The h Bar - 2016-06-03 (page 2 of 6)

« first day (2038 days earlier) ← previous day next day → last day (2907 days later) »

user116211

12:00 PM

16

A: Why is oil a better lubricant than water?

Your derivation is composed of correct statements and indeed, if something is known to act as a lubricant, we want the viscosity to be as low as possible because the friction will be reduced in this way. For example, honey is a bad lubricant because it's too viscous. However, your derivation isn...

user116211

Another classic from Lumo.

@ACuriousMind But your comments say that if I was near you, you certainly kill me.

@ACuriousMind I think I'm quite helpful!

@lucas Are you some sort of troll? I have never even implied any such thing.

@lucas I don't think "kill" means what you think it does...

user116211

12:01 PM

@lucas: this is really a BLUNT translation.

B)

user image

I want to be friend with all. But they don't want:(

@MAFIA36790 The globe is warmin' up when we fire up the blunt. - Ludacris.

Have you read any textbooks on this subject? @lucas

12:03 PM

@skillpatrol No

user image

@lucas It would be a good start :-)

user116211

1

A: Is the energy of a photon continuous/discrete?

A free particle (photon, electron etc) is not restricted to discrete energy levels. Its wavelength and therefore energy can take any value. A plane wave, with any wavelength you choose, can satisfy the Schrodinger equation for a single free particle. A free particle does not have to have a sin...

user116211

@lucas: ^^^

user image

12:04 PM

user image

@skillpatrol I want to read but I want to know why should I read QM, while I don't know classical mechanic solution.

Well I would advise reading classical physics, first, then

@ACuriousMind Is your palm through your face yet?

user116211

@lucas So, thhhhat's the point?

@Slereah This is my first ask. I want a text containing .. about 1 hour ago.

12:06 PM

user image

@Secret Is that a diagram of a sperm entering the egg?

user116211

@lucas Ok, your statements are contradictory.

nope, just pile of quantum dots solution

@0celo7 It is firmly attached to it, at least :P

user116211

For @lucas' enlightenment:

user116211

12:07 PM

41

Q: If photon energies are continuous and atomic energy levels are discrete, how can atoms absorb photons?

If photon energies are continuous and atomic energy levels are discrete, how can atoms absorb photons? The probability of a photon having just the right amount of energy for an atomic transition is $0$.

photons atomic-physics discrete

@ACuriousMind Is it possible to prove that manifolds are metric spaces without using a Riemannian metric?

user image

@MAFIA36790 Why my statements are contradictory?

A standard classical mchanics text

user116211

@lucas C'mon check yourself... you told what then and telling what now.

12:08 PM

user image

@0celo7 Yes. Urysohn's metrization theorem is much more general and encompasses the case of manifolds.

For some Rigor in your mechanics.

Is that the one that does the pendulum with fiber bundles

@Slereah Yes.

user116211

@0celo7 Lanczos' Mechanics is damn good too.

12:09 PM

goodbook

Oh hey Lanczos

I read that guy recently

Apparently he's the guy that worked on thin shell formalism in GR

user116211

@Slereah He is intuitive.

Lanczos junction and all that

@Secret Is this book containing classical mechanics solution about photoelectric effect?

user116211

What if Bourbaki wrote some physics ;/

Well Bourbaki is a lot of dudes

He might have

user116211

12:11 PM

@Slereah He is alive still today ;P

@lucas what do you mean exactly by "the classical photoelectric effect"

On what would you apply it

There are no classical atoms

@ACuriousMind Do you need paracompactness + PoU to prove that manifolds are completely regular?

@0celo7 no idea

@ACuriousMind So how do you know that manifolds are completely regular?

@Slereah Not classical photoelectric effect. Classical mechanics explanation of that phenomenon.

12:12 PM

But how

I mean, the photoelectric effect is the effect of EM waves on bound electrons

How can you do that classically

@0celo7 I have faith in the clever people who showed that, and the equally clever people who checked the proof :P

user116211

@Slereah I've lost hopes....

@ACuriousMind Oh you and your "black box" mentality.

