The h Bar

4:07 AM

@Slereah holy carp this covers a lot, but seriously, so many tiny headaches! calling velocity configuration space phase space, having the manifold coördinate mapping the opposite direction, incredibly complicated notation only to go back to old notation at the mechanics portion, wtf am i reading?

Slereah

11:01 AM

@Amit One thing I can tell you is that if you consider the projective structure of a manifold, ie the equivalence class of spacetimes with metrics $(M, g)$ such that they share the same geodesics, $\nabla_{\dot{\gamma}} \dot{\gamma} = 0$, then 1) the class of all such spacetimes contains all diffeomorphic spacetimes which are related by a constant Weyl factor 2) This isn't the only case

Ryder Rude

Hello

Slereah

There are some sporadic examples of two different spacetimes which aren't conformally related which share the same geodesics

Not sure if it relates here tho

Ryder Rude

Infinite time evolution is killing two birds with one stone. 1. It allows for quantum to classical transition, thereby solving the measurement problem.

2. It makes the infinite time path integral a fundamental descritption of reality, which makes for a fundamentally covariant quantum theory.

Slereah

But as far as you're doing it with just coordinates on Minkowski spacetime your question is essentialy just a differential equation

Ryder Rude

But the thing is... our actual experiments take place over finite time. But what if it's our clock that shows finite time, and the system's internal clock really evolves for infinite time?

But how can the system's internal clock evolve for infinite time while our clock shows finite time

Even general relativity doesnt allow for this behavior of time

ACuriousMind

11:07 AM

@RyderRude You're overthinking this: The "infinite time" is just an approximation like any other approximation. Nothing in the formalism claims infinite time actually passes.

Slereah

also if you're very bothered just think "infinite proper time"

ACuriousMind

Ordinary QM scattering theory also has the Møller operators being a limit as $t\to\pm\infty$

Ryder Rude

@ACuriousMind I was thinking that if we modify the postulates somehow to actually get infinite time evolution, we could kill these two birds with one stone

ACuriousMind

@RyderRude there are no birds to kill

physics is all perturbations and approximations

learn to live with it

Ryder Rude

@Slereah but does GR allow the system's proper time to be infinite while our clock shows finite time?

Slereah

11:09 AM

Yes, but this QFT approximation is done on Minkowski space

If you start to look into Malament-Hogarth spacetimes or spacetimes without a proper conformal boundary I'm guessing things are gonna get unpleasant

Ryder Rude

Ooh so GR does allow it!

Slereah

sure

Malament–Hogarth spacetime

A Malament–Hogarth (M-H) spacetime, named after David B. Malament and Mark Hogarth, is a relativistic spacetime that possesses the following property: there exists a worldline λ {\displaystyle \lambda } and an event p such that all events along λ {\displaystyle \lambda } are a finite interval in the past of p, but the proper time along λ {\displaystyle \lambda } is infinite. The event p is known as an M-H event. == Significance == The significance of M-H spacetimes is...

De Sitter space is an example IIRC

Ryder Rude

@Slereah I dont agree with the usual quantisation of GR anyway because it pretends that Minkowski time is the physical time of the system, which is experimentally false

Slereah

I don't believe it does such a thing

Amit

@Slereah is it spacetimes that are conformally related or the coordinate charts? or are these two actually equivalent and the same way to formulate the same thing?

Ryder Rude

11:12 AM

I mean it divides the full metric into eta and h and treats h like a dynamical field, and it makes the time give by eta into the parameter of unitary evolution @Slereah

This parameter of unitary evolution should be the physical time of the system

Slereah

@Amit Spacetimes are conformally equivalent, although of course you can describe it in coordinates

Ryder Rude

The time given by $\eta$ really has no physical significance

It has no business being the parameter of unitary evolution

Slereah

most physics books do it in coordinates as they are wont to do

The actual condition should be that if you have some map between your two spacetimes then $g_2 = f^* g_1 = \omega g_1$

for some scale factor $\omega$

Amit

okay

Slereah

But I would guess that no there's no change of coordinates that isn't a constant conformal factor that would have a zero Christoffel symbols

