The h Bar

1:54 AM

69

$SU(2)$ is the covering group of $SO(3)$. What does it mean and does it have a physical consequence? I heard that this fact is related to the description of bosons and fermions. But how does it follow from the fact that $SU(2)$ is the double cover of $SO(3)$?

Why does looking only at SO(3) lead us to miss half-interger spin representations?

Also, I don't really understand the answer. The person who answers seems to motivate looking at SU(2) rather than SO(3) because SU(2) circumvents dealing with a projective representation. However, later in their answer it turns out that SO(3) doesn't even fully represent what we want represented at all?

Moreover, physics.stackexchange.com/questions/756969/… this post says in their Quantum II course, they are looking at SO(3). Why look at SO(3) at all in detail if SU(2) is the real representation of it all?

Silly Goose

2:51 AM

Also, so in Gold's answer here, by a system having rotational symmetry, they mean "if we rotate every state there will be no observable difference"? which is different from a system being rotationally invariant, which would mean that w.r.t. time a system's generator of rotations is conserved? physics.stackexchange.com/questions/743916/…

Silly Goose

3:15 AM

Where is the representation theory of operators that are not angular momentum :0

Ryder Rude

6:50 AM

@SillyGoose the former notion of symmetry implies the latter becuz of Noether's theorem. Noether's theorem gives you conserved quantities corresponding to the transformations which leave the action invariant

@SillyGoose there is also the representation theory of creation and annihilation operators

@SillyGoose becuz in the SO(3) group, u cant have stuff like : "rotation by 2pi turns the object to its negative". The half integer representation has these properties

Silly Goose

Hm, certainly every generator of a unitary operator is not conserved always (with respect to time), no?

Ryder Rude

Put it simply, only those are conserved that commute with the Hamiltonian

By "we rotate every state and it has no observable difference", it mathematically means that the action is invariant under the rotation, or the Hamiltonian commutes with the Generator of rotation

By "no observable difference", we mean "dynmaics remain unchanged". So ofc a rotated system shud be described by the same dynamic laws, i.e. the same action or the Hamiltonian

Silly Goose

I don't see how that is true, though. For any unitary $U$, $\langle \psi | U^\dag U | \phi \rangle = \langle \psi | \phi \rangle

there is no mention of time evolution in Gold's statementt to my understanding hence nothing to do with the hamiltonian

Ryder Rude

Ill see what Gold says

Gold indeed did not mention the fact that dynamics shud remain unchanged for a transformation to b a symmetry

He points seems to imply that unitarity is sufficient

Silly Goose

If it helps here is the original definition they are working off of

Ryder Rude

7:04 AM

I'm sure he wasnt clear enough

Silly Goose

Which is from weinberg vol. I QFT, but this chapter is I think pretty much about normal QM

Ryder Rude

This also does not speak of time evolution, yes

Silly Goose

About the SO(3) and so on: Oh I see. Well so is total angular momentum a representation of SU(2)?

Ryder Rude

I really dont know whats going on with this definition then. Btw, to have conserved quantities, the dynamics must remain invarianr under the transformation. This is what the usual definition of symmetry means

But idk this other definition sorry :P

Silly Goose

And, if spin-1/2 is a representation of SU(2), then why do we not have to consider some double cover business as is motivated to do for orbital angular momentum?

ACuriousMind

7:08 AM

@SillyGoose see this Q&A of mine for the more general theory of projective representations

Ryder Rude

By looking for usual representations of SU(2), u r looking for the projective representations of SO(3)

The 1/2 representation qualifies as a projective representation of SO(3)

Silly Goose

oh. wait but i thought SO(3) is not enough to work for spin-1/2

Ryder Rude

This means that predictions are invariant under 2pi rotations

ACuriousMind

the upshot is: For most groups you will encounter outside of conformal field theory, the projective representations of that group are equivalent to normal linear representations of the universal cover of the group.

Ryder Rude

The wavefunction is allowed to become its negative under 2pi rotations

Silly Goose

7:13 AM

Well, so is the symmetry described in weinberg just the simplest type of symmetry. whereas say rotational invariance w.r.t. time occurs when you compose a rotation operator and time evolution operator and they commute (so that they can find their way to their hermitian buddy)

ACuriousMind

forget about time

the notion of symmetry here is just the notion of symmetry in the sense of Wigner's theorem, i.e. a ray transformation that leaves probabilities invariant

it is not necessary that the groups we're thinking about are dynamical symmetries in the sense that they commute with the Hamiltonian

Silly Goose

oh okay and so this is distinct from the usual noetherian symmetry?

