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4:26 AM
@ACuriousMind Hmm, it's rendering this morning. The characters that weren't rendering last night are the arrows used to denote a vector. Oh well.
 
 
2 hours later…
6:17 AM
why do we call spacelike separated points spacelike and timelike points timelike?
trying to figure out the physical intuition behind this
If A and B are spacelike separated then there is no way someone on A could reach B without either travelling back in time or faster than light. Is this correct?
 
6:35 AM
Timelike separated points means that there exists a timelike curve that connect the two
So there could exist an object going from A to B
Spacelike separated means that it is not the case
(also they are not null separated)
Also the answer depends a little if we're talking special or general relativity
 
7:12 AM
@Slereah So there is no path made by an object between these two points?
i.e. impossible for anyone to do this trip
 
Huh?
Who flagged that?
 
i by mistake
im from a laptop and accidentally touched the pad while writtin
sorry :p
 
@ShikiRyougi Basically yes
One point cannot influence the other
Things can be a little ambiguous because in some cases two points can have both a timelike curve and a spacelike curve connecting them
 
@Slereah ok that makes sense :)
 
That is why "spacelike separated" usually means "no timellike or causal curve"
 
7:26 AM
Weak Equivalence Principle (WEP): inertial and gravitational mass of any object are equal. This is directly from Carroll. In regards to a conversation we had some days ago: is this a postulate, or is there experimental evidence? As it was mentioned, you cant measure directly these two quantities to find out, so then what?
 
There is experimental evidence, yes.
Quite famously the big experiment was the Eötvös experiment
A 4000 hours experiment
They even did an entire geological survey of the neighbouring region of the experiment to have as much details on the local gravitational field as possible
Even detailed plans of the building
"The authors bow to the fate of human limitations and leave it to future times and future workers to further elaborate those observations which they themselves believe upon mature experience to be able to still improve."
 
7:44 AM
woaaah
experimentalists have so much patience
 
Things are harder when you can't assume two objects in the universe
Original paper is attributed to Baron Eötvös
 
cant assume what about them?
 
Well in the real world, there are a very large amount of objects all around
For the gravitational field, you have influences from everything around you
The experimental setting, the laboratory, the city, the entire planet, neighbouring planets and stars
Depending on your precision, those can become important
 
did they have to take into account all that though?
 
The original experiment did not, although people later checked the gravitational influence of the neighbouring region to make extra sure
Things can get even tougher for modern gravitational wave experiments
since those are even more sensitive
They require a lot of isolation to make sure a passing car doesn't set off the detector
"A group of scientists encountered a problem that the computers of the day couldn’t handle, and asked von Neumann for advice on designing a new generation of computers that was up to the task. But:

When the presentation was completed, he scribbled on a pad, stared so blankly that a RAND scientist later said he looked as if “his mind had slipped his face out of gear”, then said “Gentlemen, you do not need the computer. I have the answer.” While the scientists sat in stunned silence, Von Neumann reeled off the various steps which would provide the solution to the problem."
 
8:21 AM
:o
 
 
3 hours later…
11:37 AM
any Indian here?
 
12:01 PM
@Feynman_00 Basic level calculus, yes.
 
12:23 PM
@Shane You are asking for something at a very low level, yet you want to use it to understand chemistry. I guess you would at least need to know the hydrogen atom, not to mention how the approximation for heavier atoms works
I don't think a book that doesn't cover the hydrogen atom would be of any use
 
 
1 hour later…
1:28 PM
@Feynman_00 You see, I want to try understanding it as much as is possible, but I currently don't have the time to spend solving partial differential equations just so that I can get a gist (gist, yes, but a solid one nevertheless) of the subject. I'm not sure if a book that meets my requirements exists, but that's why I'm asking around.
 
glS
@Shane I think Feynman's six easy pieces also has a chapter about QM? They're mostly mathless if I remember correctly so they might be a good fit
that aside, there's plenty of books about QM for non-physicists
also Feynman's QED is pretty good and barely uses math: en.wikipedia.org/wiki/…
 
1:45 PM
@glS in six easy pieces he talks about electron diffraction mostly. That was my first approach ever to QM too, but I would say it would really help understanding chemistry
In addition to the last two chapter of six easy pieces that glS mentioned, a cute book is the theoretical minimum by Leonard Susskind, the one about QM of course
 
 
2 hours later…
4:08 PM
Thanks; I'll check those out!
 
