The h Bar

4:19 AM

I want to be happy, but not so happy that the screen has to be wiped. Is there really a need to start a paper with "In the beginning, praise be to Allah for helping me in everything."?

Ryder is not Rude.

5:08 AM

That sounds like something Abdus Salam would've written. RIP

123

5:39 AM

Hello Everyone...

Sir Cumference

6:34 AM

well, I have a master's in physics now

4

I guess that's cool

Ryder Rude

6:53 AM

hi

@SirCumference congrats

@SirCumference i thought u wer doing phd

Sir Cumference

@RyderRude yeah but you get the master's along the way

now I'm working on the PhD portion

Ryder Rude

@SirCumference oh

@SirCumference nice

Slereah

7:27 AM

@SirCumference grats

naturallyInconsistent

7:41 AM

congrats

Slereah

7:55 AM

This is what Gell-Mann was working on, if you were wondering :p

Arjun

9:39 AM

Shankar in in his QM book mentions that every dynamical variable $\omega$ (clasically speaking) is a function only of X,p i.e $\omega(X,p)$,Why can't a dynamic variable have explicit time dependance?Or it's a trivial matter that he wrote $\omega$ at some particular instant in time t ?

Ryder Rude

do photons interact with gluons, etc?

@Arjun in general, one can have time dependent observables, i think

e.g. the Hamiltonian itself is time dependent sometimes

@Arjun i think Shankar considers a simplified case

Arjun

@RyderRude I concur.Time dependant potentials struck me immediately after I saw the thing in shankar.

Ryder Rude

yes, there is a generalised evolution equation for time dependent observables. I don't remember if Shankar discusses it

the equation is just the usual equation plus $\frac{\partial A}{\partial t}$ on the right

Slereah

@RyderRude Not at tree level

Ryder Rude

@Slereah oh

@Slereah is the interaction mediated by fermions or is there a direct interaction

e.g. photons interact with photons but not when there's no fermions

can one say that two bosons or two fermions can't interact without mediation by a particle of the other type?

this would mean that fermions are "force carriers" for bosons

but i think at least the Higgs field is an exception to this

@Slereah what do u think

naturallyInconsistent

10:49 AM

@RyderRude you were just asking about gluons; why didn't you check that before writing down your question?

Ryder Rude

11:19 AM

@naturallyInconsistent i generalised the question

naturallyInconsistent

11:30 AM

@RyderRude that is a good generalisation, but it is falsified by that example. You did not need to ask it.

Ryder Rude

@naturallyInconsistent i am asking it for others except the Higgs boson

naturallyInconsistent

@RyderRude I said gluons. Are you blind?

Ryder Rude

@naturallyInconsistent can gluons interact with photons without mediation by fermions

naturallyInconsistent

Yes; the intermediary can be any charged boson. But I'm saying gluons can interact with gluons and so bosons can interact with bosons directly without the intermediary of fermions

now bye, i need to be out

Ryder Rude

oh. Any non linear field has self interaction

it says gluons self interact

bolbteppa

12:38 PM

Yikes

pbs.twimg.com/media/GXKxgkya4AAFDZ8?format=jpg&name=medium

PM 2Ring

12:52 PM

@bolbteppa Did you see this alarming case in the HNQ?

61

Q: A journal has published an AI-generated article under my name. What to do?

The Global International Journal of Innovative Research has published a fake research article under my name, complete with a DOI doi:10.59613/global.v1i3.42. The article appears to be entirely AI-generated. I never had anything to do with the article: I never created the text, nor did I submit ...

bolbteppa

@PM2Ring wow

Amit

weird, it was published in 12.2023 according to here but he found out only now? supposedly possible but odd

PM 2Ring

> I became aware of it, when a colleague fell for it and found it relevant to one of our department's initiatives.

If the colleague hadn't stumbled upon it, that fake article may have gone under the radar for years...

Amit

@PM2Ring But is there something in the DOI or somewhere else that uniquely refers to him? It could be just a duplicate name issue

PM 2Ring

It's not a dupe name issue: it links him to the institute he actually works for

Amit

1:07 PM

Not cool

PM 2Ring

Definitely not cool. But how do you stop it? How do you even detect it?

