I remember everyone was confused in class when we learned about what a mole is

Yeah it sounds a lot scarier than it is

@ACuriousMind "Energy does not have mass, it is can be transformed into mass" and so on and on. Try asking graduates about the history of relativity theory. You will see I am not making this up.

@MatthewChristopherBartsh I mean, if that is your experience then that of course sucks, but I really don't know where you got those interlocutors from. Really anyone with some basic understanding should have been able to explain rest/invariant mass to you.

this really sounds as if you only talked to people who had their knowledge of relativity from pop sci treatment instead of actual physics

of course they perhaps won't know the historical details of the shift in the usage of "relativistic mass", but actual physicists being unable to explain what they mean by the photon being massless sounds just absurd to me and does not match my experience at all

@ACuriousMind Not at all, one of them was a professional physicist.

you either vastly overestimated the expertise of these people or they thought you were a crackpot ("The photon can't be massless and relativity is wrong" is a common thing crackpots say) and were just trying to make you go away

Professional physicist may not mean much

I don't know anything about geophysics

@This guy was very smart.

@MatthewChristopherBartsh So? Unless their expertise was in a field that required relativity, they might not ever have actually learned relativity at a formal level

Smart people tend to be specialized :P

You never see anyone asking a vulcanology question on PSE

I don't know nothing about volcanoes

Mysterious

@ACuriousMind I thought he was dumb for thinking that a photon had no mass. I guess in a way he was, but it wasn't his fault. He had been miseducated. I think I've found a way to mitigate the problem, and the benefit to nonrelativists would greatly outweigh the harm if any to relativists. Indeed, all relativists were once nonrelativists so it might even benefit those people on balance.

@ACuriousMind He did use relativity. He used to make software that simulated relativity. I don't know how good it was, but I saw some other software he made and it was impressive.

*not dumb for thinking it had no mass, but dumb for not knowing why.

@Slereah we have, but it's from someone watching LotR and apparently being bored enough by it to wonder how hot Mount Doom is :P

Not to mention the lack of toothpaste physics questions

I have a rheologist friend and he once worked on the properties of meat

Where is the hamburger physics

Does a photon have mass or not? Im confused now... but to be fair I still havent read QED. Yukawa theory which I think is supposed to be a toy model of QED seems to give mass to the "photon"

that's a scalar, not a vector field

but there is an action for massive photons, it's called Proca theory

we generally believe the photon to be massless in that sense, though

but, as I said earlier:

Also light can acquire an effective mass via a variety of means

@ACuriousMind Even physics professors at decent universities have misconceptions about physics, and even about simple stuff like the basics of Newtonian mechanics. The focus in physics education is on calculation and lab work. Discussion and debunking of misconceptions and splitting hairs does get much emphasis. Physics puzzles catch out a surprising percentage of physics professors. I heard that even the great Richard Feynman wrongly answered in public a simple puzzle about the level of water

@ACuriousMind in a lake. Academics are not at their best when something new is presented, or something is presented from new perspective.

Well physics never gets easy :P

So in QED the photon has no mass. Can I deduce this statement from the fact that there is no mass factor in this term?

@ACuriousMind Yes, but im more interested in our theoretical models

not entirely (you need to also know that it cannot acquire a mass through renormalization because masslessness is protected by gauge symmetry)

ah.. havent reached renormalization yet so... maybe another time

@ACuriousMind As for my experience sucking, it does in a way, but OTOH all's well that ends well. In the end, as a result of never giving up, and eventually getting lucky, I did find out what was going on, and now am in the enviable position of being one of the few people to know what the true situation is (at least I've got an inkling now). But rather than just enjoy being one of the lucky few I want to make things better for those who are still in the dark.

@MatthewChristopherBartsh This somewhat reminds me of my girlfriend who asks me questions all the time about basically everything, and when I say I dont know, she responds: well, arent you a physicist?

My point is that we are not supposed to know everything in physics, especially if its not in our area of expertise

@ShikiRyougi I guess she wants you to research the question and get back to her.

@ShikiRyougi True, but physicists are not supposed to make wrong statements about physics.

No one is supposed to make wrong statements about anything lol

It's still gonna happen

@SirCumference Lawyers?

