pcalau12i

don’t mind me i have autism

Many worlds theories are rather strange.

If you take quantum theory at face value without trying to modifying it in any way, then you unequivocally run into the conclusion that ψ is contextual, that is to say, what ψ you assign to a system depends upon your measurement context, your “perspective” so to speak.

This is where the “Wigner’s friend paradox” arises. It’s not really a “paradox” as it really just shows ψ is contextual. If Wigner and his friend place a particle in a superposition of states, his friend says he will measure it, and then Wigner steps out of the room for a moment when he is measuring it, from the friend’s perspective he would reduce ψ to an eigenstate, whereas in Wigner’s perspective ψ would instead remain in a superposition of states but one entangled with the measuring device.

This isn’t really a contradiction because in density matrix form Wigner can apply a perspective transformation and confirm that his friend would indeed perceive an eigenstate with certain probabilities for which one they would perceive given by the Born rule, but it does illustrate the contextual nature of quantum theory.

If you just stop there, you inevitably fall into relational quantum mechanics. Relational quantum mechanics just accepts the contextual nature of ψ and tries to make sense of it within the mathematics itself. Most other “interpretations” really aren’t even interpretations but sort of try to run away from the conclusion, such as significantly modifying the mathematics and even statistical predictions in order to introduce objective collapse or hidden variables in order to either get rid of a contextual ψ or get rid of ψ as something fundamental altogether.

Many Worlds is still technically along these lines because it does add new mathematics explicitly for the purpose of avoiding the conclusion of irreducible contextuality, although it is the most subtle modification and still reproduces the same statistical predictions. If we go back to the Wigner’s friend scenario, Wigner’s friend reduced ψ relative to his own context, but Wigner, who was isolated from the friend and the particle, did not reduce ψ by instead described them as entangled.

So, any time you measure something, you can imagine introducing a third-party that isn’t physically interacting with you or the system, and from that third party’s perspective you would be in an entangled superposition of states. But what about the physical status of the third party themselves? You could introduce a fourth party that would see the system and the third party in an entangled superposition of states. But what about the fourth party? You could introduce a fifth party… so on and so forth.

You have an infinite regress until, at some how (somehow), you end up with Ψ, which is a sort of “view from nowhere,” a perspective that contains every physical object, is isolated from all those physical objects, and is itself not a physical object, so it can contain everything. So from the perspective of this big Ψ, everything always remains in a superposition of states forever, and all the little ψ are only contextual because they are like perspectival slices within Ψ.

You cannot derive Ψ mathematically because there is no way to get from inherently contextual ψ to this preferred nonphysical perspective Ψ, so you cannot know its mathematical properties. There is also no way to define it, because each ψ is an element of Hilbert space and Hilbert space is a constructed space, unlike background spaces like Minkowski space. The latter are defined independently of the objects the contain, whereas the former are defined in terms of the objects they contain. That means for two different physical systems, you will have two different ψ that will be assigned to two different Hilbert spaces. The issue is that you cannot define the Hilbert space that Ψ is part of because it would require knowing everything in the universe.

Hence, Ψ cannot be derived nor defined, so it can only be vaguely postulated, and its mathematical properties also have to be postulated as you cannot derive them from anything. It is just postulated to be this privileged cosmic perspective, a sort of godlike ethereal “view from nowhere,” and then it is postulated to have the same mathematical properties as ψ but that all ψ are also postulated to be subsystems of Ψ. You can then write things down like how a partial trace on Ψ can give you information about any perspective of its subsystems, but only because it was defined to have those properties. It is true by definition.

In a RQM perspective it just takes quantum theory at face value without bothering to introduce a Ψ and just accepts that ψ is contextual. Talking about a non-contextual (absolute) ψ makes about as much sense as talking about non-contextual (absolute) velocity, and talking about a privileged perspective in QM makes about as much sense as talking about a privileged perspective in special relativity. For some reason, people are perfectly happy with accepting the contextual nature of special relativity, but they struggle real hard with the contextual nature of quantum theory, and feel the need to modify it, to the point of convincing themselves that there is a multiverse in order to escape it.

There are no “paradoxes” of quantum mechanics. QM is a perfectly internally consistent theory. Most so-called “paradoxes” are just caused by people not understanding it.

QM is both probabilistic and, in its own and very unique way, relative. Probability on its own isn’t confusing, if the world was just fundamentally random you could still describe it in the language of classical probability theory and it wouldn’t be that difficult. If it was just relative, it can still be a bit of a mind-bender like special relativity with its own faux paradoxes (like the twin “paradox”) that people struggle with, but ultimately people digest it and move on.

But QM is probabilistic and relative, and for most people this becomes very confusing, because it means a particle can take on a physical value in one perspective while not having taken on a physical value in another (called the relativity of facts in the literature), and not only that, but because it’s fundamentally random, if you apply a transformation to try to mathematically place yourself in another perspective, you don’t get definite values but only probabilistic ones, albeit not in a superposition of states.

For example, the famous “Wigner’s friend paradox” claims there is a “paradox” because you can setup an experiment whereby Wigner’s friend would assign a particle a real physical value whereas Wigner would be unable to from his perspective and would have to assign an entangled superposition of states to both his friend and the particle taken together, which has no clear physical meaning.

However, what the supposed “paradox” misses is that it’s not paradoxical at all, it’s just relative. Wigner can apply a transformation in Hilbert space to compute the perspective of his friend, and what he would get out of that is a description of the particle that is probabilistic but not in a superposition of states. It’s still random because nature is fundamentally random so he cannot predict what his friend would see with absolute certainty, but he can predict it probabilistically, and since this probability is not a superposition of states, what’s called a maximally mixed state, this is basically a classical probability distribution.