Ryder Rude

Oh so they r indeed two different notions of symmetry

Silly Goose

excellent

ACuriousMind

I've seen these called "kinematic" and "dynamic" symmetry to distinguish them but unfortunately I don't think there really is a standard terminology here

Silly Goose

7:15 AM

Ah okay well that clears it up :P

I am still confused about representations of spin, orbital angular momentum, and total angular momentum. So spin-1/2 operators are representations of \mathfrak{su}(2). orbital angular momentum operators are representations of \mathfrak{so}(3). total angular momentum is?

ACuriousMind

the angular momentum operators live in the algebra, not the group

Silly Goose

oh oops

ACuriousMind

so first off they're representations of $\mathfrak{su}(2)$, not $\mathrm{SU}(2)$

and since $\mathfrak{su}(2)\cong\mathfrak{so}(3)$ that already solves part of your question: there is no difference between representations of $\mathfrak{su}(2)$ and representations of $\mathfrak{so}(3)$, they are the same algebra

the reason orbital angular momentum doesn't occur in half-integers is not representation-theoretic

it's just because the representation generated by the orbital angular momentum operators $x\times p$ on position space $L^2(\mathbb{R}^3)$ coincides with the (algebra version of the) natural representation of $\mathrm{SO}(3)$ on functions on $\mathbb{R}^3$

Ryder Rude

And the total angular momentum depends on ur system. e.g. ur system may just b a spinor, with no $x$ component. Then the total angular momentum wud just b the 1/2 representation

Or ur system may b two spinors, in which case u wud direct product the individual 1/2 representations

I mean u wud look for a representation of the total angular momentum on the direct product vector space

ACuriousMind

tensor product, not direct product

Ryder Rude

7:24 AM

Is the distinction important ? :P ive never felt a distinction

It must b subtle i gues

ACuriousMind

the distinction is fundamental to the notion of entanglement!

it's not subtle

a "direct product" is the Cartesian product of spaces, the tensor product is much bigger

Ryder Rude

Idk :P. Can u explain

Slereah

Direct product of two spaces has dimension $2n$, tensor product has dimension $n^2$

ACuriousMind

$\mathbb{C}^n\times \mathbb{C}^m = \mathbb{C}^{n+m}$ but $\mathbb{C}^n\otimes\mathbb{C}^m = \mathbb{C}^{nm}$

Ryder Rude

Oh

So when u consider two QM particles together, u do a tensor product of the spaces?

Silly Goose

7:27 AM

and then we can decompose the tensor product space into a direct sum of invariant subspaces right?

Ryder Rude

Like how the wavwfunction is $\psi (x, y) $ of the combined system

Silly Goose

or perhaps decompose is a weird word

view the tensor product space as a direct sum of invariant subspaces

ACuriousMind

the whole point of an entangled state is that, in terms of the projective state spaces, it is not in the image of the natural embedding $P(H_1)\times P(H_2) \to P(H_1\otimes H_2)$

@SillyGoose yes

and decompose is the correct word, at least mathematically

Silly Goose

oh

it feels strange to "decompose" a tensor product basis into a direct sum basis

transmute is more fun :)

Okay so to summarize so far: $\mathfrak{su}(2) \cong \mathfrak{so}(3)$, so spin and orbital angular momentum can be representations of either. But when we want to generate (in the rep theory sense) our groups, I am still not understanding for what reason we choose to map orbital angular momentum representation to SO(3). Are we forced to do so, or is it convenient?

ACuriousMind

what do you mean we "choose to exponentiate orbital angular momentum to SO(3)"?

Silly Goose

7:32 AM

or whatever the word is to go from the lie algebra being represented by total angular momentum to the lie group SO(3)

is it lift?

