Many worlds busted?

[vlaiv]

Ok, here is the argument, I'll be short and to the point as I don't feel to write too much at the moment.

Many worlds states that when there is "choice" in quantum world - worlds are split and one choice happens in one world, and the other in another world. This is of course very simplified. Some transitions have continuous distributions and are split to infinite number of copies.

Here is a question - say we have electron with a spin in some direction and we have spin detector at an angle to this direction such that it produces detections at rate 1:2. Twice as many electrons with spin up as those with spin down.

Does this mean that this event splits world into two? One having electron up and one having electron down?

Right away, I must say that this is not possible since one resulting universe will have unlikely long streak of subsequent electrons with spin down.

Obvious answer to above question would be that universe splits into 3 copies - two of those will have spin up and one will have spin down. This way probability density is maintained over all copies in future.

Let's then get back to same question. Let's again say that we have detector set at such angle to prepared electron spin that probability of measuring spin up is let's say third root of 0.25. There is such angle since formula for probability of measuring spin up electron is cos^2 ( theta / 2). Third root of 0.25 is less than one so it can be square of number less than one and of course we know that cos some angle is in 1 to -1 range (1 to 0 for this instance) - so there is such angle.

However - there is no number of universes that universe can split as to maintain ratio of cube_root_of(0.25) / 1 - cube_root_of(0.25)

This is because this number is irrational as cube_root_of(0.25) is irrational.

Quantum mechanics predicts probability for detecting electron spin that can can't be explained by splitting into multiple universes.

Does this sound right to you?

 

Edited September 30, 2020 by vlaiv

[globular]

You are suggesting worlds are split into numbers of worlds proportional to the outcome probability?

I tend to think of it splitting into one for each possible outcome (in this case 2) and it’s the “size” or “weight” of each world that is proportional to the probability.

[vlaiv]

1 minute ago, globular said:

You are suggesting worlds are split into numbers of worlds proportional to the outcome probability?

I tend to think of it splitting into one for each possible outcome (in this case 2) and it’s the “size” or “weight” of each world that is proportional to the probability.

What does weight mean in this context?

Let's say we have 2:1 event like described above.

World split into two. One world has "weight" of 2 and other has "weight" of 1.

Can you tell what weight do you have and based on what?

Since there are two copies of the world after event - you can't really say that one is "more likely" somehow.

Once you have three copies - two with one outcome and one with other outcome - then yes, out of three copies of me - two will see spin up - so it is indeed more likely that I will see spin up and that probability is indeed 2:1 given number of worlds.

 

[globular]

Each world does not know what weight it has. Just like in your scenario each version of you does not know how many other yous there are in other worlds.

[vlaiv]

1 minute ago, globular said:

Each world does not know what weight it has. Just like in your scenario each version of you does not know how many other yous there are in other worlds.

Ok, but what is the weight then? Who keeps the score?

Why is there then probability different than 1:1?

[globular]

These concepts are basically the same. The weights one doesn’t have a rational number constraint but the world counting one does. So I tend to think in terms of weights (which seems to work) rather than counting (which seems to lead to doubt and talk of busting the whole theory).

And to think you and I both exist in the same world at the same time 😀 haha.

[vlaiv]

1 minute ago, globular said:

These concepts are basically the same. The weights one doesn’t have a rational number constraint but the world counting one does. So I tend to think in terms of weights (which seems to work) rather than counting (which seems to lead to doubt and talk of busting the whole theory).

And to think you and I both exist in the same world at the same time 😀 haha.

That is true, however, weight does not account for probability but number of worlds does.

Imagine you have experiment with 3:1 ratio and 1:1 ratio - both of those create two worlds of different weights according to you. How do you distinguish them, or rather what distinguishes these two cases so we can say - look here is why this one has probability 3:1 and other has 1:1 probability.

[globular]

The weight is the probability. 

In my case a supreme being can see two worlds; one with weight 3 where thing A happened and the other with weight 1 where thing B happened.

In your case the supreme being can see 3 worlds where thing A happened and 1 where thing B happened.

Basically the same thing.

[vlaiv]

2 minutes ago, globular said:

The weight is the probability. 

In my case a supreme being can see two worlds; one with weight 3 where thing A happened and the other with weight 1 where thing B happened.

In your case the supreme being can see 3 worlds where thing A happened and 1 where thing B happened.

Basically the same thing.

It is not the same thing.

Weight approach does not explain probabilities and requires existence of some weights that are "external" to the worlds - conjecture not supported by quantum mechanics.

