The h Bar

Tryst with Freedom

00:23

probably everything (unironically) @SillyGoose

DIRAC1930

07:26

@ACuriousMind The Gellmann-Low theorem

ACuriousMind

@DIRAC1930 Gellmann-Low does not involve any actual switching on or off either because it takes the limit $\epsilon\to 0$, the switching only exists in the intermediate steps

Slereah

Some paper on the shape of planetary bodies mentions that animals and trees don't have a spherical shape and gives a bibliographical reference for this

On Growth and Form

On Growth and Form is a book by the Scottish mathematical biologist D'Arcy Wentworth Thompson (1860–1948). The book is long – 793 pages in the first edition of 1917, 1116 pages in the second edition of 1942. The book covers many topics including the effects of scale on the shape of animals and plants, large ones necessarily being relatively thick in shape; the effects of surface tension in shaping soap films and similar structures such as cells; the logarithmic spiral as seen in mollusc shells and ruminant horns; the arrangement of leaves and other plant parts (phyllotaxis); and Thompson's own...

ACuriousMind

"Cows are not spherical." [1][2][3][discuss?]

Slereah

reminds me of

ACuriousMind

08:10

@DIRAC1930 Also, note that Gell-Mann-Low more or less again assumes the existence of the interaction picture in its proof, so Haag's theorem says this is not actually a theorem about interacting QFT in continuous space. See also this answer by Chiral Anomaly.

Slereah

Gell-Mann, that WAR CRIMINAL?

> Dr. Murray Gell-Mann, a Nobel Prize-winning physicist from Cal-Tech, had come to Paris to lecture on the theory of elementary particles, but the audience which met him wanted to ask about his work for the Pentagon, through his participation in the Jason group. Gell-Mann’s response was, “I am not free to answer.”

lol

> Gell-Mann: Can we find out what effect increasing police density or ear cutting, or other negatives have on villager attitudes?

Oh apparently Wigner and Wheeler were also part of the Jason Group

Sorry Wigner's theorem has been deemed a warcrime

Jack Rod

08:37

@JohnRennie sir can protons be combined to give muons Or photons?

DIRAC1930

08:51

Ah yes I forgot about the $\epsilon\rightarrow 0$ limit

IIRC Bogolubov did something with adiabatic switching but I can't remember what he did

Is the paper 'On Quantum Field Theories' by Haag a good introduction to Haags theorem?

DIRAC1930

10:25

So can you usually use your intuition of QM to describe discrete QFT?

PM 2Ring

10:47

@JackRod If the protons hit each other with a lot of kinetic energy many different particles & antiparticles can be created. See:

2

A: Where all those particles come from - proton proton collision

If the total energy is conserved, are those particles the transformation of the kinetic energy to matter? Exactly! To understand how this happens you have to understand how quantum field theory describes particles. For every type of particle there is a quantum field that pervades all of spa...

DIRAC1930

11:07

It seems like assuming everything is discrete solves all problems

ACuriousMind

11:57

@DIRAC1930 all problems except for all the problems lattice theory has :P

fermion doubling, existence of the continuum limit, what does Lorentz invariance even mean on a lattice etc.

it's really a tradeoff: Lattice theory feels less fraught with problems "conceptually" but the devils in the details are no smaller

Ryder Rude

Hello

In a lattice theory, the free operator and the full operator can b defined to act on the same hilbert space

But still, I'm not sure about lattice theory's description of asymptotic freedom, even if the interaction picture works now

Since the interaction picture works, it is completely justified to use the eigenstates of the free operator as ur initial and final states in the S-matrix. So far, so good

But which free operator are we supposed to use here now? Is it the one with the (finite) bare mass, or the experimental mass?

DIRAC1930

So as of yet, QFT tells us nothing about what happens during an interaction, only what goes in and what comes out.

Do people see this as a problem?