ACuriousMind

I mean, if you go about this systematically we're not starting with the algebra and angular momentum here

physically, our starting point is that rotations should have a way to act on physical systems

and rotations are SO(3)

there's no choice there

Silly Goose

hm but i thought we can equivalently start with the algebra

or so some answers on stack say

ACuriousMind

not start

but when you look at SO(3), you find that its projective representations are equivalent to the linear representations of SU(2), which in turn are equivalent to linear representations of its algebra $\mathfrak{su}(2)\cong\mathfrak{so}(3)$

Silly Goose

wait so what is the starting postulate, or experimentally backed whatever? is it that orbital angular momentum is the generator of spatial rotations?

ACuriousMind

so when you're just interested in "which representations of SO(3) can occur in quantum mechanics", you can just forget about the group and just think about the algebra

@SillyGoose from my POV, the only starting postulate that makes sense is "rotations should have a way to act on physical states"

Ryder Rude

7:36 AM

@Slereah what is the difference between direct sum and direct product

ACuriousMind

and Wigner's theorem tells us that the "way" in which such transformations act on the quantum Hilbert space is by a projective representation

@RyderRude a direct sum is a direct product that is also a (direct) coproduct

for vector spaces there's no difference

Ryder Rude

Oh

Silly Goose

wait so you are saying that okay we postulate that we should be able to rotate a system in blah blah ways that makes the set of rotations a group. it is the SO(3) group since we are rotating things in 3D space (?). we can then get all the way to the lie algebras. And so what people mean by "equivalently you can go from the algebra to the group" does not mean you can go a priori from the algebra to the group, but rather that because we know the group should be SO(3) we can find some mappings

from the lie algebra to SO(3)

Ryder Rude

And also is outer product the same as tensor product? @ACuriousMind @Slereah

Slereah

The fundamental difference

Ryder Rude

7:41 AM

Yeah, i knew this stuff. Ive just been usinf wrong terms :P

Slereah

Direct sum is the points, tensor product is the lines

Ryder Rude

Yeah, i knew this stuff. Ive just been using wrong terms :P

I think outer product and tensor product r used for almost the same thing, with maaybe a subtle difference

I mixed up the terms direct product and outer product

Or is outer product also not wut im thinking?

Slereah

Outer product is the tensor product

Ryder Rude

Oh this i just conflated the terms outer product and direct product

Silly Goose

Well, so for the spin case: the rotations generated by say the pauli matrices are of a different nature than spatial rotations, right?

So how would we motivate starting from the group and getting to the algebra

Slereah

7:45 AM

Tensor product basically means that in general you can't really speak of the individual Hilbert spaces by themselves

That is what entanglement is

Ryder Rude

Yeah

U need the cross terms too

I know these ideas but i mix up the terms :P

Direct sum can b used when the systems hav nothing to do with each othr, but u r just considering then together for some reason

And outer product for interacting systems

Silly Goose

I guess observables untenable to human senses cannot be motivated starting from the group? but from experiment? or is it just pedagogical how spin is introduced in say Sakurai?

but then i would expect to be able to experimentally motivate total angular momentum :P and then you can motivate everything from one perspective

Ryder Rude

U can motivate projective representations by considering that the predictions of QM only depend on the square modulus of wavefunction @SillyGoose

This is y u wanna go out looking for weird representations too

Becuz the wavefunction is allowed to become its negative under a 2pi rotation

Slereah

You can just look for all projective reps of SO(3) for such purpose

turns out you have a bunch of weirder ones than you'd expect

Including weirder ones than spinors

some of them are real particles, some of them are not

Ryder Rude

But projective representations r the same as usual rerpesrtnations of the cover @Slereah

Silly Goose

7:57 AM

hm I'm not understanding. so projective representations are kind of like dualities in textbook QM?

Ryder Rude

@Slereah like, what kind of what kind of cursed particles hav u seen

Slereah

I guess technically it's the Lorentz group : en.wikipedia.org/wiki/Continuous_spin_particle

SO(3) reps are indexed by just the $j$ number iirc

Although that's only for vector representations

Ryder Rude

These must b spinning like crazy

@SillyGoose what do u mean by "duality" here?

