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5:22 AM

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robjohn ♦, West Hills, CA

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Acuriousmind is not the true mean squared

Note the number of down-votes^

user54412

5:56 AM

@IsaacMoses You're a new face around here

user54412

(though I've seen you around the network)

I hope I didn't offend you @ChrisWhite with any of my dumb questions :-)

user54412

Sep 1 '15 at 22:25, by Danu

@ChrisWhite You aren't invested enough in the opinion of the people in this chat ;)

So you invest your opinion of people the fashion way, they have to earn it :P

7:37 AM

*old fashion

:-/

7:50 AM

@CuriousOne Please consider avoiding strident remarks about what physics is, what physicists think, and how quantum mechanics works. Such strong comments put yourself at risk of giving hapless readers incorrect impressions if the statement is incorrect. Softer language would lessen this risk, without compromising the content of your posts.

@DavidZ Please clean up chatty comments here.

@CuriousOne Hi.

Density matrices don't give you Born.

Density matrices plus decoherence give you a diagonal density matrix, full stop.

What those diagonal elements mean is by definition the Born rule!

You can't derive it.

What science is is well defined. I am constantly surprised how many physicists don't seem to be able to apply the definition. Maybe we need to teach it better?

@CuriousOne Stick to the point. I know that's hard for you, but let's get through the Born rule first, ok?

I didn't say that one could derive it.

> The density matrix formalism explains the Born rule

I am simply saying that the Born rule is explained completely by the density matrix and the proper treatment of measurements.

7:57 AM

What did you mean by that?

Are you @CuriousOne a science teacher?

If we let science teachers define science we would be in really bad shape. :-)

:-)

@CuriousOne That sentence is nonsense.

What is?

7:58 AM

As in, it contains no information.

What does not contain information?

I'm using the chat room's feature in which my comments are linked to yours. Please mouse over my comments to understand the links.

Unless you're on mobile :(

I am not using the advances features of the interface, yet... sorry.

@CuriousOne It's not advanced. You click on the little arrow on the right of a message and then the next message you send is marked as a response.

Mousing over my comments is definitely not advanced :)

8:00 AM

I am an old guy... this is actually posted on a desktop. Can you believe that? :-)

Sure. Desktops are nice.

Anyway...

Let's get back to the physics. What, if I may ask, is so problematic about the Born rule in the first place?

@CuriousOne Nothing. Nobody said there was a problem.

You said:

> The density matrix formalism explains the Born rule

I claim that is false.

Maybe you have a higher level of explanation in mind than I do?

To me "explain" means "make obvious that it's a necessary result of other statements which are taken as given".

Does "explain" mean "stipulate" to you?

8:04 AM

I am neither a native English speaker nor a lawyer. I have no idea what you mean by that differentiation.

The ontology of a theory is only "obvious" trough the experiments that define it.

@CuriousOne That could be a problem :)

A theory doesn't pull itself out of the swamp at its own bootlegs, if that is what you mean.

@CuriousOne Of course not.

Then I don't understand what "make obvious" is supposed to mean.

We measured a bunch of stuff and figured out that quantum mechanics is a good way to cohesively describe those measurements.

@CuriousOne Suppose you ask me why it rains.

8:06 AM

That's no different from classical mechanics or any other theory.

I explain about evaporation and condensation. Now it's obvious to you why it rains.

I explained rain.

On the other hand, if you ask, "why do charges push against each other" and I answer "because charges push against each other', then I didn't explain anything.

We don't know why it "quantum-mechanics".

@CuriousOne Certainly not. In light of that statement please justify your statement that

> The density matrix formalism explains the Born rule

Neither is that related in any way shape or form to interpretations.

@CuriousOne Well I disagree with that but that's not the topic right now.

8:08 AM

OK... but you do agree that we don't have a microscopic theory of quantum mechanics?

Do you also agree that a theory does not have to supply its microscopic theory out of itself? We don't expect that from any theory.

@CuriousOne I'm not 100% sure what you mean by "microscopic". Do you mean "lower level theory"?

We do not have an explanation why the world is quantum mechanic rather than something else.

Correct.

What if I ask "Why do we take measurements?" :-)

@CuriousOne Yes, quantum mechanics sits at the "bottom" of the stack, at the present time.

8:10 AM

We do not expect to generate that explanation within the theory itself, right?

@CuriousOne Certainly not.