But you only get those classical distributions after applying the transformation to the correct perspective where such a distribution is to be found, i.e. what the mathematics of the theory literally implies is that only under some perspectives (defined in terms of any physical system at all, kind of like a frame of reference, nothing to do with human observers) are the physical properties of the system actually realized, while under some other perspectives, the properties just aren’t physically there.

The Schrodinger’s cat “paradox” is another example of a faux paradox. People repeat it as if it is meant to explain how “weird” QM is, but when Schrodinger put it forward in his paper “The Present Situation in Quantum Mechanics,” he was using it to mock the idea of particles literally being in two states at once, by pointing out that if you believe this, then a chain reaction caused by that particle would force you to conclude cats can be in two states at once, which, to him, was obviously silly.

If the properties of particles only exist in some perspectives and aren’t absolute, then a particle can’t meaningfully have “individuality,” that is to say, you can’t define it in complete isolation. In his book “Science and Humanism,” Schrodinger talks about how, in classical theory, we like to imagine particles as having their own individual existence, moving around from interaction to interaction, carrying their properties with themselves at all times. But, as Schrodinger points out, you cannot actually empirically verify this.

If you believe particles have continued existence in between interactions, this is only possible if the existence of their properties are not relative so they can be meaningfully considered to continue to exist even when entirely isolated. Yet, if they are isolated, then by definition, they are not interacting with anything, including a measuring device, so you can never actually empirically verify they have a kind of autonomous individual existence.

Schrodinger pointed out that many of the paradoxes in QM carry over from this Newtonian way of thinking, that particles move through space with their own individual properties like billiard balls flying around. If this were to be the case, then it should be possible to assign a complete “history” to the particle, that is to say, what its individual properties are at all moments in time without any gaps, yet, as he points out in that book, any attempt to fill in the “gaps” leads to contradiction.

One of these contradictions is the famous “delayed choice” paradox, whereby if you imagine what the particle is doing “in flight” when you change your measurement settings, you have to conclude the particle somehow went back in time to rewrite the past to change what it is doing. However, if we apply Schrodinger’s perspective, this is not a genuine “paradox” but just a flaw of actually interpreting the particle as having a Newtonian-style autonomous existence, of having “individuality” as he called it.

He also points out in that book that when he originally developed the Schrodinger equation, the purpose was precisely to “fill in the gaps,” but he realized later that interpreting the evolution of the wave function according to the Schrodinger equation as a literal physical description of what’s going on is a mistake, because all you are doing is pushing the “gap” from those that exist between interactions in general to those that exist between measurement, and he saw no reason as to why “measurement” should play an important role in the theory.

Given that it is possible to make all the same predictions without using the wave function (using a mathematical formalism called matrix mechanics), you don’t have to reify the wave function because it’s just a result of an arbitrarily chosen mathematical formalism, and so Schrodinger cautioned against reifying it, because it leads directly to the measurement problem.

The EPR “paradox” is a metaphysical “paradox.” We know for certain QM is empirically local due to the no-communication theorem, which proves that no interaction a particle could undergo could ever cause an observable alteration on its entangled pair. Hence, if there is any nonlocality, it must be invisible to us, i.e. entirely metaphysical and not physical. The EPR paper reaches the “paradox” through a metaphysical criterion it states very clearly on the first page, which is to equate the ontology of a system to its eigenstates (to “certainty”). This makes it seem like the theory is nonlocal because entangled particles are not in eigenstates, but if you measure one, both are suddenly in eigenstates, which makes it seem like they both undergo an ontological transition simultaneously, transforming from not having a physical state to having one at the same time, regardless of distance.

However, if particles only have properties relative to what they are physically interacting with, from that perspective, then ontology should be assigned to interaction, not to eigenstates. Indeed, assigning it to “certainty” as the EPR paper claims is a bit strange. If I flip a coin, even if I can predict the outcome with absolute certainty by knowing all of its initial conditions, that doesn’t mean the outcome actually already exists in physical reality. To exist in physical reality, the outcome must actually happen, i.e. the coin must actually land. Just because I can predict the particle’s state at a distance if I were to travel there and interact with it doesn’t mean it actually has a physical state from my perspective.

I would recommend checking out this paper here which shows how a relative ontology avoids the “paradox” in EPR. I also wrote my own blog post here which if you go to the second half it shows some tables which walk through how the ontology differs between EPR and a relational ontology and how the former is clearly nonlocal while the latter is clearly local.

Some people frame Bell’s theorem as a paradox that proves some sort of “nonlocality,” but if you understand the mathematics it’s clear that Bell’s theorem only implies nonlocality for hidden variable theories. QM isn’t a hidden variable theory. It’s only a difficulty that arises in alternative theories like pilot wave theory, which due to their nonlocal nature have to come up with a new theory of spacetime because they aren’t compatible with special relativity due to the speed of light limit. However, QM on its own, without hidden variables, is indeed compatible with special relativity, which forms the foundations of quantum field theory. This isn’t just my opinion, if you go read Bell’s own paper himself where he introduces the theorem, he is blatantly clear in the conclusion, in simple English language, that it only implies nonlocality for hidden variable theories, not for orthodox QM.

Some “paradoxes” just are much more difficult to catch because they are misunderstandings of the mathematics which can get hairy at times. The famous Frauchiger–Renner “paradox” for example stems from incorrect reasoning across incompatible bases, a very subtle point lost in all the math. The Cheshire cat “paradox” tries to show particles can disassociate from their properties, but those properties only “disassociate” across different experiments, meaning in no singular experiment are they observed to dissociate.

I ran out of charact-