The h Bar

12:11 AM

@0celo7 You need believers to be a god.

1:29 AM

@DanielSank So, Knuth, then?

I think that calls for the sacrifice of two chickens and a goat with a silver knife on a moonless night. Or a new and correct bug report on TeX or Metapost.

Secret

1:43 AM

in Mathematics, 6 mins ago, by Xander Henderson

the theory of fractal strings is related to the wave equation, which requires a Laplacian, which quickly gets you into the analysis of unbounded operators, which is basically where QM lives ;)

Secret

1:58 AM

Suppose this is a s-t vector field plot of some hypothetical two time physics s and t. Then for any frame of reference, seeing the laws of physics changing in a periodic manner is a necessary but not a sufficient condition to conclude that there is a closed path in the s-t- plane

(the other possibility is that the laws of physics just happens to change in a periodic manner along the non parallel direction of time)

In other words, for such two time physics model, CTCs will be even more weird because not only do a worldline will revisit itself some time in the past, the laws of physics will also change for each infinitesimal displacement in the s-t plane

We can thus also conclude that for causality to be preserved in such model, the curl of the vector field in the s-t plane has to be zero and there are no singularities

Sir Cumference

2:38 AM

@loocsieulb Those links went down

@Blue Thanks a ton

Secret

3:35 AM

Some entanglement thoughts:

Secret

3:53 AM

$\frac{1}{\sqrt{2}}(\lvert 0\rangle \otimes \frac{1}{\sqrt{2}}(\lvert 0\rangle + \lvert 1\rangle) + \lvert 1\rangle \otimes \frac{1}{\sqrt{2}}(\lvert 1\rangle + \lvert 0\rangle))$

Secret

4:10 AM

$= \frac{1}{2}\lvert 00\rangle + \frac{1}{2} \lvert 01 \rangle + \frac{1}{2} \lvert 11\rangle + \frac{1}{2} \lvert 10\rangle$

Physics Meta

1

Q: Do we have any particular recourse for accepted answers that are wrong?

A while back, I answered yet another perpetual motion question. The post essentially asks whether or not you can extract work from Brownian motion, which I consider a good question because of how widely spread is misunderstanding of thermodynamic noise and the importance of the temperature of a t...

discussion

Secret

$= \frac{1}{2} (\lvert 0\rangle + \lvert 1\rangle) \otimes (\lvert 0\rangle + \lvert 1\rangle)$

ok that's a product state, not useful

ok try:

$\frac{1}{\sqrt{2}}(\lvert 0\rangle \otimes \frac{1}{\sqrt{2}}(\lvert 0\rangle + \lvert 1\rangle) + \lvert 1\rangle \otimes \frac{1}{\sqrt{2}}(\lvert 0\rangle - \lvert 1\rangle))$

$=\frac{1}{2}(\lvert 00\rangle + \lvert 01\rangle + \lvert 10\rangle - \lvert 11\rangle)$

Squaring:

$\frac{1}{2}\begin{pmatrix}1 & 1 & 1 & -1\\1 & 1 & 1 & -1\\1 & 1 & 1 & -1\\-1 & -1 & -1 & 1\end{pmatrix}$

Taking partial trace wrt Bob

=$\frac{1}{4}\begin{pmatrix} 2 & 0\\ 0 & 2\end{pmatrix} = \begin{pmatrix} \frac{1}{2} & 0\\ 0 & \frac{1}{2}\end{pmatrix}$

typo at 4x4x matrix, should be $\frac{1}{4}$

Now attach measuring device at Alice's side:

$\frac{1}{\sqrt{2}}(\lvert\varepsilon\rangle \otimes \lvert 0\rangle \otimes \frac{1}{\sqrt{2}}(\lvert 0\rangle + \lvert 1\rangle) + \lvert\varepsilon\rangle \otimes \lvert 1\rangle \otimes \frac{1}{\sqrt{2}}(\lvert 0\rangle - \lvert 1\rangle))$

Equilibrate:

$\frac{1}{\sqrt{2}}(\lvert\varepsilon 0\rangle \otimes \frac{1}{\sqrt{2}}(\lvert 0\rangle + \lvert 1\rangle) + \lvert\varepsilon 1\rangle \otimes \frac{1}{\sqrt{2}}(\lvert 0\rangle - \lvert 1\rangle))$

oops typo

Secret

4:52 AM

I will explain the above later, turns out it is a bit messy

John Rennie

5:56 AM

@dmckee have you got a moment?

