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I have completely new appreciation for Many Worlds


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I never really liked many worlds interpretation - or should I better say - what I thought it was all about, until I watched this video (possibly could be used with adverb again? - can't really tell if I watched it more than once):

https://www.youtube.com/watch?v=5hVmeOCJjOU

In any case, last time I saw it - two very important sentences stuck with me, and I finally properly understood many worlds interpretation. I'm going to paraphrase them:

- Everett did not add many worlds to quantum mechanics - he simply acknowledged that they are there

- If we can accept that electron can be in superposition of two states, why can't we accept that universal wavefunction  (or wavefunction of universe) can also be in superposition of many states?

I must say that terms "Many Worlds" as well as "Branching" are very unfortunately chosen (as are many terms related to QM) - because they make it much harder to grasp what is actually going on.

In any case - interesting fact arises from MW interpretation - our physical reality is nothing but particular vibration in universal wavefunction. Yes, I'm quite aware how "new age" that sounds :D.

Other worlds are similarly - just different vibrations in same universal wavefunction that are no longer in phase with "our world" - and in that sense, yes, it can be thought of as really separate worlds (no longer able to interfere with ours) - but we are still all part of the same universe / same universal wavefunction.

Some of my original objections to MW are gone now that I have better understanding of it, however - principal objection still remains, and it is not related to MW interpretation any more - but rather our understanding of probability and how it relates to "weights" of eigenstates in wavefunction.

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On 08/06/2021 at 19:07, vlaiv said:

Other worlds are similarly - just different vibrations in same universal wavefunction

 

On 08/06/2021 at 19:07, vlaiv said:

probability and how it relates to "weights" of eigenstates in wavefunction

 

I think of the probability as proportional to the amplitude of the 'vibration'.

If you are in a particular world you no longer know what the amplitude of the wavefunction that has collapsed to 'create it' was... but if anyone could see all the possible vibrations before collapse then the probability of ending up following a particular one is related to the amplitude of that vibration.

I know I've offered this thinking before on another thread... and you were not overly impressed with my contribution.... but I thought I'd offer it again.

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3 minutes ago, globular said:

I think of the probability as proportional to the amplitude of the 'vibration'.

That is what QM says (or rather something very similar), but that is where problem lies.

Imagine we have quantum system that is like a coin - it's flipped and can land in either of two states - heads and tails. These are eigenstates of system. We will assign a bit different eigenvalues - 1/3 and 2/3 instead of usual 1/2 and 1/2 for this example.

Once coin is "thrown" (prepared in superposition) and it entangles with environment - world "branches" into two.

Heads and Tails world.

When we throw coin again - world again branches, etc.

After three flips - we will have 8 branches (2 to the power of three).

There is 8 copies of us doing this experiment. We can label those worlds as:

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

Some of our copies will be very "unlucky" and will get just a series of heads, some will get just a series of tails - however, problem is that we all are going to measure probability as 1/2 and 1/2 and not 1/3 and 2/3.

There is simply no explanation as to why branching into two distinct states would result in us seeing different type of probability than simple 1/2 - 1/2, yet there are many systems that don't have simple 1/2 - 1/2 probability - like prepare electron with spin along some axis and measure it along 30° angled axis - you'll get either spin up or spin down - but with different probability. Branching does not explain that.

We can't end up in spin up "on average two times out of three" - as there is no branching into three branches for two distinct eigenstates. That is not what QM says - it says a*|up> + b*|down> - there is not third branch we only have combination of two eigenstates.

 

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6 minutes ago, vlaiv said:

Once coin is "thrown" (prepared in superposition) and it entangles with environment - world "branches" into two.

and if the wavefunction that just collapsed had an amplitude of 100 then the H vibration will have amplitude 67 and the T vibration amplitude 33.  So the single wave of amplitude 100 is now 2 with amplitudes 67 and 33.

 

8 minutes ago, vlaiv said:

There is 8 copies of us doing this experiment. We can label those worlds as:

HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

The HHH world resulted from the collapse of a vibration of amplitude 30 (=100*2/3*2/3*2/3), HHT's amplitude was 15, HTH 15, HTT 7, THH 15, THT 7, TTH 7 and TTT 4.
They all add up to the original 100 - but we now have 8 smaller amplitude vibrations than collapse into 8 different worlds.

 

On 08/06/2021 at 19:07, vlaiv said:

Other worlds are similarly - just different vibrations in same universal wavefunction that are no longer in phase with "our world" - and in that sense, yes, it can be thought of as really separate worlds (no longer able to interfere with ours) - but we are still all part of the same universe / same universal wavefunction.

This means that someone sitting in the TTT world will not know the relative amplitude of the wavefunction that collapsed to create it compare to the other worlds that they might imagine were also created.... so while they can guess that their world is 1/2 * 1/2 * 1/2 = 0.125 compared to them... they would be wrong (it's 4/100 = .04) .... but they don't know it as there is no longer any interference between worlds.

