Question about Many Worlds branching in Quantum Mechanics

[PaleMoon]

you are right i should have said that they become rapidly orthogonal.
during decoherence, a state v><v evolves as ∑ p_i(t) v_i(t) ><v_i(t)
when t = 0 it is
(∑ p_i) v><v = v><v
and during decoherence the v_i(t) ><v_i(t) rapidly tend to be orthogonal (but never are exacty orthogonal)
it is not cleat to me why the output should be exactly on the limit

 

[PaleMoon]

during decoherence, a state v><v evolves as ∑ p_i(t) v_i(t) ><v_i(t)

i wonder if the probabilities p_i depend on time or if they are constant and equal to the transition probability
from v> to the i-th eigenvector of the measured operator

 

[Mentz114]

you are right i should have said that they become rapidly orthogonal.
during decoherence, a state v><v evolves as ∑ p_i(t) v_i(t) ><v_i(t)
when t = 0 it is
(∑ p_i) v><v = v><v
and during decoherence the v_i(t) ><v_i(t) rapidly tend to be orthogonal (but never are exacty orthogonal)
it is not cleat to me why the output should be exactly on the limit

i wonder if the probabilities p_i depend on time or if they are constant and equal to the transition probability
from v> to the i-th eigenvector of the measured operator

All I can remember about this is the basic model where a state $|s_n\rangle$ becomes coupled to the environment $|e_n(t)\rangle$ to give $\psi_n(t)=|s_n\rangle|e_n(t)\rangle$. If the $|e_n(t)\rangle$ are independent random vectors of increasing dimension, then their correlation is zero (orthogonality) in the limit. Clearly you can think of the limit as a few million degrees of freedom without everything falling apart.

The density matrix contains off-diagonal terms that have products $|e_i(t)\rangle \langle e_j(t)|$ which go rapidly to zero if $i\ne j$. So only the diagonal elements are preserved.

 

[bhobba]

I'm not sure what there is to "get". In some possible "worlds" the observed frequencies for repeated experiments will not equal the predictions of quantum mechanics.

That's what I do not get. By construction it MUST equal the predictions of QM.

After decohenece each element of the mixed state is a new world. This is exactly as QM predicts - by it's very definition. But I have only read Wallace - in a discussion a while ago evidently in some views it is possible. For example in Decoherent histories it is claimed in the paper by Gell-Mann and Hartle you can even have histories with negative probabilities. I trust what guys like that say - but haven't verified it personally.

Thanks
Bill

 

[PeterDonis]

By construction it MUST equal the predictions of QM.

No, it mustn't, at least not if you're expecting all of the observed frequencies to match the predictions of QM.

Consider a simple example: we have a source of qubits and a spin measuring device that each qubit passes through. The source emits qubits in a state which gives equal probabilities for spin up and spin down for the measurement result. We run 10 qubits through the device. We record a "1" for spin up and a "0" for spin down for each measurement.

According to the MWI, there are now 1024 different worlds, in each of which the sequence of 10 measurement results is a different sequence of 10 binary digits (0 or 1). Many of these sequences of 0s and 1s give relative frequencies of spin up and spin down that are different from 50-50 (at the extremes, there will be one sequence of all 0s and one sequence of all 1s). That is what I think @stevendaryl meant by results not matching the predictions of QM.

Btw, the fact that this will be the case according to the MWI is one of the key issues I personally see with the MWI. I understand that various physicists (including, IIRC, Bryce DeWitt) have published papers arguing that this isn't really a problem, but their arguments look like black magic to me and I've never been convinced by them. But however that may be, the fact that the MWI has the implications I've described above should be uncontroversial.

 

[bhobba]

That is what I think @stevendaryl meant by results not matching the predictions of QM.

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.

Btw, the fact that this will be the case according to the MWI is one of the key issues I personally see with the MWI. I understand that various physicists (including, IIRC, Bryce DeWitt) have published papers arguing that this isn't really a problem, but their arguments look like black magic to me and I've never been convinced by them. But however that may be, the fact that the MWI has the implications I've described above should be uncontroversial.

Wallace actually argues such a view is inconsistent - I will need to dig up the book to find the page.

Thanks
Bill

 

[PeterDonis]

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.

"Probability" has a different meaning here, though: it means "fraction of worlds". (In more general cases where there is a continuous observable, that has to become "measure of worlds", which introduces additional issues about how to define the measure.) But an observer in a particular world has no way of knowing what fraction of worlds have the same fraction of 0s/1s as his, so this "fraction of worlds" probability is unobservable. We only know it in the scenario I described because we declared by fiat what the state emitted by the source was.

But in a real experiment, we have to infer the state emitted by the source from observed frequencies of measurement results; so in a world of all 1s, we would infer that the source was emitting all spin up qubits, not an equal amplitude superposition of up and down qubits. In other words, the MWI predicts that worlds will exist in which the natural method of inferring the source state from observed frequencies does not work; yet in practice it always does work. That is an issue that I don't think is addressed adequately.

