The h Bar

12:32 AM

sciencedaily.com/releases/2016/07/160718133218.htm

Prepare an ensemble of identically prepared photon pair states, measure thrm to get interference information. Group all of them together to get the hologram formed by the wavefunction of a single photon

Will read the paper in more detail to see how they carry this out

Secret

[Something else about inteepretarions] We define the wavefunction as something that contains all the information we can learn about the quantum state. After reading the PSE answers about probability in quantum

mechanics, I am tempted to think that a hermitian operator $\hat{M }$ kind of filter out the probability amplitude that corresponds to the information of the observable $m$ only, which then, when the overlap of that with the wavefunction is computed via the inner product $\langle \psi \lvert \hat{M} \rvert \psi \rangle$

with give the sum of all values of $m$ weighted by the amplitude squared (i.e probability), thus giving the expectation value as expected. However there is an obvious question to ask. We knew that

while there are a lot of observables are noncommutative, there are some that are. This means there exists some state $\lvert K \rangle such that it is both an eigenvector of two observables $\hat{A}, \hat{B}$. Then

the interpretation of hermitian operators "filtering" out relevant information from the wavefunction will be challenging in this special case: Suppose I have the ket $\lvert K \rangle$, does it mean that it contains information of both $a$ and $b$...? In that case we cannot really say a hermitian operator $\hat{A}$ filter out information of $a$ only from the wavefunction, as the above ket also contains information of $b$

Perhaps one way to look at it is similar to the mathematical phenomenon of some equation of motion having multiple solutions at some positions in phase space, it might just happened that under a certain basis, the state vector that corresponds to some observable $a$ happened to have the same form as $b$

And since it is true for one basis, it is true for all bases as eigenvectors of linear operators are independent of basis. So maybe, if we insist on the filtering interpretation, there are actually two $\lvert K\rangle$ that look the same but contains diffetent information of the wavefunction that corresponds to the quantum state it started with. An

alternate way to think about this issue is that most filters are not perfect (because they are linear hermitian operators, there are only so many possible states they can act on and not give the same state vector), therefore when a hermitian operator $\hat{A}$ is trying to filter information of $a$ it is more common that the filtered result will contain information of, say, $b$. This will then explain noncommutativity

But even then, there is still an interpretational issue on that:

Sir Cumference

1:08 AM

@HDE226868 I give up.

@0celo7 Search for knowledge.

I've spoken with graduate students fluent in QM, yet they were giving the same definition for i that I originally gave.

They were just as surprised when I brought up the problems you showed me with the definition.

Secret

Because any state vector is linear, they can be linear combinations of other state vectors, which may contains eigenvectors corresponds to some hermitian operator. Then assuming we have the filtering information interpeetation above, we will need to deal with the issue of how can information of $a$ (say position) be added to information of $b$ (say spin projected at the z axis) to give information of a completely unrelated $c$ (say the mass of a particle)

If the above interpretation is the correct one (which I doubt it) it will imply information has a weird property that they are linear, they give different physical qualities when arranged in certain ways

and then, one may come to the conclusion that all the physical things like charge, momentum etc might be nothing but a result of different ways these information overlap with each other. And in the macroscopic scale, decoherence (may be one of thr things that) ensure we only ever observed one of the many, with some probability

Unless there's an experimental way to probe this interpretarion about information, I don't think the filtering interpretation I had make sense

Therefore, either information has such weird properties, or that the filtering interpretation is wrong, thus meaning that quantum probabilities and logic cannot simply be treated in the same way (with some modification such as linearity and superposition) of claasical probability in the notion of that propositions filter out relevant elements from the set (except that by definition it just happened that a vector space is a type of set)

Or put it more directly, quantum probabilities cannot be thought of as some form of venn diagram

0celo7

1:48 AM

Who do you think will read that?

skill patrol

2:02 AM

Shog9

Sir Cumference

2:12 AM

Okay I'm reading about degenerate gases and energy levels, so I need to know

Is energy discrete or continuous?

The whole "energy level" thing makes it sound discrete

depends

on?

your system

oh my god i'm tired

All right, say we're in a neutron star

0celo7

I know nothing about those

AFAIK they have no practical purpose

Sir Cumference

2:19 AM

Okay, give me an example of a system where energy is discrete

@0celo7 They're the epitome of awesomeness

0celo7

@SirCumference harmonic oscillator

Sir Cumference

Why is energy discrete there?