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3 minutes ago, globular said:

This means that someone sitting in the TTT world will not know the relative amplitude of the wavefunction that collapsed to create it compare to the other worlds that they might imagine were also created.... so while they can guess that their world is 1/2 * 1/2 * 1/2 = 0.125 compared to them... they would be wrong (it's 4/100 = .04) .... but they don't know it as there is no longer any interference between worlds.

But this exactly contradicts QM - we know relative frequencies of event based on eigenvalues from wavefunction.

QM tells us that probability of heads is 1/3 and probability of tails is 2/3 - however, in no worlds this is true. If we pick any branch on random after 10000 coin flips - it is very likely that we will end up in a branch that has roughly the same number of head and tails - but QM tells that we should likely end up in one having 1/3 - 2/3 ratio instead.

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You can't just count the branches, you need to weight the branches (using amplitude of the collapsed wavefunction as weight).  If you know the amplitudes (i.e. if you know the 1/3  2/3 thing) then you get the right answer.  But sitting in one of those worlds you have 'lost' all information about the wavefunction - because it has collapsed.  All you can do is theorise about the wavefunction of what might happen next - not about the ones that have already happened.  You might conclude that they are the same.... but they might not be.

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2 minutes ago, globular said:

You can't just count the branches, you need to weight the branches (using amplitude of the collapsed wavefunction as weight).  If you know the amplitudes (i.e. if you know the 1/3  2/3 thing) then you get the right answer.  But sitting in one of those worlds you have 'lost' all information about the wavefunction - because it has collapsed.  All you can do is theorise about the wavefunction of what might happen next - not about the ones that have already happened.  You might conclude that they are the same.... but they might not be.

What does it mean for me to weight the branch?

I'm an observer, I flip a coin. World splits - first one is heads + me recorded heads and second is tails + me recorded tails (and of course environment and deconherence and all entangled into particular entity).

What is justification of assigning weight of 1/3 to first copy of me, and 2/3 of second copy of me. Why is there "privilege" on any particular copy? Just because QM says so? QM only says so because there is something in actual workings of the world that makes me (single copy) - detect heads 1/3 of time. and tails 2/3 of time.

You have to show that above split leads to me (any probable copy of me - one that I am at the moment) - having basis to deduce that probabilities are 1/3 and 2/3 and verify that by experiment.

This is not something that happens sometimes - this is something that happens all the time and is one of most confirmed scientific theory. Many worlds must provide mechanism for that being so if it is to be correct interpretation.

Saying that world splits into two - one with weight of 1/3 and other with weight of 2/3 - just makes no sense if you don't explain what those weights are.

We can never test probabilities on single measurement - we need many measurements and there will be converging on particular probability.

Binary branching will never produce convergence to 1/3 - 2/3 probabilities and since coin has only two eigenstates - only binary branching is possible.

We used to kid back in school that any event has 50% probability - either it will happen or it wont. Many worlds interpretation is a bit like that :D

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18 minutes ago, vlaiv said:

just makes no sense if you don't explain what those weights are

The weights are the amplitude of the wavefunction of the vibration that has just collapsed. 

And the sum of the amplitudes of all the vibrations (in this case 2 vibrations, H and T) is the amplitude of the originating worlds wavefunction.

But once you are sitting in world H then you can't know anything about the amplitude of T... because that world is: 

On 08/06/2021 at 19:07, vlaiv said:

no longer able to interfere with ours

Therefore you can't work out the amplitude of the originating world... and so you can't work out your 'privilege' in the universe.

All you can do is postulate about the relative size of worlds that will stem from yours.

.....

This is now the conversation we had before. 
I thought the lightbulb moment that you describe above might have brought us closer together on probabilities - as it seemed to have done on the general many worlds theory.
I'm pretty comfortable with probabilities sitting nicely within many worlds - but I know you and many others are troubled by it.
I'm sure you know more about this than I do - I eagerly await your next lightbulb moment when you can explain to me how probabilities really work.

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@vlaiv what do you make of this….
https://www.anthropic-principle.com/preprints/manyworlds.html
You can safely fast forward to ‘Q23 How do probabilities emerge within many-worlds?’ - the rest can be skipped.

This isn’t really the point I was trying to make, and failing badly, but it is perhaps a more mathematical argument that probabilities and many worlds do work together?
Maybe this will give you a new way of looking at it?
Or maybe you can set out what bits of it you are not convinced by?

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10 hours ago, globular said:

@vlaiv what do you make of this….
https://www.anthropic-principle.com/preprints/manyworlds.html
You can safely fast forward to ‘Q23 How do probabilities emerge within many-worlds?’ - the rest can be skipped.

This isn’t really the point I was trying to make, and failing badly, but it is perhaps a more mathematical argument that probabilities and many worlds do work together?
Maybe this will give you a new way of looking at it?
Or maybe you can set out what bits of it you are not convinced by?

Thanks for that link.

I found following paper last night and will look into it as well as that FAQ list you provided.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6434053/

 

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