Ryder Rude

How is that any different from non rel. QM? The intermediate states r a superposition of the free hamiltonian eigenstates (assuming u r doing lattice theory)

DIRAC1930

Well in non-rel QM, particles aren't produced

Ryder Rude

U want to know how particles r produced inside the black box?

DIRAC1930

12:12

Yep

I would have thought we would have been able to experimentally determine something

Ryder Rude

i dont get it. U just hav unitary evolution on the Fock space. The wavefunction is the complete description of a system in any quantum theory, not just QFT. Particles r "produced" when this unitary evolution yields u the state vectors corresponding to those particles

U will not get any "mechanical" description of how particles r produced. The wavefunction is the complete description

DIRAC1930

So it is assumed that the event is discrete and is just an exchange of quantum numbers

Ryder Rude

Maybe if u do some weird hidden variable theory, u cud get such description. But hidden variable theories r not usually compatible with particle creation/annihilation

@DIRAC1930 yes, the quantum numbers r exchanged, conserving energy-momentum at each stage, i think. But the evolution is continuous

Also, u start ur experiment with eigenstates, but the end product is a superposition of many possible outcomes that each conserve energy-momentum @DIRAC1930

Since it's a superposition, no definite particles r being produced inside the black box. Definite products r produced at the collapse of the wavefunction.

ACuriousMind

12:30

@DIRAC1930 QM scattering theory does the same. That in one case the outgoing particles can be different kinds of particle isn't really that fundamental a difference, it just feels to you that way because as long as it's the same particle you can pretend you have a description of scattering as "it's just one particle bouncing off another"

Ryder Rude

Only a hidden variable theory can produce definite products inside the black box. You would need the "particle type" to be a hidden variable. In QFT, a state can b a superposition of different types of particles of indefinite particle numbers

I mean the particle number can b indefinite prior to collapse. Like, how many photons r produced can b indefinite depending on the state

Physics Meta

0

Q: Feedback on closed question?

So a question of mine was closed. Probability distribution for the momentum of a particle undergoing a collision? I thought it was decently written (post the edits) however I guess it's still not up to standard. From a learning perspective can I have some feedback?

DIRAC1930

Ah yes, a particle is an excited state in the same way an energy level is an excited state in QM. The same goes for multiparticle states being just another excited state above the vacuum

But this discrete change is still an assumption right since we can't prove it or measure times short enough. Is that correct?

Ryder Rude

12:49

What discrete change do u mean?

DIRAC1930

well say an electron-positron annihilating to form a photon

ACuriousMind

@DIRAC1930 if you're trying to identify particles "during" the interaction - don't. if you try to resolve such interacting states, you just get weird answers - consider the QCD description of a bound nucleon state. We like to say that it's a bound state of three quarks but when you try to resolve this by higher energy probes, you find the parton sea

Ryder Rude

this particular process is forbidden becuz the energy momentum conservation cannot be satisfied for this. At least two photons must b produced, i think

Slereah

Only Moses can part the sea

DIRAC1930

@Slereah lol

ACuriousMind

13:02

the asymptotic states are exactly the ones which you can unambiguously identify as discrete batches of particles at every energy level

bound states - and also the intermediate states during a scattering process - are a mess if you try to view them purely through the "particle lens"

DIRAC1930

Would you class this as a failure of QFT, a failure of our calculational tools or a failure in being able to measure?

Ryder Rude

But either way, i dont think u can pinpoint to any instant of time where the photon states enter the scene during the unitary evolution

ACuriousMind

@DIRAC1930 I would not say this is a failure at all, just a demonstration that the "real world" of quantum states is far stranger than our pictures of discrete little particles

in a way this is not a failure in the same way that the double slit is not a failure of QM, it's just a failure of our intuition for "particle"

Ryder Rude

If u evolve the initial state for any non-zero amount of time, u shud already hav a crazy superposition. So i dont think u can pin point a time

The initial eigenstate starts with probability 1. But this probability slowly moves like a fluid to the other energy basis vectors in the time evolution. For any non-zero time, u hav a crazy superposition.

