The h Bar

Semiclassical

3:00 PM

Hamilton-Jacobi gives you a PDE.

which is great when you can do something with it

Phase

why does Hamiltonian give twice as many variables?

I was under the [probably wrong] assumption both work using generalised co-ordinates

Secret

I wonder if there are any python people here who have encountered this problem before:

for i in some list 1:
for j in some list 2:

Semiclassical

in Hamiltonian mechanics you've got coordinates and momenta as independent

Phase

Ahhhh right

Balarka Sen

Hamiltonian mechanics is over the tangent bundle of the manifold

Phase

3:01 PM

Whereas in Lagrangian the co-ordinates encode all the information you need

Balarka Sen

which is of dimension 2n

Secret

Somehow in the 2nd layer of the loop, it is skipping the first element

Phase

Because you're minimising the functional

ACuriousMind

@BalarkaSen *cotangent. The Lagrangian is over the tangent.

Phase

@BalarkaSen you might as well me screaming the language of Cthulu in my face

What the hell even is a bundle

Balarka Sen

3:01 PM

@ACuriousMind Ah yes thanks

bolbteppa

Obviously you just average then extremize Hamilton-Jacobi for a logarithmic form of the action for no reason and magic happens physics.drexel.edu/~bob/Quantum_Papers/Schr_1.pdf

Semiclassical

my recollection of H-J is that (in the 1D case) you write $H=\frac{\partial S}{\partial t}$ and $p=\frac{\partial S}{\partial q}$

Balarka Sen

@Phase A smooth family of vector spaces parameterized by some space

Phase

What's S?

@BalarkaSen what exactly does parametrised mean here? I dont have much experience using such general terms

bolbteppa

I literally have 0 reason to do mechanics on manifolds and tangent spaces, except for Arnold's re-writing Landau in that language, 0

Semiclassical

3:03 PM

and then $H=\frac{p^2}{2m}+V(q)$ gives you the PDE $\frac{\partial S}{\partial t} = \frac{1}{2m}\left(\frac{\partial S}{\partial q}\right)^2+V(q)$

Phase

What's S sorry?

Semiclassical

I think it goes under the name of Hamilton's characteristic function?

I honestly remember the prescription more than how one gets there

Phase

Another question

bolbteppa

If $S = \int p dq - Hdt$ then $\partial S/ \partial t = - H$

Balarka Sen

@Phase If means you have a space $X$ and for each point $x \in X$ there is an associated vector space $E_x$

Semiclassical

3:04 PM

main thing is that if you can (somehow) solve that PDE for $S$, you can differentiate it w/r/t $q$ to get $p$

Phase

Probably a very difficult one to answer without making it alien to my inferior vibrational consciousness but

Semiclassical

@bolbteppa yeah, that looks right

Phase

How does one introduce a Lagrangian to [i assume] wave quantum mechanics

Balarka Sen

@bolbteppa I think it's important to mathematicians. Symplectic/contact geometry something something

Semiclassical

i think the way that's usually done is via the path integral representation

Phase

3:05 PM

@BalarkaSen sorry I dont get it

Balarka Sen

thats fine

Semiclassical

if you do that, you get the classical Lagrangian as playing a central role

bolbteppa

You can rewrite Schrodinger's equation as the EL equations for a Lagrangian

Phase

@BalarkaSen I dont get what it means for each point have it's own vector space

@bolbteppa spooky. But is action always minimised in QM?

Semiclassical

there's not a variational principle per se

Balarka Sen

3:07 PM

@Phase The classical example is the Moebius strip. To each point $x$ in the center circle of the Moebius strip, there is an associated line (vector space of dimension 1) that is "perpendicular to the circle". Look up a picture

Semiclassical

but when you compute in the path integral method, the paths with less action will carry more weight than those with more action. (this is a bit simplistic, since it doesn't take into account interference between such paths)

Phase

@BalarkaSen do I just google "moebius vector bundle"?

