The h Bar

Ryder Rude

22:00

@ACuriousMind it is the EL equation cuz it is d/dt(dL/dv)=dL/dx

it just doesn't correspond to a stationary action, which is what i write

ACuriousMind

@SignorFeynman Don't believe anything, Ron's answers are always some mix of actually correct and his own idiosyncrasies presented as obvious fact and without other sources you can never tell which is which :P

@TobiasFünke I'm not watching a program where I already know at least 50% of participants will just make my blood pressure rise whenever they open their mouth :P

Tobias Fünke

@ACuriousMind haha yeah I can relate

although it is quite funny/absurd

User198

This is I guess my question.

In CM, things evolve according to some differential equations that hold if and only if action is stationary.

In QM, things evolve according to some differential equations. Why?
Can I also say because of the Principle of stationary action? Or if referencing the path integral formalism; I get the answer "Because the integral and the maths say so."

Idk what to make of this.

Ryder Rude

in QM, the diff eqn is not a consequence of the principle of stationary action

ACuriousMind

@User198 You've just arbitrarily chosen to phrase the question in terms of the action. If you go to the Hamiltonian formalism, in both classical mechanics and quantum mechanics time evolution is generated by the Hamiltonian. Where's the problem? :P

User198

22:07

@RyderRude Ok. Thanks.

Ryder Rude

u can get to those diff eqns as simply postulates in the Heisenberg picture or u can derive them from the Schrodinger picture

User198

THan what is the cause of such diff equations?

Ryder Rude

they r pretty much postulates

ACuriousMind

@User198 What does it mean for something to be the "cause" of an equation?

Ryder Rude

but what we postulate is not the actual EL equation, but the commutator equation $dA/dt= -i/h[A,H]$

ACuriousMind

22:08

Physics does not tell you why the laws that hold hold. It should be obvious: If I say equation Y holds because of X, then you will just ask "and why does X hold?"

either you have an infinite regress of reasons, or you have to terminate at some axioms that have no "cause"

Tobias Fünke

"why" questions, in a philosophical sense, won't get you anywhere in physics, I am afraid

Ryder Rude

the EL eqn is a consequence of this postulate. Normally, the postulate u would use is the Schrodinger eqn, from which the eqn i gave is another step away

Tobias Fünke

exactly

User198

Ok, ok I guess you are right.

@ACuriousMind True.

Ryder Rude

@ACuriousMind Agrippa's trilemma also mentions circularity as an option

User198

22:11

I was just looking at CM, and thinking to myself: "Ok the principle of stationary action seems like a good way for the world around us to function. Seems nice. xD "

But than I was looking also: "QM is actually the true nature of the world around us, and there is not principle of stationary action there. So what to make of this."

Tobias Fünke

?

Ryder Rude

the path integral is the closest relative of principle of stationary action in QM

User198

Than I was looking what would be the cause of diff equations in QM, but I guess the answer is:
"The differential equations are constructed in a way as to accurately model the reality."

Ryder Rude

u can take the path integral as the postulate if u like, but i prefer Von Neumann postulates

User198

Okok

Thanks

Tobias Fünke

22:13

@User198 time evolution is generated by the Hamiltonian, just as in classical (Hamilton) mechanics

ACuriousMind

@User198 Again, the most unifying statement is "the Hamiltonian generates time evolution"

@TobiasFünke jinx

User198

Is that satisfying enought for you?

Tobias Fünke

hehe

Ryder Rude

yes. if u understand classical mech in terms of generator stuff instead of least action stuff, then QM is the same thing @User198

ACuriousMind

@User198 I do not require physics to satisfy me

Tobias Fünke

22:14

hahaha

User198

xD

Ryder Rude

@User198 it doesn't get more satisfying than lie groups

ACuriousMind

I require it to describe the world accurately :P

User198

And it doesn't make sense to ask: "Why does the Hamiltonian generate time evolution.?"

Its just the way it is.

Right?

Ryder Rude

it is the definition of the Hamiltonian. it makes sense to ask "why are there generators in the first place"

ACuriousMind

22:15

@User198 it always depends on what you want to take as your axioms

Ryder Rude

this is equivalent to asking 'why is an action minimised in the first place"

User198

True

ACuriousMind

there is great circularity between different axiomatizations of both classical and quantum mechanics, by which I mean there are several different sets of assumptions you can make that can then derive all the standard formalism

some people have strong opinions on which of these sets of axioms are more "natural"; I am not among them :P

User198

Alright

Thanks

Ryder Rude

yes. I prefer to think of a web of truths

it is not a staircase of truths

any portion of the web can be taken as an axiom

it just generates the rest of the web

while if u think of a staircase, u would imagine some preferred axioms at the bottom

so don't think staircases

User198

22:18

Alright, nice visualisation

Thanks

Ryder Rude

this is why i take "circularity" as the preferred option of Agrippa's trilemma

ACuriousMind

it's a staircase, just one of the ones drawn by M. C. Escher

Ryder Rude

it is the good kind of circularity

User198

@RyderRude You take it as the preferred option 2 times? xD

@ACuriousMind True

One more question:

The axioms of group theory are cool.

