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12:46 AM
@Slereah Gell-Mann was obviously an accomplished scientist, but I didn't really like his attitude towards other physicists. I went through snippets of his interview on youtube where he talks about other physicists, and he comes off as envious and vain.
 
 
3 hours later…
3:34 AM
@Avantgarde I only saw him talk about feynman
Who else did he talk shit about?
 
 
2 hours later…
5:07 AM
Here's a quote about Gell-Mann: "I had barely sat down when he began to tell me... that science writers were "ignoramuses" and a "terrible breed" who invariably got things wrong: only scientists were really qualified to present their work to the masses. As time went on, I felt less offended, since it became clear that Gell-Mann held most of his scientific colleagues in contempt as well."
- John Horgan, The End of Science (1996) p. 212
 
6:03 AM
These 200 clips of a Gell-Mann interview are incredible
 
6:16 AM
Hi @JohnRennie good morning
 
@cOnnectOrTR12 Hi :-)
 
Are you a teacher John. I mean what do you do
 
I'm retired. I used to be a colloid scientist, but working in industry not in university.
 
Wow a scientist
That’s great
What does a colloid scientist do
 
Colloid science is a very broad subject ...
Interface and colloid science is an interdisciplinary intersection of branches of chemistry, physics, nanoscience and other fields dealing with colloids, heterogeneous systems consisting of a mechanical mixture of particles between 1 nm and 1000 nm dispersed in a continuous medium. A colloidal solution is a heterogeneous mixture in which the particle size of the substance is intermediate between a true solution and a suspension, i.e. between 1–1000 nm. Smoke from a fire is an example of a colloidal system in which tiny particles of solid float in air. Just like true solutions, colloidal particles...
I worked in all sorts of areas. It was a fascinating job, though I did get bored with it eventually and switch to working in IT.
 
6:27 AM
What does people mean when they say they work in It
 
IT = information technology, and this covers all sorts of areas from computer programming to managing networks to analysing computer algorithms.
I worked mainly in network management and that involved maintaining the servers and the network equipment.
 
From a water scientist to a networking guy. That is not fair
 
I enjoyed both jobs. I had got a bit bored with the colloid science job by the time I left.
In fact a few years after I left the company I used to work for as a scientist closed down. So I would have lost my job anyway :-)
(I didn't know it was going to close down when I left)
 
It’s like I was working with Einstein and now I am a plumber
Sorry if it’s offensive
I mean Einstein’s second job preference was to be a plumber
 
:-)
 
6:38 AM
In India plumbing, electrical guys, carpentery are all not seen as a decent job
 
You'd be surprised how intellectually demanding IT jobs can be. ACuriousMind used to work in string theory, which is about as complicated as physics can get and now he works as an analyst/programmer.
 
Computer jobs are interesting too like all sorts of programming but it doesn’t speak that much as physics
 
The core skills are surprisingly similar
In both cases you need to combine a good capacity for learning and memorising things with a high level of concentration.
 
Oh but that is also needed in violin playing too
The thing is after doing all kinds of labour you don’t get as interesting results as in physics or bio or chemistry.
 
Looking back, I think I got as much satisfaction from the IT work as I did from working as a colloid scientist.
Possibly more, since very few scientists see any great change as a result of their work while some of the IT stuff I did made a huge difference to the company I was working for.
 
6:48 AM
What does these programmers program. I mean programming a new operating system seems interesting but other than that?
 
My main job was writing software to monitor servers. By the time I retired I had to monitor about 800 servers and there is no way you can check that many servers manually.
So I wrote a big suite of software that monitored all the servers and alerted me if there were any problems.
It was fascinating because it require a detailed knowledge of how the operating system worked at quite a low level.
 
And what is the purpose of these servers!
 
We had all sorts of servers e.g. web servers, database servers and file servers.
Like the servers that run the Stack Exchange software.
Mainly running Windows, though I had to monitor some Linux servers as well.
 
