@RyderRude Found a reference for your active vs. passive discussion in the context of Noether's theorem. See the review by Banados found

arxiv.org/abs/1601.03616

here

@Obliv it is similar in form (seemingly) to any other abstract maths

morning everyone

@NairitSahoo thanks

@NairitSahoo but they proceed to say that the distinction is irrelevant for their discussion

extremely slow day today

they're using active vs passive in the geometry sense where the distinction is about whether u moved the point or the co ordinate system

or could it be that "active" and "passive" are nebulous terms that are useless for these discussions because everyone uses them slightly differently? If only someone had pointed out that these terms aren't useful before!

in physics however, we don't just have an object and the axes. We also have a lagrangian/Hamiltonian. here, the distinction between active and passive is about whether or not the functional form of the Lagrangian/Hamiltonian is allowed to change

I can give a reference for the above

@ACuriousMind yes..i get ur point. These terms have become confused because of the geometry discussions

It's maybe best to not use them

@ACuriousMind miao miao uses it only for the specific thing, with immediate definitions of those terms, so it should be fine, right? right?

to be clear, in physics, if we move the object (a particle or a field), there is no way the functional form of a Lagrangian changes. But if we move the axes, the functional form can change

@naturallyInconsistent I would abstain entirely - I've never seen any need for these notions when being mathematically careful about what one is doing :P

We can just talk about maps $x\mapsto x'$. It does not matter one bit if what we "think" is "happening" is changing coordinates or moving objects or whatever, the math doesn't care.

the idea i wrote about above generalised really nicely. It leads to several types of active and passive transforms depending on the theory, many of which are equivalent

@ACuriousMind but physics is not maths. miehehehehe

i have written about this in a post. I can link it if naturallyinconsistent won't downvote

lol, mission accomplished

it is really enlightening. Mr Feynman liked it too

I arrived at it after a few hours of thinking

@RyderRude please do not accuse individual users of downvoting you; you can't see where the votes are coming from and you're probably underestimating how many people click on these links when someone posts them

but I'm not merely being facetious. While the maths does not care about the difference between active and passive transformations, and it is also mostly a philosophical exercise, it is still intriging to note that, if you rotate a fermion passively around once, why would it get the negative sign? What would that mean?

@naturallyInconsistent It means nothing, because you're rotating the state not the fermion :P

@ACuriousMind he has admitted many times including right now!

@RyderRude sure, but if they think your post is bad, they are allowed to downvote it

"pls don't downvote me" is not how SE works

@ACuriousMind yes, but they're doing it in bad faith!

@ACuriousMind you only are rotating the state in active view. In the passive view you are rotating the coördinates. That should not be doing anything to the fermion.

@naturallyInconsistent this comment is yet another evidence of that @ACuriousMind

@RyderRude You are vastly overestimating how many times they have done this; moderators have tools to analyze targeted voting: while we cannot see individual votes, we can see aggregates

you're not being persecuted by a single targeted voter; several people think some of your posts are not particularly good, and overall you haven't really received that many downvotes anyway

@ACuriousMind yes.. and i actually think they have downvoted me no more than 10 times by now. So it won't show in any stats. They just downvote anything i link here (which i barely do) and anything new i post (which i barely do)

@naturallyInconsistent The problem is the phrasing "rotate 360°"

It certainly does not help that the rude one often would write something that does not answer the question, which just attracts downvotes.

@RyderRude To be frank, I thought about downvoting the last two things you posted here, too, and I explicitly told you I thought they were not useful

@naturallyInconsistent both things i linked in the past two days hve zero downvoted except from u

I didn't downvote them, but perhaps I should have so that you don't develop this particular persecution complex :P

@ACuriousMind Why is that a problem? A passive rotation, i.e. a rotation of just the coördinates in observer's mind and nowhere else, still incurs the negative sign.

lol

@naturallyInconsistent The problem is what the phrase means. As an operator on the space of state, the "360° rotation" is already just -1 due to the nature of the projective representation, before you decide whether to apply that operator to the basis ("coordinates") or to the vectors themselves

@ACuriousMind What I am getting from this is that you are saying that it is an operator regardless of whether it is just in my mind, and/or this is about the projective representation. Is this correct?

when you say "rotating the coordinates 360° should not change anything" you are disregarding the nature of the quantum state space - you're not rotating the physical space coordinates in a passive interpretation here, you're rotating the basis of the quantum state space - the axes of the quantum state space are not the physical space coordinate axes, so the naive "passive idea" of what a 360° rotation should do to them does not apply

@ACuriousMind well if exactly one person actually presses the downvote on every link i post, they're doing it in bad faith. The chat has 10+ users and the website has millions. Both my answers only have one downvote

@ACuriousMind Yes, I am catching that from your earlier comment. Clears that bit up.