@guest Then I say "because it's fun".

We do expect to understand why measurements of classical expectation values take a certain form, right?

@CuriousOne Well, if by "understand" you mean "provide a theory for", then yes.

Does decoherence and the density matrix approach allow us to do that?

@CuriousOne Nope. They get close, but you have to add the Born rule as an extra ingredient.

8:12 AM

If it does, is quantum mechanics self-contained?

@CuriousOne Actually, in my opinion, no, it is not. It ignores an important and vexing question to which I already linked you in the comments of the post that sent us here.

What's the vexing question?

@CuriousOne I guess you didn't follow the link?

Suppose I have a physics experiment in my lab (which I do in fact have, so this is not a fairy tail thought experiment).

OK.

I go in there and I make a quantum state (which I am actually doing right now as we talk about this).

(my data is rather interesting this evening!)

Now, I measure my system and I get a result.

8:14 AM

Yes?

We say the wave function collapsed or some such thing. Perhaps you prefer to say that the density matrix for that subsystem diagonalized because of decoherence.

I never talk nonsense like that. :-)

Uhhh, didn't you say that not five minutes ago?

I am always thinking about what actually happened.

How would you describe it?

@CuriousOne Oh well that's admirable. What really happened?

Please enlighten me.

8:16 AM

I would describe it with the experiment that I did and I would be looking for irreversible changes in the system and the environment.

I have no idea what you mean by that.

By that I mean that I am always looking at the physics of my experiment and not some theoreticians mathematical ideas about it.

Ok, suppose I run an experiment according to Bell's prescription.

So what happens in your experiment that is so strange?

I don't care about Bell and philosophy.

I come out with a number which, according to Bell's argument, cannot exceed 2 in classical physics.

I find the value greater than 2.

Now what should I do?

I have now done an experiment which I cannot explain with classical physics. I have to use quantum, right?

8:18 AM

Assume that classical physics is the wrong description of your experiment or look for the bug. :-)

Ok, so we assume classical is wrong and invent quantum, ok?

I don't have to assume that classical is wrong. That was known many decades before Bell was even born.

@CuriousOne Please don't be difficult.

Fine whatever, quantum already exists.

Yes.

What do we mean by "quantum mechanics" if not the mathematical theory and the pile of experimental evidence supporting it?

8:20 AM

Reality.

We mean one particular approximation of reality... that's what we always mean.

ok...

So what's the problem with your experiment?

In doing my experiments I get the distinct impression that when I measure my system, it suffers changes that cannot be explained with Schrodinger's equation.

Do you agree?

1) Schroedinger's equation is not the entire description 2) Schroedinger's equation is not even a good equation.

So what's the problem... that a toy model has problems?

Let me revise.

8:24 AM

OK

3) are you using a cat :P

I find that density matrices plus decoherence plus whatever equation of motion you like still do not recover my observed data.

OK. What else do you need?

I need the Born rule.

Meaning what?

8:26 AM

Meaning the following:

I have a way of computing the density matrix for my system, including the bazillions of environmental degrees of freedom surrounding the little bitty well-controlled quantum part. I find that when I turn on the measurement-o-meter, the density matrix ought to become diagonal in a certain basis. From doing many experiments, I discover that these diagonal elements represent the probabilities of my measurements (that's part A of the Born rule).

OK...

Additionally, after the measurement, the system's state has changed to be in whatever classical state I measured it to be in.

Not really, but even if that was so... what would be the problem with that?

Decoherence gave me a diagonal density matrix, but measurement by me made the system "collapse" (dumb word but we're stuck with it) into a single state.

Yes, the collapse is a dumb word for something that never happened. So?

8:29 AM

@CuriousOne The problem is that if you put me and my lab into a box, you might think that everything going on ought to follow some unitary equations of motion, right?

Without doing measurements you expect me to behave like any other quantum system.

I didn't even think that when I didn't know about the density matrix, yet.

@CuriousOne No idea what you mean.

I mean that I never had that kind of detailed imagination.

@CuriousOne Well I do, and it's why I say that traditional quantum mechanics ignores a vexing problem.

I do not expect "you" to behave like a spin system. You aren't a spin system. You are almost completely classical.

8:31 AM

Oye gevalt.

Seriously... there is no 180 degree pulse that makes Daniel walk backwards and get younger...

