"How to derive quantum mechanics from Wolfram Physics" Transcript

The introduction of the Observer into this theory [Wolfram Physics] is fascinating because physics has had a slightly interesting relationship with the idea of an observer for a long time now. It’s always seemed very dodgy how physics deals with the observer in quantum mechanics—like collapsing the wave function. Wolfram Physics actually promises to make the concept more precise in terms of the Observer being what effectively imposes Causal Invariance and possibly reduces the multi-way graph to a single thread of time. Could you elaborate on how the Observer plays that role in Wolfram Physics?

yeah absolutely but actually you you skipped over or you briefly mentioned something which I think is actually an extremely important and deep point which is the Role of the Observer in kind of traditional science

yeah

okay first of all to relate stuff to what we said at the beginning or towards the beginning about Computational Irreducibility part of the underlying Assumption of theoretical science has traditionally been that the Observer is kind of infinitely computationally sophisticated relative to the system that they're observing

So in a sense when you choose to make a theoretical scientific model you are sort of being sufficiently arrogant as to assume that your methods of analysis your maths your physical intuition whatever it is is capable of somehow shortcutting the computational process of the system you're trying to explain is actually doing

and of course there are situations where you can do that like for instance Celestial mechanics or whatever

but there are also plenty of other situations where as far as we can tell you can't like molecular Dynamics

yeah

I mean again it doesn't normally get couched in these terms but I would argue and again this is not this is me essentially parroting stuff that comes from NKS, that the two most fundamental theories of 20th century physics General Relativity and Quantum Mechanics one way you can think about them is that they both emerge as a consequence of being more realistic about the nature of the Observer and the limitations of the Observer what the Observer can and can't do

See also The Science of Can and Can't

So relativity one way you can think about the foundation of Relativity is it's basically saying you know there are some things that observers can unambiguously know like the causal structure of space-time but then there are some things that observers can't unambiguously know like for instance The Ordering of space like separated events in their reference frame

yeah

that's something which no two observers are guaranteed to be able to agree upon and again so that's very kind of anti the traditional scientific view of the Observer but somehow by being slightly more realistic about what the Observer can and can't do we immediately get this really foundational Theory which is general relativity

similarly you know quantum mechanics one way that you can think about it I don't necessarily think it's the most useful way to think about it but one way you can think about it is that you know things like the Uncertainty Principle are a consequence I mean this is this is the basis of Heisenberg's microscope experiment and the you know the Heisenberg microscope thought experiment and things like that where you basically say well the Observer you have an observer and you've got a system that they're observing and traditionally we think of the Observer as being kind of infinitely far removed from the system they're observing that they can they can perform a completely independent experiment that's kind of isolated from both themselves and from the rest of the universe

and in a sense quantum mechanics is telling us that it isn't true that the Observer is bound by exactly the same physical restrictions physical constraints as the system that they're observing and in particular in order to be able to make an observation of that system they need to become entangled with it and as soon as they become entangled with it they become Inseparable from it and the state of them and their observations is really deeply related to the abstract state of the system and blah blah blah

and again so you know the formalism of quantum mechanics can again be thought of as a consequence of being more realistic about the nature of the Observer so yeah and then as you say in a sense war from physics the Wolfram physics project kind of takes that to and I would argue its next logical step and so this is this is the place where I mentioned the beginning that sort of one of the things that led to essentially the the start of this project was this realization I had about how you could do these Explorations without the need to impose a priori Causal Invariance on the rules

and that was based on a realization so you know when I was reading NKS it always seemed kind of ugly to me that we have to impose because causal invariance is quite a strong restriction

yeah

it's certainly not a natural restriction to impose it's a restriction that you'd only really impose either if you wanted to make an efficiency savings you didn't have to tree out big multi-way systems or