All to make the life of people easier but no one answers the fundamental questions of life ,of universe. That is still can’t be done by machines
 
There are still plenty of scientists working on the fundamental problems :-)
 
6:57 AM
Still the work of machines is very primitive. They are dumber than a dog or a bug
We can’t make them work very intelligently
It is us who are doing all the work.
All the results all the conclusions.
They just calculate
 
@cOnnectOrTR12 The unique advantage of software is that once it works, it works. If you train a dog to do something, then you can't just make 1000 other dogs do the same with no effort. If you write a program that runs on one computer, it will run on others like it with no change at all.
All the skill and knowledge of the programmer goes into the program once, and then it is available to everyone else, for eternity. (yes, it's not quite as simple, but it is a massive improvement over transmitting the ability to do certain things only from human to human or from human to book to human)
 
7:16 AM
@ACuriousMind Yes but then a update comes and many of the softwares after the update on many computers don’t work
 
"Just calculation" misses the point - while deep down everything is just numbers and bytes and bits, computers handle all sorts of structured data for us. Images, formulae, personal records, etc. The power of symbolic computation is that if something is data, you can make a computer do work on it
@cOnnectOrTR12 but updates don't just "come"! Someone programmed that update and decided it is acceptable that it might break existing programs and then you decided to install it
don't blame the computer for poor human decision-making
3
 
@ACuriousMind if it breaks some of the programs is it reliable?
 
@cOnnectOrTR12 my point is that its reliability is something the humans programming it determine. It is not an inherent fact about software that updates have to break things.
 
@ACuriousMind can it think? Can it feel? Is it conscious? It’s only doing what it’s told
 
@cOnnectOrTR12 and that's the magic - it does exactly what the programmers tell it!
it doesn't need to "feel" to crunch the terabytes of data the LHC produces, or to send the words you're typing into this chat around the world to make them appear on my screen
 
7:27 AM
Well then it’s a good loyal servant. Not a great companion. Not a friend.
After all the brain is yours behind everything, behind it’s working
 
in some cases, the brains behind the software deep down in the stack are brains of people who're dead!
 
It’s like you are the thinker and you employ a human calculator to calculate and memorise for you simply because you can’t handle such big calculations.
After all You will be appreciated
 
FWIW:
18
A: Please use the new Mod/Staff label tech to identify Community as a bot

Yaakov EllisCommunity bot now has its own label. It looks like this: A tooltip will show when hovering over the label with the following text: Community Bot — not a real person. Replies to this bot are not monitored. This is live now on MSE for testing - please report any issues as answers on this questio...

 
You know why we need it just because we can’t think and make links between more than 4or 5 entities in our brain.
 
I hope they restore Community's diamond.
 
7:35 AM
There can be three thoughts or four or maybe five but not more than that at ones or your mind will get confused
 
I really think you are insufficiently awed by the fact that we are only communicating right now because of software
 
0
Q: \mathrm or \text for units?

ACBTo edit units, some editors use \mathrm. eg.\mathrm{m/s}$\to\mathrm{m/s}$ Also some use \text. eg.\text{m/s}$\to\text{m/s}$ Recently I edited a post using the first method, and I found that someone had suggested an edit with the second method. Which one should we actually use?

 
I'm not using the computer to do a "computation too big for my brain" when I use the internet. I'm using it to do something fundamentally impossible in a world where all work on data had to be done by humans.
 
@ACuriousMind and I think you are giving it more credit than it deserves
Who is the brains behind this software!
 
Well, the credit is to the humans who developed that software
the software itself is just a tool
 
7:44 AM
Exactly
We should be doing works on advancing the ai not to make them handle large data.
You have to admit they are dumb
It’s of no use other than extending our capacity to do large amount of work
 
"dumb" or "smart" is not a category that applies to ordinary computers/programs
The computer executes exactly the instructions it gets. There is no "intelligence" involved in that.
It's not "dumb" to compute e.g. complex square roots in fractions of a second. Neither is it "smart".
@cOnnectOrTR12 And just with that we have created things like the internet.
doing a lot of work on a lot of data really fast is much more useful than you probably think
meanwhile "AI" still can't reliably tell a cat from a loaf of bread
 
Well it’s all technology so instead of celebrating computers we should be putting our mind on ai. That can well one day become smart as humans and probably more generous. To help us in our quest of finding big questions.
 