I would also like to point out that what happens in "boxes" actually depends on the size of the boxes. It already does so in classical mechanics.

Gedankenexperiments with boxes are deceptively simple until one actually thinks about the details, which Schroedinger's cat, for instance, does not.

@CuriousOne Would you agree that it is part of the program of physics to understand how to describe that changing behavior with a single unified picture of reality?

Let's get back to what you are trying to say...

No, that was never part of the program and physics was never taught that way in my university.

@CuriousOne That's absurd.

It's absurd to think otherwise.

Newtonian physics is not a dead art just because we have quantum mechanics now...

It's just as good today as it was 300+ years ago.

8:35 AM

You don't think physics should try to understand how Natural phenomena depend on the size of the box?

Who is teaching otherwise?

I never said to throw out Newton.

Physics does that, Schroedinger's car doesn't.

However, should not the "lower level" story recover the "higher level" one?

The failure of Schroedinger's cat is not a failure of physics, if that's what you mean. It was a bad idea by Schroedinger, that's all.

8:36 AM

I have no idea what you mean by that.

You seem to now be saying that microscopic theories don't need to explain the macroscopic ones.

The lower level story does recover the higher level one... IF one does it right. Schroedinger's cat doesn't do it right.

I guess they don't have to in order to be useful...

I am saying that a Gedankenexperiment is not automatically good because it has a big name attached to it.

YOU brought up Schrodinger's cat. Why do you keep injecting examples and then arguing against yourself?

That is incredibly annoying.

@CuriousOne Nobody said it did.

Stop arguing with yourself, it's boring for the spectators.

You were talking about a box... can we get back to that? Assuming it's not Schroedinger' cat now?

8:38 AM

Yes, I was talking about a box.

OK. How big is your box?

Schrodinger's cat in a box

What are the boundary conditions on a cat

Standing cat wave

@CuriousOne Well, I don't suppose you remember the example with three qubits we went through some time ago, do you?

That's a very small box, indeed. :-)

yup

8:39 AM

OK... what happens in that small box?

Wait I can find more puns

The Klein paradox is... at the boundary... cats and anticats are produced!

There we go

:-)

@CuriousOne Microwaves go in, microwaves come out.

You know I don't actually know how to solve particle in a box for Klein Gordon

OK... now the box has become much bigger. It's the size of a microwave oven. :-)

8:40 AM

It's one of those things that's never in books

I just am vaguely aware that it is somewhat complicated

@Slereah: We are not holding it against you.

Good night, everyone.

@DanielSank: Oh, come on... we are having fun here. Nature doesn't care! Remember?

@CuriousOne It's late and I have to work tomorrow.

@DanielSank: Fair. Have a good night and all the best for your experiments. I mean it!

8:45 AM

Thanks.

Have a nice evening.

user116211

@DanielSank: From me too! Good night!! LIGO is waiting :)

LIGO! LIGO LIGO! :-)

user116211

@CuriousOne: To you too ;P

Or is it LI-GO! LI-GO! LI-GO! ?

Good night everyone.

user116211

@CuriousOne: LI-GO dreams ;P

8:51 AM

I will let the gravitational waves rock me to sleep...

user116211

Some revolution is waiting, I guess !

Or just another "It's just as we expected..." result. My money is on that, but I take the revolution... if it comes.

I believe the nature of "the vexing question" allows for that possibility.

One man's "vexing question" is another man's past folly. Been there, done that...

At least LIGO is real science.

9:07 AM

Indeed, in the sense of learning how to solve every problem that has been solved.

It sure took them a while... that's a tough experiment.

Let's hope nature will give them a reward.

...and not throw the dice where they cannot be seen.

Yeah, the non-existing dice thrower behind the non-existing curtain keeps driving some people to really poor thinking while they are trying to pull the curtain away.

Perhaps the internet will help in some way.

It made it worse. There has never been so much bad thinking around... or maybe it wasn't so obvious... :-)

9:19 AM

It's still relatively "early" in the game.

They say nature has been playing it for 13.8 billion years without us...

Seems like she can manage without any thinking...

All very deep questions.

That's why it's wise to install a cover over deep wells... otherwise the kids tend to drown in them.

user116211

Well, can anyone tell me why $\partial E$ is included while writing the multiplicity function $\Gamma (E, \partial E)$? What's the meaning of that?

That's too deep for me, I am afraid.