Silly Goose

the theory of textbook quantum mechanics is invariant under switching between projective representations

Ryder Rude

Idk what that means :P

Slereah

8:15 AM

More complex forms of products

Ryder Rude

Chinese products

ACuriousMind

@SillyGoose No, they are not different from spatial rotations. The point of "spin is angular momentum" is that spin really is angular momentum in the sense that it is related to spatial rotation. It's just not angular momentum of the form $x\times p$

What makes spin different from orbital angular momentum is that the spin representations are not the straightforward "how functions on $\mathbb{R}^3$ act under rotation" you'd expect from thinking about QM in terms of wavefunctions

Ryder Rude

8:31 AM

@ACuriousMind @Slereah Is there some philosophy of mathematics which is in-between Plantonist and Formalist?

Slereah

I don't know

ACuriousMind

what is that supposed to be, "math is about formal manipulations of symbols but the symbols have objective immaterial existence"?

philosophical positions are not necessarily spectra, I don't know what "in-between" means here

Slereah

If anything platonism might be in between formalism and pythagoreanism

material objects are just math objects

ACuriousMind

@SillyGoose You can experimentally motivate total angular momentum by showing that you can "convert" spin angular momentum into orbital angular momentum, cf. Einstein-de Haas effect

i.e. the two angular momenta are, in general, not seperately conserved and it is really just total angular momentum that relates to rotation and rotational symmetry in gneeral

Ryder Rude

@ACuriousMind @Slereah I dont mean a spectrum. I mean some philosophy that has pros of both.

Pros of formalism: U dont need to define what existence means beyond what u can verify to exist. Pros of platonism : U get motivation for why ur string manipulation system must be consistent and y the rules r not just arbitrary

imbAF

8:39 AM

In fermi dirac statistics, when we see the graph that shows the dependency of the average occupation nr. from the energy value for different Temperatures, one can notice that all the plots contain the point with coordinates (fermi energy,1/2). What is the significance of this? What does it imply?

Slereah

Sounds like someone wants to have their cake and eat it too

Ryder Rude

Kinda, yes. I need some compromise

Platonism is fine, except theres no way to define that sort of existence

Slereah

What if some math objects are real but not others

like the REAL numbers

ACuriousMind

@RyderRude I don't think you appreciate that the existence of many different philosophical viewpoint to a question usually signifies that there's some sort of tradeoff that can't be solved :P

Slereah

My advice is to drop the law of non-contradiction so that you may embrace both at the same time

Ryder Rude

8:42 AM

So I cant even pick a school then :P

What if all was true

Lol

Imo truth is only defined after a statement's interpretation wrt some set

There can b no set that can interpret both P and not P as true

Oh.... except the SET OF ALL SETS

Maybe we shud just embrace that that set exists :P

It means all things r true but some things r useful :P

imbAF

What conditions should a system satisfy so that the Liouville theorem holds true ?

ACuriousMind

@imbAF depends on what kind of "systems" you're thinking about

every system in Hamiltonian mechanics obeys Liouville's theorem

but if you're thinking about some more general notion of "dynamical systems", in particular ones where energy isn't conserved, then it doesn't hold for every system

imbAF

9:02 AM

so the Liouville theorem is only valid for isolated systems? where energy is conserved, which would make that a system that satisfies the hamiltonian mechanis

ACuriousMind

I mean, it really depends on what exactly you mean by "system" and "Liouville's theorem"

in the most narrow interpretation, Liouville's theorem is just a statement about Hamiltonian mechanics

imbAF

the interpretation of it, where moving along side a trajectory in phase space the density of states is constant

ACuriousMind

my point is, what does "phase space" or "trajectory" mean if you're not doing Hamiltonian mechanics?

depending on your answer, the theorem may or may not hold for all systems you're considering

imbAF

if the trajectory is only something that occurs for when energy is conserved than that would imply Hamiltonian mechanics. As we know, the only case we studied in class was the MCE, which is an isolated system, so conserved energy. I cannot speak about other cases

Ryder Rude

9:20 AM

@Slereah @ACuriousMind This is the philosophy I've made up so far : We pretend infinite collections exist and write down what axioms they would satisfy if they existed. This is all done to hopefully come up with a consistent and useful string manipulation game to produce truths about finite collections and computations

This philosophy is more inclined toward formalism. But it also provides a motivation for y ZFC is not just any game and y it should be consistent

Amit

@RyderRude I think there's a contradiction there possibly: if we assume an infinite set exists, it means we can also prove things about it. So the truths produced will also apply to infinite sets whose existence is assumed. Perhaps you want to say that these truths can only ever be verified or made use of for finite sets. For example $$\sum_{n=1}^{\infty} \left(\frac{1}{2}\right)^n = 1$$ you can verify this expression is correct only up to a finite number of terms.

