact transformations.

Classical non-linearity has nothing to do with quantum linearity. No known exceptions to the latter.

 

[Michael Price]

Can a linear quantum theory of gravity be ruled out ? I thought classically non-linear processes can be modeled with infinitessimal linear contact transformations.

Classically non-linear processes become linear when quantized, because linear has a different meaning (sort of) in quantum theory. Causes no end of confusion to philosophers.

 

[cosmik debris]

Yes, so most "worlds" (using the Born measure to give a definition of "most") will have relative frequencies that approach the probabilities given by the Born rule. But some worlds will have relative frequencies that differ from those predicted by the Born rule.

I thought the whole point of the MWI interpretation was that each branch was a branch in which one of the eigenvalues of the observable was measured?

Cheers

 

[cosmik debris]

but what mass is, is not a mystery in our current theories.

Maybe, but where mass values come from is.

Cheers

 

[Michael Price]

Yes, that is one way or viewing MWI; one result = one branch. Another way (which I prefer) is to require that all branches at an event have the same norm. Then you can just count the relative number of number of branches to determine the probability of a result. That's how Zurek and a few other people define them to derive the Born Rule. I've tried to summarize this approach here: https://www.quora.com/How-does-the-...ding-to-the-Born-rule/answer/Michael-Price-29
No matter how you define things there will be worlds where unlikely sequences of results are observed - but that doesn't mean the Born rule has failed for those worlds; it just means unlikely events have occurred!

 

[Mentz114]

Classically non-linear processes become linear when quantized, because linear has a different meaning (sort of) in quantum theory.

Do you mean there are different linear algebras for classical and quantum dynamics ?

[edit]@Michael Price
I think I know what you mean, ie that solutions of the SE can be superposed and remain solutions, but this is not the case (generally) for classical EOMs. The former is valid for the amplitudes the latter for actual dynamical variables.

 

[stevendaryl]

Yes, that is one way or viewing MWI; one result = one branch. Another way (which I prefer) is to require that all branches at an event have the same norm. Then you can just count the relative number of number of branches to determine the probability of a result. That's how Zurek and a few other people define them to derive the Born Rule. I've tried to summarize this approach here: https://www.quora.com/How-does-the-...ding-to-the-Born-rule/answer/Michael-Price-29
No matter how you define things there will be worlds where unlikely sequences of results are observed - but that doesn't mean the Born rule has failed for those worlds; it just means unlikely events have occurred!

Well, if someone is trying to find out if QM is correct, then the way they would do it is to calculate the probabilities predicted by QM for the results of some measurement and see if the relative frequencies agree. If they don't agree, then they will assume that QM is not correct. So if QM is correct, then there are necessarily worlds where the observers are led to believe that it's not correct. Assuming that there are any observers in those worlds---it's hard to imagine that creatures like us would evolve in a world where probability doesn't work.

 

[cosmik debris]

Well, if someone is trying to find out if QM is correct, then the way they would do it is to calculate the probabilities predicted by QM for the results of some measurement and see if the relative frequencies agree. If they don't agree, then they will assume that QM is not correct. So if QM is correct, then there are necessarily worlds where the observers are led to believe that it's not correct. Assuming that there are any observers in those worlds---it's hard to imagine that creatures like us would evolve in a world where probability doesn't work.

No one will see relative frequencies will they? Each branch sees only one value for a measurement. I thought that was the whole point of MWI.

Cheers

 

[stevendaryl]

No one will see relative frequencies will they? Each branch sees only one value for a measurement. I thought that was the whole point of MWI.

You do the same experiment 1000 times, and write down 1000 results.

 

[DrChinese]

You do the same experiment 1000 times, and write down 1000 results.

Each person sees a pattern which has a quite rare 2^1000 chance of occurring. And if you do 10 more iterations, you have about 1 in a thousand chance of seeing all 1's. That's true regardless of the previous results.

 

[PeterDonis]

You do the same experiment 1000 times, and write down 1000 results.

This tells me the relative frequencies I observe in my branch of the wave function. What it doesn't tell me is the probability amplitude of my branch relative to all of the other branches. The only thing that tells me that is my assumption about what the overall wave function actually is. But my assumption about what the overall wave function actually is, in a real case, is based on the relative frequencies I observe. In other words, the MWI appears to be forcing me to argue in a circle about what the overall wave function actually is.

 

[stevendaryl]

Each person sees a pattern which has a quite rare 2^1000 chance of occurring. And if you do 10 more iterations, you have about 1 in a thousand chance of seeing all 1's. That's true regardless of the previous results.

I'm just saying that if every experiment done so far has yielded the result 1, then at some point, people will decide that it's not a 50/50 chance. Yes, if they don't give up, and perform the experiment more times, then the relative frequencies will tend to be restored to 50/50.

But in practice, we give up at a certain point. In experiments, people pick a cut-off. Maybe they perform the experiment 1000 times. Maybe 10,000 times. But if you pick a cut-off and decide "If after N trials the relative frequency for this experiment differs significantly from the theoretical prediction, then I will conclude the theory is wrong." How else could you decide that a theory is wrong?

So the point is that in a MW interpretation, there will necessarily be worlds where people have rejected QM as empirically falsified.