Amit

You can detect it by actively monitoring your personal info in new publications. Perhaps some Cyber company will turn to make a buck out of that, too.. 😉

PM 2Ring

I guess you could use an AI to regularly scan the net, looking for malicious uses / mentions of your name. But that doesn't scale well if everyone online is doing such searches.

It's not so bad if you restrict it to publications in journals. But you should probably also scan prominent blogs, and sites like Stack Exchange, Reddit, Quora, etc.

Next-gen predatory journalism: Pay us $$$ and we won't publish a deepfake crap article written in your style, under your name.

Ryder Rude

1:25 PM

is it meaningful to speak of probabilities if u have been cloned

if i toss a coin, if it lands heads, u get a clone. If it lands tails, u don't get a clone

regardless of outcome, u wake up not knowing what happened

what is the probability that u have a clone

and u don't know if u r a clone after waking up

Ryder Rude

1:52 PM

according to some views on cloning, the original object ends its existence at the moment of cloning. and neither of the clones can be called "the clone"

In popular versions of many worlds interpretation, the experimenter can't meaningfully ask "what is the probability that i will be in world A after measurement", because they will end up in all of the worlds

but after they have measured, they can meaningfully ask "what is the probability that I AM in world A". This is given by :#no of worlds that correspond to outcome A / total number of worlds

Amit

@PM2Ring Academic ransomware... 😏

Ryder Rude

but there are other versions in which both of "what is the probability that i will be in world A" and "what is the probability that am in world A" are well defined

@PM2Ring lol

Amit

@RyderRude the probabilities you calculate are always related to your state of knowledge anyway. so I don't understand the statement that it can be "unmeaningful" to apply probability theory. It's always meaningful but also dependent on your current state of knowledge

Ryder Rude

@Amit but how do u make sense of "what is the probability that i will end up in world A after measurement", when u will end up in all of the worlds

i think u can say the probability is 1

Amit

I don't, because I think MWI is a fairytale lol

Ryder Rude

2:04 PM

lolol

i think it is on the right track, but naive rn

relational interpretation is somewhat better

Amit

Did you look into TSVF?

That's another rabbit hole for you to ponder, lol

Ryder Rude

What is this

ooh this seems to be the transactional interpretation

i haven't explored it... not willing to risk wasting time :P

The risk feels big with that interpretation lolol

I'll be back

Amit

Alright Arnie

Ryder Rude

2:22 PM

I'm back

shoots h bar with rifle

PM 2Ring

> TIQM doesn't destroy causality, it just redefines it a bit. Conventional causality is like a conveyor belt, propagating "stuff" from the past to the future, so there's an intrinsic time asymmetry.

Apr 11, 2023 at 4:55, by PM 2Ring

TIQM says there's an invisible underside of that conveyor belt, which restores the symmetry. The advanced waves in TIQM aren't causal in the sense that retarded waves are causal in conventional interpretations. Instead, TIQM says that that the retarded waves aren't sufficient for causality: they need to work in conjunction with the complementary influence of the advanced waves.

Apr 11, 2023 at 5:04, by PM 2Ring

@LeakyNun No! Causality is a key issue in TIQM. It says "You guys are only looking at the retarded wave, but you also need to look at the advanced wave for causality to make sense". It says a particular outcome is observed because only in that outcome do the advanced & retarded waves reinforce each other. In contrast, MWI says you observe a particular outcome merely because you happen to be conscious of that branch. (And presumably other versions of you are conscious of other branches).

TIQM = Transactional Interpretation of Quantum Mechanics

Ryder Rude

this feels like the makers cared more about making a cool idea than figuring out the solution :P

but this is just a first impression

@PM2Ring if u have studied this, do they derive born rule?

PM 2Ring

IMHO, the MWI is like Borges' Library of Babel. At first, it appear to contain all information. But it actually contains no information because it contains every possible book (in a given format) with no useful organising structure to the collection, and no way to distinguish true books from nonsense.

@RyderRude I haven't studied it deeply. But AFAIK, nobody has been able to make it work for anything more complex than a system consisting of one atom emitting a photon and some other atom absorbing that photon.

Ryder Rude

@PM2Ring this is a good description:P if we accept MWI, most universes are non sense, as they have never followed anything resembling the Born rule or any probability rule

PM 2Ring

But I find the bidirectional causality of TIQM & TSVF appealing.

