The h Bar

12:00 AM

Or is that just one method of proof?

@0celo7 I guess you can prove it with other methods, but Atiyah's and Singer's own method is through K-theory, which has as central object equivalence classes of sheaves

0celo7

@ACuriousMind K theory is algebraic geometry?

ACuriousMind

@0celo7 It's larger than alg. geo., but your initial question was about the use of sheaves

I think that happens to most of these techniques: They are first developed in the algebro-geometric context because there you can't rely on the structure you have in all the differentiable and other cases, and then someone notices you can export the technique to actually give interesting results in all cases

0celo7

Hmm, to whom is it worth learning?

ACuriousMind

What exactly, now? I'd say that one should be familiar with the notion of a sheaf, but it's perfectly fine to don't understand any particulars of algebraic geometry.

0celo7

12:08 AM

I'll ask my advisor. Although he pretty much told me he has no interest in "algebra" as a subject. Don't know if he includes algebraic geometry in there too.

ACuriousMind

Well, you can't do algebraic geometry without a truckload of commutative algebra

That's why I'd say it's fine to not know it - the investment into the algebra is really large before you see even the smallest "geometric" result

0celo7

@ACuriousMind His "I don't know much about X" is probably different than mine.

@ACuriousMind Why do I need to know what a sheaf is?

ACuriousMind

@0celo7 Because knowing more ways to think about a mathematical object enriches your understanding of it :P

0celo7

Actually, Ward & Well's book on twistors has a section on sheaf cohomology.

So if I'm serious about learning more about twistors...I might have to learn what a sheaf is.

ACuriousMind

And many situations in which some local data is glued to global data become far more organized if you phrase them in the language of sheaves

@0celo7 Well, to learn sheaf cohomology, I'd advise to first learn ordinary cohomology to be able to see that the sheaf case reduces to the ordinary case for the case of the constant sheaf.

0celo7

12:16 AM

@ACuriousMind When proving continuity of a function $\mathbb{R}\to\mathbb{R}$, should one use analytical or topological continuity (I know that they are equivalent), or does it depend?

ACuriousMind

@0celo7 Depends if you're asked to do so by an analyst or a topologist ;)

If you're doing this by yourself, do whatever you feel is more right

If you don't feel one of the two things is more right, reevaluate your aesthetics

0celo7

@ACuriousMind My adviser said I need to get serious about learning (general and algebraic) topology. So I will eventually figure it out.

And Steenrod has a whole section on cohomology of fiber bundles (which he also said is a must-read), so I'll get it before then.

There's so much crap to read...

@ACuriousMind Fiber or fibre?

ACuriousMind

Fiber. I'm horribly inconsistent when it comes to AE/BE :P

0celo7

@ACuriousMind Is $\exists !$ common notation?

ACuriousMind

Yes, it means "there is exactly one"

0celo7

12:23 AM

Huh, I'd never seen that before today's algebra lecture.

@ACuriousMind tfw you have no clue which way the inequality goes in the triangle inequality

ACuriousMind

Draw a triangle, then!

0celo7

what

I remembered it

but I was totally lost for a second

ACuriousMind

...you do realize it is named that way because it relates the three sides of a triangle?

0celo7

no

ACuriousMind

It says the longest side of a triangle is shorter than the two other sides together.

0celo7

12:35 AM

of course

ACuriousMind

So you don't need to memorize the sign, just draw a triangle to deduce it :P

0celo7

I'm still terrible at analysis

@ACuriousMind Let $(X,d)$ be a metric space and $x_0\in X$ be given. Define $f:X\to\mathbb{R}$ by $f(x)=d(x,x_0)$. I want to show that $f$ is continuous. I must thus show $\forall \epsilon>0$ $\exists \delta >0$ s.t. $d(x,y)<\delta\Rightarrow |f(x)-f(y)|<\epsilon$.

Is the setup at least correct?

I hope I can read a definition.