8:00 AM
If we developed cheap AI as smart as humans, it could destroy the world's economies. There's also the issue of making AI friendly. lesswrong.com/tag/friendly-artificial-intelligence And not accidentally creating an AI that wants to turn the world into paperclips lesswrong.com/tag/paperclip-maximizer
 
@NiharKarve personally I think sci journalism is in trouble. They only talk about hype and never the null result. The sci books which try to explain things to common man are some kinda Zen bullshit riddle. The person doesn't know anything about physics but he does learn alot of useless analogies.
I ve seen those books do a lot of damage to students where they think physics is about constructing rubbish analogies and learn that's not the case in their degree
 
8:54 AM
Hm
when a paper has $\Xi$ in it, that's usually bad news for being easy
2
 
14
Q: How to draw the Greek letter $\xi$

iamveganI hate this letter $\xi$. I dont understand why we have to use this symbol. I mean there are many greek letters easier to draw. Do we use this letter in order to imply the level of difficulty in the topic it appeared? Anyway, I always wanted to ask how to draw this letter. Should I first draw an ...

 
$\xi$ is common enough, but nothing simple uses $\Xi$
When someone uses $\Xi$ it's usually some weird abstract thing
 
9:40 AM
0
Q: How do I write better answers?

Reet JaiswalI haven't written many answers, but after I have identified what the user is asking, I usually go with a conversational tone, going over whatever has a question mark over it and any context supporting it. Optionally(if you have the time), recently my answer https://physics.stackexchange.com/a/666...

 
 
3 hours later…
12:23 PM
@ACuriousMind if only all programmers understood that rather than the number that seem to think that the computer does what they want it to do!
 
1:13 PM
@DanielUnderwood yeah, there's a tendency to blame "software" but that's not an excuse if you're the one who wrote it :P
 
@ACuriousMind How about blaming the people who wrote the compiler/interpreter
or libraries
Plenty of blame to go around
 
@ACuriousMind I do it all the time tho. “Boy, past me was a dumbass”
Particularly when it’s “gd it why haven’t I worked on this already@
 
@Semiclassical That's doing it right - you're not blaming the computer, you're blaming past-you
 
And my past self is an idiot, too
 
1:17 PM
That said, I will yell at the computer when it does stuff out of my control
 
@Slereah well, why did you use that terrible library :P
 
Like my laptop sometimes refuses to hibernate, even at critical power levels
 
@ACuriousMind I mean you're in the computer business
You know why
 
I think b/c Windows has decided “you need to update/ restart tonight” and won’t let anything change that
Even if it entirely drains the battery to zero in the process
I will definitely yell when hitting the power button has the screen go dark and then promptly light up at the Windows lock screen
Windows: it’s their world, we just live in it
 
1:35 PM
Hello there
can anyone help me with my doubt ?
 
ask
 
how do we calculate the highest limit of force exerted by a charge on the another (i.e: k q1 q2/r^2), this shows that the force exerted is inversely proportional to the distance squared . suppose when r approaches 0, the force exerted will also approach infinity, but this is not practical and not possible. so what is the highest magnitude of force, a charge can actually exert ? how we can calculate it ?(of course I believe this is not the exact formula for calculating the force by a charge)
 
I don't have any idea about the practical case of highest limit achieved in lab, but on theory, infinite magnitude force is possible whenever you bring two electrons closer enough, but yes, how much closer enough remains a question and planks limit and quantum effects come into play
force very close to infinity is quite possible if you bring in two electrons sufficiently near even in practical case.
I don't have much idea regarding that but the people here might help you with that.
 
wondering plank has given a limit for everything
 
planks constant, gravitational constant and speed of light constant, has consequence on almost everything in this universe, even length
 