Ryder Rude

2:34 PM

@PM2Ring oh :P

@PM2Ring it is a cool idea. I think they were inspired by the quantum eraser

PM 2Ring

@RyderRude I suspect that MWI needs some additional branch-pruning rule that restores the Born probabilities. Eg, the Sun could turn into a giant marshmallow tomorrow, but the probability is so insanely tiny that you'll never find yourself on such branches.

The branch-pruning rule says that such branches aren't just low probability, they're zero probability. So you can safely ignore them.

Ryder Rude

oh

maybe we can round the probabilities, as reality maybe doesn't have the infinite precision that real numbers have

PM 2Ring

@RyderRude I think two-state vector formalism predates any thoughts of the quantum eraser.

Ryder Rude

oh. Then i think have a false memory of reading that

Also, Feynman and wheeler were doing retrocausality long ago

PM 2Ring

> Time-symmetric interpretations of quantum mechanics were first suggested by Walter Schottky in 1921,

Ryder Rude

2:42 PM

Bohr must have been soo mad at him xD

Bohr be like "u can't even understand basic stuff"

at least he didn't say that to Einstein lol

PM 2Ring

I think the Feynman-Wheeler absorber theory is from 1949. "Classical Electrodynamics in Terms of Direct Interparticle Action" doi.org/10.1103%2FRevModPhys.21.425

Ryder Rude

yes

retrocausality is cool but i think measurement is a time irreversible process, but i havent studied their interpretation

PM 2Ring

Bohr was certainly very smart, probably smarter than Einstein, and possibly with better physical intuition. But he was very opinionated and self-assured. Abraham Pais wrote a good biography of Bohr. It's not quite as good as his biography of Einstein, of course, since he was Einstein's companion for several years at Princeton. Einstein really appreciated having someone he could chat with in German.

Ryder Rude

yes. Both Bohr and Einstein are famous for coming up with physical arguments rather than mathematical. I think bohr's previous non theoretical background gave him an edge over einstein

Bohr had a tremendous intuition

PM 2Ring

2:57 PM

@RyderRude Maybe. OTOH the usual Simulation Interpretation arguments say that the universe behaves like a simulation, but there's no measurement you can do that proves you're in a sim. Because if you can tell you're in a sim it's not a very good sim. And that would affect your behaviour. There's no point running a sim if the inhabitants don't behave like they aren't in a sim.

Ryder Rude

also, i don't want to risk admiring any physicist, which is why i dont read biographies

PM 2Ring

A good biography presents a balanced picture, showing both the good bits & the bad bits.

Ryder Rude

that would be great to read then. thanks

@PM2Ring the simulation arguments are very tiresome

they say stuff like "there's hierarchies of simulations", so we r most likely in a simulation. They invoke probabilities to say this !!!

it's all piles of assumptions. worst hypothesis ever

PM 2Ring

The Pais bio of Einstein is excellent. Pais is a great writer, and a physicist. He alternates the bio material with the actual physics that Einstein was doing at the time. It doesn't go right into all the fine details, but there are plenty of equations for those of us who are familiar with calculus & matrices.

@RyderRude Not quite. They say if it's possible to build realistic ancestor sims, then we're most likely in one. But that's a very big if.

Ryder Rude

i will check it out. sounds like an interesting approach

@PM2Ring yes.. but many of them remove this if :P

maybe the point of the argument is that, if we ever find out that we r able to do that, we shud begin to contemplate that we r in a simulation

there will be a brief pause between "figures out how to build sims" and "wait a second.... looks up in the sky"

PM 2Ring

3:12 PM

I'm highly sceptical. IMHO, it would take huge computing resources to simulate even a few million atoms to the precision that modern science can observe. So unless there are some tricks that can overcome the combinatorial explosion, I don't think anyone will ever be able to do sims of the quality & resolution of what we appear to perceive.

OTOH, maybe that's a trick of the sim, and the universe isn't actually as complicated as it looks. ;)

Ryder Rude

yes. Chalmers said that they only really have to put resources in simulating Earth and some nearby stuff... the other outer space stuff is just paintings lol

like a painting of the sky

sounds like the Truman show

but even the earth is really complex ofc...