@Semiclassical stuff like that just sounds like total voodoo

Balarka Sen

@Phase Take a look at this

Semiclassical

I think a comparison to the stationary phase approximation is helpful

suppose you write down the integral $\int_{-\infty}^\infty e^{-a x^2}e^{f(x)}\,dx$

bolbteppa

Right now I just think of it as a green function for the Schrodinger equation, still have to do the string context

Semiclassical

3:10 PM

with $a$ being some large positive number, and $f(x)$ not blowing up faster than $x^2$ at infinity

Phase

@BalarkaSen so is this an example of a vector bundle? Each point $x \in X$ of the circle has an associated vector... Space? Where does the space part come from

If you got bored of answering questions lemme know, dont wanna pester

@Semiclassical ok im following I think

But does the size of a affect how fast it blows up?

Balarka Sen

@Phase By vector space I mean, you know, a copy of $\Bbb R^k$. If $k = 1$ that's the real line, if $k = 2$ that's a plane. To each point in the circle you have that line that passes through it

Semiclassical

if that integrand has a single peak, then we can approximate that integral using the stationary phase approximation

Balarka Sen

So it's a family of lines (1 dimensional vector spaces) parameterized over the circle

Also called a line bundle

Semiclassical

the peak will be located where e$\frac{d}{dx}(-ax^2+f(x))=-2ax+f'(x)=0$. solving that gives us (hopefully) a point $x_0(a)$

Phase

3:13 PM

@BalarkaSen Ok.. I guess I get it, I feel like I wouldn't understand it properly though, like if you defined what generates the vector spaces orientation. Also, how old are ya? Idk whether to trust Ocelot

he's sneaky

Semiclassical

and then you run the stationary phase approximation to get $e^{-f(x_0(a))}$ as the leading asymptotic

Balarka Sen

You don't need to know it properly; that's what it approximately is.

Phase

@Semiclassical Ive never heard of or used the stationary phase approximation

Balarka Sen

I'm 52

Phase

God damn that's a lie too

No one can be trusted

Semiclassical

3:14 PM

basically, expand the exponent in the neighborhood of a critical point

Phase

as a taylor series?

Semiclassical

yep. then the exponent is of the form $-f(x_0)-\frac{1}{2}f''(x_0)(x-x_0)^2$

Phase

Is there a reason for only taking it to second order? Is it because the exponent was x^2?

Semiclassical

so then you can pull $e^{-f(x_0)}$ out of the integrand, and what's left is a Gaussian integral

yeah

Phase

everything in physics is black magic

Semiclassical

3:16 PM

the Gaussian integral can then be computed exactly, but the key point is actually that $e^{-f(x_0)}$ factor

an example would probably have been better, tbh

i'm just not remembering one off the top of my head

Phase

dw about it dude you already took a fair bit of time explaining something interesting to me, I appreciate the time

it's also a nice change to at least understand a couple elements of it

Semiclassical

key point is that, so long as the approximation is valid, you have $x_0$ as the controlling parameter despite the fact that there's no explicit variational principle

you trade "minimize the action" for "get a good enough approximation for the integral"

Phase

I see

Semiclassical

'good enough' is a bit wishy washy, but that's sorta the name of the game when it comes to asymptotics

Phase

sorry if I missed something but where does EL enter the mix?

Semiclassical

3:19 PM

EL will be the equivalent of that $\frac{d}{dx}(-ax^2+f(x))=0$ condition

here the analogy is limited since you get a particular value of $x$

whereas for EL your solution corresponds to a particular $x(t)$

Phase

Hm. Doubt i get it but its nice to get an understanding at least, even if incredibly limited

not your fault either, just my brain

Ought to get a refund

Semiclassical

but in both cases there's some variational condition. it's calculus of variables versus calculus of variations.

0celo7

Calculus of variations in a very broad sense is just calculus of variables along lines in a vector space.

Phase

Will I learn this in my degree?

Semiclassical

in quantum, probably you'll see some stuff on stationary phase approsimation

Phase

3:22 PM

nice

Semiclassical

and if you go far enough, you'll definitely see the path integral formulation.

Phase

I'm looking forward to starting the actual mathematical physics side of things

Semiclassical

it does depend on teh scope of the course, mind

Phase

Oh crap i misused the term

Ocelot please spare me

I meant mathematical side of physics

0celo7

🔫🔫🔫

Phase

3:23 PM

atm it's very... Definition and rote based.

Semiclassical

if you're doing a single semester undergrad QM course then it probably will fall outside the scope

Phase

wait what there are emojis

Balarka Sen

@0celo7 the ting goes skrrra, boom boom boom, kka pak pak boom

Phase

Old

Old memes are punishable by ridicule

[points]

Semiclassical

the trouble is really that you only need the path integral formulation when you want to go into QFT

Balarka Sen

3:24 PM

@Phase You want me to quote Pink Season?