yeah

if you were trying to kind of reproduce physics but otherwise it feels like a very arbitrary restriction and I somehow never really I don't know it never really chilled with me particularly and similarly the explanation in the book Steven's kind of conjectural explanation of quantum phenomena where the idea is basically that you could have kind of long-range pieces of the hypergraph that connected apparently distinct regions of space in such a way that you know that so that you have long range edges that don't correspond to you know the usual three plus one-dimensional space-time structure and that you could use that to kind of set up correlations that you'd need to to reproduce quantum entanglement and violate Bell's inequalities and stuff I don't know it again seemed a little bit ad hoc I didn't I didn't particularly like that as an explanation

so what what I realized was that actually we could solve both of these problems by again just being slightly more realistic about the nature of the Observer

so let's imagine that the evolution of the universe is not just a single thread of time it's a multi-way system where you've got different branching and merging events happening and the universe is not causing the variance right yet there's no a prioriticals in the variants that's being imposed

okay

okay so what is an observer you know again normally we might think of an observer as being kind of localized to a single branch of the multi-way system that would be sort of the traditional like many worlds interpretation of quantum mechanics kind of view right that you are an observer in one Universe in the space of possible universes

yeah

but what I thought was useful was to say well okay let's imagine that's not really true I mean because if the Observer is going to be described by the same computational rules as the system itself then you know it's not just that the universe is branching and merging but the Observer is branching and merging right their their internal perception of the world is branching and merging at the same time

so you quickly realize that it's not useful it's not accurate to think of the Observer as being localized to a single multi-way Branch rather The Observer is an extended object in the multi-way system as a whole and they're moving through the entire multi-way system they're not just moving through a single Branch they're perceiving essentially all branches of History

Okay

so you might think okay well such an observer couldn't possibly you know such an observer would go insane right they couldn't possibly reach any definite conclusions about what was going on they couldn't have a single persistent notion of time they couldn't make any kind of consistent statements about about reality

but then okay then what I came to realize is well if you look at you know these individual multi-way branches at least locally the differences in the structure of the hypergraph that separate two multi-way branches are quite small right that they might be at the level of a single hyper node or a small collection of hyper nodes or something certainly Far Far Below anything that you'd expect and observer a Macross a big macroscopic Observer to be able to to distinguish right

yeah

if I show you two pictures of the universe where I've you know permuted a couple of hyper edges here or that you're not gonna be able to tell the difference between those two

yeah

so what I realized is that sufficiently macroscopic Observer is effectively going to be coarse graining their description of the of the underlying hypograph they're not seeing the micro details of the hypercraft they've got some coarse grained picture in terms of space-time and and you know these continuous structures

so the Observer is really imposing a core screening and how do you actualize that core screening well that core screening really just means that you're imposing a certain set of equivalences between different branches of the multi-way system you're saying the hypographs on these branches of the multi-way system are distinct but they differ at a level that's so small that to the Observer they are the same

so the Observer is imposing some equivalences and you can actualize those equivalences as what are called completion rules so these are rules that effectively these are rules that are not part of the evolution of the universe they're kind of fake rules that the Observer is imposing that let them effectively jump from one branch of History to another they're kind of that's a two-way rules that right enable them to jump between the two that tangle the branches of History together

yeah

those rules are a way of formally encoding the statement that to the Observer these branches of History are the same they can't tell the difference

well what I was able to show was that if you add enough of these completion rules to the system then you could take any arbitrary multi-way system and you could make it equivalent to one that was causal invariant

so in other words that any arbitrary non-causal invariant multi-way system could be reduced to one that was observationally equivalent to a causal invariant one so long as the Observer performed a sufficient amount of coarse graining as long as they added enough of these completion rules

so that had one very nice consequence which is it meant that it allowed us to study multi-way systems without having to worry about whether they were causal invariant or not because we knew that the Observer could impose causal invariance post-hoc you know whatever happened

but the other really nice and somewhat unexpected feature is it turned out to give us quantum mechanics in the following way