PM 2Ring

There are ~2^167 atoms in the Earth. That's a lot of bits. But I guess you only need to simulate to high precision the stuff we can see. And most of those atoms are buried deep inside the Earth.

Ryder Rude

This is getting too close to solipsism :P

at some point, they only have to simulate ur own mind

which is why these hypothesis have zero content lol. It's just piles of assumptions

PM 2Ring

@RyderRude True. Boltzmann Brain territory.

Ryder Rude

Einstein would be mad. The moon isn't there when not looking

@PM2Ring yes. Lol

PM 2Ring

3:25 PM

The reason I mentioned sims in chat.stackexchange.com/transcript/message/66284316#66284316 is not that I think we might be in a sim. To me, the Simulation Interpretation is occasionally useful as an alternative way of looking at stuff, to make you aware of your assumptions. The same goes for MWI.

So if your model says the universe looks like a bad sim, your model is probably wrong. ;)

Ryder Rude

yes. I too find these interesting as lines of thought to better philosophise about the world

especially the Boltzmann brain

e.g. the Boltzmann brain argument lets u know just how much of ur knowledge is based on leaps of faith

these arguments are important as philosophical tools

Slereah

I'm back on the non-Hausdorff spacetime bullshit

I think I've got something

Ryder Rude

in non Hausdorrf spaces, limits are not unique, i think

like two limits of the same sequence

@Slereah what is it

Slereah

3:40 PM

A bunch of different shit that maybe goes together

bolbteppa

4:31 PM

7 Times Michio Kaku Went Next Level Genius

►

Amit

5:55 PM

@Slereah I'm starting to get it. Some day in the future you're gonna build a time machine, which retro causally explains the time loop of QM interpretations discussions we're experiencing here for a while now

Slereah

I'm afraid it's much more boring

It's for QM

Amit

non-Hausdorff for QM?

You're gonna puncture the fourth dimension dude, don't try to deny it

Slereah

That's the main proposed use for it really

Amit

Are you publishing it?

Slereah

I'd probably need to write it first

Important step

Amit

6:08 PM

I don't think that's the difficult part is it?

For a "baked" idea

@Slereah I spy with my little eye 😉

Slereah

Have you actually read it

That shit is not at all finished

Amit

No, I'm probably not up for it even

Slereah

although for some reason I seem to be the foremost authority on the topic now according to google

i got a few mails about that page

Amit

what kind of mails?

Slereah

Physicists telling me about other stuff on the topic

Amit

6:14 PM

I see, actually when I asked about publication I meant like in a journal etc.

Slereah

see above

it would need to be finished

Amit

makes sense

imbAF

6:58 PM

In Einstein's thought experiment, with the light and two mirrors in a moving frame, from which the LT can be derived, he indirectly makes the assumption that the light has the same speed seen from any inertial reference frame. How can he justify this assumption?

ACuriousMind

@imbAF Maxwell's equations heavily suggest it, since $c = \frac{1}{\sqrt{\epsilon_0\mu_0}}$. See also physics.stackexchange.com/q/489291/50583

imbAF

Thanks for the link. But before I read it. If time contraction can be written as:
$\Delta t = \gamma \Delta t'$

If $v\rightarrow c$, than $\gamma \rightarrow \infty$

Amit

It's time dilation

imbAF

which means $\Delta t \rightarrow \infty$

Then, what is the meaning here? Of infinity time duration of some event

The clock on the ship, doesn't tick at all?

Amit

@imbAF You need to remember that massive objects can't reach $c$

imbAF

7:08 PM

Sorry time dilation**

I am being hypothetical

Amit

Hypothetically yes if you could strap a watch to a light ray, it wouldn't tick :)

imbAF

And that is what an observer from earth let's say would witness

Amit

If hypothetically he can somehow see the clock receding with light speed yes. It's even obvious classically I think

ACuriousMind

@imbAF nothing with mass can have $v=c$, the limit is never reached for any observer

imbAF

Ok

I need to fire up some questions. I have been studying some trivial GR stuff, which I need in relativistic quantum mechanics. And I have amassed some questions. The first one was about Einstein's summation, for which I have the link provided