@RyderRude No, if someone posts 10 answers I genuinely think are bad and I downvote them, I am not acting in bad faith.

I have cast more downvotes on this site than most other users by orders of magnitude and there are several users where I've downvoted every post they've posted, not because of the user, but because they consistently put out low-quality content; as long as one does not go to the profile of those users and just downvote everything they ever posted, this is not targeted voting and not forbidden by SE rules.

@ACuriousMind I'm not talking about ur motivations. people r different. naturallyinconsistent isn't doing it because he thinks they're bad.

In fact "downvote as you come across the content" is exactly what you are supposed to do to evade targeted voting

@naturallyInconsistent this comment is evidence @ACuriousMind

@RyderRude No, it is not; If someone posted stuff I thought was bad and then stopped because I kept downvoting them, that is "mission accomplished". In fact, that is exactly what downvoting is for: Getting people to stop posting things the downvoter considers not useful.

there is no need at all to suggest this is about you personally: While you construct a "they don't like me, so they downvote my stuff" narrative, the narrative "they think my content is bad, so they downvote my stuff and don't particularly like me" is equally valid - and plausible to me, since I already said I also considered downvoting some of the stuff you posted.

u r interpreting his actions in the most charitable way possible, while I'm looking at them in context. naturallyinconsistent often fights with me and other people on the chat

Yes, and you often say wrong things

now what?

naturallyinconsistent does too.everyone does

and he fights many people

I've been downvoting a LOT of stuff. I'm always on the newest questions on the site. I always find a good reason to downvote; I'd not get to downvote bolbteppa stuff because, no matter how much we disagree, his output is usually good on the site.

i can give a list. If u look at the instances, they're not about saying wrong stuff

Yes, it is not always about wrong. Because they can be vague. Or irrelevant. Or uncited.

@RyderRude please don't give me a list, we will not litigate the behaviour of any specific user in detail in public.

@naturallyInconsistent the answers i posted had 2 and 4 upvotes respectively. And 0 downvotes

if you are convinced someone has a personal vendetta against you, I can't change that. I've just tried patiently to explain to you why this is not the only possible interpretation (or rather, that no matter the personal dislike that may be there your content actually has quality problems often enough).

@RyderRude low upvote counts mean nothing, I just this week deleted an answer with +3/-0 score after a comment pointed out it was completely wrong.

i will leave it because it won't show in the stats anyway. I cant report anything

And i will consider ur viewpoint

Yesterday I read "introduction to LQG" by rovelli and found the idea really fascinating

Thanks

or rather:

And I checked it first; it is indeed not answering the question, before I downvoted it

@Davyz2 also see his debate with David Gross. Although it's really bad

but it shows that string theorists can be aggressive

Ah, interesting, why is it bad?

Gross keeps interrupting

There was one where you wrote something that is not answering the question, and then after some comments with the OP, you added enough in comments to answer the question to the OP's satisfaction. But then you did not update the answer to include the clarifications in the comments.

some physicists have a despicable behaviour, I guess they don't know how social interactions work (are they even unitary?)

@RyderRude lol, you really are living in a bubble if you havent known that already

jinx, was about to comment the same thing :P

@Davyz2 are you sure you are not looking for Hermitian?

@ACuriousMind was just talking about bolbteppa...

@Davyz2 there is a relatively fun rap battle between Rovelli and... some string theorist

nooo T_T i want reversibility in time plz

and recently many links to Lubos...

@Davyz2 interactions have to be Hermitian so that time evolution is unitary and thus reversible...

oh, then we are on the same page

i was thinking about time evolution

measurements aren't reversible

@Davyz2 While certainly some are like that, I would be wary of generally characterizing people that have successfully navigated academia to get to where they have publicly recorded debates with other people as "not knowing how social interactions work".