I also have the result $|f(x)-f(y)|\le f(x)+f(y)\ge d(x,y)$

ACuriousMind

@0celo7 Yes

0celo7

12:52 AM

@ACuriousMind Ugh, I keep getting chains of inequalities where one of them is backwards. Is there a trick to this?

Hmm, I feel like we once did someething similar...where there was a "symmetry"

ACuriousMind

@0celo7 Haven't you recently proven $\lvert \lvert x \rvert - \vert y \rvert\rvert\leq\lvert x-y\rvert$? The same logic gives you $\lvert d(x,x_0)-d(x_0,y)\vert\leq d(x,y)$.

0celo7

@ACuriousMind Exactly.

@ACuriousMind So...now what.

I adopted the proof to show just that

How do I pick $\delta$ now

ACuriousMind

I believe you can figure out that one yourself

0celo7

@ACuriousMind $\delta =\epsilon/2$, in which case $\epsilon>\delta >d(x,y)\ge |f(x)-f(y)|\Rightarrow |f(x)-f(y)|<\epsilon$.

btw I don't know right from left

ACuriousMind

I'd have picked $\delta=\epsilon$, but I guess that works, too.

0celo7

1:05 AM

...oh

@ACuriousMind Let $A\subset X$ and $D(x):=\inf \{d(x,y)\mid y\in A\}$. To be 100% certain, there exists a specific $y_1\in A$ s.t. $D(x)=d(x,y_1)$, right?

Oh, no

that's wrong

:(

@ACuriousMind I know I have to somehow use the triangle ineq to show $|D(x_1)-D(x_2)|\le d(x_1,x_2)$...but how do I deal with the $\inf$?

(this is not homework, btw)

ACuriousMind

1:26 AM

@0celo7 If $a<b$ for all $a\in A$ and $b\in B$, then $\inf A\leq \inf B$.

0celo7

1:43 AM

@ACuriousMind Assume instead that $\inf B <\inf A$. There exists a number $\epsilon$ s.t. $\inf B<\epsilon <\inf A$. But $\epsilon <\inf A\le a <b\Rightarrow \epsilon <b$ for all $b$. Thus $\epsilon$ is a lower bound for $B$, but is strictly greater than the infimum. Contradiction.

0celo7

2:00 AM

@ACuriousMind Define the set $K:=\{d(x_1,y)-d(x_2,y)\mid y\in A\}$. Then $D(x_1)-D(x_2)=\inf K$ (due to $\inf(A+B)=\inf A+\inf B$). It can be easily seen that for all $k\in K$, $k\le d(x_1,x_2)$. Then, by the previous lemma, $\inf K\le d(x_1,x_2)$. Due to symmetry, $|\inf K|\le d(x_1,x_2)$. Let $\epsilon >0$ be arbitrary and let $\delta =\epsilon$. Then $d(x_1,x_2)<\delta$ implies $|D(x_1)-D(x_2)|\le d(x_1,x_2) <\delta =\epsilon$, showing continuity of $D(x)$.

3507

2:11 AM

life is boring.

Bernard Meurer

@3507 It isn't if you do what I'm doing

try juggling with high voltage batteries

It's amazing!

3507

2:24 AM

sigh

Bernard Meurer

Correction, don't try juggling with high voltage batteries

Physics Meta

5:40 AM

0

Q: Adding an answer to a duplicate

I recently asked a question How do I show a layman that the Earth is not flat? which has become much more popular than I originally anticipated, and has since been closed as a duplicate of What is the simplest way to prove the Earth is round?. Ordinarily I wouldn't mind too much that it was marke...

vzn

7:06 AM

in theory salon, 1 min ago, by vzn

google deepmind attacks Go and AlphaGo attacks top human / Tmachine blog

Secret

8:23 AM

Msg: DanielSank, I have some quantum questions and discussions prepared to discuss with you in half an hour

Secret

9:04 AM

(NB: Please note the the following article is known to be open access, thus there is no problem screencapping various sections for discussion)

rspa.royalsocietypublishing.org/content/472/2185/…

Q1

So does that mean because for the spatial case there is no hamiltonian to evolve the states in time, thus translational symmetry cannot be violated hence why there cannot be a case where you have 2 versions of the parity operators $\hat{P}_F$ and $\hat{P}_B$?

