# I Danger for the Many-Worlds Interpretation?

#### timmdeeg

Gold Member
Summary
http://backreaction.blogspot.com/2019/09/the-trouble-with-many-worlds.html

Are the claims of Sabine Hossenfelder a danger for the many worlds?
Sabine Hossenfelder claims:

This, of course, is not what we observe. We observe only one measurement outcome. The many worlds people explain this as follows. Of course you are not supposed to calculate the probability for each branch of the detector. Because when we say detector, we don’t mean all detector branches together. You should only evaluate the probability relative to the detector in one specific branch at a time.

That sounds reasonable. Indeed, it is reasonable. It is just as reasonable as the measurement postulate. In fact, it is logically entirely equivalent to the measurement postulate. The measurement postulate says: Update probability at measurement to 100%. The detector definition in many worlds says: The “Detector” is by definition only the thing in one branch. Now evaluate probabilities relative to this, which gives you 100% in each branch. Same thing.

What does "logically entirely equivalent " which results in "same thing" mean regarding the collapse avoidance of the wave function in the MWI?

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#### martinbn

Why dont you ask this question on her blog?

#### timmdeeg

Gold Member
I tried without success. So I’m interested how experts around here interpret her message.

#### PeroK

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Why dont you ask this question on her blog?
@timmdeeg Someone already has prompted this clarification. In response to Steve Bryson she says:

"Write down the assumptions that you need to describe what you observe (including the fact that, after measurement, you know with 100% probability what has happened). I hope then you will see that you need an assumption, next to the Schrödinger equation, to replace the measurement postulate."

#### timmdeeg

Gold Member
Thanks.
Hm, doesn't "including the fact that, after measurement, you know with 100% probability what has happened " mean that the mentioned assumptions require the collapse of the wave function in contrast to what MWI claims?

If so, what do you think about that?

#### PeroK

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Thanks.
Hm, doesn't "including the fact that, after measurement, you know with 100% probability what has happened " mean that the mentioned assumptions require the collapse of the wave function in contrast to what MWI claims?

If so, what do you think about that?
The difference between the two is roughly analogous to:

You roll a die and it comes up 6:

Collapse: the probability space of the die before rolling collapsed into a single outcome of 6. The practical consequences are that you are now in a world where the die came up 6.

MWI: the probability space remains in a superposition of 1-6, with each possible outcome. The observer is, however, also superposed into these six "worlds". The result of their measurement is a definite 6. They are not aware of the other five worlds, nor can they explain why they are in the world where the die came up 6. The practical consequences are the same: you are now in a world where the die came up 6.

SH's point, I think, is that to all intents and purposes these amount to the same thing. "Logically entirely equivalent". I.e. the missing explanation in MWI is equivalent to the wave-function collapse.

#### timmdeeg

Gold Member
SH's point, I think, is that to all intents and purposes these amount to the same thing. "Logically entirely equivalent". I.e. the missing explanation in MWI is equivalent to the wave-function collapse.
This sounds just like a personal opinion, not like a physical statement which is either correct or wrong.

So I think I was mislead thinking that S.H. saying "you need an assumption, next to the Schrödinger equation, to replace the measurement postulate" means that it's an illusion to believe that the unitary evolution of the wave function holds in MWI; or in other words that this needed "assumption" contradicts Schrödinger's equation unitarity.

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Hum, I was also confused by her comments that there must be some kind of evolution beyond unitary, here and also in previous comments. But it seems all she really can say is you need an additional assumption to derive subjective collapse from unitary evolution. All the Born rule derivations do use additional assumptions so it seems likely, but she really distorts the point.

#### Demystifier

2018 Award
I think Sabine is really talking about the problem of the Born rule in the many-worlds interpretation (MWI). If that interpretation is true, then where do probabilities come from and why are they given by the Born rule? This is indeed one of the main unsolved problems in MWI. It's not that there are no proposed solutions, but neither of the proposed solutions is generally accepted in the MWI community, let alone outside of the community.

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#### Minnesota Joe

What does "logically entirely equivalent " which results in "same thing" mean regarding the collapse avoidance of the wave function in the MWI?
I'm not sure I understand what analysis leads Hossenfelder to this conclusion, except maybe that branching results in new worlds, each with pure states ("collapsed").

@PeroK 's dice analogy works as long as the die is thought of as a superposition--the universal wave-function. All sides exist at the end.

But that means collapse has been explained as only apparant, not assumed as far as I can tell.