And the initial free state is an approximate description of the actual initial state in the first place. This is becuz interactions cant b turned off

Its all approximate stuff, i think

DIRAC1930

At what point does something become an 'in' state and not an intermediate state

If I measure it for long enough such that this $sin^2 E_{mn} t/E_{mn}^2$ formula tends to a delta function?

ACuriousMind

13:14

@DIRAC1930 as soon as you can tolerate the approximation - remember, there's a limit in $t\to\infty$ here, so there's an "error term" at finite $t$. The point at which you can treat a state as effectively free hence depends on when that error term gets small enough for you to not care anymore

Slereah

Still getting votes for that answer I did

I don't know why

Ryder Rude

Particles approximately behave Newtonian outside of the very small interaction region. Becuz they r shot at high speeds

ACuriousMind

@Slereah HNQ

Slereah

It's not particularly different from the average GR answer I give and I usually get like 3 votes there

What makes it a HNQ

ACuriousMind

you can see that the question hit HNQ in the revision history

DIRAC1930

13:16

How do I show that? In a book a read they called it 'the interaction range' but they didn't define it past that

ACuriousMind

@Slereah The Algorithm

Slereah

Is it the traffic or do the Gods of SE decide

DIRAC1930

It seems dodgy that measuring a particle for long enough allows us to treat is as free

Slereah

Had I known I would have written that answer better

ACuriousMind

@Slereah it's not traffic, but a combined score from the number of votes and answers, see the formula here

Ryder Rude

13:20

@DIRAC1930 u wud need to construct asymptotically free states like in Haag Ruelle

ACuriousMind

@DIRAC1930 how do you show what

if you expect anyone to explicitly compute this error term, no one will

DIRAC1930

Well it's difficult to interpret what exactly $\hat{V}(fields)$ does

ACuriousMind

why do you need to "interpret" what it "does"

Ryder Rude

Do u mean asymptotic dressing due to V?

DIRAC1930

Well to show that farly seperated particles are non interacting

ACuriousMind

13:22

if you want a picture, just draw the corresponding Feynman vertex to whatever polynomial in the fields $V$ is

@DIRAC1930 how is that not again exactly the same question about why asymptotic states are free

you don't need any details on the interaction to show that the asymptotic limit exists

Ryder Rude

I'm worried that asymptotic particles may b free from each othr, but not free from the dressing @ACuriousMind

ACuriousMind

and by the nature of limits, that asymptotic states are free means states at large but finite time are approximately free

@RyderRude what does that even mean? What is "the dressing"?

Ryder Rude

To show they they r free from each other, we wud need to first construct position-space wavefunctions maybe

ACuriousMind

the language of "bare" and "dressed" is rooted in the ill-defined idea of the interaction picture that somehow the free and interacting theories exist alongside each other

DIRAC1930

Is it best to forget about asymptotically free particles as treated in most QFT books. Will studying Haag-Rulle answer my questions?

ACuriousMind

13:24

the masses of the asymptotic states are the interacting masses (see again that discussion of the S-matrix in Weinberg)

@DIRAC1930 no

Haag-Ruelle theory is just the formal derivation of "asymptotic states are free"

DIRAC1930

Isn't that what I need

At the moment I'm stuck on how particles can be asymptotically free if I can never switch the interaction off

ACuriousMind

oh, sure, that's the thing Haag-Ruelle theory constructs

DIRAC1930

And also how a particle we use in experiments can be treated as a free particle if it is not in the asymptotic limit

ACuriousMind

but I predict it will not sate your desire for "interpretations"

it's just a bunch of cold math

DIRAC1930

I feel like the interpretations are what is confusing me

But Haag-Ruelle seems a bit above my mathematical level

ACuriousMind

13:28

well, but that's how it is in QM: Either you get handwaves that make no sense if you start thinking about them closely, or you get a bunch of math that's far more complicated than what you bargained for :P

it's arguably already the case when you really think about how operators like position and integrals like $\int \lvert x\rangle\langle x\rvert$ work, this isn't unique to QFT

Also, a caveat: Like most of mathematical QFT, Haag-Ruelle is based on the Wightman axioms. We don't have an established formulation of e.g. the Standard Model as a Wightman QFT, this is one of the millenium problems

so while Haag-Ruelle conceptually answers the question of how we get asymptotic states, it doesn't currently explain why it works in practice for the Standard Model :P

DIRAC1930

Is pg 153 here archive.org/details/space-and-time-in-the-microworld/page/152/… of any use?

