Many Worlds and determinism

• I
I am having a hard time understanding the evolution of many worlds in the context of determinism.

If each branch evolves deterministically what can be said about a branch that splits into two branches?

I will try to give an example so the question can be understood better. For instance if my car is on the crossroad and I can go straight, turn left or turn right the MWI will say that all those possibilities/events occur. But before the branching in 3 separate branches, there was my car and the environment around it at some present state at time t=0. So considering determinism, if we knew all the factors in relation with the car and the environment at time t=0 we could predict the future and we would get only one outcome. But instead we get three. So my question is, at time t=0, is there a single state which splits into three branches and how is it possible since the state should evolve deterministically into a single state or are there hidden factors which allow determinism to occur independently at all three worlds?

AlexCaledin

mfb
Mentor
The deterministic evolution leads to three worlds. MWI is not classical physics - you let the wave function evolve in a deterministic way, and you see it splitting into three branches that decohere.

bhobba
The deterministic evolution leads to three worlds. MWI is not classical physics - you let the wave function evolve in a deterministic way, and you see it splitting into three branches that decohere.

I understand that part, and it's fine, but that's just the basic premise behind this. Wouldn't this mean that we lost all predictive power regarding any experiment, even classical? For instance, a coin toss. If we know the variables before we did the experiment we could predict whether it would land heads or tails. But it seems that in MWI we can't predict anything, with respect to the branch we would "land" in the future. Opinions?

mfb
Mentor
It depends on what you call "prediction", and how you evaluate the result of an experiment. The theories make predictions about unobservable magnitudes of amplitudes of those worlds, but you can pick a (potentially small) subset of those worlds with large amplitudes, and say "I consider the experiment as successful in those worlds". That way you can get the physics right in worlds with a large amplitude. This is equivalent to the kind of tests you can do in other interpretations - in probabilistic interpretations you have a risk to be wrong as well, because the photon can go detector one 100 times in a row - it is just unlikely.

It depends on what you call "prediction", and how you evaluate the result of an experiment. The theories make predictions about unobservable magnitudes of amplitudes of those worlds, but you can pick a (potentially small) subset of those worlds with large amplitudes, and say "I consider the experiment as successful in those worlds". That way you can get the physics right in worlds with a large amplitude. This is equivalent to the kind of tests you can do in other interpretations - in probabilistic interpretations you have a risk to be wrong as well, because the photon can go detector one 100 times in a row - it is just unlikely.

How does this correlate with single-worlds interpretation, is the future in those interpretationa still blurry and uncertain from our present perspective?

Nugatory
Mentor
Wouldn't this mean that we lost all predictive power regarding any experiment, even classical?
No. For example, all the results of classical statistical thermodynamics are inherently probabilistic.

For that matter, even the classical treatment of the classical tossed coin is probabilistic. You are thinking that if we feed the exact initial position and velocity of every particle in the coin into some massive calculation based on Newton's laws, we will come out with a deterministic prediction of how the coin will land - and in principle we will. But in practice we do not know the exact initial positions and velocities of every particle, so the calculation can yield no more than a probabilistic prediction, something like "There is a 99.999....% probability that this particular coin toss under these particular initial conditions will come up heads".

Nugatory
Mentor
How does this correlate with single-worlds interpretation, is the future in those interpretations still blurry and uncertain from our present perspective?

Quantum mechanics gives you the probability that you will observe a particular experimental result in a particular experiment in whatever world you happen to be in. Maybe that's the only world, maybe it's not, but that makes no difference as far as quantum mechanics and anything you can conceivably experience is concerned.

Quantum mechanics gives you the probability that you will observe a particular experimental result in a particular experiment in whatever world you happen to be in. Maybe that's the only world, maybe it's not, but that makes no difference as far as quantum mechanics and anything you can conceivably experience is concerned.

