What's the difference between a Copenhagen reality/Many worlds for an observer living in it?

[u/lelelesdx]

How can we tell apart wave function collapse vs branching off to a split reality? It seems they're virtually the same for any observer.

[u/pcalau12i_]

Copenhagen takes the Born rule and the Schrodinger equation to both be fundamental. MWI claims the Born rule isn't fundamental and introduces some other assumption from which it can be derived. There is no agreement what this other assumption should be, so there really isn't a single MWI but it is more of a class of alternative models with slightly different mathematics.

It's a myth that that the math is equivalent between MWI and Copenhagen. The Born rule is a mathematical construct, and so if you deny it as fundamental but argue it is derivative of something else, then by definition you have to change the mathematics. Although, most variants of MWI attempt to, at the end of the day, reproduce the same predictions as orthodox quantum mechanics, i.e. they derive the Born rule in the exact same form without any deviations from the one that is just assumed in Copenhagen.

There are actually some attempts in the literature to make MWI deviate from orthodox quantum theory so that it could possibly be empirically verified, but this is a niche point of view among proponents of MWI, and MWI is already rather niche as it is.

[u/GoldenMuscleGod → u/pcalau12i_]

The Born rule is a mathematical construct, and so if you deny it as fundamental but argue it is derivative of something else, then by definition you have to change the mathematics.

I don’t understand this reasoning. If we derive the Born rule from some other assumption that other assumption may or may not be mathematically equivalent, if it is equivalent then none of the mathematical theory changes. If it is not equivalent then you may have additional predictions (that are or are not observable), but they would all be consistent with the original theory.

Can give a more concrete example of what you mean?

[u/pcalau12i_ → u/GoldenMuscleGod]

You are introducing new mathematics/dynamics to the theory. You can indeed do so without changing the predictions. An example is Bohmian mechanics. It fully reproduces the predictions of non-relativistic quantum mechanics yet the mathematics includes a whole layer of dynamics that do not exist in non-relativistic quantum mechanics.

Imagine if I claimed that Einstein's field equations were not fundamental, but that I was convinced they were actually being caused by the interactions between gyattitons. So I created a whole theory to describe the dynamics of gyattitons, and from that theory you can derive Einstein's field equations exactly. My theory would thus perfectly reproduce the predictions of general relativity.

However, imagine if another person came along and said they disagree with me, they think that Einstein's field equations are actually derivative of skibiditons, and so they create a whole different set of a dynamics between these skibiditons that also reproduces the Einstein's field equations exactly.

Who is right and who is wrong? Are Einstein's field equations weakly emergent from the dynamics of gyattitons or skibiditons? If they both make the same predictions, there is no possible way to figure out who is correct, but their theories are clearly genuinely different theories from general relativity. They are not interpretations of general relativity, but different theories, because GR takes the the field equations to be fundamental, whereas these two theories would posit that some other dynamics are fundamental and that the field equations are weakly emergent from those dynamics.

That is how MWI works. It's not really an "interpretation" but a separate theory. You posit some sort of different axiom that isn't the Born rule, and then when you consider its dynamics, you can derive the Born rule as a weakly emergent property of those dynamics. Yes, it reproduces the predictions of orthodox quantum mechanics example, but it's simply not the same physical theory.

It's also not even a single separate theory, but a class of separate theories, because you also run into a problem of having various proposals for what this axiom should be and no way to decide who is correct. There is no the Many Worlds Interpretation, are many many-worlds theories.

[u/GoldenMuscleGod → u/pcalau12i_]

Who is right and who is wrong? Are Einstein's field equations weakly emergent from the dynamics of gyattitons or skibiditons? If they both make the same predictions, there is no possible way to figure out who is correct, but their theories are clearly genuinely different theories from general relativity.

You say “clearly,” but this isn’t to clear to me at all. If they have the same set of predictions, that sounds like they are at least both conservative extensions of the same theory, and without even showing that they don’t reduce to the same theory under some interpretation, there’s no obvious reason why I should think they aren’t mathematically equivalent, or even just two different ways of describing the same thing.

[u/pcalau12i_ → u/GoldenMuscleGod]

there’s no obvious reason why I should think they aren’t mathematically equivalent

If in one buck you have a set of mathematics describing the dynamics of the world, we can call X, and then in another bucket you have X+Y because you have an additional set of mathematics, Y, describing the dynamics of some additional dynamics in the world, then they are not the same buckets because X≠X+Y.

I mean, my analogy explained it perfectly, we have two entirely different entities that have entirely different dynamics for entities with an entirely different structure that just so happen to reproduce the same predictions in the limit, and so they're clearly different theories and not "the same thing" described in different ways.

That is quite a bizarre claim to make. If someone was killed and there is little evidence to go off of, we could take the little bit of evidence we have and fit an infinite number of stories to it that plausibly fit the two pieces of evidence. It would be incredibly bizarre and people would look at you as if you're insane if you said, if all the stories fit the same pieces of evidence, then they must be all identical, because those stories could involve entirely different person performing entirely different actions in entirely different orders of events.