Trickier to judge than for a tensor though since they don't transform as tensors

Amit

11:22 AM

it may bear some similarity to how irrotational vector fields look like

Slereah

If the Christoffel symbols are zero then the curvature is zero, so it's just flat space, so that this is just some coordinate transformation of the flat metric. The Christoffel symbols transform linearly in the first part plus some term depending on the Jacobian and its derivatives

Ryder Rude

@Slereah this spacetime is sooo badass. So we can make our experiments evolve for infinite proper time while our clock shows finite tjme

If we incorporate this idea into quantum theory, it may solve the measurement problem

Slereah

If you want your symbols to be 0 you need $$\frac{\partial x^m}{\partial x'^k \partial x'^l} \frac{\partial x'^i}{\partial x^m} = 0$$

Ryder Rude

Because perfect decoherence happens after infinite time

Amit

@Slereah just some linear coordinate transformation right

Slereah

11:28 AM

@RyderRude It may not

@Amit Feel free to solve the system to check

It is certainly true if it's just a rescaling

Ryder Rude

@Slereah yes, it also may not. But it is one promising direction, I feel.

Slereah

The point of the infinite time business in QFT is that in such circumstances, after an infinite amount of time, the various particles separate each other far enough so that they do not feel each other's influence and they move as free particles

this will not be true here

also it's just a trick, getting rid of it won't "solve" the measurement problem

Ryder Rude

Oh

We dont need this exact spacetime becuz we r not doing our actual experiments in this spacetime anyway

But it is promising that GR allows for infinite proper time

We need to achieve it in some other way than this spacetime. We need to achieve it in the process that we quantise GR

One thing is for sure, the physical time of the system is a dynamical entity. So when we quantise gravity, the system's internal proper time does not have a well-defined evolution

Because quantisation introduces uncertainty to the metric

And we experimentally know that the physical time is a dynamical entity, because the proper time is given by the full metric $\eta + h$

Amit

@Slereah The trick here would be to also make sure the transformation remains diffeomorphic I think, otherwise it's easy

Slereah

@Amit just make sure that the determinant of the Jacobia doesn't vanish

Amit

11:47 AM

maybe it's possible with an antisymmetric metric? Idk, it goes beyond my level of comfort in diff. equations :D

Slereah

that's not even differential geometry here, it's just a PDE to solve

Amit

yes

Trying something like $x^{'1} = (x^1)^2$ , $x^{'2} = (x^2)^2$ didn't work :)

I think I see intuitively now why there can't be such a transformation, no idea how to prove it though

Intuitively, we are "asking" the coordinate basis to change and that has to be reflected in a non-zero Christoffel symbols, regardless of whether there is or isn't a curvature

I mean, the moment we have a metric which is not just numerical factors times $\eta$ we are "asking" this...

Ryder Rude

General Relativity is such a chad theory

Allows for CTCs as well as infinitely long computations

What r some other badass spacetime features

Amit

It's mostly tax free

Ryder Rude

Einstein was probably communist :)

Amit

12:01 PM

a lot of intellectuals had a phase of communism back then, until they saw the implementation...

maybe it's a bit like ST?

just kidding ^_^

Ryder Rude

Wasnt Vietnam communist and doing fine

But idk. I hav not read their history

Amit

Idk... anyone who stays out of politics is doing fine in my book, lol

Slereah

The Soviet Union should not be a black mark on communism since nothing implemented in Russia ever had good results

Amit

My favorite truism in this regard is that the wrong people can conquer any type of regime, and no type of regime can eliminate all the wrong people

ACuriousMind

@Amit Einstein famously wrote "Why socialism?" in 1949; this was not a phase, he was a very public and outspoken socialist (but rejected the label "Communist"), which also earned him scrutiny in the US during the McCarthy era, cf. e.g. amnh.org/exhibitions/einstein/global-citizen

Slereah

12:06 PM

It's not like the soviet union was that much worse than czarist russia

Boy not a fun time to be around

Amit

@ACuriousMind I don't know enough about that era I guess, but today we distinguish much more between socialism and communism. Are you suggesting it was almost synonymous?