What if we had an experiment with a gun, wall and a bullet which is fired in a straight line (we just pull the trigger)? We would see it hit the wall without changing direction in mid-air because the classical probability is massive for that event to happen, right? Which is different than the coin toss in a sense that the different outcomes in the coin toss have about equal probability, but in the bullet firing the probability that it will hit the wall in a straight line is large compared to other possibilities? That's why we see our world evolve in a "normal way".

No. For example, all the results of classical statistical thermodynamics are inherently probabilistic.

For that matter, even the classical treatment of the classical tossed coin is probabilistic. You are thinking that if we feed the exact initial position and velocity of every particle in the coin into some massive calculation based on Newton's laws, we will come out with a deterministic prediction of how the coin will land - and in principle we will. But in practice we do not know the exact initial positions and velocities of every particle, so the calculation can yield no more than a probabilistic prediction, something like "There is a 99.999....% probability that this particular coin toss under these particular initial conditions will come up heads".

So QM and eventual branching applies even when we are considering a non-microscopic experiment like the double slit, the 50-50 (approximately) chance can be considered in a quantum fashion (e.g. the coin collapses, the result that we dont get is a separate world and so on..)

The thing I don't understand really is the probability density regarding MW and macroscopic objects. So, for instance it is often said that macroscopic objects have 99.9 percent of its positions in a range of few atomic diameters. Wouldn't that mean that 99.9 worlds are very similar like ours and that MWI is good when quantum events are in play but when the coin toss experiment or something macroscopic is carried out we still can rely on the classical probability which isn't 50-50 but in fact 99.9 percent in favor of one outcome?

Thanks

mfb
Mentor
Counting worlds is meaningless (and not even well-defined), you need the squared amplitudes as weight - it can be shown that this weight is the only one that is conserved.

For a real macroscopic coin toss, you'll see that the worlds with one result will have a much larger amplitude than the other.

For a real macroscopic coin toss, you'll see that the worlds with one result will have a much larger amplitude than the other.

Can you explain why is that?

mfb
Mentor
Because that's what the time-evolution of the wave function gives you.

bhobba
Because that's what the time-evolution of the wave function gives you.

And it gives us that because there's something like 99:1 ratio in favor of one outcome when we toss the coin?

mfb
Mentor
Those two statements are identical, there is no "A causes B".

bhobba
Dear durant35,

As you know, in 1926 was formulated by Erwin Schroedinger a partial differencial equation that describes how the quantic state of a physical system changes with time. For it, in 1933, he received the Nobel Prize (together with Paul Dirac).

It contains the factor Ψ, referred somewhat improperly as "wave function". The significance of it was not understood, until Max Born interpreted it as defining the probability of finding a particle in a determinate position of space. He received the Nobel Prize for it in 1932. The possibility can be represented by a Gauss curve, with maximum in the center and coming asymptotically to zero in the extremities. The mathematical formalism adopted leaves clear that in the instant the location of the particle is made, all probabilities disappear. Strangely, since the formulation to this day, numerous discussions about the significance of this disappearance occur, maintaining that there is something misterious in it (Copenhagen interpretation). Nevertheless, when we have a dice in hand before we throw it the possibility of each face falling upside is one to six. In the moment it falls upon the table and immobilize, to us it's clear one can no more speak of probabilities, as one of the faces was defined. Its obvious, there is nothing mysterious in it, as even Einstein and Niels Bohr concurred. A supposed “observator's influence” is therefore nonsense, analogous to Kant's discussion of the Moon's existence when no one is looking to it.

It's what occurs when one imagines that Physics necessarily must be described by mathematical formulas, even when they are not needed, as is the case. In this love for mystery, even today is frequent the understanding that the wave function signifies that the particle is in all places at the same time, and quantum theory would make possible the creation of a computer capable of realizing simultaneously infinite mathematical operations, a thing that would be useful, for instance, in breaking cryptographed texts. We must have present that Mathematics is a tool, albeit useful, but only an instrument. In his celebrated novel "Glory Road" Robert Heinleim created the neologism "to grock" meaning a profound, almost subconscient knowledge of some theme. Perhaps what is needed is "grocking" the physical fenomenon before using mathematics to better understand the details of it.