Slereah

6:58 AM

So many topologies

Dawood ibn Kareem

This is the last one, I promise.

John Rennie

7:12 AM

@EmilioPisanty this is the quote from my thesis:

Physics Meta

1

Q: Community Promotion Ads - 2018

It's almost February in 2018, which isn't supposed to be the proper time to cycle these, but for this year it'll be once again, so we'll be refreshing the Community Promotion Ads for this year now! What are Community Promotion Ads? Community Promotion Ads are community-vetted advertisements tha...

discussion community-ads

Emilio Pisanty

7:29 AM

@JohnRennie what?

me no understand the quote

I'm not a big fan of starting quotes in a thesis, but they're not terrible either

I did end up putting one in mine

John Rennie

In the finals at Cambridge (at least in 1983) you had a first paper that was intended to get you into the swing of doing exams, so it asked fun questions that didn't count towards the final score.

That was one of the questions on that first paper.

Emilio Pisanty

said tram tracks having contributed to the broken rib

John Rennie

You tripped over the tram tracks while walking home drunk one night? :-)

Emilio Pisanty

not quite

I was cycling and my front wheel got caught in the tracks

John Rennie

@EmilioPisanty Chester has a few cobbled streets, and that has happened to me when the wheel got stuck between two cobblestones.

Emilio Pisanty

7:36 AM

@JohnRennie ouch

John Rennie

Though so far I have suffered only bruising.

Emilio Pisanty

@JohnRennie yeah, I wouldn't recommend breaking ribs

in that fashion or otherwise

John Rennie

It probably helped that I was ... erm ... very relaxed at the time :-)

Mithrandir24601

@JohnRennie What? I wish I got that

John Rennie

@Mithrandir24601 I guess that's changed since 1983 ...

Mithrandir24601

7:39 AM

@JohnRennie Along with what seems like everything else :P

John Rennie

Whether it's really a good idea or not I don't know. I think it did help relax you, but on the other hand I suppose it was a wasted three hours that could have been put to other uses.

Emilio Pisanty

@JohnRennie I still think it's way too wordy for its own good

John Rennie

@EmilioPisanty my quote?

Emilio Pisanty

yeah

as in: please explain why you're going to do badly (i) in this exam, or (ii) in that other exam at the end of the year, or (iii) in some other aspect of your life

?

John Rennie

I think you might be taking it a bit more seriously than it was intended :-)

Emilio Pisanty

7:48 AM

@JohnRennie I just don't understand what it's actually trying to say

@PhysicsMeta ... aaaaaand, it's that time of the year, again

when I have to repeatedly try to convince SE that I'm not a robot

John Rennie

@EmilioPisanty if you have a moment spare can I ask you cast your eye over something I've written?

Emilio Pisanty

sure

John Rennie

@EmilioPisanty This

No great attention to detail is required, I'm mainly interested to know if you think it's a good analogy

Emilio Pisanty

@JohnRennie is this a draft canonical Q&A?

John Rennie

Yes

Emilio Pisanty

7:56 AM

good, we need one on that symmetry thing

John Rennie

Though there might be an existing question I can append the answer to rather than post a new canonical Q/A.

Emilio Pisanty

you write them in Word?

/ google docs?

why not stackedit?

John Rennie

I generally draft long articles in MS Word. I copied it to Google Docs to share it.

Emilio Pisanty

¯\ _(ツ)_/¯

if you did it in stackedit.io you'd have mathjax

John Rennie

Does stackedit do diagrams?

Emilio Pisanty

7:58 AM

hmmmm, no

you do the drawings in Word itself?

John Rennie

No, in Google Draw.

Emilio Pisanty

@JohnRennie ok

@JohnRennie I think it's a good analogy, but I think you need more details at the end

i.e. spell out the fact that the rotation is different in Minkowski geometries

other than that, I think it's great

John Rennie

@EmilioPisanty yes, I agree. At the moment it just says oh look the time axis is rotated without any justification. But I didn't want to put the effort into expanding it without some feedback on whether it would be comprehensible to non-experts.