Ryder Rude

Or maybe Einstein was having the old physicist phase where they keep telling other people that they're wrong about their field :P

Amit

@ACuriousMind From the link you sent:

> Einstein never backed down from his beliefs, however—and always emphasized the importance of intellectual freedom. "I have never been a Communist," he said. "But if I were, I would not be ashamed of it."

Ah, I'm sorry ACM, I missed your parenthetical comment.

Ryder Rude

People say Marx is one of the most evil people in history. Is that justified

ACuriousMind

@Amit it is not clear to me what we clearly distinguish the notion of "socialism" and "communism" today - everyone seems to have a different fuzzy notion of what the difference is supposed to be

Ryder Rude

12:11 PM

Emperors had been genociding for all of human history

It's just that emperors got replaced with dictators

Genocide continued. I dont think Marx can b blamed. But im not an expert

Amit

hah :) I think you're right. We probably like to think there's a clear line, probably because communism is indeed considered a "black mark" on the socialist movement

ACuriousMind

I mean, the easy definition would be that only actual Marxists are communists, but that's generally not how the term is used either

Slereah

I think the term predates Marx too

also bickering on terminology is truly the worst part of any field

Ryder Rude

Most countries today r like a mixture of socialism and capitalism

They now hav very complex jargon to label this stuff

Like proto meteor capitalist economy

This jargon is used to describe mixture economies

According to google, the world does produce enough food to feed everyone, but it's the supply of food that causes world hunger

Ryder Rude

1:13 PM

If we become able to harness interstellar energy, it would solve most human conflicts

Slereah

why would it

Ryder Rude

The universe has abudance of every resource. We shouldnt be needing to fight, but we are not yet able to acesss the resources outside of earth

@Slereah we are fighting for resources

Slereah

the problem isn't the production of resources

plenty of resouces are abundant enough as it is

Ryder Rude

The problem may be supply?

Technology would cure that too. I think we are not far from a future where there is no competition in life

Eventually, we should reach sort of an equilibrium where we no longer compete for small things

Right now, nations are trying to screw over each other. Nations have become vultures

It's because we are all competing for Earth

Nukes would also cease to be a problem in an inter-planetary civilisation

Ok but we may need to worry about Death Stars then :P

@Slereah But u r right. All conflics are not about resources. There are also conflicts caused by ideologies. These are caused by narcissistic dictators and they wud be a problem even in an inter-galactic civilisation

Amit

1:31 PM

Nations are worse than mobs 'cause mobs at least have the police to regulate their criminal activity... but the nations are supposed to be self regulating lol... the UN is really a bit of a joke

Ryder Rude

Yes, there is no world court to hold anyone accountable

Amit

It's a builtin problem, who watches the watchers

They tried to invent "checks and balances" to deal with that

But as long as power is concentrated anywhere it remains a problem

Ryder Rude

On a global level, countries understand that it's not about morals. It's all about being opportunist and vulturing over other countries

But still, world peace has improved a lot compared to 1000 years ago

I think technology brings world peace

Amit

Idk if world government will solve all of our problems, but because of technology, w/o a world government I'm pretty sure we'll be doomed, lol.

Everyone will have the means to destroy everything

Ryder Rude

World government sounds like an interesting idea

ACuriousMind

1:42 PM

@RyderRude it has?

Ryder Rude

Star Wars had this stuff but for a galaxy

Amit

@RyderRude You have to start somewhere :)

Ryder Rude

@ACuriousMind yes. Now u dont have emperors invading and killing becuz they felt like killing

ACuriousMind

@Amit everyone (the nuclear powers) already has the power to destroy everything

@RyderRude Which emperor thousand years ago do you think invaded "becuz they felt like killing"?

Ryder Rude

e.g. Napoleon, Alexander, Genghis were infamous genociders

ACuriousMind

1:45 PM

oh, they killed a lot of people, but not "becuz they felt like killing"

Ryder Rude

They killed for fun

They were very rage-fueled

Amit

@ACuriousMind Yes.. but they're still very expensive and messy to handle. I am projecting into a future where not only nukes are widely available but all kinds of targeted viruses and other more "elegant" means of destruction are both cheap and widely available... what happens in the Cyber "war" field is a clue: everyone is doing it because it's quite easy to deny you're doing it

ACuriousMind

@RyderRude how do you know?