I'm not a physicist

What are you then?

doing homework

2:22 AM

Oh crud, I didn't realize I was talking to you

I didn't check the username...

@0celo7 Anyway, on the chat?

0celo7

you're dumb

Sir Cumference

Perhaps

right now i'm tired tho

You know, it's funny how many people say "Schrödinger's cat is an example of quantum mechanical effects"

When really it was made to ridicule QM

Schrödinger would be rolling in his grave

0celo7

It was made to ridicule an interpretation of QM

Sir Cumference

@0celo7 And yet people are talking about how great of an example it is for QM effects

Most of them think it was made to support that interpretation of QM

0celo7

Oh, but you're smarter than them, I see

Sir Cumference

2:35 AM

I just looked up the history

I feel like it got bastardized

0celo7

very clever

Sir Cumference

>_>

You're being sarcastic...stop being sarcastic...

0celo7

I don't know why you would thing I'm being sarcastic

Did you look up some dirty pictures yet

Sir Cumference

Yeah in other news

Here's a picture of a dog

0celo7

what about it

Sir Cumference

2:40 AM

It's the beauty of photoshop

0celo7

what

Sir Cumference

Do you not see the human smile?

0celo7

Sure, so?

My dog smiles

Sir Cumference

I hope not like that

0celo7

Exactly like that

Sir Cumference

2:42 AM

Jesus christ get it exorcized

0celo7

no

Sir Cumference

yes

0celo7

you're Jewish, what do you know about that

Sir Cumference

I know that face isn't holy

You're christian I assume, you should be worried

0celo7

Don't assume

Sir Cumference

2:44 AM

Okay religion do you believe in (if any)

0celo7

it makes an ass out of you and me, but mostly you.

Sir Cumference

You know what happens when you assume, you make a you out of ass and me

0celo7

@SirCumference I worship the Nine Divines.

Sir Cumference

@0celo7 Ok

I can't really respond to that

0celo7

Depends, do you support Talos?

Sir Cumference

2:45 AM

"Support"?

0celo7

Infidel!

Sir Cumference

Wat

At least you don't worship pokemon like half the people I know

You realize how many people are obsessed with Pokemon go?

0celo7

No.

I need to show that $L(f)\cdot L(g)=L(f\times g)$...

Sir Cumference

Well a pokemon appeared in Central park, there was a riot

Pokemon Go - Vaporeon stampede Central Park, NYC

►

0celo7

never heard of "Pokemon"

Sir Cumference

2:47 AM

Wallets stolen, people stabbed

@0celo7 That's a rock worth living under

0celo7

It's called having a job

Sir Cumference

I don't see why that means you've never heard of pokemon

0celo7

Me neither

Sir Cumference

Right...

You see the wikipedia vandalism that google cached?

This here is why I don't trust Wikipedia

0celo7

There's a Vaporeon near me

By the university gym

Sir Cumference

2:51 AM

Nice knowing you

Prepare for a stampede

0celo7

People in the south are civilized

Unlike the ghetto north

HAH

Sir Cumference

@0celo7 History says otherwise >_>

skill patrol

Excuse me? <_<

0celo7

Solved the problem

Sir Cumference

With lotsa blood...

Speaking of which, I'd get out of there if there's a vaporeon

0celo7

2:54 AM

@SirCumference The North started the war

Sir Cumference

You wanna go?

breaks wine bottle

bleeds to death

0celo7

oh please

skill patrol

:runs:

0celo7

I have German warrior blood

also American weapon fondness

skill patrol

Says you.

0celo7

2:57 AM

which part do you doubt

skill patrol

as he rus...

0celo7

what

lucas

I hope (wish) you are not a German.

0celo7

@lucas based on your behavior, the feeling is mutual

assuming that means I might be related to you

user218912

3:18 AM

lolwut roger penrose authored a book with deepak chopra? amazon.com/Consciousness-Universe-Quantum-Physics-Evolution/dp/…

user218912

that's ridiculous

user218912

if you don't understand why that's retarded watch this youtube.com/watch?v=tZXewVWUKAM

user218912

"consciousness is defined as a superposition of possibilities"

Secret

en.m.wikipedia.org/wiki/Spinor

0celo7

Penrose is insane @3750

Secret

3:24 AM

I wonder, if spinors are a linear way to track the topologies of special orthogonal groups...?

user218912

@0celo7 how do you know?