One question which I find tricky to formulate is the following:
Let\s consider primed symbols, the coordinates of the moving frame while not-primed ones those of the non-moving frame

First of all, describing that situation, doesn't indirectly implies that a 3rd reference frame is present here, with an observer

Because we are able to distinguish between two frames, one which is in motion and one which is idle

ACuriousMind

7:14 PM

no, there is no "non-moving frame", the whole point of relativity is that no notion of absolute rest exists

imbAF

Yes but the problem, which I read about a while back is the following

ACuriousMind

that's what's relative about it - all speeds are only relative to some arbitrarily chosen zero; "non-moving" is not a property of a frame, it's just that an observer in an inertial frame will put their own velocity as zero, but this is importantly only their own view of their velocity, not some statement made about the frame from outside

imbAF

I understand, and perhaps I expressed myself incorrectly. But with the following example a distinction is made

If you have an observer on earth and one on the spaceship, moving with relativistic velocity, if they see each others clocks, they will, both perceive, that the clock of the other moves slower then their own clock. But, if they would meet after sometime, the one that was in the spaceship will be younger then the one who was on earth.

Right?

ACuriousMind

It depends very much on what you mean by "meet"

imbAF

like meet after some time has passed. The spaceship guy returns for a game of Uno

ACuriousMind

7:19 PM

no, that's not the point

imbAF

What is it then?

ACuriousMind

the crucial question is whether by "meet" you mean that they are both at rest w.r.t. each other or not

we have dozens of questions on the twin paradox, the difference between the spaceship and the earth is that the spaceship accelerates when it launches and decelerates when it lands

whether something undergoes acceleration is, in contrast to having velocity, an absolute notion

see physics.stackexchange.com/q/383248/50583

imbAF

@ACuriousMind I don't understand what you mean by this

@ACuriousMind this is what I was referring earlier

thanks for this as well

ACuriousMind

@imbAF All observers agree whether something undergoes acceleration, i.e. changes its velocity. They may not agree about the value of velocity (velocity is relative), but they do agree it is changing (acceleration is absolute)

imbAF

but do they agree on how much it changes per unit of time?

meaning the value of acceleration

Agreeing that acceleration occurs, I believe is not the same as agreeing on it's value

ACuriousMind

7:24 PM

"changes per unit of time" is a loaded phrase (whose time? whose units?) but the magnitude of proper acceleration is a Lorentz invariant and hence a quantity all observers can agree on

imbAF

That's wild to comprehend. All observers regardless of their relative motion perceive the same acceleration but once that is done, the velocity is different

ACuriousMind

I didn't necessarily say they "perceive" the same acceleration

imbAF

If it is lorentz invariant, they will measure the same thing, no?

ACuriousMind

sure, but they need to actually measure the proper acceleration

imbAF

Just, so I do not have the false understanding, the addition of "proper", implies observing a physical quantity where the system that exhibits this quality is at rest?

like proper length of a rod

would be the length of it, in a reference frame where the rod is at rest

right ?

ACuriousMind

7:29 PM

the acceleration you naively "perceive", i.e. the change of velocity in your units of space over your unit of time, is coordinate acceleration and it varies

Amit

@imbAF It looks like you need to take your time with kinematics of SR from the beginning. There you get to the distinction between the four acceleration vector, whose magnitude is invariant under LT and equal to the proper acceleration. The three acceleration however is frame dependent and it's a good exercise to find the relation of the three acceleration for an object, that two distinct inertial observers moving relative to one another measure

imbAF

@ACuriousMind Ok I understand this part.

ACuriousMind

@imbAF "Proper" means it's Lorentz covariant or invariant property. In many cases, it turns out that these proper quantities have particularly simple meanings in the inertial frame in whjch the object whose property it is is at rest, such as proper time being the time the clock of an observer measures, or proper length being the length they would measure with their ruler

imbAF

And judging from what Amit said, what doesn't change is the proper acceleration

One second

How can the time an observer measures be anything else than not proper?

Like understand not measuring proper lenght, because the object moves

but the time? How?

ACuriousMind

I don't understand the question

imbAF

7:34 PM

Yeah cuz I have hard time formulating it. That is why I gave the example of the rod after asking it, in the hopes that you would be able to deduce

So let me go step by step

And observer measures the time of something, duration of an event or w/e that might be

In which case the measured time would be proper and when not?

