...perhaps there's simply no point trying to understand entanglement, or it's implications, without a proper quantum background first

when they say 'hidden variables' is that shorthand for saying "actually deterministic, but too complex to calculate so random variables are easier, mathematically?"

so the findings of no hidden variables means it truly is random, as distinct from the classical approach to modelling complex systems with randomness?

@antimony (roughly speaking) yes. hidden variables capture the idea that there is an underlying "reality", i.e. systems have some properties which we are not aware of, for one reason or the other, and the observed probabilities for these values are because we cannot prepare the system in some suitable state. So long story short: yes, hidden variables would mean that the situation is similar to e.g. in (classical) statistical mechanics

but of course, what is ruled out by e.g. Kochen-Specker or Bell are certain types of hidden variables, i.e. you need some further specification of these entities, how they behave, so to say. The topic is very complex and non-trivial, especially the consequences of the mathematical theorems, because one has to interpret them

@Relativisticcucumber yeah, I think thats the rough idea. :)

Regarding the Mandelstam variables

Invariants are constructed from the metric tensor and determinant

So in 4 dimension with 2 vectors it's only with the metric

So $g(p,k)$, $g(p,p)$ and $g(k,k)$

Ingoing mass, outgoing mass and the boost

That's for one particle btw

For more you have to check out more combinations

And use constraints like conservation of energy momentum

Isn't an LI quantity the scalar productt?

Well yes, that's what the metric is

yes but then the process is 2 in and 2 out

so for one consideration

the invariant quantities is the scalar product of the total four momenta before collision and the one after the collision

@DIRAC1930 hi. i can explain this stuff

we have a function $B(x)$. if we transform it to another function while keeping the co ordinate system the same, it becomes another function $B'(x)$

@DIRAC1930 so u r right here

however, P&S is also correct. We have to understand the nuance

sometimes, we take a function and consider a one parameter family of transformations. Like, all possible translations of the function. We will write it as $f_{\epsilon} (x)$ $\epsilon \in (-\infty, \infty)$

this is so far consistent with the previous notation. we have just added an eplison subscript instead of a ' superscript. we are recognising that $f_{\epsilon}$ is a different function from $f$

now, since we are e.g. considering translations, we have the equality $f_{\epsilon} (x)=f(x+\epsilon)$. on the right, we just have $f$

so u could alternatively right the translated function as $f(x+\epsilon)$. it just expresses the fact that $f_{\epsilon}$ is the composition $fog$ where $g(x)=x+\epsilon$

Hello and welcome back pal.

@DIRAC1930 so P&S is correct in writing $u'(p)$ as $u(\Lambda p)$. It just expresses the fact that $u'$ is composition $uog$ of $u$ and $g(p)=\Lambda p$

@think_meaning_buildß tears

@DIRAC1930 sorry for the late reply. i was banned for a week

Come on, water off a duck's back ;-)

also, one doesn't need to consider a one parameter family of transforms to use this technique. I think P&S doesn't explicitly consider it

e.g. u have a function f(x). after reflection, it becomes a function g(x) which u could write as f(-x)

@RyderRude Thanks, I ended up just accepting it since it was the only calulation I could find that gives an example of $U^\dagger \Phi^i(x) U = D(\Lambda)^{i}{}_j \Phi^j(\Lambda^{-1}x)$

For some reason, textbooks just quote that result without giving an example

@DIRAC1930 make sure u r convinced by it... u don't have to just accept it

we are just alternatively writing $f'(x)$ as f(g(x))

because the equality $f'=fog$ is satisfied

@naturallyInconsistent In the case of gamma spectroscopy of real samples, this difference is drastic and certainly not crazy. We measure almost a hundred samples here every day and I would hate to have our work called crazy.

In the context of the 2 to 2 process and Mandelstam variables, what does an independent LI quantity mean? Independent of what?

Does knowing how $\rho(t,\vec{r})$ depends on time and knowing $\vec{j}(t,\vec{r})$ completely fix $\rho$ via the continuity equation?

I mean take the case of a 0 current and constant charge density

it doesn't fix the value of the charge at all

it could be anything

and any distribution

merp to all

@TobiasFünke thank god

Are techniques from Loop Quantum Gravity useful for NON-loop quantum gravity? I may be interested in working on quantum gravity in the future, not LQG tho. There is a really good 12 days summer school on LQG taught by the main guys, and I am deciding whether to go. I don't want to spend that time learning ultra-specific tools and never use them again

It seems quite broad to me but I don't know enough to judge

Also, when did table-top experiments come up in LQG lol

Can someone help me understand the theory behind what is being asked here?