Ryder Rude

@Amit no, i dont mean that we assume infinite collections exist. I mean we pretend. The goal is to ultimately motivate why we wrote down the "meaningless" string which is the axiom of infinity

Amit

which isn't really verifying the equality. To verify the equality you have to use the closed formula which is again finite...

but pretending is not a mathematically defined process lol

Ryder Rude

We just be sloppy and use our feeling about infinite collections

@Amit but this is pre-mathematics!

We r trying come up with mathematics

Amit

I don't think it is only pre-mathematics. For example when you start defining a limit by saying for any $n\in\mathbb{N}$ such that $n>N$ ... I claim you are already assuming infinity, not only on some metaphysical level. The statement that you can always pick a greater number assumes infinity

Ryder Rude

9:34 AM

The problm with assuming an infinite collection exists, is how do u define that existence? Does it objectively exist in nature? @Amit

Amit

It doesn't have to exist in nature for you to define it

Ryder Rude

@Amit i mean...$n \in N$ it is still just a string. It can b used to make useful deductions about the finite world that we encounter. It's not necessary to interpret that string using an infinite collection

Amit

that's correct, but what about the other part. For any $N$ I can pick a strictly larger number...

You can even put that on an automated theorem prover and it will probably be able to use it to prove various theorems.

Even though the prover itself certainly can't represent infinite quantities

Ryder Rude

@Amit You don't need that sentence to do mathematics. Thr sentence "I can pick any larger number" is human intuition that we use to come up with mathematics. Mathematics is just strings

I mean this sentence is not mathematics

@Amit but i really want to know a definition of this. I'm struggling to define it @Amit

Amit

You are trying to separate totally the interpretation of the strings from the strings themselves if I get you correctly

Definition of infinity?

Ryder Rude

9:40 AM

@Amit i mean we interpret those strings to verify truths about finite collections and computations. This is where interpretation is necessary imo

@Amit definition for what it means for infinity to exist

Im thinking that this sentence means that an infinite collection objectively exists out there in nature

Amit

Well since the "machine language" of all this is as you say just string manipulation according to certain rules that also don't need to be interpreted, why are you bothered about whether you interpret a certain symbol as referring to infinity or not?

Ryder Rude

Sorry, I meant that we dont need that particular interpretation for any application of math. For applications, we need to relate math with finite collections and computations. That interpretation is necessary

But the interpretation of any string in terms of infinite collections is not necessary

I mean the latter interpretation is still useful for human intuition @Amit

But it's not necessary to assume such a collection exists

Amit

I don't agree that we don't need it, I think it is essential in some cases. Again suppose you are handling a very complex sum, something like a taylor expansion. It is essential to know whether it converges in a way that each term is a smaller correction, so that you know you're always safe in computing the next term and adding it. It makes a great deal of difference to know "no matter how many terms I compute, my sum only gets more accurate, never less"

this is not true for all series

as we know from renormalization etc.

Ryder Rude

@Amit that is a truth about finite computations that you interpret from the string manipulation that is your proof about the infinite sum

I mean you can verify that truth for finite computations that it keeps converging

Amit

Yeah but you just said, we don't need the interpretation of something being infinite. I am saying this is the interpretation that allows you to know you're taking correct action here

Ryder Rude

9:49 AM

But any computation that you will ever do is finite in nature. You can interpret from ur string manipulation that ur finite compitation will b alright. In saying u need not assume that there exist an infinite collection of objects

Amit

I agree, every computation is finite, every verification is finite

Ryder Rude

So this is y u r justified in doing that computation. Becuz u hav interpreted thaat ur finite computation is fine

Amit

But we need apparently some ideas beyond computation and verification to make skilled use of our math :)

Ryder Rude

@Amit Yeah, I agree. In practice, platonism is useful for human intuition

Humans have a feeling of infinity

Even tho nothing infinite ever exists in our brain

Amit

Platonism is somewhat of an exaggeration but yeah it's in that general "direction"

Ryder Rude

9:51 AM

Lol

Amit

To see a world in a grain of sand...