Ryder Rude

@ACuriousMind Genghis used to kill countries if they didnt surrender in 3 days

And also when he felt like it

It was very unpredictable times

ACuriousMind

@RyderRude What about that is "rage-fueled" and not "effective military strategy"?

Ryder Rude

1:47 PM

@ACuriousMind they did used to be irrational tho. They often order to kill everyone AFTER winning

Amit

Conquering the world by killing a lot of people was something that people used to look at like we look at Mars exploration nowadays in the modern "enlightened" world. It was just obviously cool and the right thing to do, a great use of everyone's time :D lol

Ryder Rude

U cant expect these emperors to b rational

ACuriousMind

@RyderRude just because we generally call that a war crime today doesn't mean that doesn't happen anymore

Have you looked at the stuff that went down in the World Wars?

Ryder Rude

@ACuriousMind it has improved becuz in many countries u can now live a lifetime without getting invaded and mass murdered

ACuriousMind

@RyderRude most people in the past also lived a lifetime without getting invaded or mass murdered

Amit

1:48 PM

It's not irrationality it's just rationality by different standards... spreading your own culture and way of life and way of thinking to as many places and people across the world. Now we don't need that, we have the media, we have so many political and social ideologies... we don't need to kill so much, we just brainwash people :D lol

Ryder Rude

@ACuriousMind Genghis killed 15% of world population

I think Genghis may b an outlier tho

ACuriousMind

@RyderRude So? That's over 20 years of war, and it was very much a singular historical event rather than the norm

Ryder Rude

Perhaps in other generations than Genghis, u cud live a lifetime just like today. But I will doubt it because there didnt used to be a UN back then @ACuriousMind

Countries werent connected

Amit

It's also a bit difficult to digest that the world population in 1760 was 10% of what it is today!

Ryder Rude

The environment encouraged raiding and murdering. It wss the norm

ACuriousMind

1:50 PM

I really don't know what you imagine the past to be like

people didn't go around just killing each other

they thought, in general, that killing was wrong just like we do

and yet they waged war - but again, just like we do

Ryder Rude

Yes. I also dont buy moral relativism. The common people had to be good @ACuriousMind

But do u really think that wars didnt used to be more common back then @ACuriousMind

It was the culture of the time to go to war

ACuriousMind

depends on how you count, what's a "war", etc.

@RyderRude There's wars going on right now, too!

You can't really claim that we don't go to war anymore

Ryder Rude

Yes. I'm just saying it's less common today. Back then, a king wud b lucky to go thru his life without fighting a war

Today, most country governments live without wars

ACuriousMind

[citation needed] for both of these claims

Amit

@RyderRude If you work out the percentage of losses in the Russian-Ukraine war to the total world population at say, only 500 years ago, you'll be surprised at the result!

Ryder Rude

1:55 PM

I have not read history :P

@Amit but this is unfair. We shud actually b comparing the% of people who died in war in modern era to the% from history

ACuriousMind

@RyderRude so why are you so confidently making these claims?

Ryder Rude

@ACuriousMind I still think they r true because there wasnt any UN back then. It was considered right for an emperor to go to war. Genghis, Alexander r examples

Amit

@RyderRude But you realize what this means right... it means we got better at killing but at the same time value human life less because there's more of us? That sounds a bit grotesque isn't it?

Ryder Rude

But yeah, I will have to find sources to back it up @ACuriousMind

@Amit yes. That is another way to look at it. I'm looking at it in terms of the probability of dying

ACuriousMind

@RyderRude So? The predecessor of the UN did not prevent WWII, nor did the UN prevent e.g. the various wars the US has waged during and after the cold war

Ryder Rude

1:58 PM

In absolute terms, human suffering as increased @Amit

Amit

@RyderRude So technology hasn't really delivered yet on its promises, I mean, tech can't promise anything really, it's the promises made on behalf of it :)

Ryder Rude

@ACuriousMind u r right. There is still no world court to hold anyone accountable

ACuriousMind

@RyderRude there literally is a world court

Ryder Rude

@Amit but tbf, in absolute terms, human non-suffering has increased a lot too. This is y the probabilty argument cannot be dismissed completely

@ACuriousMind i knew about that court. This is y i said "There is no world court which actually holds US accointable" :P

ACuriousMind

what does that even mean

Amit

2:01 PM

@RyderRude Yeah I'm not dismissing it... I mean to say, technology alone doesn't promise us a bright future, that was the only point I objected to

Ryder Rude

@ACuriousMind i mean no court has the actual power to punish for war crimes

ACuriousMind

@RyderRude and where would such power come from?