In number of worlds approach - you don't need any external weights and probabilities work - with simple assumption - there is no preference to any one copy in any way (a sort of cosmological principle - same rules apply to all).

[globular]

maybe thinking of weight as being the proportion of the universes particles that the world occupies might the helpful?

Your 3 worlds where A happened would use 3 times the particles as the 1 world where B happened.

My single A world would be 3 times the weight of the B world too.

[vlaiv]

4 minutes ago, globular said:

maybe thinking of weight as being the proportion of the universes particles that the world occupies might the helpful?

Your 3 worlds where A happened would use 3 times the particles as the 1 world where B happened.

My single A world would be 3 times the weight of the B world too.

Ok, I'm not going to go in circles.

Can you explain probability in case of weights? In repeated experiments why do we see about twice as many spin up electrons then spin down electrons if each time world splits in two with some "weights"?

[globular]

It splits in two but the pieces are not equal in size. The size is proportional to the probability.

Not sure how else I can describe it.  I guess I’ve failed to convince you.

[vlaiv]

1 minute ago, globular said:

It splits in two but the pieces are not equal in size. The size is proportional to the probability.

Not sure how else I can describe it.  I guess I’ve failed to convince you.

Size of what? Of universe?

Many worlds postulates that each split produces exact copies of universe except for outcome of quantum "measurement". No way they can be different in size.

[globular]

You are breaking the postulation by changing the ‘splits into 2’ into ‘splits into a whole number of bits proportional to probability’ and then go on to show that that can’t work because there can’t always be a whole number of splits in other scenarios.

I was trying to say that there can an irrational number of splits if you weight rather than count them. While at the same time trying to say that thinking of it as probability proportional splitting is not really necessary.

Indeed it seems to me that your proof that the postulation is wrong is actually a proof that your change to the postulation is wrong.

 

[Synchronicity]

Sorry to but in but my understanding is that the 'splitting' happens at the point of detection so at event 1 we have a spin up world and a spin down world.  At event 2 each of those worlds splits (we have 4) and at event 3 each of those 4 split again... and so on.

Michael

[globular]

Agreed.

[andrew s]

@vlaiv, with respect, I think if such a logical flaw in MWT existed it would have been discounted by now. As with all interpretations experiment can't  differentiate between them.

Personally,  I dislike it and find it unsatisfactory, but its motivation was to take quantum probabilities seriously and literally. On the plus side looking into it led me to "dechoherence" and the quantum classical transition, which greatly enhanced my understanding.

Regards Andrew 

Edited October 1, 2020 by andrew s

[vlaiv]

@Synchronicity and @globular

I understand that you think that there is only two worlds being split, however in such approach there is no way to account for probabilities, and as @andrew s mentioned, probabilities lie at the heart of this interpretation.

Try making tree diagram of split worlds for spin up / spin down 2:1 case with only two branches and try to explain probabilities. It simply does not work.

If you make tree diagram of this case for 3 worlds splitting - 2 with up and one with down - then explaining probabilities becomes trivial - only assumption needed is that all copies exist simultaneously and we might be any one of those copies (we traced any one path down the tree without bias - since bias can't be here - why would we be "this" copy rather than "that" copy?).

If you have problem with world splitting in more than two, then just look at event that has continuous probability distribution - like detecting particle along X axis. There are infinite number of outcomes, and not only that - there is probability density that must be observed.

@andrew s

I don't mind being wrong, however, I'm not prepared to accept "smarter people would have thought of it by now" as explanation where I did wrong. I'm sure simple explanation why my argument is flawed can be given.

[vlaiv]

Here is what I've found on wiki article on MWI regarding probabilities:

Given the state of affairs, I wonder how did MWI end up to be mainstream interpretation?

 

[Synchronicity]

21 minutes ago, vlaiv said:

If you have problem with world splitting in more than two, then just look at event that has continuous probability distribution - like detecting particle along X axis. There are infinite number of outcomes, and not only that - there is probability density that must be observed.

The probability of detection only exists where there is a detector.  As each detector is passed the particle is either detected or not, so it becomes a binary split again.  Effectivly the quantum waveform 'collapses at that point into a specific result.  Repeating the experiment multiple times gives the liklihood that you would see an even distribution between detectors but there should also be a split version where all particles were detected at the same point.  The liklihood of you or I being in that version is tiny simply because there are more vesrions where an even spread happens.

27 minutes ago, vlaiv said:

(we traced any one path down the tree without bias - since bias can't be here - why would we be "this" copy rather than "that" copy?).

As I understand it we are in both, probably typing the same messages, but we can't percieve the other versions of us.