1:44 PM
The Planck constant doesn't give limits for everything
It's just a scale at which some other effects are maybe important
 
Again I must warn, bringing two electrons close enough for almost infinite repulsion force is not feasible as it'd require a very large amount of energy to do so and measurement there after,,
@Slereah Yes, that's what I meant, quantum effects at planks scale, not limit actually
but the article is correct
practically we don't know much about it
so can't say much about it
 
@Ishwaran there is no "highest limit of force"
the highest force you'll get from two charges attracting each other is the force at the distance right before they smash into each other
 
@ACuriousMind who knows, we all have limits :P
 
two macroscopic charged objects just have a size, and you can't get to $r=0$ with them - there's just some finite distance where you can't push them into each other further
 
@ACuriousMind what of the Schwarzschild limit
 
1:55 PM
for two particles or whatever, quantum mechanics becomes relevant - they aren't actually little balls, and $r=0$ can't "happen" in the way you probably imagine it
@Slereah sure, if you're unlucky you get black holes
 
@ACuriousMind So two charges cannot actually stick together ?
 
but that's also not the caes $r=0$
@Ishwaran what do you mean by "two charges"?
I can have two giant ballons, charge them differently, and they'll stick together
 
@Ishwaran yes, you need infinite energy for infinite force and incredible pressure to stick them together
and they'll do it
 
but that's not $r=0$ in the sense you're asking about because they are not point charges
 
(I was talking about point charges)
 
1:57 PM
@RewCie me too
 
it is important to realize that physical laws works with idealizations of reality
there are no "point charges" in the real world
the electron comes closest to that, but it's a quantum object, not a classical point
 
At what age you discovered the nonsense physicist call Lagrangian mechanics is just the nonsense engineers call D'Alembert principle which is just a different same nonsense in different face
 
so the moment you try to "defeat" Coulomb's law by saying "the force exerted will also approach infinity, but this is not practical and not possible", you really also need to stop thinking about point charges
if you want to be practical, there indeed are no infinite forces, but also no point charges, so there is no problem
just removing one part of the idealization but not the other is inconsistent
 
@ACuriousMind my assumption works only "mathematically" ?
 
Mathematically, there's also no problem - the force for $r=0$ is just undefined
 
2:00 PM
@ACuriousMind When I say "practical" case I don't mean point charges
 
@RewCie I'm not talking about you, that was a direct quote from Ishwaran
 
k
 
can we say the force has infinite range ?
 
2:16 PM
@Ishwaran sure - it's never zero
 
^
 
@Ishwaran This reminds of the question can 2 point particles ever touch? (the answer is no)
 
@MoreAnonymous Explain this
 
@MoreAnonymous :)
 
@Slereah Hahahaa ... emphasis on the "point" word in the sentence
 
2:52 PM
here's something I know how to establish by brute force but not in a nice way
suppose I have the usual singlet state $|\psi\rangle$. Since this has total spin 0, we have $S^x_{12} |\psi\rangle = 0\implies S_1^x |\psi \rangle= -S_2^x|\psi\rangle$, and simialrly for $y,z$.
as such, the outcomes for $S_1^x$ and $S_2^x$ are anticorrelated and the same holds for $y,z$
 
cryptography ?
 
just elementary quantum
Is there a state such that the outcomes are perfectly correlated?
it's definitely "no" for pure states but I only know how to confirm that by brute force
 
@Semiclassical perfect correlation would necessarily mean that total spin is non-zero
 
what is a brute force ?
 