They might just not be nice people :P

if you interrupt another person, you belong in the garbage bin, i am sorry

it's a matter of basic human respect

couldn't care less about "navigating academia" it's not like these people are geniuses or something

...I think you didn't understand me

@Davyz2 he has the Nobel prize..

you said "they don't know how social interactions work"; I say - they probably do understand, they might just be rude

oh alright, yes true that

@RyderRude big deal, they give nobel prizes for all kinds of stuff

it's a ceremony

@Davyz2 i think he has one for theoretical stuff

the dirac medal?

no, the Nobel prize

They also gave to it to Penrose who also does theory

@Davyz2 Do you let aggressive people just talk over you all the time and never interrupt them?

aggressive people are not people

couldn't care less about talking to them

let alone interrupt them

That's a rather dangerous line of thinking.

Let's try to not dehumanise people

@Davyz2 hey hey hey, let's perhaps not dehumanize people regardless of what they do, okay?

i mean i guess it depends on how aggressive somebody is

i don't know what I would do to be fair

probably nothing?

usually an aggressive person doesn't listen anyway, I guess

I think "aggressive" might be a wrong word. he just interrupts a lot

u can see the video for urself

yeah i wouldn't put that into the aggressive category either

Pushy, perhaps.

he was also behaving as if Rovelli's ideas were dumb, while Rovelli was respectful to his ideas

Interrumpting means you're just dumb and not willing to listen, so yeah it doesn't probably even qualify as "aggressive"

I guess that's what age does

Penrose is calm

But he is like 90

yeah it was just a joke, not all old men get grumpy ahah

@Davyz2 I mean, do you listen to every cold fusion practitioner wasting your time with their hour-long spiels?

I guess no, i don't

wait, hold-up how did we get to cold-fusion practicioners?

exactly. Gross thinks Rovelli is talking nonsense, so you kinda dont expect him to be so respectful. We get to judge whether we think Gross is being fair or respectful or justified or not, but we don't get to insist that he be nice

@Davyz2 just from my day job. Soooo much nonsense to block

Also, just upvoted a rather nicely asked question on the site. So rare to see something showing so much effort

I am at work right now, hbar is literally an antidote to extreme boredom

@naturallyInconsistent yeah I agree with you here

@Davyz2 do u do physics as hobby?

yeah more or less

same

couldn't turn it into a carreer

i got severe impostor syndrome after reviewing some stuff about confinement and dropped out of the master's to avoid permanent brain damage

@Davyz2 QCD confinement or plasma confinement?

QCD

would have been my thesis if I continued

instead I got into pentesting, basically lego toys compared to physics

Yeah, when I received a paper to review that was basically doing what I did, mostly better than what I did, that was very sad. I mean, the research they were doing is solid, except for small mistakes, but because I got to publish before them, it blocked their journal requirement of being novel.

I think mine was a wise choice, I would have gone mad in academia

mew mewth

Yes, mew mewth indeed

@Davyz2 looking forward to study QcD

PTSD triggered

I can only wish you good luck

@Davyz2 come come, miao miao pat head

r u interested in philosophy or the measurement problem?

@Davyz2 it's very far on my road...

@naturallyInconsistent you like cats?

yeppu~

cats are cute and clever

Most cats like meow meow too. Only rarely does one just bite and bite

@Davyz2 and devious

This is my cat

she cute innit?

@RyderRude Yeah that's an interesting topic

KAWAIII~~~

tickle her head for meow

_ yeeesss

she called spinny, coz she spins around me when she wants food

miahahahaha

@Davyz2 heh, we also had pics of a stray called spinor in here for a while, @Relativisticcucumber she still around?

spinooor :D such a cute name

@Davyz2 awwww

cuteness overload

@Davyz2 what interpretation do u like

i don't understand QM well enough to say anything about it, i can only calculate spectrums

you need ACM power to understand QM

ahahahahah

i like Copenhagen or panpsychism interpretations

jokes aside, i think there is some value in trying to intuitively understand QM, but i don't think it's a matter of interpretation

Quantum Gravity will resolve this problem

@Davyz2 i also don't refer to those as interpretations. it's just an unfortunate terminology

@Davyz2 but i also don't think it's a matter of intuitively understanding

The measurement problem is a mathematical problem

as the postulates are inconsistent. Several physicists agree with this

U can see Carroll, Sabine, Penrose straight up calling out the inconsistency

In the Copenaghen interpretation, there is an objective collapse of the physical state, meaning that in principle it's possible to devise an experiment in which the result of a measurement is fixed before the measurement itself

that is, it's a hidden variable theory

as such, it must be non-local, thus can't be the right explanation

"The Copenhagen interpretation" doesn't really exist, it's just the thing people proclaim to believe in when they don't want to worry too much; debating it without first defining what exactly one means by that term is generally useless

yes that's right, by "Copenaghen" i just mean ordinary QM

if you need the state collapse to play a role in the time evolution (which we need), you get an hidden variable theory

for example, in a Wigner's friend scenario, the isolated observer receives a mixed state from another isolated observer which makes a measurement

this cannot be true, as the experimental outcome of this observer is now fixed before the measurement itself