Phase

I just like learning things for the sake of it

Semiclassical

for undergrad QM you usually don't, so it's not a high priority

0celo7

@Semiclassical not really

Just do Schwinger

Phase

@BalarkaSen $_{Sure \space you \space don't \space wanna \space quote \space the \space older \space album?}$

0celo7

Weinberg gets very far without path integrals. Not sure how gauge theory works without it tho

Balarka Sen

3:26 PM

@Phase Pink Guy is also a great album

Phase

I have a gun is probably my favourite pink season song

Just because of how dumb it is

Semiclassical

"need" is probably too strong a word

but the motivation for the path integral method is its use in moving from QM to QFT

I mean, there's a reason we talk about the QED Lagrangian and not the QED Hamiltonian

Balarka Sen

I love Rice Balls 'cuz it's lit

Phase

edups diss track XXX mashup is surprisingly good

Balarka Sen

lol

Phase

3:30 PM

have you heard it?

0celo7

@Semiclassical Weinberg does QED with hamtiltonians :)

Balarka Sen

yes

Semiclassical

:S

Phase

Damn

Did you see Dan Bull's rap roast on edups?

0celo7

You know maybe if you memed less you'd understand topoi

Balarka Sen

3:32 PM

@Phase Absolutely. Idubbbz tweeted it up

I love it

Semiclassical

ew topoi

Phase

@BalarkaSen I don't own Tweetor

@0celo7 what's a topoi

Balarka Sen

me neither

i look at these guys to catch up with meme trends

Phase

I have FB but I mostly just use that to... Torture myself with flat earthers..

Semiclassical

the most pretentious reference to topoi i've ever seen was in a music theory paper, amusingly enough

0celo7

3:34 PM

There's a book like "topoi of music"

It's 800 pages of algebraic geometry and topoi

Semiclassical

Yeah, and that was the context

Phase

btw for vector bundles

Semiclassical

Mazzola wrote a book arguing that topoi theory was necessary to do music theory

Phase

Is there something that functions like a metric? I.e. something that coupled with a set of points $X$ generates the vector bundles at those points?

Semiclassical

so for instance Dmitri Tymoczko responded to that book with this article: dmitri.mycpanel.princeton.edu/files/publications/mazzola.pdf

opening paragraph is relevant: "For an American music theorist, Guerino Mazzola’s The Topos of Music (henceforth Topos) can be a forbidding book: dense, intricately systematic, and more complex in its mathematics than the writings of Allen Forte, John Clough, or David Lewin.
And where American theorists can be somewhat apologetic in their invocations of advanced mathematics, offering simplified tutorials for untrained readers, Mazzola can seem almost aristocratic in his disdain for nonmathematicians. If you can’t learn algebraic geometry, he sometimes seems to be saying, then you have no bu…

Phase

3:37 PM

Wow

Semiclassical

had to split it up to have it in one message

now, Mazzola wrote a response to that

Phase

To be fair you have to have a high IQ to understand Mozart

without a deep knowledge of theoretical physics a lot of the jokes will go over the listeners head

Semiclassical

here: encyclospace.org/special/answer_to_tymoczko.pdf

and again the opening paragraph or so is relevant

>>Once a writer was asked for the population of Mexico City by a German citizen. When the writer answered “it is about 6 million people, a million more, a million less”, his interlocutor replied “But a million is about the population of my hometown!”. Perhaps as our German friend, we could wish to know the aforementioned figure down to every single individual, but determining this number is an extremely complex labor. For some purposes, it is good enough to count with some approximation, but for many others we need more powerful mathematical tools in order to refine our knowledge.

sorry for the lenght of that

and right there is the most pretentious use of topoi theory I've ever seen

equating “If you cannot learn algebraic geometry [...], then you have no business trying to understand Mozart” to “If you cannot learn probability and statistics, then you have no business trying to count the population of a city.”

bolbteppa

At least it's been done

Semiclassical

is just hilarious in its incongruity

bolbteppa

3:42 PM

Imagine a world where algebraic geometry did not apply to music :o

The most ridiculous thing I've seen is point set topology applied to psychology

Phase

Imagine a world where pure maths applied to real life

$_{bait}$

Semiclassical

to act as though the connection between AG and Mozart is as obvious/compelling as between prob & stats and population count

is just laughable to me

Phase

When they say that Newtonian Mechanics is affine

bolbteppa

Wish Mozart wrote his AG down in book form without all the music symbols

Phase

Do they just mean that for instance things like velocity is additive according to galilean invariance

bolbteppa

3:45 PM

Velocity vector need not always be at the origin, hence affine

Phase

Yeah

Ty

0celo7

@Phase once you pick an origin you've got a vector space.