ACuriousMind

depends on what that book does with the switching function

Slereah

A lot of axiomatizations of QFT basically just list cool ideas

would be cool if QFT obeyed all of these things in my opinion

Get someone to work on it

ACuriousMind

again, the usual constructions that start like that usually want to construct a limit at the end where they turn the switching to "always on", i.e. $g\to 1$, but the intermediate steps depend on taking another limit first

you don't want your S-matrix to depend on the switching function

(also I associate switching-dependent S-matrices more with renormalization than asymptotics)

@Slereah I mean the Wightman axioms are much more than that, since we know a lot of 2d and 3d theories for which we can establish them

Slereah

@ACuriousMind Plenty of them do but the theories that work for them are added on top

It's not really a way to get those theories

ACuriousMind

13:35

I'm not sure what you mean

DIRAC1930

Also section 32 here archive.org/details/space-and-time-in-the-microworld/page/182/…

Slereah

If you have just the axioms of QFT you're not gonna be able to do much as far as actual QFT goes :p

DIRAC1930

This talks about initial and final states

interaction radius is mentioned on page 183

ACuriousMind

@Slereah Oh, no, but the idea is that all the statements you can deduce from just the axioms follow once you've shown your construction fulfills the axioms

it's not "these axioms should give us the Standard Model", it's "If we could show that the Standard Model fulfills these axioms, we'd actually rigorously understand it"

Slereah

it always feels a little weird how detached it is from most constructions of "basic" QFT, though

Part of why I kinda like nlab rly

As weird and abstruse as it is, their QFT stuff is still basically just "quantize the classical theory"

ACuriousMind

13:39

@Slereah is it really that more farfetched than going from Heisenberg's "hey, these matrices do interesting stuff" to Dirac-von Neumann axioms for QM?

Slereah

@ACuriousMind Dirac-von Neumann is kind of like that too yeah

Basically too broad a spectrum of QM to be that helpful

Just in case you want to work on a quantum theory that doesn't have an underlying space or classical theory like a weirdo

ACuriousMind

I think it's once again this bias that because QFT isn't as finished as older fields, we tend to view all the discrepancies and abstractions as flaws, or misguided, or whatever because we don't see how everything fits together yet

the other fields looked like this too when they were in the process of being formalized

Slereah

true enough

Boy people did not know how to handle covariance in the 20's

DIRAC1930

Is section 32 the secret to the whole of QFT

(me trying to trick people into reading it) lol

Slereah

I hold the secret to the whole of QFT and I will reveal it for low prices

I think it would help if QFT books had like little roadmaps or something where they decompose it into different aspects of the theory and how they relate

since QFT is kind of a lot of different areas that aren't that connected

like whatever the hell Souriau was doing

Daniel Underwood

13:52

Schwichtenberg does something like that in his books, though they aren't exactly the typical mainstream textbook

Also mechanique quantique sounds much more elegant than quantum mechanics

Slereah

What doesn't sound better in French

What I always find surprising in QFT books is that most of them don't even have the same kind of variety of problems as QM books

you're not gonna see the particle in a box in QFT

and rarely even the hydrogen atom

AXensen

14:11

iirc peskin/schroeder actually has exactly such a roadmap so you can know which chapters to read in which order if you don't want to learn everything

edit: I was wrong. must be remembering another book

it has a very brief "if you want to read this... read this first" table in the introduction

Slereah

It is hard writing a book because you are torn between doing some kind of historical order, some bottoms up approach, top down approach or some ideal pedagogical order

it's basically impossible to do a good ordering because if you try to somehow sort by topics every topic will eventually use methods introduced elsewhere

DIRAC1930

@ACuriousMind It looks like Haag's book 'Local Quantum Physics' has some useful information

Slereah

I don't know why the historical approach is so common really

I guess it's some sort of thinking that if people thought about it first, it's probably a more obvious idea?