Q2

I understand that there are distinct states $| Y \rangle$ that are labelled with different clock times as the number of steps N increases. But what happened to the curves on the left. The article does not seemed to discuss much about them. What do the negative values imply here in the graph?

Q3

So experimentally, are we looking for deviation of $\hat{H}_{phen}$ from $\hat{H}_F$ and $\hat{H}_B$ due to a phase difference?

Q4

Q5

All the construction in the article does not seemed to imply anything about space and time, nor the parity and time reversal operators (except their usual properties).

Would the result in this article may well be applicable in the relativistic case as I remember to go from non relativistic to relativistic quantum mechanics one simply use $E^2=\sqrt{m^2c^4+p^2c^2}$? for the energy?

Q6 (Extended question)

(This is more a discussion than an actual question) I am wondering since the t violation effects hinges on $\hat{H}_Fa_+-\hat{H}_Ba_-$ and that the commutation of this quantity with its time reversed counterpart is a phase factor.

We knew from many experiments in quantum mechanics that the phase of a wavefunction depends and can be influenced by many things such as electromagnetic potentials, geometry and other things. I wonder, if backward time travel can be realise if this phase difference is shifted by applying a potential such that the net evolution $t_c=a_+-a_-$ becomes slightly negat…

Secret

9:44 AM

NB: I will ask daniel about the quantum questions later...

John Duffield

1:41 PM

@SirCumference : it bothers me. A lot.

@SirCumference : it's resistance to change-in-motion. And "the mass of a body is a measure of its energy-content".

@SirCumference : science is how we study the universe. Don't be distracted by people who don't even know what mass is.

ACuriousMind

2:48 PM

@Secret No. There are no two different parity operators for "forward" and "backward" because parity commutes with time reversal (already abstract as elements of the Lorentz group), so $P_B = T^{-1} P_F T = P_F$.

@Secret Look at the expression for $t_c$. You could have defined the substraction the other way around. The negative values just imply a certain value of $n$ and $N$ w.r.t. each other.

0celo7

@ACuriousMind Is my proof ok...?

ACuriousMind

@Secret Stop thinking about time travel. Seriously, a lot of your confusion results from you wanting to use some completely innocuous result to travel back in time, or to communicate FTL, or whatever. First, how do you think making the net evolution "negative" corresponds to "backward time travel"? Secondly and more importantly, that explicitly says: "We will need, however, to depart from conventional quantum mechanics in three important ways. " They disregard the Schrödinger equation.

And then they claim the Hamiltonian creates translations in time

But the Schrödinger equation is the equation that says that the Hamiltonian is translation in time.

So the whole construct in that article falls apart: It is internally inconsistent.

Danu

@ChrisWhite I'm an artist ;)

ACuriousMind

@0celo7 Yes

Secret

3:04 PM

(forget about time travel for the following question)
They seemed to be able to derive a schrodinger looking equation (it has a time derivative, it has a hamiltonian and also the correct factor of i)

However I am not sure if I have overlooked something in their derivation. The maths seems ok to me...?

" Imagine that observations of the galaxy are made with a resolution in time that is much larger than the width of the Gaussian weighting function g±ngn± in equation (3.19). Under such coarse graining, the summation in equation (3.19) can be replaced by the term corresponding to the maximum in g±ngn± and so, for example,"

Is my understanding of the above statement correct: That if we measure the state at some time interval much larger than the width of the gaussian function of the state in the time direction, the interference effects effectively averages out and thus its evolution can then…

ACuriousMind

@Secret It's a "Schrödinger" equation for their $t_c$. But the problem is far earlier: Note the point where they say that $H_F$ translates forward, but $H_B$ instead of $-H_F$ translates backward. That's impossible. By Stone's theorem, $H_F$ generates a full one-parameter group, that is, to every forward translation it also generates the back translation simply by exponentiating $-H_F$ instead.