I bet you can't even prove Stone's theorem

Do you mean Stokes

@Slereah They draw two diagram. 1 by classical mechanics and 1 by QM. How they draw that? By which calculations?

12:13 PM

@Slereah No.

But I bet he can't prove that either.

@Slereah Do the Einstein Field Equation allow for CTC solutions such that there are more than one CTC that share at least one common event?

No

You can't have curves splitting

@Slereah Proof?

Isn't that just like

Hausdorff property

Uh, no?

12:17 PM

I dunno then

Picard Lindyhop mb

He's not asking if there's one curve $c:(-\epsilon,\epsilon)\to M$ that splits at $c(0)=p$

But if there are two CTCs $c$ and $\tilde c$ for which $c|_{(-\epsilon,0]}=\tilde c|_{(-\epsilon,0]}$ but afterwards they disagree.

Like this: i.stack.imgur.com/91UJV.jpg

@Secret Something like that?

Well geodesics are locally unique for the same spacetime point and tangent vector, no?

CTCs are not necessarily geodesics.

12:19 PM

Hm

What about the...

Identity theorem?

If two curves are identical over a compact region they are the same curve, or some shit

(if they are somewhat smooth)

@0celo7 I am guessing they basically only agree on one event, and then they go their separate ways, thus there's only one c such that they have the same spacetime coordiantes

so in some sense, it might be suggesting the curve splitting property that Slereah is mentioning about

That's a thing?

I don't belive it for a second.

@Slereah What? That's clearly not true for arbitrary curves.

Identity theorem

In complex analysis, a branch of mathematics, the identity theorem for holomorphic functions states: given functions f and g holomorphic on a connected open set D, if f = g on some non-empty open subset of D, then f = g on D. Thus a holomorphic function is completely determined by its values on a (possibly quite small) neighborhood in D. This is not true for real-differentiable functions. In comparison, holomorphy, or complex-differentiability, is a much more rigid notion. Informally, one sometimes summarizes the theorem by saying holomorphic functions are "hard" (as opposed to, say, continuous...

Hence the smoothness

>holomorphic functions

12:21 PM

@Slereah Holomorphy is a much stricter requirement than smoothness

Well there you go

You can have that if the curves ain't holomorphic

maybe I dunno

@Slereah come on even this 18yo knows better

@Slereah wtf is a holomorphic curve :D

Who knows

Pretty sure it involves ghosts

@Secret Maybe that can happen

Although, aren't CTCs integral curves of a timelike vector field?

Those are unique, locally at least.

By Picardy Lindelhofer.

12:22 PM

*Picard Lindyhop

user image

Who's that?

Picard

@Slereah lol

Not exactly dancing a Lindyhop, though, I think

user image

Something like this, which I suspect something will be violated at A if this configuration is impossible

...why did you think anyone needs a picture for "two curves agreeing on one event"?

12:24 PM

He likes to draw

At least it's not freehand

like most people

Since the past and future are set to stone in CTC, it should be reasonable that their could be conditions where more than one event can lead to the same past or future

(I need to wait 10 years later before I have the rigorous terminology to formulate the above guess)

@Secret I doubt Sam can prove it either way :P

Rude

12:28 PM

Ok, prove it?

Oh easy to do

Take the Deutsche spacetime

cf. Hawking Ellis?

Add an arbitrary curve between the two cuts

Bam

Same past, different future

What?

That's not a proof...

A counterexample is a proof!

12:30 PM

I don't see how it's a counterexample

What are you counterexampling

In both case the initial conditions are an empty spacetime

@Slereah Not this again :D

It can develop into either a still empty spacetime or one with some arbitrary curves in between the cuts

@ACuriousMind what?

hmm, sounds like the final configuration is quite undetermined as any curve in between the cuts can satisfy the condition. hmm....

12:37 PM

@0celo7 I seem to remember you have a philosophical issue with counterexamples as proofs that something is not true :P

I also recall a weird example for a non-unique scalar field development with CTCs

But the example was like

user image

Nice title :D

CP2 is complex projective plane?

yes

Making non-unique developments with CTCs isn't hard

But, as far as I know

It's mostly curves going nowhere

Rather than curves splitting

so that equation is suggesting the spacetime is R^4 with a handle and a klein bottle (because if I recall correctly, connected sums of projective planes give klein bottles) attached to it, thus this spacetime will have genus = 2?