Michael

[andrew s]

11 hours ago, vlaiv said:

Right away, I must say that this is not possible since one resulting universe will have unlikely long streak of subsequent electrons with spin down.

If all possible outcomes are considered then such a universe is inevitable. A long run of the same result is just as likely as any other sequence. If tossing  a coin hhhh or tttt is just as likely as thht, etc

That's what I don't like about MW or any theory that implies everything possible happens in one universe or another.

They explain everything  and nothing.

Regards Andrew 

[vlaiv]

1 minute ago, andrew s said:

If all possible outcomes are considered then such a universe is inevitable. A long run of the same result is just as likely as any other sequence. If tossing  a coin hhhh or tttt is just as likely as thht, etc

That's what I don't like about MW or any theory that implies everything possible happens in one universe or another.

They explain everything  and nothing.

Regards Andrew 

Both cases will have ttttttttt ad infinitum sequence in them - question is - how likely it is?

Interpretation of QM (if there is in fact need for such thing) should account for what QM is telling us. QM is telling us that such sequence is possible but very improbable.

In fact we have a mathematical framework to calculate probability of it.

22 minutes ago, Synchronicity said:

As I understand it we are in both, probably typing the same messages, but we can't percieve the other versions of us.

We are in infinitesimally small number of world . All other worlds simply don't contain us and there is so much more of such worlds

Sheer number of worlds is one thing that I object with MWI - Occam's razor epic fail.

24 minutes ago, Synchronicity said:

The probability of detection only exists where there is a detector.  As each detector is passed the particle is either detected or not, so it becomes a binary split again.  Effectivly the quantum waveform 'collapses at that point into a specific result.  Repeating the experiment multiple times gives the liklihood that you would see an even distribution between detectors but there should also be a split version where all particles were detected at the same point.  The liklihood of you or I being in that version is tiny simply because there are more vesrions where an even spread happens.

Ok, imagine following scenario

We have biased coin that lands heads one million times more likely than tails.

We toss that coin two times.

If there is two worlds split per coin toss and we toss the coin two times, we will end up with 4 resulting copies of universe.

hh, ht, th, tt

How likely is that we are any one out of four resulting copies? Well we could be third copy with probability 1 in 4 or 25%.

How likely it is that we are fourth copy? Well exactly the same probability 25%. There should be no bias which copy we end up being.

Now, probability to lend hh is extremely big and probability to lend tt is extremely small.

If we are 1/4 chance fourth person, we just witnessed extraordinary event one in a million in a million chance happened before our eyes.

We do another two consecutive coin flips. There is again 1/4 chance that we will end up being tt copy. What is that? We had two consecutive one in a million in a million events just happen before our eyes?????

Do this ten times, or how ever many times you need to understand that probability as we know it would be broken in this system.

Now, let's consider approach where 1,000,000:1 weighted coin produces 1,000,001 worlds - 1,000,000 heads worlds and 1 tail worlds.

Do coin flip two times.

hh will be in 1,000,000 * 1,000,000 worlds

ht will be in 1,000,000 * 1 worlds

th will be in 1,000,000 * 1 worlds and

tt will be in 1*1 = 1 world

We can equally be any one copy after we finish tossing the coin.

There is 1,000,002,000,001 worlds in total

Probability that we end up in one of hh worlds is 1,000,000,000,000 / 1,000,002,000,001 and probability that we end up in tt world is 1 / 1,000,002,000,001

Hold on, but that is just the same as probability that we will have hh or tt respectively - so if we are randomly chosen copy - we will still have proper probabilities

If we by any chance land tt in first two flips, what is probability that we will land another tt in two subsequent flips? It's certainly not 1/4 - it is the same as it should be 1 / 1,000,002,000,001

Two states outcome can't always split in two worlds - that would mess up our probabilities as we know them - chain of events would not have probability that we expect it to have based on math that we have established.

This is what I meant when I said "resulting universe will have unlikely long streak of subsequent electrons with spin down. "

[andrew s]

@vlaiv the point is any specific sequence is just as likely as any other. 

The probability of all t or all h is low compared to all the possible 50/50 t and h  configurations but that is not the point. In MW it is not an ensemble but a branching sequence. There is only a single (infinite?) set of MW.

Regards Andrew 

Edited October 1, 2020 by andrew s

[andrew s]

Each of the MW will have unique sequence. Only one tttt... or hhhh.... and many more with a near 50/50 split but each will have a different sequence.

Regards Andrew 

[andrew s]

@vlaiv you might find this discussion interesting mwi-with-probability-of-outcomes Regards Andrew