When the spatial coordinates of where the event takes place, wouldn't change

then he would measure proper time?

ACuriousMind

that's...not how the words are used, I'm afraid :P

imbAF

Well, ignoring my poor vocabulary

I would want the answer to the question:
In which case the measured time would be proper and when not?

ACuriousMind

Let's imagine a situation where some observer runs along some track from start to finish

another is watching them from the sidelines

Amit

@RyderisnotRude. ?

imbAF

@RyderisnotRude. I did take my time with it, and the professor just touched the surface of it. Because GR is not what he is aiming. His next lecture is on dirac equation. really not realted to Gr. So I cannot right now study that, when my lecture is about QM. That is why I opt to have a feeling of what is going on

ACuriousMind

7:38 PM

Both carry clocks; the time the clock of the observer running the track shows is the proper time of that observer, the time the clock of the observer on the sidelines shows is the proper time of that observer.

Amit

@imbAF I wonder why he copy pasted part of what I wrote and then deleted it...

Ryder is not Rude.

Pardon the interruption, then.

imbAF

@ACuriousMind YES I AGREE

ACuriousMind

@imbAF So what is the question?

Amit

@RyderisnotRude. Why are you spoofing ryder's name?

imbAF

7:41 PM

Nothing, since you confirmed my assumption that the time each observer measures in his own frame is the proper time. The non-symmetry, that I feel exist is when you consider for example the rod length case

What I mean

If a frame of reference where the rod is at rest, the observer measures the proper length. An observer, for which the rodes moves with velocity v, clearly is not measuring the proper length, right?

@RyderisnotRude. I feel like, what I am discussing right now, has to do more with intuitive understanding rather than calculations. Might be wrong though

ACuriousMind

@imbAF well, what do you mean by "measuring"? Of course, if they just use their own ruler, no, they're not measuring proper length, that's what length contraction is

imbAF

what is called the length measured in the rest frame of the rod

ACuriousMind

but the point of "proper" length is that it is well-defined - they can observe how fast the rod is moving relative to them, and compute the proper length with the length contraction formulae

imbAF

Yes

Amit

I wish you weren't

imbAF

7:44 PM

@RyderisnotRude. Thanks for the irony bro

ACuriousMind

so this "proper" quantity is a quantity each observer can compute, and if two observers (no matter how they moved relative to each other during their measurements) compare their results, it's the same

imbAF

Ok I understand

ACuriousMind

that's what "proper" about it: everyone can compute it without coordinating with each other or knowing anything about the other observers, and when they compare their results, it's the same - these quantities are absolute

imbAF

I understand

Amit

@RyderisnotRude. Why are you spoofing @RyderRude 's name?

imbAF

7:46 PM

But then, why would it be wrong to say that proper length (in this case) coincides with the length of the rod that an observer at rest with it would measure

Is this statement inaccurate ?

And then, you can add this part

@ACuriousMind .

ACuriousMind

@imbAF no, it's true

imbAF

Ah ok, than I understand

Same with the proper time

But then, why did you say

they measure the proper time

which you didn't say for the length

Couldn't you say: "They measure their own times, and via LT they can find the proper time"

ACuriousMind

I mean, they also both measure their own proper lengths

imbAF

aha their own

I see

Perspective

Ok I understan. And also the nice wording of yours

Another thing, I want to ask is regarding the LT. The question might sound confusing. so instead of asking one big question with a large description I will ask a list of them, And you can stop me where I make the wrong assumption

ACuriousMind

The point is that "proper" properties are always properties of some specific object or event. A rod has a proper length - the length that an observer in an inertial frame at rest w.r.t. the rod would measure. An observer moving relative to it would not measure the rod's proper length with their naive rules - but if the observer measured the length of their own finger, that would be the proper length of the finger, since the observer is at rest w.r.t. to their finger (hopefully)

imbAF

7:51 PM

I will copy paste this answer

I understand

Ok, let's say obs.1 is in frame S and obs.2 is in frame S', which relative to S moves

You also can take the case where S moves relative to S'

So idk how important is for me to say which moves relative to which

But w/e I will follow the wording of the problem like it was done in the lecture

Amit

not important for inertial motion

imbAF

Yeah

ACuriousMind

@imbAF these are not different cases, that's the same case ;)

imbAF

Yeah same case

different something something

perspective

or just totally not say this at all

SO for S' : x' = $\gamma (x-vt)$ y'=y,z'=z, t'=\gamma(t - \frac{v}{c^2}x) these are the LT for a boost in x direction. And perhaps is important for what we will discuss, I am
considering that S' moves in the positive x direction relative to...S (can I say this?)