@Davyz2 you cannot be having played with QCD and then tell us you dont understand QM

i don't understand the slightest thing about QM, let alone QFT, you could say I understand the math behind it tough

@Davyz2 do u have a source on this

@Davyz2 ACM is trying to say that you have to first define "ordinary QM"

I don't think normal QM is at all related to hidden variable thwories

It's as far away from hidden variables as possible

ordinary QM is a set of four postulates

i don't think we disagree about what ordinary QM says

Also, Copenhagen (even when somewhat well-defined) is not generally considered an objective collapse theory

@Davyz2 usually symmetrisation is another postulate. There is nothing in single-particle quantum theory that prohibits, say, anyons.

@Davyz2 oh now i get ur viewpoint

@ACuriousMind then what is it? a subjective collapse theory?

@Davyz2 but note that this is not necessarily a hidden variable theory. It is in fact the classical-quantum divide tht Bohr envisioned

What's happening is that "big things" like humans can collapse the wavefunction, while small things are still quantum. For the measurement of Wigner's friend, there is no hidden variable @Davyz2

But for the measurement of Wigner, there is a hidden variable

@Davyz2 Plenty of people would probably say yes when pressed, i.e. turning it into a kind of relational interpretation; again, this isn't really a single well-defined interpretation and it is not useful to argue "against" it, you're trying to hit a nebulous and moving target

objective collapse has a specific meaning in this context and people usually do not list Copenhagen under those interpretations

That's wrong, because the theory doesn't work without a collapse mechanism anyway

every theory of QM must have a collapse mechanism of some sort

because that's what we see in experiments, right?

No, you're not using those words in the sense that people discussing interpretations use them

@ACuriousMind the reason Copenhegan is not listed here is because it lists specific mathematical models. Copenhagen is still very much an objective collapse interpretation with a classical-quantum divide. It's just not mathematically precise enough to be called an objective collpse theory

E.g. MWI is a collapse-free interpretation

there is no collapse-free interpretation, you cannot get outcome statistics and you have no theory

U can say that Copenhagen is a vague prototype for objective collapse theories which r actually precise

@Davyz2 That you say that just means you don't understand what the technical terms mean in this context

@ACuriousMind also, people might be bringing "subjective stuff" into Copenhagen these days. But Bohr envisioned a classical quantum divide as I've read on wiki

i don't understand what you mean by "collapse-free", i am sorry, if you don't collapse the input state, you don't get measurement statistics, no?

@Davyz2 no, you can

But these days, Copenhagen has become the vague-est interpretation possible

how

see e.g. Wiki's list where there is a prominent column "Wavefunction collapse?" which has several "no" entries

with people bringing in subjective collapse

@Davyz2 "collapse" has agin become a confused term these days. What u mean is that every theory has state reduction from the PoV of the experimenter, but not necessarily collapse

yes by collapse I mean a non-unitary evolution at some point

The term collapse is now used to refer to ontology. In many worlds ontology, there is no collapse

@RyderRude stop pretending you know anything about the history here, collapse has not "become confused", this goes back to the original works of Bohm at least

@Davyz2 many worlds doesn't have that either, in the ontological sense

@Davyz2 but it may be unitary and yet appear to "have collapsed"

you have this really irritating habit of saying things that sound like historical explanations but which really really aren't

if you don't know the history, don't pretend to

Alright, what I mean is that a QM theory cannot exist without a non-unitary evolution law

@Davyz2 Yeah, and that's wrong

The collapse-free interpretations do exactly that

like MWI

How? I don't understand, in MWI how do you get the measurement statistics then?

Like, it is not really that I like MWI, but the proponents there are correct to point out that you can just have Hamiltonian evolution without collapse and yet get that every observer sees distinct measurement outcomes.

To be clear, collpse free interpretation still require state reduction and Born rule, which is non unitary indeed

They just add some extra philosophy on top, like other universes which make the ontological wavefunction unitary

@RyderRude There is no state reduction, but one might have to postulate the Born rule. And FFS just get out of the conversation.