Emilio Pisanty

@JohnRennie no, I think it's great and you should push ahead at full steam

John Rennie

Thanks. I'll search around the site and see if there is an existing question that I can append to or whether it is best posted as a new question.

Slereah

8:04 AM

What are the unitarily equivalent reps of the CCR, is it just \begin{eqnarray}\hat x \psi &=& (x + a)\\ \hat p \psi &=& (\frac{\partial }{\partial x} + b) \psi\end{eqnarray}

Emilio Pisanty

hmmmmm

News! As of today, we're retiring the name oaDOI. All its services/features will continue to work, but now they're part of larger Unpaywall project. Reason: saves us time and effort explaining how Unpaywall and oaDOI relate. The relation is now: "same project." :)

Tweeted by unpaywall_data on January 27, 2018 at 10:49 PM

this is unwelcome

Emilio Pisanty

8:20 AM

btw this one is the one I care the most about

0

A: Community Promotion Ads - 2018

not that I'm soliciting for upvotes on it

ok, no, maybe I am

Emilio Pisanty

8:47 AM

hey @Slereah @ACuriousMind @other-topologists

suppose I have a group $G=\mathrm{SO}(3)\times \mathrm{SO}(2)$ and I want to find interesting continuous closed subgroups

I could e.g. fix an axis on the first factor and do rotations $R_z(\theta)$ on the first one coupled with some other rotation on the other

so, say, $\theta\mapsto (R_z(2\theta),R(3\theta))$

so if I then look at the projection on the first factor, I get $\{R_z(0),R_z(2\times 2\pi/3),R_z(4\times 2\pi/3)\} \cong C_3$

(i.e. the elements that correspond to $R(0)$ on the second factor)

is there a way to thread that so that instead of getting a cyclic group on the first-factor projection, I get some other discrete subgroup of $\mathrm{SO}(3)$ that's more three-dimensional?

say, the tetrahedral group $A_4$

Physics Meta

9:16 AM

0

Q: A possible canonical Q/A on symmetric time dilation?

We have lots and lots of questions on the symmetry of time dilation. That is when two observers are heading towards each other how can each think their clock is running faster? These questions typically come from people who have just started studying special relativity. I think I have come up wi...

discussion

Slereah

9:51 AM

hey @0celo7

Up early?

or late

Secret

10:04 AM

amp.theguardian.com/environment/planet-oz/2018/jan/24/…

Well, in some sense, they are easy to identify. A lot of predatory journals have the string "International Journal of" in that exact order

bolbteppa

Maybe simple question, if $f(x)$ is monic and $p_i(x)$ is monic, $i = 1,\dots,n$, then from $P(x)Q(x)f(x) = \Pi_{i=1}^n p_i(x)$, why must $P(x)Q(x) = 1$?

Slereah

Monic?

bolbteppa

Highest term has $1$ as it's coefficient, e.g. $x^2 + 2x + 1$

Slereah

Ah

Are the $p_i$'s of the same degree?

And what is $f$'s degree

Well, $\prod p_i$ will have some degree $x^k$

with coefficient $1$

bolbteppa

Oh yeah

Slereah

10:14 AM

But if $f(x) = 1$ then $PQ$ could be equal to $x^k$

So without more informations this seems false

bolbteppa

Degree of $f(x)$ and $g(x) = \Pi_{i=1}^n p_i(x)$ are the same

Slereah

Well then there you go

$f(x) = x^k + ...$

Hence if you multiply by a non-one thing

It won't be equal

bolbteppa

If something is not monic, how does it make $PQ$ not equal to 1

Slereah

Well then you could have $g = 2 x^k + ...$ and $f = x^k + ...$

And then $PQ$ can be $2$

bolbteppa

Hmm

Slereah

10:18 AM

for instance $p_1 = x$, $p_2 = 2x$, $f = x^2$

Then you can just pick $P = 1$, $Q = 2$

bolbteppa

Yes, the degrees of $f$ and $\Pi_i p_i(x)$ need to be the same, then $PQ$ can be a constant, and if everything was monic they need to be $1$, but this relation allows $P$ and $Q$ to be non-trivial if the degrees of $f$ and $\Pi_i p_i(x)$ are different...