@MatthewChristopherBartsh No exception

Ask an IP lawyer about stuff decided by the supreme court, and the guy won't be much better off than a layman

People tend to be wrong about some stuff in their specialty too. It's just humans not being perfect

@SirCumference Right now most physicists, and nearly every nonphysicist, when they use the word "mass" when relativity is relevant they are in danger of making no sense at all, or making an untrue statement, because they don't know that there are two definitions of "mass", and they are very different. Using one definition, photons have mass, and mass increases with speed, using the other, not at all.

@So I'm not just trying to help the public, but also physicists to not make fools of themselves.

Trying to clean up the terminology usage is probably a hopeless endeavor

Mathematicians use "derivative" to mean a bunch of different things, for instance

Chemists use "acids" to mean different things too

@SirCumference I have no hope at all here. I don't expect anyone to listen to me about anything. As you say, it makes it worse that it's a matter of terminology. They'll just say, shut up and calculate.

@SirCumference Does use of "derivative" cause misconceptions, though?

@SirCumference What can "acid" mean, then?

This is true of every word

Every word can mean different things in different contexts

@MatthewChristopherBartsh For sure. Some people use it to refer to differentiation (a linear operation on the set of differentiable functions), others to refer to the derivative of a function (e.g. cosine being the derivative of sine, which isn't linear), and others to refer to the derivative at a point (which again, gives you something linear)

All this reminds me of a good meme

@SirCumference you mean there are people who mean something other than LSD? ;)

The case of "derivative" being overloaded brought me a lot of confusion since people tend to say "derivatives are linear". That's true in definitions 1 and 3 (e.g. a Jacobian matrix is indeed linear), but not definition 2

@SirCumference "Sketch of a proof" made me laugh.

@SirCumference Mind you, you could say the same about the "proofs" of high school math, right?

@SirCumference I mean, someone doing a degree in math could.

If you're talking about the stuff in US public school geometry, those are fake proofs invented by people who've never written a real proof :P

obligatory: Lockhart's lament

@SirCumference No, it was actually something a British guy doing a degree in math said about what he'd seen in British high school.

I was thinking of those stupid column proofs

> All proofs are separated into two columns. There are statements on the left-side and reasons on the right-side. See the diagram below to see how they look.

@SirCumference He told me that at uni the word "proof" has a whole other meaning.

I'd argue "proof" means the same at every level, but what's different is the kind and amount of scrutiny something is subjected to before it's accepted as proof :P

@It's rock solid. There are no gaps.

@ACuriousMind I don't agree with everything there (I think the history of math ought to be separated from math classes), but it is a shame most of the good stuff in the essay was ignored by educators

@ACuriousMind I mean forcing people to use a stupid column structure is just bad preparation

Especially bizarre that it comes up in geometry classes of all places and then is never used again

Most of the "proofs" there are obvious to anyone with eyes

@SirCumference quoth Lockhart: "Instead of a witty and enjoyable argument written by an actual human being, and conducted in one of the world’s many natural languages, we get this sullen, soulless, bureaucratic formletter of a proof."

@MatthewChristopherBartsh I think math in general is just completely different in uni compared to most high schools

You're expected to understand what's going on at a deep level rather than memorize

It's no wonder so many high schoolers find math confusing when they're offered none of the intuition

People look at e.g. the fundamental theorem of calculus and see some abstract equation they gotta memorize, when it's really just a (brilliant) way of saying "the sum of all changes equals the net change"

All the fun of math is lost when the intuition is discarded

the people working on formal proof verification assistants might disagree ;)

Formal proofs don't need to be unrelated to intuition :P

A lot of proofs and conjectures I've come up with began with an intuition, and then were made more rigorous

yes, sure

You can generally make connections more easily when everything seems simple to understand

Is there any historical reason why annihilation and creation operators don't have hats? $\hat{a}^\dagger$

@Feynman_00 it's not about c/A operators

after intro QM (where it is important to not additionally confuse people about what's a number and what's an operator when they're already being confused by QM itself) people simply often stop putting hats on operators because it gets annoying to put hats on everything

Oh, that's just it

I had this question because some people hat all operators except c/a even in introductory qm

hm, that sounds like an interesting quirk - maybe it's because $a$'s eigenvalues are usually written $\alpha$ and $a^\dagger$ has no eigenvalues so there's no risk of confusing the operators with their eigenvalues like for most self-adjoint operators (where $\hat{x}$ is the operator and $x$ an eigenvalue)?