 
1 hour later…
5:33 PM
what is a timelike curve...? I know what timelike separated points are: points inside the future and past light cone of another point. A timelike curve then is, a curve whose any pair of points are timelike separated. Does that sound like a good definition? Idk I just made that up. Keep in mind im looking for the definition of everywhere timelike curve.
 
6:04 PM
@ShikiRyougi it's one where the tangent vector is everywhere timelike
 
ahh alright alright
makes sense
 
6:37 PM
what is the meaning of a : normally distributed random number? A random number is an arbitrary, in fact as the name suggests a variable with a randomized value. What does this has anything to do with distribution? The normal distribution, is a characteristic of a function. Can anyone explain to me what is the meaning of :normally distributed random number?
 
@ACuriousMind I was looking at this precisely. I still cannot see how a single random variable can have something as normal distribution??? It is a cluster of randomized variables, that represent the normal distribution. How can a evaluated single variable represent anything else other than what it is. A randomly valued single variable
 
I think you are confused about what a random variable is :P
 
a random variable is a variable with a random value
what else xD ?
 
sure, but that doesn't actually mean anything
what does it mean for a variable to have a "random value"?
 
6:42 PM
it does
 
how is it different from having a "non-random value"?
 
it's not important
whether the value taken is non-random or random
a single variable
cannot possibly be considered a distribution
 
for a variable $x$ that takes values in the real numbers, a probability distribution is essentially the definition of what a random variable is, namely that the probability of $x$ taking a value between $a$ and $b$ is given by $\int^a_b f(y)\mathrm{d}y$ for some "distribution" or "probability density" $f$.
I'm not sure what your problem is, you can't really argue against a definition (actually the formal definition is in terms of the cumulative distribution function, but that's a minor detail)
 
so what you are saying is that, there is a normal probability distribution, and a variable is taking a value from the possible values of this distribution ?
 
the variable is just taking values in $\mathbb{R}$
all the possible distributions are functions on $\mathbb{R}$ that, when integrated as above, tell you how likely it is that the variable takes a value in any specific interval $[a,b]\subset \mathbb{R}$
the "normal distribution" is just when you look at a variable for which that function is a Gaußian
 
6:52 PM
"all the possible distributions are functions ". There are multiple functions? In our class it was said:"We consider a function, a region from which values can be taken as input, and ultimately the values given from this function. Ploting this, gives us a bell shaped graph, which is the normal distribution of it." So we considered a single one.
 
If that's what was said verbatim, that does indeed sound very confusing to me :P
in that I have no idea what that sentence is supposed to mean, really, or what it has to do with random variables
 
Well welcome to my world lol
 
Do I interrupt your conversation If I ask something?
 
Not really
 
chat is asynchronous and multi-threaded, don't worry ;)
 
6:59 PM
@ACuriousMind I was wondering. If for a physical quantity that can be measured, such as energy for example, there is a corresponding operator in QM, why isn't there an operator for time? Isn't time a physical quantity that you can measure?
 
After a point transformation $q=q(Q)$ the generalized velocities transform as $\dot{q}=\frac{\partial q}{\partial Q}\dot{Q}$
This looks like a time derivative of a function of time, but generalized velocities and coordinates are not time dependent unless evaluated on a specific path. So is this analogy just formal?
I mean, this is just the way vectors of tangent space transform, right?
 
@imbAF Who claims that there is a corresponding operator in QM for "a physical quantity that can be measured"? In any case, you can't have a time operator because that contradicts the boundedness of the Hamiltonian from below (we want to have a minimum energy!), see also physics.stackexchange.com/a/268344/50583
 
well for some physical quantities, such the example I gave
 
@Feynman_00 I wouldn't say it is "just formal" - one representation of tangent vectors is as the actual tangent vectors to infinitesimal curves, i.e. the "time derivative" of these curves, after all
I mean, you're right there is no "true time derivative" there, but neither is this an accident or anything like that
 
Yes, derivatives are strongly related to tangent and that is why it works for functions of time, my wording was poor in that part
I didn't mean it is an accident
Maybe a better way of posing that question would be the following: to prove that generalized velocities transform like that you wouldn't use "true time derivative"
What you are really saying is that the transformation matrix is the jacobian matrix
 
7:10 PM
I mean, you can just think about the velocities in the formulation of tangent vectors as derivations and then this is just the chain rule: $\partial_q = \frac{\partial q}{\partial Q}\partial_Q$
there isn't a lot to prove :P
 
hi
is anyone here familiar with screw gauge
hello?
 