The whole setup of theirs saying that $-H_F$ "inverts" $H_F$, while $H_B$ "evolves back". So..."inverting" an evolution is not the same as "evolving back"?!

I'm very sceptical of this approach, and it is definitely not a statement in standard quantum mechanics

That is, okay, if you want to assume the world evolves differently forward than backward, then, okay, fine, but what reason do you have to model the world like that?

So, to "answer" your question: None of what is done in that article relates at present to any measurement that I can see. It's not a well-tested theory, it's a research hypothesis. You may read it, but don't take it as a description of quantum mechanics, or even reality, as you seem to do

Perhaps it's an ingenial way to get the direction of the arrow of time? Yes. Maybe it's completely wrong? Also possible. You can't tell from that paper alone

Secret

You are right about stone's theorem. Actually I had a feeling that their formalism is experimentally motivated by the kaon decay results (as covered in their previous article http://dx.doi.org/10.1007/s10701-011-9568-x)

This is because near that line when they mention $\hat{T}\hat{H}_F\hat{T}^{-1}=\hat{H}_B$ they simply wrote that because they knew the experiments showed T violating events. I had a feeling they just insert the B and F into the formalism. That is, the B and F statements seemed to be something independent of their formalism (that 2011 article I have not read in detail yet, h…

ACuriousMind

3:20 PM

@Secret Well...I have a feeling that trying to model the T-violation in some particle experiment with non-relativistic quantum mechanics instead of QFT or at least relativistic quantum mechanics is not really a sensible approach.

As in, I cannot understand why someone would expect to be able to use non-rel QM to model that.

Danu

@Secret But the kaon decay stuff is satisfactorily explained within the standard model, no?

ACuriousMind

^Yes, the weak T-asymmetry arises from the chirality of the weak interaction

A phase in the fermion mass matrix is enough to give T-violation at loop level. I think. We did only mention that, not calculate that

Secret

Actually, unlike some past articles, time travel is not the first thing that came to mind (in fact it is the sciencedaily article's quote(?) of the author's statement that inspire the idea). When I first read the article, I am thinking more about the question of the arrow of time, which is always something I wondered about since little

---
@Acuriousmind I have not read much about the relativistic QM yet, thus I am not sure if their formalism will generalise easily to it

@Danu umm.. I am kinda only aware it violates parity, but at that time (it was 2011 when I was still in high school) I h…

0celo7

@Danu what is Chern-Weil theory actually about

ACuriousMind

The secret relationship of Chern and Weil, obviously.

Danu

3:29 PM

@0celo7 Topological invariants of vector bundles.

Via the Weil homomorphism

0celo7

@Danu is that related to Atiyah-Singer in any way?

@ACuriousMind right in the feels reddit.com/r/AskReddit/comments/43b3h8/…

ACuriousMind

He's out there somewhere, running his tests on seashells

Secret

(Clarification) I guess you might have answered that question here
http://chat.stackexchange.com/transcript/message/27213408#27213408
so taking the negative does not really affect the physics

In fact, near the introduction of their 2011 paper also saying something along the lines that the formalism wil give an arrow of time, but there is no difference between choosing $\hat{H}_F$ or $\hat{H}_B$ as the one that makes the arrow

0celo7

I wonder what he says if you side with the salarian gov't

@ACuriousMind have you ever done that

ACuriousMind

@0celo7 Nope

0celo7

3:38 PM

Is there any possible way to get him to survive?

Secret

Right now, I am reading this again:
https://en.wikipedia.org/wiki/Path_integral_formulation
Because I felt like I have misunderstood something

ACuriousMind

@0celo7 I'd have to look that up again, but I think there is one convoluted way which basically ends up being the worst?

