Question about Many Worlds branching in Quantum Mechanics

[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.