Phew

user228700

10:36 AM

Hello, everyone :-)

Slereah

Hello

skullpatrol

Hi

Secret

(cont.) Ok, here's what I am trying to model:

I have a double slit apparatus (in fact, any apparatus with some observables that can give an interference pattern will do), which constantly firing electrons towards the screen, thus the computer will be recording some interference pattern building up.

To this apparatus, I also have the electron being entangled with a qubit located in a trap some meters away from the apparatus (so as not to put two bulky things too close)

Therefore I have the following entangled state, where stuff on the left side of the $\otimes$ corresponds to the qubit and the superposition on the right side of the $\otimes$ corresponds to the which slit observable in the double slit apparatus. i.e.

$\lvert s\rangle = \frac{1}{\sqrt{2}}(\lvert 0\rangle \otimes \frac{1}{\sqrt{2}}(\lvert 0\rangle + \lvert 1\rangle) + \lvert 1\rangle \otimes \frac{1}{\sqrt{2}}(\lvert 0\rangle - \lvert 1\rangle))$

which expands to:

$=\frac{1}{2}(\lvert 00\rangle + \lvert 01\rangle + \lvert 10\rangle - \lvert 11\rangle)$

when wrote as a density matrix we get:

$\lvert s\rangle\langle s\rvert = \frac{1}{4}\begin{pmatrix}1 & 1 & 1 & -1\\1 & 1 & 1 & -1\\1 & 1 & 1 & -1\\-1 & -1 & -1 & 1\end{pmatrix}$

Actually typo

$\lvert s\rangle = \frac{1}{\sqrt{2}}(\lvert 0\rangle \otimes \frac{1}{\sqrt{2}}(\lvert L\rangle + \lvert R\rangle) + \lvert 1\rangle \otimes \frac{1}{\sqrt{2}}(\lvert L\rangle - \lvert R\rangle))$

$=\frac{1}{2}(\lvert 0L\rangle + \lvert 0R\rangle + \lvert 1L\rangle - \lvert 1R\rangle)$

(and the density matrix is the same as it is written under the basis generated by $\{\lvert 0L\rangle, \lvert 0R\rangle, \lvert 1L \rangle,\lvert 1R\rangle\}$

We can easily take a partial trace wrt the qubit to confirm that we will get 50:50 on which slit the electron passes through

$\frac{1}{4}\begin{pmatrix} 2 & 0\\ 0 & 2\end{pmatrix} = \begin{pmatrix} \frac{1}{2} & 0\\ 0 & \frac{1}{2}\end{pmatrix}$

Now I am preparing to measure the spin of the qubit along the z direction. The measuring device, being macroscopic, has many degrees of freedom, hence it is basically like an environment to the system in question

Just before measurement, I should have the following system-environment state:

$\lvert\varepsilon \rangle\otimes \lvert s\rangle = \frac{1}{\sqrt{2}}\lvert\varepsilon\rangle \otimes ( \lvert 0\rangle \otimes \frac{1}{\sqrt{2}}(\lvert L\rangle + \lvert R\rangle) + \lvert 1\rangle \otimes \frac{1}{\sqrt{2}}(\lvert L\rangle - \lvert R\rangle))$

$=\frac{1}{2}(\lvert \varepsilon 0L\rangle + \lvert \varepsilon 0R\rangle + \lvert \varepsilon 1L\rangle - \lvert \varepsilon 1R\rangle)$

Then the environment absorbs the system's states and give:

$=\frac{1}{2}(\lvert \varepsilon_{0}L\rangle + \lvert \varepsilon_{0}R\rangle + \lvert \varepsilon_{1}L\rangle - \lvert \varepsilon_{1}R\rangle)$

Thus by einselection and decoherence, $\langle \varepsilon_i\vert \varepsilon_j\rangle = \delta_{ij}$

However, what I am not sure now, is whether I have the correct system-environment state to query the statistics of the double slit experiment after the measurement of the qubit is being done. By unitarity and no communication theorem, a local operation at one subsystem of the entangled system will not change the reduced density matrix of the other subsystem, so I should still have the interference pattern building up unaltered before and after measurement?