@Ishwaran checking all possibilities rather than using a more natural argument
 
2:58 PM
but you can't have total non-zero spin but definite values for all three total spin components due to the uncertainty principle
 
@ACuriousMind would you have a definite value for the total spin components, though? correlation means $(S_1^x-S_2^x)|\psi\rangle=0$
and $S_1^x+S_2^x$ isn't a spin component
 
@Semiclassical is this something that involves Bloch sphere ?
 
yes
obviously that's linked to crypto stuff but i'm not aiming there at the moment
 
hmmm
 
@Semiclassical nice
 
3:00 PM
i think it still won't work, because you'd have $\psi$ being annihilated by three different operators
but that's not quite precise enough, because the singlet state is annihilated by infinitely many such combinations
@ACuriousMind the context underlying this, btw. in quantum computing one usually sees the Bell state given by $|00\rangle+|11\rangle$, which differs from the singlet state $|01\rangle-|10\rangle$
the prof whose i'm grading for noted in lecture that the bell state displays perfect correlations in X and Z, and added in passing that it's also perfectly correlated for any observable
buuuuuut
that didn't seem right
easiest way to check that it's not: $|00\rangle+|11\rangle = (1\otimes -i\sigma^y)[|01\rangle-|10\rangle]$
the action of $-i\sigma^y$ on the second qubit will exchange the X2- and Z2-basis states, but leave the Y2-basis states unchanged
 
Let's take a step back - what exactly is the definition of "perfect correlation"?
 
good point
in terms of qubits, i'd say it means that a spin observable S displays perfect correlation on a two-qubit state if it's of the form $|00\rangle + |11\rangle$ in the S-basis, up to phases on the coefficients
and perfect anticorrelation if it's $|01\rangle +|10\rangle$ in that basis
 
I mean, in words "perfect correlation" means "both spin measurements always give the same result", right?
 
right
 
so that's where your annihilation condition comes from - "both give the same result" means that $S^i_1 - S^i_2$ is measured to be 0 always, i.e. this is an eigenstate of $S^i_1 - S^i_2$ with eigenvalue 0 for all $i = x,y,z$
 
3:11 PM
right
 
I don't see any obvious way to deduce this can't happen, either
 
I assume "brute force" means writing the state out in a basis and explicitly deriving equations for the coefficients from each of the three annihilation conditions?
 
If I am right then the E field vectors at points don’t tell about the strength of field. It’s the flux of field that tells us where the field is stronger and weaker.
 
yeah. pick a generic state $|\psi\rangle = |00\rangle + e^{i\theta} |11\rangle$ and show that it's never annihilated by all 3.
(the annihilation in Z is guaranteed)
and comes down to the fact that you can't have $1=e^{i\theta}=-1$
 
3:18 PM
@cOnnectOrTR12 what do you mean by "strength of the field" if not the actual value of the field at a point?
Flux is something through a surface, not at a point
 
by contrast, i'm not at all sure how to check it for arbitrary mixed 2-qubit states
16 complex parameters is not my idea of a fun time
(though i think it's pretty unlikely that mixed states will make the situation any better)
this does all come out of looking at the usual Bell states, tho
 
Hm, maybe there's something funny like the identity being a linear combination of the three annihilating operators?
 
In griffiths it is explained like this. You draw field vectors at points around the charge. The vector lengths decreases as we move away from the charge. Then it says join the vectors and we get field lines.
But doing so have we lost the information about the field strength. No , the strength of field is determined by how close the lines are . Near the charge it’s closer so more strength and away the field lines are apart so field is weaker. So the density is what tells us about the strength and that is defined as flux. This flux is directly proportional to charge enclosed by the surface and that is gauss law.
 
field lines are a convenient visual representation. but ultimately they're not the actual physical thing. the physical thing is $\vec{E}(x,y,z)$
@acm what i have:
|00> + |11> is (perfectly) correlated in X and Z, anti-correlated in Y,
|00> - |11> is correlated in X, anti-correlated in Y and Z,
|01> + |10> is correlated in X and Y, anti-correlated in Z,
|01> - |10> is anticorrelated in all 3.
for the four Bell states
the fact that some combos of correlated/anticorrelated are missing is probably due to the usual bell states avoiding $i$'s
 
Analytic topological hairy dyonic black holes and thermodynamics - admit it, that title was made up using a random word generator as a bet to see if it could get past the referees.
 
3:30 PM
Is a black-hole an ideal black body?
 