Ryder Rude

But can we ever take this idea FULLY seriously? I mean, not just as a feeling to motivate string manipulation. To take it fully seriously, how do we define what existence means beyond what one can ever verify?

Would this mean sets objective exist in nature? Or can there be other camps too?

Amit

define existence of infinity?

Ryder Rude

Yeah, how do we define that existence

It surely exists as a string. But as a collection, does it exist in nature?

Amit

Nothing in math has a pretense to exist in nature... I mean if you take Platonism as a kind of an ideal for math, Platonic forms are not supposed to enter reality, reality is only in their image

Ryder Rude

9:55 AM

Yeah, but then they r just extending nature to another universe which exists

How is that existence defined

ACuriousMind

@RyderRude Honestly, I think the correct response from a scientific/falsificationist standpoint here is that this is a meaningless question

Ryder Rude

@ACuriousMind That's wut im thinking!

ACuriousMind

there is no experiment I can run that would distinguish "a world in which infinity exists" from " a world in which infinity doesn't exist"

@RyderRude if it is, then it is not what you're saying

you've been debating the "existence" of mathematical objects for days here

if you think it's a meaningless question, I don't know why you're talking about it so much

just say "doesn't matter" and move on

Amit

It's sometimes hard to put into words what's bugging one, that I can understand :)

Ryder Rude

Hmmm.. Yeah im mostly in the formalist camp @ACuriousMind

Ok let's forget about whether infinity exists from the scientific verification PoV. Im interested in if theres any other definition of existence

Becuz the scientific question is settled

Platonists say that things exist but they dont define existence.

Amit

10:00 AM

For a scientist what exists is what the experimenter recorded in his notebook :)

Ryder Rude

@Amit @ACuriousMind What if we, suppose, say that physics IS nature? I mean the sets that physics uses objective exist? Is this a good definition of existence

ACuriousMind

scientific verification? what is this, logical positivism?

Slereah

There are no experimenters recording me

Do I exist?

ACuriousMind

@RyderRude why would you say that?

Amit

@Slereah You think the h bar is not an experiment?? :D

Slereah

10:01 AM

Nobody even used sets until the 20th century

Although I guess people used universals

which were essentially sets

Ryder Rude

Becuz most scientists believe in an objective reality. Suppose life gets wiped out. Does the set of planets exist objectively now?@ACuriousMind

And does spacetime exist objectively now

Let's say we say that spacetime IS nature

Slereah

How do you even know the past exist

or the future

Ryder Rude

Then an infinite set can objectively exist

Amit

@RyderRude here's a famous dissenter from that view: en.wikipedia.org/wiki/…

Slereah

Can you be sure that the informations you get from your senses are fundamentally differenty from the ones you get from your mind

etc etc

Amit

10:04 AM

@RyderRude Suggestion: Question the demand for certainty!

Slereah

Are you even sure that the basic rules of reason that you use make sense since you cannot prove them from themselves in any satisfying ways

Ryder Rude

I mean... What other definition do we even have of nature? Y not just say the sets of physics ARE nature? @ACuriousMind @Amit @Slereah

Slereah

Plenty of schizophrenics have no problem holding contradictory ideas

Ryder Rude

I mean the sets that physics uses like spacetime

Slereah

what if you are insane and don't know it

Amit

10:06 AM

lol, sometimes the insane person is the one who suffers from an excess of logic and not from the lack of it

Ryder Rude

Ummm.... this is devolving into a discussion of consciousness

Amit

sets are only in the consciousness! :)

Slereah

You can start questioning just about anything if you really want to

Ryder Rude

Im asking, what other definition to we have of nature

Amit

definitions are consciousness

Slereah

10:07 AM

I'm afraid in 3000 yeqrs of philosophy nobody has really given an argument to convince everyone

Maybe you're not gonna fond an answer there

Amit

@Slereah If anyone is convinced the fun of debating is over ^_^

ACuriousMind

@RyderRude the basic idea of falsificationism is that we never gain certainty about what "is"

we just have models, and these models can be differently accurate

Ryder Rude

Yeah. It can b that no model is perfect. Then nature cannot b described using sets

ACuriousMind

that's been on a technical level the mainstream scientific position for decades now

the question "do sets exist in nature?" just doesn't make sense

Slereah

I'd say it's not quite true

ACuriousMind

10:09 AM

the question is "Can we use sets to model nature?"