That is actually a good explanation. I can't think of another operator whose eigenvalues are denotes with a different symbol, except of course the hamiltonian

Oh well, no, angular momentum

another explanation: $a$ and $a^\dagger$ are not the quantized version of classical observables

if you're using the hat to mean "this is the canonically quantized version of the classical thing below the hat", then it's just correct to not put hats on them

I was thinking about that too

You cannot confuse them with something that doesn't exist in the first place

Ya know, considering how much the world tends to disagree on the units for temperature, mass, length and other stuff, I'm just glad there's a universally accepted unit of time

Imagine if Europe used the second and the Americas used some other unit equal to 1.3 seconds

I'd argue time zones are already much more terrible than different units :P

I guess so lol

Imo the worst is how some countries use d/m/yr and others m/d/yr

With time zones you can specify which one you're in, but here there's no indication

@ACuriousMind Every day I fear of having to write code that will involve using datetimes

fortunately most stuff is on the unix time which is easy to deal with, but when the standards come

Don't want to be the one who has to code second-level precision with standard dates

Come to think of it, do other countries use versions of e.g. Python or JS that are modified to align with their spoken language?

Like a country that doesn't have Latin letters on their keyboard, for instance

@SirCumference Not really (although there are occasional attempts), but they will usually have localization libraries

So that the dates, currencies, etc are printed in the correct format

People have tried making localized programming languages but it never catches on that well

So most code is in english these days

Hmm, I guess I should consider myself kinda lucky they're usually written in my native language. I imagine it'd be much harder for me to learn a programming language that strictly uses e.g. Japanese characters

@SirCumference That reminds me the preface to Griffiths's Introduction to Electrodynamics, where he writes "Neanderthals still speak of pounds and feet". That was savage

Yup lol

Living in the US but being more familiar with SI units is weird

I have no concept of how much an ounce is supposed to be

Well books nowadays are written in SI units

The only thing I know is that I haven't worked with numbers for a long time and I have this test where I have to. It takes more time to use the calculator and convert units than solving the problem

Hopefully this will be my last test using numbers :P

I feel like a reasonable grader will give you credit as long as your derivation was correct

Granted requiring calculators is still dumb

Yes, a reasonable grader would do that.

Or rather you should be asked the numerical result only there is something to say about it. Why would you make an exercise about Zeeman effect and ask for the numerical value of 10 wavelenghts?

I still have a few books written in the cgs system

I have Gravitation in cgs

I wanted Jackson in gaussian but 3rd edition is SI

Hello everyone

I have a question if I may

When quantising the Dirac field, do we have the freedom to quantise with the spin directed towards a particular axis? I.e. do we quantise "the particle in the $S_z$ eigenstate"?

I dont remember such thing as where the spin points when quantizing the dirac field, but maybe someone more qualified could answer.

I mean that I havent heard of it, at least i dont remember it

Hmm

The choice of basis in the solution space of the Dirac equation amounts to choosing one of the Pauli spin matrices to diagonalize, which we generally take as $S_z$. I can't think of a point at which this enters during quantization but I am unsure

Im not sure if this helps but Ill send it anyways

I haven't actually encountered the spin operator acting on the full Fock space yet

@Charlie yes you have this "freedom" - but you're just picking a "random" basis to expand the field in, there's nothing particular about the choice of spin axis (you're not somehow only quantizing particles with spin in that direction or something like that)

Ok great I definitely see what you mean, thank you

I would be extremely grateful if someone will entertain my stupid confusions.

So I was thinking about 1-loop matching in EFT, and how it's supposed to capture all correlation functions to some desired accuracy in E/M, where E is the typical energy scale of measurements, and M is the mass of the particle I've integrated out.

There are many cases in which the effective potential has a different vacuum than what you originally expanded around to do perturbation theory. Eg. the classic coleman-weinberg potential.

However, unlike the coleman-weinberg potential, I'm thinking about a Wilsonian effective action, not the quantum effective action. Therefore there's still a path integral to perform when computing observables.

Aren't the following two statements contradictory? 1) the 1-loop effective potential reproduces observables to the desired accuracy 2) The original vacuum is unstable, so that 2-pt functions in particular, do not match?

can strings pass through each other and not interact?