12:47 PM

@ACuriousMind Correct.

@ACuriousMind Can you prove that counterexample is a valid proof technique?

By definition

Not an argument.

$\forall$ is defined as $\neg \exists \neg$

What

If $\exists \neg$, that's equivalent to $\neg \forall$

12:51 PM

What^2

@0celo7 wants to debate logic but can't actually read it

@Slereah I just don't like proof by contradiction

Why not

for all is defined as not (for some that are not)
if for some that are not, that's equivalent to not for all

I see...

because

12:54 PM

If your theorem doesn't work for a specific example, then you can't say it works for all

Proposed Theorem: All whole numbers are positive.

False because 0 is not positive.

But that does not answer the question: For which subset of the whole numbers is this true?

But you didn't ask a question

You proposed a theorem

The false theorem implies a question.

This is logic 101 m8

No

That is more

~philosophy~

Usually the complement of the counterexample is generally a more difficult question

12:55 PM

Hoity toity stuff

My maths solving speed is slow because I tend to solve probelms on trying to find the counterexample by deriving the general case and then make it fail

If you want me to solve the Cauchy problem for non-causal spacetimes

That's a pretty tall order

Agreed, though it is nice to be aware of nonunique CTC evolution and the possibility of "conjoined CTCs"

*Looks like I have extra scenarios need to consider in my time travel theory formulation*

for an illustration of this statement, see my answer to someone in MSE here
http://math.stackexchange.com/questions/53926/ideas-of-finding-counterexamples/1367616#1367616

This is why I usually took 3x more time than me peers in solving counterexample problems unless I am familiar with it

I don't think this is gonna be really a CTC related problem

I think this will be more like

Can somewhat smooth curves split like that

mb I dunno

@ Slereah Hmm, I would check this out when I got back to the revision of differential geometry after my QFT and QM revision

1:05 PM

Please stop using ---

However, while this is hard work, arguably it closed the pseudo-loophole that @0celo7 proposed

Since this generally time consuming way allow you to find the set of all counterexamples of a problem, we can easily take the complement to find the condition that give you the set of all examples that satisfy the problem

My maths professors and my MSE friends however cautions me that in general, doing this is the same as asking "what is the tree of knowledge" thus... (...)

What loophole

The false theorem (end of sentence)
open loophole = implies a question.

Therefore, time consuming method mentioned above answered both questions at the same time, thus closing the loophole

(I must have used my vocab wrongly, due to a persistent habit of equating "loophole" with "loose end")

@0celo7 us.metamath.org/mpegif/exnal.html

:p

what does that mean

1:12 PM

>This means the values a,d,e,h and the traces of AA and BB does not affect whether the matrices will satisfy the condition required by the counterexample. Thus we can set them all to zero to save ourselves some trouble

I don't think mathematicians solve problems like this. From my memory, only physicists do such things

Mathematicians only do similar things if there is no loss of generality

@Secret I don't see a reason why it shouldn't be possible

Unless @Slereah proved otherwise

what

I'd like him to write a formal proof that explains everything

I don't even know what this sentence means

ask the German.

1:13 PM

Alright

YODELAIHIHOO

@Slereah you called?

haha holy shit

Wrong German

:-(

@Loong do you have a thing that alerts you when someone says "German"

1:14 PM

Yodelling - Franzl Lang

^possibly @ACuriousMind

Ayy Franzl

@0celo7 no ;-)

>Here AA has eigenvalues 2√2 and −2√−2, BB has eigenvalues 1 and -1, while A+BA+B has eigenvalues −6√−6 and 6√6 and ABAB has eigenvalues 2 or 1. It is then easy to check that no possible products or sums of eigenvalues of AA and BB matches at least one of those in A+BA+B and ABAB (in fact, it turns out this particular counterexample, even the sum and products of eigenvalues in just AA or BB cannot equal to those of A+BA+B or ABAB thus making it a pretty broken (hence almost perfect) counterexample.