Wallace actually argues such a view is inconsistent - I will need to dig up the book to find the page.

I'd be interested in seeing his arguments.

 

[bhobba]

"Probability" has a different meaning here, though: it means "fraction of worlds"

Got it now - yes I see that point - that for some worlds the probability will be so small they will FAPP just peter out. Fine in probability theory - but we are talking about worlds here - yes that is a strange consequence. A physicist in this world of all 1's would likely reach different conclusions about the laws of nature - its a good thing it peters out - but of course never actually vanishes. Is it a problem - I suppose that's a personal opinion.

I'd be interested in seeing his arguments.

He examines a number of alternative ideas for assigning probabilities in section 5.8 - page 189 of the Emergent Multiverse.

Here is one I remember. Suppose you have an observational black box with lights representing each outcome. Let's say you adopt the rule all worlds are equally probable ie if you have N outcomes from the black box then the probability of each outcome is 1/N If you have two outcomes you get 2 worlds with 1/2 chance, 3 outcomes 1/3 and so on. Now let's form a compound observation inside our black box - with three outputs from two, two output observations. You do the first observation - and light 1 goes on - but for the second outcome we observe it with another two output observation and you display those lights. What you would get knowing the contents of the black boxes is probabilities of 1/2, 1/4, 1/4. But if you didn't know what was inside, and the rule says nothing about that, you would say it was 1/3, 1/3, 1/3.

He examines a lot of ideas like that and all show similar logical flaws. Admittedly he has not considered every possible scheme you could come up with, but he does look at a lot. This is suggestive that in the MW scheme the only one that is feasible is the Born Rule. Indeed Gleason more or less says that must be the case because he has a non-contextuality theorem which basically means there is no real out for the theorem. On page 196 he explains in words without using the explicit theorem why in his decision theory approach it must be non contextual - it would mean a rational agent preferring a given act in one situation to the same act in another situation.

To me this is the real issue with MW - at least as Wallace presents it - this rational agent thing they introduce and how a rational agent would act. Yes it would be irrational to prefer a given act in one situation to the same act in another situation (or would it?). But rational behavior is hardly something you can pin down exactly. Why would it be irrational to do so? That would seem the key point. Lots of unstated assumptions being smuggled in via back door IMHO. I would say its fatal actually - except he has proofs based on axioms he states from the start. Its those axioms that need challenging. They are very very reasonable - but that's the point - science is correspondence with experiment - not reasonableness. I love reasonable proofs of thing like Maxwell's equations - it fact giving reasonableness augments for physical theories is one of my favorite things. But Feynman said it straight:


These arguments mean nothing - only experiment matters.

Thanks
Bill

.

 

[Chris Miller]

Isn't the current thinking that the universe is infinite in time and mass also refutable via "reductio ad absurdum." Or are there really infinite me's inhabiting infinite observable universes exactly identical to this one?

 

[bhobba]

Isn't the current thinking that the universe is infinite in time and mass also refutable via "reductio ad absurdum." Or are there really infinite me's inhabiting infinite observable universes exactly identical to this one?

I am not sure what you mean, but we have all sorts of theories in accord with current observation about cosmology. What mass is, is well known, but technical. There is an advanced argument based on irreducible representations of the Poincare group. That obviously makes no sense at the B level - but what mass is, is not a mystery in our current theories.

As to infinite me's inhabiting infinite worlds I urge you to watch Murray Gell -Mann's video I posted about the Everett interpretation. Its 'meaning' of what a world is, is more subtle than presented in some literature. So let's just say at the B level these sorts of things are just conjectures on which further research is needed.

My personal favorite for what its worth is eternal inflation:
http://cds.cern.ch/record/485381/files/0101507.pdf

Although not a proper reference here I am reading book by Penrose right now - Fashon, Faith and Fantasy In The New Physics Of The Universe that looks at a lot of these things. The interesting thing about Penrose is he does not hide the math, explaining definitively non trivial stuff like analytical continuation, and equations are used freely. It's not like his good friend and collaborator Hawking who believed every equation he used cut book sales in half. I much prefer Penrose to other popularizes - but he does reach some weird conclusions - he is a literal Platonist - its surprising how many math types are - but then again as the great physicist Ken Wilson noted when he was invited to a dinner in his honor by the math department for being named a Putman Fellow at an early age (he entered Harvard at 16) they were all excellent mathematicians, but quite mad. Wilson was a two time Putman Fellow at 17 and 19, so was Feynman who didn't even prepare for it - people usually go through a special preparation program for that tough test:
https://en.wikipedia.org/wiki/William_Lowell_Putnam_Mathematical_Competition

Thanks
Bill

 

[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.