#### timmdeeg

Gold Member
But it seems all she really can say is you need an additional assumption to derive subjective collapse from unitary evolution.
The key point regarding the additional assumption is:

Some people have a problem with the branching because it’s not clear just exactly when or where it should take place, but I do not think this is a serious problem, it’s just a matter of definition. No, the real problem is that after throwing out the measurement postulate, the many worlds interpretation needs another assumption, that brings the measurement problem back.

No, the real problem is that after throwing out the measurement postulate, the many worlds interpretation needs another assumption, that brings the measurement problem back.
Can you really say that without specifying which assumption you are making? What is the assumption and the problem?

#### timmdeeg

Gold Member
What is the assumption and the problem?
I think the problem is this:

The wave-function collapse, I have to emphasize, is not optional. It is an observational requirement. We never observe a particle that is 50% here and 50% there. That’s just not a thing. If we observe it at all, it’s either here or it isn’t. Speaking of 50% probabilities really makes sense only as long as you are talking about a prediction.

If Hossenfelder's statement is true then I think the MWI fans have a problem, because they can't deny that outcomes are observed which then requires the wave-function collapse.

But is this statement true?

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#### PeterDonis

Mentor
doesn't "including the fact that, after measurement, you know with 100% probability what has happened " mean that the mentioned assumptions require the collapse of the wave function in contrast to what MWI claims?
No, because the word "you" means two different things in the two interpretations. In Copenhagen, "you" means the single "you" that observes the single die outcome. In MWI, "you" means one of six copies, each of which observes one of the six possible outcomes.

Part of the problem in even talking about the MWI is that ordinary words have to mean very different things.

#### entropy1

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the many worlds interpretation needs another assumption, that brings the measurement problem back.
Could it be that the outcomes of for instance $\sqrt{\frac{1}{4}}|A \rangle+\sqrt{\frac{3}{4}}|B \rangle$ might be viewed as $\frac{1}{4}$ % real outcome $|A \rangle$ and $\frac{3}{4}$ % real outcome $|B \rangle$, in other words labeling the outcome with the probability?

#### Minnesota Joe

Why isn't it available for your copy in one of the branch worlds to realize that the collapse is only apparent? That the full wave function does satisfy the Schrodinger equation?

And those copies know the amplitudes of the original wave function too since by assumption you knew the amplitudes.

I don't know. Maybe she is attacking the Born Rule derivations instead of how the collapse is explained by MWI . I say this because Hossenfelder's comments at the end of the video about that seems like a bigger problem to me and that is where the amplitudes and choice of where to calculate the probability come in first.

#### DarMM

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dice analogy works as long as the die is thought of as a superposition--the universal wave-function
In Perok's dice analogy we have an outcome space $\Omega = \left\{1,2,3,4,5,6\right\}$ and a probability distribution over it $p(\omega)$. Many Worlds corresponds to stating that rather than the elements of $\Omega$ being what occurs, the actual "reality" is $p(\omega)$. The primary claim is not so much that all the dice outcomes exist.

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#### Minnesota Joe

In Perok's dice analogy we have an outcome space $\Omega = \left\{1,2,3,4,5,6\right\}$ and a probability distribution over it $p(\omega)$. Many Worlds corresponds to stating that rather than the elements of $\Omega$ being what occurs, the actual "reality" is $p(\omega)$. It's not so much that all the dice outcomes exist.
It seems crucial for MWI to explain the collapse. All the dice outcomes must occur and there is a different macroscopic person (or detector) assessing the microscopic outcomes.

Instead of entangled die states, consider measuring an entangled spin state with spins $\uparrow$ and $\downarrow$ and person $A$ (you are the detector) in world environment $0$. This state evolves via the Schrodinger equation ($\longrightarrow$) into worlds $1$ with person $B$ and world $2$ with person $C$:
$$a_1 |\uparrow,A,0> + a_2 |\downarrow,A,0> \longrightarrow a_1 |\uparrow,B,1> + a_2 |\downarrow,C,2>$$
Person $B$ and $C$ are copies of person $A$ (you).

Look at the first term on the right of the arrow. It describes a different world environment $1$ with a copy of you, person $B$, but a definite value of spin: $\uparrow$.

Is that real "collapse"?

Why isn't it available to your copy, person $B$, to realize that the full universal wave-function--the superposition--does satisfy the Schrodinger equation (by assumption)? Person $B$ understands why it seems like a "collapse" but realizes that is only seeming because person $B$ cannot observe the outcome in world $2$. Only person $C$ can do that.

ETA: Fixed repeated word.

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#### DarMM

Gold Member
Note the dice states are not entangled. That's impossible in a classical probability theory.