Not sure that's true

DIRAC1930

I remember being completely lost in my first QFT course

I thought it would be similar to QM i.e. finding eigenstates of the Hamiltonian etc.

Slereah

I don't know why people don't do more of showing that it's actually the quantization of a field, for a start

Showing second quantization can wait

DIRAC1930

14:25

I didn't even know what second quantization was throughout the whole course

Slereah

Wait until you get to third quantization

DIRAC1930

The more you learn about QFT, the more you realize that it is alot like non-rel QM

When I was in my first QFT course, it seemed like something completely different

Slereah

why does QM not need distribution-valued operators anyway

It's still a one dimensional QFT

Why isn't the time dependence of the operators distributional in nature

or is it

Mr. Feynman

@Slereah The Dirac $\delta$s in the CCR appear due to spatial variables, don't they?

Slereah

The spatial variables aren't part of it technically

That's a whole different hog

The base space of non-relativistic QM in that description is just the time

Mr. Feynman

14:38

@Slereah That's what I mean (?)

ACuriousMind

But Mr.Feynman is correct that the $\delta$s are spatial

what you're looking at are the equal-time commutation relations of $N$ fields $\phi_i$, which are $[\phi_i(\vec x,t),\pi_j(\vec y,t)] = \delta_{ij}\delta(\vec x - \vec y)$

Slereah

yeah but then those are unrelated to the distributionalness in QFT

ACuriousMind

in 1d QM that's just $[x_i(t),\pi_j(t)] = \delta_{ij}$

Slereah

Although I guess if our CCRs need equal times, then it would just be a single point

ACuriousMind

no continuous $\delta$, so no distributions

the $\phi_i(\vec x,t)$ therefore have to be distributions in $\vec x$, and if we remember that we're actually in a relativistic theory this then means that $\phi(x)$ as a whole is a distribution

you get no such requirement for the $x_i$, and in fact they're just operators with continuous spectrum, but not distributions

It is interesting to remark that classically the $\delta(\vec x - \vec y)$ is not problematic because the PB bracket is not just multiplication but also a functional derivative, so there the $\phi_i(x)$ can be normal functions, but it is not exactly clear to me what lesson exactly I should draw from this

Slereah

14:48

I never really know how accurate those ancient greek portraits are

I know some of them are from contemporary busts and some are made up, but it's hard to really know which is which

ACuriousMind

first of all you have to imagine most of them in really garish colors :P

Slereah

Menelaus of Alexandria was apparently the first guy to compare great circles on a sphere to straight lines of the plane

The OG non-Euclidian man

Mr. Feynman

How did we get from QFT distributions to ancient Greek portraits?

Slereah

People talk as they please :p

Mr. Feynman

Prove it

Slereah

14:51

I just did

ACuriousMind

@Mr.Feynman Slereah was probably looking at some Wiki article on QFT and then started clicking random links until he ended up on one that had a Greek portrait on it

Slereah

@ACuriousMind Just reading some history of astronomy stuff

Is that anything like Mr. Menelaus or is that just a greek looking dude

there's almost never a reference for portraits of that era

I'm guessing the standard Euclid portrait is fake since we basically know nothing of the guy

Smurf looking guy

Mr. Feynman

@ACuriousMind this is so Slereah-like :P

Slereah

I'm guessing most mathematician portraits are fake since I don't think most of them were that influential in their days

Nobody's keeping a bust of Euclid around

DIRAC1930

I feel like QFT can be summarized in 20 pages

Slereah

15:02

I mean sure, but would it be readable

ACuriousMind

everything can be summarized in 20 pages

just depends on the audience and how small the print is how useful that summary will be to them :P