Emilio Pisanty

11:32 AM

@dmckee You're not. But surely you go through moments like this with some regularity, right?

bolbteppa

Oh my god they made a cartoon about (part of) my life the past 3 years :p

Poor blue hat just needs to learn about projective reps :'(

Balarka Sen

Spin is the double cover of SO :3

Emilio Pisanty

11:49 AM

@bolbteppa bluehat already knows about projective reps

he's explicitly saying that he doesn't think it's enough

sadly, bluehat stopped cartooning =(

wait

no

there's two new ones!

to some extent

bolbteppa

Blue hat must be afraid of the gruppenpest

John Rennie

Abstruse Goose?

bolbteppa

Yup

Emilio Pisanty

@bolbteppa I stand by my claim that this is what happened to Majorana. Think about it: how would this look like to historians in the intervening years? It would look like the mysterious disappearance of the woman.

John Rennie

It's a shame he/she/it stopped publishing cartoons. I guess everyone runs out of ideas eventually.

bolbteppa

11:53 AM

I vaguely remember a discussion on Majorana the person on here, hmm

Try defining Majorana in higher dimensions, fun times

Secret

ok, so $s$ is an entangled since $\text{tr}\rho_{qubit}^2 = \frac{1}{2} < 1$

Emilio Pisanty

Ettore Majorana

Ettore Majorana (; Italian: [ˈɛttore majoˈraːna]; born on 5 August 1906 – probably died after 1959) was an Italian theoretical physicist who worked on neutrino masses. On March 25, 1938, he disappeared under mysterious circumstances while going by ship from Palermo to Naples. The Majorana equation and Majorana fermions are named after him. In 2006, the Majorana Prize was established in his memory. == Life and work == There are several categories of scientists in the world; those of second or third rank do their best but never get very far. Then there is the first rank, those who make important...

specifically the section "Disappearance at sea and suggested explanations"

Secret

and similarly for $\text{tr}\rho_{doubleslit} = \frac{1}{2} < 1$

Emilio Pisanty

@JohnRennie there's two new (non-)cartoons

bolbteppa

He's with 2pac and the rest on that island along with the RH solution

11pm, hmm

'On February 4, 2015, the Rome Attorney's Office released a statement declaring that Majorana was alive between 1955 and 1959, living in Valencia, Venezuela.'

In all fairness, they say was Hitler around there too right

miamiherald.com/news/local/news-columns-blogs/…

Slereah

12:05 PM

Majorana was Hitler all along

Secret

12:19 PM

I need skullpatrol to further The Plan

Angels & Demons

►

Quantum Transport, Lecture 20: Majorana fermions

►

and then, there's this issue of recording...

cbronline.com/news/microsoft-set-5-year-quantum-computing

Still more error correction needed

29 mins ago, by John Rennie

It's a shame he/she/it stopped publishing cartoons. I guess everyone runs out of ideas eventually.

don't we all? just look at the mess of hollywood

abstrusegoose.com/577

bolbteppa

Turns out 91 is not prime

2

Secret

2

and why is bolbteppa get caught in this seething mess?

arrrrrrggh

of to math chat you go

Secret

It cannot even cut a stone

91=3*17

and 17 is a curse, unlike 7

The what???

and this movie sucks than the original

I mean, come on, in the first movie, the whole organisation is being wiped out, and then you do that again in the second movie?

I am guessing, in the 3rd movie, they are going to wipe the whole thing out again leaving only the main casts

Tbh, I do wish WWIII will wipe out every single human being, because we are just a pitful existence that never knew how to fix a problem

in Mathematics, 38 secs ago, by Vrouvrou

hello

Slereah

Feel free to set the example

Secret

12:35 PM

and $$\text{SHUT UP!}$$ vrou

Abcd

@JohnRennie Where can I see 3D molecules? Any site?

Secret

@Abcd what software you are looking for to visualise 3D molecules?

cause there are many

Abcd

Its very difficult to visualise everything

@Secret i don't know any software

But I face real problems while studying stereochemistry, coz I just can't imagine everything in my head.

John Rennie

@Abcd that's an awfully vague question. Are you interested in specific molecules, or do you want a site where you can put in any molecule and have it show you a 3D image?

Abcd

@JohnRennie Umm...both?

Generally, what I do is google the compound and see its google image.

But many times there's no image.

