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17:00
@JohnRennie is it what gravitational length mean??
Yes, the Schwarzchild radius for a mass $M$ is $\frac{2GM}{c^2}$.
kpv
kpv
@JohnRennie Once experiment is conducted, and data is recorded, that point onward, everything is about data but should still remain about physics, isn't it?
@JohnRennie you mean that question is wrong, because electrons are not point particles?
@kpv to a degree these are judgemnt calls and different people will reach different conclusions. But if a data analysis question didn't have anything that made it especially relevant to a physics expt I'd say it was out of place here.
@2physics Basically yes. When you start looking in detail at what exactly an electron is it turns out to be a very strange object indeed. It is certainly not the usual classical idea of a point particle.
@Shing What?
17:05
ACM has tried several times to explain to me exactly how particles emerge from quantum field theory, but even now my grasp on the concept is a bit tenuous.
@0celo7 I was studying introduction to complete analysis. and I couldn't remember many things in advanced calculus. one of them is: if the union set of x' and (x',x] equivalent to the set [x',x]
That's not advanced calculus, that's straight from the definitions
I can't be sure if there are gaps between x' & (x',x]
Suppose there is a gap, and produce a contradiction.
@0celo7 during your GR reading, do you encounter any invariance laws or rules for some tensors in accelerated frames?
17:08
@Secret Can you be more specific?
@kpv incidentally, publishing on Vixra will destroy your career unless you're already so well known and famous you can get away with it. Everyone in the physics world will automatically assume you're a crackpot if you publish on Vixra.
Maybe that's unfair, but that's the way it is.
@JohnRennie do other theories of physics put any constraint on the smallest measurable length theoretically?(except QM)
@0celo7 We knew that tensors are invarient under coordinate transformations, but what if the coordinates themselves have a time dependence?
What does that even mean?
Time is a coordinate.
@2physics No. The limit basically emerges from the uncertainty principle, which exists only in quantum mechanics.
17:10
@0celo7 I mean suppose I have a tensor, if I transform the coordinates from some inertial frame to an accelerated frame, will the tensor remains invariant in general?
invariant or covariant?
invariant
@JohnRennie That is a black hole of confusion.
@0celo7 ok to be more specific, suppose my tensor is the stress energy tensor, will it remain invariant in an accelerated frame compared to when in an inertial frame
kpv
kpv
@JohnRennie This is relavent to whether measurement outcomes of entangled pairs remain independent over time, or not. How this can not be related to physics. Thanks for the information about vixra. I am not affiliated to any institution so have no way to post it elswhere. I am not looking to build a career in the field though. Just trying to remove my doubts so that I can believe in quantum weirdness. Without actually verifying, I can not.
17:12
@Secret What do you mean by "invariant" anyhow
@kpv Whether you're trying to build a career or not, publishing on Vixra means no-one will take you seriously.
mayeb similar to how when we do coordinate transformations in vectors and tensors, the components will change under some transformation rule, but the geoemtric object as a whole remains unchanged
@Secret I believe that's what physicists call covariant, not invariant.
ok, in that case, does covariance of tensors hold in general when transforming between accelerated frames?
Anyhow, I have this weeks New Scientist to read, and my armchair and a bottle of cold beer are both looking seductively at me. Time to chill I think.
@Secret Covariance holds, yes.
17:14
@Secret Yes.
ok thanks
kpv
kpv
@JohnRennie I get your point. But as I said, I am trying to verify my own doubts and I am also not looking to build any credibility either. Just seeking answer to specific questions. Moreover, I do not have any options other than vixra. Could you suggest some.
FYI background of the question:
54 mins ago, by Sanya
@JohnRennie anyone here for discussing material objectivity? :|
and then (omitting a bunch of logs) I started to wonder about an analogous notion in GR
@JohnRennie should QM conform relativity principles , I mean does violation of these principles violates any of QM principles?
@yuggib hi
17:20
@0celo7 hi
@2physics The basic principles of QM and relativity are completely disjoint. Quantum field theory is what you get when you want to do special relativistic QM. The proper way to do general relativistic QM is unknown.
@Secret see e.g. Bampi, Morro: Foundations of Physics, Vol. 10, Nos. 11/12, 1980, section 4 or arXiv.org/abs/math-ph/0608065v2
@ACuriousMind most QFT is mysterious as well ;-P
I have never found the time to go into relativistic continuum theory though, but those papers talk about some relativistic analogon
@yuggib I have a hard analysis problem
17:24
@0celo7 like?
@ACuriousMind I got it; thanks..
@yuggib First, does it make sense to talk about smooth functions $F\to \Bbb R$, $F$ Banach?