Phase

Im surprised I've never heard the term affine before

Semiclassical

it's a fine term

Phase

...

ACuriousMind

3:45 PM

@Phase They just mean that there is no god-given choice of origin, so an affine space faithfully represents our freedom to choose the origin.

Phase

@ACuriousMind yeah, in Newtonian mechanics that comes from the notion of Galilean invariance though right?

and then in SR it comes from the postulates

John Rennie

In SR it comes from Lorentz invriance

Slereah

Poicaré invariance*

ACuriousMind

@Phase Uh. Galilean invariance entails, among other things, that physics remains unchanged under translations. It's just another name for "we're free to choose the origin" in that respect.

Phase

Yeah

I was just checking that my statement was equivalent

and that I wasn't misunderstanding

ACuriousMind

3:48 PM

So saying "the freedom to choose the origin comes from Galilean invariance" is pretty much tautological

Phase

yeah ik I was just trying to check if I was right :c

Semiclassical

"comes from"->"basically is"

John Rennie

@Phase Handlebar moustache emoticon?

ACuriousMind

I think it's just an exceptionally sad :(

Phase

Idd

There's an emoji for exceptionally sad and exceptionally frustrated

for sad it's :c

for frustrated, the more spaces between the colon and the up arrow in ": ^)" the more the frustration

$: \space \space \space \space \space \space \space \space $^)

damn SE prevents it.

Balarka Sen

3:50 PM

..c

John Rennie

:         ^)

Semiclassical

:c

Phase

John did you do the same as me? Just copy paste \space multiple times? : p

John Rennie

No. Put four spaces first and it switches to fixed font

Fixed font

Fixed                      font

Phase

fixed

Whoa weird.

I assume this is for sharing code then

John Rennie

3:53 PM

Useful if you feel the urge for writing ASCII art :-)

Balarka Sen

I think the same happens if you do shift+enter

fixed

fixed font

yep

a fixed font button appears

Semiclassical

huh

 code line 1
 code line 2

so that's how i can get code to show up in multiple lines

i've tried using "`" for that before, but it has problems with multiple lines

John Rennie

Bohmian mechanics and code formatting in a single day!!! :-)

Phase

god damn it.

Slereah

Oh bloody hell

another LED fried

it actually smells burnt

0celo7

3:56 PM

@Semiclassical whoaaaaa

How do do that

Phase

4 spaces

Semiclassical

________
| o | o|
|  ..> |
| ____ |
| |  | |
|______|

Phase

Balarka Sen

posts the infinite centipede emoji art

0celo7

It will take my Fortran game to a whole nother level

Semiclassical

3:57 PM

there we go

Phase

You stole my son

You will pay

0celo7

Test

Phase

$test$

makes sense

was just curious how the web script worked with it

Semiclassical

geeeeeeeet dunked on

Balarka Sen

+1

Phase

3:58 PM

if dunked:
    print(":c")

huh.

I need to add 8 spaces for embedding

and tab doesnt work either

that could be tedious

Balarka Sen

now I have got that sick boss fight tune stuck in my head again

Semiclassical

lolyes

Balarka Sen

dudud dum dum du du du dudu

Phase

dudududu dudududu dudududududududududududu

Balarka Sen

This ain't Darude Sandstorm

Phase

4:00 PM

Ok i'm memed out im gonna play witcher, thanks for answering my questions chums

maybe not for you @BalarkaSen

But for some of us every day is dead meme day

Balarka Sen

@Semiclassical Sick minecraft cover

Phase

hang on before I go

question

I get that energy is poorly defined a lot of the time in GR, but energy can be defined sometimes, and the concensus is that not conserved right? And this is a consequence of Noether's theorem not applying to time. Can energy be gained?