9:38 AM

At the very least, put a warning sign over them.

Zeno's paradox would be a good example of this.

A paradox is when a wise man over-thinks, jumps into a well he dug himself and not so wise men follow him down the well.

Yup, that's one way of looking at it.

Q: What can be the way of the light

Another way is by stuffing a dead cat into a box to scare the children.

sytolk

12:30 PM

0

All we know that from the Sun to the Earth is comming light. But what can be the motion of the one particle of the light? Its have the source of the light Sun and opened eye on the finish of this motion. I think that this particle from the Sun have only two options: (One way ticket to the Eart...

visible-light

it seems that all my questions are unclear :)

北美館│物．理 The Way Things Go

12:54 PM

►

Physics in some sense is just sufficiently analysed magic that follow patterns and readily reproducible

Q: Book recommendations: On-topic, on-topic but community wiki, or off-topic?

1:29 PM

I realized we never made this official:

12

Yes, we've had this debate before. Unfortunately, there's no definite consensus to be found about their community wiki status: Good list, bad list (from July 2013) has the top voted answer (with a meager +11/-2) saying that book recommendation questions need to be actively moderated by the comm...

discussion policy books

Any objections before I do?

user116211

1:48 PM

Is Qmechanic dead?

Yes.

He was put in a box

With some cyanide

So he would be dead and alive now, I guess (jokes)

user116211

$$\lvert dead\rangle+\lvert alive\rangle$$

user116211

Who would measure it?

user116211

1:51 PM

Probably it collapses to....

Q: In praise of "... and links therein"

You forgot the normalization

Jeez

user116211

7

We've all seen them: short comments saying Related: http://physics.stackexchange.com/..., and links therein. Also, we've all seen bunches of useful links to closely-related questions on the Linked sidebar over on the right, which are a very useful way to navigate the site. Also, you know what...

discussion moderators users

user116211

That must be the elegy from EP to QMechanic :(

@user36790 just traveling

user116211

Or, he might be a member of LIGO ;P

1:54 PM

For anyone interested, there is a CERN webcast following the LIGO press conference

2

user116211

@DavidZ Oh! So, you know more of him ;/

@user36790 mods notify each other when we die :-P

(or are going to be away for a while)

@Secret $A/S$ would be the quotient. The "without" is the backslash $A\backslash S$.

I see

user116211

@DavidZ: I'm a theoretical physicist.

user116211

1:57 PM

Do we know more of him apart from he is from Europe?

@user36790 Don't be nosy, he obviously wants to remain anonymous.

I don't

user116211

BTW, how to quote something here?

Isaac Moses

@ChrisWhite Hi. I came in to see if I could detect evidence of excitement waves.

@user36790 start the line with >

user116211

1:59 PM

> I'm a theoretical physicist.

user116211

@DavidZ Got that.

@ Acuriousmind
As for the motivation of that algebra: It is me wondering about how similar are complex numbers to $\mathbb{R}^2$ vectors and thus I wrote that out as an experiment.

what I found is that in some sense they are not exactly the same, even if you consider the polar form, because attempt to treat those two properties (argument and modulus) as separate means it is necessary to suddenly have a continuum of absorbing elements appeared that is not found in $\mathbb{C}$ (The set $S$)

I tend to randomly construct number systems in my free time to wonder aand test about the properties of existing number systems

@Secret Of course $\mathbb{R}^2$ and $\mathbb{C}$ are the same, your $A$ just isn't $\mathbb{R}^2$, it is $\mathbb{R}^2$ with an infinitely duplicated origin due to the $(0,\theta)$. Your taking it out is just making it be $\mathbb{R}^2$, can you not see that?

OK well I can't stick around for the LIGO announcement, I have a plane to board :-(

in order to gain a better understanding

2:01 PM

save some physics for me

user116211

@DavidZ safe journey :)

Q: Difference between $\mathbb C$ and $\mathbb R^2$

I mean, I am demonstrating what happens if people just naively treat the two properties of complex numbers as independent variables, then they will end up with that infinitely duplicated origin

I am never aware of the difference between $\mathbb{C}$ and $\mathbb{R}^2$ (because if they are the same for all intent and purpose, we won't be given two names for it) until 3 days ago I stumbled upon this MSE answer

14

What are the basic differences between $\mathbb C$ and $\mathbb R^2$? The points in these two sets are written as ordered pairs, I mean the structure looks similar to me. So what is the reason to denote these two sets differently?