@Secret actually, forget about that arXiv thing, I mixed that up with something else I kind of remembered
I recall from Jost one can differentiate functions on Banach spaces
but does smoothness make sense
@Sanya Well, based on what johnrennie and 0celo7 said, it seems most GR tensors work fine in accelerated frames as they are covariant. However I am not sure if the continuum mechanics tensors can be generalised to GR ones
17:26
@0celo7 well, there should be a smooth structure on some infinite dimensional manfiolds
@yuggib Let's avoid manifolds now
I think also Banach ones
what I learned today: 1- nothing is constant. 2-nothing is related to anything else. unknowns doubled :D
While my analysis result will be transferred to a manifold, I'm just doing it in a coordinate neighborhood
So I'll do it on $\Bbb R^n$, but I wonder if it transfers to all Banach spaces
@Secret the problem is usually the derivative of a tensor - or a non-tensor so to speak because the object does not have the tensor transformation properties, that is the core of the problem in the end
17:27
@2physics 2 basically sums up whenevr ACM tries to figure out how various points of mine are strung together
You can take derivatives on Banach spaces, it's either Frechet or gateaux derivative
The lemma is: let $\gamma:I\to\Bbb R^n$ be a smooth curve, $I$ a closed interval.
Smoothness in Banach spaces does make sense. You can define differentation in the usual Frechet way, and since the space of linear operators between two Banach spaces is itself Banach you can iterate this to define smoothness.
Let $g$ be a smooth function defined on $I$. Then there is a smooth $G:\Bbb R^n\to\Bbb R$ such that $G(\gamma(t))=g(t)$ for $t\in I$.
@ACuriousMind only if they are continuous
17:29
We also assume the image of $\gamma$ has no double points.
@yuggib Yes, the space of bounded/conitnuous linear operators, my bad
What is the Frechet way?
@Secret lol those various points must be as complicated as general theories of physics then
@yuggib I guess what I need to know is: do Banach spaces admit partitions of unity?
@0celo7 Use the Power Of Google(TM)
17:32
@ACuriousMind Oh, I didn't know that's what it was called.
@2physics I suggest you to read that log when I and ACM discuss about magic. If you can underrstand that, it means you are somehow similar to me in my worldview (thus does not require those cues)
@yuggib Do Banach spaces admit exhaustions by compact sets?
Which ironically is not kinda good because it turns out it is people who said they don't understood me understood me more than anyone else including myself
The usual proof for $\Bbb R^n$ fails because closed balls need not be compact.
...closed balls are not generally compact, right?
@0celo7 I doubt you can have partitions of unity in general
17:35
No, a Banach space is finite-dimensional if and only if the closed unit ball is compact.
And yes, balls need not be compact
Ok, so once compact exhaustion fails there goes the usual PoU proof.
I hope someday we hear somebody's theory has predicted the existence of an object smaller than the planck length which is travelling faster than C lol
But Banach spaces are paracompact.
People who are at odds with my view but not antagonistic, in some sense understood me better than most people including myself because they are unaffected by that chrisma side effect of me when I talk passioonately about something and thus can see deep into personality traits that I am not aware of
17:36
Although you can choosing different topologies in which the unit ball does become compact
Weak*
@ACuriousMind Other than the metric topology you mean?
Yes
E.g. for the weak-* topology on the dual there is the theorem of Banach and Alaoglu
@ACuriousMind This seems to be nontrivial to prove, is that true?
wtf
@0celo7 it's not so hard, there is a scaling argument somewhere
17:38
A scaling argument?
Google seems to think I need the Riesz lemma.
@0celo7 skim math.se, I saw it there somewhere
I did skim, they all say to use the Riesz lemma.
@2physics Well it will either mean we are doomed (because something is unstable), or we need to start think in a way throwing causlaity out of the window
@Secret I don't know what you talk about actually.. maybe that's because my English's kinda lame
Well then you are not alone, my text communication skills is a WIP. but basically that sentence is saying people who think differently than me, tend to be better at picking out habits I don't aware within myself
17:41
Is the intuition that you have enough degrees of freedom to construct a Cauchy sequence that does not converge in the ball?
Yes, in a Banach space you need something like the Riesz lemma. For Hilbert spaces, just pick any orthonormal Hilbert basis.
@Secret yup maybe
@0celo7 Not exactly. Compactness means that every sequence has a convergent subsequence, so you construct a sequence where the distance of every element to every other element is larger than some fixed $\epsilon$, so no subsequence can be Cauchy.
who understands QM ?
i think I understand it..
lol
ACM (general), yuggib (mathematical formulation and some experiments), danielsank (qubits and quantum information)
17:44
@ACuriousMind In some sense, you just pick each point to lie on a different "axis" of the Banach space?
