@Amit i would say GR is already a "purely mathematical model" just like QM. GR spacetimes need not have a space-like foliation. I have no way to visualize GR. It just seems like a purely mathematical universe
But where GR and QM are different is that GR gives us an objective ontology and it's hard to connect it to experiments, while QM gives u what experiments would measure and it's hard to get an objective mathematical universe out of it
MWI is an attempt to get an objective mathematical universe out of QM. Just like GR says universe is a manifold, MWI tries to make the universe a time-dependent Hilbert space vector
Yeah, that's what I was trying to say there. Einstein was driven by an Ontology. I think he was rare in Physics in that he got so far by just hitting on the right ontology
So many physicists stuck to various principles until the end and it turned out to be either wrong or lead nowhere. But he did it right at least twice lol. But he tried to do the same with QM and failed, his Ontology told him that it can't be a complete theory, and he could never show that
Yes. I've also read that Heisenberg's conception of QM was extremely unconventional for scientific theories at the time. Before that, everyone was trying to get a picture of "what the electrons were really doing", becuz everyone was used to Newton. And Heisenberg was like "we shouldnt talk about anything other than what we measure". This idea turned out to be extremely successful
Heisenberg came up with the matrix mechanics stuff, which literally just talks about the observables u observe. Even Schrodinger's wave mechanics was more pictorial than this.
Did you ever dig into the Bohmian stuff? I am very interested to do that. Just 'cause I listened to lots of interviews with Bohm and he was really an interesting guy
Yes, "Bohmian trajectories", I think it is interesting to see how he cooked that up
It was not only an interpretation though, he did add some mathematics to explain it. It's just that whatever was added also doesn't come into play experimentally :)
Because he doesnt say that other observables are hidden variables. So it's not easy to explain
@Amit possibly. I guess the wavefunction is "aware" of the entire Aaron Bohm magnetic field.
Cuz the wavefunction is everywhere. It allows the particle to get access to global information
Bohm's interpretation has also survived all the no-go theorems. Bell's inequality and PBR theorem
Becuz Bohm's interpretation is pretty much usual QM. The more modern approach to hidden variable theories is to not treat the wavefunction as ontological, becuz then it pretty much ends up being usual QM
T Hooft is working on such a hidden variable theory
The Kochen Specker theorem says that hidden variable theories must be contextual. I'm not seeing anything in the definition of Bohmian mechanics that makes the hidden variable variable assignments dependent on the measurements. Bohmian mechanics seems to revolve around the Newtonian idea that hid...
I am trying to do a small write up which involves detailing superficially the differencce between topological quantum computing and usual quantum computing
I wrote that TQC uses anyons to construct its qubits whereas usual QC uses bosons and femions...is this accurate?
Hm well it sounds like anyons are the qubits and braiding their worldlines is equivalent to performing logic gate operations? or like the topological characteristics of a particular braid can be mapped to performing a logic gate operation
@RyderRude Heisenberg (and most of the other founding fathers of quantum physics) was strongly influenced by Logical Positivism. en.wikipedia.org/wiki/Logical_positivism
> This theory of knowledge asserted that only statements verifiable through direct observation or logical proof are meaningful in terms of conveying truth value, information or factual content
@RyderRude BTW, MWI doesn't necessarily create new branch universes. Some MWI advocates prefer to say that the branches are pre-existing, but they diverge. See my answer:
You would need an uncountably infinite number of branches to be able to represent arbitrarily precise probability ratios, and then subsets of those branches would contain uncountably infinite universes that are 100% degenerate and identical to each other.
What's the problem with having an i...
"Consider a unitary matrix U which acts on a d-dimensional Hilbert space. In this section we explain how U may be decomposed into a product of two-level unitary matrices; that is, unitary matrices which act non-trivially only on two-or-fewer vector components." hm it seems like you can just decompose an arbitrary nxn unitary into a nxn which acts trivially on all but a subspace corresponding to a 2x2 block...so maybe you can then decompose the nxn
into a tensor product of the form of an operator on two qubits?
@Mr.Feynman oh i mean the quantum computation stack chat is inactive heh
it's just that in practice of course, a classical computer won't be built this way, which is apparently the difference from what you're saying from a quantum computer
Try Erlang or some other functional programming language :) Otherwise it's just a different syntax for roughly the same ideas. Although if you are only familiar with C, there's also the whole OOP thing to get familiar with
Yeah C++ is kind of the dinosaur of OOP. C# & Java are a bit more modern in that genre. Then there's Python, which is just too "cool" to be "just OOP" -- it is very multi-paradigm
I wanted learning Python some months ago but had to stop because I had a lot going on. Anyways, I suppose that going from C to Python can be quite traumatic :P
I don't really like doing numerical simulations but suppose I had to. C isn't very convenient to work with in that regard
But I can't really rant on this. A bunch of my astrophysicists colleagues are being taught Fortran in 2023...
Do you want to see an object system bolted on to the manual memory management, with a Turing complete sublanguage where you'll write boilerplate code that generates more tedious boilerplate code for you? Go for C++! (don't @ me :P )
personally I've become a big fan of Rust, or more generally anything with nice algebraic data types
@Mad this is an annoying technicality: you cannot just talk about the subspace of functions that vanish at infinity because it's not a Hilbert space (it is not complete)
the subspace of nice functions falling off at infinity e.g. Schwartz functions is dense in $L^2(\mathbb{R}^n)$, so you cannot really avoid having the "weird" $L^2$ functions in there that don't converge to 0 at $\infty$ - when you try to complete your nice functions into a Hilbert space you inevitably get those
@PM2Ring thanks for this. I think this version of MWI does escape my betting thought experiment becuz there is no world splitting here. MWI is very resilient
@PM2Ring But this version is just a bunch of stacked worlds, where each world independently obeys the Copenhagen interpretation. So I think it is just adding redundancy to Copenhagen
@PM2Ring But it is a very cool redundancy. We can think about Marvel-like multiverses using this philosophy
this version does not interpret the Born rule in a crazy world splitting philosophy
@PM2Ring Each world in this stack has a unique future, which is non-deterministic and adheres to the Born rule. This is in accordance with either Copenhagen or Relational QM. This is y i say that it is like a stack of worlds with each world effectively functioning like in Copenhagen interpretation or Relational QM
And becuz each world has a unique future, this escapes my thought experiment. My thought experiment works if the world has non-unique future involving world-splitting and world-duplication
@PM2Ring I'm sorry. I shouldnt say each world is in accordance with relational QM. Because Relational QM has the concept of relative states describing the same world. .