I read about the Mandelstam variables and also on and off shell mass

And I don't really have the faintest idea what this exercise is talking about

And I find this weird, since I believe I must be able to have an understanding

to certain level

The first question is about the nr. of invariant quantities

lorentz invariant*

If we simply consider 4 four momentum, one has 10 pairs of 2 four vectors multiplying each other, if you consider the sum of 3 and the square of them, you'd have even more etc

What I don't understand is what is meant with independent

and how does the consideration of four momenta conservation affects the independence

I don't understand

I'm suspicious. A new member physics.stackexchange.com/users/466216/luigi-m has just posted 6 extensive answers in the space of 2 hours. Most of them make extensive use of MathJax. I suspect undisclosed use of high-quality GenAI. Admittedly, the answers do seem pretty good, as far as I can tell, but I don't have the expertise to be certain. However, they do seem to ramble a bit and have the odd repetition that you often get in long streams of GenAI output.

hmmh I've seen another user some days ago, too, where I had this feeling

@PM2Ring I think the "repetition" can be seen quite nicely here: physics.stackexchange.com/questions/837131/…

the question/problem is (also in general terms): How do proof this? What to do about it?

This one? physics.stackexchange.com/users/315779/badri-narayanan Totally quiet for 3 years, then 4 long answers in 18 minutes!

nope, someone else

Oh dear. The invasion has begun...

yes. I was afraid of this anyway...

...yes, but what do you want to do about it?

It will become harder and harder to detect AI generated content

it will make SE so much less valuable...

He answered a thread of mine

Pretty extensive

Right now, I just want a few other people to check these guys answers, and let me know if they agree that GenAI was very likely to have been used. And if so, we can flag one of the answers with a custom mod flag.

I couldn't understand the post. But I thought it's the result of me not knowing much about the topic I asked

However, mods can take a while to verify & act on suspected GenAI flags...

and yet you accepted the answer?

Of course I did

the extremely long answers are a red flag to me

Me not understanding doesn't mean the answer is wrong or has missing info

It, in most cases, means that I lack the knowledge

@imbAF how you know? but I mean, sure, your decision

@imbAF You should not accept an answer if it hasn't actually helped you.

I know from the fact that his answer, on a general scale gives the answer to my question. Additional stuff

related to my question

I don't understand

But I don't believe I need to know 100% of what is being talked about

I can link the thread here and you can check his answer

if you so desire

@imbAF I bet he won't respond if you ask him to clarify stuff in a comment. Or if he does, his comment won't actually help.

I did ask

I don't know whether he will reply or not and whether it will help or not

But his answer was extremely loaded

I could partially understand stuff

But he also used to make connections between concepts etc

that I had never encountered before

we probably need some sort of AI detector before posting an answer or a question or so

@TobiasFünke There are no reliable AI detectors - and even if there were, you could just train the models to evade it

@PM2Ring indeed, some answers are only 7 minutes apart or so... so very likely AI generated

@ACuriousMind yeah, I guess you are right

this **** will haunt us, not only here but also as a society in general

I guess someone who has the knowledge can tell whether the answer is A.I generated or not

knowledge about what?

the topic of the thread

Our site does permit some use of GenAI, but it must be disclosed. I'd prefer it if we were a no-GenAI zone, but ...

His answer on my thread was convoluted, but I thought that it's me who lacks knowledge

@PM2Ring yes, but given only a very few minutes between several long answers, it is very likely fully AI generated...

If they were new answers to old questions, then it's possible that they were produced offline & then posted in quick succession. But that's clearly not the case here.

yes

the problem is, of course, that in the many cases you won't know for sure...

also, what is interesting, that the user does not respond to comments (also the one I had in mind)

which by itself is not suspicious, but if they cannot clarify certain aspects, it is another hint (?)

Often people do not reply to comments

In any case, I don't know why anyone would answer by just copy-paste e.g. ChatGPT. What's the point?

It baffles me. I guess it's a quick way to get the rep needed for various site actions. But still...

while we were chatting, they put two other answers. I am out for today

see you around

And people post GenAI stuff who clearly don't need the rep.

See you