It seems crucial for MWI to explain the collapse. All the all dice outcomes must occur and there is a different macroscopic person (or detector) assessing the microscopic outcomes.
The point though is that the "dice outcomes" are secondary to the primary reality in MWI, which is $p\left(\omega\right)$

Instead of entangled die states, consider measuring an entangled spin state with spins $\uparrow$ and $\downarrow$ and person $A$ (you are the detector) in world environment $0$. This state evolves via the Schrodinger equation ($\longrightarrow$) into worlds $1$ with person $B$ and world $2$ with person $C$:
$$a_1 |\uparrow,A,0> + a_2 |\downarrow,A,0> \longrightarrow a_1 |\uparrow,B,1> + a_2 |\downarrow,C,2>$$
Person $B$ and $C$ are copies of person $A$ (you).

Look at the first term on the right of the arrow. It describes a different world environment $1$ with a copy of you, person $B$, but a definite value of spin: $\uparrow$.

Is that real "collapse"?
Well yes in a sense, it's essentially equivalent. The bigger issue in MWI is explaining why $A$ should expect to find themselves in the $B$ situation with probability $|a_1|^{2}$.

#### Minnesota Joe

Note the dice states are not entangled. That's impossible in a classical probability theory.
They definitely are entangled if you are talking about MWI as far as I understand. Otherwise there aren't any branches unless you measure a different property than the die values. And it is entanglement between microscopic things and macroscopic things that is key because decoherence provides the mechanism for splitting. Entanglement is the most important feature of MWI this means I suppose.

The point though is that the "dice outcomes" are secondary to the primary reality in MWI, which is $p\left(\omega\right)$
I disagree with this as I noted. I don't think that is what MWI is saying. The outcomes occur with probability $p\left(\omega\right)$ and which outcome-world your copies are in decides what they see. See the importance of an initial entangled state above.

Well yes in a sense, it's essentially equivalent. The bigger issue in MWI is explaining why $A$ should expect to find themselves in the $B$ situation with probability $|a_1|^{2}$.
I agree this is a bigger issue and probably this is where I part ways with MWI.

If I understand him correctly, Sean Carroll tries to derive the Born Rule by assigning probabilities from a branch world of $B$ (or $C$). He argues from the amplitudes. (Since $A$ knows the amplitudes by assumption so do copies $B$ and $C$). If the amplitudes are equal assign a probability of $1/2$. Of course in that case $1/2=|a_1|^2=|a_2|^2$. This is the uninformative prior rule I guess. And, presumably, this model should adjust with the amplitudes accordingly if they are different. So the Born Rule is a rational weighting. I don't fully understand this argument yet so I don't want to say too much more.

#### WWGD

Gold Member
If I may ask, as someone uninitiated: does the issue of the dice extend to other events with larger, say infinite, possible outcomes, and if so, does this bring about branching? Say we consider a voltage measurement, which can take infinitely- many values, each value being realized in a different world. Then, in each of these worlds, a similar measurement is made, leading to infinitely- many more worlds where outcomes are realized, and so on? Or does this come about only with a finite potentiality of outcomes?

#### PeroK

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If I may ask, as someone uninitiated: does the issue of the dice extend to other events with larger, say infinite, possible outcomes, and if so, does this bring about branching? Say we consider a voltage measurement, which can take infinitely- many values, each value being realized in a different world. Then, in each of these worlds, a similar measurement is made, leading to infinitely- many more worlds where outcomes are realized, and so on? Or does this come about only with a finite potentiality of outcomes?
As far as I am aware, Everett believed there should be an uncountable infinity of worlds.

#### Minnesota Joe

If I may ask, as someone uninitiated: does the issue of the dice extend to other events with larger, say infinite, possible outcomes, and if so, does this bring about branching? Say we consider a voltage measurement, which can take infinitely- many values, each value being realized in a different world. Then, in each of these worlds, a similar measurement is made, leading to infinitely- many more worlds where outcomes are realized, and so on? Or does this come about only wiAsth a finite potentiality of outcomes?
Yeah, as far as I understand it is turtles all the way down .

I guess the number of branches created depends on larger questions like whether or not things like space-time is quantized and the number of degrees of freedom at a point in space-time, are there really a continuum of voltages?, and so on.

#### WWGD

Gold Member
And I guess no two of these worlds ( physically) overlap?

#### Minnesota Joe

And I guess no two of these worlds ( physically) overlap?
As I understand they don't interact in any way, ever.

ETA: This is incorrect and I amend it in a later post.

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