Slereah

On a practical level we have plenty of heuristics

Ryder Rude

Okaay. Then nature is "something" unknowable. And sets and strings are human interpretation of it

Slereah

We don't go purely by verificationism methods

It just wouldn't work

Ryder Rude

But the key point is... "Nature is something". It's not nothing. Something objectively exists

Slereah

There's infinitely many different models you can fit on just about any data

ACuriousMind

10:10 AM

oh, sure, you have to add Occam's razor and some sort of disclaimer about incommensurability etc.

Amit

Not even necessarily an interpretation. The main thing today is to use these models to extract juicy predictions about what nature will do in a given situation. You don't need to interpret what it does to predict what it does

Slereah

I'd say we have tons of heuristics really

Just unspoken ideas as to what constitutes a good physical model

Amit

@RyderRude That's about as much as we'll ever know for certain. Even solipsists agree that "something" exists (themselves)

Slereah

People aren't trying to literally find every possible mathematical model

Ryder Rude

Ive been holding this viewpoint for long, that it doesnt make sense for sets to exist out there. Im just trying to clear the loose ends now

ACuriousMind

10:12 AM

@Slereah that's just Feyerabend's and Kuhn's critique of falsificationism, really

Ryder Rude

The one looose end is... what IS nature

ACuriousMind

It's true: We have "external" rules about how we select the field of theories we then actually test via falsificationism

Slereah

It is Azathoth

Ryder Rude

We interpret sets out of it. Nature must have enough structure to allow for sets in its interpretation @ACuriousMind @Slereah @Amit

Slereah

Ryder Rude

10:13 AM

I mean.. Nature cant b ONE structureless blob

Slereah

Toot toot

Are you sure

Maybe all physical observations have been random so far

ACuriousMind

@RyderRude Again: What does it mean to say that "nature" has structure?

Amit

@RyderRude Or we have enough structure to impose our ideas on nature :)

Slereah

But by coincidence they fit some model

ACuriousMind

all we know for certain is that the structure is in our models, not "in nature"

Ryder Rude

10:15 AM

Lol. But then again u get the concept of randomnes and observations out of nature @Slereah

Slereah

And tomorrow the world will fail to obey any previous rule

Ryder Rude

Is there any intel on what IS nature

ANYTHING

Slereah

Maybe the past does not exist and our memories are in place from the rules of the universe

Ryder Rude

Or is all of it undescribable by definition

Slereah

And then what can we say of physics

ACuriousMind

10:16 AM

@RyderRude not if you actually commit to consistently thinking about science just as a body of models

Amit

Any intel you get is colored by the limitations of your biology, possibly also your culture education and society... we have no way to look at it differently. Even if we ask our alien friends, we have to interpret what they're saying into our framework lol

ACuriousMind

that this is...not satisfying to many is the primary reason people still debate epistemology, I think :P

Ryder Rude

So this is where any such discussion must end. NOTHING can b said about nature. Not even that nature is nothing or structureless. Becuz even the concept of nothing has been borrowed from our own experience

ACuriousMind

I mean, if people agreed that this is the end epistemology would have ended with Humean skepticism

yet we kept going :P

Slereah

No actually we are all spirits in the mind of God, nevermind what I said

Ryder Rude

10:18 AM

we r not allowed to ask "Why is there something instead of nothing? ". Its beyond our pay-grade

Slereah

It's all water

Amit

@ACuriousMind I can see one place where epistemology is helpful: when coming up with new theories/models, it seems that epistemology can lead you in very different directions. And we need different directions to come up with an improved body of models

ACuriousMind

@RyderRude "beyond our pay-grade" implies there is a reason, we just can't know it

but actually the question just doesn't make sense

@Amit oh, I'm not saying we should have stopped at Humean skepticism!

PM 2Ring

@RyderRude You might enjoy reading about Stephen Wolfram's concept of the Ruliad. writings.stephenwolfram.com/2021/11/the-concept-of-the-ruliad I must admit that I didn't finish reading that whole article, but it does have some intiguing ideas. OTOH, maybe you should get a bit more background in philosophy & metaphysics first...