@ACuriousMind what i -want- this to come down to: (x,y,z) -> (-x,y,-z) is a proper rotation, but (x,y,z) -> (-x,-y,-z) is not
 
@RonaldVilliers If Hawking is right it is, but we don't know for certian.
 
@ACuriousMind ?
 
@cOnnectOrTR12 !
 
3:32 PM
When was the first black body theorized? and for what reason?
 
@ACuriousMind what?
 
black holes have nothing particular to do with black bodies as far as i remember
 
@cOnnectOrTR12 we keep telling you to not focus on the "field lines" so much, and everytime you come back and it's a field lines argument again. At this point I have nothing to add.
 
for one, black bodies radiate
i guess "hawking" is indeed the natural response there
 
@RonaldVilliers "black body" just means "something that radiates only because of its temperature"
 
3:33 PM
@ACuriousMind all these introductory books are filled with lines. What do I do?
 
so we sorta automatically theorized it when we first started thinking about thermal radiation
 
accept that those are introductory books, and focus on the parts that deal with the math
 
Well if light was only thought of as a wave back in the Young,Newton days, we didn't quite understand radiation or temperature right?
 
and thereby move to books which aren't
 
Although I think newton predicted light to be a particle even before the double slit
 
3:35 PM
i said my combinations wrong above. should have been:
|00> + |11> is (perfectly) correlated in X and Z, anti-correlated in Y,
|00> - |11> is correlated in Y and Z, anti-correlated in X,
|01> + |10> is correlated in X and Y, anti-correlated in Z,
 
@ACuriousMind ok! But tell me am I right. Have I understood it correctly
 
so each of the other Bell states makes two of the three correlations from negative to positive
but can't turn all three positive
each of them should be related to the singlet state by making a pi-rotation on one of the axes for the second qubit
so (x,y,z) -> (-x,y,-z), (x,-y,-z), and (-x,-y,z) respectively
 
Don’t leave me in the middle guys ,in doubt
 
if you have questions that aren't resolved by introductory books, then move on to other books
there's no royal road to this stuff
 
@Semiclassical ah, this probably comes down to the Pauli matrices/rotations being a basis for all operators in 2d then
 
3:39 PM
yeah
 
so if we start with a perfectly anti-correlated state, every possible non-trivial operation on it is some combination of rotations on the 1st qubit and rotations on the 2nd qubit
 
right. and since we started with a singlet state, a rotation on the first qubit is equivalent to (the opposite) rotation on the 2nd
 
as you've already said, there's no rotation that flips all three axes, so we can't get to a perfectly correlated state
 
yeah
if one wants to get perfect spin correlations, one should just start out with a single spin in the maximally mixed state :P
(i.e., measure the same observable twice, and you get the same result)
 
@RonaldVilliers Wiki says that Kirchhoff originated the black body idea in 1860
and then it didn't take long to get to the ultraviolet catastrophe and the beginnings of QM
 
3:43 PM
yeah, though the "catastrophe" only existed in retrospect
 
History of electricity&magnetism seems to tie right into the study of light & QM
 
given that classical light = electromagnetic wave, that's hardly shocking
 
Right, but it's easy to say something isn't shocking when you know all the details :P
I can imagine Hoang-Ti of the Chinese empire in 2635 BC thought his magnetic compass was a divine gift to rule with divinity
Or something along those lines
 
yeah
and definitely wouldn't have understood that there's a link between it and lightning
(though lightning strikes can produce natural magnets)
 
Yeah back then I don't know what idea of electricity was available and how it differed based on location/civilization
Static electricity was around in ancient greece
 
3:52 PM
well, static electricity as such has been around for billions of years :P
 
Lightning was likely the first widely observed phenomena
 
well, not quite. light itself is EM phenomena, after all :P
 
so the easiest EM phenomena to observe, was also historically one of the last to be understood as EM
 
It was hard for sure, it took most of the 18th and 19th century to finally arrive at maxwells equations
It was definitely a collaborative effort
 
4:24 PM
@MoreAnonymous Bogolyubov, Sheldon Glashow and Einstein. Seems like he always explicitly stated something he didn't like about other physicists (at least these 4, which are the ones I saw in that video).
 