You also have the inverse LT for S :
x = $\gamma (x'+vt)$ y=y',z=z', t=\gamma(t' - \frac{v}{c^2}x')

Anything I need to know up to this point, or is everything accurate?

In what I described, and how I worded everything ?

Amit

@imbAF Looks ok but you might wanna recall sometimes one uses $\beta = v/c$ instead which makes the matrix formulation nicer

ah and $ct$ instead of $t$ as time coordinate

imbAF

8:00 PM

Yeah I also have that notation

right about ct

Ok, now an event takes place. I don't know if it is important for the discussion to mention where it takes place, in the reference frames of one of the two observers or in some other reference frame, a 3rd one. So if it is important later on, someone needs to draw my attention

Each observer measures some physical quantity that can be observed in that event, And each of them attaches a set of coordinates to that event

S(x,y,z,ct), S'(x',y',z',ct')

Amit

@imbAF actually you need a plus in the last relation here as well.

imbAF

where?

ah

Amit

i replied to the place :)

imbAF

yes

sorry

yeah, yeah the inverse

Well I can't change it now

Amit

no matter

@imbAF that's true in Galilean relativity as well ;)

imbAF

8:07 PM

Of course

Amit

the spacetime interval equality is maybe what you wanted to write next. but you need a pair of events for that, not one

imbAF

Now, I believe that the reason the observer in S would perform the LT (where the primed components are expressed as functions of non-primed ones), is so that he can experience what the observer in S' experiences, meaning he can observe what the observer in S' observes. So the LT where the primmed components are being measured is performed by the observer in S. And the total opposite when we consider the LT where the non-primed components are measured, which I labeled inverse LT.

Example of what I am saying for confirmation:

Rod at rest in S and moving at S'.
Observer in S performs LT (where he measures the primed components), calculates the length of the rod, and finds out that the values is smaller than what he gets, which means contraction

And the observer in S is aware that the observer in S' is experiencing this

is measuring this value for the rod

Am I correct?

ACuriousMind

yes

imbAF

Ahhhhh thank god

It makes me happy

ACuriousMind

:)

Amit

8:13 PM

yes but I think you're going to be confused if you keep thinking it's a specific observer that "performs the LT". I think a better way is just to say, there are two inertial observers. you are finding out about how they measure a certain length. because this length can be of a rod that's neither at rest at S nor S'. It can be moving with respect to both of them...

imbAF

Was I not correct in saying that this discussion has to do more with intuition rather than calculations ?

@Amit Yes

I just lack in properly expressing myself

there is not LT and inverse LT that belongs to any of them

But how else can I be general in what I say but specific enough for people to understand what I want to say

Amit

@imbAF I honestly don't know, I usually just copy the style of the best textbook I come across :D

Ryder is not Rude.

@imbAF perhaps, slow down a bit?

Relativisticcucumber

@ACuriousMind hm interesting. i wonder why hydrogen is not a metal usually?

imbAF

@RyderisnotRude. no thanks

Amit

8:16 PM

@imbAF Is this fake Ryder your stalker or something? lol

ACuriousMind

@RyderisnotRude. will you stop heckling useless platitudes while someone is asking earnest questions here? If the 30 min timeout you got for your last condescending message was not enough you can have a longer timeout, that's no problem.

imbAF

Idk but I am not here to amuse people who waste my time

Amit

Ofc not, was just curious

imbAF

Another thing I wanted to ask

Relativisticcucumber

and i have read that, if the frequency of electromagnetic radiation meets sufficient criteria (plasma frequency) that it can penetrate metals, thus making them transparent. i have also read that metals can support charge density waves (plasmons?), and i am wondering what the relation between these two phenomena are. they both seem to have the requirement of reaching the plasma frequency

imbAF

8:19 PM

@Amit The dude is the type of guy how acts in a way that annoys others, so he can get attention out of them. That's what I used to do about until the age of reason, 7th grade