@Davyz2 All the results exist at the same time: You get states of the form $\lvert \text{obs sees 1}\rangle \otimes \lvert 1\rangle + \lvert \text{obs sees 2}\rangle \otimes \lvert 2 \rangle +\dots$ unitarily (via decoherence or similar)

But many worlds has the subjective wavefunction, which must have state reduction

In Pilot Wave, you have a hidden variable that determines what "actually happens", but it will appear to have superpositions turn into distinct outcomes

@RyderRude stop stating things as if they are standard if you just made them up, do you have a single published reference where an MWI proponent talks about a "subjective wavefunction"?

@ACuriousMind And why don't you get states of the form (|0> + |1>)|Obs sees 0 + 1>?

Decoherence is such an important concept to understanding how quantum theory actually functions, that it is quite sad that it is not taught at all

@Davyz2 because of the form of the measurement interaction, decoherence, etc.

The concept that certain pointer states are special is called einselection

@ACuriousMind i just mean that an experimenter would not use the MWI universes's wavefunction to model anything, but they would use the reduced wavefunction, just like ordinary QM uses. This wavefunction is defined after the experimenter is part of the world

@RyderRude Then why bold "subjective wavefunction", without an accompanying definiiton, as if it were some standard technical term?

@ACuriousMind sorry... I should not have bolded that. It's not a standard term

@RyderRude There is no reason why the experimenter cannot use the MWI universes's wavefunction, appropriately handled, to model stuff. It will mathematically just work, only just be inconvenient.

Also, the whole point is that it makes no difference whether one uses the full or what you call "reduced" wavefunction, since the other parts of the wavefunction are decohered and cannot interfere anymore

That's precisely why we don't need collapse here, as the parts that other interpretations need to "collapse away" simply become irrelevant

Every time we have a discussion about interpretations, or about history, you always get mistakes pointed out.

@ACuriousMind that is a good point... But at some point, they have to use the born rule, which means their wavefunction will turn into density matrix

This is not implied by unitarity.. it is an extra postulate for MWI

@RyderRude What part of "makes no difference" and "don't need collapse" do you not understand?

one still needs some remnant of the Born rule to say that the probability of finding "oneself" in "one of the branches" of the universal wavefunction is proportional to its overall coefficient in there, but this no longer implies any kind of state change or collapse (but perhaps it makes the nature of "reality" or "the observer" even more nebulous)

I agree on this, I also think state collapse is somewhat of a trick and that MWI is the correct idea, because of locality

Also, one has to consider that trading a postulate of abrupt non-unitary evolution for a postulate for Born rule is a vastly good trade

I just don't know how MWI deals with the fact that you observe a single outcome

Oh, I'm not saying MWI is correct, I'm just explaining it :P

@Davyz2 it is not just MWI, but a whole host of interpretations use decoherence to explain how you observe a single outcome

yeah I mean the class of collapse-free theories

@ACuriousMind i would say "finding urself in a universe" and subsequently modeling ur own state by a probabilistic mixture, is no different from abandoning the universe's unitary wavefunction and just using ordinary QM state reduction :P

The unitarity is ultimately irrelevant in MWI and is just philosophy

By the way, this is why talking about interpreations is misleading

@RyderRude Of course it's "ultimately the same"! The whole point of my disdain for these interpretational discussions is that they do not affect the actual prediction of the physics one bit!

you're just making the very point why this is pointless and yet you still always want to discuss it

it's bizarre

I'm not a fan of MWI to be fair... What im interested in is just the inconsistency of QM postulates, which is not an interpretation issue. MWI is just one approach to remove inconsistency (but it's mathematically vague still)

It's not vague at all

Does it specify when exactly ur wavefunction is supposed to be modelled by a mixture

Decoherence is a continuous process

no idea what you mean

where does the mixture come from?