I would just say each world in the stack effectively functions like in Copenhagen interpretation. It is unaware of the other worlds in the stack. And when we zoom out to the MWI multiverse, the universal wavefunction looks like a pilot wave guiding this stack of worlds.
It would be impossible to translate this picture to mathematics tho lol. It's a cool story
Consider the Schwarzschild metric in Schwarzschild coordinates, why do books (e.g. Carroll) only impose that null radial curve condition $d\Omega=0$ and $ds^2=0$ and then call them null geodesics?
If you look at the geodesic equations and its symmetries, you end up with $$-E^2 + (\frac{dr}{d\lambda})^2 + (1 - \frac{2GM}{r}) (\frac{L^2}{r^2} + \epsilon) = 0$$
Where epsilon is the type of curve
For a radial null curve that's just like $$\dot{r} = E$$
Up to reparametrization I think that's any radial null curve?
These days they don't but I would say 1910 muons did carry a pocket watch
man those were different times
More seriously, I think this can be made more general. I've found this Qmechanic's answer proving that null curves in 1+1 dimensional spacetime are non-affinely parametrized geodesics
And if we restrict to radial curves, the spacetimes is 1+1 dimensional
@naturallyInconsistent / others could you tell me the shortfalls of the method of ensemble averaging of microscopic quantities to bring out macro ones in EnM?
@nickbros123 There are actually physical systems where, for some reason or another, the time it takes to explore a significant fraction of the ensemble is tremendously large. Say, for example, a system where some constraint or so forth makes the energy hypersurface in phase space become two almost isolated pieces, with only a tiny bridge linking them. Then the time it takes for one system to explore enough of the phase space to swap over to the other piece, may be really long.
Then the ensemble average could be entirely different from the ensemble average of either of the two isolated pieces, and the actual experimental result will be closer to one of the isolated pieces rather than the ensemble average
@Slereah surprisingly, the answers do not mention this simple explanation. They cud just say that in 1+1, u have V-shapes. And in multiple dimensions, u can hack it because the light cone becomes a surface
You know it's kind of weird that ancient people thought that Euclidian geometry was true but also that the universe stopped at the sphere of fixed stars
Why worry about parallel lines, you don't even have an infinite space
It just doesn't apply for higher dimensions because we usually consider Penrose diagrams to just be spherically symmetric spacetimes with angles suppressed
@RyderRude "each world in the stack effectively functions like in Copenhagen interpretation". Right, but instead of objective collapse we have divergence. However, rather than thinking of individual worlds in the stack it's better to think of substacks which share identical pasts that can diverge in the future.
All (genuine) interpretations are mathematically identical and therefore make the same predictions. The interpretation "merely" tells us what the mathematics implies for the underlying physical reality. The "Shut Up & Calculate" interpretation says that it's meaningless to ask about any purported underlying physical reality.
@Mr.Feynman Python can be a bit disconcerting coming from C because it uses a different data model.
However, the official Python tutorial was written for people who already know how to program, probably in C (or at least a language with similar syntax). So you should find it pretty easy to follow and work through. docs.python.org/3/tutorial
Is this because temperatures concerned are very high and quantum stat goes to classical at high temperatures?
But again, in a similar calculation , while calculating the lattice specific heat of the solid using Einstien's model or the Debye model, I have seen books calculate the average energy of oscillators using MB distribution only, but we use this formula to predict specific heats at very low temperatures also. So I don't understand, what is the reason?
If this is not a suitable question for this room, kindly tell what are the rules, or how should one in general frame suitable questions :)
In Dirac's book... he pulls that thing out of a hat $$ g_{,\nu} = gg^{\lambda\mu}g_{\lambda\mu,\nu} $$ and he says that $g$ is the determinant... is he just skipping a lot of steps or is there a simple way to see why that's true?
@Obliv What are you trying to do? Which OS? Windows tends to dislike such things, it has all its important system files signed by MS, which you won't be able to reproduce
I mean, won't be able to forge such a signature. And if you can, don't tell NSA
Ah, if it's reverse engineering you wanna do you can do a lot...
It's not simple... I mean, for starters you don't have the source code. The security updates you get are binaries, meaning, machine code. The programmers at MS however actually create that with some programming language, and you can't see that source code
It's so they can prevent other ppl stealing and reproducing it, which kills their income. That $100 windows license slapped on every computer makes so much money :O
Actually I'm not sure that's still true, there are many open source models. For example they could release the code and have a policy that if you change anything you no longer receive updates (both general and security ones for that matter)...
I think one main motivation not to release the code is how many security issues will be exposed
Even as it is, being closed source, clever reversers find new exploits every month...
If it becomes open source it'll be a shit storm, lol
You would need an uncountably infinite number of branches to be able to represent arbitrarily precise probability ratios, and then subsets of those branches would contain uncountably infinite universes that are 100% degenerate and identical to each other.
What's the problem with having an i...