Secret

12:39 PM

If you only need something to visualise molecules, you can try Avogadro (which is free) which you can simply build your molecule. If you want to convert 2D representation to 3D ones, then you can use this app called molview molview.org

But it seems you want something that you input the name of a molecule and it gives you an image...

John Rennie

Wow, molview.org is well cool! :-)

Secret

not very good for professional work, but does it well when it comes to quick visualisation.

It even tries to compute the 3D geometry for you expected from the 2D drawings

Abcd

will it give correct structure always?

I wonder how it works !

bolbteppa

I don't know why I never just set up LSZ in terms of path integrals for a specific example like Compton, you unify so many things in one go, like most of pre-renorm basic qft just falls out of this thing

Future Historian

Hmmmm.

John Rennie

12:42 PM

@Abcd why not get yourself a kit for building models of molecules?

Future Historian

How hard is it to make a pure fusion bomb with antimatter as a catalyst?

Abcd

@JohnRennie Man, there are so many molecules I study. How will I prepare every molecule?

John Rennie

@FutureHistorian it's not obvious why antimatter would be useful for making fusion bombs. It wouldn't catalyse a fusion reaction.

@Abcd amazon.co.uk/Molymod-MMS-008-Molecular-Organic-Chemistry/dp/…

Slereah

Wasn't there some idea of muon catalyzed fusion in the 70's

I don't remember if that ever went anywhere

Abcd

@Secret Please give the link to avogadro too.

Future Historian

12:44 PM

@JohnRennie. I mean in the sense that a pure fusion bomb could be made with 10^18 micrograms' worth of antiprotons as a means to ignite the explosion.

Secret

avogadro.cc

Future Historian

Basically a modern thermonuclear bomb using antimatter as the ignition mechanism instead of another fission bomb.

Could it work? Or fail?

Secret

@Slereah large.stanford.edu/courses/2016/ph241/yoon1 Here's a good summary, it seems the muons cannot catalyse enough events to make the reaction sustainable

bolbteppa

$\not{\partial}$ how do you get the Dirac slash, (horrible)

John Rennie

@FutureHistorian But why use antimatter? Given that it's exceedingly hard to make and exceedingly difficult to store what makes it better for igniting fusion than a fission bomb?

Future Historian

12:46 PM

Less radiation?

:P

That and I was thinking..........more politically acceptable as a result of reduced radioactive fallout.

Slereah

@JohnRennie More compact?

Future Historian

^

That as well.

Slereah

I think the popular mean of ignition was a while was laser primed fusion

Secret

@bolbteppa I think you need to load a package, there is no latex symbol in the database with the dirac slash by itself

John Rennie

More compact? You know a compact way to store antimatter and keep it in the form of a shaped charge?

bolbteppa

12:48 PM

Yeah the slashed package is better than \not

Future Historian

@JohnRennie. He means that the need for the fission bomb becomes unnecessary.

Secret

and if I recall, we can load packages now in chat?

Future Historian

Since only 10^18 micrograms' worth of antiprotons are used to ignite the big BOOM BOOM.

Slereah

@JohnRennie I just keep it in my pocket

John Rennie

@FutureHistorian yes, but fission bombs are already very compact. You're proposing replacing a nice compact fission bomb with a hugely complicated containment system to stop your antimatter blowing itself and you up.

Future Historian

12:52 PM

*fusion

John Rennie

I mean the fission bomb component of your fusion bomb.

Slereah

I just flex my biceps and crush the hydrogen between my rippling muscles

Emilio Pisanty

has its imperfections though

@Abcd no

John Rennie

@EmilioPisanty still cool though

Abcd

@EmilioPisanty ya, read that.

@JohnRennie Is this fine?

Emilio Pisanty

12:55 PM

@Abcd looks fine

Future Historian

Sorry.

John Rennie

@Abcd it looks fine to me. I can't give a personal recommendation since I've never used it.

Future Historian

I just thought it would be a good idea.

John Rennie

@Abcd hang on. Is that the kit or just the book to go with the kit?

Abcd

Avogadro isn't easy to use.

@JohnRennie Nothing is mentioned.