Slereah

You could probably summarize it in one awful categorical diagram but I don't think it would be super useful

DIRAC1930

Might try reading the last chapter of Dirac on QED

pg 303

sophiararebooks.com/pages/books/5883/paul-dirac/…

$12,500

Wow sophiararebooks.com/pages/books/5812/ludwig-boltzmann/…

$12,500 also

Old textbooks look way better

Slereah

15:25

That's because poor people didn't go to university in the 20's

DIRAC1930

I dunno, textbooks cost an insane amount nowadays

Mr. Feynman

@DIRAC1930 why would you want to do that?

DIRAC1930

20 pages showing everything including radiative corrections. 20 pages doing scattering. And then 160 pages doing conceptual understanding

Slereah

15:48

physics education is a little weird because they spend a lot of time teaching you unintuitive ideas that were historically very hard to accept and then teaching you that actually those ideas are WRONG

DIRAC1930

Thats true

More Anonymous

@Slereah ahmen

DIRAC1930

I feel like the physics high school syllabus needs to overhauled

Look how complicated chemistry is in high school

compared with physics

Slereah

well that's true even outside of high school

DIRAC1930

Most people think physics is just $F=ma$

IIRC, in chemistry, we were taught about the $n,l,m$ quantum numbers in a hydrogen atom

And physics was just $F=ma$

Also, statistical mechanics was taught in chemistry albeit in a different form

But free energy etc. was all there

In maths we were integrating to find the volume of a some weird shaped item with radial symmetry

I feel like the Schrodinger equation is simpler than that

Even if it is taught at a very basic level

Tbf I dropped physics in the last 2 years of high school

Ryder Rude

16:04

@ACuriousMind we shud also note that non rel QM can b translated into the language of non. Rel. QFT, which does have distributions. Hence, Haag's theorem may be an issue. But im not sure

ACuriousMind

@RyderRude Haag's theorem in its strong form - saying that a free and an interacting field necessarily have two different representations - does not hold for non-relativistic theories, Poincaré invariance is necessary (and hence putting your theory into a finite box an escape)

Slereah

what part of Poincaré invariance causes issues exactly

Ryder Rude

Oh. This is y it doesnt hold for lattice theories too

Slereah

Like what happens if you use different kinematic groups

I'm guessing the causal structure is the issue there

ACuriousMind

@Slereah There are Euclidean QFTs where the interacting and free field representations are unitarily equivalent, i.e. we know actual counterexamples

Slereah

16:13

what about CFTs?

ACuriousMind

I mean a "CFT" is still either Euclidean or Lorentzian depending on the signature of the underlying manifold, right?

you can't escape the theorem by enlarging the symmetry group

Slereah

oh wait I guess that's a larger group, not smaller :p

what's the smaller example

I guess AdS/dS symmetry is a case of a different group

ACuriousMind

@Slereah one view on the fundamental issue is that the equal-time commutation relations essentially determine the correlation functions of the fields at all times because time translations are equivalently a boost + spatial translations + a boost

so relativity allows you to prove that the representation of the eq. t. CCR already determines at least the first four Wightman functions

Ryder Rude

16:28

I have made a new philosophy. Is there anything similar to this : So basically 1. math is extractible from the universe's ontology 2. A subset of that math is ur brain brain 3. We know that there exists such a thing as "what it is like to be our brain". As in, there is a personal experience associated with the brain that cant b shared.