@0celo7 yes
Ok.
So, let's go back to the $\Bbb R^n$ case because I don't want to deal with functional analysis.
"If you think you understand quantum mechanics, you don't understand quantum mechanics" Feynman
I completely understand it :D
@yuggib So it it believable that a smooth function defined along a compact curve can be extended to all of $\Bbb R^n$?
@JohnRennie what about you , do you understand it?
17:46
I will never say I completely understood anything because to be qualified for that, I will need to be able to answer any question in that field with ZERO errors
::The problem of being a perfectionist::
The idea is to locally extend it and piece together the sections with a PoU.
But the details are hard.
@Secret how does it feel , being a perfectionist?
Especially because each local extension requires a PoU.
I might start to have more physics questions for ACM once I took care of that PhD application forms and continue to read classical mechanics theoretical minimum
@2physics it is tiring because msot things are simply unrealistic, but when you can doen it, a sense of accomplishment
@Secret but I think most things being unrealistic can be kinda more interesting than being realistic sometimes
17:52
Well yes, for starters, out of control free associations do sometimes came up interesting topics to ponder about
@0celo7 probably there are many ways to do it
Anyway its 3:53 here and I am heading to sleep. Big day tmr in resolving that annoying PhD appplication chores
@yuggib The question is then transferred to a manifold.
I think it requires three separate uses of a partition of unity.
I hate analysis sometimes
@0celo7 analysis is annoying
@2physics the word "understand" is not well-defined in this question
Oh, it also uses the implicit function theorem.
18:01
@yuggib well it has the definition of what Feynman referred to. you can ask him for more clarifications :P
I still don't understand how to do that integral.
@2physics I don't know what you're talking about
@yuggib "If you think you understand quantum mechanics, you don't understand quantum mechanics" Feynman
I was just kidding
I see
@JohnRennie@ACuriousMind thank you for the help on the plank units and relativity issues
18:05
@ACuriousMind Am I just supposed to know that $$\int dx\,\exp\left(-\frac{(x-2i(k-p'/\hbar))^2}{2d^2}\right)=\int dx\,\exp\left(-\frac{x^2}{2d^2}\right)$$
kpv
kpv
@ACuriousMind Looks like only you can help now. Is there a way that I can satisfy your expectations to have the hold removed and get the question answered. You are right, I do not believe in QM workings (only in case of entanglement correlations) but would like to remove my doubts so I can believe. Or if reasonable, can raise more doubts. Please let me know.
@0celo7 I have no idea what you're supposed to know, but isn't that straightforward by substitution?
@ACuriousMind No, the constant is complex.
You have to use Cauchy's theorem.
18:20
At the physics level of rigor, it is just substitution. You're formally correct, but I think you're approaching these problems with the wrong mindset - this is a QM class, not analysis.
kpv
kpv
18:31
@ACuriousMind Can you please elaborate little, I did not understand it. May be that is the issue, we do not understand one another's style.
@ACuriousMind Grumble.
I should have taken Modern Algebra instead of QM.
kpv
kpv
@JohnRennie Thank you for your time and input today
@ACuriousMind Are smooth functions Lipschitz on any compact set or just locally Lipschitz on any compact set?
I guess if they're locally Lipschitz on a compact set they're Lipschitz on the compact set.
kpv
kpv
@ACuriousMind Are you going to engage or I should leave the chat, just waiting for your response.
@ACuriousMind
18:46
@kpv He probably put you on ignore.
Can anyone help me with an electrical engg. question?
@HariPrasad Yes, the people at Electrical Engineering.
kpv
kpv
@Ocelo7 Thanks, looks like. what an arrogant dude, but I know he may be afraid of facing new questions.
@0celo7 I don't think all smooth functions are locally Lipschitz.
But being locally Lipschitz indeed implies being Lipschitz on compact sets.
@ACuriousMind Pretty sure all $C^1$s are locally Lipschitz
Use the mean value theorem
18:50
Ah, yes
kpv
kpv
That is what happens to people who believe like religion
Then smooth functions are Lipschitz on compact sets.
@ACuriousMind but i need a quick answer and the Electrical Engineering chat is not that active. :(
Ok. I'm being super anal now and reviewing all ODE stuff in geometry
19:21
@kpv calling people arrogant is kind of inappropriate. Remember our policy on civility (a.k.a. the "be nice" rule), which applies in chat too.
kpv
kpv
@DavidZ: I agree, I kind of forced myself to use that word. But is it polite to not even respond to someone waiting for your response? What would you call that behavior?