John Rennie

12:57 PM

@Abcd Hmm

Slereah

Can't you just buy some play doh and toothpicks

CooperCape

@JohnRennie I'm liking the new vid

John Rennie

@CooperCape have you nothing better to do? :-)

CooperCape

Hah somehow I had you on my chrome notifications

Was a bit weird

John Rennie

I bought a cheap USB hub on eBay and one of the ports doesn't work. The seller asked me to upload a video to prove it.

CooperCape

1:03 PM

Hence the aptly named "Hubfault"

John Rennie

Given that the hub only cost me £2 I very nearly didn't bother, but it's the principle of the thing! :-)

skullpatrol

Are you aware of this etymology? @JohnRennie

:-)

Slereah

Wigner's theorem is p. dense in math

gee

0celo7

1:19 PM

@Slereah If I don’t close chrome on my phone it keeps refreshing the PSE tabs when I’m asleep

I’m never on in the dead of the night but it can sometimes appear as if I am

skullpatrol

I think David Z. appears on 24/7?

::kinda creepy, actually::

Slereah

maybe you're sleepwalking

also hello

does the quantum theory associated to the Pauli equation obey the CCR

Or is it some anti-commuting thing

0celo7

Is the Pauli equation the nonrelativistic Dirac equation?

Slereah

yes

If it obeys the CCR, is there some unitary map between the Hilbert space $L^2(\Bbb R^n, \mu)$ and the Hilbert space of $SU(2)$ spinors

Oh wait, is the momentum $\vec \sigma \cdot \vec p$

0celo7

Good question

Slereah

1:35 PM

Weinberg was hiding things from me

Look at all this bullshit

Is a "conjugate linear isometry" just the fancy talk for a unitary linear operator

I believe so

I think it just means "unitary operator up to a phase"

all that nonsense

0celo7

It means conjugate linear unitary

Slereah

what does conjugate refer to here

0celo7

I think physicists call it antilinear

Slereah

ah, antiunitary

unitary or antiunitary operator

\begin{eqnarray}
\{ \sigma p , x \} \psi &=& \sigma p x \psi + x \sigma p \psi
\end{eqnarray}

Let's see

component by component that would be...

$$\partial_z (x \psi) + x \partial_z \psi = 2x \partial \psi$$

$$- \partial_z (x \psi) - x \partial_z \psi = -2x \partial \psi$$

No that doesn't really seem to be CCA

CAR*

Apparently it does obey the CAR

for the sigma matrices

arxiv.org/pdf/math-ph/0511030.pdf

There's the anticommuting version of Stone-von Neumann

Apparently you just get two copies of the usual Hilbert space

not much surprise

"Strictly speaking the formulas (1) and (2) are ill defined because it is not clear how to interpret the commutator of unbounded operators"

What, even the commutator isn't defined?

Oh, is it one of those domain problem again

Slereah

2:39 PM

dtic.mil/dtic/tr/fulltext/u2/400925.pdf

Phew, the paper on infinite dimensional CCR is declassified

QFT has fallen to the communists

Future Historian

2:54 PM

Back.

So, let me guess: antimatter-catalysed pure fusion bomb = fail?

Secret

2 hours ago, by John Rennie

@FutureHistorian yes, but fission bombs are already very compact. You're proposing replacing a nice compact fission bomb with a hugely complicated containment system to stop your antimatter blowing itself and you up.

Future Historian

I will take that as a "yes".

Secret

Meanwhile, I don't know of any way to produce huge amount of antimatter in situ

Future Historian

So, use normal thermonuclear weapons?

Great......

Slereah

Muon-catalyzed fusion

Muon-catalyzed fusion (μCF) is a process allowing nuclear fusion to take place at temperatures significantly lower than the temperatures required for thermonuclear fusion, even at room temperature or lower. It is one of the few known ways of catalyzing nuclear fusion reactions. Muons are unstable subatomic particles. They are similar to electrons, but are about 207 times more massive. If a muon replaces one of the electrons in a hydrogen molecule, the nuclei are consequently drawn 196 times closer than in a normal molecule, due to the reduced mass being 196 times the mass of an electron. When the...

Might wanna look this up

It's not really great either

Future Historian

2:57 PM

:(

Slereah

but it has been discussed

Future Historian

So, I suppose I will have to remain with regular nuclear warheads for that "torpedo" design.

Which is really just an autonomous suicide drone that is basically a rocket with a bunch of MIRVs in it.

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