real-analysis abstract-algebra complex-analysis

and then I realise the imaginary part and real part are in some sense, not completely independent of each other when all the binary operators are considered

this is unlike the x and y axis in $\mathbb{R}^2$ if one have not defined a multiplication on it

@Secret No, that is not true. You end up with the duplicated origin if you insist on using polar coordinates for the point they are not made for

I see, well... I am kinda aware that the argument of the orign/the compelx nuumber 0 is undefined, but I kinda ignored it because I want to impose as little assumptions I have for the algebra experiments as possible in order to see all the possible results that will pop up, then fix them later

so you mean when defining/constructing some mathematical structures one has to be aware right away for these special cases and not just wrote down general things like "elements in $\mathbb{R}$" without thinking ahead what would the possible cases where you end up with "points you not made for" thus r…

2:16 PM

@Secret Uh...yes, if you write down something that is supposed to be "elements of $\mathbb{R}$", you better make sure its elements, well, are actually $\mathbb{R}$! What's the point in writing down something that is not what it is supposed to be?

And 0 is not "a special case". Use real and imaginary parts as your real coordinates and everything works fine.

ok I see, yes, the Cartesian case works fine

(clarification: I realise the complex numbers are not exactly the same thing as vectors in $\mathbb{R}^2$ in the most general sense not because from that algebra expeirment, but from reading in the MSE link that there's simply no notion of multiplying two vectors in $\mathbb{R}^2$. Specifically

$$i\cdot 1=i$$ but the analogous

$$\begin{pmatrix}1 \\ 0\end{pmatrix} \cdot begin{pmatrix}0 \\ 1\end{pmatrix}=\begin{pmatrix}0 \\ 0\end{pmatrix} \text{ or not defined for the usual \mathbb{R}^2 in high school textbooks}$$ thus making the x and y unit ve…

user54412

So, does anyone have an actual link for the press conference? Like it will be streamed live, right?

@ChrisWhite It says: "For press not based in the Washington, D.C. area, this event will be simulcast live online"...maybe only for "press"?

tpg2114

^ That was my impression also

grr LaTex is failing me in the above message. Need to revise how to build column vectors correctly

2:24 PM

@Secret The problem is the usage of \mathbb inside text.

user54412

Hmm, well we'll be having a viewing here, which sounded like there would be something to... watch.

tpg2114

Time to pretend to be a campus newpaper journalist for some secret media access?

I see

Anyway, $$i^2=-1$$ makes $\mathbb{C}$ behave differently than the usual $\mathbb{R}^2$ because it allows the imaginary and real parts to be transformed into each other, as the MSE link said/implied

This is why I said they are in some sense, not "independent", though not in the mathematical sense (probably?)

One of my algebra hobby is
1. Learn a new number system
2. Compute the cayley table for the interesting case
3. Delete or modify some of the given axioms
4. Watch how the Cayley table changes
5. Experimenting with messing around the axioms and see if it can produce a Cayley table with some kind of structure (e.g. symmetric wrt the first and second argument of the binary operator)
6. Look up google to see if the final result correspond to something known
7. Repeat step 1 with the new thing

Ultimately the final goal of this messing around is to define a mathematical object that acts like a function, but that its argument is a mathematical structure, and upon applying it. changes the axioms based on some rules

Then starting to wonder whether it can be generalise to something with the notion of "infinitesimally transforming the axioms of the mathematical structure" and deriving something simialr to a derivative that measrues how much the axioms are being changed

So basically, the notion of maps generalised to accpet arguments that are the axioms of a given mathematical structure

Q: Why is the detection of gravitational waves so significant?

2:40 PM

0

Since there is to be an announcement about this today, I was wondering what the significance was of detecting gravitational waves. I know it is another confirmation of GR, but I thought we had already confirmed GR beyond much doubt. What extra stuff would finding gravitational waves teach us? Is ...

gravitational-waves

> with no time-space cross terms in the metric). Gravitational waves, on the other hand, involve a time-varying spacetime

Time varying spacetime???

@Secret A "function" that sends a mathematical structure to another mathematical structure is called a functor (if it plays nice with the respective structures). "infinitesimally transforming" a structure is possibly known as deformation theory.

https://en.wikipedia.org/wiki/Functor
Wow, treading into category theory territory without realising...