LSS
Guys
 
Electricity was barely a thing for most of history
there wasn't a lot you could do with static electricity back then
Magnetism was the cooler topic
there was the idea that there was a giant magnetic landmass in the north pole
Hence the compass
 
4:40 PM
@Slereah i mean, thunderstorms aren't exactly "barely a thing". what they weren't was controlled in any useful way
 
Also people did not think static electricity and storms were related
 
yeah, that's true
 
IIRC the ancient opinion was that it was due to cloud friction
 
i wonder when that was first recognized
 
Not the worst hypothesis
Probably when people started making decent electricity
 
4:41 PM
yeah, lightning as a kind of cloud-generated static electricity
 
17th-18th century maybe
 
i do find questions like this interesting even if they're in practice unanswerable
 
Benjamin Franklin was famously involved
 
the one i remember thinking about: When did the concept of "phase" originate? e.g., water/ice/vapor as basically the same substance
 
Probably old?
 
4:44 PM
yeah
 
People have been watching substances change phase for a long time
although famously the old idea for that process was a little weird
the whole 4 element thing
 
sure, but it's one thing to say "we start with substance A and end with substance B"
another thing to recognize that substance A is another form of substance B
it probably depends a ton on what 'substance' we're talking about tho
 
Well it was probably at least there in the 18th century since that was when people realized that substances didn't go away
 
yeah. the ancient example someone gave was distillation of water, dating back to 200 AD
 
I mean people have been boiling water for a while
melting metals
 
4:46 PM
sure. what makes distillation special is that you convert water to vapor and then back to water
which makes it a lot more plausible that the vapor was just another form of the water
 
but it's not entirely trivial I think, since if you put yourself in their situation, it's not obvious how boiling water would be very different from burning wood
 
ya. very substance-dependent
and they definitely would've had no way of assessing whether a substance was 'pure'
except via stuff via distillation i guess, and even that is only "up to a certain point"
 
they certainly thought water was pure to some extent, since that was one of the 4 elements
 
right
metal is an interesting case, b/c in metallurgy you work so much with alloys
and i could imagine that people thought that heating a metal up effectively "added" fire to it
(come to think of it, you could probably think of distillation like that. add fire to water, converting it into steam, and then remove the fire to get back water)
 
there is a bit of that in that old theory
Elements had two characteristics, they could be hot or cold, and they could be light or heavy
 
4:57 PM
right
different ways of thinking about combining substance properties
 
 
2 hours later…
glS
7:07 PM
@Semiclassical can't tell if you then solved it, but perfectly correlated can be understood in this context e.g. as maximal mutual information when performing local projective measurements. |00>+|11> is perfectly correlated just as |01>+|10> is. A maximally entangled state is indeed maximally correlated wrt any local projective measurement, your example also shows max correlation as it gives |00>+|11>
a simple way to see that this is the case is the fact that any local unitary operation, applied to a bipartite state, doesn't change its Schmidt coefficients (i.e. the singular values if you think it as a matrix)
another way to state this more generally is that the eigenvalues of the partial trace of $(U\otimes V)\rho(U^\dagger\otimes V^\dagger)$ are the same as those of $\operatorname{Tr}_2\rho$, for any bipartite $\rho$ and unitaries $U,V$
 
 
2 hours later…
9:23 PM
@glS I suspect the terminology might be throwing me a little, then. The distinction I was using was perfect correlation vs perfect anti-correlation, ie, are Alice’s values always equal to Bob’s or always opposite to Bob’s
But you could also view those both as “perfect correlation, just with positive vs negative correlation
I definitely concur that all four Bell states are maximally correlated in the sense that knowing Alice’s value for an observable suffices to predict Bob’s value
So to combine the points: the Bell states are all maximally correlated, but none of them display positive correlation for all observables
 
 
2 hours later…
11:24 PM
Anyone know why boris johnson's cabinet is still wank?
 

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