Secret

given their path dependence that depends on only two nonequivalent rotational classes

0celo7

@3750 he's gone into old physicist mode

Secret

which is related to the topology of the rotational group being not simply connected (i need to check whether SO(n) is also mot simply connected later...)

0celo7

SO(n) is not simply connected for $n>2$.

Secret

3:46 AM

Ok, so it seems we are fine (for now)

> Lorentz transformations include 3-dimensional rotations as well as boosts. A boost transfers to a frame of reference with a different velocity, and is mathematically like a rotation into time.

(the above quoted block of text is unrelated to the spin discussion)

I wonder, since lorentz boost mathematically act like a rotation in spacetime, surely there is a way to measure the rapidity, maybe it is tan (v)...?

We can directly see a rotational angle (by measuring how much something is spatially displaced by a rotation). Do similar notions for direct measurement of rapidity exist...?

> Additionally, the assumption (known as microcausality) that spacelike separated fields either commute or anticommute can be made only for relativistic theories with a time direction.

Might need to ask Acuriousmind later on why microcausality means spacelike separated fields can only be of the form $[/phi_1, /phi_2]=/pm 1$

Obliv

4:06 AM

@0celo7 do you study all day or something?

0celo7

@Oblivno

John Rennie

5:18 AM

Ah, erm, yes, my latest badge. Erm, perhaps I shouldn't be too proud of this one :-)

physics.stackexchange.com/help/badges/1332/…

skill patrol

Congrats, I guess.

:-)

Are you the first? @JohnRennie

John Rennie

Yes, though I'm not boasting about it. The (gold) badge of shame :-)

Secret

5:57 AM

en.m.wikipedia.org/wiki/Spin_(physics) I might need to revise again why spin of a particle is always aligned with magnetic moment of a particle

Also if spin basically describe the topology of SO(n) and in 3+1 spacetime, lorentz invariance result in spacelike separated field operators to tranform in a symmetric or antisymmetric way, then how is one of the two classes of action of SO(3) being assigned to what field operator.

KNP

@0celo7 what's wrong with it?

Secret

For example, why do field operators that creates something with lepton number 1, charge -1, $mass m_e$ (i.e. Electron) will have a SO(3) topology that is of the class that corresponds to "rotations by 4$\pi$"...?

I might get my answer when I revise how the value of spin of particles are calculated, such as the Higgs, the photon etc.

skill patrol

6:35 AM

Hi @JohnDuffield

John Duffield

@Skill patrol: hi. I thought I'd look in while I wait for the wife to bring me my morning cup of tea.

Ah, here it is. I am English you know.

skill patrol

Yes, I know :-)

What kind of tea? @JohnDuffield

John Duffield

Not as obviously English as some. You won't be getting too many toodle pips from me.

@skillpatrol : Tetley!

skill patrol

Golly good :D

Enjoy your Tetley.

Hi @lucas

lucas

Hi

Nice day!

@skillpatrol

John Duffield

6:44 AM

@skillpatrol : would you believe it, I have to go already.

skill patrol

:-)

user116211

23

A: Mathematician trying to learn string theory

Many string theorists would like to know more algebraic geometry. There are a few of us who know algebraic geometry at a pretty high level (not me) but many more who would like to learn more and feel it would help with their research but find the literature very difficult. I think the optimal sol...

user116211

I think the optimal solution would be to find such a string theorist and agree that you will teach them algebraic geometry if they will teach you string theory.

user116211

7:22 AM

Holy Lord!

user116211

Bourbaki did write a treatise on Algebraic Geometry!!

user116211

90

A: Did Bourbaki write a text on algebraic geometry?

Wrong! Here is Bourbaki document on algebraic geometry, taken from the now available Master's Archives: click on Autres rédactions, then on Chap.I Théorie globale élémentaire (91 p.) This preliminary draft was apparently written (according to a penciled annotation on the first page) for Bourb...

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