Do you think it would be a cool thing to somehow describe all of physics just by starting from the axioms of group theory?

I think this can not be achieved, because the math axioms don't have anything physiciccal /or experimental in them.

ACuriousMind

It would be a bizarre thing to expect since physics with its differential equations requires notions of smoothness not inherent in the pure algebra of group theory

Signor Feynman

22:20

@ACuriousMind I typically don't believe, I just wanted to make sure I wasn't being too biased and it seems I wasn't ;)

User198

But it just occured to me like a cool thing.

@ACuriousMind But smooth Lie groups also obay the axioms of group theory.

Tobias Fünke

oO

ACuriousMind

@User198 so?

User198

You said: "differential equations requires notions of smoothness not inherent in the pure algebra of group theory"

ACuriousMind

you're not starting from the "axioms of group theory" if you then have to add the axioms of smooth manifolds to them :P

User198

22:21

Maybe I missunderstood you.

Signor Feynman

@RyderRude you can still build a Lagrangian for the Schrödinger equation, just like you do for other fields (formally it's still the SE)

User198

@ACuriousMind Aha I got you.

Alright

Thanks

Ryder Rude

@SignorFeynman yes

@SignorFeynman the diff eqn I was talking about there was the Heisenberg eqns tho

Signor Feynman

And you can find a sense in which the SE descends from a variational principle too :P

Basically the TISE is the energy functional minimization with the normalization constraint. Some introductory books don't stress that the variational principle yields the SE and thus you can get the entire spectrum, and they seem to focus on the GS only

Ryder Rude

nvm

it is resolved now

CPlus

22:33

del-pls 20k+ Opinion-based/off-topic physics.stackexchange.com/q/842098/359074

ACuriousMind

@CPlus I know SO has chat rooms that work like that, but we don't do that here.

CPlus

Are there any rooms here that work like that?

Signor Feynman

And since I brought it up, why does there seem to be a RM cult on some places of the internet? Some sort of unsung hero cult

ACuriousMind

@CPlus no, we're much smaller than SO and do not have dedicated rooms where high-rep users would coordinate moderation

@SignorFeynman people love a charismatic writer (regardless of the accuracy of the content, he is a good writer) posing as an iconoclast :P

obviously as a defender of the orthodoxy, I'm biased :P

Signor Feynman

It's scary what charisma can still do to people as of today

Ryder Rude

22:45

Ron always expresses strong opinions

Signor Feynman

Although the guy is somehow quoted in some papers or thanked for useful discussion

Ryder Rude

like, in philosophy, he says everything except logical positivism is useless

Signor Feynman

I'm talking about physics, which is the only thing I have some knowledge on :P

Ryder Rude

like, any questions that is not validated by logical positivism is meaningless to ask

@SignorFeynman oh

Signor Feynman

I have read some posts of his basically saying that entire branches of math are trash

Ryder Rude

22:47

yeah... he expresses strong opinions. not too open minded.

strangely, he is open minded about LQG and String theory being compatible :P

cuz he takes string theory as fact. So it was unexpected to read

@SignorFeynman he says that any math that isn't constructible is useless. e.g. axiom of choice stuff

@SignorFeynman i think he has a really deep knowledge of physics

ACuriousMind

@SignorFeynman To be realistic, we don't know what it would look like if the early 20th century physicists would have been able to post here :P

if you look at the non-technical stuff some of them wrote or said and poured it into an SE post, it perhaps wouldn't look all that different

or just look at what 't Hooft posted

Ryder Rude

@ACuriousMind it sounds similar

i think it is the tradition of Bohr and Einstein to make these physical arguments in natural language

these people r probably inspired by that

Signor Feynman

@ACuriousMind you're implicitly comparing RM to big names, bud :P

Ryder Rude

it is about preference. i don't like natural language arguments too much cuz it sounds like u could argue anything that way. but the people who can do it right do have some great physical knowledge

Signor Feynman

23:02

Incidentally, I have the impression we don't wanna know would SE would look like in a 20th century spin off

Landau and Pauli would get a permaban

ACuriousMind

@SignorFeynman I wasn't saying anything about relative merit compared to the "big names", and more trying to point out that we have a lot less records of this kind of informal discussions between physicists in the past

@SignorFeynman von Neumann just gets suspended every year like clockwork for posting unhinged screeds about bombing the Soviets after the previous suspension runs out :P

2

DIRAC1930

What did people think of Pauli spinors when they were first introduced?

Like did people have the same bewilderment as when Dirac spinors were introduce? It seems like people didn't know what to make of Dirac spinors at first since the projective representations are missed by the tensor calculus used at the time

But it seems like they just accepted Pauli spinors immediately

Signor Feynman

23:24

@ACuriousMind I guess this deserves a spin off fan fiction

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