 

[AlexCaledin]

in a MW interpretation, there will necessarily be worlds where people have rejected QM as empirically falsified.

- and even worlds with miracles happening so frequently that almost everybody rejects any physics as unbelievable superstition

 

[pBrane]

Supposing the Many Worlds interpretation of QM is true... If a branching occurs during what we perceive is a wave function collapse, why would this be perceptible to us as probabilties? Wouldn't we just branch, leaving it just as imperceviable as the passage of time? That is, it just happens. By way of analogy, there is no intermediate process in the passage of time. And this is how I envision the branching of many worlds.

In other words, why would we have any evidence of our own branching?

My mind cannot contain MWI. I don't want it to.

If MWI, were to be, is true (grammar??) then somewhere in the MW;

David Hockney is going to burst into your room, car, swimming pool..
carrying a painting of you, your environment, your ipad, newspaper.
Dave painted this picture 50 years ago.

That is not going to happen.

Causal paths are needed to 'navigate' to a space-time event. They don't do backwards.

 

[DrChinese]

... somewhere in the MW;

David Hockney is going to burst into your room, car, swimming pool..
carrying a painting of you, your environment, your ipad, newspaper.
Dave painted this picture 50 years ago.

This is an incorrect analysis of MWI. All conceivable events do not occur.

All quantum branching options occur, but this is not the same thing as all macroscopic options occurring. For example, there would not be a world in which my son was born before myself and his mother. Or where I am born with 52 fingers and 6 brains. Etc.

I couldn't say what the specific limits are of course, but hopefully you can see the difference.

 

[pBrane]

This is an incorrect analysis of MWI. All conceivable events do not occur.

All quantum branching options occur, but this is not the same thing as all macroscopic options occurring. For example, there would not be a world in which my son was born before myself and his mother. Or where I am born with 52 fingers and 6 brains. Etc.

I couldn't say what the specific limits are of course, but hopefully you can see the difference.

Thanks DrChinese, I could cope with that type of MWI. I am not familiar with it (I am MWI blind).

It sounds like all MWI that can sustain a coherent path.
That makes sense.

 

[QuantumConfusion]

This is an incorrect analysis of MWI. All conceivable events do not occur.

All quantum branching options occur, but this is not the same thing as all macroscopic options occurring. For example, there would not be a world in which my son was born before myself and his mother. Or where I am born with 52 fingers and 6 brains. Etc.

I couldn't say what the specific limits are of course, but hopefully you can see the difference.

Isn't this incorrect? AFAIK, all non-zero probabilities are realized in at least 1 branch, so even though those instances are EXTREMELY rare, they (as long as they don't violate physics) are realized. The macro world is built up by the micro world. So for instance in one branch DrChinese would suddenly have 52 fingers and 6 brains, because it's just configurations of atoms?

 

[DrChinese]

Isn't this incorrect? AFAIK, all non-zero probabilities are realized in at least 1 branch, so even though those instances are EXTREMELY rare, they (as long as they don't violate physics) are realized. The macro world is built up by the micro world. So for instance in one branch DrChinese would suddenly have 52 fingers and 6 brains, because it's just configurations of atoms?

No, such a configuration would require a previous world in which this could branch into. And a precursor to that one. You don't necessarily get all possibilities, just all possibilities that can follow from an earlier world.

Keep in mind that the laws of physics still apply. You can't have an electron decay into a proton, for example, because of conservation laws.

 

[QuantumConfusion]

No, such a configuration would require a previous world in which this could branch into. And a precursor to that one. You don't necessarily get all possibilities, just all possibilities that can follow from an earlier world.

Keep in mind that the laws of physics still apply. You can't have an electron decay into a proton, for example, because of conservation laws.

I agree that the laws of physics still apply, naturally otherwise there'd be no reason to contemplate MWI in the first place. However, let's imagine a classical game of dice, the dice rolling are affected by the air surrounding them, the friction on the surface they land on, the strength by which you tossed them. But MOST of those variables are macroscopic, but those are again comprised of quantum particles, so wouldn't you agree that MWI predicts that when I toss a regular classical dice, that all outcomes will occur in at least one branch, even if the required effect is highly improbable, like the surface changing from a wood table top to stone?

 

[DrChinese]

I agree that the laws of physics still apply, naturally otherwise there'd be no reason to contemplate MWI in the first place. However, let's imagine a classical game of dice, the dice rolling are affected by the air surrounding them, the friction on the surface they land on, the strength by which you tossed them. But MOST of those variables are macroscopic, but those are again comprised of quantum particles, so wouldn't you agree that MWI predicts that when I toss a regular classical dice, that all outcomes will occur in at least one branch, even if the required effect is highly improbable, like the surface changing from a wood table top to stone?

Definitely not. It must be a quantum outcome, and transmuting from one substance to another is not a possible quantum outcome. Now, there is a certainly a "chance" a particle could decay to any viable decay product. But those are relatively limited in most cases. Electrons are stable, protons are probably stable, etc. Even considering exotic combinations (spontaneous electron capture for example), you don't get every possible outcome as you envision.

 

[AlexCaledin]

... transmuting from one substance to another is not a possible quantum outcome...

- but we have the whole universe sending all the known and unknown particles here - the "cosmic rays" - and those may come focused as to synthesize the required stone or something.