Nobody is obligated to respond to anyone.
kpv
kpv
Is that "be nice" category?
@kpv Not exactly, it is a passive agressive behavior, but it is tolerated
@kpv Also I am on their "persona non grata" list since a while, it is quite easy to get into that list.
kpv
kpv
Yes, because he is in a position to effectively use the passive aggressiveness. I am not. That is misuse of discretion.
19:28
@kpv But don't worry on it, they could probably even expel you from here if they had really wanted it, a little bit of ignorance is not the world. Actually, the community would profit from it, if not they would be in its centre, and this is what they get with this ignore.
It's not even necessarily passive-aggressive. Sometimes people just walk away from the computer or just can't think of a good response, or any of many other things.
@kpv You can't do anything with it, they didn't say any bad word to you, so they are perfectly correct. ;-) Or not? :-)
kpv
kpv
@DavidZ He was there responding to others, I asked if he was going to respond, he could have said some other time, but no response. That is explicit ignoring, it is kind of insulting but I would not feel it that way.
Perhaps. Regardless of whether it's explicit or not, intentional or not, etc., it is every participant's right to ignore whoever they like.
kpv
kpv
also whether it is reasonable or not? All I asked him was how I can meet his expectations on my question. I was not arguing with him.
19:35
@DavidZ is there any chat session concerning the reworking of the homework policy planned?
@Sanya I feel like almost every regular chat session in the last months has touched on that issue.
It'll probably come up in the next one
@ACuriousMind Not every one ;-) There was a span of a couple months or so where we didn't talk about it
@ACuriousMind that might well be, but I feel like it still needs a bit of talking and discussing and the meta is a bad place to get a brainstorm-discussion
@DavidZ thanks :)
@kpv As I said, it's everyone's right to ignore whoever they like. Nobody is ever obligated to respond to you.
btw, @ACuriousMind , 21,4% AfD, did you see that? :<
19:38
@kpv out of curiosity, what question is this about?
@Sanya Sadly, it is not unexpected.
The truth... breakthrough :-)
@ACuriousMind I am unteachable and can't stop believing in common sense until I am disappointed once again
kpv
kpv
Emilio, it is below I have reworded it today, you also put it on hold yesterday, if you could please revisit your hold/close vote.
-4
Q: Does this observation in a probabilistic experiment indicate presence of a balancing mechanism?

kpvI will ask the question in terms of an observation on a hypothetical coin toss experiment. If you like, you may answer the question based upon the coin toss description alone. For little more curious and patient readers, I have provided link to a paper that I wrote about an observation on an ac...

@Sanya Ah, the idealism of the youth ;)
19:41
@ACuriousMind thanks - but I fear that I'm older than you ^^"
@kpv Ping him with a @
Hi, everybody.
@Sanya I'm at least eighty in cynicism years ;)
:D
@DanielSank good evening :)
kpv
kpv
@EmilioPisanty , it is below I have reworded it today, you also put it on hold yesterday, if you could please revisit your hold/close vote
-4
Q: Does this observation in a probabilistic experiment indicate presence of a balancing mechanism?

kpvI will ask the question in terms of an observation on a hypothetical coin toss experiment. If you like, you may answer the question based upon the coin toss description alone. For little more curious and patient readers, I have provided link to a paper that I wrote about an observation on an ac...

19:47
@kpv To be frank, it's still not particularly clear exactly how the imbalance is defined. This is a single experiment? Or is it four independent experiments? You jump all over the place.
Similarly, is the imbalance defined as (heads-tails)/(heads+tails)? If there are four experiments, are the coins the same (i.e. "heads" corresponds with "heads" on all experiments)? Are you still defining the imbalance as (heads-tails)/(heads+tails) then, or do you switch to (tails-heads)/(heads+tails)?
These are the sort of details which would be very easy to make crystal clear but you somehow don't
I'm not saying that fixing this would fix the question, which is improved but I still think does not pass the bar.
You also don't need any more interaction from me - all you need is five 3k+ users (any such users) to agree that this is reopen-worthy.
kpv
kpv
@EmilioPisanty Let me fix these issues first and will ping you here. I do not know any 3K+ users how I can reach them and make them agree.
@kpv You don't 'reach them'. You hope that people will see your question and agree, and there is a review queue where people will see the question.
And (assuming the question should actually be reopened) if not enough people see it, then use that as a prompt to get the question right the first time.
If you edit the question you can ping me here, just keep in mind that people are busy and you're not entitled to any response as such.

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