@ACuriousMind What about a time dependent transformation? $q=(Q,t)\implies\dot{q}=\frac{\partial q}{\partial Q}\dot{Q}+\frac{\partial q}{\partial t}$. Same thing but in extended phase space?
 
time-dependent stuff is annoying
 
@Feynman_00 are u familiar with screw gauge
or @ACuriousMind are u familiar with screw gauge
I have a little problem
 
No, I'm not
And I'm not the real Feynman either...
 
7:14 PM
@SamyakMarathe I'm pretty sure if anyone here is and wants to talk you to, they'll reply to you
 
if anyone from u guys ca help
 
you don't need to ping random people
 
@Feynman_00 yeah ofc Iknow, 1st: he is dead and 2nd: He would know
@ACuriousMind but then why are u ignoring
u could just say, 'No I am not familiar.'
but u are ignoring
so I thought u are
anyways
 
@Feynman_00 but sure, if we add $t$ to the generalized coordinates (why "phase space"? This isn't Hamiltonian mechanics if you have velocities and not momenta) then it's just the chain rule again
@SamyakMarathe if everyone in the room always replied to every question where they can't (or don't want to) give a useful answer that would be a lot of pretty pointless messages
 
@ACuriousMind Ops, I guess I'm sleepy :P
 
7:22 PM
@ACuriousMind Any book you can recommend me about probability and statistics that has a fundamental explanation of different concepts, taxing terminology and possibly visual representation ? I want to spend like 2-3 months focusing on this in particular
 
That was a stupid question indeed, not knowing differential geometry gets me in trouble with lagrangian mechanics
In this case tangent vectors and derivations
 
Nov 29, 2021 at 13:50, by ACuriousMind
Nov 30 '19 at 17:05, by ACuriousMind
@yuvrajsingh I haven't read many textbooks so I'm about the worst person in here to recommend any books on basic topics.
we've been over this before :P
 
lmaooo you are an elephant xD
 
Why an elephant of all animals?
 
@Feynman_00 I wouldn't think about it that way because physics also often doesn't teach it that way - indeed, this is obvious in the differential geometry formulation, but physics often doesn't do Lagrangian mechanics that way
 
7:26 PM
@Feynman_00 elephant have strong memory
 
@Feynman_00 they're famous for having long memories
 
Oh, I didn't know that
I knew German Shepherds do, though
 
lol, so you thought they randomly called me a grey fatass :P
 
"In addition, Proclus and Sextus Empiricus mention several criticisms of Euclid that they attribute to an unnamed Epicurean and that are similar to Zeno’s criticisms: for instance, that there is no axiom establishing the infinite divisibility of curves, which is connected with a discussion of various consequences following from the assumption that curves are not infinitely divisible but, rather, are composed of the smallest units of indivisible lines."
People have known that Euclid's axioms are bad for 2000 years and nobody fixed them
smh
 
@ACuriousMind Yeah I was trying to ease things up
 
7:28 PM
I usually hear people making excuses on how the ancients just understood math differently back then but they knew the whole time
 
@Slereah relatable
I also only fix things when it's absolutely necessary :P
 
also the QFT people
 
@ACuriousMind In most universities in Italy we study analytical mechanics like that, just that we don't have a differential geometry background and it messes things up
 
@Feynman_00 ciao fratello come va?
 
That's Italian, if non-Italian users are wondering
 
7:31 PM
@Slereah could you recommend me a book about probability and statistics ?
 
I cannot
Not sure why you'd ask me
 
Well I asked AcuriousMind but he couldn't recommend any, so I thought of asking you.
 
Knowing you are Italian I can recommend one
Loreti
 
@Feynman_00 I am not but can speak well enough and fully understand
 
Search "Maurizio Loreti Statistica" and you'll find a pdf online
I used it back in my freshman days
 
7:34 PM
Ok Ill check it rn
 
That were actually two years ago
 
8:19 PM
While some of his Manhattan Project collaborators came to regret or at least agonize over their role in inventing the Bomb, von Neumann was disinclined to waste time questioning past decisions. Instead, he goaded the government to get to work building bigger, deadlier hydrogen bombs before the Russians managed the same.

His most controversial opinion was urging an immediate pre-emptive nuclear strike on Russia. And he meant immediate - he famously said “If you say why not bomb [Russia] tomorrow, I say why not today? If you say today at five o' clock, I say why not one o' clock?”
 

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