0celo7

How can it be the worst if the doctor survives

Seems like the best to me.

Secret

(The following question is a quantum question and it has nothing to do with the questions on the article (except this question is produced by a statement in the article because it caused me to get confused when I go back and read the wikipedia article)

@Acuriousmind I am not sure if I have confused (because of reading that statement highlighted in the article), but say if we are trying to compute probabilities using path integrals for a system that can exhibit tunneling, then how on earth you can have a potentially classical path that crosses the barrier (because classically a particle not having enough energy cannot go through the barrier)

Are the paths that are being integrated in the path integral already quantum, thus they are not actually trajectories in the sense of of waves or billard balls?

ACuriousMind

@Secret The path integral measure is the Wiener measure, which integrates over all continuous paths with the same start- and end-points. If you only integrated over the classical solutions to the equations of motion, you'd mostly get exactly one trajectory except in pathological cases.

FenderLesPaul

3:48 PM

@Secret that's a very good question

you have to use a Euclidean action and analytically continue to the Lorentzian action

the saddle points of the Euclidean action will include not only the usual classical trajectory you'd think of but also the tunneling

c.f. instantons

0celo7

@ACuriousMind It is possible to do it.

You have to kill Wrex in the first game and destroy Maelon's data in the second.

ACuriousMind

@FenderLesPaul: You're answering a different question, namely why the tunneling contribution is significant (it's a saddle point), not why we integrate over it at all.

FenderLesPaul

@ACuriousMind his/her question was how you can have a classical path that includes tunneling probability because classically tunneling can't occur

ACuriousMind

Classically it can also not occur that a free particle moves in a zig-zag, yet that is a "classical path" - just not a solution to the e.o.m.

FenderLesPaul

and classical paths are fixed points of the path integral; the point is that the tunneling path does exist as a saddle in the Euclidean action along with the saddles for the usual paths

ACuriousMind

3:53 PM

@FenderLesPaul Oh, we may be operating with different terminologies here

FenderLesPaul

@ACuriousMind probably haha

because I don't disagree with anything you're saying

ACuriousMind

A "(potentially) classical path" is what the path integral integrates over, here to me, because I thought that's what Secret is asking about in "how on earth you can have a potentially classical path that crosses the barrier"

You're talking about "classical path" as a point we expand the exponent in the path integral around

FenderLesPaul

yeah

Secret

(clarification)

FenderLesPaul

Oh ok so you're talking about what @ACuriousMind was talking about

not what I was talking about

Secret

3:56 PM

My understanding of what the author said in this section about feymann leads me to the following picture. I thought she means all potentially realisable classical paths that (say a ball) can roll form A to B

which is why the tunneling quesiton pop up, because a ball without enough eneegyr can never cross the barrier, but feymann path integral also sum that tunneling path

Which caused me to wonder whether potentially classical path is something more abstract

ACuriousMind

@Secret A potentially classical path is just a continuous path in space. Nothing more.

Secret

Ah I see

ACuriousMind

It doesn't obey any equations, it doesn't know about any potentials, it's just a path.

Secret

Hmm... I guess I have enough questions clarified to help me to shot down my misunderstanding of something (to be detailed later..)

0celo7

@ACuriousMind Why does $$\langle (d\exp_p)_v(v),(d\exp_p)_v(v)\rangle=\langle v,v\rangle$$

ACuriousMind

4:02 PM

@0celo7 What does $\mathrm{d}\exp_p$ do, in words?

0celo7

Carries the target vector along the geodesic $(p,v)$

ACuriousMind

Exactly. What does a geodesic do with its tangent vector rather by definition?

0celo7

Parallel transport. I know that.

But how do I "prove" that.

ACuriousMind

Yes, and parallel transport in particular preserves the norm, doesn't it?

0celo7

@ACuriousMind yeah yeah

I can't come up with the rigorous proof of that.

ACuriousMind

4:04 PM

That looks like a rigorous enough proof to me.