One of the reasons why quantum mechanics is considered to be sort of philosophically somewhat unpleasant and and why it's still considered to be kind of an incomplete theory is because there's a distinction made between evolution and measurement

so evolution which is how the quantum system evolves through time is performed by applying these so-called unitary operators these operators where if you take a conjugate transpose whatever you you get the time reversal

but then measurement is this sort of mysterious and somewhat magical procedure that you do at the end where you then take your pure Quantum system that's been evolving according to the Schrodinger equation you know it's just a pure kind of superposition of of eigenstates and then you apply not a unitary operator but what's called a hermitian operator an operator with a different set of algebraic conditions that say now if you take a conjugate transpose you don't get the time reversal you just get the same thing back

and then that performs a measurement and that collapses the wave function and you recover a single eigenstate with some classical probability associated with it

and so somehow quantum mechanics has tended to make this distinction between the time Evolution unitary Evolution and the measurement the application of the mission operator

well in the multi-way system there's actually a very natural encoding of these things so the application of the conjugate transpose operation this adjoint operation is effectively like just flipping the orientation of an evolution Edge so if you've got an evolution Edge from A to B you just flip it around so now it goes from B to A

so for the edges that evolve you down the multi-way system if you apply this inversion operation you get a Time reversal

so they basically algebraically they act like unitary evolutions

these completion rules that the Observer imposes that allow you to hop from one branch to another they're symmetric right you can go from Branch a to Branch b and Branch b to Branch a

yeah

so if you apply the adjoint operation there you get the same thing and so they act effectively like her Mission operators and we were able to show and this is in the series of papers that I wrote immediately prior to the launch of the physics project I was able to prove that the algebra that you get out from considering these unidirectional edges that evolving forwards in time and these bi-directional edges that map between the different branches of History which are crucial for giving you this kind of Observer imposed causlin variants their algebraic properties are the same as the algebraic properties of the unitary and emission operators that you get in quantum mechanics

and so there's a well-defined sense in which you can say these completion rules are the Observer adds to coarse grain out these different branches of history and make their causal structure equivalent there's a well-defined sense in which you can say those completion rules are isomorphic to Quantum measurements

and so that in position of those coarse grainings all those completions becomes a kind of actualization of the process of quantum measurement

so not only does it reproduce the mathematical formalism of quantum mechanics but it also kind of gives you a physical explanation for why that measurement operation happens why the wave function collapses it's not that anything magical is happening it's just that the apparent wave function collapse is a consequence of the macroscopic nature of the Observer and the fact that the Observer caught you know you got the superposition of these different branches of history but because they differ on scales that are much smaller than the Observer can macroscopically measure the Observer imposes an equivalence between them that treats them as being sort of the same at least up to their causal structure and that imposition of the equivalence that collapses the multi-way system down to just a single thread is the collapse of the wave function

and so this very pragmatic way of trying to avoid having to do systematic searches for causal variants accidentally gave us a formulation of quantum mechanics

that is fantastic that's amazing so so just to be clear that's that's always possible to take a system that's not causally a variant and if you get at a high enough level of observation you can always reduce it to a causally invariant system?

It's always possible with a very significant footnote so one problem is when you add these completion rules they enable you now to reach new states of the system that maybe you couldn't reach before yeah so the Observer can see effectively in the observer's perception of the world they can see multi-way states that maybe were not permitted in the original you know pure formulation of the multi-way system before they impose the completion

and that's okay in fact you can show that if you want to reproduce phenomena like say Quantum interference those kind of spurious observer-produced states are the essence of a phenomena like Quantum interference and Quantum tunneling and so on

so it's important that they exist but it comes with a rather negative side effect which is if you want to collapse the the multi-way system down to something that's purely causal invariant then every time you get a branch that doesn't resolve you need to add some completion rule that resolves that branch

but those completion rules can introduce new branches right because they can introduce new states that weren't previously reachable and so you can end up in the rather undesirable situation where each completion rule you add to resolve one branch creates two new branches

right

and then that procedure won't ever terminate it So eventually it will terminate it will eventually terminate once you essentially exhaust the complete rule your multi-way system for that hypercraft signature which is trivially causal invariant so there's a sense in which yes okay eventually if you keep on adding lesion rules add infinitum you will get something called some variant which is why I say yes it's guaranteed you can always do it yeah you can't always do it in a finite number of steps and in order to be kind of physically plausible you need to be able to do it in a finite number of steps

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