Ryder Rude

@ACuriousMind if there was a world government like in Star Wars :P

ACuriousMind

also: plenty of courts have the power to punish for war crimes: It's usually the courts of the victor in a conflict judging all the other side's war criminals

@RyderRude And how does that work?

Ryder Rude

@ACuriousMind lmao

Yes. "History is written by winners"

@ACuriousMind it requires a radical change of world system. Im not sure if its practical tho

Becuz there r too many cultures to b under uniform laws

Maybe there cud b prejudice

ACuriousMind

2:05 PM

@RyderRude also: You realize that the "world government" in Star Wars was corrupted into a tyrannical empire, right? That is, Star Wars is a story of an overarching government being instrumentalized to oppress everyone, not a utopian vision of how a universal government should work

Ryder Rude

And also, the majority population countries wud screw over democracy

Amit

lol

Ryder Rude

@ACuriousMind yes. It was again corrupted by the Sith ideologies

Amit

Holy sith

Ryder Rude

Technology can only resolve resouce conflicts. Ideology conflicts r there to stay with us till the end of civilisation

Or perhaps AI overlords can solve all human conflicts :P

I think AI species may b the good guys aftr all. There need to b more movies presenting them in good light

Who's to say they wont b friendly and wont follow "live and let live"

They wud b the bad guys only if there's a resource conflict between us. Then we r screwed

Amit

2:11 PM

Maybe we'll just genetically engineer ourselves to the point where we don't think it makes sense not to cooperate... like the Borg!

They did it with cybernetics too... I think that's redundant

ACuriousMind

ah, yes, the Borg, another famously utopian concept

Amit

lmao

I was hoping that it would be read sarcastically

Maybe there's like a nice version of the Borg though right? Like, hippie Borg or something

They always cooperate but never at the expense of another civilization

ACuriousMind

that's the Federation

Amit

Yes, but the federation just put that as an ideal, I am talking about hardwiring

ACuriousMind

at least on old Trek, the Federation is a genuine utopia

Amit

2:15 PM

Everyone likes the phrase "cooperate freely" but if everyone is free to cooperate it means inevitably not everyone will cooperate :D that's the human condition

Ryder Rude

Borg sounds a lot like Googl's AI Bard :P

@ACuriousMind I cant believe that, on average, world peace isnt higher today compared the emperor times. Do u hav a study about this

ACuriousMind

@RyderRude What does "world peace is higher" even mean

Ryder Rude

Yes, there is no way to measure it. But a study wud create some criteria

U r sure that today isnt much better. What is the data on this @ACuriousMind

ACuriousMind

Also, you should not take my questioning of your claims as evidence that I believe the world is less peaceful todoy

Ryder Rude

Yes. I mean u r saying it's not much better today

Not necessarily less

ACuriousMind

2:26 PM

@RyderRude Oh, I am absolutely sure that for someone like me - born in a rich European country - the world today is much better than it would have been 1000 years ago in many ways

Ryder Rude

I thought people in the past were always fearing to get invaded and mass murdered lol :P

ACuriousMind

What I am cautioning against is imagining the past as being inhabited by barbarians that did nothing but pillage and murder each other

Ryder Rude

Yes. There still had to be more-or-less normal lives without being constantly paranoid

Silly Goose

I was wondering: a photon is not a classical concept right?

ACuriousMind

no

Silly Goose

2:32 PM

Oh it is a classical concept?