Secret

The thing is too long, I'll post it as a word doc. Download if interested in what I have misunderstood and how you guys have helped me greatly to get to the right path throughout these 3 weeks

ACuriousMind

Do you want to see all the horrible $\epsilon$-$\delta$s that are hidden in the words?

0celo7

@ACuriousMind Yes.

ACuriousMind

(I, for one, don't)

0celo7

I'm trying to get comfortable with that stuff

@ACuriousMind The proof you just outlined (and which I came up with myself before) is a "proof by picture"

Because nowhere did I prove that $d\exp$ is equivalent to parallel transport.

ACuriousMind

4:07 PM

How would you define parallel transport, then?

0celo7

@ACuriousMind A vector is parallel transported if it satisfies $\mathrm{D}V/\mathrm{d}t=0$.

ACuriousMind

Where $V$ is the tangent vector field along a curve, right? And you know tangent vectors are parallel transported along geodesics? Okay, so you need to show that $(\mathrm{d}\exp_p)_{tv}(v)$ is the tangent vector to the geodesic to $(p,v)$? That follows directly from the geodesic being itself $\exp_p(tv)$.

You see, it's a completely general thing that if $\gamma$ is a curve and $\phi$ a map, then $\phi(\gamma)$ has tangent vector $\mathrm{d}\phi(\dot{\gamma})$ (just chain rule, basically).

0celo7

Hmm.

But $tv$ is not a curve.

Or do you mean a curve in the tangent space?

ACuriousMind

@0celo7 Exactly.

0celo7

And then you set $t=1$ to get the result?

ACuriousMind

4:16 PM

Yep

0celo7

Ok, now to prove that the tangent vector of $\phi(\gamma)$ is $d\phi(\dot\gamma)$...I want to say that's obvious, but I don't know the actual proof.

I shall think on that.

@ACuriousMind Hmm, $d\gamma=\dot\gamma$?

Where we view $d\gamma$ as a linear map on the tangent space to $\mathbb{R}$.

ACuriousMind

Yes

0celo7

Ok, then it is indeed just the chain rule, thanks.

Secret

4:32 PM

http://chat.stackexchange.com/search?q=secret&Room=71&User=121322&page=4&pagesize=50&sort=newest

Finding my questions I asked in the chatroom is often easy, because I just need to type "secret" as mentioned by "<insert answer>"
Above for example

0celo7

@ACuriousMind wait

the tangent vectors are derivations, not linear maps on the tangent space to something

I'm confusing myself again

ACuriousMind

@0celo7 I thought you were thinking about $\dot{\gamma} : \mathbb{R}\to TM, t\mapsto \dot{\gamma}(t)$. Then it is true that this is the map $\mathrm{d}\gamma : T\mathbb{R}\to TM$ after identifying $T\mathbb{R}\cong \mathbb{R}$.

0celo7

Oh. My. God. I've been giving my aunt tech support for her Apple TV. I eventually figured out she doesn't even have an Apple TV...

@ACuriousMind blargh I'm confused

let me stew a bit

ACuriousMind

@0celo7 lolwat

0celo7

@ACuriousMind she wants to AirPlay her pictures, like I did for her at my house once

She doesn't even have an Apple TV...I've been going through all the standard Apple troubleshooting things

Great, now she claims "Apple" told her she doesn't need an Apple TV to do this

morphic

4:53 PM

@0celo7 would you ever work for Apple

0celo7

@morphic I don't know, why

$$\frac{\tau P_{\circ A}^{\circledS Q \circ A}}{\tau A_{\circ P}^{\circ Q}}$$

C'mon that's just made up

Danu

5:10 PM

Not very directly no, @0celo7

but both have to do with topological structure of vector bundles AFAIK

0celo7

@Danu what is CW theory used for

(Besides topology of vector bundles)

Danu

No idea

I'm by no means an expert.