ACuriousMind

@Relativisticcucumber I mean that's a bit like asking why any substance is in its "usual" state of matter and not one of the other ones at usual conditions, right? Maybe some condensed matter folk have a good answer to that; I don't :P

Relativisticcucumber

@ACuriousMind but hydrogen is in the column of other metals in the p table, right?

so my naive mindset was whether smth is a metal or not depends on valence number

ACuriousMind

I don't think many people would be happy about calling hydrogen an alkali metal :D but formally you're right

Amit

@imbAF This theory definitely fully explains the phenomena... 😉

imbAF

We say that the S.E is not lorentz covariant, because the LHS and the RHS transform differently under LT. Is that an accurate statement?

ACuriousMind

8:21 PM

@Relativisticcucumber the periodic table is where our naive hopes of the world making sense go to die :P

@imbAF yeah, you can say that

there's a bunch of other problems with relativity + naive QM, but that's one of them

imbAF

My question is about "differently"

Slereah

Even astronomers don't call hydrogen a metal

And they're very generous with the word

imbAF

They transform differently in relation to what? to each other, to what they were prior ?

Slereah

Although of course there is metallic hydrogen

imbAF

In what sense differently? Do the expressions of each side are different then before? Or they are the same and the quantities have somehow changed ?

ACuriousMind

8:23 PM

@imbAF it's more about that if you take the usual "shape" of the SE - first-order time derivative, but second-order spatial derivatives - and do a Lorentz transform on it, the result is not an equation that has first-order time derivatives and second-order spatial derivatives

Slereah

Metallic hydrogen

Metallic hydrogen is a phase of hydrogen in which it behaves like an electrical conductor. This phase was predicted in 1935 on theoretical grounds by Eugene Wigner and Hillard Bell Huntington. At high pressure and temperatures, metallic hydrogen can exist as a partial liquid rather than a solid, and researchers think it might be present in large quantities in the hot and gravitationally compressed interiors of Jupiter and Saturn, as well as in some exoplanets. == Theoretical predictions == === Hydrogen under pressure === Though often placed at the top of the alkali metal column in the p...

ACuriousMind

because the Lorentz transformations mix time and space, you get something that has first and second order derivatives of both

imbAF

@ACuriousMind so the mathematical expression differs

@ACuriousMind I see, thanks

ACuriousMind

meaning it is no longer a first-order evolution equation in time that can start from an initial condition $\psi(x,t=0)$ and derive the result

imbAF

Yes

ACuriousMind

8:24 PM

@Slereah that was my message that started this discussion :P

imbAF

@ACuriousMind I will upload something in german. Because it will take me forever to try and explain it. It has to do with "wrikung", which is used to derive the relativistic dispersion relation

Slereah

Dang ir

imbAF

@ACuriousMind what is this wirkung, and how does the first step in the calculations is made?

ACuriousMind

@imbAF Wirkung is just the German word for the action

imbAF

Ok and what is going on here? Or maybe you can give me a link

I don't understand the first equalization

ACuriousMind

8:33 PM

see en.wikipedia.org/wiki/…

imbAF

Ok

Another thing, is something about the Dirac equation, which was derived in a way, that I don't know how to name it

heuristic perhaps

But assumptions were made, and the Hamiltonian that appears in the equation, which is a matrix, it is said that it must not have complex components. Which to me is an apriority, since the Hamiltonian represents a measurable quantity, the energy. I don't know whether it's the case in the dirac equation. But the lecturer goes on and says:
H is complex then H is not invariant under spatial rotation.
I have no clue of the implications made here

Why would having or not complex components play a role in the invariance under rotation

Am I missing something ?

ACuriousMind

I suspect this is an extremely strange way to talk about observables being Hermitian/self-adjoint

imbAF

8:49 PM

Here it is, in case I say something inaccurate

Additionally, after we deduce that $\alpha_i$ are nxn type matrices, it is said that n=2 is not possible because there exist only 3 anti-commutable matrices with each other: the pauli ones.
So i literally have no idea how this statement explains why n=2 is not possible for the Dirac equation

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