ACuriousMind

no

Silly Goose

Oh okay

ACuriousMind

questions with negations in them in English just suck because you never know how to interpret a "yes" or "no" answer :P

Ryder Rude

ACM meant "no, it's not" @SillyGoose

Silly Goose

Lol yeah i should have ohrased the question so an unambiguous answer was given easily

I think the same is in korean i had trouble w this grammar lesson even though the same situation happens in english xD

So then does the logic in the top answer here make sense? physics.stackexchange.com/questions/765961/….

The claim is that the chargelessness of the photon can be seen from the fact that in CFT the maxwell equations are linear. But isn’t it like just serendipitous that the form of the maxwell equations are pretty resilient to advancements in physical theory. So a priori CFT maxwell’s being linear has nothing to do with QFT maxwell’s being linear? Also photons arent a thing in CFT

ACuriousMind

2:39 PM

I'm not sure where the serendipity here is

Ryder Rude

U can at least talk about the charge of a classical field becuz of the appropriate symmetries

ACuriousMind

both the classical and the quantum theory have uncharged light/are linear because there are no terms of higher order than $\propto A^2$ in the Lagrangian

Silly Goose

Hm i see

@ACuriousMind i guess my impression was that the form of the Maxwells stays the same from classical through quantum as well as through relativity which just seems to be a convenience. Unless there is an explanation for why the form is “correct” for both frameworks

ACuriousMind

@SillyGoose what do you mean "convenience"

why would the form of Maxwell's equations change during quantization?

and what does "through relativity" mean? Maxwell's equations are inherently relativistic (because they fix the speed of light to be a constant), there isn't really a non-relativistic version of them

Silly Goose

Right but the intention wasn't for them to be relativistic

ACuriousMind

2:47 PM

whose intention?

Silly Goose

Maxwell perhaps :P im not sure the founders of the theory

ACuriousMind

oh, sure, we didn't right away understand they already had relativity built into them

but I'm not sure what question you're trying to ask about that

Silly Goose

I think this is what i mean by convenient that the maxwells were made before relativity and before quantum and they just work for both and that is convenient or serendipitous is what i mean

Although i do not know about what the quantizing procedure looks like

Like newton’s laws dont work for relativity so they had to be supplanted

But not maxwell

ACuriousMind

@SillyGoose Maxwell's equations and their constant speed of light were the whole trigger for the development of relativity (and aether theories)!

Silly Goose

Hm okay i see i suppose in that sense they must be relativistic :P—or relativity was constructed to fit the maxwells

Slereah

2:51 PM

I mean you could indeed have made Maxwell non-relativistic, but all of it was hinged on the ether

It turned out not to work

ACuriousMind

@SillyGoose Of course it was, where do you think the postulate of the constancy of the speed of light in relativity comes from?

why would anyone start to believe that the speed of light is constant if not because they knew that if you didn't have an aether that's the "obvious" option left to explain why the heck Maxwell's equations work

Slereah

people just expected that the Maxwell equations were only valid in the ether's frame of reference

and that the speed of light would change depending on the frame

ACuriousMind

the paper in which Einstein introduced relativity is called "On the electrodynamics of moving bodies"!

Slereah

Most people just assumed at EM was basically like a fluid's wave motion overall

like sound

which was a pretty sound idea back then

ACuriousMind

sure, until we failed to detect the aether there wasn't a lot of reason to doubt it

Silly Goose

2:56 PM

okay so then is it just a trivial sort of thing that when you "quantize" the maxwell equations (i am not sure what this actually means to do) that the form is retianed?

ACuriousMind

I'm not sure how to answer that question except by "you have to learn about quantization in QFT"

Ryder Rude

Yes, this follow from the Heisenberg's eqns in quantum mechanics

It is true even for Newtonian mechanics. They hold in the quantum theory

ACuriousMind

because probably you don't even really understand what it even means when we talk about Maxwell's equation in a quantum context - it's not an equation for a wavefunction as you might assume.

Ryder Rude

I mean for the operators

Silly Goose

arent they still equations whose solutions are the fields :0

Ryder Rude

2:58 PM

Yes, operator fields

ACuriousMind

@SillyGoose but what does that mean?