Often when I do counterexample questions, I also end up optimising the solution for it
Rather than just finidng one counterexample, I found the whole set of them and pick the worst possible one

(Problem of being a perfectionist...)

@Slereah Franzl is not skinny.

Hm

Thinking about it

I can think of an example of a smooth curve being able to do that

1:18 PM

However, the problem "optimisation of a counterexample for a given problem A" is in general no different to "what is the tree of knowledge", which is why they are hard

@Slereah a smooth curve splitting is trivial...

take a bump function and its negative

The function $f(x) = 0$ and $f(x) = $ some test function with a domain outside of 0

That works too

So yeah I think you'd need more than smoothness

Maybe analyticity?

Also of course

59 mins ago, by ACuriousMind

@Slereah What? That's clearly not true for arbitrary curves.

@Slereah uhh

1:19 PM

There's the classical example of CTC pool game

I don't even think you can have analytic curves

what does that even mean

For a manifold, not sure

The CTC pool game is an example of interacting fields with CTCs

> Browsing the internet during class is fully inappropriate and inexcusable.

>:(

You get such splitting behaviours from it

But that involves a particle getting bumped by itself

Under "7. Slightly More Realistic Models of Time Travel"
http://plato.stanford.edu/entries/time-travel-phys/
This one is the CTC pool game?

1:23 PM

yes

Ah, Klinkhammer

I like that name

It sounds like a whacky nazi name

"Obersturmfuhrer Klinkhammer!"

user116211

@Slereah o/

user image

@Slereah Ja, mein

Uh

I think the pool game describes an ordinary CTC

...unless

user image

oh god

1:27 PM

If we add an extra pair of time portals after the future ball bounces away from the past ball so it becomes its past

then we recover the structure we are investigating. So that question is as you raised whether it would be possible on a spacetime manifold

Stop drawing butts

user116211

hehehehe.

All I want for my birthday is a big booty hoe. - 2 Chainz.

user116211

Oh! @yuggib didn't come today :(

user116211

@0celo7 Where do you get these?

1:35 PM

@MAFIA36790 Uh, I listen to music?

user116211

ohh.

imgur.com/a/YEVxZ

good old Black Mesa

You dun goofed son

@MAFIA36790 I leave for japan tomorroww...I have to get prepared. I may post on meta about my ama questions tomorrow (even if the date is not officially set)

user116211

@0celo7 what again ;_;

user116211

@yuggib Have a sweet journey! Don't forget to bring back souvenir :D

1:46 PM

@MAFIA36790 And I done killed more cats than curiosity, snitch! - Busta Rhymes.

Always remember that.

@MAFIA36790 thanks! yeah, I most probably will get back a lot of souvenirs ;-)

@yuggib I need analysis halp

pls

what?

@yuggib If $f,g$ are smooth and $f\circ h\circ g$ is smooth, is $h$ smooth?

I'll try but I don't have much time right n

1:47 PM

It's simple

Or actually, if $f, g\circ f$ are smooth, is $g$ smooth?

right?

@0celo7 : What about if $f$ is 0 and $h$ is not smooth

by smooth you mean c-infty

@Slereah Oh good point

@yuggib I'm taking about maps on open sets of $\mathbb R^n$ to $\mathbb R^k$

yeah, but then the smooth structure is differentiability right?

you lnow I don't like geometry

1:52 PM

@yuggib how is this geometry

it's pure analysis

I'm not talking about $\mathbb R^n$ as a manifold

@0celo7 smooth structures are geometry

@yuggib "smooth" means "all partial derivatives of $f,$ etc. are continuous to all orders"

$C^\infty$.

@yuggib so you won't help?

I have not much time as I said

I am on mobile now

@yuggib I would think an analyst would know this...

« first day (2038 days earlier) ← previous day next day → last day (2907 days later) »

Transcript for

Jun '163

The h Bar

General chat for Physics SE (physics.stackexchange.com). For M...

join this room
about this room

00:00

06:00

12:00

18:00

all times are UTC

site design / logo © 2024 Stack Exchange Inc; legal

mobile