Another common mistake that has the same origin consists in "multiple universes interpretation", that erroneously affirms the objective reality of the universal wave function. As I see it, that makes no sense at all. Observe that Schroedinger's equation is completely deterministic, the aleatority surges in it as an emergent property.

Strilanc
I remember, when I learned about cell division, wondering something along the lines of "But which of the two cells at the end is the parent?". Which is really not the right way to be thinking about cell division.

This is kind of an analogous situation, except instead of "Which cell is the parent?" you're asking "But which world will I end up in?". It's not really the right way to think about it. Taking MWI extremely literally for the rest of this paragraph I'd say you always end up in both worlds, but in an isolated way without cross talk between your two descendant selves. Your inability to predict outcomes isn't because they're random, it's because you aren't informed of which descendant copy you are. The uncertainty is indexical.

Imagine if cell division happened to people, and someone about to divide was asked "but which copy will you be?". Even if the person-division process was deterministic, there's not really a well-defined answer to that question.

bhobba
Mentor
that erroneously affirms the objective reality of the universal wave function. As I see it, that makes no sense at all. Observe that Schroedinger's equation is completely deterministic, the aleatority surges in it as an emergent property.

Well what makes sense to you, or me for that matter, is not what determines if an interpretation is valid or not. That it contains the QM formalism is all that is required - and MW does.

These days MW is very elegant and beautiful:
http://users.ox.ac.uk/~mert0130/books-emergent.shtml [Broken]

Do I hold to it? No - but that means diddly squat.

Thanks
Bill

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bhobba
Mentor
"But which world will I end up in?".

Of course you end up in all worlds - but you only experience one. Decision theory is used to determine the probability of what world will be experienced (IMHO its really non contextuality that is the basis Gleason in another guise - but that is a whole new thread). The woolly thinking about this compels me to say, just like the Bayesian view of probability not requiring a rational agent to be present to assign a probability, the probability of what world is experienced has nothing to do if anyone is there or not.

Thanks
Bill

I red one post from a forum member which is related to my thread and it answes the question of why we don't experience a history where someone throws heads on the coin 10000 times in a row, which should happen in some other branch. The answer was:

"There are a lot more histories with about 5000 heads than with 10000 heads, so chances are we'd find ourselves having lived through one of them."

Now my real issue with this is the following, if we had ideal and same conditions each throw, we could throw the coin and deterministically make it fall on one side repeatedly, every single time. That's because it is a macroscopic object, so the chances of it following on the other in conditions which favor one outcome are miniscule. So how on earth would all these branches where 5000 heads fall occur, if each time flipping we would get 2 worlds with a relative amplitude of something like 99:1.

bhobba
Mentor
So how on earth would all these branches where 5000 heads fall occur, if each time flipping we would get 2 worlds with a relative amplitude of something like 99:1.

Because only the Born rule is basis independent.

Any other rule singles out a particular basis over another, which is against the spirit of the Hilbert space formalism.

In a nutshell the issue is this. Suppose we have an observation with two outcomes. Your idea would be they occur 50-50. Now lets form a compound observation where one of the outcomes fire off a second observation. That will have 3 outputs - one with 50% probability and the other two with 25% probability. The equally likely idea would assign 1/3 to each. Its obviously wrong. As I said the only one that works is basis independence - all others run into problems. And via Gleason basis Independence means the Born rule.

These and other 'objections' are examined in section 5.8 of Wallace's book:
https://www.amazon.com/dp/0198707541/?tag=pfamazon01-20

Thanks
Bill

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mfb
Mentor
"There are a lot more histories with about 5000 heads than with 10000 heads, so chances are we'd find ourselves having lived through one of them."
That has the implicit assumption that all those worlds have the same amplitude. This is not true in your scenario.

Now I get it, thank you very much Bill and mfb

bhobba