Ryder Rude

Not classical fields

ACuriousMind

just like in ordinary QM you don't have definite positions or momenta anymore, in QFT you don't have definite fields anymore

Silly Goose

well id have to think about that :P

hm but so are you saying that fields are not physical states

@ACuriousMind with this comment

ACuriousMind

@SillyGoose yes

the fields are operators, not states

just like position and momentum become operators instead of definite properties of states

Ryder Rude

3:01 PM

But there is some related shit where Maxwell's eqn somehwat becomes the eqn of position space wavefunction from rel. QM

But this is besides the main point

For e.g. Dirac eqn is also the eqn of position space wavefunction

Silly Goose

but then is a photon not a physical state :P; or maybe a photon is a system and within this system you associate a hilbert space of states

ACuriousMind

what

A photon is a specific quantum state

so far we've only talked about fields, not particles

and really, if you want to know what's going on, you just need to learn QFT

Ryder Rude

@ACuriousMind tbf the terminology on this is really ambigous. Do u identify an electron as a state $|p\rangle$?

I think there r some problems with this idea

Silly Goose

@ACuriousMind this does seem to be a good idea :P

ACuriousMind

@RyderRude which kind of electron? The kind of electron I have in a collider beam? Sure. The kind of electron I have in an atom? Of course not, that's at least a superposition of $\lvert p\rangle$s such that average momentum is zero.

Silly Goose

3:05 PM

what other maths are quite important in qft? it seems like representation theory (and Lie theory) but i am not sure about others

Ryder Rude

@ACuriousMind yes this is the problem i mean. Many people define particles as the eigenstates of field hamiltonian, which is wrong terminology

Slereah

@ACuriousMind I would expect them to be a little localized

ACuriousMind

a little localization, as a treat

Ryder Rude

@ACuriousMind but ur terminology is correct where u also identify a superposition as a single particle

But it is very common in QFT to refer to particles as energy eigenstates

This makes for confusing terminology

Silly Goose

i thought particles were mathematically irreps of the poincare group 0.0

ACuriousMind

3:07 PM

@RyderRude I think you're misreading whatever sources you're talking about

Everyone agrees that for a free field you have a Fock space, and there's of course a one-excitation part of the Fock space. That's the space spanned by the $\lvert p\rangle$, and it's the one-particle space

I would be surprised if anyone disagreed with that. There are a lot of subtleties to the notion of particle in practice, but restricting the term "particle" specifically to eigenstates of the Hamiltonian is not something I have commonly seen

Ryder Rude

Yes, I think this is correct. I may have misread it. But i can support this mis-use of terminology with evidence

For e.g. havent u seen photons being called discrete chunks of energy of light?

ACuriousMind

@RyderRude of course, but that's not really a claim based in QFT, that's just a description of what the photoelectric effect looks like

Ryder Rude

Yes, but it is the most commonly perpetrated view of photons

It confused me for a bit :P

ACuriousMind

pop-sci communication about QFT is universally terrible

Slereah

I'd say never believe anything called a particle in QM

ACuriousMind

3:10 PM

^the sanest approach

Slereah

Particles were invented in the 16th century or so, they don't really fit modern notions of physics

Due to this a lot of things are called "particles" based on whether or not they have some commonality with them

ACuriousMind

@SillyGoose There's lots of math you can introduce, but I firmly believe that for a good intro to QFT you need not so much a lot of math and much rather a firm understanding of classical physics and ordinary QM

because the most confused questions about QFT I've seen are always people who have never seen a classical field and haven't really understood the basics of QM either and then they get horribly confused about which parts of the arguments they're reading are supposed to be specific to QFT and which aren't

Ryder Rude

One other massive mis-use of terminology is conflating the "quantum field" with the "operator field"

This is one i have realised myself

ACuriousMind

what

I don't know what "the operator field" is and how it is supposed to be different from "the quantum field"

Ryder Rude

"Quantum field" should ideally be the term of the physical system we are studying

"Operator field" is just a heisenberg picture term

ACuriousMind

3:14 PM

what

"operator field" is just shorthand for "operator-valued field"

when people say "quantum fields are operator fields" they mean that the fields we deal with in QFT are operator-valued

Ryder Rude

I'm saying that "electron field" or "electromagnetic field" is the abstract physical system we r studying in QFT

And these r quantum fields becuz of uncertainty stuff

"Operator field" shud b a distinct idea

@ACuriousMind the fields we deal with is the physical thingy that we measure. It is distinct from the Heisenberg picture field

ACuriousMind

who said anything about "Heisenberg picture"?