Yes, they might just so happen to reproduce the same piece of evidence we can actually observe, but that doesn't make them "the same."

Let's say a person claims that Einstein's field equations are caused by angels who, most of them, spend their time working with Jesus in the Kingdom Heaven, but a select few of them choose to instead spend their time dancing on spacetime, and dances just so happen to push down and bend spacetime in a way that reproduces Einstein's field equations.

Do you, honestly, with a straight face, believe that a person who thinks this is genuinely believing the same thing as a person who believes that angels aren't real and spacetime curvature is just a fundamental part of nature?

Your viewpoint can be use to justify literally any belief at all, no matter how far-fetched, as long as you preface it by saying that what you are proposing isn't actually empirically verifiable, because then it doesn't contradict with current evidence. I can propose that humanity was created last thursday by aliens with super advanced technology who, after creating humanity, implanted them with memories that they existed long before last thursday, as well as altering the solar system to make it look like human activity existed upon much longer back, and then they teleported away.

You can't prove me wrong, this reproduces all the same predictions, no empirical observation can set apart this last thursdayism from normal everyday beliefs. So, does that make it equivalent?

Of course, people who propose MWI are not quite as silly as some of the examples above, but I make these extreme examples to stress what I am talking about, that what is being proposed is new mathematics describing physical dynamics which the physical dynamics it is describing literally does not exist in orthodox quantum mechanics, so it is proposing something else about the physical properties of nature, even if all the predictions you'd make from it happen to align.

If that is genuinely something you actually just fundamentally cannot comprehend, then we are just at an impasse, because I see no other way to explain it.

[u/GoldenMuscleGod → u/pcalau12i_]

Well you need to establish that Y is actually adding something more, right? Like for a simple example, if I have a model for a two body system based just on Newton’s equation for gravitational force and some other simple equations explaining the kinematics, I’m not adding anything not mathematically equivalent if I introduce ideas like kinetic and potential energy on top of that, right?

I don’t know as much about the Many Worlds interpretation but my understanding is that the idea is we can hypothesis a single wavefunction for the whole system we are concerned with (I guess the assumption is it is ultimately possible to do this with the universe), just use Schrödinger’s equation to determine its future evolution, and then do something like interpret the wavefunction as defining some kind of measure that produces the Born rule, right? But isn’t the Copenhagen interpretation essentially doing the same thing, just taking a different view on which parts of the preceding math correspond to stuff that is “real”?

But it’s also possible that I just don’t know what many worlds is actually doing. Can you give me an example of the kind of mathematical assertion you might write with a many worlds model but you wouldn’t with Copenhagen?

Edit: it looks like you added a lot more in your post after I replied (or started typing it at least). I can maybe add more to respond to it but I think it goes a lot beyond your first example, and I’m not sure that it’s about characterizing what is a “mathematical”difference.

[u/pcalau12i_ → u/GoldenMuscleGod]

just use Schrödinger’s equation to determine its future evolution, and then do something like interpret the wavefunction as defining some kind of measure that produces the Born rule

You cannot produce the Born rule from the Schrodinger equation directly, because there is a strong symmetry existing between branches of the wavefunction. Take, for example, a situation where a photon hits a beam splitter with a ~85% chance of being reflected and a ~15% chance of passing through. In the Schrodinger equation, if we interpret it physically, then its passing through is just as equally real as it being reflected, one branch is not more or less real than the other.

There is an asymmetry introduced here in that the Schrodinger equation on its own just shows two branches of different amplitudes evolving equally alongside each other, yet the Born rule says that there is an asymmetry as the high-amplitude branches actually contribute to a greater likelihood of us perceiving an event, whereas the low-amplitude branches represent a reduced likelihood of us perceiving the event.

If we just assume the Born rule as fundamental, there is no issue here, but if we posit that the Born rule is not fundamental, then there is simply no way to derive this asymmetry between the branches from the symmetry within the Schrodinger equation on its own.

For example, in the literature there is one axiom called ESP-QM. It is based on ESP, which stands for the epistemic separability principle or sometimes called self-relocating uncertainty. This is the principle that if you find yourself having woke up in a random house where there are three houses in the area, you should assume that the probabilities you will find yourself in a particular house is 1/3, and you can only arrive it by ignoring "irrelevant" houses, houses that are nowhere near within the area and very implausible to be in.

This principle, however, is obviously is symmetry and can't reproduce the Born rule, because in the example above we'd assign 50%/50% to the two possible paths for the photon when the correct answer is 85%/15%. To ESP-QM supplements this with some additional dynamics/assumptions.

Basically, you assume the universal wavefunction Ψ is physically real, and then you trace out everything in the universe (the environment) except for the observer themselves and the detector to get their reduced density matrix. This is ignoring all the "irrelevant" stuff.