ACuriousMind

that we can't know any potential objective reality for certain is "true", but still we need methods of talking about what we colloquially mean by reality and "truth", like factual statements that correspond in some sense to our sensual perception

we just shouldn't fool ourselves into thinking we're talking about objective reality - no, we're talking more about a kind of shared hallucination

Amit

10:21 AM

Yes, the discussion of epistemology becomes less productive when we expect to get to some final "objective conclusion"

Slereah

If you wish to reach such a point I recommend joining a cult

ACuriousMind

human minds are pattern-matching machines, they impose structures and mental models upon their perceptions and the task of epistemology is to provide a framework that provides a meaningful sense in which some of these structures can be better ("scientific", "true") than others ("delusional", "wrong")

it's not about what "really is" and more about what kind of beliefs about the nature of the world are useful to us

Amit

@Slereah lol, I'd recommend asking where is the need to reach it. People in cults sometimes realize there was no need after spending decades in the cult...

Slereah

How did you acquire the certainty that the mind is a pattern matching machine

ACuriousMind

@Slereah I have a mind. It matches patterns

just very basic Cartesian cogito, ergo sum

Amit

10:26 AM

'Cause it's curious

PM 2Ring

But it's not just about usefulness, though. Memes (in Dawkins' original sense) can propagate even when they aren't particularly useful. They just happen to have the right attributes to appeal to enough minds and to fit the prevailing memetic landscape.

Slereah

I take it back I think the world just doesn't exist

PM 2Ring

10:50 AM

Of course the world exists. It was created last Thursday. rationalwiki.org/wiki/Last_Thursdayism

I used to love thinking and talking about this stuff when I was young. But I decided that it's not healthy to invest too much energy in it. It didn't help Cantor, Boltzmann, Gödel, etc...

Amit

Amen

When such discussions get serious I always wonder whether they in fact should be seen as inadvertent therapy sessions lol

ACuriousMind

11:16 AM

@PM2Ring my point was that is we accept the basic premise of radical skepticism then it is exactly the task of epistemology to provide a framework that separates useful "memes" about the nature of the world from non-useful ones

Slereah

But how do you assign usefulness if you have no epistemology

If you don't assume induction you're not gonna be able to!

ACuriousMind

I mean that it's the epistemology that defines "useful"

I don't believe in objective usefulness of beliefs about the nature of the world either :P

Physics Meta

0

Q: When are modified closed question reviewed again, and how is this visible?

I got my question closed (by a bot? Looks like it from the first comment) and when I saw this, I rephrased and tried to abide to the comments (should be more focused). This happened yesterday, the question is still closed but I cannot understand whether it's been reviewed and rejected a second ti...

discussion specific-question closed-questions reopen review

PM 2Ring

11:40 AM

@ACuriousMind Fair enough.

And yet, it can be very difficult to get rid of less useful concepts that have managed to survive. It can be difficult to even notice that they exist, although you can get glimpses by studying other cultures and religions. And other times.

Physics Meta

11:57 AM

0

Q: What is wrong with this question?

How can the entire system be at rest irrespective of how much external force you apply? What is wrong with this question? Seriously? I even got an upvote by some sensible dude. Do you think Muhammed Ali would be the greatest boxer by just reading BOXING theory and asking theoretical doubts to his...

discussion closed-questions close-reasons

PM 2Ring

We lost Jacob Ziv a couple of days ago, and Abraham Lempel several weeks ago. They aren't exactly household names, but LZ based compression algorithms are executed billions (or trillions) of times a day. en.wikipedia.org/wiki/Abraham_Lempel en.wikipedia.org/wiki/Jacob_Ziv

Slereah

What if that man was the only man making sense

Shub

12:33 PM

In thermodynamics, Q=U+W and G=H-ST. Are Q and H the same thing? Else how are they related?(I dunno if this is the right place though)

Physics Meta

12:49 PM

0

Q: What do you think about moderators editing your English form in the quesitons?

I just got a recently posted question edited by a third person - a moderator I suppose - for what I consider very small elements that do not really add or subtract from the understanding or the meaning of the conveyed message. I don't know how to relate to this, I find it slightly intruding. Mayb...

discussion

PM 2Ring

1:57 PM

^ I find it slightly disturbing that someone can be a member for >9 years and not understand such basic things about how Stack Exchange works.

Slereah

the hell is Stack Exchange

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