I conclude : 4: Every piece of math in the universe's ontology has a personal experience associated with it

It's just that a chair's personal knowledge is inaccessible to us. But all objects have a personal quality that the math doesnt deal with

It's like how there's supposed to be more to chair than an abstract representation of information about its particles. There's smthing more to everything out there.... just like there's smthing more to us that we cant share to others

Ryder Rude

16:43

I wud like to reverse my conclusion 4: Everything has a personal quality first-and foremost. The math or information is the secondary property attached to everything. But this property is always approximate in nature becuz there is probably no final model of physics

So it's like how we used to attach a phase space description to objects. But now we attach a wavefunction to them. These attached objects will always be approximate in nature

Mr. Feynman

@Slereah I think that it is very pedagogical to go through this. A lot of old ideas are not wrong, just true in a given limit

Slereah

@Mr.Feynman they are drilled a lot though

Ryder Rude

I have made a corollary of this philosophy : We will never be able to accurately attribute mathematical object to the brain. So this means computationalism is technically wrong in this philosophy

@Slereah @ACuriousMind Please give any comment on this philosophy, if you are free

Obliv

17:32

How much tech could you build from scratch if placed in a natural environment

Like assuming you don't have to worry about food, water or shelter

You only have the knowledge you have, and some pen and paper, and you can have servants

@ACuriousMind I feel like you could build a lot

And what would be your strategy, building a generator or something first?

human tech evolution any% lol

u could probably skip some stages, maybe stone/bronze age

Slereah

@Obliv There's plenty of youtube channels on that topic

you can check them if you wish, it is interesting

apparently one big challenge of doing this is that the world isn't as it was back during the paleolithic

For instance most of the good metal ore has been mined out

Obliv

I knew of primitive technology, but I don't think he's going up the tech tree lol

Slereah

Starting the Stone Age

►

you can try this one too

general vibe is that if you tried doing it you probably wouldn't go that far in one lifetime

even smelting decent metal at all from scratch is very hard

ACuriousMind

17:48

@Obliv worldbuilding has a lot questions about that e.g. worldbuilding.stackexchange.com/q/242375/13662; the main impediment is that much of 20th century tech requires certain materials or production processes that need a lot of people to produce them

Slereah

You can tell that they are struggling partly because they're not that good at the various crafts involved

It's pretty hard to become skilled at pottery, smithing, weaving, etc

ACuriousMind

I mean, to even start smelting stuff like iron you need someone to properly figure out charcoal production

Slereah

also like they have to cheat a lot because getting some of the materials needed for this is like

thousands of miles away

if you're a caveman you can't go to Mexico to get whatever type of fancy minerals you need

ACuriousMind

not "caveman" but e.g. long-distance tin trade was an essential feature of the bronze age

Obliv

@Slereah Thanks this is exactly what I was thinking about. I think it's common in sci-fi shows to depict some super genius that, if left on some stranded place, can build a spaceship or something to get back home.

Slereah

17:55

yeah that is one of those things needed

Obliv

Even rimworld has that idea in a game.

Slereah

IIRC there is was some breakdown of tin trade at some point during the bronze age so for a while people not living near tin deposits just had to do without

user4539917

don't forget wars will still be fought, but with sticks and stones :P

Slereah

Natural materials are just very messy and it's super hard to make them do what you want

Metal ores are mostly full of trash and if you just have fire to smelt it it is very hard

Obliv

Who even thought to smelt ores?

Some smart cavemen..

"I cook food it taste good, I try cook rocks"

Slereah

18:01

well a lot of "heating things" technology prior to this was for pottery

IIRC it's generally thought that the idea came from there

user 85795

18:32

Does that mean that Man is inherently a warlike creature?

imbAF

@ACuriousMind Because current density is something related to a physical world, i.e matter that passes through a cross section per unit of time (fluid/charges etc). While probability current density is something abstract. Probability is not a physical thing

Slereah

@Obliv Temperature for smelting ore isn't quite the same as oven temperature

Except for lead I guess

Loong

18:56

@Slereah You need > 950 °C for lead.

Silly Goose

19:09

any% to create a gps satellite from scratch

Mr. Feynman

hey @SillyGoose

Silly Goose

honk

Mr. Feynman

HONK

Silly Goose

i have been occupied with the throes of real analysis lately but today is the last day of class for it >:D

Mr. Feynman

I miss the sweet old days of Real Analysis :P

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20:01

If you are inside a black hole, could you detect whether the black hole is a rotating one?

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