Even getting to the Weil homomorphism was a pretty big achievement in a course called "Riemannian geometry" :P

well, Riemannian geometry is an "easy application", for one!

ncatlab.org/nlab/show/Chern-Weil+theory

0celo7

Frikken nlab

"Sorry Ryan I am watching YouTube tutorials. "

My aunt thinks I'm stupid

I wonder if this is how @ACuriousMind feels when I ask a question but end up finding the answer in Lee, etc. in the end

ACuriousMind

5:27 PM

@0celo7 No

0celo7

@ACuriousMind what do you mean

How do you know how I feel

ACuriousMind

I know that I don't feel anything.

0celo7

@ACuriousMind because you're heartless or just don't give a crisp

Crisp, lol

GG phone

Sir Cumference

Does non-euclidean geometry require calculus or differential geometry?

FenderLesPaul

This place needs more physics chat

John Duffield

5:35 PM

@Secret : maybe you're not understand many paths. Think of a big flat plain with houses on it. Mark one location as A, mark another ten miles away as B, and draw a line from A to B. Now contrive a seismic wave emission that starts at A and propagates towards B, where you contrive the absorption of the seismic wave. It isn't just the houses sitting on top of the AB line that shake. That seismic wave takes many paths.

ACuriousMind

@FenderLesPaul So, did you ever figure out that position space optical theorem?

FenderLesPaul

@ACuriousMind I kind of did. I had to understand this thing called wedge reflection positivity (arxiv.org/pdf/1009.3832v1.pdf) and based on it I think the basic idea is that in position space causality gives you a sum rule for the imaginary part of the correlator in the complex plane and wedge reflection then lets you write the imaginary part as a purely positive number

which isn't as strong as the usual momentum space optical theorem but it was enough for my needs

0celo7

@SirCumference non-Euclidean geometry?

you mean differential geometry?

FenderLesPaul

so now we're using the method of obtaining position space causality constraints that we have to try and derive a generalization of the so called CEMZ argument (arxiv.org/pdf/1407.5597v1.pdf)

0celo7

as soon as you abandon Euclideanness you bring in nontrivial topological and analytical notions

FenderLesPaul

5:41 PM

which says, based on causality constraints, that you cannot have a finite number of higher spin fields in a UV theory; you can only have an infinite tower of them or none at all

0celo7

@FenderLesPaul still no letters?

FenderLesPaul

@0celo7 nope

nothing

ACuriousMind

@FenderLesPaul I see

FenderLesPaul

yep fun stuff

:)

@0celo7 I think my brain fried worrying about grad school emails

and just stopped caring

Secret

@Acuriousmind @Fenderlespaul @yuggib @Danielsank
The reason (and my workings) on why the 3 quantum questions in these 3 weeks were asked, are all summarised here
https://drive.google.com/file/d/0B7G7KMGhji_lVHNMRjZjU0FqSzg/view

Tldr: Basically, reading the faymann lecture notes caused me to have a quantum interpretation. And throughout these 3 weeks I have been working with you guys so that I can poke holes in it and shoot it down (because my understanding must be wrong (as I don't know too much about quantum mechanics and made conceptual errors without nowing) and thus my interpretaton mu…

ACuriousMind

5:46 PM

@FenderLesPaul That's nice

Secret

PS I also now learnt some time dependent PT in the process

user54412

@SirCumference Classically, no. But nowadays non-Euclidean can be synonymous with manifolds

0celo7

@ACuriousMind If $a_n\to 0$, then $\lim\frac{(a_n+2)^2-4}{a_n}$ does not exist. The algebraic limit theorem gives division by zero in the answer.

Hmm, or does it...

Ignore me!

@ACuriousMind I need the binomial formula

ACuriousMind

@0celo7 k

Secret

(Let me know if I still made mistakes I am not aware of)
*Continues reading feymann lecture*

3507

5:57 PM

I was writing my university application for the past 3 hours, and right before I was finished and ready to submit. "logged out for inactivity" and it didn't save :(

lol

user54412

"caused me to have a quantum interpretation" oh no

5

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