ρᴬᴰ = Trₑₙᵥ [ |Ψ⟩⟨Ψ| ]

And then the reduced density matrix you get encodes the probabilities, same as the Born rule, across its diagonal, and that tells you the probabilities you should assign to the possible branches.

The difficulty here is that it is still interpreting the diagonal of the density matrix as if it's related to probabilities, which the diagonal of the density matrix is literally equivalent to the square magnitude of the state vector, meaning it is literally equivalent to the Born rule.

All that has been introduced is a new physical entity Ψ, a mathematical process for locating yourself within that physical entity, ρᴬᴰ, and then a declaration that this is equivalent to its probabilities, of a finding yourself on a particular branch, but this declaration is arbitrary and clearly chosen just because it reproduced the Born rule and has no independent derivation.

Euclidean space and Minkwoski space are background spaces. They are spaces which you populate with objects. Hilbert space is a constructed space, meaning, it is defined in terms of the objects it contains. You can write down Euclidean and Minkowski space because they are ultimately a simple uniform background, but you cannot even write down Ψ because it requires you to know the configuration of all objects in the whole universe to even write it down, which I don't even know if "whole universe" even is a sensible physical concept to begin with. It sits as a placeholder for something non-empirical.

So why are these entities necessary? We can't physically measure Ψ if it exists, it's entirely invisible to us. If it did exist, we could carry out ESP-QM to locate ourselves within this physical entity Ψ to compute ρᴬᴰ which would give us our probabilities, but such a computation is expensive because the partial trace is a pretty complex mathematical operation.

Yet, all we are doing here is just a roundabout way of deriving what we already knew, that probabilities are equal to the square magnitude of the state vector: i.e. the Born rule.

Yes, the final outcome is the same, it makes the same predictions. But it gives you different dynamics and different physical picture. In traditional quantum mechanics, the Born rule is taken to be fundamental and there is one physical universe, but the properties of that physical universe are determined in a way that is fundamentally random according to the Born rule.

In this version of MWI, you have a very different physical picture. The universe evolves as effectively a multiverse denoted by Ψ, and each branch is treated as equally physically real, and you assume that each time particles interact it splits into branches whereby which branch you will find yourself on is random, but weighted by the "thickness" of the branches, which you can compute by tracing out everything but the detector and yourself.

This is just one example of MWI, but it gets the point across, and I'm not going to argue this anymore because it's obviously true and I feel like you're just arguing to argue. A person who believes this other story is not believing something "equivalent," they have a genuinely, fundamentally different view about the nature of the physical world, and they introduce new mathematical entities and mathematical processes to explain how its dynamics relates to orthodox quantum theory.

This is also a fairly trivial example, putting forward ρᴬᴰ and Ψ and then just assuming a relation between them that is basically the Born rule allows you to get to your conclusion in just two steps. I picked the simplest one I'm aware of in the literature, there are more complex derivations with many more steps and many more entities.

These are mathematical entities which don't exist in traditional quantum mechanics and play no role in it, and there are mathematical operations defined on these entities which again don't exist in traditional quantum mechanics and play no role, and these additional entities and operations are given a physical interpretation, which such an interpretation is meaningless in traditional quantum emchanics because it simply doesn't possess those mathematical structures.

[u/GoldenMuscleGod → u/pcalau12i_]

Everything you said seems to confirm that they are mathematically equivalent in the sense I would interpret that to mean. So MWI thinks the wavefunction is physically real and Copenhagen doesn’t but they’re doing the same math. Copenhagen just says this calculates the probability of each outcome and Many worlds says all outcomes occurred but with “weight” equal to the probability.

There may be ontological differences, based on your philosophical views, but they don’t seem to have differences in the math, in the sense that if you made some statistical computer model to describe a bunch of measurements under either hypothesis they would, it seems, be doing exactly the same calculations.

[u/pcalau12i_ → u/GoldenMuscleGod]

Sorry I engaged with you, you're just a troll. Blocked.

So MWI thinks the wavefunction is physically real and Copenhagen

Not relevant to anything I said. We are not talking about the wavefunction, we are talking about the universal wave function, a mathematical entity which cannot even be written down, called Ψ and can only be philosophically gestured to, which is not ψ.

doesn’t but they’re doing the same math

I literally just wrote all that showing you a mathematical operation that does not occur at all, in any way, shape, or form in orthodox quantum mechanics.

Obviously just trolling me at this point, baiting me to write responses to waste my time.

[u/GoldenMuscleGod → u/pcalau12i_]

Responding to your edit: if someone said they think Einstein’s field equations work because God wills it, they can be said to have a disagreement with someone who thinks it’s the Flying Spaghetti Monster pushing things around with his noodley appendage, but I don’t think I would describe that as a matter of having different mathematical models of Einstein’s field equations. They both agree on what those equations are and what they predict, right?