After measurement, ur state becomes a mixture? But in MWI, a measurement is a continuous process being the usual time evolution, so what moment counts as "after measurment"?

why would my state become a mixture after measurement

when you measure something you get an eigenstate, not a mixture

Because of born rule... I'm saying that u would model ur uncertainty by a mixture

what uncertainty

with respect to an isolated observer, the output state after a measurement by another isolated observer is a mixed state

please use the technical terms in the correct way

But i can formulate the issue using eigenstates. When exactly does it become an eigenstate ?

in MWI, it is a pure state

@RyderRude you're just asking about decoherence

@ACuriousMind the uncertainty of what branch u r in. Born rule pobabilities

that's not something particular to MWI

yeah... I'm familiar with decoherence...

no, you're just not understanding with decoherence or MWI :P

I think the conversation is too vague because of the nature of MWI. I don't even know what to say :P

if you are familiar with decoherence, you should know that the off-diagonal terms are killed off exponentially typically, resulting in the kind of eigenstate-observer entangled state I sketched above

yeah

Okay so MWI gives this decohered state for the universe. But at what time does ur own (experimenter's) state become "an eigenstate with probability p"?

@Davyz2 But you can get back the mixed state! It's just tracing out stuff - the giant pure state of the universe is highly entangled, and so when you trace out most of the universe to get a state for the subsystem you're interested in, you get a mixed state

it's just how entanglement works

Yes, that's true

Mixed states are not quantum states however

they are in every standard meaning of the word "quantum state"

Mixed states r just pure states with ignorance. It's completely allowed

why is everyone trying to debate interpretations and invent new terminology at the same time :P

@Davyz2 u can formulate a Schrodinger eqn equivalent for mixed states

It looks like the Heisenberg picture with a change of sign

@RyderRude In MWI? It doesn't, all the possibilities exist at the same time; there's a me that saw "1" and there's a me that saw "2" in the universal wavefunction and we both exist

really, this is the most basic part of MWI

True, but mixed states are not physical states they are classical information states and these are prohibited by quantum mechanics

@Davyz2 I don't know what that is supposed to mean

it is an elementary fact that when you take an entangled pure state and ask for the corresponding state of a subsystem, you get a mixed state

@ACuriousMind sorry. I mean, as in, if u were a practitioner of QM (ideal practitioner. U use exact calculations) : at what point would u use the born rule

And did MWI give u a precise answer for that

But that's not the physical state of the subsystem, after the trace you get a probability mixture representing knowledge

@RyderRude no, does anything else?

the measurement is "done" when the decoherence has done its work "enough"

physics is inherently approximative, deal with it

@Davyz2 ah, but the claim that there is such a thing as a "physical state of the subsystem" is already an interpretational issue

that's what I am saying, there is no physical state in quantum mechanics that can be represented with a mixed state, mixed states are informational

if there was, the result of the measurement would be fixed before the measurement, right?

Okay what I'm getting at is this : imagine the universe's ontology given by MWI. When does the change in ontology happen after the measurment? When does the ontology store a pure eigenstate for the experimenter who is in a world branch?

I mean, I could just commit to "the physical state" of the subsystem being represented by that density matrix :P

The reason i insist on ontology is that having a mathematical ontology removes inconsistencies in the postulates

no, because then you are claiming that there are hidden variables, because the "physical state" truly is in |0> or |1> with probability 1/2 but the observer doesn't know

this can't happen in QM

@RyderRude I don't know what it means for the "ontology to store a pure eigenstate"

the universe is not a warehouse

it doesn't store eigenstates

and ontology is an abstract concept, not something that can do anything

@Davyz2 No, I make no claims about "truly"

neither does decoherence or MWI

@Davyz2 usually the opposite is true. For example, the quantum state that comes out of the oven and into the Stern-Gerlach apparatus is best described by the completely mixed state density operator.

but that's not a quantum state, it's the state of knowledge with respect to a whole ensemble of output states

Quite many Copenhagen-ists think that only the density operator defined quantum state, i.e. ensemble, is real.

before I look at the other observer and their measurement, the universal wavefunction contains $\lvert \text{me}\rangle \otimes ( \lvert \text{obs saw 1}\rangle \otimes \lvert 1\rangle + \lvert \text{obs saw 2}\rangle \otimes \lvert 2\rangle )$. After the measurement interaction, it contains $\lvert \text{me saw 1}\rangle \otimes \lvert \text{obs saw 1}\rangle \otimes \lvert 1\rangle + \text{same with 2}$

Before the interaction, the "physical state" of the subsystem from my point of view isn't "truly" 1 or "truly" 2, it's in an an entangled state

and if I trace out everything else, I end up with a mixed state for the measured system

you mean the physical state the global system?

that one is entangled

And in MWI, the tracing operation is merely mathematical convenience. The universe's wavefunction is still a pure state evolving unitarily.

yes exactly

meaning that sub-systems are not physical states at all

in MWI there is one physical state

@Davyz2 that is not how we use those words