I dont wanna sound like a crank tho

0celo7

@Phase The ADM energy is conserved when it is defined

John Rennie

Energy is conserved if the action is unaffected by displacing the system in time.

Phase

But i thought for GR as the metric isn't flat, displacing the system in time means that you'll end up with different action

John Rennie

4:08 PM

In some, but not all, spacetimes the action is changed by a shifting in time so energy is not conserved. The expanding universe is the obvious example.

Phase

spooky

anyway im gonna go play the Witcher DLCs, thanks for answering that last question

John Rennie

@Phase as an example, the Schwarzschild metric is static i.e. time independent. So shifting in time makes no difference.

Semiclassical

to me the point is really that energy is not generically meaningful in GR

that doesn't mean there aren't cases where it becomes meaningful, to be sure

0celo7

@Semiclassical I invite you to read Christodoulou's book

Semiclassical

yeah, uh

0celo7

4:10 PM

Take some heroin and get ready for the buuuuundles

Semiclassical

no way

i got 99 problems but a bundle aint one

theDoctor

4:31 PM

@JohnRennie: It is my opinion that the universe is scale free. So, then, the scale of particle physics is a convenience for humans, not a particular order in the universe.

Bernardo Meurer

@0celo7 @ACuriousMind Tarski uses $\forall$ upside down and $\exists$ mirrored

John Rennie

@theDoctor you are of course free to hold whatever opinions you choose

Balarka Sen

@BernardoMeurer Ugh

John Rennie

In fact particle physics does become scale free at a high enough energy. Specifically this happens when particles are massless or their masses are insignificant compared to their energies.

This is known as conformal symmetry.

theDoctor

"Scale-free": the application of relativity and the lack of an absolute reference frame implies that ideas such as "planch length" and even the notion of the atom may be inapplicable in some domains.

Bernardo Meurer

4:34 PM

I mean, why?!

theDoctor

interesting

Balarka Sen

@Bernardo What are you reading

theDoctor

i think energies should not be in the equation to notice this.

masslessness maybe

i mean masslessness is probably a prerequisite.

Bernardo Meurer

a.co/0zuCGd5

@BalarkaSen His intro to Logic ^

theDoctor

it is us, of couse, who apply the scale onto perception.

Balarka Sen

4:35 PM

ah

theDoctor

course

Bernardo Meurer

I think it's just old notation

Balarka Sen

I don't know much about mathematical logic. Maybe you should learn and teach me

John Rennie

@theDoctor: most of us hereabouts are physicists (or their poor relation mathematicians) who work with physics all the time and are used to physical reasoning. We tend not to be easily impressed by vague statements.

theDoctor

otherwise a particle is a phenomen occuring in an otherwise n-dimensional space with no relation to distance of other particles except through entanglements.

0celo7

4:36 PM

@BalarkaSen why do you want to know?

Balarka Sen

'cuz it's cool

theDoctor

i understand, yet models of physics start with vague ideas, yes?

i think for example, that the bias for neat equations has biased the understanding of reality, such that if the universe WERE actually scale-free, you wouldn't know it, because you couldn't encode it in an equation with physical units.

ACuriousMind

@theDoctor Not in the last 200 years or so, no.

Bernardo Meurer

@BalarkaSen I got a couple books on it yesterday. Tarski and this one:

amazon.com/gp/product/0486425339/…

theDoctor

@ACuriousMind: even einstein started with a vague idea -- it was just so radical he had to develop the formalisms himself

Balarka Sen

4:40 PM

@Bernardo Sweet

theDoctor

but isn't science, by its nature, collaborative? I mean equations impress students, but

Balarka Sen

I once wrote up a bunch of nonsense on the Godel's theorem

ACuriousMind

@theDoctor Tell that to Poincaré and Minkowski. Or Hilbert. You should read up on the relativity priority debate before making grandstanding claims.

Bernardo Meurer

@BalarkaSen I'm aiming to try and really understand consistency, completeness and so on

0celo7

@ACuriousMind to be fair GR was only Einstein. He showed notes to Hilbert who stole the idea.

Einstein had a fully developed theory independently of Hilbert, but Hilbert came up with the action before Einstein.

theDoctor

4:42 PM

IT's not a grandstanding claim at all. It is the orthodoxy which has the burden of explaining why there should be a preferntial order to the universe. A scale-free system is prior to such.