Ryder Rude

I will explain using non rel QM. Imagine calling the position and momentim operators "an electron" @ACuriousMind

ACuriousMind

a quantum field is an operator field, meaning it is a function that assigns to each point in spacetime an operator (this is untrue, but it is the mathematical fiction we work with in intro QFT)

Ryder Rude

Yes, but i dont agree with naming it a "quantum field". It shud just b an " Operator valued field"

Maybe it's just me

ACuriousMind

3:20 PM

it's just you

Ryder Rude

Idk :P

Slereah

I think ryder has been having a stroke for the past few months he's been talking here

Ryder Rude

I dont type full words because im on mobile :P @Slereah

Slereah

Do you also type nonsense because you're on a mobile

Ryder Rude

But i do agree with calling the field as "Quantum Field Theory", because we r studying " Quantum Electromagnetic field", "Quantum Electron Field", etc

These are the physical systems we are studying

I just thinking that calling "operator fields" as "quantum fields" is like calling "position and momentum operators" as "electron"

Sorry i have a better analogy. Imagine calling the position and momentum operators as "a quantum particle"

naturallyInconsistent

3:36 PM

@RyderRude Why is it always the most ignorant of history that love to repeat this falsehood?

that is a misunderstanding of the direction of understanding. Theorists must first make mathematical models of our universe to explain the physical phenomena, and if those models are any good, then they would include physical insights that are way beyond that conceived in the minds of the theorists who found the correct mathematical models.
Similarly, it is the quantum and relativistic models that have a simple classical approximation, thus not surprising that the same equations would work after discovery of new physics.

@ACuriousMind Michelson and Morley interpreted their results as supporting one type of æther over another. It is impossible to settle that question experimentally.

Slereah

You have to do a lot of song and dance to pretend the ether is still a good idea

Ryder Rude

@naturallyInconsistent dont u think its true to some extent

naturallyInconsistent

@RyderRude if you studied some history, you will know this is manifestly refuted by evidence.

ACuriousMind

3:51 PM

@naturallyInconsistent I know, but no one really believes in the kind of aether that's still technically possible - Occam's razor in action

Ryder Rude

@naturallyInconsistent i hav not studied history very well, yes. But i think there are some instances of winners making them look like saints

Slereah

I mean have you actually read Ockham

His real big idea is that the pope should be in charge

naturallyInconsistent

@ACuriousMind I'm not disagreeing/denying. I am just saying that those who insist upon an extremist empirical position to physics will never get to understand the limitations of pure experimentation. One has to understand that theory and experiment go hand in hand, and some things can only be settled by having scrutinised the theoretical aspects.

ACuriousMind

Clearly the simplest solution

Ryder Rude

For e.g. Alexander is called "The Great" while Genghis Khan is called barbarian and stuff @naturallyInconsistent

naturallyInconsistent

3:54 PM

@RyderRude That is the opposite of the scientific method. You are supposed to look for when it fails, not when it works.

Ryder Rude

Also, Japan were losers but they didnt teach their population that they did wrong @naturallyInconsistent So the truth doesnt always come out because the ruling state controls education

naturallyInconsistent

@RyderRude That is also manifestly a false statement.

Ryder Rude

I dont think British teach their history in bad light either

But Germany does

naturallyInconsistent

@RyderRude lol at the actual nuances involved in this

ACuriousMind

@RyderRude Alexander got the epithet most likely from the Romans, cf history.stackexchange.com/q/706

Ryder Rude

3:57 PM

Idk i havent seen textbooks frm these countries :P

@ACuriousMind thanks for the link

naturallyInconsistent

@RyderRude Chances are, you live closer to them than me.

Ryder Rude

@naturallyInconsistent Do u think these countries teach the stuff in an honest way?

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