I understand the respect to physics history, but the universe doesn't conform to physicists.

John Rennie

@0celo7 that's not really true. Other people also had the idea that gravity might eb a metric theory. Nordstrom for example.

0celo7

@JohnRennie did they communicate?

John Rennie

@0celo7 yes

0celo7

proof?

John Rennie

Nordström's theory of gravitation

In theoretical physics, Nordström's theory of gravitation was a predecessor of general relativity. Strictly speaking, there were actually two distinct theories proposed by the Finnish theoretical physicist Gunnar Nordström, in 1912 and 1913 respectively. The first was quickly dismissed, but the second became the first known example of a metric theory of gravitation, in which the effects of gravitation are treated entirely in terms of the geometry of a curved spacetime. Neither of Nordström's theories are in agreement with observation and experiment. Nonetheless, the first remains of interest insofar...

bolbteppa

4:48 PM

Einstein apparently had (most of?) the right answer in 1912 but thought it was wrong for 3 years

theDoctor

I'm an information theory person. It is abnormally improbable to have a scale like atomic physics suggests.

0celo7

@bolbteppa yeah because GR violates Mach's principle which was holy at the time

lılostafa

GR has no direct applications at all, right? Imagine we didn't have GR. Is there any useful (with real-life applications) physical theory X that its development was (indirectly) dependent on GR, so that if there was no GR, there was no theory X?

0celo7

It's unclear if GR has applications

theDoctor

GR is related to a scale-free system, so that implies there could be applications.

0celo7

4:51 PM

what?

lılostafa

@0celo7 If you mean GPS, it suffices to know that GPS can work without GR

bolbteppa

Not sure about that, contentious issue

What about black holes, cosmology, corrections to Kepler problem, perihelion, abbheration etc

0celo7

those are not applications as of 2017

theDoctor

..will try to explain under the context of you orthodoxonauts.

first need to work out the relationship between a scale-free system and an n-dimensional space.

i believe they imply each other

Balarka Sen

i.stack.imgur.com/vUSph.jpg?s=328&g=1

theDoctor

4:55 PM

as if there are n-dimensions and no priveleged dimensions, then there is no basis in which to anchor a scale of atoms upwards to the cosmos.

bolbteppa

@theDoctor you mean conformality

0celo7

The Einstein equations are not conformally invariant...

theDoctor

possibly @bolbteppa. Thank you for anchoring my thinking to the language used by the orthodoxy.

conformal: is there a nice, succinct definition?

bolbteppa

@theDoctor have you read any GR textbooks?

John Rennie

Conformal symmetry

In mathematical physics, the conformal symmetry of spacetime is expressed by an extension of the Poincaré group. The extension includes special conformal transformations and dilations. In three spatial plus one time dimensions, conformal symmetry has 15 degrees of freedom: ten for the Poincaré group, four for special conformal transformations, and one for a dilation. Harry Bateman and Ebenezer Cunningham were the first to study the conformal symmetry of Maxwell's equations. They called a generic expression of conformal symmetry a spherical wave transformation. == Generators == The conformal group...

theDoctor

4:56 PM

i've only read biolgraphies of Einstein

and several informal presentations of GR, SR

bolbteppa

@theDoctor why ignore the books which explain the actual details?

John Rennie

@theDoctor And that qualifies you to scorn us as orthodoxonauts?

ACuriousMind

Everytime I hear the word "orthodoxy" applied to mainstream physics, I can't help but think its original meaning fits perfectly: Belief in that which is correct.

theDoctor

I ignore them, with all due respect, because there is an unacknowledged ASSUMPTION in them all.

@ACuriousMind: lol

Balarka Sen

"I have seen the movie Interstellar, I know everything about GR"

John Rennie

4:58 PM

And yet they work i.e. they correctly predict the results of experiments.
Funny that ...

bolbteppa

@theDoctor what is the assumption

@theDoctor at least you admit you purposely ignore the books which actually explain the logic of the subject and conceded you do not understand it in advance

theDoctor

It is totally unacceptible, except to those perhaps in the Middle Ages, to assume a preference of scale.

I think this comes after understanding the dual nature of light.

John Rennie

And yet that is what experiment tells us is the case

bolbteppa

@theDoctor what is the preference for scale, what does that mean?

John Rennie

@theDoctor And light doesn't have a dual nature

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